Are Gauss-Legendre methods useful in molecular dynamics?

AbstractWe apply the two-stage Gauss-Legendre method to the numerical simulation of liquid argon, a typical problem in molecular dynamics. It is found that the scheme is less efficient than the Verlet/leapfrog method, standard in this sort of simulation

Nanostructure Modeling in Oxide Ceramics Using Large Scale Parallel Molecular Dynamics Simulations.

The purpose of this dissertation is to investigate the properties and processes in nanostructured oxide ceramics using molecular-dynamics (MD) simulations. These simulations are based on realistic interatomic potentials and require scalable and portable multiresolution algorithms implemented on parallel computers. The dynamics of oxidation of aluminum nanoclusters is studied with a MD scheme that can simultaneously treat metallic and oxide systems. Dynamic charge transfer between anions and cations which gives rise to a compute-intensive Coulomb interaction, is treated by the O(N) Fast Multipole Method. Structural and dynamical correlations and local stresses reveal significant charge transfer and stress variations which cause rapid diffusion of Al and O on the nanocluster surface. At a constant temperature, the formation of an amorphous surface-oxide layer is observed during the first 100 picoseconds. Subsequent sharp decrease in O diffusion normal to the cluster surface arrests the growth of the oxide layer with a saturation thickness of 4 nanometers; this is in excellent agreement with experiments. Analyses of the oxide scale reveal significant charge transfer and variations in local structure. When the heat is not extracted from the cluster, the oxidizing reaction becomes explosive. Sintering, structural correlations, vibrational properties, and mechanical behavior of nanophase silica glasses are also studied using the MD approach based on an empirical interatomic potential that consists of both two and three-body interactions. Nanophase silica glasses with densities ranging from 76 to 93% of the bulk glass density are obtained using an isothermal-isobaric MD approach. During the sintering process, the pore sizes and distribution change without any discernable change in the pore morphology. The height and position of the first sharp diffraction peak (the signature of intermediate-range order) in the neutron static structure factor shows significant differences in the nanophase glasses relative to the bulk silica glass. Enhancement of the low-energy vibrational modes is observed. The effect of densification on mechanical properties is also examined

