相关论文: A kinetic equation for linear fractional stable mo…

The resolution of Brownian motion in simulations of micro-particle suspensions can be crucial to reproducing the correct dynamics of individual particles, as well as providing an accurate characterisation of suspension properties. Including…

We propose here a testing methodology based on the autocovariance, detrended moving average, and time-averaged mean-squared displacement statistics for tempered fractional Brownian motions (TFBMs) which are related to the notions of…

Fractional Brownian motion, a Gaussian non-Markovian self-similar process with stationary long-correlated increments, has been identified to give rise to the anomalous diffusion behavior in a great variety of physical systems. The…

Continuous Time Random Walks (CTRWs) are jump processes with random waiting times between jumps. We study scaling limits for CTRWs where the distribution of jumps and waiting times is coupled and varies in space and time. Such processes…

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…

Efficiency of search for randomly distributed targets is a prominent problem in many branches of the sciences. For the stochastic process of L\'evy walks, a specific range of optimal efficiencies was suggested under variation of search…

A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…

The well-scaled transition to the diffusion limit in the framework of the theory of continuous-time random walk (CTRW)is presented starting from its representation as an infinite series that points out the subordinated character of the CTRW…

In this paper, we construct operator fractional L\'evy motion (ofLm), a broad class of non-Gaussian stochastic processes that are covariance operator self-similar, have wide-sense stationary increments and display infinitely divisible…

The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…

We show the asymptotic long-time equivalence of a generic power law waiting time distribution to the Mittag-Leffler waiting time distribution, characteristic for a time fractional CTRW. This asymptotic equivalence is effected by a…

In a continuous time random walk (CTRW), each random jump follows a random waiting time. CTRW scaling limits are time-changed processes that model anomalous diffusion. The outer process describes particle jumps, and the non-Markovian inner…

We perform extensive simulations and systematic statistical analyses of the structural dynamics of amorphous silicon. The simulations follow the dynamics introduced by Wooten, Winer and Weaire: the energy is obtained with the Keating…

We investigate the impact of intermittent energy injections on a Brownian particle, modeled as stochastic renewals of its kinetic energy to a fixed value. Between renewals, the particle follows standard underdamped Langevin dynamics. For…

Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy…

While it is very common to model diffusion as a random walk by assuming memorylessness of the trajectory and diffusive step lengths, these assumptions can lead to significant errors. This paper describes the extent to which a physical…

Anomalous diffusion, in particular subdiffusion, is frequently invoked as a mechanism of motion in dense biological media, and may have a significant impact on the kinetics of binding/unbinding events at the cellular level. In this work we…

The linear Boltzmann equation approach is generalized to describe fractional superdiffusive transport of the Levy walk type in external force fields. The time distribution between scattering events is assumed to have a finite mean value and…

Space-fractional quantum mechanics (SFQM) is a generalization of the standard quantum mechanics when the Brownian trajectories in Feynman path integrals are replaced by L{\'e}vy flights. We introduce L{\'e}vy quasicrystal by discretizing…

Based on the Langevin description of the Continuous Time Random Walk (CTRW), we consider a generalization of CTRW in which the waiting times between the subsequent jumps are correlated. We discuss the cases of exponential and slowly…