The Diffusion Equation on a Hypersphere

We study the diffusion equation on the surface of a 4D sphere and obtain a Kubo formula for the diffusion coefficient

Liquid-Vapor Transition and Critical Behavior of The Ultrasoft Restricted Primitive Model of Polyelectrolytes : a Monte Carlo Study

We present a Monte-Carlo study of the liquid-vapor transition and the critical behavior of a model of polyelectrolytes with soft gaussian charge distributions introduced recently by Coslovich, Hansen, and Kahl [J. Chem. Phys. \textbf{134}, 244514 (2011)]. A finite size study involving four different volumes in the grand canonical ensemble yields a precise determination of the critical temperature, chemical potential, and density of the model. Attempts to determine the nature of the criticality and to obtain reliable values for the critical exponents are not conclusive.Comment: 14 pages, 4 figure

Statistical field theory for simple fluids: the collective variables representation

An alternative representation of an exact statistical field theory for simple fluids, based on the method of collective variables, is presented. The results obtained are examined from the point of another version of theory that was developed recently by performing a Hubbard-Stratonovich transformation of the configurational Boltzmann factor [J.-M. Caillol, Mol. Phys. 101 (2003) 1617]. The analytical expressions for the pressure and the free energy are derived in two-loop approximation for both versions of theory and it is shown that they are indeed equivalent.The results yield a new type approximation within an untested approximation scheme

Sine-Gordon theory for the equation of state of classical hard-core Coulomb systems. II. High-temperature expansion

We perform a high-temperature expansion of the grand potential of the restrictive primitive model of electrolytes in the frame of the extended sine-Gordon theory exposed in the companion paper. We recover a result already obtained by Stell an Lebowitz (J. Chem. Phys., 49, 3706 (1968)) by means of diagrammatic expansions

Monte Carlo simulations of the screening potential of the Yukawa one-component plasma

A Monte Carlo scheme to sample the screening potential H(r) of Yukawa plasmas notably at short distances is presented. This scheme is based on an importance sampling technique. Comparisons with former results for the Coulombic one-component plasma are given. Our Monte Carlo simulations yield an accurate estimate of H(r) as well for short range and long range interparticle distances.Comment: to be published in Journal of Physics A: Mathematical and Genera

Exact Renormalization Group : A New Method for Blocking the Action

We consider the exact renormalization group for a non-canonical scalar field theory in which the field is coupled to the external source in a special non linear way. The Wilsonian action and the average effective action are then simply related by a Legendre transformation up to a trivial quadratic form. An exact mapping between canonical and non-canonical theories is obtained as well as the relations between their flows. An application to the theory of liquids is sketched

Absolute and convective instabilities of an inviscid compressible mixing layer: Theory and applications

This study aims to examine the effect of compressibility on unbounded and parallel shear flow linear instabilities. This analysis is of interest for industrial, geophysical, and astrophysical flows. We focus on the stability of a wavepacket as opposed to previous single-mode stability studies. We consider the notions of absolute and convective instabilities first used to describe plasma instabilities. The compressible-flow modal theory predicts instability whatever the Mach number. Spatial and temporal growth rates and Reynolds stresses nevertheless become strongly reduced at high Mach numbers. The evolution of disturbances is driven by Kelvin -Helmholtz instability that weakens in supersonic flows. We wish to examine the occurrence of absolute instability, necessary for the appearance of turbulent motions in an inviscid and compressible two-dimensional mixing layer at an arbitrary Mach number subject to a three-dimensional disturbance. The mixing layer is defined by a parametric family of mean-velocity and temperature profiles. The eigenvalue problem is solved with the help of a spectral method. We ascertain the effects of the distribution of temperature and velocity in the mixing layer on the transition between convective and absolute instabilities. It appears that, in most cases, absolute instability is always possible at high Mach numbers provided that the ratio of slow-stream temperature over fast-stream temperature may be less than a critical maximal value but the temporal growth rate present in the absolutely unstable zone remains small and tends to zero at high Mach numbers. The transition toward a supersonic turbulent regime is therefore unlikely to be possible in the linear theory. Absolute instability can be also present among low-Mach-number coflowing mixing layers provided that this same temperature ratio may be small, but nevertheless, higher than a critical minimal value. Temperature distribution within the mixing layer also has an effect on the growth rate, this diminishes when the slow stream is heated. These results are applied to the dynamics of mixing layers in the interstellar medium and to the dynamics of the heliopause, frontier between the interstellar medium, and the solar wind. (C) 2009 American Institute of Physics