Browsing Statistical Physics by Subject "anomalous diffusion"
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Centreofmass like superposition of OrnsteinUhlenbeck processes: A pathway to nonautonomous stochastic differential equations and to fractional diffusion
(20181025)We consider an ensemble of Ornstein–Uhlenbeck processes featuring a population of relaxation times and a population of noise amplitudes that characterize the heterogeneity of the ensemble. We show that the centreofmass ... 
Crossover from anomalous to normal diffusion: truncated powerlaw noise correlations and applications to dynamics in lipid bilayers
(20181018)The emerging diffusive dynamics in many complex systems shows a characteristic crossover behaviour from anomalous to normal diffusion which is otherwise fitted by two independent powerlaws. A prominent example for a ... 
Finiteenergy Lévytype motion through heterogeneous ensemble of Brownian particles
(20190201)Complex systems are known to display anomalous diffusion, whose signature is a space/time scaling $x \sim t^\delta$ with $\delta \neq 1/2$ in the probability density function (PDF). Anomalous diffusion can emerge jointly ... 
Fractional Brownian motion in a finite interval: correlations effect depletion or accretion zones of particles near boundaries
(201902)Fractional Brownian motion (FBM) is a Gaussian stochastic process with stationary, longtime correlated increments and is frequently used to model anomalous diffusion processes. We study numerically FBM confined to a finite ... 
Fractional Diffusion and Medium Heterogeneity: The Case of the Continuos Time Random Walk
(20210724)In this contribution we show that fractional diffusion emerges from a simple Markovian Gaussian random walk when the medium displays a powerlaw heterogeneity. Within the framework of the continuous time random walk, the ... 
Fractional kinetics emerging from ergodicity breaking in random media
(2016)We present a modelling approach for diffusion in a complex medium characterized by a random lengthscale. The resulting stochastic process shows subdiffusion with a behavior in qualitative agreement with single particle ... 
Gaussian processes in complex media: new vistas on anomalous diffusion
(201909)Normal or Brownian diffusion is historically identified by the linear growth in time of the variance and by a Gaussian shape of the displacement distribution. Processes departing from the at least one of the above conditions ... 
A generalized Stefan model accounting for system memory and nonlocality
(202005)The Stefan problem, involving the tracking of an evolving phasechange front, is the prototypical example of a moving boundary problem. In basic one dimensional problems it is well known that the front advances as the ... 
Langevin equation in complex media and anomalous diffusion
(20180730)The problem of biological motion is a very intriguing and topical issue. Many efforts are being focused on the development of novel modelling approaches for the description of anomalous diffusion in biological systems, such ... 
Singletrajectory spectral analysis of scaled Brownian motion
(201906)A standard approach to study timedependent stochastic processes is the power spectral density (PSD), an ensembleaveraged property defined as the Fourier transform of the autocorrelation function of the process in the ... 
Stochastic processes for anomalous diffusion
(2019)Anomalous diffusion is a diffusion process which Mean Square Displacement (MSD) is not a linear funtion of time, what is known as normal diffusion. When the relation is faster than linear, it is called superdiffusion and ...