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Trajectories of an overdamped particle in a highly unstable potential diverge so rapidly, that the variance of position grows much faster than its mean. Description of the dynamics by moments is therefore not informative. Instead, we…
We study the large-time behaviour of Brownian particles moving through a viscous medium in a confined potential, and which are further subjected to position-dependent driving forces that are periodic in time. We focus on the case where…
We discuss the statistics of first-passage times of a Brownian particle moving in a highly unstable nonlinear potential proportional to an odd power of position. We observe temperature-induced shortening of the mean first-passage time and…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
Statistical properties of Brownian motion that arise by analyzing, separately, trajectories over which the system energy increases (upside) or decreases (downside) with respect to a threshold energy level, are derived. This selective…
In this Letter, we clarify the physical origin of effective transport in periodic and tilted periodic systems. When Brownian dynamics is examined on the scale of a single period, the particle displacement admits a natural separation into a…
The motion of particles in random potentials occurs in several natural phenomena ranging from the mobility of organelles within a biological cell to the diffusion of stars within a galaxy. A Brownian particle moving in the random optical…
A system reservoir model, where the associated reservoir is modulated by an external colored random force, is proposed to study the transport of an overdamped Brownian particle in a periodic potential. We then derive the analytical…
Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results have indicated transport by…
Consider a chaotic dynamical system generating Brownian motion-like diffusion. Consider a second, non-chaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in…
For systems out of equilibrium and subjected to a static bias force it can often be expected that particle transport will usually follow the direction of this bias. However, counter-examples exist where particles exhibit uphill motion…
Fractional Brownian motion is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically fractional Brownian motion confined to a finite…
We present an analysis of the stationary distributions of run-and-tumble particles trapped in external potentials in terms of a thermophoretic potential, that emerges when trapped active motion is mapped to trapped passive Brownian motion…
Statistical description of stochastic dynamics in highly unstable potentials is strongly affected by properties of divergent trajectories, that quickly leave meta-stable regions of the potential landscape and never return. Using ideas from…
We study the behaviour of a Brownian particle in the overdamped regime in the presence of a harmonic potential, assuming its diffusion coefficient to randomly jump between two distinct values. In particular, we characterize the probability…
We study the biased diffusion of particles moving in one direction under the action of a constant force in the presence of a piecewise linear random potential. Using the overdamped equation of motion, we represent the first and second…
Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…
Diffusive transport of particles or, more generally, small objects is a ubiquitous feature of physical and chemical reaction systems. In configurations containing confining walls or constrictions transport is controlled both by the…
In this work we study the transition from normal to anomalous diffusion of Brownian particles on disordered potentials. The potential model consists of a series of "potential hills" (defined on unit cell of constant length) whose heights…
Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…