201 research outputs found
Characterization of the stretched exponential trap-time distributions in one-dimensional coupled map lattices
Stretched exponential distributions and relaxation responses are encountered
in a wide range of physical systems such as glasses, polymers and spin glasses.
As found recently, this type of behavior occurs also for the distribution
function of certain trap time in a number of coupled dynamical systems. We
analyze a one-dimensional mathematical model of coupled chaotic oscillators
which reproduces an experimental set-up of coupled diode-resonators and
identify the necessary ingredients for stretched exponential distributions.Comment: 8 pages, 8 figure
Dynamics at the angle of repose: jamming, bistability, and collapse
When a sandpile relaxes under vibration, it is known that its measured angle
of repose is bistable in a range of values bounded by a material-dependent
maximal angle of stability; thus, at the same angle of repose, a sandpile can
be stationary or avalanching, depending on its history. In the nearly jammed
slow dynamical regime, sandpile collapse to a zero angle of repose can also
occur, as a rare event. We claim here that fluctuations of {\it dilatancy} (or
local density) are the key ingredient that can explain such varied phenomena.
In this work, we model the dynamics of the angle of repose and of the density
fluctuations, in the presence of external noise, by means of coupled stochastic
equations. Among other things, we are able to describe sandpile collapse in
terms of an activated process, where an effective temperature (related to the
density as well as to the external vibration intensity) competes against the
configurational barriers created by the density fluctuations.Comment: 15 pages, 1 figure. Minor changes and update
Asymptotics for the Wiener sausage among Poissonian obstacles
We consider the Wiener sausage among Poissonian obstacles. The obstacle is
called hard if Brownian motion entering the obstacle is immediately killed, and
is called soft if it is killed at certain rate. It is known that Brownian
motion conditioned to survive among obstacles is confined in a ball near its
starting point. We show the weak law of large numbers, large deviation
principle in special cases and the moment asymptotics for the volume of the
corresponding Wiener sausage. One of the consequence of our results is that the
trajectory of Brownian motion almost fills the confinement ball.Comment: 19 pages, Major revision made for publication in J. Stat. Phy
Diffusion with critically correlated traps and the slow relaxation of the longest wavelength mode
We study diffusion on a substrate with permanent traps distributed with
critical positional correlation, modeled by their placement on the perimeters
of a critical percolation cluster. We perform a numerical analysis of the
vibrational density of states and the largest eigenvalue of the equivalent
scalar elasticity problem using the method of Arnoldi and Saad. We show that
the critical trap correlation increases the exponent appearing in the stretched
exponential behavior of the low frequency density of states by approximately a
factor of two as compared to the case of no correlations. A finite size scaling
hypothesis of the largest eigenvalue is proposed and its relation to the
density of states is given. The numerical analysis of this scaling postulate
leads to the estimation of the stretch exponent in good agreement with the
density of states result.Comment: 15 pages, LaTeX (RevTeX
Approach to Asymptotic Behaviour in the Dynamics of the Trapping Reaction
We consider the trapping reaction A + B -> B in space dimension d=1, where
the A and B particles have diffusion constants D_A, D_B respectively. We
calculate the probability, Q(t), that a given A particle has not yet reacted at
time t. Exploiting a recent formulation in which the B particles are eliminated
from the problem we find, for t -> \infty, , where
is the density of B particles and for .Comment: 8 pages, 2 figures; minor change
Trapping of a random walk by diffusing traps
We present a systematic analytical approach to the trapping of a random walk
by a finite density rho of diffusing traps in arbitrary dimension d. We confirm
the phenomenologically predicted e^{-c_d rho t^{d/2}} time decay of the
survival probability, and compute the dimension dependent constant c_d to
leading order within an eps=2-d expansion.Comment: 16 pages, to appear in J. Phys.
Onsager reciprocity relations without microscopic reversibility
In this paper we show that Onsager--Machlup time reversal properties of
thermodynamic fluctuations and Onsager reciprocity relations for transport
coefficients can hold also if the microscopic dynamics is not reversible. This
result is based on the explicit construction of a class of conservative models
which can be analysed rigorously.Comment: revtex, no figure
Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise
The Freidlin-Wentzell large deviation principle is established for the
distributions of stochastic evolution equations with general monotone drift and
small multiplicative noise. As examples, the main results are applied to derive
the large deviation principle for different types of SPDE such as stochastic
reaction-diffusion equations, stochastic porous media equations and fast
diffusion equations, and the stochastic p-Laplace equation in Hilbert space.
The weak convergence approach is employed in the proof to establish the Laplace
principle, which is equivalent to the large deviation principle in our
framework.Comment: 31 pages, published in Appl. Math. Opti
Self-intersection local times of random walks: Exponential moments in subcritical dimensions
Fix , not necessarily integer, with . We study the -fold
self-intersection local time of a simple random walk on the lattice up
to time . This is the -norm of the vector of the walker's local times,
. We derive precise logarithmic asymptotics of the expectation of
for scales that are bounded from
above, possibly tending to zero. The speed is identified in terms of mixed
powers of and , and the precise rate is characterized in terms of
a variational formula, which is in close connection to the {\it
Gagliardo-Nirenberg inequality}. As a corollary, we obtain a large-deviation
principle for for deviation functions satisfying
t r_t\gg\E[\|\ell_t\|_p]. Informally, it turns out that the random walk
homogeneously squeezes in a -dependent box with diameter of order to produce the required amount of self-intersections. Our main tool is
an upper bound for the joint density of the local times of the walk.Comment: 15 pages. To appear in Probability Theory and Related Fields. The
final publication is available at springerlink.co
Diffusion with random distribution of static traps
The random walk problem is studied in two and three dimensions in the
presence of a random distribution of static traps. An efficient Monte Carlo
method, based on a mapping onto a polymer model, is used to measure the
survival probability P(c,t) as a function of the trap concentration c and the
time t. Theoretical arguments are presented, based on earlier work of Donsker
and Varadhan and of Rosenstock, why in two dimensions one expects a data
collapse if -ln[P(c,t)]/ln(t) is plotted as a function of (lambda
t)^{1/2}/ln(t) (with lambda=-ln(1-c)), whereas in three dimensions one expects
a data collapse if -t^{-1/3}ln[P(c,t)] is plotted as a function of
t^{2/3}lambda. These arguments are supported by the Monte Carlo results. Both
data collapses show a clear crossover from the early-time Rosenstock behavior
to Donsker-Varadhan behavior at long times.Comment: 4 pages, 6 figure
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