Understanding the mechanism of crystal growth through oriented attachment of nanoparticles, such as in the self-assembly of metal oxide minerals in aqueous solution, poses many challenges, but also opens vast opportunities for materials design. We present a theoretical approach for modeling solvent controlled interactions between nanoparticles that reaches into the mesoscale, while retaining molecular details of the interacting particle surfaces and intervening solvent. The total Hamiltonian of the system includes contributions from long-range particle-particle dispersion interactions across solvent, that accounts for the influence of solvent structuring on the high frequency dielectric response and ion screening of the static response, and contributions from ion-mediated interactions. The latter include direct Coulomb interactions between ions and mineral surfaces with discrete facet-dependent distribution of charges, image interactions, interactions arising from density (excluded volume) and charge density (ion correlation) fluctuations, ion-mineral and ion-water dispersion interactions. The, ion-mineral dispersion contribution depends on dynamic excess polarizabilities of ions in water and on the dynamic dielectric function of the mineral surfaces providing the link between macroscopic and microscopic dispersion terms.
The model was validated against its ability to reproduce ion activity in 1:1, 2:1 and 3:1 electrolyte solutions in the 0-2M concentration range, and its ability to capture the qualitative ion-specific effect in 1:1 electrolytes at the air-water interface. We apply the approach to understand the influence of pH on facet-dependent interactions between anatase TiO₂ nanoparticles.

Progress in high-resolution electron and probe based, real space imaging techniques like (Scanning) Transmission Electron Microscopy (STEM) and Scanning Probe Microscopy (SPM) has consistently delivered imaging of atomic columns and surface atomic structures with ever growing precision. As the instruments evolve, the basic data processing principle - analysis of structure factor, or essentially a two point correlation function averaged over probing volume - remains invariant since the days of Bragg. We propose a multivariate statistics based approach to analyze the coordination spheres of individual atoms to reveal preferential structures and symmetries. The underlying mechanism is that for each atom, i, on the lattice site with indices (l, m), we construct a near coordination sphere vector , where is the radius-vector to j/2-th nearest neighbor. Once the set of N_i vectors is assembled, it is analyzed though cluster analysis and other multivariate methods to reveal and extract regions of symmetry, distortions, different phases, boundaries, defects, etc., that can be back projected on the atomically mapped surface. Results are presented on various model and real material systems including La_0.7Sr_0.3MnO₃, BiFeO₃, LaCoO₃ and discussed in light of physical parameter extraction.
Acknowledgement:
Research for (AB, QH, AB, SJ, SVK) was supported by the US Department of Energy, Basic Energy Sciences, Materials Sciences and Engineering Division. Research was conducted at the Institute for Functional Imaging of Materials and Center for Nanophase Materials Sciences, which is sponsored at Oak Ridge National Laboratory by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy.

We describe the formulation, development, implementation and applications of Objective Density Functional Theory - a novel first principles simulation methodology for Objective Structures.
Objective Structures are atomic/molecular configurations which generalize the notion of crystals and are such that all the constituent atoms/molecules of the structure “see” the same environment up to orthogonal transformations and translations. Some of the most widely studied atomic/molecular structures in materials science and nanotechnology fall into the category of objective structures. The list of objective structures includes nanotubes, buckyballs, tail sheaths and capsids of viruses, graphene sheets and molecular bilayers. The presence of high degrees of symmetry in objective structures makes them likely to be associated with remarkable material properties - particularly, collective material properties such as ferromagnetism and ferroelectricity.
A systematic study of objective structures is likely to lead to the discovery of novel materials. At the same time, formulation and implementation of theoretical and computational methods specifically designed for studying objective structures, is likely to lead to the development of novel nanomechanics and materials simulation methodologies.
Following this line of thought, we have been developing Objective Density Functional Theory (Objective DFT) - a suite of rigorously formulated quantum mechanical theories and numerical algorithms for carrying out abinitio simulation studies of objective structures. The essential ingredients of Objective DFT include:
1) Usage of Group Representation Theory techniques for formulation of symmetry adapted cell problems for the equations of Kohn-Sham Density Functional Theory as applied to objective structures.
2) Spectral discretization schemes of these cell problems.
3) Efficient solution of the discretized problems using various state-of-the art numerical schemes.
These ingredients make Objective DFT a natural extension of the traditional plane-wave density functional theory method (for studying crystals), just as objective structures form a natural generalization of periodic structures.
We have incorporated these key ideas into a powerful, efficient and reliable computational package called ClusterES (Cluster Electronic Structure) that we have developed from scratch, in order to be able to study objective structures generated by finite groups (such as isolated clusters and molecules). We briefly describe some of the key features and capabilities of this novel computational tool. We end with a discussion of the large variety of applications of Objective DFT, including (but not limited to) the use of the ClusterES package to study the vibrational and optical properties of nanoclusters, the mechanics of nanobeams as well as the investigation of material properties such as flexo-electricity.

Why is NiTi the best shape memory alloy? In recent years desirable features of phase transformations such as low hysteresis and reversibility have been linked to compatibility conditions between phases. We review these conditions and propose a route to highly reversible shape memory alloys. NiTi does not satisfy any of these conditions of compatibility, not even close. Ren and Otsuka (Scripta Mat. 38 (1998), 1669) theorized that the unique properties of NiTi are due to the simultaneous softening of two moduli of the B2 austenite phase, which they took as suggestive of a coupling of two modes of deformation, and this mechanism has been examined in more detail recently by first principles calculations. Based on results of an mathematical algorithm that systematically finds transformation mechanisms, we suggest that the widely accepted mechanism of transformation in NiTi is incorrect. A revised mechanism provides a new view of the origins of reversible shape memory in NiTi, and unexpectedly links the ideas of Ren and Otsuka with the conditions of compatibility.

I will present a family of continuum models for active liquid crystals and study their inherent instability due to activities and their ramifications to flows of the active liquid crystal system. Various patterns and spatial-temporal structures will be identified and classified in relation to the instability of the model system. Applications of the continuum model to model cell motility and bacterial colonies will be discussed in the end.

Spatial multiscale methods have been useful for extending the length scales accessible by conventional molecular dynamics at zero temperature. Recently, extensions of these spatial multiscale methods such as the finite-temperature quasicontinuum (hot-QC) methods have been used to allow for molecular dynamics simulations at finite temperature. In an effort to increase our understanding of such methods and their applications to dynamics, we examine how coarse-graining an atomistic system held at constant temperature affects transition rates. Specifically, we analyze the transition state theory (TST) rate approximation made by coarse-grained molecular dynamics (CGMD) and compare it to the TST rate of the fully atomistic system. The validity of such an approach to computing the TST rate is verified through a relative error analysis, and the resulting analysis is then used to determine the major contributions to the error. Finally, we perform numerical simulations using the method for the case of a 1-D chain before relating these results and the error analysis back to the hot-QC methods. Joint with A. Binder, W.-K. Kim, D. Perez. E. Tadmor. and A. Voter.

Nonlocal continuum models are used in many scientific and engineering applications where the material response and dynamics depend on the micro-structure. Such models differ from the classical, local, models in the fact that interactions can occur at distance, without contact; for this reason they are used for accurately resolve small scale features such as crack tips or dislocations that can affect the global material behavior. However, nonlocal models are often computationally too expensive, sometimes even intractable. Therefore, methods for the coupling of nonlocal and local models have been proposed for efficient and accurate solutions; these methods employ nonlocal models in small parts of the domain and use local, macroscopic, models elsewhere. We propose an optimization-based coupling method for nonlocal diffusion problems; we split the domain in a nonlocal and local domain such that they feature a non-zero intersection and we minimize the difference between the nonlocal and local solutions in the overlapping regions tuning their values on the common boundaries and volumes. We formulate the problem as a control problem where the states are the solutions of the nonlocal and local equations, the controls are the nonlocal volume constraint and the local boundary condition, and the objective of the optimization is a matching functional for the state variables in the intersection of the domains. The problem is treated in a variational sense and its analysis is conducted using the nonlocal vector calculus, a recently developed tool that allows one to solve a nonlocal problem similarly as the local counterpart. Specifically, we show that the coupling problem is well-posed, we study the modeling error and, for finite element discretizations, we analyze the approximation error. Furthermore, we present numerical results in a one-dimensional setting; though preliminary, our tests show the consistency of the method, illustrate the theoretical results and provide the basis for realistic simulations.

By using theoretical and computational approaches, we study Brownian motion of a massive and large particle, which is subject to a harmonic potential and suspended in an ideal gas confined by two parallel walls. This system corresponds to an optical trap experiment of a macromolecule in a slit pore filled with a gas. Based on that diffusion-related physical quantities such as the mean squared displacement and velocity autocorrelation function of the Brownian particle can be calculated from its memory function, we analyze diffusion phenomena of the system by investigating the memory function. More specifically, compared with the unbounded case, an enhanced long-time tail appears in the memory function, from which we study the effects of confinement and the dependence on the shape of the Brownian particle and the stochastic character of the thermal walls.
As an analytic model, we consider a d-dimensional (dge;2) hypercube and elastic walls. Under the infinite-mass limit, we obtain analytic expressions for the force autocorrelation function and the memory function. The transverse-direction memory function possesses a nonnegative tail decaying like t^-(d-1) at large time t, from which anomalous diffusion is expected for d=2. For d=3, the position-dependent friction coefficient becomes larger than the unconfined case and the increment is inversely proportional to the square of the distance from the wall. We also perform molecular dynamics simulations with thermal walls and/or a finite-mass hypercube. We observe faster decay due to the thermal wall (t^-3 for d=2 and t^-5 for d=3 under the fully thermalizing wall) and convergence behaviors of the finite-mass memory function, which are different from the unconfined case.
For a disk (d=2) and a sphere (d=3), we observe from molecular dynamics simulations that the longitudinal direction memory function also contains a power-law decaying tail. Its dependence on the stochastic character of the walls and implications on the normal/anomalous diffusion along the longitudinal direction of the channel are discussed.

The classic Smoothed Particle Hydrodynamics (SPH) is a particle-based method commonly used to solve fluid dynamics equations. SPH is amenable to parallelization and it has been applied successfully to fluids with low viscosity. However, it can perform poorly when applied to low Reynolds number flows in complex geometry. In this talk we present an accurate implicit implementation of SPH that can be used with unsteady low Reynolds number flows and that features good parallel scalability. The fluid dynamics equations are discretized in a Lagrangian fashion using an incremental pressure projection scheme and second-order accurate differential operators. The implementation uses the molecular dynamics library LAMMPS exploiting the common computational structure of particle methods. In our formulation of implicit SPH the solutions to Poisson and Helmholtz linear systems, required at each timestep, are performed using linear solvers provided in the Trilinos library. Using the same framework we solve the nonlinear Poisson-Bolztman (PB) equations which, in fact, reduce to a Poisson system after the application of the Newton method. We demonstrate the efficiency, accuracy and scalability of the implementation on large-scale three-dimensional simulations. Finally we show results for realistic electrokinetic applications in the micro-/nano-scale.

We derive an asymptotic method for solving the steady Boltzmann equation describing phonon transport in the small Knudsen number limit. We show that accurate solutions can be obtained by expanding the unknown phonon distribution function by treating the Knudsen number (Kn) as a small parameter. This procedure can be used to show that, in the bulk, the temperature field obeys the Laplace (steady heat conduction) equation to all orders in Kn. As expected, deviations from the classical heat equation as Kn increases (from very small values) first appear at the boundaries. Specifically, the inhomogeneity introduced by the boundaries requires the presence of a kinetic boundary layer of thickness on the order of a few mean free paths. Matching this boundary layer to the bulk solution yields boundary conditions for the heat conduction equation.
For the case of a boundary at a prescribed temperature, this analysis shows that the traditional no-jump boundary conditions provide solutions consistent with the Boltzmann equation only to zeroth order in Kn. Considering first and second order terms in Kn can be used to show that the appropriate boundary conditions for the heat conduction equation are of the jump (slip) type, with jump coefficients that depend on the material model and the phonon-boundary interaction model. In this work we consider various types of boundaries, such as adiabatic diffusive and adiabatic specular walls, as well as interfaces characterized by frequency-dependent transmission coefficients.
In addition to providing a prescription for obtaining solutions consistent with the Boltzmann equation at significantly less complexity or numerical cost, these results also provide physical insight on the role of size effects and the mechanism by which classical heat conduction theory breaks down. They also provide rigorous justification and quantitative characterization of temperature jumps at material boundaries/interfaces observed in previous studies of size effects.

Electron-phonon coupling is one of the main incoherent inelastic scattering mechanisms in a wide variety of crystalline material systems at room temperature. Therefore, it is necessary to incorporate those effects in any realistic calculation of transport or thermoelectric properties. We do so by extending our density functional theory (DFT) based Korringa-Kohn-Rostocker (KKR) Green's function formalism code.
Instead of including the electron-phonon coupling in the Kohn-Sham Hamiltonian via an adjusted effective potential V_eff, we calculate the Green's function of the 'free' system (i.e., free of electron-phonon coupling, but containing the electron-electron interaction in local density approximation (LDA)) and employ Dyson's equation G = G_free + G_free × Σ_e-ph × G to obtain the dressed Green's function.
The self-energy Σ_e-ph is calculated using Keldysh NEGF formalism, which - in conjunction with Wick's theorem - lends itself to a perturbative diagrammatic approach. Within this method it can be shown, that any term represented by a disconnected Feynman diagram must vanish. This feature makes an exact re-summation of all diagrams in terms of the reference Green's function G_free possible and leads to the customary electron-phonon self-energy formulas. Especially, both the so-called First Born Approximation (FBA) and Self-Consistent First Born Approximation (SCFBA) can be recovered.

In type II superconductors, there are two critical magnetic field values and when the applied magnetic field strength is in between of these two values, vortices with quantum magnetic fluxes appear in these superconductors. The Bogoliubov-de Gennes formalism [1] provides a microscopic description of the vortex formation, vortex symmetry and interaction between vortices. On the other hand, the generalized Hubbard model, which includes first- and second-neighbor correlated hopping interactions besides the onsite and nearest-neighbor Coulomb interactions, has been used to investigate the d-wave superconductivity in high-Tc ceramic superconductors [2]. In this work, we report an extension of the Bogoliubov-de Gennes formalism for the mentioned generalized Hubbard model, which leads to 2N coupled self-consistent equations for a supercell of N atoms. These equations allow to determine the spatial variation of the superconducting gap as a function of the electron concentration and electron-electron interactions. The supercell averaged superconducting gap shows a qualitatively different dependence on the external magnetic field, being larger the second critical magnetic field of d-wave superconductors than those corresponding to isotropic and anisotropic s-wave ones. Finally, the electronic specific heat as a function of the temperature for a given applied magnetic field is calculated and compared with experimental data.
This work has been partially supported by CONACyT 131596, UNAM IN106714 and IN113714. Computations were performed at Miztli of DGTIC-UNAM.
[1] P.G. de Gennes, Superconductivity of metals and alloys (Addison-Wesley Pub. Co., New York, 1989).
[2] C.G. Galvan, L.A. Perez, and C. Wang, Phys. Lett. A 376, 1380 (2012).

Various promising applications such as acoustic cloaking, sub-wavelength imaging, acoustic wave manipulation, transmission or reflection control etc. are feasible because of the ability of manipulating sounds and vibrations using artificially engineered “Acoustics meta-materials”. Recent works on space-coiling acoustic metamaterials show their extreme constitutive parameters like large refractive index, double negativity and zero mass density. Three dimensional structures have a wide application in sub-wavelength broadband acoustic wave suppression due to huge attenuation. Here we report the study of propagated and transmitted wave through self-designed 2D and 3D acoustic metamaterials structure using finite element method. Our simulations on 2D structure show large refractive index, double negativity and zero mass density for a broad frequency range and 3-D structure show a huge absorption/damping over few hundreds kilohertz frequency range. Simulation studies of refractive index, impedance, bulk modulus and mass density using S-parameter for both 2D and 3D structures along with experimental results will be presented.

Quantum dots have discrete energy levels that can be engineered by tuning their composition, density, organization, size and morphology. These features make quantum dots attractive for the design and fabrication of novel electronic, magnetic and photonic devices. Stranski-Krastanow (SK) growth technique leads to the formation of dislocation-free nano-islands, which are interconnected with a thin flat wetting layer, and hence has attracted great attention. In the formation of such nano-systems, the diffusion anisotropy, crystallographic orientation and the surface roughness may have a significant influence. Here, we based our study on continuum level dynamical simulations for the spontaneous evolution of quantum dots on stochastically rough thin films having random (white noise) surface undulations with well-defined strengths. During the development of SK islands through the mass accumulation at randomly selected regions of the film via surface drift-diffusion (induced by the capillary and mismatch stresses), we observed the formation of an extremely thin wetting layer. Above a certain threshold level of the mismatch strain and/or the size of the patch, the formation of multiple islands separated by shallow wetting layers is also observed as metastable states such as doublets even multiplets. These islands are converted into a distinct SK islands after long annealing times by coalescence through the long range surface diffusion. Based on the simulation results, we generated stability (including the equilibrium shape) phase diagrams as a function of the misfit stress and the equilibrium dihedral angle between the film and the substrate or the amplitude of the surface undulations. Supported by TUBITAK grants no 111T343 and 213M481, and TUBA GEBIP award to Oren EE.

