129 research outputs found
Universal first-passage statistics of aging processes
Many out of equilibrium phenomena, such as diffusion-limited reactions or
target search processes, are controlled by first-passage events. So far the
general determination of the mean first-passage time (FPT) to a target in
confinement has left aside aging processes, involved in contexts as varied as
glassy dynamics, tracer diffusion in biological membranes or transport of cold
atoms in optical lattices. Here we consider general non-Markovian
scale-invariant processes in arbitrary dimension, displaying aging, and
demonstrate that all the moments of the FPT obey universal scalings with the
confining volume with non trivial exponents. Our analysis shows that a
nonlinear scaling of the mean FPT with the volume is the hallmark of aging and
provides a general tool to quantify its impact on first-passage kinetics in
confinement
Averaged residence times of stochastic motions in bounded domains
Two years ago, Blanco and Fournier (Blanco S. and Fournier R., Europhys.
Lett. 2003) calculated the mean first exit time of a domain of a particle
undergoing a randomly reoriented ballistic motion which starts from the
boundary. They showed that it is simply related to the ratio of the volume's
domain over its surface. This work was extended by Mazzolo (Mazzolo A.,
Europhys. Lett. 2004) who studied the case of trajectories which start inside
the volume. In this letter, we propose an alternative formulation of the
problem which allows us to calculate not only the mean exit time, but also the
mean residence time inside a sub-domain. The cases of any combinations of
reflecting and absorbing boundary conditions are considered. Lastly, we
generalize our results for a wide class of stochastic motions.Comment: 7 pages, 3 figure
Mean first-passage times of non-Markovian random walkers in confinement
The first-passage time (FPT), defined as the time a random walker takes to
reach a target point in a confining domain, is a key quantity in the theory of
stochastic processes. Its importance comes from its crucial role to quantify
the efficiency of processes as varied as diffusion-limited reactions, target
search processes or spreading of diseases. Most methods to determine the FPT
properties in confined domains have been limited to Markovian (memoryless)
processes. However, as soon as the random walker interacts with its
environment, memory effects can not be neglected. Examples of non Markovian
dynamics include single-file diffusion in narrow channels or the motion of a
tracer particle either attached to a polymeric chain or diffusing in simple or
complex fluids such as nematics \cite{turiv2013effect}, dense soft colloids or
viscoelastic solution. Here, we introduce an analytical approach to calculate,
in the limit of a large confining volume, the mean FPT of a Gaussian
non-Markovian random walker to a target point. The non-Markovian features of
the dynamics are encompassed by determining the statistical properties of the
trajectory of the random walker in the future of the first-passage event, which
are shown to govern the FPT kinetics.This analysis is applicable to a broad
range of stochastic processes, possibly correlated at long-times. Our
theoretical predictions are confirmed by numerical simulations for several
examples of non-Markovian processes including the emblematic case of the
Fractional Brownian Motion in one or higher dimensions. These results show, on
the basis of Gaussian processes, the importance of memory effects in
first-passage statistics of non-Markovian random walkers in confinement.Comment: Submitted version. Supplementary Information can be found on the
Nature website :
http://www.nature.com/nature/journal/v534/n7607/full/nature18272.htm
First exit times and residence times for discrete random walks on finite lattices
In this paper, we derive explicit formulas for the surface averaged first
exit time of a discrete random walk on a finite lattice. We consider a wide
class of random walks and lattices, including random walks in a non-trivial
potential landscape. We also compute quantities of interest for modelling
surface reactions and other dynamic processes, such as the residence time in a
subvolume, the joint residence time of several particles and the number of hits
on a reflecting surface.Comment: 19 pages, 2 figure
Survival probability of stochastic processes beyond persistence exponents
For many stochastic processes, the probability of not-having reached a
target in unbounded space up to time follows a slow algebraic decay at long
times, . This is typically the case of symmetric compact
(i.e. recurrent) random walks. While the persistence exponent has been
studied at length, the prefactor , which is quantitatively essential,
remains poorly characterized, especially for non-Markovian processes. Here we
derive explicit expressions for for a compact random walk in unbounded
space by establishing an analytic relation with the mean first-passage time of
the same random walk in a large confining volume. Our analytical results for
are in good agreement with numerical simulations, even for strongly
correlated processes such as Fractional Brownian Motion, and thus provide a
refined understanding of the statistics of longest first-passage events in
unbounded space
Windings of the 2D free Rouse chain
We study long time dynamical properties of a chain of harmonically bound
Brownian particles. This chain is allowed to wander everywhere in the plane. We
show that the scaling variables for the occupation times T_j, areas A_j and
winding angles \theta_j (j=1,...,n labels the particles) take the same general
form as in the usual Brownian motion. We also compute the asymptotic joint laws
P({T_j}), P({A_j}), P({\theta_j}) and discuss the correlations occuring in
those distributions.Comment: Latex, 17 pages, submitted to J. Phys.
Discrete Feynman-Kac formulas for branching random walks
Branching random walks are key to the description of several physical and
biological systems, such as neutron multiplication, genetics and population
dynamics. For a broad class of such processes, in this Letter we derive the
discrete Feynman-Kac equations for the probability and the moments of the
number of visits of the walker to a given region in the phase space.
Feynman-Kac formulas for the residence times of Markovian processes are
recovered in the diffusion limit.Comment: 4 pages, 3 figure
Force-velocity relation and density profiles for biased diffusion in an adsorbed monolayer
In this paper, which completes our earlier short publication [Phys. Rev.
Lett. 84, 511 (2000)], we study dynamics of a hard-core tracer particle (TP)
performing a biased random walk in an adsorbed monolayer, composed of mobile
hard-core particles undergoing continuous exchanges with a vapor phase. In
terms of an approximate approach, based on the decoupling of the third-order
correlation functions, we obtain the density profiles of the monolayer
particles around the TP and derive the force-velocity relation, determining the
TP terminal velocity, V_{tr}, as the function of the magnitude of external bias
and other system's parameters. Asymptotic forms of the monolayer particles
density profiles at large separations from the TP, and behavior of V_{tr} in
the limit of small external bias are found explicitly.Comment: Latex, 31 pages, 3 figure
Exit and Occupation times for Brownian Motion on Graphs with General Drift and Diffusion Constant
We consider a particle diffusing along the links of a general graph
possessing some absorbing vertices. The particle, with a spatially-dependent
diffusion constant D(x) is subjected to a drift U(x) that is defined in every
point of each link. We establish the boundary conditions to be used at the
vertices and we derive general expressions for the average time spent on a part
of the graph before absorption and, also, for the Laplace transform of the
joint law of the occupation times. Exit times distributions and splitting
probabilities are also studied and several examples are discussed.Comment: Accepted for publication in J. Phys.
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