22 research outputs found
Multimodal stationary states under Cauchy noise
A L\'evy noise is an efficient description of out-of-equilibrium systems. The
presence of L\'evy flights results in a plenitude of noise-induced phenomena.
Among others, L\'evy flights can produce stationary states with more than one
modal value in single-well potentials. Here, we explore stationary states in
special double-well potentials demonstrating that a sufficiently high potential
barrier separating potential wells can produce bimodal stationary states in
each potential well. Furthermore, we explore how the decrease in the barrier
height affects the multimodality of stationary states. Finally, we explore a
role of the multimodality of stationary states on the noise induced escape over
the static potential barrier.Comment: 10 pages, 11 figure
Deterministic force-free resonant activation
Combined action of noise and deterministic force in dynamical systems can
induce resonant effects. Here, we demonstrate a minimal,
deterministic-force-free, setup allowing for occurrence of resonant, noise
induced effects. We show that in the archetypal problem of escape from finite
intervals driven by -stale noise with the periodically modulated
stability index, depending on the initial direction of the modulation,
resonant-activation-like or noise-enhanced-stability-like phenomena can be
observed.Comment: 8 page
Underdamped, anomalous kinetics in double-well potentials
The noise driven motion in a bistable potential acts as the archetypal model
of various physical phenomena. Here, we contrast the overdamped dynamics with
the full (underdamped) dynamics. For the overdamped particle driven by a
non-equilibrium, -stable noise the ratio of forward and backward
transition rates depends only on the width of a potential barrier separating
both minima. Using analytical and numerical methods, we show that in the regime
of full dynamics, contrary to the overdamped case, the ratio of transition
rates depends both on widths and heights of the potential barrier. The
analytical formula for the ratio of transition rates is corroborated by
extensive numerical simulations.Comment: 9 page
Drifted escape from the finite interval
Properties of the noise-driven escape kinetics are mainly determined by the
stochastic component of the system dynamics. Nevertheless, the escape dynamics
is also sensitive to deterministic forces. Here, we are exploring properties of
the overdamped drifted escape from finite intervals under the action of
symmetric -stable noises. We show that the properly rescaled mean first
passage time follows the universal pattern as a function of the generalized
P\'ecklet number, which can be used to efficiently discriminate between domains
where drift or random force dominate. Stochastic driving of the -stable
type is capable of diminishing the significance of the drift in the regime when
the drift prevails.Comment: 8 page
Random acceleration process on finite intervals under stochastic restarting
The escape of the randomly accelerated undamped particle from the finite
interval under action of stochastic resetting is studied. The motion of such a
particle is described by the full Langevin equation and the particle is
characterized by the position and velocity. We compare three resetting
protocols, which restarts velocity or position (partial resetting) and the
whole motion (position and velocity -- full resetting). Using the mean first
passage time we assess efficiency of restarting protocols in facilitating or
suppressing the escape kinetics. There are fundamental differences between
partial resetting scenarios which restart velocity or position, as in the limit
of very frequent resets only the position resetting (regardless of initial
velocity) can trap the particle in the finite domain of motion. The velocity
resetting or the simultaneous position and velocity restarting provide a
possibility of facilitating the undamped escape kinetics.Comment: 23 page
Multimodal stationary states in symmetric single-well potentials driven by Cauchy noise
Stationary states for a particle moving in a single-well, steeper than
parabolic, potential driven by L\'evy noise can be bi-modal. Here, we explore
in details conditions that are required in order to induce multimodal
stationary states having more than two modal values. Phenomenological arguments
determining necessary conditions for emergence of stationary states of higher
multimodality are provided. Basing on these arguments, appropriate symmetric
single-well potentials are constructed. Finally, using numerical methods it is
verified that stationary states have anticipated multimodality.Comment: 15 pages 10 figure
Optimization of escape kinetics by reflecting and resetting
Stochastic restarting is a strategy of starting anew. Incorporation of the
resetting to the random walks can result in the decrease of the mean first
passage time, due to the ability to limit unfavorably meandering, sub-optimal
trajectories. In the following manuscript we examine how stochastic resetting
influences escape dynamics from the interval in the presence of
the single-well power-law potentials with . Examination
of the mean first passage time is complemented by the analysis of the
coefficient of variation, which provides a robust and reliable indicator
assessing efficiency of stochastic resetting. The restrictive nature of
resetting is compared to placing a reflective boundary in the system at hand.
In particular, for each potential, the position of the reflecting barrier
giving the same mean first passage time as the optimal resetting rate is
determined. Finally, in addition to reflecting, we compare effectiveness of
other resetting strategies with respect to optimization of the mean first
passage time.Comment: 7 page
Physics of free climbing
Theory of stochastic processes provides theoretical tools which can be
efficiently used to explore properties of noise induced escape kinetics. Since
noise facilitated escape over the potential barrier resembles free climbing,
one can use the first passage time theory in analysis of rock climbing. We
perform the analysis of the mean first passage time in order to answer the
question regarding the optimal, i.e., resulting in the fastest climbing, rope
length. It is demonstrated that there is a discrete set of favorable rope
lengths assuring shortest climbing times, as they correspond to local minima of
mean first passage time. Within the set of favorable rope lengths there is the
optimal rope giving rise to the shortest climbing time. In particular, more
experienced climbers can decrease their climbing time by using longer ropes.Comment: 7 pages, 6 figure
Epidemics spread in heterogeneous populations
Individuals building populations are subject to variability. This variability affects progress of epidemic outbreaks, because individuals tend to be more or less resistant. Individuals also differ with respect to their recovery rate. Here, properties of the SIR model in inhomogeneous populations are studied. It is shown that a small change in model’s parameters, e.g. recovery or infection rate, can substantially change properties of final states which is especially well-visible in distributions of the epidemic size. In addition to the epidemic size and radii distributions, the paper explores first passage time properties of epidemic outbreaks
Nonlinear friction in underdamped anharmonic stochastic oscillators
Stationary states of overdamped anharmonic stochastic oscillators driven by
L\'evy noise are typically multimodal. The very same situation is recorded for
an underdamped L\'evy noise driven motion in single-well potentials with linear
friction. Within current manuscript we relax the assumption that the friction
experienced by a particle is linear. Using computer simulations, we study
underdamped motion in single-well potentials in the regime of nonlinear
friction. We demonstrate that it is relatively easy to observe multimodality in
the velocity distribution as it is determined by the friction itself and it is
the same as the multimodality in the overdamped case with the analogous
deterministic force. Contrary to the velocity marginal density, it is more
difficult to produce multimodality in the position. Nevertheless, for
fine-tuned nonlinear friction, the spatial multimodality can be recorded.Comment: 10 page