In contrast to multiscale methods, which often encompass multiple simulation techniques, multiresolution models use the same general modeling technique with representations of a system at varying length and time scales. We present work on a complete framework for modeling of semidilute polymer solutions, containing both coarse-graining and reconstruction steps. The coarse-graining approach is based on the wavelet-accelerated Monte Carlo (WAMC) method [1], which forms a hierarchy of resolutions to model polymers at length scales that cannot be reached via atomistic or even "standard" coarse-grained simulations. Using multiple stages of resolution, it is possible to simulate polymers of up to millions of repeat units in length. Although previously applied only to individual chain statistics [2], we show here how it can be extended to the study of polymer solutions. Bonded and non-bonded potentials between coarse-grained superatoms are computed. The non-bonded potential is computed using the same approach used previously in the study of single chains while the bonded potentials are computed using reverse Monte Carlo. A universal scaling function is obtained so that potentials do not need to be recomputed as the scale of the system is changed. To model polymer solutions, the intermolecular potential between the CG beads is assumed to be equal to the non-bonded potential, which is a reasonable approximation in case of semidilute systems. Using these potentials, various radial distribution functions are calculated from the coarse-grained representation at different resolutions, which compare favorably with the results from the atomistic simulations. We show that coarse-grained polymer solutions can reproduce results obtained from the simulations of the more detailed atomistic system to a reasonable degree of accuracy.
The reconstruction proceeds in much the same way: using probability distributions obtained from the coarse-graining procedure with respect to bond lengths, angles, and torsions, as well as the non-bonded potentials, we can reconstruct a more detailed version of the polymer that is consistent both with geometric constraints as well as energetic considerations. Using a quality estimator model for the reconstruction process, we can successfully “reverse map” entire atomistic configurations from coarse-grained descriptions. Applications for the reconstruction of atomistic models from united-atom models and detailed models from coarse-grained models will be shown, using semi-dilute polymer solutions and self-assembled monolayers as test cases.
References
[1] A. E. Ismail, G. C. Rutledge, and G. Stephanopoulos, The Journal of Chemical Physics 118, 4414 (2003)
[2] A. E. Ismail, G. C. Rutledge, and G. Stephanopoulos, The Journal of Chemical Physics 118, 4424 (2003)

Bismuth is known for the measurements of quantum oscillations in magnetic field due to its semi-metallic band structure with electron and hole pockets of small effect masses, low charge carrier density and small energy overlap. Progress in fabricating single crystal Bismuth nanowires and the experiments on magneto-resistance provide access to the characters of surface states and bulk states with the confinement effect of nanowires. In this work, we study the theory of confinement in semi-metallic Bismuth nanowire and its effect on the change in the band structure and magnetoresistance. The band structure is investigated by density functional calculation, empirical tight-binding models and effective low-energy band models around the Fermi level. The understanding provides the method to engineer the bulk and surface states in nanowires.

Phenomena such as solute strengthening in lightweight alloys and alloyed high strength steels, and embrittlement of bimaterial interfaces and grain boundaries are controlled by quantum mechanical interactions of solutes or impurities with defects (dislocations, grain boundaries, interfaces, or cracks). The local stresses driving these atomic-scale process are determined by behavior occurring at much larger spatial and temporal scales. To maintain high resolution at large special scales, we will use a “Coupled Atomistic/Discrete-Dislocation” (CADD) to represent grain boundaries, crack tips and other defects while handling dislocation plasticity at both atomistic (MD) and continuum scales (FEM) simultaneously. The temporal scale of simulations at the atomic level, are typically about 8-10 orders of magnitude smaller than the temporal scale at other spatial levels. As a result, until now MD simulations can generally only probe behavior at high stresses and sliding rates that are not practically relevant.
We present a new model that provides a general purpose approach to couple the disparate temporal scales in existing concurrent multi-scale simulations. Kinetic Monte Carlo is used as the temporal scale buffer between the continuum and atomistic regions of the model. Since KMC is capable capturing atomistic rare events at the appropriate time scale, our innovative approach provides a means to synchronize MD and FEM based on events occurring in KMC. A domain with an initial Guassian distribution of vacancies is considered. Model details are presented for the temporal evolution of vacancy concentration in domain represented by (a) FEM/KMC, (b) KMC/MD and (c) FEM/KMC/MD. The FEM/KMC coupling involves iteratively solving for the correct vacancy concentration at the interface between the regions. The KMC/MD coupling requires careful synchronization of temporal scales during an event at this interface. Finally results of the coupled approach are presented for vacancy assisted climb of an atomistically represented dislocation for a range of temperatures from 300K to 900K.

The unique geometry, structure, and physical properties of the paddlefish rostrum enhance swimming when the fish is moving at different angles. Fish velocity is also believed to increase as the swimming angle increases and when the fish is swimming in the opposite direction of the flow. In this article, a 3D multiphysics, fluid-structure interaction study of the performance of the rostrum concerning the swimming enhancements of a sub-adult paddlefish was performed. Simulations were carried out in which the fish is swimming at two different velocities, similar to those encountered by the paddlefish in its natural habitat, and at three angles of attack 0, 5, and 10 degrees. These angles of attack are along and against the direction of longitudinal axis of fluid flow to simulate filter feeding and spawning migrations, respectively. Results show that the shape and position of the rostrum help the paddlefish swim efficiently. Maximum velocity enhancements were found when the fish swim against the flow direction and the optimum angle of attack was determined to be 0 degrees. Finally, a progressive collapse analysis of the paddle fish rostrum will be demonstrated and preliminary results on the ability of this structural composition to dissipate energy when submitted to high rate loading will be also discuss.

Combinatorial material science (CombiSci) is a recently developed branch of combinatorial optimization, which seeks to find the best configuration of a material to a target set. Some topics covered by CombiSci are the synthesis of polymers and metal alloys. Another area, also innovative, is the scaffold for tissue engineering, which are porous structures that can serve as cell supports. Depending on the condition variations of the processing technique can be obtained scaffolds of various configurations, i.e. different architectures and properties. The properties and architecture of the scaffolds can affect cell proliferation, but the studies performed usually cover only a short range of possibilities, since biological studies are expensive and time consuming. Therefore in the present work we proposed a model optimization which aims to maximize the growth of osteoblasts by controlling the properties and architecture of polymeric scaffolds processed by electrospinning technique. Based on the optimization model was implemented a Genetic Algorithm (which is inspired by the Darwin&’s evolution theory). The algorithm calculated wire diameter, pore diameter, porosity, Young's modulus and contact angle of the scaffolds through of four electrospinning technique processing parameters: voltage (kV), concentration (% w/V), flow rate (mL/hr) and distance (cm). Later, is assigned a fitness value to each scaffold and the scaffold with more value represent the best conditions for osteoblasts growth. The optimization model and the Genetic Algorithm can be easily adapted to different types of polymers and cells. Also the optimization model can be applied not only by means of heuristic method, like a genetic algorithm, but also by exact methods.

Molecular dynamics (MD) simulations in atomistic detail have become available as powerful and reliable tools to explore the properties of organic-inorganic interfaces. Chemically and thermodynamically consistent parameters of inorganic components developed for common harmonic force fields (INTERFACE force field combined with CHARMM, AMBER, PCFF, CVFF force fields) reproduce measured bulk and surface properties of organic and inorganic materials in quantitative agreement with experimental measurements. For noble metals, however, polarizability due to induced charges in polar environments with ionic surfactants, DNA, or ionic liquids had not been well integrated. For example, available fixed-dipole models lack validation of induced charges against known image potentials, require artificially fixed metal atoms, and can only be applied to gold. Here, we introduce a polarizable model to extend the well performing Lennard-Jones (LJ) potential for fcc metals (Ag, Al, Au, Cu, Ni, Pb, Pd, Pt) to accurately include polarizability at the interface. The electronic structure of metal atoms is approximated by negatively charged (-q) dummy atoms that are coupled via a spring constant (k) to the positively charged (+q) metal core. In addition to the charge and spring constant, the core metal and dummy atoms are represented by their LJ parameters (ε and σ). This model leads to accurate results, is easy to use, and requires no modification of MD source codes. Validation included the computation of the polarization energy of positive and negative point charges as a function of distance from the metal surface in comparison to classical and quantum-mechanical calculations of image potentials, which yields the expected (1/r) distance dependence and near-quantitative agreement. The new polarizable model retains full mobility of all metal atoms, quantitative agreement of computed and experimentally measured surface tensions, densities, and interfacial properties with water and (bio)organic molecules, as well as mechanical properties as in the original LJ potential. The polarizable LJ parameters for metals can be integrated in major biomolecular simulation platforms, including CHARMM, AMBER, OPLS-AA, PCFF, CVFF, and GROMACS. It is applicable to metal nanocrystals regardless of shape and {hkl} bounding facets to study selective adsorption and crystal growth.

The molecular dynamics (MD) simulations have contributed to understanding of the thermodynamic and kinetic properties of the solid-liquid interface during solidification of metals and alloys [1,2]. On the other hand, it requires a large number of atoms for precise description of the curvature effect of the solid-liquid interface properly, which is computationally demanding and is however essential to discuss the morphological evolution during the solidification. To overcome the above situation, we have developed our own code for carrying out MD simulation on a graphics processing unit (GPU), which enabled handling of a million atoms in MD simulations over a period of nanoseconds within several days [3,4]. Using this code on the GPU architecture, spontaneous evolution of anisotropy in the solid nucleus in the undercooling melt of iron is achieved by million-atom molecular dynamics simulation [5]. The spherical nucleus grows preferentially in <100> directions. Based on the simulation results [5], it is emphasized that achieving fourfold symmetry in the solid nucleus in the undercooled melt in the MD simulation naturally without an anisotropic parameter is a major step forward for computational metallurgy, which is enabled by the drastic acceleration of the MD simulation performed on the GPU architecture.
[1] Y. Shibuta, S. Takamoto, T. Suzuki, ISIJ Int., 48 (2008) 1582.
[2] Y. Watanabe, Y. Shibuta, T. Suzuki, 50 (2010) 1158.
[3] K. Oguchi, Y. Shibuta, T. Suzuki, J. Jpn. Inst. Metals, 76 (2012) 462.
[4] Y. Shibuta, K. Oguchi, T. Suzuki, ISIJ Int., 52 (2012) 2205.
[5] Y. Shibuta, K. Oguchi, M. Ohno, Scripta Mater., article in press. (doi:10.1016/j.scriptamat.2014.04.021)

With tremendous progress in computer technologies and applications during the last decade, atomistic-level simulation is rapidly becoming an essential tool in materials science for the study of the physical and chemical properties of various materials. Here, we have demonstrated the combined approach that allows us to construct a p-T phase diagrams of various nanoporous materials (or inclusion compounds) with complex gas compositions without resorting to any empirical parameter fittings. First, in order to evaluate the parameters of weak interactions, a time-dependent density-functional formalism and local density technique entirely in real space have been implemented for calculations of vdW dispersion coefficients for atoms/molecules within the all-electron mixed-basis approach [1]. Next, computation approach based on the solid solution theory of van der Waals and Platteeuw with some modifications describing host lattice relaxation, guest-guest interactions and the quantum nature of guest behavior inside cavities has been developed and applied for the estimation the thermodynamic properties of nanoporous compounds with weak guest-host interactions using the obtained parameters of weak interactions [2].
We applied this approach to construct the phase diagrams of gas hydrates, three-dimensional hydrogen-bonded water structures in which water molecules arrange themselves in a cage-like structure around guest molecules. The thermodynamic stabilities of hydrogen and mixed hydrogen-propane, hydrogen-methane, hydrogen-ethane hydrates as well as the He hydrate based on different ice structures have been studied and obtained results are in agreement with available experimental data [2-4]. Recently, the formation of binary CH₄-CO₂ hydrate has been investigated at different gas phase compositions, pressures and temperatures using original thermodynamic approach. Equilibrium compositions of the formed hydrates have been determined as a function of the gas phase composition. It was also demonstrated that carbon dioxide can replace methane in the hydrate phase at temperatures and pressures typical for the permafrost regions or below the seafloor.
The proposed method is quite general and can be applied to the various nanoporous compounds with weak guest-host interactions. From this point of view, the present methodology can support experimental explorations of the novel gas storage and separation materials.
REFERENCES
[1] R. V. Belosludov et al. in Handbook of Sustainable Engineering, ed. by K-M. Lee and J. Kauffman, Springer, New York, (2013) pp. 1215-1247.
[2] R.V. Belosludov et al., J. Chem. Phys. 131 (2009) 244510.
[3] R. V. Belosludov et al.Mol. Simul.38 (2012) 773.
[4] R. V. Belosludov et al.J. Phys. Chem. C118 (2014) 2587.

The plastic deformation of metals is the result of the motion and interaction of dislocations, line defects of the crystalline structure. Continuum models of plasticity remained largely phenomenological to date and do not consider dislocation motion as the origin of permanent plastic deformation. Here we present a novel plasticity theory based on systematic physical averages of the kinematics and dynamics of dislocation systems. We demonstrate that this theory can predict microstructure evolution and size effects in accordance with experiments and discrete dislocation simulations. The CDD formulation is based on only four internal variables per slip system and features physical boundary conditions, dislocation curvature, dislocation pile ups and mutual dislocation interaction. We have realised a numerical implementation of CDD to demonstrate examples of these features.

With advancement in parallel computing, molecular dynamic (MD) simulation serves as a powerful tool to study the interface between hard and soft materials at atomic level. In this work, MD simulations of single walled carbon nanotube (SWNT) and pulmonary surfactant proteins (PSP) are presented. Hydrophilic proteins SP-A and SP-D and hydrophobic proteins SP-B, and SP-C have their unique functions in keeping the integrity of pulmonary fluid. Hence their interactions with SWNT are very important for potential protein device sensory applications. Spatial trajectory of PSP adsorption on surface of SWNT is computed for 100 ns. Results showed a stable adsorption of all proteins on SWNT surface. In 100 ns the root mean square deviation of proteins fluctuates around stable values leading optimal stability. As the distance between center of mass of PSP molecule and SWNT attends equilibrium it stabilizes the number of atoms of proteins within 5 Angstrom of SWNT surface. Results also show adsorption of both polar and non-polar residues of PSP on the surface of SWNT. Computation of interaction energy between SWNT and proteins indicate Van der Waals forces of attractions. The adsorption process of protein on surface of SWNT also changes its secondary structure these changes may occur temporally in protein structure but are important in changing many protein properties. The adsorption process is result of π - π stacking which helps in understanding of specific and non-specific binding of protein and SWNT and hence the nature of soft-hard interface. This computational interactions between SWNT and pulmonary proteins may give rise to NEMS device of SWNT for selective protein attachments.

Cellular networks are ubiquitous in nature. Most engineered materials are polycrystalline microstructures composed of a myriad of small grains separated by grain boundaries, thus comprising cellular networks. The grain boundary character distribution (GBCD) is an empirical distribution of the relative length (in 2D) or area (in 3D) of interface with a given lattice misorientation and normal. During the coarsening, or growth, process, an initially random grain boundary arrangement reaches a steady state that is strongly correlated to the interfacial energy density. In simulation, if the given energy density depends only on lattice misorientation, then the steady state GBCD and the energy are related by a Boltzmann distribution. This is among the simplest non-random distributions, corresponding to independent trials with respect to the energy. Why does such simplicity emerge from such complexity?
Here we describe an entropy based theory which suggests that the evolution of the GBCD satisfies a Fokker-Planck Equation, an equation whose stationary state is a Boltzmann distribution. The properties of the evolving network that characterize the GBCD must be identified and appropriately upscaled or `coarse-grained'. This entails identifying the evolution of the statistic in terms of the recently discovered Monge-Kantorovich-Wasserstein implicit scheme. The undetermined diffusion coefficient or temperature parameter is found by means of a convex optimization problem reminiscent of large deviation theory.
Joint work with K. Barmak (Columbia), M. Emelianenko (George Mason). Y. Epshteyn (Utah), R. Sharp (Globys), and S. Ta'asan (CMU)

The corrosion of steel components in sour (H₂S-containing) conditions encountered in the oil and gas industry is partially mitigated by the formation of a passive film composed of iron-sulfide phases. While this barrier layer retards the rate of general corrosion, they are susceptible to localized degradation, which, due to its difficulty of detection, can lead to catastrophic failure through pitting corrosion. Due to challenges in characterization of these sulfide passive films, even fundamental mechanistic information such as the nature of the rate-controlling process is not established [1]. Therefore, existing models for predicting the susceptibility of these materials to failure rely largely on empirical formulae that have little basis in the actual mechanism of sulfide corrosion [2].
In this study, we present a multiscale model for the growth and breakdown of iron-sulfide films based on elementary reaction steps such as charge transfer and ionic migration. The relative rates of these elementary processes depend upon a host of local factors, including temperature, sulfur activity and film thickness, necessitating a multiscale model that can span all the requisite time and length scales at which these elementary processes happen. Specifically, our model couples activation barriers for surface reactions calculated ab initio using Density Functional Theory (DFT) with a kinetic Monte Carlo model of pit initiation at the iron sulfide surface [3]. These atomic-scale processes are, in turn, coupled with a mesoscale phase-field model of film growth. The calculated activation barriers are validated with experimental results from the authors&’ work and literature. We also provide a mechanistic pit initiation model adapted from the well-known Point Defect Model [4].Taken together, these two results lead to a more deterministic description of the growth and degradation kinetics of sulfidic passive films on iron.
References
1. Amri, J., J. Kvarekvaring;, and B. Malki. Simulation Of Solid-State Growth Of Iron Sulfides In Sour Corrosion Conditions. in Corrosion 2011. 2011. Houston, Texas: NACE International.
2. Persson, K.B., S.J. Kaukas, and U.H. Kivisäkk. Corrosion Performance Of Alloy 29 In Simulated Sour Environments. in Corrosion 2010. 2010. San Antonio, Texas: NACE International.
3. Herbert, F.; Krishnamoorthy, A.; Ma, W.; Van Vliet, K.; Yildiz, B., Dynamics of point defect formation, clustering and pit initiation on the pyrite surface. Electrochimica Acta 2014.127: p. 416-426.
4. Macdonald, D., The Point Defect Model for the Passive State. Journal of the Electrochemical Society, 1992. 139(12): p. 3434-3449.

We have developed an island dynamics model for epitaxial growth with the level-set technique, where islands are treated as continuous in the x-y-plane, while individual atomic layers are resolved in the z-direction. Adatoms are treated as a mean field quantity by solving a diffusion equation. The effect of an additional step-edge barrier is incorporated via a mixed Robin-type boundary condition for the diffusion equation. We will present a numerical scheme to solve such a boundary condition on a fixed grid with moving boundaries. We will show how the inclusion of the step-edge barrier leads to the formation of mounds that become progressively steeper as the step-edge barrier increases. Finally, we will discuss how we can include the effect of downward funneling in our model, and how it leads to the stabilization of the slope of the mounds.

