415 research outputs found
Optimal first arrival times in L\'evy flights with resetting
We consider diffusive motion of a particle performing a random walk with
L\'evy distributed jump lengths and subject to resetting mechanism bringing the
walker to an initial position at uniformly distributed times. In the limit of
infinite number of steps and for long times, the process converges to a
super-diffusive motion with replenishment. We derive formula for a mean first
arrival time (MFAT) to a predefined target position reached by a meandering
particle and analyze efficiency of the proposed searching strategy by
investigating criteria for an optimal (a shortest possible) MFAT.Comment: 10 pages, 6 figure
Activation process driven by strongly non-Gaussian noises
The constructive role of non-Gaussian random fluctuations is studied in the
context of the passage over the dichotomously switching potential barrier. Our
attention focuses on the interplay of the effects of independent sources of
fluctuations: an additive stable noise representing non-equilibrium external
random force acting on the system and a fluctuating barrier. In particular, the
influence of the structure of stable noises on the mean escape time and on the
phenomenon of resonant activation (RA) is investigated. By use of the numerical
Monte Carlo method it is documented that the suitable choice of the barrier
switching rate and random external fields may produce resonant phenomenon
leading to the enhancement of the kinetics and the shortest, most efficient
reaction time.Comment: 11 pages, 8 figure
Resonant activation driven by strongly non-Gaussian noises
The constructive role of non-Gaussian random fluctuations is studied in the
context of the passage over the dichotomously switching potential barrier. Our
attention focuses on the interplay of the effects of independent sources of
fluctuations: an additive stable noise representing non-equilibrium external
random force acting on the system and a fluctuating barrier. In particular, the
influence of the structure of stable noises on the mean escape time and on the
phenomenon of resonant activation (RA) is investigated. By use of the numerical
Monte Carlo method it is documented that the suitable choice of the barrier
switching rate and random external fields may produce resonant phenomenon
leading to the enhancement of the kinetics and the shortest, most efficient
reaction time.Comment: 9 pages, 7 figures, RevTeX
On subdiffusive continuous time random walks with stochastic resetting
We analyze two models of subdiffusion with stochastic resetting. Each of them
consists of two parts: subdiffusion based on the continuous-time random walk
(CTRW) scheme and independent resetting events generated uniformly in time
according to the Poisson point process. In the first model the whole process is
reset to the initial state, whereas in the second model only the position is
subject to resets. The distinction between these two models arises from the
non-Markovian character of the subdiffusive process. We derive exact
expressions for the two lowest moments of the full propagator, stationary
distributions, and first hitting times statistics. We also show, with an
example of a constant drift, how these models can be generalized to include
external forces. Possible applications to data analysis and modeling of
biological systems are also discussed.Comment: 11 pages, 5 figure
Subordinated diffusion and CTRW asymptotics
Anomalous transport is usually described either by models of continuous time
random walks (CTRW) or, otherwise by fractional Fokker-Planck equations (FFPE).
The asymptotic relation between properly scaled CTRW and fractional diffusion
process has been worked out via various approaches widely discussed in
literature. Here, we focus on a correspondence between CTRWs and time and space
fractional diffusion equation stemming from two different methods aimed to
accurately approximate anomalous diffusion processes. One of them is the Monte
Carlo simulation of uncoupled CTRW with a L\'evy -stable distribution
of jumps in space and a one-parameter Mittag-Leffler distribution of waiting
times. The other is based on a discretized form of a subordinated Langevin
equation in which the physical time defined via the number of subsequent steps
of motion is itself a random variable. Both approaches are tested for their
numerical performance and verified with known analytical solutions for the
Green function of a space-time fractional diffusion equation. The comparison
demonstrates trade off between precision of constructed solutions and
computational costs. The method based on the subordinated Langevin equation
leads to a higher accuracy of results, while the CTRW framework with a
Mittag-Leffler distribution of waiting times provides efficiently an
approximate fundamental solution to the FFPE and converges to the probability
density function of the subordinated process in a long-time limit.Comment: 10 pages, 7 figure
Resonant effects in a voltage-activated channel gating
The non-selective voltage activated cation channel from the human red cells,
which is activated at depolarizing potentials, has been shown to exhibit
counter-clockwise gating hysteresis. We have analyzed the phenomenon with the
simplest possible phenomenological models by assuming discrete
states, i.e. two normal open/closed states with two different states of ``gate
tension.'' Rates of transitions between the two branches of the hysteresis
curve have been modeled with single-barrier kinetics by introducing a
real-valued ``reaction coordinate'' parameterizing the protein's conformational
change. When described in terms of the effective potential with cyclic
variations of the control parameter (an activating voltage), this model
exhibits typical ``resonant effects'': synchronization, resonant activation and
stochastic resonance. Occurrence of the phenomena is investigated by running
the stochastic dynamics of the model and analyzing statistical properties of
gating trajectories.Comment: 12 pages, 9 figure
Levy--Brownian motion on finite intervals: Mean first passage time analysis
We present the analysis of the first passage time problem on a finite
interval for the generalized Wiener process that is driven by L\'evy stable
noises. The complexity of the first passage time statistics (mean first passage
time, cumulative first passage time distribution) is elucidated together with a
discussion of the proper setup of corresponding boundary conditions that
correctly yield the statistics of first passages for these non-Gaussian noises.
The validity of the method is tested numerically and compared against
analytical formulae when the stability index approaches 2, recovering
in this limit the standard results for the Fokker-Planck dynamics driven by
Gaussian white noise.Comment: 9 pages, 13 figure
Heat and work distributions for mixed Gauss-Cauchy process
We analyze energetics of a non-Gaussian process described by a stochastic
differential equation of the Langevin type. The process represents a
paradigmatic model of a nonequilibrium system subject to thermal fluctuations
and additional external noise, with both sources of perturbations considered as
additive and statistically independent forcings. We define thermodynamic
quantities for trajectories of the process and analyze contributions to
mechanical work and heat. As a working example we consider a particle subjected
to a drag force and two independent Levy white noises with stability indices
and . The fluctuations of dissipated energy (heat) and
distribution of work performed by the force acting on the system are addressed
by examining contributions of Cauchy fluctuations to either bath or external
force acting on the system
- …