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 concer