Francis J. Alexander

CELL SIZE DEPENDENCE OF TRANSPORT COEFFICIENTS IN STOCHASTIC PARTICLE ALGORITHMS

Using the Green–Kubo theory, the dependence of the viscosity and thermal conductivity on cell size is obtained explicitly for stochastic particle methods such as direct simulation Monte Carlo (DSMC) and its generalization, the consistent Boltzmann algorithm (CBA). These analytical results confirm empirical observations that significant errors occur when the cell dimensions are larger than a mean free path.

The direct simulation Monte Carlo method

Numerical simulation of the hydrodynamics of gas flow and fluid flow is described using the Direct Simulation Monte Carlo method. (AIP)

Direct Simulation Monte Carlo for Thin Film Bearings

The direct simulation Monte Carlo (DSMC) scheme is used to study the gas flow under a read/write head positioned nanometers above a moving disk drive platter (the slider bearing problem). In most cases, impressive agreement is found between the particle‐based simulation and numerical solutions of the continuum hydrodynamic Reynolds equation which has been corrected for slip. However, at very high platter speeds the gas is far from equilibrium, and the load capacity for the slider bearing cannot be accurately computed from the hydrodynamic pressure.

Ensemble Filtering for Nonlinear Dynamics

Abstract A method for data assimilation currently being developed is the ensemble Kalman filter. This method evolves the statistics of the system by computing an empirical ensemble of sample realizations and incorporates measurements by a linear interpolation between observations and predictions. However, such an interpolation is only justified for linear dynamics and Gaussian statistics, and it is known to produce erroneous results for nonlinear dynamics with far-from-Gaussian statistics. For example, the ensemble Kalman filter method, when used in models with multimodal statistics, fails to track state transitions correctly. Here alternative ensemble methods for data assimilation into nonlinear dynamical systems, in particular, those with a large state space are studied. In these methods conditional probabilities at measurement times are calculated by applying Bayess rule. These results show that the new methods accurately track the transitions between likely states in a system with bimodal statistics,...

Big Data

This introduction to the special issue on big data discusses the significant scientific opportunities offered by massive amounts of data, along with some directions for future research.

The consistent Boltzmann algorithm for the van der Waals equation of state

The direct-simulation Monte Carlo method is generalized by introducing an advection displacement that models a hard-core exclusion with a weak and constant interparticle attraction. Simulation results demonstrate that both the van der Waals equation of state and its Maxwell tie-line construction can be obtained.

Adaptive mesh refinement for multiscale nonequilibrium physics

In this paper, the authors demonstrate how to use adaptive mesh refinement (AMR) methods for the study of phase transition kinetics. In particular, they apply a block-structured AMR approach to investigate phase ordering in the time-dependent Ginzburg-Landau equations.

Statistical mechanics of kinks in 1+1 dimensions

We investigate the thermal equilibrium properties of kinks in a classical [phi][sup 4] field theory in 1+1 dimensions. The distribution function, kink density, and correlation function are determined from large scale simulations. A dilute gas description of kinks is shown to be valid below a characteristic temperature. A double Gaussian approximation to evaluate the eigenvalues of the transfer operator enables us to extend the theoretical analysis to higher temperatures where the dilute gas apparoximation fails. This approach accurately predicts the temperature at which the kink description breaks down.

Noise in algorithm refinement methods

Hybrid or algorithm refinement (AR) schemes have focused mainly on the mean behavior of system states. However, variances in these behaviors, such as spontaneous fluctuations, are important for modeling certain phenomena. This paper discusses the effects of statistical fluctuations on hybrid computational methods that combine a particle algorithm with a partial differential equation solver.

A particle method with adjustable transport properties—the generalized consistent Boltzmann algorithm

The consistent Boltzmann algorithm (CBA) for dense, hard-sphere gases is generalized to obtain the van der Waals equation of state and the corresponding exact viscosity at all densities except at the highest temperatures. A general scheme for adjusting any transport coefficients to higher values is presented.