Emergent Lorentzian-, parity- and parabolic- symmetries are analytically proven to govern the
facet statistics of slightly undercooled crystal-melt interfaces
Novel translating fronts whose asymptotic inclinations are offset from the thermodynamic Wulff angles are proven to provide the motive ordering force here.
For each thermodynamically unstable crystal interface that undergoes thermo-kinetic spinodal decomposition,
we predict and numerically validate that the characteristic facet length is governed by a universal coarsening law, which includes not only a power law dependency on time, but also the dependence on the orientation of the intial unstable interface.

The kinematic structure of the field dislocation mechanics (FDM) is shown to predict the precise location of dislocation nucleation. We validate the predictions of the linear stability analysis of FDM in computational atomistic simulations performed for EAM-Al. and LJ potential crystals. The simulations are performed for hexagonal lattice for two crystallographic orientations in 2D and one in 3D. Apart from the accuracy in predicting the location of dislocation nucleation, the FDM based analysis also demonstrates superior performance than existing nucleation criteria in not persisting in time beyond the nucleation event, as well as differentiating between phase boundary/shear band and dislocation nucleation. Interestingly, the proposed technique discriminates between objective tensor rates; a naturally emergent convected rate succeeds while its substitution by a corresponding rate based on the skew part of the velocity gradient is shown to never predict nucleation.

Vanishing condition of the first order derivative of a free energy determines the phase equilibria. While the second order derivative provides us with the measure of the stability of the system. In materials science community, major of works of alloy physics have been centered around phase equilibria calculations and not much attentions have been paid to stability analysis. By employing a free energy described based on Cluster Variation Method, we derived an order-disorder phase diagram and placed a locus of Spinodal Ordering line below which a disordered system becomes inherently unstable against configurataional fluctuation and spontaneous ordering reaction takes place. Such an analysis may be extended to another mode of fluctuation driven by atomic displacement, which leads to displacive type phase transition.

In this talk we discuss path-space information theory-based sensitivity analysis and parameter identification methods for complex high-dimensional dynamics, as well as information-theoretic tools for parameterized coarse-graining of non-equilibrium extended systems. Furthermore, we relate such information-theoretic methods with observables and goal-oriented approaches through the derivation of path-space Cramer-Rao-type inequalities, which also allow us to address transferability questions in coarse-graining.
The combination of proposed methodologies is capable to tackle molecular-level models with a very large number of parameters, as well as non-equilibrium processes, typically associated with coupled physicochemical mechanisms, boundary conditions, etc. (such as reaction-diffusion and/or driven systems), and where even steady states are unknown altogether, e.g. do not have a Gibbs structure. Finally, the path-wise information theory tools yield a surprisingly simple, tractable and easy-to-implement approach to quantify and rank parameter sensitivities, as well as provide reliable molecular model parameterizations based on fine-scale data through suitable path-space (dynamics-based) information criteria.
The proposed methods are tested against a wide range of high-dimensional stochastic processes, ranging from complex biochemical reaction networks with hundreds of parameters, to spatially extended Kinetic Monte Carlo models in catalysis and Langevin dynamics of interacting molecules with internal degrees of freedom.

EBSD is a method of measuring the local orientation of crystals at the scale down to nanometer, while Young measure is a mathematical tool of analyzing deformation with fine microstructure at the continuum scale (often larger than micrometer). For martensitic materials without external stressing, local crystal orientation is sufficient to determine the local deformation, given the transformation stretch tensor and the assignment of variants to regions of homogeneous deformation. Therefore, EBSD is potentially a tool of accurately measuring the deformation distribution in a small (at the continuum scale) neighborhood of a point in such materials. The distribution can be further utilized to construct the Young measure field.
This manuscript discusses a scheme for measuring the Young measure using EBSD in a
material that undergoes a martensitic phase transformation. The scheme is based on the (weak) Cauchy-Born rule. The scheme first includes an algorithm of determining the transformation stretch metric. Then by assigning phases or variants for regions in the EBSD images, the distribution of deformation gradients in a small neighborhood of a point in the sample is measured. Besides, the scheme also includes specific algorithms to check whether certain zero elastic energy microstructures, which have been associated with low hysteresis and enhanced reversibility, are present in the sample. The treatment is geometrically exact: no assumptions of smallness of the deformation are made in the interpretation of the measurements.
We acknowledge the financial support of MURI project FA9550-12-1-0458 (administered by AFOSR). This research also benefited from the support of NSF-PIRE grant number OISE-0967140.

The length-scale required for semi-crystalline materials or rare-event-phenomena involving low to medium defect concentrations, such as crack initiation, aggregation, or strain-induced crystallization, is on the order of 10 mu;m (see Figure 1), which exceeds current capabilities by three orders of magnitude due to the increased 10⁶-10⁹-times computational cost. The computational cost is due to two factors: the number of degrees of freedom (DoFs) and the timestep needed to equilibrate the system. The timestep depends on the highest vibrational timescale associated with a DoF. A reduction of DoFs is commonly achieved by combining several atoms to form coarse-grained “beads.” As an alternative to this approach, we exploit without further expert input the topology and sparsity of the bonding structure of large polymers to derive a hierarchical set of DoFs that not only solves the arbitrariness of bead selection, but also provides a clear framework for full multiresolution beyond the common two-level representation. The diffusion wavelet approach to operator compression was used with a temperature-dependent accuracy to establish the hierarchy of linear combinations of particle DoFs. The resulting hierarchy separates local modes, such as a single C-C vibrational mode, from increasing chain level, e.g., long-range concerted backbone vibrational modes. Our approach correctly captures small-scale chemical features, such as the ring structures in polystyrene or cellulose, alkane side chains, or CH₂ units, as well as large-scale features of the backbone. In particular the first level of coarse graining comprises DoFs similar to united atom models and other generally hand-selected coarse-graining models. At coarser levels, the DoFs describe increasingly large connected portions of the target polymers. For polyethylene and polystyrene, spatial coordinates and their associated forces were compressed by up to two orders of magnitude. The compression in forces is of particular interest as this allows larger timesteps as well as reducing the number of DoFs.

To obtain energy density, power density, and cycle life far beyond the current Lithium-ion battery technology, we aim to exploit the next generation lithium-ion batteries, specifically the high-voltage spinel cathode (LNMO) with an operation voltage of ~4.7 V and a capacity of ~135 mA h g^-1. Recent study shows that applying a chemically protective lithium titanate (LTO) and/or anatase (Ti₂O) layer to LNMO can further increase the voltage of 3.4 - 5 V [1]. However, its commercialization is plagued by the manganese deposition at high operating voltage and SEI layer formation due to Li⁺ consumption, particularly at elevated temperatures. The studies have elucidated the SEI composition, growth rate, and impact on the capacity fade, but the morphology evolution of the SEI layer and its interaction with manganese deposition are still not fully understood, especially in term of the SEI structure prediction. In this work, we will investigate the morphology evolution of the SEI using phase field method.
Numerically, a lot of attention is focused on the phase dynamic boundary (interface). However the available methods for modeling an interface separating fluids and formation possess are limited. Therefore, physical approach is a good choice for a numerical technique, handling the morphological changes of the interface. A phase field model offers an attractive alternative to more established methods for solving multiphase flow problems. Instead of directly tracking the interface between multiple phases, which may affect the results in non-trivial way, the interfacial layer is governed by a phase field variable, #120593;. In phase field model, the time evolution of phase field variable is governed by the gradient of a free energy functional. During the long-range diffusion, the concentration field can be regarded as a conserved property. Hence, we can apply the Cahn-Hilliard equation, which is a fourth-order PDE, to formulate the diffusion [2]. And the phase field interface decomposes the Cahn-Hilliard equation into two second-order PDEs. In addition, the Cahn-Hilliard equation shows the fluid interface is simply convected with the flow field. And it also ensures that the total energy of the system diminishes correctly. Therefore, the phase field method includes more physics than the other level set methods. The phase field can model the phenomena as roughness formation and electronically mediated reactions between interfaces in electronic contact. In addition, the phase field model is more accurate in regions with sharp composition gradients and can treat phase boundaries without explicitly tracking the interfaces. In this work, the phase field model is employed as a powerful tool to model SEI layer morphology evolution.
References
[1] X. Hao, B.M. Bartlett, Journal of The Electrochemical Society, vol. 160, 2013, pp. A3162-A3170.
[2] B.C. Han, A. Van der Ven, D. Morgan, G. Ceder, Electrochimica Acta, vol. 49, 2004, pp. 4691-4699.

Dislocation dynamics (DD) simulations have been developed to advance the understanding of crystal plasticity through the evolution of dislocation microstructure. In 2D DD models, dislocations are assumed to be infinitely long, parallel lines that are represented by points on a 2D plane perpendicular to the lines. The simplicity of the 2D model (compared with the 3D line DD model) allows us to examine a number of important physical and computational issues that have been largely ignored to date.
For example, it has proven difficult for 3D DD simulations to achieve large strains. Utilizing more efficient time integrators as in the 3D case [1], has allowed for 2D simulations to achieve larger strains. This allows for a more thorough investigation of dislocation configurations well past the yield point and into stage I hardening. Initially in the case of single slip, many planes have active (non-pinned) dislocations near yielding due to the locations and strengths of both sources and obstacles. However, at higher strains, the dislocation activity is confined to a smaller subset of glide planes [2]. This occurs due to dislocation pileups at obstacles and the resulting back stress shutting down most of the dislocation sources. Multislip simulations are investigated to see if evidence of stage II hardening can be found in a 2D model.
However traditional multislip simulations often miss a key result from intersecting slip: a group of dislocations on the same glide plane will end up on different (parallel) planes after the original planes are cut by dislocations moving on an intersecting glide plane. Similarly, dislocations on different (parallel) planes can also be brought to the same plane by intersecting slip. This has been suggested as a mechanism that promotes formation of persistent slip bands. However, this mechanism is excluded in existing DD models because the glide planes of non-screw dislocations remain unchanged throughout the simulation. We developed a method to account for shifting of dislocation glide planes by intersecting slip.
The DD code uses a non-singular formulation for dislocation stresses, as well as the newly developed analytic solution to the conditional convergence problem in 2D DD models [3]. The simulation uses an implicit trapezoid integrator to achieve more strain than a simple forward Euler implementation. The predictions of this new model are compared with previous results in the literature to show the effect of slip plane cutting on dislocation microstructure evolution and crystal plasticity.
This work was supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award No. DE-SC0010412.
[1] R. Sills and W. Cai, Model. Sim. Mater. Sci. Eng. 22, 025003 (2014).
[2] E. van der Giessen and A. Needleman, Model. Sim. Mater. Sci. Eng. 3, 689-735 (1995).
[3] W. P. Kuykendall and W. Cai, Model. Sim. Mater. Sci. Eng. 21, 055003 (2013).

We employ discrete dislocation dynamics to establish a continuum-based model for the evolution of the dislocation structure in polycrysshy;talline thin films. The Taylor equation is evaluated and expressions are developed for the density of active dislocation sources, as well as dislocation nucleation and annihilation rates. We demonstrate how the size effect naturally enters the evolution equation. Very good agreement between the simulation and the model results is obtained. The current approach is based on a two-dimensional discrete dislocation dynamics model, but can be extended to three-dimensional models.

We formulate a theory of non-equilibrium statistical thermodynamics for ensembles of atoms or molecules. The theory is an application of Jayne's maximum entropy principle, which allows the statistical treatment of systems away from equilibrium. In particular, neither temperature nor atomic fractions are required to be uniform but instead are allowed to take different values from particle to particle. In addition, following the Coleman-Noll method of continuum thermodynamics we derive a dissipation inequality expressed in terms of discrete thermodynamic fluxes and forces. This discrete dissipation inequality effectively sets the structure for discrete kinetic potentials that couple the microscopic field rates to the corresponding driving forces, thus resulting in a closed set of equations governing the evolution of the system. We complement the general theory with a variational meanfield theory that provides a basis for the formulation of computationally tractable approximations. We present several validation cases, concerned with equilibrium properties of alloys, quasistatic-to-dynamic nanovoid cavitation in metals, heat conduction in silicon nanowires and hydrogen desorption from palladium thin films, that demonstrate the range and scope of the method and assess its fidelity and predictiveness. These validation cases are characterized by the need or desirability to account for atomic-level properties while simultaneously entailing time scales much longer than those accessible to direct molecular dynamics. The ability of simple meanfield models and discrete kinetic laws to reproduce equilibrium properties and long-term behavior of complex systems is remarkable.

Logarithmic structural relaxation is a ubiquitous process that typically appears in disordered materials. Using adaptive kinetic Monte Carlo (aKMC) methods, the kinetic Activation Relaxation Technique (k-ART) and the self-evolving atomistic kinetic Monte Carlo (SEAKMC), we show that such long-tailed aging also appears when point defects in bcc-Fe undergo aggregation. aKMC permits modeling of materials over timescales out-of-reach for traditional atomistic simulation techniques while fully capturing the microscopic features involved in the kinetics. These off-lattice methods based on transition-state-theory couple the kinetic Monte Carlo algorithm to on-the-fly searches for events. The k-ART handles the event catalog using topology analysis, leading to a self-learning algorithm, while SEAKMC introduces the concept of active volumes to efficiently sample the energy landscape.
We simulate the clustering of 25 self-interstitial atoms (SIA) at 100 K and 50 vacancies at 323 K, both in 10-lattice-parameter boxes, with simulated time reaching more than 1 second. In both cases, relaxation occurs over several orders of magnitude in time. The microscopic details of theses processes closely follow what was observed when annealing ion-implanted c-Si, which also ages logarithmically, described by the so-called “Replenish-and-relax” mechanism, which indicates it is not only applicable to covalently-bonded materials, but to metals as well. The logarithmic decay in potential energy is associated to the increase of activation barriers necessary to unlock the system, which is otherwise trapped in an energy landscape that has no accessible relaxation events. However, these unlocking events do not directly lead to relaxation, but rather replenish a distribution of activated processes that contains relaxation events, which will be executed later on.
Furthermore, self-defect-induced hydrostatic stress is identified as an important driver of this behavior. Initially, the point defects exert large pressure on the system, which in turn decreases the migration barriers relative to an unstrained system. As point defects cluster, the pressure decreases and the migration barriers increase, leading to logarithmic relaxation. While the role of pressure is probably not generally applicable to all logarithmically relaxing systems, it is plausible that the interaction of localized defects explain many features of more disordered materials.

During a cell cycle, mitosis is a process, in which a mother cell duplicates into two generically similar daughter cells. In the initial stage of mitosis, the mother cell, attached on a substrate, would undergo a dramatical shape change by detaching from the substance and forming a round surface. At the late stage of mitosis, a contractile ring would form in cell equator and the mother cell would split into two daughter cells, which is known as cytokinesis for eukaryotic cells.
By treating a cell and extra celluar matrix as complex viscolestic fluid mixture, we have developed a series of three-dimensional hydrodynamic multi-phase models by a phase field approach, studying mitosis cell rounding and cytokinesis. Patterns of mitotic cell rounding (MCR) and cell division process have been observed. In this talk, our current study on the mechanism and controlling factors for cell mitosis would be present. 3D numerical simulations will be shown, as well.
Our 3D hydrodynamic models for cell mitosis agree quantitatively with the experiment data from our collaboratos. The experimental-validated macroscopic models are effective tool for analysing the mechanism and dynamics of cell mitosis.

Modern instruments and creative experimentalists combine to produce remarkable data for diverse biological materials. I will discuss the biological questions posed by my experimental collaborators, the experimental probes of biological materials to gain insight into these questions, the modeling efforts by my theoretical collaborators, and some results toward understanding fundamental questions about DNA packaging in yeast nuclei, mechanochemical mechanisms of oscillatory rounded cell phenotypes, and how diverse particles (viruses, bacteria, drug carriers, environmental particulates) diffuse in human mucus barriers.

The movement of nanoparticles in biological fluids like blood, mucus and cytoplasm is heavily influenced by physical and chemical interactions with a wide variety of environmental factors. Microscopy has revealed evidence that supports using the generalized Langevin equation and fractional Brownian motion to describe this motion in some settings while in other settings the movement is better described by state-dependent diffusion. In this talk I will give a brief survey of the physical mechanisms that give rise to these distinct behaviors as well as the statistical approaches that have been implemented to move toward rigorous model selection.

Fibrous materials are ubiquitous in the biological world. The extracellular matrix, the cellular cytoskeleton, connective tissue are all composed from random fiber networks made from different types of fibers. Composite networks are often encountered in the engineering world as well, with gels, paper and non-wovens being prominent examples. In this work we use two and three dimensional computer models of networks composed from fibers of different properties and investigate the effect of the network composition on the system-scale properties, in particular, the network stiffness. We observe that a small concentration of stiff fibers has a weak effect on the mechanics of affinely-deforming networks, but has a spectacular effect on the mechanics of the non-affine networks. As a special case of composite networks we also consider structures made from the same type of fiber, but in which the contour length of some fibers is larger than their end-to-end distance. A model allowing mapping the behavior of these networks to that of homogeneous networks without slack is proposed.

