9,952 research outputs found
First Passage Time Distribution for Anomalous Diffusion
We study the first passage time (FPT) problem in Levy type of anomalous
diffusion. Using the recently formulated fractional Fokker-Planck equation, we
obtain an analytic expression for the FPT distribution which, in the large
passage time limit, is characterized by a universal power law. Contrasting this
power law with the asymptotic FPT distribution from another type of anomalous
diffusion exemplified by the fractional Brownian motion, we show that the two
types of anomalous diffusions give rise to two distinct scaling behavior.Comment: 11 pages, 2 figure
Mean First Passage Time in Periodic Attractors
The properties of the mean first passage time in a system characterized by
multiple periodic attractors are studied. Using a transformation from a high
dimensional space to 1D, the problem is reduced to a stochastic process along
the path from the fixed point attractor to a saddle point located between two
neighboring attractors. It is found that the time to switch between attractors
depends on the effective size of the attractors, , the noise, ,
and the potential difference between the attractor and an adjacent saddle point
as: ; the
ratio between the sizes of the two attractors affects . The
result is obtained analytically for small and confirmed by numerical
simulations. Possible implications that may arise from the model and results
are discussed.Comment: 14 pages, 3 figures, submitted to journal of physics
First passage time density for the Ehrenfest model
We derive an explicit expression for the probability density of the first passage time to state 0 for the Ehrenfest diffusion model in continuous time
Optimal first-passage time in gene regulatory networks
The inherent probabilistic nature of the biochemical reactions, and low copy
number of species can lead to stochasticity in gene expression across identical
cells. As a result, after induction of gene expression, the time at which a
specific protein count is reached is stochastic as well. Therefore events
taking place at a critical protein level will see stochasticity in their
timing. First-passage time (FPT), the time at which a stochastic process hits a
critical threshold, provides a framework to model such events. Here, we
investigate stochasticity in FPT. Particularly, we consider events for which
controlling stochasticity is advantageous. As a possible regulatory mechanism,
we also investigate effect of auto-regulation, where the transcription rate of
gene depends on protein count, on stochasticity of FPT. Specifically, we
investigate for an optimal auto-regulation which minimizes stochasticity in
FPT, given fixed mean FPT and threshold.
For this purpose, we model the gene expression at a single cell level. We
find analytic formulas for statistical moments of the FPT in terms of model
parameters. Moreover, we examine the gene expression model with
auto-regulation. Interestingly, our results show that the stochasticity in FPT,
for a fixed mean, is minimized when the transcription rate is independent of
protein count. Further, we discuss the results in context of lysis time of an
\textit{E. coli} cell infected by a phage virus. An optimal lysis
time provides evolutionary advantage to the phage, suggesting a
possible regulation to minimize its stochasticity. Our results indicate that
there is no auto-regulation of the protein responsible for lysis. Moreover,
congruent to experimental evidences, our analysis predicts that the expression
of the lysis protein should have a small burst size.Comment: 8 pages, 3 figures, Submitted to Conference on Decision and Control
201
First Passage Time in a Two-Layer System
As a first step in the first passage problem for passive tracer in stratified
porous media, we consider the case of a two-dimensional system consisting of
two layers with different convection velocities. Using a lattice generating
function formalism and a variety of analytic and numerical techniques, we
calculate the asymptotic behavior of the first passage time probability
distribution. We show analytically that the asymptotic distribution is a simple
exponential in time for any choice of the velocities. The decay constant is
given in terms of the largest eigenvalue of an operator related to a half-space
Green's function. For the anti-symmetric case of opposite velocities in the
layers, we show that the decay constant for system length crosses over from
behavior in diffusive limit to behavior in the convective
regime, where the crossover length is given in terms of the velocities.
We also have formulated a general self-consistency relation, from which we have
developed a recursive approach which is useful for studying the short time
behavior.Comment: LaTeX, 28 pages, 7 figures not include
First-passage time for superstatistical Fokker-Planck models
The first-passage-time (FPT) problem is studied for superstatistical models assuming that the mesoscopic system dynamics is described by a Fokker-Planck equation. We show that all moments of the random intensive parameter associated to the superstatistical approach can be put in one-to-one correspondence with the moments of the FPT. For systems subjected to an additional uncorrelated external force, the same statistical information is obtained from the dependence of the FPT moments on the external force. These results provide an alternative technique for checking the validity of superstatistical models. As an example, we characterize the mean FPT for a forced Brownian particle.Fil: Budini, Adrian Adolfo. Universidad TecnolĂłgica Nacional; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; Argentina. ComisiĂłn Nacional de EnergĂa AtĂłmica. Centro AtĂłmico Bariloche; ArgentinaFil: Caceres Garcia Faure, Manuel Osvaldo. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; Argentina. ComisiĂłn Nacional de EnergĂa AtĂłmica. Gerencia del Ărea de EnergĂa Nuclear. Instituto Balseiro; Argentin
Mean first-passage time of quantum transition processes
In this paper, we consider the problem of mean first-passage time (MFPT) in
quantum mechanics; the MFPT is the average time of the transition from a given
initial state, passing through some intermediate states, to a given final state
for the first time. We apply the method developed in statistical mechanics for
calculating the MFPT of random walks to calculate the MFPT of a transition
process. As applications, we (1) calculate the MFPT for multiple-state systems,
(2) discuss transition processes occurring in an environment background, (3)
consider a roundabout transition in a hydrogen atom, and (4) apply the approach
to laser theory.Comment: 11 pages, no figur
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