Effects of Cutoff Functions of Tersoff Potentials on Molecular Dynamics Simulations of Thermal Transport

Past molecular dynamics studies of thermal transport have predominantly used Stillinger-Weber potentials. As materials continuously shrink, their properties increasingly depend on defect and surface effects. Unfortunately, Stillinger-Weber potentials are best used for diamond-cubic-like bulk crystals. They cannot represent the energies of many metastable phases, nor can they accurately predict the energetics of defective and surface regions. To study nanostructured materials, where these regions can dominate thermal transport, the accuracy of Tersoff potentials in representing these structures is more desirable. Based upon an analysis of thermal transport in a GaN system, we demonstrate that the cutoff function of the existing Tersoff potentials may lead to problems in determining the thermal conductivity. To remedy this issue, improved cutoff schemes are proposed and evaluated

Equilibration of Long Chain Polymer Melts in Computer Simulations

Several methods for preparing well equilibrated melts of long chains polymers are studied. We show that the standard method in which one starts with an ensemble of chains with the correct end-to-end distance arranged randomly in the simulation cell and introduces the excluded volume rapidly, leads to deformation on short length scales. This deformation is strongest for long chains and relaxes only after the chains have moved their own size. Two methods are shown to overcome this local deformation of the chains. One method is to first pre-pack the Gaussian chains, which reduces the density fluctuations in the system, followed by a gradual introduction of the excluded volume. The second method is a double-pivot algorithm in which new bonds are formed across a pair of chains, creating two new chains each substantially different from the original. We demonstrate the effectiveness of these methods for a linear bead spring polymer model with both zero and nonzero bending stiffness, however the methods are applicable to more complex architectures such as branched and star polymer.Comment: 12 pages, 9 figure

Sensitivity analysis of a computational model of the IKK-NF-{\kappa}B-I{\kappa}B{\alpha}-A20 signal transduction network

The NF-{\kappa}B signaling network plays an important role in many different compartments of the immune system during immune activation. Using a computational model of the NF-{\kappa}B signaling network involving two negative regulators, I{\kappa}B{\alpha} and A20, we performed sensitivity analyses with three different sampling methods and present a ranking of the kinetic rate variables by the strength of their influence on the NF-{\kappa}B signaling response. We also present a classification of temporal response profiles of nuclear NF-{\kappa}B concentration into six clusters, which can be regrouped to three biologically relevant clusters. Lastly, based upon the ranking, we constructed a reduced network of the IKK-NF-{\kappa}B-I{\kappa}B{\alpha}-A20 signal transduction.Comment: 32 pages, 8 figure

Evaporation of Lennard-Jones Fluids

Evaporation and condensation at a liquid/vapor interface are ubiquitous interphase mass and energy transfer phenomena that are still not well understood. We have carried out large scale molecular dynamics simulations of Lennard-Jones (LJ) fluids composed of monomers, dimers, or trimers to investigate these processes with molecular detail. For LJ monomers in contact with a vacuum, the evaporation rate is found to be very high with significant evaporative cooling and an accompanying density gradient in the liquid domain near the liquid/vapor interface. Increasing the chain length to just dimers significantly reduces the evaporation rate. We confirm that mechanical equilibrium plays a key role in determining the evaporation rate and the density and temperature profiles across the liquid/vapor interface. The velocity distributions of evaporated molecules and the evaporation and condensation coefficients are measured and compared to the predictions of an existing model based on kinetic theory of gases. Our results indicate that for both monatomic and polyatomic molecules, the evaporation and condensation coefficients are equal when systems are not far from equilibrium and smaller than one, and decrease with increasing temperature. For the same reduced temperature $T/T_c$, where $T_c$ is the critical temperature, these two coefficients are higher for LJ dimers and trimers than for monomers, in contrast to the traditional viewpoint that they are close to unity for monatomic molecules and decrease for polyatomic molecules. Furthermore, data for the two coefficients collapse onto a master curve when plotted against a translational length ratio between the liquid and vapor phase.Comment: revised version, 15 pages, 15 figures, to appear in J. Chem. Phy

A relative entropy rate method for path space sensitivity analysis of stationary complex stochastic dynamics