In order to evaluate the mechanical quality of forming engineered soft tissues, it is essential to predict the forming extracellular matrix (ECM) phase mechanical properties from the overall composite response. Without a proper formulation, it is impossible to know, in a quantitative sense, to what degree the measured mechanical response is influenced by the remaining scaffold component. Previous modeling efforts have resulted in a descriptive mechanical model for intact needle non-woven (NNW) scaffolds. When applied to tissue-scaffold composites using the rule of mixtures, however, this model was not able to account for the observed increases in stiffness of the composite and substantially underestimated the predicted composite stiffness compared to the experimentally measured values. The models was also restricted to small deformations, and the meso-scale composite model relies heavily on an empirically determined coupling factor to account for observed scaffold-ECM interactions. Moreover, structural measurements indicated that scaffolds experience reduced volume fractions. Further, after extended in vivo durations, the scaffold becomes highly fragmented and discontinuous. Both previous model formulations do not account for such scaffold changes and may ultimately underestimate tissue properties. In this work, we develop a structural constitutive model that separates the scaffold mechanical contributions to enable estimation of forming engineered tissue mechanical properties for NNW scaffolds. The new model is proposed with the following assumptions:
The strain energies of the scaffold, ECM, and scaffold-ECM interactions are additive.
A measurable amount of scaffold will degrade with time, but the overall continuity of the scaffold phase will remain intact.
The scaffold remains in intimate contact with the ECM phase.
The ECM phase can be modeled as an incompressible anisotropic soft tissue.
Scaffold-ECM interactions manifest as shearing and extensional effects between the scaffold fibers that are in effect embedded in the ECM.
Scaffold-ECM interactions are additive and thus can be separated.
NNW scaffolds were seeded with vascular smooth muscle cells and incubated for up to 4 weeks using standard methods. Another group of NNW scaffolds were imbedded with PAM gels of graduated, known stiffnesses to calibrate the model with a known standard. Both groups were subjected to biaxial mechanical evaluation. A strong relationship between effective scaffold fiber stiffness and matrix shear modulus was found. Additionally, the model was shown to estimate the ECM shear modulus accurately. We hope that the insights gained from our simulations will be used to guide the design of scaffolds and selection of process variables so that the resulting engineered tissues mimic the non-linear mechanical behavior of the native tissues.

A genome is a complete copy of the entire set of genetic material that makeup a specific organism. The genome of eukaryotes is distributed into chromosomes. For example, the human genome (actually, two copies of it) is divided among 23 pairs of chromosomes. Chromosomes are made up of DNA, whose main function is to carry genetic information. All organisms, from bacteria to humans, face the daunting task of replicating, packaging, and segregating up to two meters of DNA when each cell divides. This task is carried out up to a trillion times during the development of a human from a single fertilized cell.
Chromosome segregation is challenging because the cell&’s packing strategy needs to retain organizational mechanism that are responsible for delineating gene activity, as well as the higher order spatial interactions that dictate the propensity of chromosomes to reside in specific domains. A the same time, chromosome segregation must be executed with high fidelity so that, after division, both the mother cell and the daughter cell receive precisely the same DNA content. Although many of the chemical processes that take place during cell division and interphase have been detailed, our understanding of the physical and topological properties of chromosomes during these stages of the cell cycle is still far from conclusive. It is widely recognized that both theoretical and experimental breakthroughs are in order before a satisfactory picture can be reached.
In this talk we highlight our efforts to develop mathematical models of chromosomal DNA using principles from polymer physics, anchored in our current biological understanding, closely guided by and benchmarked against experimental data. Kerry Bloom&’s lab at UNC has developed real-time imaging of yeast for purposes of quantitating the progression of mitosis, including spindle assembly/disassembly dynamics and chromosome movement in living cells. These efforts allow the visualization of the nucleus and mitotic spindle for the first time in live yeast and the quantification of dynamic readouts of DNA spatial organization throughout the cell cycle.
In this lecture, we will report progress from our collaborations and new directions. From the perspective of mathematics and materials, there is tremendous insight that can be gained from understanding how biological systems exploit mechanics and chemistry to perform remarkable tasks. In this respect, yeast provides an ideal model system to understand the principles behind chromosome organization and segregation.

We consider the effects of aspect ratio and orientational order of nanoparticles on the dielectric properties of nanocomposites. The motivation is to determine the effects of orientational order, since ambiguities exist in the literature. We focus on metallic nanoparticles, and show that, in dilute systems, theory, experiments and numerical simulations all indicate that the effective dielectric constant increases with increasing aspect ratio and degree of alignment.

In this talk, we will present some recent work concerning the derivation of bounds on the volume fraction occupied by an inclusion in a body (or one of the phases in a two-phase composite). We assume that both the inclusion and the body are isotropic and homogeneous with complex-valued conductivities. The bounds we derive correlate the average electric field, average current field, and volume fractions of the phases; practically, the average electric field and average current field can be measured in terms of boundary measurements of the complex potential and electric current flux. These bounds could have potential applications in nondestructive testing and medicine, such as in the screening of organs prior to transplantation.

Poroelastic materials are composites of elastic frame with pore space filled with fluid, eg. rock, sea ice and cancellous bone. The dynamic tortuosity is an effective property which quantifies the effective friction arising from the interaction between the solid frame and the viscous fluid in the tortuous pore space; it plays an important role in the energy dissipation of the poroelastic wave equations, which have been used to model ultrasound propagation in cancellous bones. However, dynamic tortuosity is difficult to measure. In this talk, I will present the recent results on using the dynamic permeability, which is easier to measure, at different frequencies to reconstruct the dynamic tortuosity function for poroelastic materials with any pore space geometry. The key ingredient in the reconstruction is the integral representation formula (IRF) of tortuosity and its analytical structure. The mathematical structure of the reconstructed tortuosity leads to an effective numerical treatment of the memory term appearing in the high-frequency poroelastic wave equations.The IRF, the reconstruction scheme with numerical results, together with the relations between pore space geometry and moments of the measure in the IRF will be presented. This research is partially sponsored by NSF-DMS.

Rechargeable lithium-air (Li-air) battery has been considered as a promising battery technology candidate to provide power sources for next-generation electric vehicles, primarily because of its high theoretical energy density that is about 5-10 times higher than that of the state-of-the-art lithium-ion batteries. However, the commercialization of rechargeable Li-air batteries is still limited by many barriers. One of the major challenges in the design of air electrode is the blocking of oxygen and Li⁺ pathways by the precipitation of Li₂O₂ during battery discharge thus limiting the full utilization of air electrode. A good understanding on the morphology and microstructure of the air electrode developed during the discharge process can lead to a pathway to circumvent the drawbacks of the current electrode designs and improve the battery performance.
Here, a multiscale modeling approach with high predictive capabilities has been used to analyze the discharge process of Li-air batteries. Specifically, we propose a nano pore-scale model that bridges the gap between 1D continuum models and atomistic models. The model includes the following mechanisms: 1) diffusion-limited transport of oxygen across the porous structure of the cathode, 2) varying pore size distributions and surface-to-volume ratios, 3) adjustment of distribution of defects and functional groups on carbon surfaces, and 4) rate-dependent morphology of Li₂O₂ growth. We examine how the above mechanisms affect the discharge capacity of Li-air battery at different current densities. The calculated discharge curves are compared with experimental measurements. Our studies provide an insightful fundamental understanding and diagnostics to the electrode process, which can be used to direct the cathode structure design and operating condition setup for Li-air batteries. In addition, this approach can be easily applied to other metal-air batteries with metals such as Zn, Na, and Mg, etc.

Anomalous localized resonance phenomena is observed at the interface between positive index and negative index materials. We analyze cloaking due to anomalous localized resonance in the quasistatic regime in the case when a general charge density distribution is brought near a slab superlens. It is well known from previous works that if the charge density distribution is within a critical distance of the slab,
then the power dissipation within the slab blows up as certain electrical dissipation parameters go to zero inside the slab. On the other hand,
if the charge density distribution is further than this critical distance from the slab, then the power dissipation within the slab remains bounded. We will analytically show how the critical distance explicitly depends on the rate at which the dissipation outside of the slab goes to zero and present relevant numerical support.

Dynamic materials are artificially constructed structures (like metamaterials) which may vary their characteristic properties in space or in time, or both, by an appropriate arrangement or control. These controlled changes in time can be provided by the application of an external (non-mechanical) field, or through a phase transition. Such materials exhibit very unusual behavior.
In principle, all materials change their properties with time, but very slowly and smoothly. To avoid any misunderstanding, we specify that these controlled changes in properties of dynamic materials should be realized in a short or quasi-nil time lapse and over a sufficiently large material region.
The characteristic phenomenon for dynamic materials is wave propagation because it is also space and time dependent. As a simple example of the complex behavior of dynamic materials, the one-dimensional elastic wave propagation is studied numerically in periodic structures whose properties (mass density, elasticity) can be switched suddenly in space and in time. It is shown that dynamic materials have the ability to dynamically amplify, tune, and compress initial signals over a wide range of carrier frequencies.
The thermodynamically consistent high-resolution finite-volume numerical method was successfully applied to the study of the behavior of dynamic materials. The extended analysis of the influence of inner reflections on the energy accumulation and concentration in the dynamic materials is presented.

A complete characterization is given of the possible macroscopic deformations of periodic nonlinear affine unimode metamaterials constructed from rigid bars and pivots. The materials are affine in the sense that their macroscopic deformations can only be affine deformations: on a local level the deformation may vary from cell to cell. Unimode means that macroscopically the material can only deform along a one dimensional trajectory in the six dimensional space of invariants describing the deformation (excluding translations and rotations). We show by explicit construction that any continuous trajectory is realizable to an arbitrarily high degree of approximation provided at all points along the trajectory the geometry does not collapse to a lower dimensional one. In particular, we present two and three dimensional dilational materials having an arbitrarily large flexibility window. These are perfect auxetic materials for which a dilation is the only easy mode of deformation. They are free to dilate to arbitrarily large strain with zero bulk modulus.

Nanowire metamaterials are a class of composite photonic media formed by an array of aligned plasmonic nanowires embedded in a dielectric matrix. Numerous applications in modern optics can be realized through the study and understanding of light interaction with nanowire metamaterials. These range from imaging, sensing, security, to solar power, optical information processing, and photonic circuits making nanowire metamaterials a material platform of choice. Depending on exact composition, geometry, and excitation wavelength, nanowire structures are known to exhibit elliptical, hyperbolic, or epsilon-near-zero (ENZ) responses. It was shown however that the optical properties of these composites deviate from the predictions of effective-medium theories (EMTs).
The reason for this deviation is a longitudinal electromagnetic wave that only exists in nonlocal systems. We have previously shown that this wave originates from the coupling of cylindrical surface plasmon modes propagating along the nanowires and analyzed its dispersion numerically. We also developed an analytical technique that provides an adequate description of the optical response of wire-based metamaterials, once the dispersion for the longitudinal wave is known. However, the existing formalism maps this dispersion to the solution of an eigenvalue problem that is computationally intensive and, depending on implementation, may become numerically unstable.
In this work we present a simplified analytical approach that can be used to approximate the dispersion of the longitudinal wave in the wire-based metamaterials, avoiding numerical solutions to an eigenvalue problem. The results of nonlocal effective medium theory based on such approximate solutions are shown to agree with the numerical solutions of Maxwell&’s equations and with predictions of the earlier developed formalism. Extension of the developed approximation to describe the optics for other anisotropic plasmonic metamaterials is discussed.

Multi-stability is important for sustainable design of multi-functional structures. Unlike many actuators, they don't need energy to be maintained in their functional states - but only to effect the transitions between them. Geometry can be used to amplify material responses, store and couple elastic energy to other stimuli.
We use combinations of experimental and modelling approaches to uncover novel phenomena in seemingly common object deformations.
We show new features in the inversion of a magnetic spherical cap using high speed photography, which we model by finite element methods. We also show interesting instabilities/multi-stabilities in several other shell structures, which are explained with structural energy minimization.

A traveling wave tube amplifier can be thought of as a cylindrical dielectrically loaded waveguide with an electron beam running through its center. The beam is surrounded by a dielectric jacket, and, when the dielectric constant is greater than unity, it is possible to get amplification from the traveling wave tube. Most dielectric materials, however, are insufficient for high power applications. A possible approach is the use of sub-wavelength all-metal interaction structures that effectively act as a dielectric medium with dielectric constant greater than unity. This provides the opportunity for design of TWTs with metal beam-wave interaction structures. In this talk, we investigate the influence of metal interaction structures on the anisotropy of effective dielectric tensors and on the gain, bandwidth and frequency of operation for short traveling wave tube amplifiers.

Nano-scale surface undulations have been observed in numerous biological materials such as DNA in human cells, cellulose in plant cell walls, chitin in arthropods cuticles, and collagen in human compact bones that display the twisted plywood architecture. These biological nano-structured surfaces display unique optical effects such as the iridescent colors observed in some flower petal surfaces that closely resembles the spontaneous free surfaces of cholesteric liquid crystals. To understand what is the origin of undulation length scales and which parameters control its wavelength and amplitude, a theoretical scaling and computational analysis of the formation and structural characteristics of surface nano-wrinkling for a well-known cellulose chiral liquid crystals (LC) material model system is presented. Using a generalized LC shape equation here adapted to cholesteric free surfaces we derive a model in terms of Laplace pressure (area dilation), Herrings pressure (area rotation), and director orientation gradients pressure. The capillary pressure generated by surface orientation gradients is shown to drive the wrinkling. The period and depth of the surface structure are shown to be dependent on the plywood&’s helical pitch. It is shown that the ratio of amplitude to period of the surface undulation scales linearly with the anisotropic surface tension. To study the surface water-based actuation mechanism, the interaction of anisotropic interfacial tension, swelling through hydration, and capillarity at free surfaces are incorporated. As hydration changes the molecular chirality of fibers and as a result the helix pitch, the effect of hydration on the nano-surface profile is captured by a cholesteric with a linearly varying pitch. These new finding can be used to characterize plant-based plywoods as well as in bio-inspired design of optical devices.

The melting of a solid is an example of the wider class of first-order phase transitions, which are ubiquitous in nature and have been studied intensely for over a century. However, due to the intrinsic time-scale disparity in the problem -- the average time spent by the system in metastable states is generally orders of magnitude longer than transition times between these states -- the microscopic mechanism of melting remains unelucidated. I will present a method to efficiently explore the free energy surface and search of reaction pathways at finite temperature conditions and illustrate its capability by studying the melting of a prototypical metal - copper. We find that melting can occur via multiple, competing pathways involving the formation of point defects or dislocations. Moreover, each path is characterized by multiple barrier crossing events arising from multiple metastable states within the solid basin. A common signature of the melting trajectories is the existence of a metastable liquid embryo. Our results suggest the existence of different regimes of melting regimes as a function of temperature.

Using the calculus of variations it is shown that important qualitative features of the equilibrium shape of a material void in a linearly elastic solid may be deduced from smoothness and convexity properties of the interfacial energy. In addition, short time existence, uniqueness, and regularity for an anisotropic surface diffusion evolution equation with curvature regularization are proved in the context of epitaxially strained two-dimensional films. This is achieved by using the $H^{-1}$-gradient flow structure of the evolution law, via De Giorgi's minimizing movements. This seems to be the first short time existence result for a surface diffusion type geometric evolution equation in the presence of elasticity.

Two dimensional crystal materials such as graphene and hexagon boron nitride (h-BN) hold great potential for various applications. However, their surface geometry, adsorption and wetting as well as multi-field coupling significantly influence the actual properties and behaviors of those dimensional materials when they are integrated into nano-electromechanical system (NEMS). By using and combining mechanical modeling, molecular dynamics simulations, first-principles calculations, we have extensively studied the coupled physical and mechanical properties, tuning surface structure and properties of graphene and h-BN materials. We provide an energy conversion mechanism by using graphene wrinkle thermophoresis and demonstrate that wrinkled graphene could be a good candidate for field emitter; suggest a viable way to modify water adsorption on a graphene-coated surface and unveil the role of graphene as a passivation layer for the wetting of a charged substrate; provide insights into modulating the electronic properties of substrate-supported h-BN nanosheets through charge injection mediated O adsorption. The unveiled mechanisms afford feasible ways and routes for the design and developing of new nanofunctional and nanoelectronic devices.
References
1.Y. F. Guo, W. L. Guo, Insulating to metallic transition of an oxidized boron nitride nanosheet coating by tuning surface oxygen adsorption. Nanoscale, 6 (7), 3731-3736 (2014).
2. Y. F. Guo, W. L. Guo, Effects of graphene coating and charge injection on water adsorption of solid surfaces. Nanoscale 5, 10414-10419 (2013).
3. Y. F. Guo, W. L. Guo, Soliton-like thermophoresis of graphene wrinkles, Nanoscale 5, 318-323, (2013)
4. Y. F. Guo, W. L. Guo, Electronic and Field Emission Properties of Wrinkled Graphene, J. Phys. Chem. C 117, 692-696 (2013).

We consider carbon nanostructures that consist of one or more graphene sheets. Each graphene sheet is a one-atom thick and contains carbon atoms arranged in a hexagonal lattice. Neighboring atoms within a sheet interact via strong covalent bonds, making graphene essentially inextensible, but amenable to large elastic bending deformation. The interaction between the sheets is of a weak Van-der-Waals-type and allows for a relatively easy sliding.
When upscaled to the macroscopic level, each graphene sheet can be represented by an elastic shell and the energy of interactions within a sheet reduces to an elastic energy. The macroscopic analog of weak interactions is typically thought of as a pressure-type term that depends only on the local distance between the sheets.
In my talk, I will demonstrate that this reduction is not always correct as the weak interactions also depend on relative arrangements of atoms of the neighboring shells. I will discuss how one can borrow from the idea of a Gamma-development from calculus of variations to obtain a macroscopic Ginzburg-Landau-type model for carbon nanostructures. I will also connect mathematical predictions to experimental observations.

A multi-walled carbon nanotube consists of several concentric tubes formed by graphene sheets---one-atom thick layers of carbon atoms arranged in a hexagonal lattice. A typical cross-section of a multi-walled tube can be modeled as several closed, nested, one-dimensional chains of atoms. In this talk, we present a rigorous atomistic-to-continuum procedure that upscales the energy of this discrete system of atoms to a continuum energy defined over curves in the plane. This continuum energy retains important atomistic information about lattice registry between the nested chains of atoms. In particular, the continuum model explains polygonization of cross-sections of large multi-walled nanotubes as a competition between the bending component of the energy and the component due to weak van der Waals interactions between adjacent walls.

