Systolic and Hyper-Systolic Algorithms for the Gravitational N-Body Problem, with an Application to Brownian Motion

A systolic algorithm rhythmically computes and passes data through a network of processors. We investigate the performance of systolic algorithms for implementing the gravitational N-body problem on distributed-memory computers. Systolic algorithms minimize memory requirements by distributing the particles between processors. We show that the performance of systolic routines can be greatly enhanced by the use of non-blocking communication, which allows particle coordinates to be communicated at the same time that force calculations are being carried out. Hyper-systolic algorithms reduce the communication complexity at the expense of increased memory demands. As an example of an application requiring large N, we use the systolic algorithm to carry out direct-summation simulations using 10^6 particles of the Brownian motion of the supermassive black hole at the center of the Milky Way galaxy. We predict a 3D random velocity of 0.4 km/s for the black hole.Comment: 33 pages, 10 postscript figure

Path integral Monte Carlo simulations of silicates

We investigate the thermal expansion of crystalline SiO$_2$ in the $\beta$-- cristobalite and the $\beta$-quartz structure with path integral Monte Carlo (PIMC) techniques. This simulation method allows to treat low-temperature quantum effects properly. At temperatures below the Debye temperature, thermal properties obtained with PIMC agree better with experimental results than those obtained with classical Monte Carlo methods.Comment: 27 pages, 10 figures, Phys. Rev. B (in press

The Dynamics of Non-Crystalline Silica: Insight from Molecular Dynamics Computer Simulations

Using a large scale molecular dynamics computer simulation we investigate the dynamics of a supercooled melt of SiO_2. We find that with increasing temperature the temperature dependence of the diffusion constants crosses over from an Arrhenius-law, with activation energies close to the experimental values, to a power-law dependence. We show that this crossover is related to the fact that at low temperatures the dynamics of the ions is dominated by hopping processes, whereas at high temperatures it shows the continuous flow-like motion proposed by the ideal version of mode-coupling theory (MCT). Finally we show that at low temperatures the dynamics of the system in the beta-relaxation regime obeys the factorization property, in agreement with MCT.Comment: Invited talk given at 8th Tohwa University International Symposium on "Slow Dynamics in Complex Systems", Fukuoka Nov. 1998; 12 pages of Latex, 6 figures; uses aipproc.st

Effect of long range forces on the interfacial profiles in thin binary polymer films

We study the effect of surface fields on the interfacial properties of a binary polymer melt confined between two parallel walls. Each wall attracts a different component of the blend by a non-retarded van der Waals potential. An interface which runs parallel to the surfaces is stabilized in the center of the film. Using extensive Monte Carlo simulations we study the interfacial properties as a function of the film thickness, the strength of the surface forces and the lateral size over which the profiles across the film are averaged. We find evidence for capillary wave broadening of the apparent interfacial profiles. However, the apparent interfacial width cannot be described quantitatively by a simple logarithmic dependence on the film thickness. The Monte Carlo simulations reveal that the surface fields give rise to an additional reduction of the intrinsic interfacial width and an increase of the effective interfacial tension upon decreasing the film thickness. These modifications of the intrinsic interfacial properties are confirmed by self-consistent field calculations. Taking account of the thickness dependence of the intrinsic interfacial properties and the capillary wave broadening, we can describe our simulation results quantitatively.Comment: to appear in J.Chem.Phy

Application of Pfortran and Co-Array Fortran in the parallelization of the GROMOS96 molecular dynamics module

After at least a decade of parallel tool development, parallelization of scientific applications remains a significant undertaking. Typically parallelization is a specialized activity supported only partially by the programming tool set, with the programmer involved with parallel issues in addition to sequential ones. The details of concern range from algorithm design down to low-level data movement details. The aim of parallel programming tools is to automate the latter without sacrificing performance and portability, allowing the programmer to focus on algorithm specification and development. We present our use of two similar parallelization tools, Pfortran and Cray's Co-Array Fortran, in the parallelization of the GROMOS96 molecular dynamics module. Our parallelization started from the GROMOS96 distribution's sharedmemory implementation of the replicated algorithm, but used little of that existing parallel structure. Consequently, our parallelization was close to starting with the sequential version. We found the intuitive extensions to Pfortran and Co-Array Fortran helpful in the rapid parallelization of the project. We present performance figures for both the Pfortran and CoArray Fortran parallelizations showing linear speedup within the range expected by these parallelization methods

