On the dependence of the Navier Stokes equations on the distribution of moleular velocities

In this work we introduce a completely general Chapman Enskog procedure in which we divide the local distribution into an isotropic distribution with anisotropic corrections. We obtain a recursion relation on all integrals of the distribution function required in the derivation of the moment equations. We obtain the hydrodynamic equations in terms only of the first few moments of the isotropic part of an arbitrary local distribution function. The incompressible limit of the equations is completely independent of the form of the isotropic part of the distribution, whereas the energy equation in the compressible case contains an additional contribution to the heat flux. This additional term was also found by Boghosian and by Potiguar and Costa in the derivation of the Navier Stokes equations for Tsallis thermostatistics, and is the only additional term allowed by the Curie principle

Navier-Stokes Equations for Generalized Thermostatistics

Tsallis has proposed a generalization of Boltzmann-Gibbs thermostatistics by introducing a family of generalized nonextensive entropy functionals with a single parameter $q$. These reduce to the extensive Boltzmann-Gibbs form for $q=1$, but a remarkable number of statistical and thermodynamic properties have been shown to be $q$-invariant -- that is, valid for any $q$. In this paper, we address the question of whether or not the value of $q$ for a given viscous, incompressible fluid can be ascertained solely by measurement of the fluid's hydrodynamic properties. We find that the hydrodynamic equations expressing conservation of mass and momentum are $q$-invariant, but that for conservation of energy is not. Moreover, we find that ratios of transport coefficients may also be $q$-dependent. These dependences may therefore be exploited to measure $q$ experimentally.Comment: RevTeX and epsf macros required, 19 pages, 8 figure

Type-II Quantum Algorithms

We review and analyze the hybrid quantum-classical NMR computing methodology referred to as Type-II quantum computing. We show that all such algorithms considered so far within this paradigm are equivalent to some classical lattice-Boltzmann scheme. We derive a sufficient and necessary constraint on the unitary operator representing the quantum mechanical part of the computation which ensures that the model reproduces the Boltzmann approximation of a lattice-gas model satisfying semi-detailed balance. Models which do not satisfy this constraint represent new lattice-Boltzmann schemes which cannot be formulated as the average over some underlying lattice gas. We close the paper with some discussion of the strengths, weaknesses and possible future direction of Type-II quantum computing.Comment: To appear in Physica

A Particulate Basis for an Immiscible Lattice-Gas Model

We show that a phenomenological hydrodynamic lattice-gas model of two-phase flow, developed by Rothman and Keller in 1988 and used extensively for numerical simulations since then, can be derived from an underlying model of particle interactions. From this result, we elucidate the nature of the hydrodynamic limit of the Rothman-Keller model.Comment: 11 pages. Accepted for publication in Computer Physics Communication