Biomimetic polymers (BMPs) are useful for materials science and bioenergy applications like CO₂ separation because of a diverse availability of monomers, high thermostability, and resistance to biodegradation. We have been developing a multi-scale simulation framework to facilitate experimental design and development of BMP systems, with the goal of forming ordered structures and pore networks. These simulations also provide insights about the key forces governing folding and assembly in such systems, which are currently poorly understood.
For example, experiments show that amphiphilic peptoid BMPs form fibers in solution and/or micron-scale bilayers on a mica surface. Peptoids are challenging to simulate because the amide bonds between residues can isomerize between cis and trans and the peptoid amide cannot form backbone-backbone hydrogen bonds. In addition, replica-exchange molecular dynamics (REMD) atomistic simulations of dimers of these 12-residue peptoids do not reproduce the experimental structural forms. Thus, we are developing a MARTINI-based coarse-grained (CG) force field for the peptoid backbone to model cooperative assembly at larger length scales. For bonded terms, atomistic simulations show that the backbone N_i-N_j distance is consistently 0.37 nm, while the N_i-N_j-N_k pseudo-angle clearly distinguishes the cis and trans states of the amide bond between residues i and j. For non-bonded parameters, we create a new particle type from the MARTINI P3 type that reflects the unusual hydrogen bonding properties of the peptoid amide. CG simulations of all-trans sarcosine 12-mer recover the bonded potentials seen in a corresponding atomistic simulation, and they also qualitatively reproduces the atomistic radius of gyration (R_g) distribution.
In a parallel example, we are structurally modeling different sequences of a new polymer architecture, in which variable-length non-amide linkers connect core elements bearing sidechains, to inform experimental designs. The cores and linkers are parameterized using the generalized amber force field, and 500-ns REMD simulations are used to explore the conformational space of short polymers. K-means clustering is used to identify favored structures. Simulations of hexamers suggest several favored motifs with different backbone/backbone hydrogen bonding and π stacking configurations. The simulations also suggest that imine sidechains increase helical propensity, chiral linkers increase conformational order, and longer linkers promote more globular structures. We are currently performing experiments to test these simulation-based hypotheses. In simulations of 12-mers, more globular and elaborate tertiary structures form that are reminiscent of proteins. This suggests significant promise of the novel polymer architecture for applications where intramolecular conformational and structural order are functionally important.

Jazmín Yanel Juárez-Chávez^1*, Bernardo Campillo-Illanes³, Maraolina Domínguez-Díaz¹, Sergio Alonso Serna-Barquera², Marco Antonio Cruz-Chávez².
1Posgraduate Studies in Engineering and Applied Sciences Research Center,
2Engineering and Applied Science Research Center - UAEM
3Institute of Physical Sciences/Faculty of Chemistry-UNAM.
Av. Universidad 1000, Cuernavaca, Morelos, C.P. 62209, MÉXICO
Corresponding author:{jazmin*, mcruz}@uaem.mx
Keywords: Alloy, Chemical Composition, Heuristics, Maximize Strength, Lower Cost.
Steel has a great importance for several types of industries especially for the construction, the petroleum and gas industry. Therefore, the continuously improvement and design of their mechanical properties to achieve suitable characteristics for its many and new challenging applications are still in vogue. However, this can lead to complex experimentation including a big number of variables at elevated costs that could made their development unaffordable. An intend to solve this economic and technological barriers, computational heuristics methods can find the best possible configuration between different possibilities and also can be very useful to get results quickly at low cost. This has been applied in the steel manufacture with sounded successful, contributing substantially on savings in both time and money for their development and production. The purpose of this investigation is to maximize the strength of a commercial X52 microalloyed steel, using computational heuristics methods like Simulated Annealing and Iterated Local Search Algorithms. Thirteen chemical elements contained in this microalloyed steel were used: Carbon, Chromium, Copper, Manganese, Molybdenum, Nickel, Vanadium, Nitrogen, Niobium, Titanium, Phosphorus, Sulfur and Silicon. The concentration selected for each of these elements is within the commercial alloy established ranges. When executing the algorithm with the implemented heuristics, it was found that it is possible to improve the steel mechanical resistance and could reduce its production expenses. With the implementation of the Simulated Annealing and Iterated Local Search Algorithms, it was also possible to perform tests with another composition ranges typically used in the fabrication of X65 and X70 microalloyed steel grades. Finally these results were compared to those obtained for the X52 microalloyed steel.

Finding a prosthetic for knee and hip replacements is challenging due to the fact that the implant must be biocompatible, able to withstand substantial stresses, and have an elasticity closely matching that of bone. Titanium (Ti) is biocompatible and can withstand the stress needed to be a very good candidate for knee and hip implants. The elastic modulus of pure Ti is also much lower than most materials but still higher than that of bone. A large difference in elastic modulus between bone and implants leads to stress shielding, tissue dying around the bone and implant failure. The present work aims to study the effects of alloying elements Mo, Nb, Ta, Zr, and Sn on the elastic modulus. To this purpose, systematic single crystal elastic stiffness constants (cij&’s) are predicted for five binary systems of Ti-Mo, Ti-Nb, Ti-Ta, Ti-Zr, and Ti-Sn based on first principles calculations as well as the ordered and the special quasirandom structures. In addition, the polycrystalline aggregate properties of bulk modulus, shear modulus, Young&’s modulus, and Poisson ratio are also calculated for these alloys. The data gathered from these efforts are then compared with available experimental and other first-principles results, which set a fundation to design biocompatible Ti alloys in terms of elastic properties.

Generally, the electrodes are regarded as free electron gases when we calculate the transport characteristics of nanostructure materials or devices. However, the electrons inside the electrodes interact with each other by Coulomb force. Therefore, they are never free electrons. In three dimensional electrodes, there are little electron correlation. However, in low-dimensional electrodes, electron correlation becomes much larger than that in three dimensional ones. Recently, nanotechnology has made much progress to fabricate quasi-two-dimensional (2D) electrodes precisely and easily. As a result, we must consider whether two-dimensional electrodes can be regarded as free electron gases. In this study, we investigate the electron energy spectrum of 2D electrodes, taking into consideration the electron correlation. We treat the Coulomb interaction as a perturbation within GW approximation. The one-particle Green&’s function for a dressed electron with momentum pand energy E is expressed by
G(p, E)=1/(E-xi;(p)-Σ(p, E)+iδ),
where Σ(p, E) is the selfenergy, δ is an infinitesimal positive quantity, and xi;(p) is the kinetic energy estimated from the Fermi energy. We can describe the selfenergy within the GW approximation in the following equation:
Σ(p, E)= i Tr[ G₀(p+ q, E+omega;)W(q,omega;)],
where Tr stands for integration over momentum q and energyomega;, G₀(p, E) is the bare one-particle Green&’s function, and W(q,omega;) is the screened Coulomb interaction. Finally, we calculate the spectral function A(p, E) to obtain the quasi-particle energy spectrum of 2D electron liquid using the following equation:
A(p, E)= -1/π Im[G(p, E)],
where Im stands for the imaginary part. In this study, we assume that the 2D electrodes consist of high-doped GaAs semiconductors because the recent nanotechnology enables us to make very thin quasi-2D electrodes of semiconductors. Since the GW approximation is precise for high density electron liquid, we set r_s parameter to be 1.5. Here, the dimensionless r_s parameter is an average distance between electrons in units of effective Bohr radius. The real part of the selfenergy corresponds to an energy shift from bare electron energy. The imaginary part of the selfenergy is proportional to the inverse of the lifetime of the dressed electron. The calculated results show that the real part of the selfenergy is large due to the large electron correlation and that the renormalized Fermi energy is -2.15 in units of E_F which is the Fermi energy of free electron gas. Although the lifetime at the renormalized Fermi energy is infinity, the lifetime of the dressed electron at the other momenta is very short except for Fermi momentum. For example, the lifetime is about 40 fs at the momentum of p=0.4p_F. These results suggest that the free electron model is justified only at Fermi momentum and that we should not regard the low-dimensional electrodes as free electron gases without careful consideration under high electric filed or high temperature.

The thermal interface conductance between Al and Si was simulated by a non-equilibrium molecular dynamics method. In the simulations, the coupling between electrons and phonons in Al are considered by using a stochastic force.
The results show the size dependence of the interface thermal conductance and the effect of electron-phonon coupling on the interface thermal conductance. To understand the mechanism of interface resistance, the vibration power spectra are calculated. We find that the atomic level disorder near the interface is an important aspect of interfacial phonon transport, which leads to a modification of the phonon states near the interface. There, the vibrational spectrum near the interface greatly differs from the bulk. This change in the vibrational spectrum affects the results predicted by AMM and DMM theories and indicates new physics is involved with phonon transport across interfaces.
Moreover, The effect of defects on the thermal interface conductance was investigated. The results showed that, as the size of defects increases, the interface resistance is considerably increased. The heat current is decreased and the interface temperature difference is increased in the meantime, which contributes to the deduction of thermal interface conductance. Besides the contribution of atomic level disorder at interface, the cylindrical protruding/hollow defects provide more interface resistance. The defects at the interface not only decrease the contact area but add more boundary scattering of phonons. The MD simulation results suggest that the nano-structured defects has significant effect on the thermal transport across the interface.
Keywords:
Molecular Dynamics, Thermal Interface Conductance, Electron-Phonon Couplings, Metal/Semiconductor, Defects

Abstract: In this study, five polynitro-hexahydropyrimidine derivative compounds as a potential candidate for high energy density materials (HEDMs) have been investigated by using quantum chemical treatment. Geometric features, electronic structures and other energetic properties of these compounds have been systematically studied using density functional theory (DFT, B3LYP). Analysis of the bond dissociation energies (BDEs) for C-NO2, N-NO2, O-NO2 and C-N3 bonds at B3LYP/6-31+G(d,p) level, indicates that substitutions of the -N3 group is favorable for enhancing the thermal stability of the designed molecules. From computational results it is noted that substituent groups strongly affect the heat of formation. The research demonstrated that the heat of formation of the compound 5-azidomethyl-1,3,5-trinitro-hexahydropyrimidine that contain -N₃ group as a substituent has larger heat of formation value. Detonation performances were evaluated by the Kamlet-Jacobs equations based on the calculated densities and heats of formation. It is found that 5-nitratomethyl-1,3,5-trinitro-hexahydropyrimidine derivative with the predicted density of 1.78 g/cm³, detonation velocity of 9.13 km/s, and detonation pressure of 36.91 GPa may be novel potential candidate of high energy density materials among the designed compounds.
Key words: Polynitro-hexahydropyrimidine, DFT, energetic materials, detonation performance.

Although heat conduction in crystalline solids is reasonably studied, heat transfer mechanisms in complex fluids are currently poorly understood. For liquids composed of molecular chains, the bulk thermal conductivity is the result of intermolecular and intramolecular interactions. This presentation uses octane as a model to study the contribution of each type of atomic interaction to the bulk heat transfer to further the understanding of thermal conductivity in complex fluids. The experimental bulk thermal conductivity of liquid octane is around 0.2 W/mK, although previous studies suggest that heat conduction along molecular chains can be very high. Equilibrium molecular dynamics and the Green-Kubo formula are used to study heat transfer in bulk octane at the atomic level. An effective thermal conductivity for each type of atomic interaction is defined based on the Green-Kubo formula and used to separate the contribution to the bulk thermal conductivity. The calculations reveal that the thermal conductivities of complex fluids are limited not only by heat transfer between molecules but the additional interactions also reduce heat transfer along the chain.

The presence of structural defects such as dislocations, stacking faults, and grain boundaries (GBs) affects significantly the electrical, magnetic and optical properties of ZnO [1,2]. Complexes of native point defects with impurities can create p-type conductivity in low angle GBs [3]. To understand atomic structure and the effect of point defects near GBs, we have performed first principles calculations on a 45⁰ GB in ZnO, using the Vienna Abinitio Simulation Package (VASP) with the generalized gradient approximation. A Monkhorst Pack k-grid (1x1x6) and projected augmented wave pseudo potentials are used along with a kinetic energy cut off of 400eV. The GB is formed by attaching two wurtzite ZnO [0001] crystals oriented at an angle of 45⁰ to each other. The atomic coordinates of the supercell are relaxed with energy and force tolerance of 0.0001 eV and 0.004 eV/Å, respectively. The relaxed GB consists of 8 and 10 rings and has no dangling bonds, where the Zn and O atoms are 4 and 3 coordinated. The formation energy of Zn and O vacancies shows that they prefer to be located at the GB. Zn vacancies at the GB have low formation energy and induce spin polarization. The O atoms surrounding the Zn vacancy show magnetic moments of about 0.5mu;_B/atom, whereas no magnetism can be introduced by O vacancies.
References
1. V. Srikant et al. J. App. Phys. 81, 6357 (1997).
2. Y. Sato et al. Phys. Rev. Lett. 97, 106802 (2006).
3. J. M. Carlsson et al. Phy. Rev. Lett. 91, 165506 (2003).

With current technology moving rapidly towards smaller scales, nanoparticles are synthesized in increasing numbers and explored for various useful applications such as catalysis, magnetic storage media, photonics, and drug delivery. The structure of metallic nanoparticles can be assessed accurately by various experimental techniques. Experiments, however, may be costly and time demanding. A viable alternative for providing structural information is through inexpensive theoretical models obtained from density functional theory (DFT) and molecular dynamics (MD). Although DFT is successful in studying the atomic and electronic structure of small size nanoparticles, it is inapplicable to a few nm size metallic nanoparticles because of the large number of atoms. To overcome DFT model size limitations, approximations accounting for the movement of positively charged metallic atoms in terms of Newtonian mechanics and treating the see of fast moving electrons forming metallic bonds as an effective medium have been developed. All approximations, however, have been tested and optimized mostly against ab initio or experimental data for bulk metals possessing perfectly 3D periodic, i.e. largely regular, atomic-scale structure. This leaves an open question about how accurate these approximations are when applied to nanometer-size metallic particles where otherwise like atoms may not necessarily exhibit like coordination spheres and, hence, like interatomic interactions very likely leading to irregularities at the atomic scale structure. We present theoretically derived models that are matched against the experimental pair distribution function (PDF) data. It is found that particular information derived from structure-sensitive experimental studies such as atomic PDFs studies needs to be incorporated in the theoretical modeling effort so that its outcomes represent the atomic-scale structure of real metallic nanoparticles accurately enough for a rational consideration of their synthesis and properties targeted for optimization.

Single crystals of the metal halide class of materials are widely used in scintillator-based detectors of high energy electromagnetic radiation with applications in high energy physics, natural resource exploration, homeland security, and medical imaging. Metal halide compounds of interest to national security combine chlorine, bromine or iodine with one or more Group I, Group II or rare earth elements. While promising scintillators, single crystals of such compositions can be difficult to synthesize due to anisotropic thermal expansion, low symmetry and supercooling. These factors necessitate carefully designed gradients to ensure ideal growth.
Due to the time and resource-intensive process of optimizing the bulk growth processes and equipment for successful single crystal synthesis of novel materials, predictive numerical thermal models were developed using CGSim® software to analyze and explore the thermal fields in various commercially available experimental multi-zone tube furnaces. The aim of this study was to take an existing furnace as received from the manufacturer and through simulations of multiple heater settings and optional augmentation by diaphragm and heat sink geometries, produce a model which approaches an ideal processing environment using the melting point for a novel material as the sole constraint in the optimization process. The model was ultimately used to eliminate the tedious task of repeated trial and error growth experiments, thereby reducing the optimization procedure from several weeks to a few days of modeling.
The resulting model was used to design and implement diaphragms and heat-sinks in the experimental furnace, and benchmark measurements were shown to closely approximate the predictive model. The information gained from simulations was combined with experimentally determined melting and solidification temperatures to design the actual thermal set-up that is used for crystal growth. A Oslash; 1” crystal of CsCaI₃:Eu 3% was successfully grown using an augmented three-zone furnace, a modified zone regime featuring a higher temperature just above the heat sink (i.e. the top two zones were hotter than the bottom zone, and the central zone was hottest of the three) and a slow translation rate of 1 mm/hr.

While the remarkable optical efficiency and size-tunable material properties of semiconductor nanostructures have been the focus of much research, less attention has been paid to understanding their unique heat-related processes, which are also of paramount importance. Thermal processes play a critical role in a variety of energy-related, semiconductor-based technologies; heat generation is a major energy loss mechanism in all semiconductor devices. Additionally, technologies such as light-emitting diodes and thermoelectric power converters require high and low thermal conductivity, respectively, in the active layer to maintain ideal performance.
In the nanometer size regime, bulk theories of thermal transport often produce qualitatively incorrect rate predictions. This is due to the elevated importance of diffusive boundary scattering and phonon confinement. Here, we employ fully atomistic modeling to simulate thermal transport in semiconducting nanomaterials. Specifically, we employ non-equilibrium molecular dynamics, a method which is well suited to the description of the crowded, heterogeneous environments presented by nanoscale, condensed-matter systems. Specifically, we investigate the roles played by chemical composition, surface chemistry, surrounding environment, and surface curvature in thermal conductivity. Our results provide new insight into thermal transport in nanoscale systems and yield guidelines for the design of materials with tailored thermal properties.

Boron nitride nanotubes have superior physical, thermal and mechanical properties and are being considered for various structural applications. One of the interesting advantages of BNNTs is their capability in shielding space radiation alongside with their superior mechanical strength which makes them a perfect choice to be used in space structures. Although these unique combinations of properties promise a brighter future for long duration human space exploration, but like their counterpart Carbon Nanotubes (CNTs), adding them to polymeric matrix brings new processing challenges. Non-homogeneous dispersion due to agglomeration and weak surface interaction between polymer molecules and nanotubes results in limiting their role as reinforcement, and even in some case degrades existing properties of the matrix. Therefore, it is essential to use functionalization to improve the atomic interaction at the interface and avoid agglomeration. This paper studies the interfacial interaction between different functional groups, BNNTs and matrix (Diglycidyl Ether of Bisphenol F and curing agent Diethylmethylbenzenediamine “W”). Various functional groups including NH₃ and NH₂ structures, Silane (APTES), methoxy-poly (ethylene glycol) (mPEG) were chosen due to their compatibility with the matrix and their ability to form significant bonding with nanomaterials. The choice of Epoxy system for adding BNNTs was due to their application in space structures. BNNTs with different functional groups at multiple doping spots (adding functional group to the Boron atom or Nitrogen) were added to the epoxy system. The stability of different functional groups to enhance the interfacial interaction between the Epon 862/W resin system and BNNTs was investigated by quantifying the total energy of the system. Molecular Dynamics simulations were conducted using Materials Studio by Accelrys Inc. which is commercially available software. Universal forcefield was used to run fixed number of atoms, fixed volume and fixed temperature (NVT) and fixed number of atoms, fixed pressure and fixed temperature (NPT). The presence of functional group seems to improve the interface between the nanotubes and the Epoxy molecules. BNNTs have a better interfacial interaction with matrix atoms compared to CNTs. Therefore, while functionalizing CNTs is an absolute necessity in most cases, hydrogen bonding between Nitrogen in BNNTs and alcohol groups in the matrix reduces the need for adding new components to the system. Also, adding functional group will reduce the asymmetric charge distribution in BNNTs which is the main cause of hydrogen bonding between N and H. The result indicates a preference towards the NH₂ and NH₃ functional groups which may have been due to the similarity between these groups and the hardener structure.

