Publications

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Peridynamics is a nonlocal extension of classical continuum mechanics. The discrete peridynamic model has the same computational structure as a molecular dynamics model. This document provides a brief overview of the peridynamic model of a continuum, then discusses how the peridynamic model is discretized within LAMMPS. An example problem is also included.

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Many of the most important and hardest-to-solve problems related to the synthesis, performance, and aging of materials involve diffusion through the material or along surfaces and interfaces. These diffusion processes are driven by motions at the atomic scale, but traditional atomistic simulation methods such as molecular dynamics are limited to very short timescales on the order of the atomic vibration period (less than a picosecond), while macroscale diffusion takes place over timescales many orders of magnitude larger. We have completed an LDRD project with the goal of developing and implementing new simulation tools to overcome this timescale problem. In particular, we have focused on two main classes of methods: accelerated molecular dynamics methods that seek to extend the timescale attainable in atomistic simulations, and so-called 'equation-free' methods that combine a fine scale atomistic description of a system with a slower, coarse scale description in order to project the system forward over long times.

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The most feasible way to disperse particles in a bulk material or control their packing at a substrate is through fluidization in a carrier that can be processed with well-known techniques such as spin, drip and spray coating, fiber drawing, and casting. The next stage in the processing is often solidification involving drying by solvent evaporation. While there has been significant progress in the past few years in developing discrete element numerical methods to model dense nanoparticle dispersion/suspension rheology which properly treat the hydrodynamic interactions of the solvent, these methods cannot at present account for the volume reduction of the suspension due to solvent evaporation. As part of LDRD project FY-101285 we have developed and implemented methods in the current suite of discrete element methods to remove solvent particles and volume, and hence solvent mass from the liquid/vapor interface of a suspension to account for volume reduction (solvent drying) effects. To validate the methods large scale molecular dynamics simulations have been carried out to follow the evaporation process at the microscopic scale.

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In this presentation we examine the accuracy and performance of a suite of discrete-element-modeling approaches to predicting equilibrium and dynamic rheological properties of polystyrene suspensions. What distinguishes each approach presented is the methodology of handling the solvent hydrodynamics. Specifically, we compare stochastic rotation dynamics (SRD), fast lubrication dynamics (FLD) and dissipative particle dynamics (DPD). Method-to-method comparisons are made as well as comparisons with experimental data. Quantities examined are equilibrium structure properties (e.g. pair-distribution function), equilibrium dynamic properties (e.g. short- and long-time diffusivities), and dynamic response (e.g. steady shear viscosity). In all approaches we deploy the DLVO potential for colloid-colloid interactions. Comparisons are made over a range of volume fractions and salt concentrations. Our results reveal the utility of such methods for long-time diffusivity prediction can be dubious in certain ranges of volume fraction, and other discoveries regarding the best formulation to use in predicting rheological response.

LAMMPS is a classical molecular dynamics code, and an acronym for Large-scale Atomic/Molecular Massively Parallel Simulator. LAMMPS has potentials for soft materials (biomolecules, polymers) and solid-state materials (metals, semiconductors) and coarse-grained or mesoscopic systems. It can be used to model atoms or, more generically, as a parallel particle simulator at the atomic, meso, or continuum scale. LAMMPS runs on single processors or in parallel using message-passing techniques and a spatial-decomposition of the simulation domain. The code is designed to be easy to modify or extend with new functionality.

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The kinetic Monte Carlo method and its variants are powerful tools for modeling materials at the mesoscale, meaning at length and time scales in between the atomic and continuum. We have completed a 3 year LDRD project with the goal of developing a parallel kinetic Monte Carlo capability and applying it to materials modeling problems of interest to Sandia. In this report we give an overview of the methods and algorithms developed, and describe our new open-source code called SPPARKS, for Stochastic Parallel PARticle Kinetic Simulator. We also highlight the development of several Monte Carlo models in SPPARKS for specific materials modeling applications, including grain growth, bubble formation, diffusion in nanoporous materials, defect formation in erbium hydrides, and surface growth and evolution.