Novel simulation methods for coulomb and hydrodynamic interactions

Novel simulation methods for Coulomb and hydrodynamic interactions This thesis presents new methods to simulate systems with hydrodynamic and electrostatic interactions. Part 1 is devoted to computer simulations of Brownian particles with hydrodynamic interactions. The main in uence of the solvent on the dynamics of Brownian particles is that it mediates hydrodynamic interactions. In the method, this is simulated by numerical solution of the Navier{Stokes equation on a lattice. To this end, the Lattice{Boltzmann method is used, namely its D3Q19 version. This model is capable to simulate compressible ow. It gives us the advantage to treat dense systems, in particular away from thermal equilibrium. The Lattice{Boltzmann equation is coupled to the particles via a friction force. In addition to this force, acting on point particles, we construct another coupling force, which comes from the pressure tensor. The coupling is purely local, i. e. the algorithm scales linearly with the total number of particles. In order to be able to map the physical properties of the Lattice{Boltzmann uid onto a Molecular Dynamics (MD) uid, the case of an almost incompressible ow is considered. The Fluctuation{Dissipation theorem for the hybrid coupling is analyzed, and a geometric interpretation of the friction coe cient in terms of a Stokes radius is given. Part 2 is devoted to the simulation of charged particles. We present a novel method for obtaining Coulomb interactions as the potential of mean force between charges which are dynamically coupled to a local electromagnetic eld. This algorithm scales linearly, too. We focus on the Molecular Dynamics version of the method and show that it is intimately related to the Car{Parrinello approach, while being equivalent to solving Maxwell's equations with freely adjustable speed of light. The Lagrangian formulation of the coupled particles{ elds system is derived. The quasi{Hamiltonian dynamics of the system is studied in great detail. For implementation on the computer, the equations of motion are discretized with respect to both space and time. The discretization of the electromagnetic elds on a lattice, as well as the interpolation of the particle charges on the lattice is given. The algorithm is as local as possible: Only nearest neighbors sites of the lattice are interacting with a charged particle. Unphysical self{energies arise as a result of the lattice interpolation of charges, and are corrected by a subtraction scheme based on the exact lattice Green's function. The method allows easy parallelization using standard domain decomposition. Some benchmarking results of the algorithm are presented and discussed. Supervisor PD Dr. Burkhard Dunweg May 17, 2004 Neue Methoden zur Simulation von Systemen mit elektrostatischer und hydrodynamischer Wechselwirkung Die vorliegende Dissertation stellt neue Methoden zur Simulation von Systemen mit hydrodynamischer und elektrostatischer Wechselwirkung vor. Teil 1 widmet sich der Computersimulation von Brown'schen Teilchen mit hydrodynamischer Wechselwirkung. Der wichtigste Ein u des Losungsmittels auf die Dynamik der Brown'schen Teilchen besteht darin, da es hydrodynamische Wechselwirkungen vermittelt. In der vorgestellten Methode wird dies simuliert durch numerische Losung der Navier{Stokes{Gleichung auf einem Gitter. Hierzu wird die \Lattice Boltzmann"{Methode benutzt, und zwar in ihrer sogenannten \D3Q19"{Version. Dieses Modell ist imstande, kompressible Stromungen zu simulieren. Dies hat den Vorteil, da dichte Systeme studiert werden konnen, insbesondere auch unter Nichtgleichgewichtsbedingungen. Die \Lattice Boltzmann"{Gleichung wird mit den Teilchen uber eine Reibungskraft gekoppelt. Zusatzlich zu dieser Kraft, die auf Punktteilchen wirkt, konstruieren wir eine weitere Kraft, die vom Drucktensor herruhrt. Diese Kopplung ist streng lokal, d. h. der Algorithmus skaliert linear mit der Gesamtzahl der Teilchen. Um imstande zu sein, die physikalischen Eigenschaften der \Lattice Boltzmann"{Flussigkeit auf diejenigen einer Molekulardynamik{Flussigkeit abzubilden, wird der Fall einer fast inkompressiblen Stromung betrachtet. Die Analyse des Fluktuations{Dissipations{Theorems fur die Hybridkopplung fuhrt auf eine geometrische Interpretation des Reibungskoe zienten im Sinne eines Stokes{Radius. Teil 2 widmet sich der Simulation geladener Teilchen. Wir prasentieren eine neue Methode, um Coulomb{Wechselwirkungen als das \potential of mean force" zwischen Ladungen zu erhalten, die dynamisch an ein lokales elektromagnetisches Feld angekoppelt werden. Dieser Algorithmus skaliert ebenfalls linear. Wir konzentrieren uns auf die Molekulardynamik{Version der Methode, und zeigen, da ein enger Zusammenhang zum Car{Parrinello{Verfahren besteht. Au erdem wird gezeigt, da die Methode auf die Losung der Maxwell{Gleichungen mit frei anpa barer Lichtgeschwindigkeit hinauslauft. Die Lagrange'sche Formulierung des gekoppelten Systems Teilchen{Felder wird hergeleitet. Die quasi{Hamilton'sche Dynamik des Systems wird im Detail studiert. Zur Implementation auf dem Computer werden die Bewegungsgleichungen sowohl raumlich als auch zeitlich diskretisiert. Die Diskretisierung der elektromagnetischen Felder auf dem Gitter sowie die Interpolation der Teilchenladungen auf das Gitter werden angegeben. Der Algorithmus ist so lokal wie nur moglich: Nur die nachsten Nachbarn des Gitters wechselwirken mit einem geladenen Teilchen. Die Gitter{Interpolation der Ladungen fuhrt zu unphysikalischen Selbstenergien; diese werden durch ein Subtraktionsverfahren korrigiert, welches auf der exakten Gitter{Greensfunktion beruht. Die Methode la t sich mit Standard{ Gebietszerlegung leicht parallelisieren. Einige \Benchmark"{Testergebnisse des Algorithmus werden vorgestellt und diskutiert. Betreuer PD Dr. Burkhard Dunweg 17. Mai 200

Nanoscale Structures and Fracture Processes in Advanced Ceramics: Million-Atom MD Simulations on Parallel Architectures.

Properties and processes in silicon nitride and graphite are investigated using molecular-dynamics (MD) simulations. Scalable and portable multiresolution algorithms are developed and implemented on parallel architectures to simulate systems containing 10\sp6 atoms interacting via realistic potentials. Structural correlations, mechanical properties, and thermal transport are studied in microporous silicon nitride as a function of density. The formation of pores is observed when the density is reduced to 2.6 g/cc, and the percolation occurs at a density of 2.0 g/cc. The density variation of the thermal conductivity and the Young\u27s modulus are well described by power laws with scaling exponents of 1.5 and 3.6, respectively. Dynamic fracture in a single graphite sheet is investigated. For certain crystalline orientations, the crack becomes unstable with respect to branching at a critical speed of $\sim$60% of the Rayleigh velocity. The origin of the branching instability is investigated by calculating local-stress distributions. The branched fracture profile is characterized by a roughness exponent, $\alpha\sim0.7,$ above a crossover length of 50A. For smaller length scales and within the same branch, $\alpha\sim0.4.$. Crack propagation is studied in nanophase silicon nitride prepared by sintering nanoclusters of size 60A. The system consists of crystalline cluster interiors, amorphous intercluster regions, and isolated pores. These microstructures cause crack branching and meandering, and the clusters undergo significant rearrangement due to plastic deformation of interfacial regions. As a result, the system can withstand enormous deformation (30%). In contrast, a crystalline sample in the same geometry cleaves under an applied strain of only 3%