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Entropy increase and comparison principles are found for the Fokker–Planck equation for the radiation field in a homogeneous plasma with constant electron temperature. When emission– absorption is neglected, this is used to find equilibrium distributions that have the form of a Planck distribution plus a δ function at zero photon energy. For distributions below the Planck and with emission–absorption included, a rate of entropy increase is obtained. Numerical results confirm these conclusions. [ABSTRACT FROM AUTHOR]

Presents criteria for monitoring the validity of the Navier-Stokes approximation during the simulation of a rarefied gas. Construction of non-dimensional, non-negative definite matrices; Comparison of stationary planar shock profiles computed using the Navier-Stokes equations with those computed using Monte Carlo simulations.

Density variations in real fluids are related to both pressure and entropy variations, even in the incompressible limit. The behavior of density variations depends crucially on the relative sizes of the pressure, temperature, and entropy fluctuations. It is shown how this arises from a formal asymptotic expansion of the compressible Navier–Stokes equations about a uniform state. Direct numerical simulations of the full compressible equations verify the consistency of different asymptotic regimes. In the case of turbulent flow, the Kolmogorov–Obukhov theory allows one to predict inertial range scalings for the density fluctuation power spectra in various situations. The results may be relevant to observations of the interstellar medium. [ABSTRACT FROM AUTHOR]

The hydrodynamic mixing of shell material into the fuel region of an inertial confinement fusion (ICF) target during compression will suppress the thermonuclear yield due to the loss of charged fusion reaction products to the entrained shell material. Adopting a binary Markovian model for this mixture an exact formula for the fraction of particles lost is derived. [ABSTRACT FROM AUTHOR]

Renewal theory is used to analyze linear particle transport without scattering in a random mixture of two immiscible fluids, with the statistics described by arbitrary (non-Markovian) fluid chord length distributions. One conclusion (for unimodal distributions) that is drawn is that the mean and variance of the chord length distributions through each fluid is sufficient knowledge of the statistics to give a reasonably accurate description of the ensemble averaged intensity. Expressions for effective cross sections and an effective source to be used in the usual deterministic transport equation are also obtained. The use of these effective quantities allows statistical information to be introduced very simply into a standard transport equation. An analysis is given which shows how the transport description, including scattering, in a Markovian mixture can be modified to yield an approximate description of transport in a nonMarkovian mixture. Numerical results are given to assess the accuracy of this model, as well as the simpler model involving the effective cross sections and source. [ABSTRACT FROM AUTHOR]

The time-independent linear transport problem in a purely absorbing (no scattering) random medium is considered. A formally exact equation for the ensemble averaged distribution function 〈ψ〉 is derived. Under the assumption of a two-fluid statistical mixture, with the transition from one fluid to the other assumed to be determined by a Markov process, an exact solution to this equation for 〈ψ〉 is obtained. In the source-free case, this solution is shown to agree with the result obtained by ensemble averaging simple exponential attenuation. Several approximations to the exact equation for 〈ψ〉 are considered, and numerical results given to assess the accuracy of these approximations. [ABSTRACT FROM AUTHOR]