Related papers: Markovian embedding of fractional superdiffusion
Diffusive motion is a fundamental transport mechanism in physical and biological systems, governing dynamics across a wide range of scales -- from molecular transport to animal foraging. In many complex systems, however, diffusion deviates…
Langevin equations or generalized Langevin equations (GLEs) are popular models for describing the motion of a particle in a fluid medium in an effective manner. Here we examine particles immersed in an inherently nonequilibrium fluid, i.e.,…
In this work, we propose a new semi-Lagrangian (SL) finite difference scheme for nonlinear advection-diffusion problems. To ensure conservation, which is fundamental for achieving physically consistent solutions, the governing equations are…
A Langevin process diffusing in a periodic potential landscape has a time dependent diffusion constant which means that its average mean squared displacement (MSD) only becomes linear at late times. The long time, or effective diffusion…
Despite the success of fractional Brownian motion (fBm) in modeling systems that exhibit anomalous diffusion due to temporal correlations, recent experimental and theoretical studies highlight the necessity for a more comprehensive approach…
We study the generalized Langevin equation approach to anomalous diffusion for a harmonic oscillator and a free particle driven by different forms of internal noises, such as power-law-correlated and distributed-order noises that fulfil…
In the present work, by using the method of accumulation of phase shifts in the rotating frame, the attenuation function S(t) of the NMR signal from an ensemble of spin-bearing particles in a magnetic-field gradient is expressed through the…
Levy walks define a fundamental concept in random walk theory which allows one to model diffusive spreading that is faster than Brownian motion. They have many applications across different disciplines. However, so far the derivation of a…
The impact of thermal fluctuations on the translocation dynamics of a polymer chain driven through a narrow pore has been investigated theoretically and by means of extensive Molecular-Dynamics (MD) simulation. The theoretical consideration…
Levy flights and fractional Brownian motion (fBm) have become exemplars of the heavy tailed jumps and long-ranged memory seen in space physics and elsewhere. Natural time series frequently combine both effects, and Linear Fractional Stable…
A Markov process fluctuating away from its typical behavior can be represented in the long-time limit by another Markov process, called the effective or driven process, having the same stationary states as the original process conditioned…
Given nonstationary data from molecular dynamics simulations, a Markovian Langevin model is constructed that aims to reproduce the time evolution of the underlying process. While at equilibrium the free energy landscape is sampled,…
In this article integro-differential Volterra equations whose convolution kernel depends on the vector variable are considered and a connection of these equations with a class of semi-Markov processes is established. The variable order…
Capturing the correct dynamics at the Coarse-Grained (CG) scale remains a central challenge in the advancement of systematic CG models for soft matter simulations. The Generalized Langevin Equation (GLE), rooted in the Mori-Zwanzig…
Einstein's explanation of Brownian motion provided one of the cornerstones which underlie the modern approaches to stochastic processes. His approach is based on a random walk picture and is valid for Markovian processes lacking long-term…
The underdamped, non-linear, generalized Langevin equation is widely used to model coarse-grained dynamics of soft and biological materials. By means of a projection operator formalism, we show under which approximations this equation can…
Overdamped Brownian motion of a self-propelled particle is studied by solving the Langevin equation analytically. On top of translational and rotational diffusion, in the context of the presented model, the "active" particle is driven along…
Stretched-exponential relaxation is a widely observed phenomenon found in ordered ferromagnets as well as glassy systems. One modeling approach connects this behavior to a droplet dynamics described by an effective Langevin equation for the…
We present the Fokker-Planck equation (FPE) for an inhomogeneous medium with a position-dependent mass particle by making use of the Langevin equation, in the context of a generalized deformed derivative for an arbitrary deformation space…
We investigate single-particle diffusion in a two-state Langevin model where the friction coefficient randomly switches between low-friction (liquid-like) and high-friction (glassy-like) states. The dynamics are governed by the ratio…