Design of experiments (DOE) methods are basic procedures used to obtain good data about variation of responses as function of process variables. More than one response can be involved in process optimization, so, to optimize many response it are normalized by desirability functions, which are unify in a global desirability function. Derringer & Suich desirability functions are useful to unify all responses from a process resulting a global optimization function. Nanoscale metal particles have been intensively studied because of their potential application in surface enhanced Raman spectroscopy (SERS), catalysis, microelectronics an biological action (bactericidal and fungicidal). Physical and chemical properties of materials at nanoscale are distinct from those at microscale (or higher). These properties changes comes from higher percentage of atoms in the surface of particles. In the presented work, silver colloids were prepared by means of the Turkevich Method. It was obtained nanoparticles which were characterized by X-ray diffraction, ultraviolet-visible absorption spectroscopy and scanning and transmission electronic microscopy. Temperature and pH were valuated parameters in the synthesis process and particle size (PS), reaction time (RT), conversion rate (CR) and standard deviation of particle size (SD) were monitored responses. Derringer & Suich multiresponse optimization method was employed to find the optimum temperature and pH to produce good results simultaneously for all responses by minimizing PS, RT and SD and maximizing CR. The temperature does not have effect on on particle size, this could be verify in the model, which is only function of pH. Small particles are more desirable and the results indicates that high pH values aid yielding of small particles and temperature have any influence on particle size. The pH have more influence on conversion rate than temperature. When pH increase, desirability of CR increase too. When temperature increase, desirability of response increase, but this increment is significantly smaller if compared with pH increase. The pH presented great influence in all responses while temperature had significantly influence only in reaction time response. So, it is expected that a optimal condition for all variables present high values of pH. In the reaction time response, when temperature increase, reaction time decrease and desirability increase. Then to a global optimization is expected that both pH and temperature parameters will be at high levels. Predict values for a global optimization are according with better results obtained to particle size and conversion rate responses. Reaction time was minimized but due lack of fit of model (caused by large range in the values of this response), predict value can be super estimated if this predict value is compared with experimental values. Particle size standard deviation was also minimized but predict value is significantly lower than experimental values.

First principles quantum mechanics based materials modeling schemes, such as density functional theory (DFT), are powerful tools to study the dynamical evolution of processes (e.g., chemical reactions, phase transformations, transport). Nevertheless, such methods have several practical drawbacks. For instance, owing to the computational expense, a typical DFT-based molecular dynamics (MD) simulation can span timescales of the order of just picoseconds (with a maximum reachable timescale of about a nanosecond). Here, we show that DFT-based MD simulations can be significantly accelerated using machine learning—a branch of artificial intelligence that enables rapid and high-fidelity predictions based on past data or knowledge. The basic premise underlying our concept is the following. A typical MD simulation results in innumerable configurations many of which are similar to each other. The bottleneck of a DFT-based MD simulation is the prediction of energy and atomic forces for each of these configurations. If we are able to rapidly estimate (with acceptable accuracy) the energy and atomic forces of a new configuration, given these for past similar configurations (determined, say, using DFT), then we can significantly speed up the MD simulation. The ‘training&’ underlying this property prediction capability is referred to as machine learning, and requires a critical amount of prior information or results, adequate descriptors (or fingerprints) that uniquely represent our configurations, and a suitable measure of (dis)similarity between configurations. We show here that such training, prediction, and consequently, the acceleration of DFT-based MD simulations, are indeed possible. Illustrations of this new development are made for the case of the self-diffusion of vacancies in bulk Al, and the diffusion of an Al adatom on an Al surface.

We present a new method to characterise electrically heterogeneous electroceramics for a full three-dimensional system that includes randomly shaped grains, grain boundaries and electrical contacts. This model does not require the use of either the bricklayer model for the microstructure or equivalent circuits to describe the electrical response but instead uses a finite element approach, solving Maxwell&’s equations in space and time, to simulate impedance spectroscopy data. This method overcomes several deficiencies associated with previous approaches, allowing comprehensive treatment of a full three-dimensional granular representation of a ceramic microstructure. The use of extra, unphysical components such as constant phase elements to describe any non-ideality of the response is thereby avoided. This method is applied to determine the influence of the ceramic microstructure on the impedance spectra by first analysing simple brick layer models and then via complex multi-granular systems that include varying grain size and electrical properties. We present the simulated impedance spectroscopy plots and use these to highlight the limitations of the brick-layer model in impedance data analysis of electroceramics.

Owing to the desirable dielectric and electronic properties of compounds containing Sn^[1,2,3], we introduce Sn-based units (such as SnF₂, SnCl₂^[4] or Sn-ester^[5,6] units) into the backbone of a polyethylene chain. Density functional theory calculations along with the minima hopping method^[7,8] were used for determining relaxed geometries, energies, dielectric constant and band gap (thus generating the necessary “data”). Machine learning techniques were then utilized to develop a predictive model of the computed properties and to recommend chemical environment rules ideal to achieve favorable dielectric and electronic properties of organotin polymers.
A database of organotin compounds was created, including the SnF₂, SnCl₂ and Sn-ester containing polymers as well as a number of Sn-organic frameworks procured from the Crystallography Open Database^[9]. A fingerprint was developed based on the structure and bonding information that would represent each system in the database uniquely. Kernel ridge regression (KRR) is used to form a mapping between the fingerprint and the properties; it is seen that this mapping works extremely well in predicting dielectric constants and band gaps of a test set of systems based on a training set. Correlation analysis helps determine the specific features in the fingerprint that contribute most to the properties, based on which a decision tree is prepared to establish the ideal chemical environment for organotin polymer dielectrics. Further, an inverse design mechanism is developed that will provide the fingerprint corresponding to a desired value of dielectric constant and band gap, and thus enable us to identify the specific organotin polymer that would possess these properties.
References
[1] C.C. Wang, G. Pilania, & R. Ramprasad, Phys. Rev. B 87, 035103 (2013).
[2] G. Pilania, C.C. Wang, K. Wu, N. Sukumar, C. Breneman, G. Sotzing, & R. Ramprasad, J. Chem. Inf. Model 53, 879 (2013).
[3] A. Mannodi-Kanakkithodi, C.C. Wang, & R. Ramprasad (submitted)
[4] A. Mannodi-Kanakkithodi, T.D. Huan, & R. Ramprasad (submitted)
[5] A. F. Baldwin, T.D. Huan, Rui Ma, A. Mannodi-Kanakkithodi, N. Katz, R. Ramprasad & G. Sotzing, (submitted)
[6] A.F. Baldwin, Rui Ma, A. Mannodi-Kanakkithodi, T.D. Huan, C.C. Wang, J.E. Marszalek, M. Cakmak, R. Ramprasad, & G. Sotzing, (submitted)
[7] S. Goedecker, J. Chem. Phys. 120, 9911 (2004).
[8] M. Amsler & S. Goedecker, J. Chem. Phys. 133, 224104 (2010).
[9] Grazulis, S., Chateigner, D., Downs, R. T., Yokochi, A. T., Quiros, M., Lutterotti, L., Manakova, E., Butkus, J., Moeck, P. & Le Bail, A. (2009) "Crystallography Open Database - an open-access collection of crystal structures". J. Appl. Cryst.42, 726-729.

Discovering new approaches to self assemble nanoparticles (NPs) into mesoscopically-ordered structures can lead to novel materials with new functionality. Using a hybrid Brownian Dynamics-Cahn Hilliard (BD-CH) computational model, the coupled morphology of an immiscible binary polymer blend, with and without dispersed NPs, is investigated in a confined thin-film geometry. This model combines Eulerian (grid-based) and Lagrangian (particle-based) approaches to simulate the mutual evolution of the phase-separating mixture and the suspended NPs, which adsorb on the polymer-polymer interfaces ultimately leading to a stabilized morphology. We investigate cases in which one polymer type preferentially wets the top and bottom film surface. Large-scale, 3D simulations were executed to perform a parametric study to determine how the final, stabilized state transitions from a bicontinuous structure to a discrete structure depending on the NP volume fraction and film thickness. This talk will discuss both the numerical implementation of the model, including parallelization, and the simulation results. From a practical standpoint, these thin-films have applications as catalytic membranes upon selectively etching one of the polymer domains, thereby leaving mesoscopic channels with nanoparticle-coated surfaces.

Determining upconversion parameters is of high interest in laser material development. For many materials these parameters cannot be directly measured by experimental methods. These upconversion coefficients appear as unknown parameters in the laser rate equations which are a system of coupled nonlinear differential equations that are used to model the dynamics of population densities in different energy levels. Currently in the literature they are determined by searching for the set of parameters that will fit the experimentally measured fluorescence data. Specifically, the nonlinear differential equations are solved numerically for each set of guessed parameter values and the set that reasonably fits the experimental data is taken to be the actual set of parameters. When no single set of parameters is found to fit the experimental data, the rate equation model is concluded to be invalid and proper modification to the model is seek. In this paper we propose the well established system theoretic tools pertaining to the system inversion to be applied in this case. The unknown parameters can be considered as the input and the fluorescence signal can be considered as the output of the dynamical system. Therefore the determination of the unknown parameters in the system equations from the output data is a classical system inversion problem and control system theorists routinely apply this method to various applications. In this paper we argue that the sufficient conditions of the invertibility of the dynamical system, the rate equation model , must be verified in order to guarantee the existence and uniqueness of the unknown parameters to be determined.

Traditional thermoelectric materials suffer from low efficiencies due to inverse coupling of the Seebeck coefficient and electrical conductivity, which limits the power factor. Decoupling of these two physical prshy;shy;operties represents an exciting opportunity, and has previously been demonstrated in single molecule junctions. While it was shown that the Seebeck coefficient and electrical conductance can be simultaneously increased in these molecular junctions, scaling of these concepts to full material systems is unknown. Using molecular junction design principles for guidance, gold nanocrystal arrays were designed with varying molecular ligands, drawing inspiration from the single molecule literature. Both non-conjugated and aromatic ligands were used in these nanocrystal arrays, along with different binding groups, to identify trends that map the single molecule experiments to thin film nanocrystal arrays.
The conductivity of these nanocrystal arrays follows a conventional tunneling model, where the length between nanoparticles dictates conductance, as expected from previous theoretical and experimental work. The tunneling decay constant changes strongly based on molecular backbone, as expected from single molecule electrical studies. The binding group is not seen to strongly affect the electrical conductivity, while in single molecule junctions the binding group strongly defines the electrical conductance of the system.The Seebeck coefficient is observed to switch signs with alkyl ligands, indicating a switch from hole to electron transport. The change in the Seebeck coefficient with length parallels the single molecule literature, albeit with a switch in carrier. When phenyl based and thiophene based aromatic ligands are exchanged in the nanocrystal array, the Seebeck coefficient is seen to follow the single molecule results. In addition, a variety of binding groups were studied, ranging from thiols, amines and direct-bonded ligands. Binding groups are seen to strongly affect the thermoelectric properties, as with single molecule junctions, where the binding groups are paramount to defining the thermoelectric properties.
The results are explained using metal induced gap states from single molecule junction theory, along with the Landauer transmission model. A comparison is made between macroscale thin film transport properties to single molecule electronic transmission measurements reported in previous studies, comparing results with ligand length, binding groups and aromaticity. These results will lend further insight into how molecular junctions and nanocrystal arrays can be integrated for materials with higher power factors, and further enhance understanding of the hybrid inorganic-organic interface.

We perform the extensive Brownian dynamics simulation on monolayer identical colloids and binary colloids with repulsive interactions. The binary colloids consist of large (L) particles and small (S) particles. We fully investigate the time dependences of the mean-square displacement, the radial distribution functions, the bond-orientational order function of colloids, and the number of nearest neighbors in the process of crystal growth at different number ratio and size ratio of L particles and S particles. The differences between the crystal growth of identical colloids and that of binary colloids are compared and discussed. The segregation and dislocations are affected by the size ratio of L and S particles and the number ration of those.

The principle of operation of magnetically controlled MEMS is based on switching the electrodes under the effect of the magnetic field. To provide the working capacity and durability of MEMS switches the electroerosion-resistant materials are necessary.
Cardinal increase of the lifetime is possible with the use of specialized electrode coatings like "sandwich", meeting the requirements of the local heat resistance, high heat conductivity and small value of the electric resistance. In general, such coatings consist of several layers: the top layer consists of high-melting metal having high erosion resistance, the second, adhesive layer, consists of the material providing good material adhesion to the substrate.
The prospective direction of increase is the use of an additional high heat conductivity underlayer intended for the temperature profile alignment along the electrode surface. To achieve the erosion resistance optimum parameters it is necessary to calculate the coatings operating modes at local temperature influence and current flow through the film structure.
The paper provides the mathematical model of the local temperature and electric current effect on the film structure in axially symmetric approximation, taking into account the electric current spreading, ohmic heating and temperature and electric variations of the coatings materials under heating.
By the means of the model the calculation of local temperature and electric current influence on the film structure that is equivalent to the impact of the channel microdischarge on electrodes contact areas has been carried out. The temperature and current spot diameter changed within 0.1-50 nm, the current density varied from 0.1 to 100 A/mm², the thermal stream average power - 0.05 - 2 W. As the material of external (high-melting) coating layer, tungsten with the thickness of 1-100 nm was used, as the adhesive layer -titan (0-20 nm thickness), as the heat-conducting layer - copper (20-400 nm thickness) were used.
The calculation results of the temperature distribution inside the coating, the distributions of the electric current density, dependence of internal mechanical stresses on temperature are given.
It is shown that at quasisteady operation the layer thickness increase of high-melting material (tungsten) for more than 50-100 nm leads to considerable rise of the thermal spot temperature. It is established that the maximum temperature value on the coating surface decreases with the thickness increase of the copper layer. The analysis of the temperature mode and thermomechanical stress value resulting from coating heating shows the expediency of introduction of the heat-conducting copper layer with the thickness of 100-200 nm for ensuring equalized temperature distribution.
On the basis of the obtained data the requirements for the coating structure providing high erosion resistance have been formulated.

Liquid crystal (LC) and nanoparticles (NPs) mixtures are both of fundamental interest in the development of advanced materials and can serve as a paradigm by which to better understand the process of self-assembly in nano-materials. The interactions in LC-NP mixtures are still under active research, although important tendencies have been established. Little attention has been given to morphological instability patterns, especially to those mediated by the diffusion of NPs.
Directed self-assembly is an exciting process for patterning novel microstructures to control materials functionality in a wide class of systems, ranging from quantum dots in semiconductors to carbide orientation in composite ceramics. It can lead to materials with high processability, self-healing properties, and reversible control.
Using numerical simulations, we study the growth of isolated nematic droplets in an isotropic LC doped with NPs. We employ the continuum model of Soule et al., [1], representing a mixture of calamitic nematic LC (cylinders) and NPs (hard spheres) of comparable size. The numerical implementation is based on the adaptive mesh refinement scheme developed by Provatas et al, which dramatically extends the time and length scales in which this system can be explored numerically. We report the largest times and lengthscales to date, which allows us to capture the NPs diffusive instabilities from their inception up to morphologies in the microns scale.
To date, directed self-assembly of NPs in LC-NPs mixtures have been addressed in two ways: trapping in defect cores, and enrichment in grain boundaries where NP expulsion is isotropic and the boundaries are those of micron size spherulites. Our work reveals a new dual mechanism where defect trapping coexists with anisotropic expulsion on the nanoscale. This expulsion mechanism is linked to a diffusive instability at the Nematic-Isotropic phase boundary that leads to branching morphologies not reported yet in the context of isolated nematic spherulitic growth, demonstrating that the morphological diversity in liquid crystal hybrid systems is much richer than previously anticipated.
References:
[1] Soft Matter, 2012, 8, 2860

Models of visco-elastic fluids couple the momentum equation with an
equation governing the evolution of the elastic components, and
numerical simulation is notoriously difficult (the high Weisenberg
problem). This system of partial differential equations can be derived
from Hamilton's principle which reveals a subtle balance between
inertia, transport, and dissipation effects. This talk will focus on
the structural properties of these equations which provide insight
into why naive numerical schemes may fail, and the ingredients
required to construct stable numerical schemes.

