982 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
Entropic descriptor of a complex behaviour
We propose a new type of entropic descriptor that is able to quantify the
statistical complexity (a measure of complex behaviour) by taking
simultaneously into account the average departures of a system's entropy S from
both its maximum possible value Smax and its minimum possible value Smin. When
these two departures are similar to each other, the statistical complexity is
maximal. We apply the new concept to the variability, over a range of length
scales, of spatial or grey-level pattern arrangements in simple models. The
pertinent results confirm the fact that a highly non-trivial, length-scale
dependence of the entropic descriptor makes it an adequate complexity-measure,
able to distinguish between structurally distinct configurational macrostates
with the same degree of disorder.Comment: 14 pages, 7 figures, extended versio
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
Field induced stationary state for an accelerated tracer in a bath
Our interest goes to the behavior of a tracer particle, accelerated by a
constant and uniform external field, when the energy injected by the field is
redistributed through collision to a bath of unaccelerated particles. A non
equilibrium steady state is thereby reached. Solutions of a generalized
Boltzmann-Lorentz equation are analyzed analytically, in a versatile framework
that embeds the majority of tracer-bath interactions discussed in the
literature. These results --mostly derived for a one dimensional system-- are
successfully confronted to those of three independent numerical simulation
methods: a direct iterative solution, Gillespie algorithm, and the Direct
Simulation Monte Carlo technique. We work out the diffusion properties as well
as the velocity tails: large v, and either large -v, or v in the vicinity of
its lower cutoff whenever the velocity distribution is bounded from below.
Particular emphasis is put on the cold bath limit, with scatterers at rest,
which plays a special role in our model.Comment: 20 pages, 6 figures v3:minor corrections in sec.III and added
reference
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
Anthologies of contemporary Polish poetry in English translation : paratexts, narratives, and the manipulation of national literatures
No abstract provided
Effective conductivity in association with model structure and spatial inhomogeneity of polymer/carbon black composites
The relationship between effective conductivity and cell structure of
polyethylene/carbon composites as well as between effective conductivity and
spatial distribution of carbon black are discussed. Following Yoshida's model
both structures can, in a way, be said to be intermediate between the well
known Maxwell-Garnett (MG) and Bruggeman (BR) limiting structures. Using TEM
photographs on composites with various carbon blacks we have observed that the
larger is Garncarek's inhomogeneity measure H of two-dimensional (2D)
representative distribution of the carbon black, the smaller is the effective
conductivity of the composite.Comment: 7 pages, 9 figure
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