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Peridynamics (PD) is a continuum theory that employs a nonlocal model to describe material properties. In this context, nonlocal means that continuum points separated by a finite distance may exert force upon each other. A meshless method results when PD is discretized with material behavior approximated as a collection of interacting particles. This paper describes how PD can be implemented within a molecular dynamics (MD) framework, and provides details of an efficient implementation. This adds a computational mechanics capability to an MD code, enabling simulations at mesoscopic or even macroscopic length and time scales. © 2008 Elsevier B.V.

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Nanoparticles are now more than ever being used to tailor materials function and performance in differentiating technologies because of their profound effect on thermo-physical, mechanical and optical properties. The most feasible way to disperse particles in a bulk material or control their packing at a substrate is through fluidization in a carrier, followed by solidification through solvent evaporation/drying/curing/sintering. Unfortunately processing particles as concentrated, fluidized suspensions into useful products remains an art largely because the effect of particle shape and volume fraction on fluidic properties and suspension stability remains unexplored in a regime where particle-particle interaction mechanics is prevalent. To achieve a stronger scientific understanding of the factors that control nanoparticle dispersion and rheology we have developed a multiscale modeling approach to bridge scales between atomistic and molecular-level forces active in dense nanoparticle suspensions. At the largest length scale, two 'coarse-grained' numerical techniques have been developed and implemented to provide for high-fidelity numerical simulations of the rheological response and dispersion characteristics typical in a processing flow. The first is a coupled Navier-Stokes/discrete element method in which the background solvent is treated by finite element methods. The second is a particle based method known as stochastic rotational dynamics. These two methods provide a new capability representing a 'bridge' between the molecular scale and the engineering scale, allowing the study of fluid-nanoparticle systems over a wide range of length and timescales as well as particle concentrations. To validate these new methodologies, multi-million atoms simulations explicitly including the solvent have been carried out. These simulations have been vital in establishing the necessary 'subgrid' models for accurate prediction at a larger scale and refining the two coarse-grained methodologies.

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Peridynamics is a nonlocal formulation of continuum mechanics. The discrete peridynamic model has the same computational structure as a molecular dynamic model. This document details the implementation of a discrete peridynamic model within the LAMMPS molecular dynamic code. This document provides a brief overview of the peridynamic model of a continuum, then discusses how the peridynamic model is discretized, and overviews the LAMMPS implementation. A nontrivial example problem is also included.

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We have enhanced our parallel molecular dynamics (MD) simulation software LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator, lammps.sandia.gov) to include many new features for accelerated simulation including articulated rigid body dynamics via coupling to the Rensselaer Polytechnic Institute code POEMS (Parallelizable Open-source Efficient Multibody Software). We use new features of the LAMMPS software package to investigate rhodopsin photoisomerization, and water model surface tension and capillary waves at the vapor-liquid interface. Finally, we motivate the recipes of MD for practitioners and researchers in numerical analysis and computational mechanics.

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Chemically Induced Surface Evolution with Level-Sets--ChISELS--is a parallel code for modeling 2D and 3D material depositions and etches at feature scales on patterned wafers at low pressures. Designed for efficient use on a variety of computer architectures ranging from single-processor workstations to advanced massively parallel computers running MPI, ChISELS is a platform on which to build and improve upon previous feature-scale modeling tools while taking advantage of the most recent advances in load balancing and scalable solution algorithms. Evolving interfaces are represented using the level-set method and the evolution equations time integrated using a Semi-Lagrangian approach [1]. The computational meshes used are quad-trees (2D) and oct-trees (3D), constructed such that grid refinement is localized to regions near the surface interfaces. As the interface evolves, the mesh is dynamically reconstructed as needed for the grid to remain fine only around the interface. For parallel computation, a domain decomposition scheme with dynamic load balancing is used to distribute the computational work across processors. A ballistic transport model is employed to solve for the fluxes incident on each of the surface elements. Surface chemistry is computed by either coupling to the CHEMKIN software [2] or by providing user defined subroutines. This report describes the theoretical underpinnings, methods, and practical use instruction of the ChISELS 1.0 computer code.

