Session H27: Computational Methods: Multiscale Modeling

Coarse Molecular Dynamics Applied to the Study of Structural Transitions in Condensed Matter

We report results from application of two coarse molecular-dynamics (MD) methods to determining the onset of structural transitions in condensed matter focusing on the melting of crystalline silicon. The two techniques require properly defined coarse variables that are slow and attracting. The first method is coarse projective integration. It allows wrapping a coarse time stepper around an MD simulator to extract the corresponding \textit{coarse}-level description resulting from short MD bursts, which is used to extrapolate forward over coarse time steps. The second method is used to construct the underlying effective free energy landscape. Proper multi-system initialization at representative points in coarse-variable space along with analysis of the coarse-variable trajectories yields the effective free energy landscape upon integration of the reconstructed Fokker-Planck equation. Subsequent application of a coexistence criterion yields the thermodynamic melting point.   

Adaptive Resolution Molecular Dynamics Scheme

A new adaptive resolution scheme for efficient particle-based multiscale molecular dynamics (MD) simulations is presented. The key feature of the method is that it allows for a dynamical change of the number of molecular degrees of freedom during the course of the MD simulation by an on-the-fly switching between the atomistic and coarse-grained levels of detail. The new approach is tested on a model system of a liquid of tetrahedral molecules. The simulation box is divided into two regions: one containing only atomistically resolved tetrahedral molecules, and the other containing only one particle coarse-grained spherical molecules. The molecules can freely move between the two regions while changing their level of resolution accordingly. The hybrid and the corresponding all-atom systems have the same statistical properties.   

A Multiscale Field Theory for Atomistic Multi-element Systems

Formulas for local densities of fundamental physical properties, including stress and heat flux fields, are derived for atomistic systems with many-body potentials. The obtained formulas are then generalized to multi-element systems and the field representation of the corresponding conservation equations is obtained. The resulting formulas are calculable within an atomistic simulation, in consistent with the conservation laws of the thermodynamics continuum, and can be applied to single- and multi-element systems involving general two- and three-body interaction forces. It is found that, for multi-element systems, fluxes are composed of homogeneous and inhomogeneous parts and the energy conservation equation takes a different form from single-element systems. At atomic level, stress is nonlinear and nonlocal in displacements and consists of higher order strain gradients, and heat flux is a function of both strain and temperature gradients. With the derived balance equations and constitutive relations, it is shown that the atomistic formulation is able to completely define a field theory that exactly represents the classical many-body dynamics and is able to work as an alternative to, but computationally more efficient than, atomic-level molecular dynamics simulations in studying statistical and finite temperature properties of finite size multi-element materials. Numerical examples will be presented. Potential applications of the obtained field theory will be discussed. .   

Wavelet-based Multiresolution Particle Methods

Particle methods offer a robust numerical tool for solving transport problems across disciplines, such as fluid dynamics, quantitative biology or computer graphics. Their strength lies in their stability, as they do not discretize the convection operator, and appealing numerical properties, such as small dissipation and dispersion errors. Many problems of interest are inherently multiscale, and their efficient solution requires either multiscale modeling approaches or spatially adaptive numerical schemes. We present a hybrid particle method that employs a multiresolution analysis to identify and adapt to small scales in the solution. The method combines the versatility and efficiency of grid-based Wavelet collocation methods while retaining the numerical properties and stability of particle methods. The accuracy and efficiency of this method is then assessed for transport and interface capturing problems in two and three dimensions, illustrating the capabilities and limitations of our approach.   

Multiscale model for the study of phase separation in alloys with elastic misfit

We present a multiscale model developed for the study of phase separation and microstructure evolution in binary alloys. The model is based on the classical time-dependent DFT formalism for lattice systems generalized so that elastic effects are taken into account. A multi-scale implementation of this formalism is then performed using the finite volume method to obtain the evolution of the diffusive degrees of freedom while the quasicontinuum method is used to relax the elastic degrees of freedom. The combination of these two methods allows for a seamless coupling between different length-scales using a single formalism, while reducing exactly to the original TDDFT model as the mesh size is reduced to atomic dimensions. As a first application of this model, we study the effect of elastic heterogeneity on the chemical potential of inclusions as a result of inclusion-matrix and inclusion-inclusion interactions, and infer the consequences on the coarsening behaviour of a collection of inclusions.   

Multiscale Modeling of Polymer Rheology

We propose a novel simulation method which can be used to readily parallelizesimulations on systems with a large spatial extent. We simulate small parts of thesystem with independent molecular dynamics simulations, and only occasionally passinformation between these simulations through a constitutive model free continuumapproach. We illustrate the power of this method in the case of a polymeric fluidundergoing rapid one dimensional shear flow. Since we show that this flow problemcannot be modeled by using a steady-state constitutive model, this method offersthe unique capability for accessing the non-linear viscoelasticity of complex fluids.   

PUPIL: A New Concept of Software Integration in Multi-scale Simulations.

We present a relatively straightforward way to incorporate existing software packages systematically into a fully automated multi-scale simulation framework. The \textbf{PUPIL} (\textit{Program for User Package Interfacing and Linking}) architectural concept is to provide a simulation manager, enabled by small, minimally intrusive wrapper routines installed within each software package. Thus prepared, the different packages (``Calculation Units'') are plugged into the \textbf{PUPIL} system which one then operates as a software driver. A protocol is defined to communicate between the different Calculation Units and the \textbf{PUPIL} system to exchange information. The system has been designed using the OO paradigm and implemented in Java as a fast prototyping language. A test has been carried out joining three different packages to do a MD calculation with pattern recognition to identify the QM region and an external QM force calculation. The results show the ease of operation and maintenance of this software system with little overhead. Work supported by NSF ITR award DMR-0325553.   