We study the problem of packing a filament of DNA in a prescribed domain of typical length scale within the range of 20 to 100 nm. The goal is to understand the packaging of the genome of a bacteriophage virus and its release from the capsid during the bacteria infection process.
This problem is motivated by research on development of antibiotics.
We model the DNA in the capsid domain as an electrically charged semiflexible polymer gel in a water environment, in the presence of ions. Mechanical properties such as resistance to bending and splay, the persistence and Kuhn length of the chain, as well as electrostatic interaction determine the spooling ordering (If any) of the DNA as well as the size of the melted core. We show that nematic point defects are the source of kinks in the chain and loss of injectivity of the filament deformation map relates to the density of knot crossings.
From the point of view of statics, the study provides two types of information:
1. Size of the ordered DNA region and that of of the melted core, and
2. Evaluation of the osmotic pressure inside the capsid. This is relevant to determine the onset of release of the virus genome in the process of infection.
A wealth of experimental data on the stress-strain response of a capsid to mechanical loading as well as the availability of electron micrograph images of capsids allows us to determine the parameters of the model.
Tools that are used in this work include models of nematic liquid crystals, lyotropic liquid crystal elastomers, nonlinear elastic rods as well as molecular dynamics studies of DNA. The following articles served as part of the mathematical background of the problem:
Investigation of viral DNA packaging using molecular mechanics models, Javier Arsuaga, Robert K.Z. Tan, Mariel Vazquez, De Witt Sumners and Stephen C. Harvey, Biophysical Chemistry 101-102 (2002),
475-484.
Axisymmetric configurations of bipolar liquid crystal droplets, Quan Chen, Chun Liu and M.Carme Calderer, Continuum Mech. Thermodyn. 14 (2002), 363-375.
Liquid crystal elastomers and phase transitions in actin rod networks, M.Carme Calderer, Carlos Garavito and Chong Luo, SIAM J. Appl. Math. 74 (2014), 649-675.
A dynamic model of polyelectrolyte gels, Haoran Chen, Catherine Micek, Yoichiro Mori and M. Carme Calderer, SIAM J. Appl. Math., 73 (2014), 104-123.
The work presented was done in collaboration with Javier Arsuaga and Mariel Vazquez.

Cells have evolved a mechanism to maintain integrity while dynamically adopting a variety of shapes in response to specific internal and external signals. This requires that the cell body be both highly flexible and possess the material properties to oppose external forces. We use periodic morphological protrusions exhibited by many rounded cells as a simple model system to investigate this question. Cell morphology is dictated mainly by the plasma membrane (PM) and the underlying actomyosin cortex. Periodically protruding cells exhibit a highly dynamic actomyosin cortex that is polarized in different regions at different time points. We demonstrate that compression (folding) and subsequent dilation (unfolding) of the coupled plasma membrane-cortex layer provides a mechanism for these periodic transformations in rounded cells. Our live-cell images show that the cyclic process of membrane-cortex compression and dilation results in a traveling wave of cortical actin density around cell periphery. Our findings provide insight into the mechanisms that drive the rapid morphological changes that occur in many physiological contexts, such as in amoeboid migration and cytokinesis.
Supported by NIH GM078994 & NSF DMS-1200535

Background and Objective: The brain, a mixture of neural and glia cells, vasculature, and cerebrospinal fluid (CSF), is one of the most complex organs in the human body. In order to understand brain responses to traumatic injuries and diseases of the central nervous system, it is necessary to develop accurate mathematical models and corresponding computer simulations which can predict brain biomechanics and help designing better diagnostic and therapeutic protocols. Brain tissue has been modeled as either a poroelastic mixture saturated by CSF or as a viscoelastic solid. However, it is still not obvious which model is more appropriate when investigating brain mechanics under certain conditions. In this study we propose to model the brain as a Kelvin-Voight (KV) model of a one-phase viscoelastic solid as well as a Kelvin-Voight-Maxwell-Biot (KVMB) model of a two-phase (solid and fluid) mixture and explore the limit between these two models. In order to account for the evolving microstructure in brain, we replace the classic integer order time derivatives by Caputo fractional order derivatives and thus generalize the above mentioned models to corresponding fractional KV and KVMB models. In these fractional models, the fractional order is a measure of the amount of microstructures in brain.
Modeling Approach: We start with the classic KVMB model where the brain is a poroelastic mixture made of two phases: 1). CSF, an incompressible Newtonian fluid, and 2). brain tissue which is assumed to be an incompressible, linear elastic solid. The model links the dynamic viscosity of CSF, the permeability and tortuosity of brain. We solve the corresponding system of first order linear differential equations using the eigenvalue method. These eigenvalues are then used to build an equivalent classic KV model where the brain is seen as a one-phase viscoelastic solid. Similarly, we propose the fractional KVMB model whose analytic solutions, found using a generalization of the eigenvalue method, are used to determine the equivalent fractional KV model. Inspired by Michaels' work in soil mechanics (Michaels, 2006), we use the displacement of the solid phase in the classic (fractional) KVMB model and the displacement in the classic (fractional) KV model to define a poroelastic-viscoelastic limit.
Results: When the CSF and brain tissue in the KVMB (classical/fractional) model have similar velocities, then the KV (classical/fractional) and KVMB (classical/fractional) models are indistinguishable. As the fraction order approaches 1, the analytic solutions of the fractional KVMB model converge to the analytic solutions of the classic KVMB model. Our numerical simulations provide threshold values for poroelastic-viscoelastic limits for the classic as well as fractional models.
References:
Michaels, P. (2006). Relating Damping to Soil Permeability. International Journal of Geomechanics, 6(3), 158-165.

We study the stability of a gel material in contact with a fluid that exerts a pressure at the interface.We assume that the gel is an interactive mixture of polymer and viscous fluid, the former characterized also by viscous as well as elastic behavior. The total energy of the gel includes the elastic contribution of the polymer, the Flory-Huggins energy of polymer-fluid interaction and the surface energy. The governing equations consist of a system of partial differential equations for the balance of mass and linear momentum of the solid and fluid components. The boundary conditions at the fluid interface express the degree of permeability of the gel to the fluid. We consider equilibrium states of the gel under an applied pressure at the gel surface and with the gel substrate being subject to displacement boundary conditions. Parameters of the model include the elastic moduli of the polymer, the fluid and solid viscosities, the permeability coefficient, and the strength of the surface energy. We assume that the external pressure experiences a perturbation of the form Aexp(at+ikx), where a is the decay rate and k the wave number. We look material parameters such that a < 0. Our model predicts the stability of a given (a,k)-tuple with respect to the material parameters. The time dependent system is reduced to a set of ordinary differential equations that, in combination with the boundary conditions generate a matrix whose determinant determines the stability of a pair (a,k). In addition our model, provide dimensionless numbers that have an essential role in describing the physics of the model. We construct stability diagrams considering a range of possible values for (a,k). Our model provides a tool-box to determine sets of parameters that give stability of the equilibrium states. This work is motivated by the need to determine appropriate material parameters that guarantee stability of body implantable medical devices.

Acoustic radiation force (ARF) imaging techniques have been developed to characterize the viscoelasticity of biological soft materials by measuring the motion excited by the ARF noninvasively. Due to the unknown stress distribution induced by the ARF, it is hard to accurately solve the inverse problem, and simplified single degree-of-freedom (SDF) models have been developed to analyze it. In this study, an inverse finite element (FE) procedure based on a Bayesian formulation is developed. In the presence of measurement noise and prior parameter uncertainties, the Bayesian approach aims to estimate a distribution of the mechanical properties rather than a best-fit value that is generally obtained with an optimization procedure. In this approach, prior parameters, such as ARF distribution, local heterogeneity profile and known mechanical property estimations, are represented as probability distributions. Gaussian process metamodels based on a small number of FE model runs are used in the uncertainty quantification. An analytical approximation technique based on Taylor expansion is applied to solve the integral for the computation of the posterior distribution of the material parameter. Simulation results demonstrate the computational efficiency of the proposed approach and provide practical probability distributions for the estimated material properties. In a comparison study with the SDF models, the Bayesian approach improves the estimation results even when the prior parameters have large uncertainty levels.

Experiments show that a colloidal particle placed in a liquid crystal matrix will come to rest at some nonzero distance, h, from the bottom of the container. The same particle placed in an isotropic liquid matrix would sink to the bottom. Our goal is to model this behavior mathematically. For this, we assume that the energy of the system consists of the Landau-de Gennes contribution of the liquid crystal including the gradient and the bulk terms, the gravitational energy of the fluid and the particle, and the anchoring energy of the liquid crystal on the surface of the particle. Strong anchoring boundary conditions are prescribed on the walls and the bottom of the container. The incompatibility of the liquid crystal anchoring at the bottom of the container and on the surface produces topological defects that oppose the sinking of the particle. We study global and local minimizers of the energy and show that the latter satisfy h>0.

We describe results on the nature, number, and location of defects for minimizers of the Landau-De Gennes Q-tensor energy in thin liquid crystal materials. We also describe properties of minimizers for a Q-tensor energy constrained by the Maier-Saupe potential, and discuss differences observed in these models.

A broad range of systems undergoing change, such as the temperature-dependent eutectoid transformation in steels, crystallization in supersaturated solutions, the propagation of information in social systems, or the spread of infection, exhibit behavior similar to classical nucleation and growth. In all cases, a driving force for change exists due to a difference between some variable and its equilibrium value. For crystallization in melts, the driving force is a consequence of supersaturation that results from a change in temperature. In the case of crystallization from solution, the driving force can also be a consequence of supersaturation that results from a change in composition.
While detailed models exist for predicting the behavior of many such systems on a case by case basis, a broad view is beneficial to communicating (and understanding) the principles of nucleation and growth based transformations more generally, and to developing useful graphical representations that can aid with process design.
We present a means of generalizing the classical model for nucleation and growth in systems that are undergoing a phase transformation or analogous process. Our approach is based on the thermodynamics of nucleus formation and diffusion-limited reactant transport. We then expand the general model from 3-D nucleation and growth with one system variable to include phase transformations that are dependent on m arbitrary system variables. Furthermore, we have laid out the mathematics necessary to consider nucleation and growth in an arbitrary number of n spatial dimensions. This is particularly interesting for explaining fractal growth, and for abstracting of the model to fields outside of materials science, such as epidemiology.
We use (i) the formation of crystalline phases during the drying of protein solutions and (ii) the formation of a nematic phase from an isotropic solution as examples to illustrate the utility of the generalized model. We show that, at constant temperature, contours of constant transformed fraction plotted in the concentration-time plane have a C-shaped profile, similar to the well-known time-temperature-transformation (TTT) diagrams for the eutectoid transformation in steel. Furthermore, it follows that the contours of constant transformed fraction are cup-shaped when plotted in time-concentration-temperature space.
The lack of a concise representation of drying kinetics is a bottleneck in organic synthesis and pharmaceutical development. Prediction of such time-concentration-temperature-transformation (“TCTT”) diagrams will allow for improved process design in crystallization of proteins and other macromolecules.

We present a finite element method (FEM) for computing equilibrium configurations of liquid crystals with variable degree of orientation. The model consists of a Frank-like energy with an additional "s" parameter that allows for line defects with finite energy, but leads to a degenerate elliptic equation for the director field. Our FEM uses a special discrete form of the energy that does not require regularization, and allows us to obtain a stable (gradient flow) scheme for computing minimizers of the energy. Simulations in 2-D and 3-D are presented to illustrate the method.

The combination of low elastic modulus, anisotropy, and responsiveness to external fields drives the rich variety of experimentally observed pattern formation in nematic liquid crystals under capillary confinement. External fields of interest in technology and fundamental physics are flow fields, electro-magnetic fields, and surface fields due to confinement. In this work we present theoretical and simulation studies of pattern formation of nematic liquid crystals disclination loops under capillary confinement including a branching processes from m=+1 disclination line to two m=+1/2 disclination curves that describes the post nucleation and growth regime of the textural transformation from radial to planar polar textures. The early post-nucleation and growth of emerging disclination loops in cylindrical capillaries is characterized using analytical and computational methods based on the nematic elastica that takes into account line tension and line bending stiffness. Using sub diffusive growth and constant loop anisotropy, we find that the solution to the nematic elastica is a cusped elliptical geometry characterized by exponential curvature variations. The scaling laws that govern the loop growth reflect the tension/bending elasticity balance and reveal that the loop dilation rate depends on the curvature and normal velocity of the disclination. The line energy growth is accommodated by decrease in total curvature. These finding contribute to the evolving understanding of textural transformations in nematic liquid crystals under confinement using the nematic elastica methodology.

Atomistic simulations of crystalline solids often involve creation, recombination and transformation of defect structures. Such defects can be of various shapes, sizes and kinds, from isolated vacancies or interstitial atoms to large clusters, voids, dislocations and grains boundaries. To understand the behavior of these defects and their consequences on other material properties, they need to be properly detected, isolated and characterized.
For point defects, this is usually done using a parameter representing the local structural order (like the centro-symmetry parameter, or the common neighbor analysis), and a threshold separating the atoms in a defect and the bulk. These methods are problematic because of the arbitrary character of the threshold value and the definition of the structural parameters.
More recently, methods based on Wigner-Seitz analysis have been used. While they do not rely on as many arbitrary parameters, they depend on a reference configuration to detect the point defects. Besides the fact that this prevents the detection of defects already present in the reference, it makes the method unusable when a part of the simulation box undergoes structural changes, like during the motion of a dislocation or a grain boundary, or the nucleation of a secondary phase.
A technique will be shown, based on the statistical analysis of the considered atomistic configuration, which allows the creation of a graph representing the topology of the crystal [1]. This graph can be processed to automatically determine the positions of point defects and clusters, and perform higher-level analysis, like dislocation extraction [2]. The lack of need for a reference configuration makes it suitable to the analysis of complex microstructures like dislocations and poly-crystals.
This will be illustrated by three example showing different cases in which this methods provides accurate and valuable information:
the motion of a dislocation in presence of high concentrations of point defects and solute atoms;
the automatic characterization of the local microstructure in a poly-crystal;
and the super-ionic transition in mixed actinide oxides.
Each of these examples underlines some key benefits of this method applied to configuration resulting from Molecular Dynamics simulations.
[1] Linn W. Hobbs, “Topological approaches to the structure of crystalline and amorphous atom assemblies”, Engineering of Crystalline Materials Properties: State of the Art in Modeling, Design and Applications (2008).
[2] Alexander Stukowski and Karsten Albe, “Dislocation detection algorithm for atomistic simulations”, Modelling and Simulation in Materials Science and Engineering, (2010).

Excited states and dynamics in materials and at interfaces underpin a wide range of important physical processes such as light harvesting, spectroscopy, and photochemistry. Modeling these processes from first-principles is challenging for density functional methods, however, largely due to deficiencies in exchange-correlation functionals and basis set limitations. In this talk I will discuss time-dependent density functional theory (TDDFT) approaches to optical and X-ray absorption of insulators using bulk-mimicking finite clusters. Combining range-separated hybrid functionals with non-Hermitian real-time propagation enables TDDFT to accurately capture Rydberg-like and post-ionization states without input from experiment. Application to valence and core-level spectra of various SiO₂ polymorphs will be presented, along with methodological details including embedding, time propagation, and high-performance computing aspects.

Over the past few years, my group (with various collaborators) have shown how density functional approximations can be derived systematically, in terms of a very special type of semiclassical expansion, as first pointed out by Lieb and Simon 41 years ago. I will explain how this expansion works, show how many of the most useful approximations can be understood (and even derived), and report on recent progress.

Understanding the underlying physics of superconductive materials can be greatly facilitated by establishing a relationship between atomic structure and electronic properties at the nanoscale. Here, the structural data is obtained from high-resolution scanning tunneling microscopy imaging, whereas tunneling spectroscopy mapping provides information on the local electronic properties such as band structure and, in our case, the superconductor gap. We further explore local interactions with statistical methods such as Principle Component Analysis (PCA) and Bayesian Statistics to perform unsupervised classification and cross-correlative analysis of these data to establish the internal data structure and reveal the correlations between structure and functionality. We further explore the pathways to map these behaviors on the atomistic models parameterized via interaction Hamiltonian terms. In this approach, the statistically significant atomic configurations are established and further used as an input into first principle modelling. Thus, the determined electronic structure is then compared to the local tunneling spectra. This approach is applied to explore local behavior of the chemically phase separated FeSeTe superconductor, identifying effects of local phase separation, structural defects, and magnetic impurities on superconductive behavior. This research was conducted (AG, SK, PG, PM, AB, GS) at the CNMS, sponsored at ORNL by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. DOE, Materials Science and Energy Division (AB), the Compute and Data Environment for science at ORNL (GS), and the Institute for Functional Imaging of Materials. Fellowship support (AG) from the UT/ORNL Bredesen Center for Interdisciplinary Research and Graduate Education.

State-of-the-art ab initio methods are currently used to predict the lowest-energy structure of hypothetical compounds by performing total energy calculations in a high-throughput fashion on a set of candidate structure types. For a given class of materials, e.g., the compounds with ABX composition, the library of candidate structure types is assembled by surveying compilations of synthesized solid-state compounds and the related literature to identify as many as possible of the structure types that materials with that composition exhibit. The effectiveness of such a prediction approach relies on the assumption that hypothetical materials with a certain composition will likely have one of the structure types that is exhibited by one of the materials in that family.
A drawback of a high throughput ab initio approach is that it might miss the lowest energy structure of a material if it belongs to a structure type that is yet unknown, or known but not reported in the current databases of materials. This problem can be addressed by applying a crystal structure prediction method that is unbiased and not constrained to a given set of structure types. We have previously highlighted how the application of an evolutionary algorithm that starts from a set of structures produced by randomly selecting the lattice vectors and the atomic positions in a supercell, is an efficient approach to search for the lowest-energy structure of a solid without constraints.
Here, we will discuss another possible scenario in which stable or metastable structure might be overlooked in automatic high-throughput calculations. This is the case of a solid that presents local minima that might be competing in energy and metastable and that can be all formally described by the same structure type, that is, by the same space group symmetry and set of general Wyckoff positions. In such a case, a high-throughput approach will select one of the possible minima of same “structure type” depending on the initial configurations from which the total energy calculation is performed. We will illustrate the emergence of such metastable phases sharing the same structure type through total energy calculations and crystallographic analysis of selected I-I-VI systems in the family of ABX half Heusler compounds.

The last 10 years have seen an explosion of efforts in computational materials design. NREL&’s Solid State Theory and Computational Science groups, as well as the NREL-led Center for Inverse Design (an Energy Frontier Research Center), have been at the forefront of many of them. In this talk we highlight three areas fertile for cross cutting research between mathematics, computer science, and materials physics.
First is the obvious but tantalizing role that optimization should play. However, we observe that for a combination of reasons—lack of fast-enough robust and accurate solvers, lack of efficient search algorithms, failure to formulate the search in practical terms—these efforts remain in a “reach-exceeds-grasp” stage. We note: perhaps not for long.
For the present, though, the relative failure of direct optimization, as well as the application of “design rules” that act as constraints on the otherwise exponentially large search spaces, and the usual desire for comprehensive information leads to the importance of high-throughput computations. Therefore, we next discuss computational materials science workflows and software to support them, including our recently released “pylada”, a flexible python framework enabling end-to-end (structure generation to results database) management of many thousands of simultaneous calculations and results.
Finally, the constraints of crystal chemistry lead to a fascinating array of computational geometry problems. We report here on recent efforts at automated characterization of the surface faceting of nanostructures as a function of temperature using a combination of surface-reconstruction optimization, the well-known Wulff construction, and Monte Carlo simulation.

