40 research outputs found
Nonextensive statistics in viscous fingering
Measurements in turbulent flows have revealed that the velocity field in
nonequilibrium systems exhibits -exponential or power law distributions in
agreement with theoretical arguments based on nonextensive statistical
mechanics. Here we consider Hele-Shaw flow as simulated by the Lattice
Boltzmann method and find similar behavior from the analysis of velocity field
measurements. For the transverse velocity, we obtain a spatial -Gaussian
profile and a power law velocity distribution over all measured decades. To
explain these results, we suggest theoretical arguments based on Darcy's law
combined with the non-linear advection-diffusion equation for the concentration
field. Power law and -exponential distributions are the signature of
nonequilibrium systems with long-range interactions and/or long-time
correlations, and therefore provide insight to the mechanism of the onset of
fingering processes.Comment: 8 pages including 3 figures; to appear in PHYSICA
Propagation-Dispersion Equation
A {\em propagation-dispersion equation} is derived for the first passage
distribution function of a particle moving on a substrate with time delays. The
equation is obtained as the continuous limit of the {\em first visit equation},
an exact microscopic finite difference equation describing the motion of a
particle on a lattice whose sites operate as {\em time-delayers}. The
propagation-dispersion equation should be contrasted with the
advection-diffusion equation (or the classical Fokker-Planck equation) as it
describes a dispersion process in {\em time} (instead of diffusion in space)
with a drift expressed by a propagation speed with non-zero bounded values. The
{\em temporal dispersion} coefficient is shown to exhibit a form analogous to
Taylor's dispersivity. Physical systems where the propagation-dispersion
equation applies are discussed.Comment: 12 pages+ 5 figures, revised and extended versio
Viscous fingering in miscible, immiscible and reactive fluids
With the Lattice Boltzmann method (using the BGK approximation) we
investigate the dynamics of Hele-Shaw flow under conditions corresponding to
various experimental systems. We discuss the onset of the instability
(dispersion relation), the static properties (characterization of the
interface) and the dynamic properties (growth of the mixing zone) of simulated
Hele-Shaw systems. We examine the role of reactive processes (between the two
fluids) and we show that they have a sharpening effect on the interface similar
to the effect of surface tension.Comment: 6 pages with 2 figure, to be published in J.Mod.Phys
Propagation and organization in lattice random media
We show that a signal can propagate in a particular direction through a model
random medium regardless of the precise state of the medium. As a prototype, we
consider a point particle moving on a one-dimensional lattice whose sites are
occupied by scatterers with the following properties: (i) the state of each
site is defined by its spin (up or down); (ii) the particle arriving at a site
is scattered forward (backward) if the spin is up (down); (iii) the state of
the site is modified by the passage of the particle, i.e. the spin of the site
where a scattering has taken place, flips (). We consider one dimensional and triangular lattices, for which we give a
microscopic description of the dynamics, prove the propagation of a particle
through the scatterers, and compute analytically its statistical properties. In
particular we prove that, in one dimension, the average propagation velocity is
, with the probability that a site has a spin
, and, in the triangular lattice, the average propagation velocity is
independent of the scatterers distribution: . In both cases, the
origin of the propagation is a blocking mechanism, restricting the motion of
the particle in the direction opposite to the ultimate propagation direction,
and there is a specific re-organization of the spins after the passage of the
particle. A detailed mathematical analysis of this phenomenon is, to the best
of our knowledge, presented here for the first time.Comment: 30 pages, 15 separate figures (in PostScript); submitted to J. Stat.
Phy
Dependence of the liquid-vapor surface tension on the range of interaction: a test of the law of corresponding states
The planar surface tension of coexisting liquid and vapor phases of a fluid
of Lennard-Jones atoms is studied as a function of the range of the potential
using both Monte Carlo simulations and Density Functional Theory. The
interaction range is varied from to and the surface
tension is determined for temperatures ranging from up to the
critical temperature in each case. The results are shown to be consistent with
previous studies. The simulation data are well-described by Guggenheim's law of
corresponding states but the agreement of the theoretical results depends on
the quality of the bulk equation of state.Comment: 13 pages, 5 figure
Phase behavior of a confined nano-droplet in the grand-canonical ensemble: the reverse liquid-vapor transition
The equilibrium density distribution and thermodynamic properties of a
Lennard-Jones fluid confined to nano-sized spherical cavities at constant
chemical potential was determined using Monte Carlo simulations. The results
describe both a single cavity with semipermeable walls as well as a collection
of closed cavities formed at constant chemical potential. The results are
compared to calculations using classical Density Functional Theory (DFT). It is
found that the DFT calculations give a quantitatively accurate description of
the pressure and structure of the fluid. Both theory and simulation show the
presence of a ``reverse'' liquid-vapor transition whereby the equilibrium state
is a liquid at large volumes but becomes a vapor at small volumes.Comment: 13 pages, 8 figures, to appear in J. Phys. : Cond. Mat
Long-range correlations in non-equilibrium systems: Lattice gas automaton approach
In systems removed from equilibrium, intrinsic microscopic fluctuations
become correlated over distances comparable to the characteristic macroscopic
length over which the external constraint is exerted. In order to investigate
this phenomenon, we construct a microscopic model with simple stochastic
dynamics using lattice gas automaton rules that satisfy local detailed balance.
Because of the simplicity of the automaton dynamics, analytical theory can be
developed to describe the space and time evolution of the density fluctuations.
The exact equations for the pair correlations are solved explicitly in the
hydrodynamic limit. In this limit, we rigorously derive the results obtained
phenomenologically by fluctuating hydrodynamics. In particular, the spatial
algebraic decay of the equal-time fluctuation correlations predicted by this
theory is found to be in excellent agreement with the results of our lattice
gas automaton simulations for two different types of boundary conditions.
Long-range correlations of the type described here appear generically in
dynamical systems that exhibit large scale anisotropy and lack detailed
balance.Comment: 23 pages, RevTeX; to appear in Phys. Rev.
Effects of protein size on the highconcentration/low-concentration phase transition
SCOPUS: ar.kinfo:eu-repo/semantics/publishe
Hydrodynamique statistique des gaz sur réseau
Doctorat en Sciencesinfo:eu-repo/semantics/nonPublishe