Three-dimensional lattice-Boltzmann simulations of critical spinodal decomposition in binary immiscible fluids

We use a modified Shan-Chen, noiseless lattice-BGK model for binary immiscible, incompressible, athermal fluids in three dimensions to simulate the coarsening of domains following a deep quench below the spinodal point from a symmetric and homogeneous mixture into a two-phase configuration. We find the average domain size growing with time as $t^\gamma$, where $\gamma$ increases in the range $0.545 < \gamma < 0.717$, consistent with a crossover between diffusive $t^{1/3}$ and hydrodynamic viscous, $t^{1.0}$, behaviour. We find good collapse onto a single scaling function, yet the domain growth exponents differ from others' works' for similar values of the unique characteristic length and time that can be constructed out of the fluid's parameters. This rebuts claims of universality for the dynamical scaling hypothesis. At early times, we also find a crossover from $q^2$ to $q^4$ in the scaled structure function, which disappears when the dynamical scaling reasonably improves at later times. This excludes noise as the cause for a $q^2$ behaviour, as proposed by others. We also observe exponential temporal growth of the structure function during the initial stages of the dynamics and for wavenumbers less than a threshold value.Comment: 45 pages, 18 figures. Accepted for publication in Physical Review

Parallel simulations of reacting two-phase flows - A DoD Grand Challenge progress report

Parallel simulation of unsteady turbulent combustion is carried out for a range of precursor test problems leading to the development of a new methodology for reacting two-phase flows. Simulations are carried out using large-eddy simulations (LES) which allows full spatio-temporal resolution of all scales larger than the grid resolution with the unresolved small-scales modeled by a localized dynamic one-equation subgrid models. For two-phase applications, Lagrangian tracking of a range of droplets is carried out and is fully coupled to the Eulerian gas phase flow. An extension of this approach to accurately deal with small-scale scalar mixing and chemical reactions has been carried out using an innovative model that is implemented within each LES cell, to account for the effects of small-scale mixing and molecular diffusion on the chemical processes. The first year&apos;s effort focused on validating this methodology using both simple and complex test configurations. Highly optimized parallel LES codes are used for these studies. In addition to parallel scaleup data, results discussed in this paper include stagnation point premixed flame, opposed jet diffusion flame, highly swirling premixed flame in a General Electric combustor and two-phase mixing and vaporization in mixing layers. Comparison with experimental data wherever possible, clearly demonstrates the unique capabilities of the new subgrid combustion LES model

Molecular Dynamics Simulations

A tutorial introduction to the technique of Molecular Dynamics (MD) is given, and some characteristic examples of applications are described. The purpose and scope of these simulations and the relation to other simulation methods is discussed, and the basic MD algorithms are described. The sampling of intensive variables (temperature T, pressure p) in runs carried out in the microcanonical (NVE) ensemble (N= particle number, V = volume, E = energy) is discussed, as well as the realization of other ensembles (e.g. the NVT ensemble). For a typical application example, molten SiO2, the estimation of various transport coefficients (self-diffusion constants, viscosity, thermal conductivity) is discussed. As an example of Non-Equilibrium Molecular Dynamics (NEMD), a study of a glass-forming polymer melt under shear is mentioned.Comment: 38 pages, 11 figures, to appear in J. Phys.: Condens. Matte

On two intrinsic length scales in polymer physics: topological constraints vs. entanglement length

The interplay of topological constraints, excluded volume interactions, persistence length and dynamical entanglement length in solutions and melts of linear chains and ring polymers is investigated by means of kinetic Monte Carlo simulations of a three dimensional lattice model. In unknotted and unconcatenated rings, topological constraints manifest themselves in the static properties above a typical length scale $dt \sim 1/\sqrt{l\phi}$ ($\phi$ being the volume fraction, $l$ the mean bond length). Although one might expect that the same topological length will play a role in the dynamics of entangled polymers, we show that this is not the case. Instead, a different intrinsic length de, which scales like excluded volume blob size $\xi$, governs the scaling of the dynamical properties of both linear chains and rings.Comment: 7 pages. 4 figure