A parametrization scheme for the density-functional based tight-binding (DFTB) method that covers the periodic table is presented. A two-stage semiautomatic parametrization scheme has been developed. First, Kohn-Sham energies and band structure curvatures of real and fictitious homoatomic crystal structures are used as reference data to obtain the electronic part of the method. A confinement potential is used to tighten the Kohn-Sham orbitals, which includes two free parameters that are used to optimize the performance of the method. In the second step, the double counting terms to obtain total energy and gradients are obtained using the same philosophy, that is, to compute these terms using a confined electron density. This time, structural data of molecules and solids and relative energies are used as reference data. The method is tested on more than 100 systems and shows excellent overall performance.

Solar thermal fuels (STFs) are an unconventional paradigm for solar energy conversion and storage which is attracting renewed attention. A material absorbs sunlight and stores the energy chemically via an induced structural change, which can later be reversed to release the energy as heat. Two important factors for STFs are the absorption cross-section and the quantum yield for photoisomerization. We employ massively parallel time-dependent density-functional theory (TDDFT) calculations with the Octopus real-space code [www.tddft.org/programs/octopus] to obtain the optical absorption and follow the structural changes after absorption for candidate STF molecules such as azobenzene and norbornadiene/quadricylcane. We use our new excited-state forces formulation for TDDFT in the Casida or Tamm-Dancoff approaches, which is based on density-functional perturbation theory and does not require any additional sums over unoccupied states. Our results show the photoisomerization mechanism in these molecules, to aid in further improvement of STF materials by functionalization and attachment to templates [A. M. Kolpak et al., Nano Lett.11, 3156 (2011); T. Kucharski et al., Nat. Chem.6, 441 (2014)].

Molecular-dynamics (MD) simulation is one of the most important computational methods to study the properties of materials on the atomistic scale. While parallel MD codes have been available for a long time, computing technology has evolved. For the last years, the computational power of CPUs has been increased primarily through increases of the number of cores and SIMD units with wider vector registers. This presentation addresses the question of how MD simulation programs can take full advange of the computational power provided by modern CPUs.
A novel parallel algorithm for MD simulations with short-ranged forces is discussed. The cell-task method uses a task-based programming approach. The calculation of forces is divided into a large number of small tasks that are executed by a thread pool. This approach avoids the load balancing problems that can occur with the spatial decomposition method in simulations of inhomogeneous systems. Benchmark calculations are presented which show that the cell task method significantly outperforms spatial decomposition in the case of inhomogeneous, porous systems. For homogeneoeus systems both methods perform equally well. Tests on an Intel Xeon-Phi co-processor show that the method scales very well to large numbers of threads and is thus suitable for many-core processors with hundreds of CPU cores.
Recent CPUs contain SIMD vector units that allow simultaneous operations on short vectors (typically 2 - 8 elements). Unfortunately, the sparse and irregular interaction pattern in MD simulations with short-ranged forces makes it difficult to take advantage of SIMD vectorization. In the second part of this presentation a blocking algorithm is discussed which allows vectorization of some parts of the force calculation of short-ranged MD simulations. Bechmakr caclulations showing signifcant speed-up factors of two and above will be presented.

Ab initio plane-wave methods based on density-functional theory (DFT) such as ultrasoft pseudopotential and projector augmented wave methods coupled with efficient iterative ground-state computations enable us to deal with various defects, surfaces and interfaces in materials. In the plane-wave methods, total energies and stress tensors are given as integrated or averaged quantities in the supercell, and we cannot obtain local distributions of energies or stresses. If we could obtain such local distributions by the plane-wave methods, it should greatly contribute to the understanding of the nature of defects, surfaces and interfaces. We are engaged in the development of the computational technique for such local energies and stresses within the plane-wave DFT framework. In this talk, we present our recent development and applications [1-4] by using QMAS code [5]. The energy-density and stress-density schemes were proposed for the plane-wave methods, while there are inherent gauge-dependent problems. The kinetic terms in these densities depend on the selection of symmetric or asymmetric forms, leading to non-uniqueness. The differences between the symmetric and asymmetric forms in these densities, namely the gauge-dependent terms, are naturally integrated to be zero throughout the supercell. We consider local regions for which the gauge-dependent terms are also integrated to be zero. By integrating the energy and stress densities in such local regions, we can obtain unique local quantities. About the computational schemes to define such local regions, we use the layer-by-layer method [1] for layered structures, and the Bader method with the recent algorithm [6] for general systems. For grain boundaries (GBs) in Al, Cu and Fe, the local-energy and local-stress analyses showed general presence of tighter and looser sites at the interfaces. The tighter sites with smaller atomic volumes show lower local energies and compressive stresses, while the looser sites with larger atomic volumes show higher local energies and tensile stresses. These two kinds of sites show quite different magnetic moments in bcc Fe and quite different behaviors of impurity segregation in all the GBs. During ab initio tensile tests of such GBs, local-energy and local-stress analyses revealed contrasting behaviors of such tighter and looser sites. For coherent Fe/TiC (NbC) interface models, we observed that the distributions of energy and stress at the interface seriously depend on the local configurations.
[1] Y. Shiihara et al., Phys. Rev. B 81, 075441 (2010); ibid.87, 125430 (2013)
[2] H. Wang et al., J. Phys.: Condens. Matter 25, 305006 (2013)
[3] S. Kr. Bhattacharya et al., J. Phys.: Condens. Matter 25, 135004 (2013); J. Mater. Sci. 49, 3980 (2014)
[4] V. Sharma et al., submitted (2014)
[5] S. Ishibashi et al., Phys. Rev. B 76 (2007) 153310
[6] M. Yu and D. R. Trinkle, J. Chem. Phys. 134, 064111 (2011); M. Yu et al., Phys. Rev. B 83, 115113 (2011)

In this talk we discuss mathematical and computational strategies for obtaining coarse-grained stochastic approximations of extended (many-body) microscopic systems. Examples of such models include stochastic lattice models of reaction kinetics in catalysis modeling, or more complex off-lattice models of macromolecules (e.g., polymers). We explain how information theory based methods (e.g., using relative entropy, Fisher information) can be used for analysis of the derived approximation schemes and acceleration of simulation algorithms (e.g., kinetic Monte Carlo). We present an extension of these tools to analysis on the path space and its application to the treatment of non-equilibrium systems. (joint work with M.A. Katsoulakis).

There is a significant amount of experimental research on the production of hydrogen through photocatalytic water splitting. Of existing research, titanium dioxide has been the subject of study as the catalyst due to it being inexpensive and abundant. However, the deposition of more expensive transition metals such as platinum on titanium dioxide, which enhances the photocatalytic activity, made large scale production costly. We develop a nanoscale model of the interface between titanium dioxide and water to simulate the molecular behavior which leads to water decomposition. Rutile and anatase forms of titanium dioxide are simulated for water adsorption using atomistic molecular dynamics in LAMMPS. Platinum atoms supported on the surfaces represent the co-catalyst. Properties such radial distributions functions, diffusion coefficients, and catalyst coordination residence time are used to characterize the transport phenomena of the system. Kinetic Monte Carlo simulations of the mesoscale system provide yield estimates of water splitting based on initial conditions and experimental data.

Molecular Dynamics (MD) is a powerful computing tool that can give us insight into how bio-molecules interact without doing hands-on experiments. However, MD is limited by the fact that current computing resources can only simulate a handful of molecules on a microsecond timescale. Hence, a coarse-grained model with reduced degrees of freedom can be useful, since it can give us the same useful information with orders of magnitude reduced computational time. We present a coarse-grained model based on the Mori-Zwanzig formalism. Our approach leads to the computation of a rigorously correct generalized Langevin equation (GLE), which reproduces the correct kinetics. As an example, we show that the model reproduces the distribution of first passage times and velocity correlation functions for alanine dipeptide. In addition, we show that the memory part of the GLE is essential to reproduce the correct kinetics. In other words, in our example, Markovian models fail to reproduce brute force MD results, whereas the GLE succeeds. Finally, we apply our model to bigger bio-systems to measure rates of rare events. Specifically, we will present results for the rate of flip-flop (80 degree orientation change) of protonated oleic acid molecules in a phospholipid bilayer.

Fluctuating hydrodynamic descriptions provide a promising approach for developing materials models that bridge the gap between atomistic molecular dynamics and continuum mechanics descriptions. Many coarse-grained models have been introduced for this purpose to provide a simplified description allowing access to large spatial and temporal scales. However, these models either treat the solvent using explicit degrees of freedom, which is costly, or treat these contributions implicitly through an effective free energy of interaction between the retained coarse-grained degrees of freedom. To study dynamic processes using such models requires further advances to account efficiently for important kinetic effects mediated by the solvent. We discuss our recent progress on developing thermostats based on continuum fluctuating hydrodynamics for implicit-solvent coarse-grained models. We show our approach can be used to capture many of the correlations exhibited in explicit solvent calculations. We present results for lipid bilayer membranes and vesicles making comparisons with other coarse-grained modeling approaches and continuum theory. We also present results for the electrokinetic transport of charged colloids in nanochannels.

We present a bottom-up coarse-graining procedure to construct mesoscopic force fields directly from microscopic dynamics. By grouping many bonded atoms in the molecular dynamics (MD) system into a single cluster, we compute both the conservative and non-conservative interactions between neighboring clusters. In particular, MD simulations of polymer melts are performed to provide microscopic trajectories for evaluating coarse-grained (CG) interactions. Subsequently, dissipative particle dynamics (DPD) is considered as the effective dynamics resulting from the Mori-Zwanzig (MZ) projection of the underlying atomistic dynamics. The forces between finite-size clusters have, in general, both radial and transverse components and hence we employ four different DPD models to account differently for such interactions. Quantitative comparisons between these DPD models indicate that the DPD models with MZ-guided force field yield much better static and dynamics properties consistent with the MD system compared to standard DPD with empirical formulae. When the rotational motion of the particle is properly taken into account, the whole curve of the velocity autocorrelation function of the MD system as well as the pair correlation function can be accurately reproduced by the MD-informed DPD model. Since this coarse-graining procedure is performed on an unconstrained MD system, our framework is general and can be used in other systems in which the clusters can be faithfully defined as CG particles.

The strive towards smaller electronic devices will result in damage and failure due to processes such as electromigration becoming a central impediment. As the size of the devices reach the nanoscale, where quantum effects become important, the current densities flowing will be huge and this will give rise to large current-induced forces acting on the constituent atoms in the device. The current-induced force consists of fluctuating forces (due to the corpuscular nature of electrons and responsible for processes such as Joule heating [1]) and the average force. The average force contains, amongst other contributions, the electron wind force [2]. The electron wind force has the remarkable feature of being non-conservative [3 - 5] and can therefore do net work on atoms around closed paths. Understanding this new energy exchange mechanism between the current and the atomic motion will be necessary in the continued miniturization of electronic devices and may also be exploited for the manipulation of matter at the atomistic level, and/or in the development of nanoscale motors.
Non-conservative dynamics are investigated in a system containing many degrees of freedom: defect-free metallic nanowires. Electron-ion interactions are modelled at the level of the Ehrenfest approximation, which neglects Joule heating. This leaves work by the non-conservative current-induced forces as the only energy injection mechanism into the atomic motion, enabling us to isolate and study its effect. As a result of the competition between the non-conservative forces and electronic friction the ionic kinetic energies saturate at a bias-dependent steady-state. The dependence of the ionic saturation kinetic energy on length, bias and mass, observed in the non-equilibrium non-adiabatic molecular dynamics simulations can be understood with the help of a simple analytical model. Two key results are that the saturation kinetic energy per atom under non-conservative current-induced dynamics dies out with increasing atomic wire length and with decreasing atomic mass. The results therefore define the limit in which low dimensional metallic conductors should be expected to be most stable against this novel mechanism for energy transfer from current into atomic motion. This material also highlights the benefit of simple preliminary steady-state calculations in anticipating aspects of brute force dynamical simulations, and provides rule of thumb criteria for the design of stable quantum wires.
[1] M. Galperin, M. A. Ratner, and A. Nitzan, J. Phys.: Cond. Matt. 19, 103201 (2007).
[2] R. Landauer and J. W. F. Woo, Phys. Rev. B 10, 1266 (1974).
[3] S. R. Sorbello, Sol. Stat. Phys. 51, 159 (1997).
[4] D. Dundas, E. J. McEniry, and T. N. Todorov, Nature Nanotech. 4, 99 (2009).
[5] J.-T. Lü, M. Brandbyge, and P. Hedegaring;rd, Nano. Lett. 10, 1657 (2010).

The GW-Bethe-Salpeter Equation (BSE) approach has over the last couple of decades proven to be a highly accurate approach for predicting excited-state properites of a wide class of materials. However, in practice, this appoach has been prohibitively expensive to carry out on systems with more than approximately 50 atoms. In this talk, I will show that through a combination of methodological and algorithmic improvements, the standard GW-BSE approach can be applied to systems with many hundreds to thousands of atoms. I will discuss the massively parallel GW-BSE implementation in the BerkeleyGW package including the importance of hybrid MPI-OpenMP parallelism, parallel IO and library performance. I will discuss optimization strategies for, and performance on, many-core architectures such as machines using the Intel Xeon-Phi processor. I will discuss the mathematical and computational challenges in applying the conventional GW method to large systems and the approaches and approximations we use to overcome these. I will additionally present multiple applications of the GW-BSE approach as carried out in BerkeleyGW on systems ranging from molecules to nanostructures to bulk semiconductors.

The free energy surface (FES) describes the equilibrium behavior of a system in terms of a limited number of collective coordinates while taking into account the effects of disorder, fluctuations, and finite temperature. In atomistic simulations, either the relative free energy or its gradient can be sampled by biasing the dynamics so they explore all the important configuration space, and averaging the probability density or mean force (conjugate to the collective coordinates) during constant temperature simulations. Gaussian process regression (GPR), a Bayesian multidimensional interpolation technique, can be used to robustly reconstruct a smooth FES from noisy samples from such molecular dynamics simulations. By breaking down a wide range of FES calculation and exploration methods into three components, the form of the bias, the sampled quantity, and the reconstruction method, we can recombine these components and take advantage of GPR to develop a new and more efficient method. This method combines elements of metadynamics and adaptive biasing force to more efficiently explore and reconstruct the low-free-energy regions of the full collective-coordinate space, providing more accurate FESes at fixed computational cost (or equal accuracy at reduced cost). We show tests of our free energy exploration and reconstrution method for both low (D = 1-2) and high (D ge; 10) dimensional FESes of solvated molecular systems, such as polyalanine and other polypeptides, and compare our results to existing methods.

The phase behavior of systems that are termed thermodynamically small has been the subject of intensive theoretical study over the past two decades. These systems contain a small number of particles, on the order of 100 or less; as such, they are far removed from the infinite limit of traditional bulk-scale thermodynamics. Developing a fundamental understanding of the phase behavior of these systems has direct application for the self and directed assembly of structures within materials and devices, having wide-ranging technological impact. The phase behavior of these small systems is qualitatively different from the typical thermodynamic behavior in bulk phases. Specifically, thermodynamically small colloidal assemblies exhibit coexistence of phases or configurations over a broad range of physical conditions. In this presentation, we report results of a systematic investigation of the phase behavior of thermodynamically small colloidal assemblies, which interact via electrostatic repulsion and Asakura-Oosawa (AO) depletion potentials. The interparticle potential has been validated experimentally and used for accurate statistical mechanical analyses of the fundamental thermodynamics and kinetics of the colloidal clusters.
In order to study the phase behavior of these small clusters, we have constructed free-energy landscapes (FELs) using the windowed Monte Carlo-umbrella sampling (MC-US) technique. The FELs were generated with respect to a well justified coarse-variable space, capable of capturing both order-to-disorder and polymorphic structural transitions. The dimensionality of coarse-variable space was determined by analysis based on the machine learning technique of diffusion mapping on data sets generated by Brownian-dynamics simulations of the colloidal clusters of interest. Local minima in these FELs correspond to (meta)stable configurations of the clusters. Moreover, we have characterized the equilibrium shape of the locally stable cluster configurations, which exhibit a relaxed face-centered cubic (FCC) packing, following a generalized Wulff-construction approach.
We constructed FELs over a range of interparticle interaction strength, interaction range, and cluster size and obtained a comprehensive picture regarding the possible stable configurations of such colloidal assemblies at equilibrium, as well as the phase changes that may occur between them. In particular, we have found an order-to-disorder transition between fluid-like and crystalline phases, as well as a polymorphic transition between relaxed FCC and relaxed hexagonal close-packed structures. The analysis of these FELs yields phase-diagram information, which can describe not only the bulk-like phase behavior (i.e., coexistence at a single point) but also the complex phase behavior arising from the system smallness inherent to these colloidal clusters.

At temperatures higher than 1150K up to the melting point and at normal pressure, titanium exhibits a stable bcc phase. However, harmonic phonon analysis of bcc titanium suggests that it is mechanically unstable. It is known that this apparent paradox can be explained by noting that the system is hopping between local minima, which occur away from ideal bcc position, in a way such that the average atomic positions stay at the bcc sites. However, a practical way to determine the free energy of such a system has remained elusive.
We propose a general method for free energy calculations in these mechanically unstable but dynamically stabilized phases. The energy surface is explored by discrete sampling of the various local minima via a cluster expansion approach and by a continuous sampling in the viscinity of each local minimum using a harmonic approximation. Given the proximity of the local minima, it is necessary to carefully partition phase space using a Voronoi tessellation to constrain the domain of integration, during the calculation of the free energy within a harmonic approximation, in order to avoid double-counting artifacts.