Related papers: Langevin equation in complex media and anomalous d…
Distributed order fractional Langevin-like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent. It is shown that these fractional Langevin equations of distributed order can be…
We investigate the influence of a self-propelling, out-of-equilibrium active particle on generalized elastic systems, including flexible and semiflexible polymers, fluid membranes, and fluctuating interfaces, while accounting for…
Financial markets have long since been modeled using stochastic methods such as Brownian motion, and more recently, rough volatility models have been built using fractional Brownian motion. This fractional aspect brings memory into the…
In this paper we present a dynamical system to generate Brownian motion based on the Langevin equation without stochastic term and using fractional derivatives, i.e., a deterministic Brownian motion model is proposed. The stochastic process…
Brownian yet non-Gaussian phenomenon has recently been observed in many biological and active matter systems. The main idea of explaining this phenomenon is to introduce a random diffusivity for particles moving in inhomogeneous…
Many complex systems are described by Langevin-type equations in which the noise exhibits long-range correlations and couples to the system in a state-dependent, multiplicative manner, leading to heterogeneous non-Markovian diffusion. Here,…
Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on…
Motivated by subdiffusive motion of bio-molecules observed in living cells we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and…
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…
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…
Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is…
The time dependent Tsallis statistical distribution describing anomalous diffusion is usually obtained in the literature as the solution of a non-linear Fokker-Planck (FP) equation [A.R. Plastino and A. Plastino, Physica A, 222, 347…
It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
We present analytical results for the biased diffusion of particles moving under a constant force in a randomly layered medium. The influence of this medium on the particle dynamics is modeled by a piecewise constant random force. The…
Langevin dynamics has become a popular tool to simulate the Boltzmann equilibrium distribution. When the repartition of the Langevin equation involves the exact realization of the Ornstein-Uhlenbeck noise, in addition to the conventional…
Standard continuous time random walk (CTRW) models are renewal processes in the sense that at each jump a new, independent pair of jump length and waiting time are chosen. Globally, anomalous diffusion emerges through action of the…
Functionals of Brownian motion have diverse applications in physics, mathematics, and other fields. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, which is a Schrodinger equation in…
Linear dynamical systems, driven by a non-white noise which has the Levy distribution, are analysed. Noise is modelled by a specific stochastic process which is defined by the Langevin equation with a linear force and the Levy distributed…
Pervasive across diverse domains, stochastic systems exhibit fluctuations in processes ranging from molecular dynamics to climate phenomena. The Langevin equation has served as a common mathematical model for studying such systems, enabling…