1,661 research outputs found
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
The critical catastrophe revisited
The neutron population in a prototype model of nuclear reactor can be
described in terms of a collection of particles confined in a box and
undergoing three key random mechanisms: diffusion, reproduction due to
fissions, and death due to absorption events. When the reactor is operated at
the critical point, and fissions are exactly compensated by absorptions, the
whole neutron population might in principle go to extinction because of the
wild fluctuations induced by births and deaths. This phenomenon, which has been
named critical catastrophe, is nonetheless never observed in practice: feedback
mechanisms acting on the total population, such as human intervention, have a
stabilizing effect. In this work, we revisit the critical catastrophe by
investigating the spatial behaviour of the fluctuations in a confined geometry.
When the system is free to evolve, the neutrons may display a wild patchiness
(clustering). On the contrary, imposing a population control on the total
population acts also against the local fluctuations, and may thus inhibit the
spatial clustering. The effectiveness of population control in quenching
spatial fluctuations will be shown to depend on the competition between the
mixing time of the neutrons (i.e., the average time taken for a particle to
explore the finite viable space) and the extinction time.Comment: 16 pages, 6 figure
Fractional Brownian motion with a reflecting wall
Fractional Brownian motion, a stochastic process with long-time correlations
between its increments, is a prototypical model for anomalous diffusion. We
analyze fractional Brownian motion in the presence of a reflecting wall by
means of Monte Carlo simulations. While the mean-square displacement of the
particle shows the expected anomalous diffusion behavior , the interplay between the geometric confinement and the
long-time memory leads to a highly non-Gaussian probability density function
with a power-law singularity at the barrier. In the superdiffusive case,
, the particles accumulate at the barrier leading to a divergence of
the probability density. For subdiffusion, , in contrast, the
probability density is depleted close to the barrier. We discuss implications
of these findings, in particular for applications that are dominated by rare
events.Comment: 6 pages, 6 figures. Final version as publishe
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