1,256 research outputs found
Stretched Exponential Relaxation in the Biased Random Voter Model
We study the relaxation properties of the voter model with i.i.d. random
bias. We prove under mild condions that the disorder-averaged relaxation of
this biased random voter model is faster than a stretched exponential with
exponent , where depends on the transition rates
of the non-biased voter model. Under an additional assumption, we show that the
above upper bound is optimal. The main ingredient of our proof is a result of
Donsker and Varadhan (1979).Comment: 14 pages, AMS-LaTe
Entropic and gradient flow formulations for nonlinear diffusion
Nonlinear diffusion is considered for
a class of nonlinearities . It is shown that for suitable choices of
, an associated Lyapunov functional can be interpreted as thermodynamics
entropy. This information is used to derive an associated metric, here called
thermodynamic metric. The analysis is confined to nonlinear diffusion
obtainable as hydrodynamic limit of a zero range process. The thermodynamic
setting is linked to a large deviation principle for the underlying zero range
process and the corresponding equation of fluctuating hydrodynamics. For the
latter connections, the thermodynamic metric plays a central role
Privatisering onder de loep
Sinds de jaren twintig van de vorige eeuw is overheidsinterventie met openbaar vervoer manifest. Politieke stromingen, tijden van crisis maar ook van economische voorspoed, innovatie en de invloeden vanuit Europa dragen bij aan de wisselende koers die de Nederlandse politiek de afgelopen 50 jaar heeft gevaren. Ontwikkelingen als marktwerking (publiek vs. privaat}, (de}centralisering (rijk vs. regio} en liberalisering vs. regulering, zijn onlosmakelijk verbonden met de organisatie van openbaar vervoer in Nederland
Minimum entropy production principle from a dynamical fluctuation law
The minimum entropy production principle provides an approximative
variational characterization of close-to-equilibrium stationary states, both
for macroscopic systems and for stochastic models. Analyzing the fluctuations
of the empirical distribution of occupation times for a class of Markov
processes, we identify the entropy production as the large deviation rate
function, up to leading order when expanding around a detailed balance
dynamics. In that way, the minimum entropy production principle is recognized
as a consequence of the structure of dynamical fluctuations, and its
approximate character gets an explanation. We also discuss the subtlety
emerging when applying the principle to systems whose degrees of freedom change
sign under kinematical time-reversal.Comment: 17 page
Binary data corruption due to a Brownian agent
We introduce a model of binary data corruption induced by a Brownian agent
(active random walker) on a d-dimensional lattice. A continuum formulation
allows the exact calculation of several quantities related to the density of
corrupted bits \rho; for example the mean of \rho, and the density-density
correlation function. Excellent agreement is found with the results from
numerical simulations. We also calculate the probability distribution of \rho
in d=1, which is found to be log-normal, indicating that the system is governed
by extreme fluctuations.Comment: 39 pages, 10 figures, RevTe
Relaxation Height in Energy Landscapes: an Application to Multiple Metastable States
The study of systems with multiple (not necessarily degenerate) metastable
states presents subtle difficulties from the mathematical point of view related
to the variational problem that has to be solved in these cases. We introduce
the notion of relaxation height in a general energy landscape and we prove
sufficient conditions which are valid even in presence of multiple metastable
states. We show how these results can be used to approach the problem of
multiple metastable states via the use of the modern theories of metastability.
We finally apply these general results to the Blume--Capel model for a
particular choice of the parameters ensuring the existence of two multiple, and
not degenerate in energy, metastable states
Tunneling and Metastability of continuous time Markov chains
We propose a new definition of metastability of Markov processes on countable
state spaces. We obtain sufficient conditions for a sequence of processes to be
metastable. In the reversible case these conditions are expressed in terms of
the capacity and of the stationary measure of the metastable states
Entropy production and fluctuation relations for a KPZ interface
We study entropy production and fluctuation relations in the restricted
solid-on-solid growth model, which is a microscopic realization of the KPZ
equation. Solving the one dimensional model exactly on a particular line of the
phase diagram we demonstrate that entropy production quantifies the distance
from equilibrium. Moreover, as an example of a physically relevant current
different from the entropy, we study the symmetry of the large deviation
function associated with the interface height. In a special case of a system of
length L=4 we find that the probability distribution of the variation of height
has a symmetric large deviation function, displaying a symmetry different from
the Gallavotti-Cohen symmetry.Comment: 21 pages, 5 figure
The target problem with evanescent subdiffusive traps
We calculate the survival probability of a stationary target in one dimension
surrounded by diffusive or subdiffusive traps of time-dependent density. The
survival probability of a target in the presence of traps of constant density
is known to go to zero as a stretched exponential whose specific power is
determined by the exponent that characterizes the motion of the traps. A
density of traps that grows in time always leads to an asymptotically vanishing
survival probability. Trap evanescence leads to a survival probability of the
target that may be go to zero or to a finite value indicating a probability of
eternal survival, depending on the way in which the traps disappear with time
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