Biomedical subjects

M H Ernst

Publications and source records attributed to M H Ernst.

7 recordsLinked to original sources

PubMed2005

Generalized Green-Kubo formulas for fluids with impulsive, dissipative, stochastic, and conservative interactions.

We present a generalization of the Green-Kubo expressions for thermal transport coefficients mu in complex fluids of the generic form [equation see text], i.e., a sum of an instantaneous transport coefficient muinfinity, and a time integral over a time correlation function in a state of thermal equilibrium between a current J and its conjugate current Jepsilon. The streaming operator exp(tL) generates the trajectory of a dynamical variable J(t)=exp(tL)J when used inside the thermal average <...>0. These formulas are valid for conservative, impulsive (hard spheres), stochastic, and dissipative forces (Langevin fluids), provided the system approaches a thermal equilibrium state. In general muinfinity not equal 0 and Jepsilon not equal J, except for the case of conservative forces, where the equality signs apply. The most important application in the present paper is the hard sphere fluid.

Journal Article↗

PubMed2005

Power law tails of time correlations in a mesoscopic fluid model.

In a quenched mesoscopic fluid, modeling transport processes at high densities, we perform computer simulations of the single particle energy autocorrelation function C(e) (t) , which is essentially a return probability. This is done to test the predictions for power law tails, obtained from mode coupling theory. We study both off and on-lattice systems in one- and two-dimensions. The predicted long time tail approximately t(-d/2) is in excellent agreement with the results of computer simulations. We also account for finite size effects, such that smaller systems are fully covered by the present theory as well.

Journal Article↗

PubMed2005

Model system for classical fluids out of equilibrium.

A model system for classical fluids out of equilibrium, referred to as a dissipative particles dynamics (DPD) solid, is studied by analytical and simulation methods. The time evolution of a DPD particle is described by a fluctuating heat equation. This DPD solid with transport based on collisional transfer (high-density mechanism) is complementary to the Lorentz gas with only kinetic transport (low-density mechanism). Combination of both models covers the qualitative behavior of transport properties of classical fluids over the full-density range. The heat diffusivity is calculated using a mean-field theory, leading to a linear-density dependence of this transport coefficient, which is exact at high densities. Subleading density corrections are obtained as well. At lower densities the model has a conductivity threshold below which heat conduction is absent. The observed threshold is explained in terms of percolation diffusion on a random proximity network. The geometrical structure of this network is the same as in continuum percolation of completely overlapping spheres, but the dynamics on this network differs from continuum percolation diffusion. Furthermore, the kinetic theory for DPD is extended to the generalized hydrodynamic regime, where the wave-number-dependent decay rates of the Fourier modes of the energy and temperature fields are calculated.

Journal Article↗

PubMed2005

Universal power law tails of time correlation functions.

The universal power law tails of single particle and multiparticle time correlation functions are derived from a unifying point of view, solely using the hydrodynamic modes of the system. The theory applies to general correlation functions and to systems more general than classical fluids. Moreover, it is argued that the collisional transfer part of the stress-stress correlation function in dense classical fluids has the same long-time tail approximately t(-1-d/2) as the velocity autocorrelation function in Lorentz gases.

Journal Article↗

PubMed2003

Exact steady-state solution of the Boltzmann equation: a driven one-dimensional inelastic Maxwell gas.

The exact nonequilibrium steady-state solution of the nonlinear Boltzmann equation for a driven inelastic Maxwell model was obtained by Ben-Naim and Krapivsky [Phys. Rev. E 61, R5 (2000)] in the form of an infinite product for the Fourier transform of distribution function f(c). In this paper we have inverted the Fourier transform to express f(c) in the form of an infinite series of exponentially decaying terms. The dominant high-energy tail is exponential, f(c) approximately A0 exp(-a|c|), where a identical with 2/square root[1-alpha(2)] and amplitude A0 is given in terms of a converging sum. This is explicitly shown in the totally inelastic limit (alpha-->0) and in the quasielastic limit (alpha-->1). In the latter case, the distribution is dominated by a Maxwellian for a very wide range of velocities, but a crossover from a Maxwellian to an exponential high-energy tail exists for velocities |c-c(0)| approximately 1/square root[q] around a crossover velocity c(0) approximately ln q(-1)/square root[q], where q identical with (1-alpha)/2<<1. In this crossover region the distribution function is extremely small, ln f(c(0)) approximately q(-1) ln q.

Journal Article↗

PubMed2002

Driven inelastic Maxwell models with high energy tails.

The solutions of the homogeneous nonlinear Boltzmann equation for inelastic Maxwell models, when driven by different types of thermostats, show, in general, overpopulated high energy tails of the form approximately exp(-ac), with power law tails and Gaussian tails as border line cases. The results are compared with those for inelastic hard spheres, and a comprehensive picture of the long time behavior in freely cooling and driven inelastic systems is presented.

Journal Article↗

PubMed2001

Randomly driven granular fluids: collisional statistics and short scale structure.

We present a molecular-dynamics and kinetic theory study of granular material, modeled by inelastic hard disks, fluidized by a random driving force. The focus is on collisional averages and short-distance correlations in the nonequilibrium steady state, in order to analyze in a quantitative manner the breakdown of molecular chaos, i.e., factorization of the two-particle distribution function, f((2))(x(1),x(2)) approximately chif((1))(x(1))f((1))(x(2)) in a product of single-particle ones, where x(i)=[r(i),v(i)] with i=1,2 and chi represents the position correlation. We have found that molecular chaos is only violated in a small region of the two-particle phase space [x(1),x(2)], where there is a predominance of grazing collisions. The size of this singular region grows with increasing inelasticity. The existence of particle- and noise-induced recollisions magnifies the departure from mean-field behavior. The implications of this breakdown in several physical quantities are explored.

Journal Article↗