303 research outputs found
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 . These reduce to the extensive Boltzmann-Gibbs form for
, but a remarkable number of statistical and thermodynamic properties have
been shown to be -invariant -- that is, valid for any . In this paper, we
address the question of whether or not the value of 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 -invariant, but that for conservation
of energy is not. Moreover, we find that ratios of transport coefficients may
also be -dependent. These dependences may therefore be exploited to measure
experimentally.Comment: RevTeX and epsf macros required, 19 pages, 8 figure
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
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
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
From Dirac to Diffusion: Decoherence in Quantum Lattice Gases
We describe a model for the interaction of the internal (spin) degree of
freedom of a quantum lattice-gas particle with an environmental bath. We impose
the constraints that the particle-bath interaction be fixed, while the state of
the bath is random, and that the effect of the particle-bath interaction be
parity invariant. The condition of parity invariance defines a subgroup of the
unitary group of actions on the spin degree of freedom and the bath. We derive
a general constraint on the Lie algebra of the unitary group which defines this
subgroup, and hence guarantees parity invariance of the particle-bath
interaction. We show that generalizing the quantum lattice gas in this way
produces a model having both classical and quantum discrete random walks as
different limits. We present preliminary simulation results illustrating the
intermediate behavior in the presence of weak quantum noise.Comment: To appear in QI
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