1,160 research outputs found
Efficient kinetic method for fluid simulation beyond the Navier-Stokes equation
We present a further theoretical extension to the kinetic theory based
formulation of the lattice Boltzmann method of Shan et al (2006). In addition
to the higher order projection of the equilibrium distribution function and a
sufficiently accurate Gauss-Hermite quadrature in the original formulation, a
new regularization procedure is introduced in this paper. This procedure
ensures a consistent order of accuracy control over the non-equilibrium
contributions in the Galerkin sense. Using this formulation, we construct a
specific lattice Boltzmann model that accurately incorporates up to the third
order hydrodynamic moments. Numerical evidences demonstrate that the extended
model overcomes some major defects existed in the conventionally known lattice
Boltzmann models, so that fluid flows at finite Knudsen number (Kn) can be more
quantitatively simulated. Results from force-driven Poiseuille flow simulations
predict the Knudsen's minimum and the asymptotic behavior of flow flux at large
Kn
Microscopic Derivation of Causal Diffusion Equation using Projection Operator Method
We derive a coarse-grained equation of motion of a number density by applying
the projection operator method to a non-relativistic model. The derived
equation is an integrodifferential equation and contains the memory effect. The
equation is consistent with causality and the sum rule associated with the
number conservation in the low momentum limit, in contrast to usual acausal
diffusion equations given by using the Fick's law. After employing the Markov
approximation, we find that the equation has the similar form to the causal
diffusion equation. Our result suggests that current-current correlations are
not necessarily adequate as the definition of diffusion constants.Comment: 10 pages, 1 figure, Final version published in Phys. Rev.
Blow-up of the hyperbolic Burgers equation
The memory effects on microscopic kinetic systems have been sometimes
modelled by means of the introduction of second order time derivatives in the
macroscopic hydrodynamic equations. One prototypical example is the hyperbolic
modification of the Burgers equation, that has been introduced to clarify the
interplay of hyperbolicity and nonlinear hydrodynamic evolution. Previous
studies suggested the finite time blow-up of this equation, and here we present
a rigorous proof of this fact
Explicit coercivity estimates for the linearized Boltzmann and Landau operators
We prove explicit coercivity estimates for the linearized Boltzmann and
Landau operators, for a general class of interactions including any
inverse-power law interactions, and hard spheres. The functional spaces of
these coercivity estimates depend on the collision kernel of these operators.
They cover the spectral gap estimates for the linearized Boltzmann operator
with Maxwell molecules, improve these estimates for hard potentials, and are
the first explicit coercivity estimates for soft potentials (including in
particular the case of Coulombian interactions). We also prove a regularity
property for the linearized Boltzmann operator with non locally integrable
collision kernels, and we deduce from it a new proof of the compactness of its
resolvent for hard potentials without angular cutoff.Comment: 32 page
A Continuum Description of Rarefied Gas Dynamics (I)--- Derivation From Kinetic Theory
We describe an asymptotic procedure for deriving continuum equations from the
kinetic theory of a simple gas. As in the works of Hilbert, of Chapman and of
Enskog, we expand in the mean flight time of the constituent particles of the
gas, but we do not adopt the Chapman-Enskog device of simplifying the formulae
at each order by using results from previous orders. In this way, we are able
to derive a new set of fluid dynamical equations from kinetic theory, as we
illustrate here for the relaxation model for monatomic gases. We obtain a
stress tensor that contains a dynamical pressure term (or bulk viscosity) that
is process-dependent and our heat current depends on the gradients of both
temperature and density. On account of these features, the equations apply to a
greater range of Knudsen number (the ratio of mean free path to macroscopic
scale) than do the Navier-Stokes equations, as we see in the accompanying
paper. In the limit of vanishing Knudsen number, our equations reduce to the
usual Navier-Stokes equations with no bulk viscosity.Comment: 16 page
Real time plasma equilibrium reconstruction in a Tokamak
The problem of equilibrium of a plasma in a Tokamak is a free boundary
problemdescribed by the Grad-Shafranov equation in axisymmetric configurations.
The right hand side of this equation is a non linear source, which represents
the toroidal component of the plasma current density. This paper deals with the
real time identification of this non linear source from experimental
measurements. The proposed method is based on a fixed point algorithm, a finite
element resolution, a reduced basis method and a least-square optimization
formulation
Composition profiles of InAs–GaAs quantum dots determined by medium-energy ion scattering
The composition profile along the [001] growth direction of low-growth-rate InAs–GaAs quantum dots (QDs) has been determined using medium-energy ion scattering (MEIS). A linear profile of In concentration from 100% In at the top of the QDs to 20% at their base provides the best fit to MEIS energy spectra
Entropic force, noncommutative gravity and ungravity
After recalling the basic concepts of gravity as an emergent phenomenon, we
analyze the recent derivation of Newton's law in terms of entropic force
proposed by Verlinde. By reviewing some points of the procedure, we extend it
to the case of a generic quantum gravity entropic correction to get compelling
deviations to the Newton's law. More specifically, we study: (1) noncommutative
geometry deviations and (2) ungraviton corrections. As a special result in the
noncommutative case, we find that the noncommutative character of the manifold
would be equivalent to the temperature of a thermodynamic system. Therefore, in
analogy to the zero temperature configuration, the description of spacetime in
terms of a differential manifold could be obtained only asymptotically.
Finally, we extend the Verlinde's derivation to a general case, which includes
all possible effects, noncommutativity, ungravity, asymptotically safe gravity,
electrostatic energy, and extra dimensions, showing that the procedure is solid
versus such modifications.Comment: 8 pages, final version published on Physical Review
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