We propose a new sensitivity analysis methodology for complex stochastic dynamics based on the Relative Entropy Rate. The method becomes computationally feasible at the stationary regime of the process and involves the calculation of suitable observables in path space for the Relative Entropy Rate and the corresponding Fisher Information Matrix. The stationary regime is crucial for stochastic dynamics and here allows us to address the sensitivity analysis of complex systems, including examples of processes with complex landscapes that exhibit metastability, non-reversible systems from a statistical mechanics perspective, and high-dimensional, spatially distributed models. All these systems exhibit, typically non-gaussian stationary probability distributions, while in the case of high-dimensionality, histograms are impossible to construct directly. Our proposed methods bypass these challenges relying on the direct Monte Carlo simulation of rigorously derived observables for the Relative Entropy Rate and Fisher Information in path space rather than on the stationary probability distribution itself. We demonstrate the capabilities of the proposed methodology by focusing here on two classes of problems: (a) Langevin particle systems with either reversible (gradient) or non-reversible (non-gradient) forcing, highlighting the ability of the method to carry out sensitivity analysis in non-equilibrium systems; and, (b) spatially extended Kinetic Monte Carlo models, showing that the method can handle high-dimensional problems

Transient dynamics simulations: Parallel algorithms for contact detection and smoothed particle hydrodynamics

Transient dynamics simulations are commonly used to model phenomena such as car crashes, underwater explosions, and the response of shipping containers to high-speed impacts. Physical objects in such a simulation are typically represented by Lagrangian meshes because the meshes can move and deform with the objects as they undergo stress. Fluids (gasoline, water) or fluid-like materials (earth) in the simulation can be modeled using the techniques of smoothed particle hydrodynamics. Implementing a hybrid mesh/particle model on a massively parallel computer poses several difficult challenges. One challenge is to simultaneously parallelize and load-balance both the mesh and particle portions of the computation. A second challenge is to efficiently detect the contacts that occur within the deforming mesh and between mesh elements and particles as the simulation proceeds. These contacts impart forces to the mesh elements and particles which must be computed at each timestep to accurately capture the physics of interest. In this paper we describe new parallel algorithms for smoothed particle hydrodynamics and contact detection which turn out to have several key features in common. Additionally, we describe how to join the new algorithms with traditional parallel finite element techniques to create an integrated particle/mesh transient dynamics simulation. Our approach to this problem differs from previous work in that we use three different parallel decompositions, a static one for the finite element analysis and dynamic ones for particles and for contact detection. We have implemented our ideas in a parallel version of the transient dynamics code PRONTO-3D and present results for the code running on a large Intel Paragon

Confined granular packings: structure, stress, and forces

The structure and stresses of static granular packs in cylindrical containers are studied using large-scale discrete element molecular dynamics simulations in three dimensions. We generate packings by both pouring and sedimentation and examine how the final state depends on the method of construction. The vertical stress becomes depth-independent for deep piles and we compare these stress depth-profiles to the classical Janssen theory. The majority of the tangential forces for particle-wall contacts are found to be close to the Coulomb failure criterion, in agreement with the theory of Janssen, while particle-particle contacts in the bulk are far from the Coulomb criterion. In addition, we show that a linear hydrostatic-like region at the top of the packings unexplained by the Janssen theory arises because most of the particle-wall tangential forces in this region are far from the Coulomb yield criterion. The distributions of particle-particle and particle-wall contact forces $P(f)$ exhibit exponential-like decay at large forces in agreement with previous studies.Comment: 11 pages, 11 figures, submitted to PRE (v2) added new references, fixed typo

Icarus: A 2D direct simulation Monte Carlo (DSMC) code for parallel computers. User`s manual - V.3.0

Icarus is a 2D Direct Simulation Monte Carlo (DSMC) code which has been optimized for the parallel computing environment. The code is based on the DSMC method of Bird and models from free-molecular to continuum flowfields in either cartesian (x, y) or axisymmetric (z, r) coordinates. Computational particles, representing a given number of molecules or atoms, are tracked as they have collisions with other particles or surfaces. Multiple species, internal energy modes (rotation and vibration), chemistry, and ion transport are modelled. A new trace species methodology for collisions and chemistry is used to obtain statistics for small species concentrations. Gas phase chemistry is modelled using steric factors derived from Arrhenius reaction rates. Surface chemistry is modelled with surface reaction probabilities. The electron number density is either a fixed external generated field or determined using a local charge neutrality assumption. Ion chemistry is modelled with electron impact chemistry rates and charge exchange reactions. Coulomb collision cross-sections are used instead of Variable Hard Sphere values for ion-ion interactions. The electrostatic fields can either be externally input or internally generated using a Langmuir-Tonks model. The Icarus software package includes the grid generation, parallel processor decomposition, postprocessing, and restart software. The commercial graphics package, Tecplot, is used for graphics display. The majority of the software packages are written in standard Fortran

Parallel contact detection algorithm for transient solid dynamics simulations using PRONTO3D

An efficient, scalable, parallel algorithm for treating material surface contacts in solid mechanics finite element programs has been implemented in a modular way for MIMD parallel computers. The serial contact detection algorithm that was developed previously for the transient dynamics finite element code PRONTO3D has been extended for use in parallel computation by devising a dynamic (adaptive) processor load balancing scheme