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A nonlinear theory of quantum Brownian motion in classical environment is developed based on a thermodynamically enhanced nonlinear Schrodinger equation. The latter is transformed via the Madelung transformation into a nonlinear quantum…
In the present review we survey the properties of a transcendental function of the Wright type, nowadays known as M-Wright function, entering as a probability density in a relevant class of self-similar stochastic processes that we…
We demonstrate experimentally that a Brownian particle is subject to inertial effects at long time scales. By using a blinking optical tweezers, we extend the range of previous experiments by several orders of magnitude up to a few seconds.…
The density distribution function of the integral of the exponential Brownian motion is determined explicitly in the form of a rapidly convergent series.
We discuss the distribution of various estimators for extracting the diffusion constant of single Brownian trajectories obtained by fitting the squared displacement of the trajectory. The analysis of the problem can be framed in terms of…
We study diffusion processes driven by a Brownian motion with regular drift in a finite dimension setting. The drift has two components on different time scales, a fast conservative component and a slow dissipative component. Using the…
The process of diffusion is the most elementary stochastic transport process. Brownian motion, the representative model of diffusion, played a important role in the advancement of scientific fields such as physics, chemistry, biology and…
A relativistic diffusion model with cylindrical symmetry, which propagates an initial state based on quantum chromodynamics in time towards a thermal equilibrium limit, is derived from nonequilibrium-statistical considerations: Adapting an…
The Lorenz 1963 dynamical system is known to reduce in the steady state to a one-dimensional motion of a classical particle subjected to viscous damping in a past history-dependent potential field. If the potential field is substituted by a…
We discuss a relativistic diffusion in the proper time in an approach of Schay and Dudley. We derive (Langevin) stochastic differential equations in various coordinates.We show that in some coordinates the stochastic differential equations…
A new asymptotic method is presented for the analysis of the traveling waves in the one-dimensional reaction-diffusion system with the diffusion with a finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics. The analysis makes use of…
Diffusion rates through a membrane can be asymmetric, if the diffusing particles are spatially extended and the pores in the membrane have asymmetric structure. This phenomenon is demonstrated here via a deterministic simulation of a…
The distribution of the initial short-time displacements of particles is considered for a class of classical systems under rather general conditions on the dynamics and with Gaussian initial velocity distributions, while the positions could…
We formulate the generalized master equation for a class of continuous time random walks in the presence of a prescribed deterministic evolution between successive transitions. This formulation is exemplified by means of an…
Our purpose in this paper is to determine the limiting distribution and the evolution rate of particles near the frontier of branching Brownian motions. Here the branching rate is given by a Kato class measure with compact support in…
We introduce exact methods for the simulation of sample paths of one-dimensional diffusions with a discontinuity in the drift function. Our procedures require the simulation of finite-dimensional candidate draws from probability laws…
Although first-order rate constants are basic ingredients of physical chemistry, biochemistry and systems modeling, their innermost nature is derived from complex physical chemistry mechanisms. The present study suggests that equivalent…
Low-dimensional periodic arrays of scatterers with a moving point particle are ideal models for studying deterministic diffusion. For such systems the diffusion coefficient is typically an irregular function under variation of a control…
A finite-time fluctuation theorem is proved for the diffusion-influenced surface reaction A<->B in a domain with any geometry where the species A and B undergo diffusive transport between the reservoir and the catalytic surface. A…
The random propagation of molecules in a fluid medium is characterized by the spontaneous diffusion law as well as the interaction between the environment and molecules. In this paper, we embody the anomalous diffusion theory for modeling…