Browsing Mathematical Physics (MP) 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
(Fractional Calculus and Applied Analysis, 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
(New Journal of Physics, 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
(Journal of Physics A: Mathematical and Theoretical, 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
(New Journal of Physics, 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 kinetics emerging from ergodicity breaking in random media
(Physical Review E, 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
(Front. Phys., 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
(International Communications in Heat and Mass Transfer, 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
(Journal of the Royal Society Interface, 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
(New Journal of Physics, 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 ...