342 research outputs found
Anomalous Drude Model
A generalization of the Drude model is studied. On the one hand, the free
motion of the particles is allowed to be sub- or superdiffusive; on the other
hand, the distribution of the time delay between collisions is allowed to have
a long tail and even a non-vanishing first moment. The collision averaged
motion is either regular diffusive or L\'evy-flight like. The anomalous
diffusion coefficients show complex scaling laws. The conductivity can be
calculated in the diffusive regime. The model is of interest for the
phenomenological study of electronic transport in quasicrystals.Comment: 4 pages, latex, 2 figures, to be published in Physical Review Letter
Scaling laws and vortex profiles in 2D decaying turbulence
We use high resolution numerical simulations over several hundred of turnover
times to study the influence of small scale dissipation onto vortex statistics
in 2D decaying turbulence. A self-similar scaling regime is detected when the
scaling laws are expressed in units of mean vorticity and integral scale, as
predicted by Carnevale et al., and it is observed that viscous effects spoil
this scaling regime. This scaling regime shows some trends toward that of the
Kirchhoff model, for which a recent theory predicts a decay exponent .
In terms of scaled variables, the vortices have a similar profile close to a
Fermi-Dirac distribution.Comment: 4 Latex pages and 4 figures. Submitted to Phys. Rev. Let
Weak Disorder in Fibonacci Sequences
We study how weak disorder affects the growth of the Fibonacci series. We
introduce a family of stochastic sequences that grow by the normal Fibonacci
recursion with probability 1-epsilon, but follow a different recursion rule
with a small probability epsilon. We focus on the weak disorder limit and
obtain the Lyapunov exponent, that characterizes the typical growth of the
sequence elements, using perturbation theory. The limiting distribution for the
ratio of consecutive sequence elements is obtained as well. A number of
variations to the basic Fibonacci recursion including shift, doubling, and
copying are considered.Comment: 4 pages, 2 figure
Self-gravitating Brownian particles in two dimensions: the case of N=2 particles
We study the motion of N=2 overdamped Brownian particles in gravitational
interaction in a space of dimension d=2. This is equivalent to the simplified
motion of two biological entities interacting via chemotaxis when time delay
and degradation of the chemical are ignored. This problem also bears some
similarities with the stochastic motion of two point vortices in viscous
hydrodynamics [Agullo & Verga, Phys. Rev. E, 63, 056304 (2001)]. We
analytically obtain the density probability of finding the particles at a
distance r from each other at time t. We also determine the probability that
the particles have coalesced and formed a Dirac peak at time t (i.e. the
probability that the reduced particle has reached r=0 at time t). Finally, we
investigate the variance of the distribution and discuss the proper form
of the virial theorem for this system. The reduced particle has a normal
diffusion behaviour for small times with a gravity-modified diffusion
coefficient =r_0^2+(4k_B/\xi\mu)(T-T_*)t, where k_BT_{*}=Gm_1m_2/2 is a
critical temperature, and an anomalous diffusion for large times
~t^(1-T_*/T). As a by-product, our solution also describes the growth of
the Dirac peak (condensate) that forms in the post-collapse regime of the
Smoluchowski-Poisson system (or Keller-Segel model) for T<T_c=GMm/(4k_B). We
find that the saturation of the mass of the condensate to the total mass is
algebraic in an infinite domain and exponential in a bounded domain.Comment: Revised version (20/5/2010) accepted for publication in EPJ
Theory of the temperature and doping dependence of the Hall effect in a model with x-ray edge singularities in d=oo
We explain the anomalous features in the Hall data observed experimentally in
the normal state of the high-Tc superconductors. We show that a consistent
treatment of the local spin fluctuations in a model with x-ray edge
singularities in d=oo reproduces the temperature and the doping dependence of
the Hall constant as well as the Hall angle in the normal state. The model has
also been invoked to justify the marginal-Fermi-liquid behavior, and provides a
consistent explanation of the Hall anomalies for a non-Fermi liquid in d=oo.Comment: 5 pages, 4 figures, To appear in Phys. Rev. B, title correcte
Analytical results for random walk persistence
In this paper, we present the detailed calculation of the persistence
exponent for a nearly-Markovian Gaussian process , a problem
initially introduced in [Phys. Rev. Lett. 77, 1420 (1996)], describing the
probability that the walker never crosses the origin. New resummed perturbative
and non-perturbative expressions for are obtained, which suggest a
connection with the result of the alternative independent interval
approximation (IIA). The perturbation theory is extended to the calculation of
for non-Gaussian processes, by making a strong connection between the
problem of persistence and the calculation of the energy eigenfunctions of a
quantum mechanical problem. Finally, we give perturbative and non-perturbative
expressions for the persistence exponent , describing the
probability that the process remains bigger than .Comment: 23 pages; accepted for publication to Phys. Rev. E (Dec. 98
Anisotropic Coarsening: Grain Shapes and Nonuniversal Persistence
We solve a coarsening system with small but arbitrary anisotropic surface
tension and interface mobility. The resulting size-dependent growth shapes are
significantly different from equilibrium microcrystallites, and have a
distribution of grain sizes different from isotropic theories. As an
application of our results, we show that the persistence decay exponent depends
on anisotropy and hence is nonuniversal.Comment: 4 pages (revtex), 2 eps figure
Finite mass self-similar blowing-up solutions of a chemotaxis system with non-linear diffusion
For a specific choice of the diffusion, the parabolic-elliptic
Patlak-Keller-Segel system with non-linear diffusion (also referred to as the
quasi-linear Smoluchowski-Poisson equation) exhibits an interesting threshold
phenomenon: there is a critical mass such that all the solutions with
initial data of mass smaller or equal to exist globally while the
solution blows up in finite time for a large class of initial data with mass
greater than . Unlike in space dimension 2, finite mass self-similar
blowing-up solutions are shown to exist in space dimension
Nontrivial Exponent for Simple Diffusion
The diffusion equation \partial_t\phi = \nabla^2\phi is considered, with
initial condition \phi( _x_ ,0) a gaussian random variable with zero mean.
Using a simple approximate theory we show that the probability p_n(t_1,t_2)
that \phi( _x_ ,t) [for a given space point _x_ ] changes sign n times between
t_1 and t_2 has the asymptotic form p_n(t_1,t_2) \sim
[\ln(t_2/t_1)]^n(t_1/t_2)^{-\theta}. The exponent \theta has predicted values
0.1203, 0.1862, 0.2358 in dimensions d=1,2,3, in remarkably good agreement with
simulation results.Comment: Minor typos corrected, affecting table of exponents. 4 pages, REVTEX,
1 eps figure. Uses epsf.sty and multicol.st
A precise approximation for directed percolation in d=1+1
We introduce an approximation specific to a continuous model for directed
percolation, which is strictly equivalent to 1+1 dimensional directed bond
percolation. We find that the critical exponent associated to the order
parameter (percolation probability) is beta=(1-1/\sqrt{5})/2=0.276393202..., in
remarkable agreement with the best current numerical estimate beta=0.276486(8).Comment: 4 pages, 3 EPS figures; Submitted to Physical Review Letters v2:
minor typos + 1 major typo in Eq. (30) correcte
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