Bruce M. Boghosian

Thermodynamic description of the relaxation of two-dimensional turbulence using Tsallis statistics

Two-dimensional Euler turbulence and drift turbulence in a pure-electron plasma column have been experimentally observed to relax to metaequilibrium states that do not maximize the Boltzmann entropy, but rather seem to minimize enstrophy. We show that a recent generalization of thermodynamics and statistics due to Tsallis [Phys. Lett. A 195, 329 (1994); J. Stat. Phys. 52, 479 (1988)] is capable of explaining this phenomenon in a natural way. In particular, the maximization of the generalized entropy

An exact quantum Monte Carlo calculation of the helium–helium intermolecular potential

{S}_{q}

Simulating quantum mechanics on a quantum computer

with

Entropic lattice Boltzmann methods

q=\frac{1}{2}

Galilean-Invariant Lattice-Boltzmann Models with H-Theorem

for the pure-electron plasma column leads to precisely the same profiles predicted by the restricted minimum enstrophy theory of Huang and Driscoll [Phys. Rev. Lett. 72, 2187 (1994)]. These observations make possible the construction of a comprehensive thermodynamic description of two-dimensional turbulence.

Lattice-Boltzmann model for interacting amphiphilic fluids

We report “exact” ab initio calculations with reduced statistical error for the potential energy of interaction of two helium atoms. For the equilibrium internuclear distance of 5.6 bohr, the calculated electronic energy is −5.807 483 53±0.000 000 06 hartrees and the corresponding well depth is (e/k) 10.98±0.02 K.

Quantum chemistry by random walk: Exact treatment of many‐electron systems

Abstract Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrodinger equation for interacting many-body systems are presented in some detail. These algorithms would make it possible to simulate nonrelativistic quantum systems on a quantum computer with an exponential speedup compared to simulations on classical computers. Issues involved in simulating relativistic systems of Dirac or gauge particles are discussed.

A Lattice-Gas Model of Microemulsions

We present a general methodology for constructing lattice Boltzmann models of hydrodynamics with certain desired features of statistical physics and kinetic theory. We show how a methodology of linear programming theory, known as Fourier‐Motzkin elimination, provides an important tool for visualizing the state‐space of lattice Boltzmann algorithms that conserve a given set of moments of the distribution function. We show how such models can be endowed with a Lyapunov functional, analogous to Boltzmanns H, resulting in unconditional numerical stability. Using the Chapman‐Enskog analysis and numerical simulation, we demonstrate that such entropically stabilized lattice Boltzmann algorithms, while fully explicit and perfectly conservative, may achieve remarkably low values for transport coefficients, such as viscosity. Indeed, the lowest such attainable values are limited only by considerations of accuracy, rather than stability. The method thus holds promise for high‐Reynolds‐number simulations of the Navier‐Stokes equations.

NEKTAR, SPICE and Vortonics: using federated grids for large scale scientific applications

We demonstrate that the requirement of Galilean invariance determines the choice of H function for a wide class of entropic lattice-Boltzmann models for the incompressible Navier-Stokes equations. The required H function has the form of the Burg entropy for D=2, and of a Tsallis entropy with q=1-(2/D) for D>2, where D is the number of spatial dimensions. We use this observation to construct a fully explicit, unconditionally stable, Galilean-invariant, lattice-Boltzmann model for the incompressible Navier-Stokes equations, for which attainable Reynolds number is limited only by grid resolution.

A Ternary Lattice Boltzmann Model for Amphiphilic Fluids

We develop our recently proposed lattice-Boltzmann method for the nonequilibrium dynamics of amphiphilic fluids [H. Chen, B. M. Boghosian, P. V. Coveney, and M. Nekovee, Proc. R. Soc. London, Ser. A 456, 2043 (2000)]. Our method maintains an orientational degree of freedom for the amphiphilic species and models fluid interactions at a microscopic level by introducing self-consistent mean-field forces between the particles into the lattice-Boltzmann dynamics, in a way that is consistent with kinetic theory. We present the results of extensive simulations in two dimensions which demonstrate the ability of our model to capture the correct phenomenology of binary and ternary amphiphilic fluids.