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Understanding the properties and behavior of biomembranes is fundamental to many biological processes and technologies. Microdomains in biomembranes or ''lipid rafts'' are now known to be an integral part of cell signaling, vesicle formation, fusion processes, protein trafficking, and viral and toxin infection processes. Understanding how microdomains form, how they depend on membrane constituents, and how they act not only has biological implications, but also will impact Sandia's effort in development of membranes that structurally adapt to their environment in a controlled manner. To provide such understanding, we created physically-based models of biomembranes. Molecular dynamics (MD) simulations and classical density functional theory (DFT) calculations using these models were applied to phenomena such as microdomain formation, membrane fusion, pattern formation, and protein insertion. Because lipid dynamics and self-organization in membranes occur on length and time scales beyond atomistic MD, we used coarse-grained models of double tail lipid molecules that spontaneously self-assemble into bilayers. DFT provided equilibrium information on membrane structure. Experimental work was performed to further help elucidate the fundamental membrane organization principles.

Molecular dynamics calculations are performed to study the effect of deformation sequence and history on the inelastic behavior of copper interfaces on the nanoscale. An asymmetric 45 deg tilt bicrystal interface is examined, representing an idealized high-angle grain boundary interface. The interface model is subjected to three different deformation paths: tension then shear, shear then tension, and combined proportional tension and shear. Analysis shows that path-history dependent material behavior is confined within a finite layer of deformation around the bicrystal interface. The relationships between length scale and interface properties, such as the thickness of the path-history dependent layer and the interface strength, are discussed in detail.

A conforming representation composed of 2D finite elements and finite Fourier series is applied to 3D nonlinear non-ideal magnetohydrodynamics using a semi-implicit time-advance. The self-adjoint semi-implicit operator and variational approach to spatial discretization are synergistic and enable simulation in the extremely stiff conditions found in high temperature plasmas without sacrificing the geometric flexibility needed for modeling laboratory experiments. Growth rates for resistive tearing modes with experimentally relevant Lundquist number are computed accurately with time-steps that are large with respect to the global Alfven time and moderate spatial resolution when the finite elements have basis functions of polynomial degree (p) two or larger. An error diffusion method controls the generation of magnetic divergence error. Convergence studies show that this approach is effective for continuous basis functions with p {ge} 2, where the number of test functions for the divergence control terms is less than the number of degrees of freedom in the expansion for vector fields. Anisotropic thermal conduction at realistic ratios of parallel to perpendicular conductivity (x{parallel}/x{perpendicular}) is computed accurately with p {ge} 3 without mesh alignment. A simulation of tearing-mode evolution for a shaped toroidal tokamak equilibrium demonstrates the effectiveness of the algorithm in nonlinear conditions, and its results are used to verify the accuracy of the numerical anisotropic thermal conduction in 3D magnetic topologies.

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As current experimental and simulation methods cannot determine the mobility of flat boundaries across the large misorientation phase space, we have developed a computational method for imposing an artificial driving force on boundaries. In a molecular dynamics simulation, this allows us to go beyond the inherent timescale restrictions of the technique and induce non-negligible motion in flat boundaries of arbitrary misorientation. For different series of symmetric boundaries, we find both expected and unexpected results. In general, mobility increases as the grain boundary plane deviates from (111), but high-coincidence and low-angle boundaries represent special cases. These results agree with and enrich experimental observations.

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The traditional, serial, algorithm for finding the strongly connected components in a graph is based on depth first search and has complexity which is linear in the size of the graph. Depth first search is difficult to parallelize, which creates a need for a different parallel algorithm for this problem. We describe the implementation of a recently proposed parallel algorithm that finds strongly connected components in distributed graphs, and discuss how it is used in a radiation transport solver. © 2005 Elsevier Inc. All rights reserved.