Multi-scale Simulation of Ferroelectric Properties in Perovskite Solid

The first principles calculations provide us with the fundamental information for the study of ferroelectric materials, including the atomic structures of morphotropic phases, ferroelectric double-well potentials, dynamical effective charges and phonon spectra. Building on such information obtained from the electronic-structure calculations by density functional theory, we developed a multi-scale approach with parameterization of the classical Buckingham potential. Applying the empirical potentials to the atomistic modeling method and a newly developed continuum theory, the ferroelectric behaviors of BiScO3 are investigated through dynamical simulations. This approach illustrates the capability to study ferroelectric materials with finite temperature and external electromechanical loadings, with no limitation to a small system with zero temperature as being imposed in the first principles calculations.   

Anisotropy of Step Stiffness and Its Implications

Based on a lattice gas viewpoint, we have derived \footnote{T. J. Stasevich et al., Phys. Rev. B 70, 245404 (2004); 71, 245414 (2005)} a simple expression for the [in-plane] orientation dependence of step stiffness which is accurate for, e.g., noble metals at room temperature except near orientations with close-packed steps. We have extended our result to deal with this narrow but important range of angles. In addition to previous applications to Cu (001) and (111), we consider, e.g., simulations of fluctuations of island edges on Pb (111) in conjunction with experimental data.\footnote{F. Szalma et al., Phys. Rev. B 71, 035422 (2005) \& to be published.} We find that the numerical data in an Arrhenius plot is dominated by the contributions from highly kinked regions of the step edge. We emphasize that our expression is far superior to the standard phenomenological forms and is continuous and differentiable, so well suited to continuum models and finite-element calculations.   

Grain Boundary Cohesive Laws as a Function of Geometry

Cohesive laws are stress-strain curves used in finite element calculations to describe the debonding of interfaces such as grain boundaries. It would be convenient to describe cohesive laws as a function of the parameters needed to describe the grain boundary geometry; two parameters in 2D and 5 parameters in 3D. However, we find that the cohesive law is not a smooth function of these parameters. In fact, it is discontinuous at all geometries for which the two grains have repeat distances that are rational with respect to one another. Using atomistic simulations, we extract cohesive laws of grain boundary fracture in 2D with a Lennard-Jones potential for all possible geometries which can be simulated within periodic boundary conditions with a maximum box size. We connect the atomistic result to analytic calculations of fracture toughness as a function of dislocation density.   

Water-Silica Interactions from Quantum Calculations and Non-Markovian Meta-Dynamics

The interaction of silica clusters and water molecules has been investigated using first-principles Born-Oppenheimer molecular dynamics (BOMD) method. A small silica nano-rod that contains 108 atoms is chosen to illustrate the effects of external stress. Our results show clearly that the hydration energy between the nano-rod and water increases as a function of strain, which suggests that the water is more reactive under stress. Further simulations have been performed in which the nano-rod is twisted or squashed. We have also implemented a meta-dynamics based on the ideas of the extended Lagrangian and coarse-grained Non-Markovian dynamics. Hopefully, the method can be used to explore free energy barriers of chemical reactions.   

POP-ART: thermodynamically correct activated event sampling in complex materials

Dynamics of complex systems with a rugged energy landscape can be represented as a sequence of rare activated events during which the system jumps between different potential energy minima. The activation-relaxation technique (ART) [1] is an efficient method of sampling such events; however, because of an unknown bias in selecting these events it cannot easily provide thermodynamical information. We present a modification of ART, the properly obeying probability ART (POP-ART) [2]. POP-ART combines short molecular dynamics runs with ART-like activated moves, with an additional accept/reject step designed to satisfy detailed balance and thus reproduce correct thermodynamics. Both correctness and efficiency of the method have been tested using a variety of systems. We mention briefly some ways of extending the approach to obtain correct dynamics as well.\\ \noindent [1] G.T. Barkema and N. Mousseau, Phys. Rev. Lett. 77, 4358 (1996)\\ \noindent [2] H. Vocks, M.V. Chubynsky, G.T. Barkema and N. Mousseau, J. Chem. Phys., accepted   

Microstructural Effects in a Fully-Resolved Simulation of 1,024 Sedimenting Spheres

The results of a fully-resolved simulation of 1,024 particles settling under gravity in a periodic domain are described and analyzed. The particle volume fraction is about 13\% and the single-particle terminal Reynolds number about 10. Single and two-particle diffusivities are explored in the vertical and horizontal directions and their values related to the anisotropy of the system. Examination of the microstructure reveals that that the formation of nearly-horizontal particle pairs is an important phenomenon affecting the mean settling velocity as well as the velocity fluctuations.   

Information-Based Examination of Variable Hierarchy in Radiation Detection

Of considerable importance in the development of a general program of information-based materials design is the manner in which materials data are stored, retrieved and analyzed. In the area of radiation detection materials, the variable spaces tend to be large and property measurements (and computations) of candidate materials are not abundant. Moreover, measurements and calculations of the same nominal quantity (e.g. bandgap) are typically based on differing and incompletely defined environments, and may not be directly comparable. The identification of parameter degeneracies, reduced spaces and transferability within the information hierarchy have become critical issues for the development of effective structure mappings for making inferences on these systems. As the initial framework for a materials-informatics approach to radiation detection materials, we have explored the use of both supervised (Support Vector Machines( SVM); Linear Discriminant(LDA)) and unsupervised (Principal Component (PCA)) learning methods for the development of structural signature models. Application of these methods yields complementary results, both of which are necessary to reduce parameter space and variable degeneracy. Using a crystal structure classification test, nonlinear SVM significantly increases predictive performance, suggesting trade-offs between smaller descriptor spaces and simpler linear models.