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In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions…
Modeling human ratings data subject to raters' decision uncertainty is an attractive problem in applied statistics. In view of the complex interplay between emotion and decision making in rating processes, final raters' choices seldom…
This paper tackles the problem of generating safe exit controllers for continuous-time systems described by stochastic differential equations (SDEs). The primary aim is to develop controllers that maximize the lower bounds of the exit…
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic…
Rare events are processes that occur upon the emergence of unlikely fluctuations. Unlike what their name suggests, rare events are fairly ubiquitous in nature, as the occurrence of many structural transformations in biology and material…
Rare events in stochastic processes with heavy-tailed distributions are controlled by the big jump principle, which states that a rare large fluctuation is produced by a single event and not by an accumulation of coherent small deviations.…
Reliability assessment of distribution system, based on historical data and probabilistic methods, leads to an unreliable estimation of reliability indices since the data for the distribution components are usually inaccurate or…
We use an effective Hamiltonian to characterize particle dynamics and find escape rates in a periodically kicked Hamiltonian. We study a model of particles in storage rings that is described by a chaotic symplectic map. Ignoring the…
A fission decay of highly excited periodically driven compound nuclei is considered in the framework of Langevin approach. We have used residual-time distribution (RTD) as the tool for studying of dynamic features in a presence of periodic…
To assess the possibility of evacuating a building in case of a fire, a standard method consists in simulating the propagation of fire, using finite difference methods and takes into account the random behavior of the fire, so that the…
Statistical limits are defined relaxing conditions on conventional convergence. The main idea of the statistical convergence of a sequence l is that the majority of elements from l converge and we do not care what is going on with other…
Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic…
In this paper, we propose a stochastic dynamic model for earthquake rupture and suggest that the Langevin equation of frictions may be used for interpreting the slip distributions of rupture processes in earthquakes. The steady-state…
Throughout physics Brownian dynamics are used to describe the behaviour of molecular systems. When the Brownian particle is confined to a bounded domain, a particularly important question arises around determining how long it takes the…
Rare events in molecular dynamics are often related to noise-induced transitions between different macroscopic states (e.g., in protein folding). A common feature of these rare transitions is that they happen on timescales that are on…
We present an approximate analytical expression for the escape rate of time-dependent driven stochastic processes with an absorbing boundary such as the driven leaky integrate-and-fire model for neural spiking. The novel approximation is…
We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar…
We study the effects of noise-intensity fluctuations on the stationary and dynamical properties of an overdamped Langevin model with a bistable potential and external periodical driving force. We calculated the stationary distributions,…
We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which…
A simple tight-coupling model of a molecular chemical engine is proposed. The efficiency of the chemical engine and its average velocity can be explicitly calculated. The diffusion constant is evaluated approximately using the fluctuation…