31 research outputs found
Lorentz's model with dissipative collisions
Propagation of a particle accelerated by an external field through a
scattering medium is studied within the generalized Lorentz model allowing
inelastic collisions. Energy losses at collisions are proportional to
, where is the restitution coefficient. For
(elastic collisions) there is no stationary state. It is proved in
one dimension that when the stationary state exists . The
corresponding velocity distribution changes from a highly asymmetric
half-gaussian () to an asymptotically symmetric distribution , for . The identical scaling
behavior in the limit of weak inelasticity is derived in three dimensions by a
self-consistent perturbation analysis, in accordance with the behavior of
rigorously evaluated moments. The dependence on the external field scales out
in any dimension, predicting in particular the stationary current to be
proportional to the square root of the external acceleration.Comment: 13 pages, no figures, submitted to Physica
Approach to a non-equilibrium steady state
We consider a non-interacting one-dimensional gas accelerated by a constant
and uniform external field. The energy absorbed from the field is transferred
via elastic collisions to a bath of scattering obstacles. At gas-obstacle
encounters the particles of the gas acquire a fixed kinetic energy. The
approach to the resulting stationary state is studied within the Boltzmann
kinetic theory. It is shown that the long time behavior is governed by the
hydrodynamic mode of diffusion superposed on a convective flow. The diffusion
coefficient is analytically calculated for any value of the field showing a
minimum at intermediate field intensities. It is checked that the properly
generalized Green-Kubo formula applies in the non-equilibrium stationary state.Comment: 2 figures, accepted in Physica
The Bose gas beyond mean field
We study a homogeneous Bose gas with purely repulsive forces. Using the Kac
scaling of the binary potential we derive analytically the form of the
thermodynamic functions of the gas for small but finite values of the scaling
parameter in the low density regime. In this way we determine dominant
corrections to the mean-field theory. It turns out that repulsive forces
increase the pressure at fixed density and decrease the density at given
chemical potential (the temperature is kept constant). They also flatten the
Bose momentum distribution. However, the present analysis cannot be extended to
the region where the mean-field theory predicts the appearence of condensate.Comment: 19 pages, 3 figure
Ballistic annihilation kinetics for a multi-velocity one-dimensional ideal gas
Ballistic annihilation kinetics for a multi-velocity one-dimensional ideal
gas is studied in the framework of an exact analytic approach. For an initial
symmetric three-velocity distribution, the problem can be solved exactly and it
is shown that different regimes exist depending on the initial fraction of
particles at rest. Extension to the case of a n-velocity distribution is
discussed.Comment: 19 pages, latex, uses Revtex macro
Front formation in a ballistic annihilation model
We study a simple one-dimensional model of ballisticaly-controlled
annihilation in which the two annihilating species are initially spatially
separated. The time dependent properties of the annihilation front are exactly
derived. It is shown that the front wanders in a brownian fashion around its
average value.Comment: Typeset using Latex, with Elsevier macros (elsart); 17 pages with one
Latex figure and two Encapsulated Postscript figures (need epsf
Search for universality in one-dimensional ballistic annihilation kinetics
We study the kinetics of ballistic annihilation for a one-dimensional ideal
gas with continuous velocity distribution. A dynamical scaling theory for the
long time behavior of the system is derived. Its validity is supported by
extensive numerical simulations for several velocity distributions. This leads
us to the conjecture that all the continuous velocity distributions \phi(v)
which are symmetric, regular and such that \phi(0) does not vanish, are
attracted in the long time regime towards the same Gaussian distribution and
thus belong to the same universality class. Moreover, it is found that the
particle density decays as n(t)~t^{-\alpha}, with \alpha=0.785 +/- 0.005.Comment: 8 pages, needs multicol, epsf and revtex. 8 postscript figures
included. Submitted to Phys. Rev. E. Also avaiable at
http://mykonos.unige.ch/~rey/publi.html#Secon
On the first Sonine correction for granular gases
We consider the velocity distribution for a granular gas of inelastic hard
spheres described by the Boltzmann equation. We investigate both the free of
forcing case and a system heated by a stochastic force. We propose a new method
to compute the first correction to Gaussian behavior in a Sonine polynomial
expansion quantified by the fourth cumulant . Our expressions are compared
to previous results and to those obtained through the numerical solution of the
Boltzmann equation. It is numerically shown that our method yields very
accurate results for small velocities of the rescaled distribution. We finally
discuss the ambiguities inherent to a linear approximation method in .Comment: 9 pages, 8 eps figures include
Casimir force induced by imperfect Bose gas
We present a study of the Casimir effect in an imperfect (mean-field) Bose
gas contained between two infinite parallel plane walls. The derivation of the
Casimir force follows from the calculation of the excess grand canonical free
energy density under periodic, Dirichlet, and Neumann boundary conditions with
the use of the steepest descent method. In the one-phase region the force
decays exponentially fast when distance between the walls tends to
infinity. When Bose-Einstein condensation point is approached the decay length
in the exponential law diverges with critical exponent , which
differs from the perfect gas case where . In the two-phase region
the Casimir force is long-range, and decays following the power law ,
with the same amplitude as in the perfect gas
Kinetics of ballistic annihilation and branching
We consider a one-dimensional model consisting of an assembly of two-velocity
particles moving freely between collisions. When two particles meet, they
instantaneously annihilate each other and disappear from the system. Moreover
each moving particle can spontaneously generate an offspring having the same
velocity as its mother with probability 1-q. This model is solved analytically
in mean-field approximation and studied by numerical simulations. It is found
that for q=1/2 the system exhibits a dynamical phase transition. For q<1/2, the
slow dynamics of the system is governed by the coarsening of clusters of
particles having the same velocities, while for q>1/2 the system relaxes
rapidly towards its stationary state characterized by a distribution of small
cluster sizes.Comment: 10 pages, 11 figures, uses multicol, epic, eepic and eepicemu. Also
avaiable at http://mykonos.unige.ch/~rey/pubt.htm