Related papers: Relaxation time distributions for an anomalously d…
An equation describing subdiffusion with possible immobilization of particles is derived by means of the continuous time random walk model. The equation contains a fractional time derivative of Riemann--Liouville type which is a…
The L\'evy-Lorentz gas describes the motion of a particle on the real line in the presence of a random array of scattering points, whose distances between neighboring points are heavy-tailed i.i.d. random variables with finite mean. The…
We solve a model of sluggish stochastic motion in which a Brownian particle diffuses with a diffusion coefficient that decays algebraically with the distance to the origin, as $|x|^{-\alpha}$. Additionally, the particle resets with a…
The diffusion of a particle in a crowded environment typically proceeds through three regimes: for very short times the particle diffuses freely until it collides with an obstacle for the first time, while for very long times diffusion the…
Superslow diffusion, i.e., the long-time diffusion of particles whose mean-square displacement (variance) grows slower than any power of time, is studied in the framework of the decoupled continuous-time random walk model. We show that this…
In this paper, by comparing the time scales associated with the velocity relaxation and correlation time of the random force due to dust charge fluctuations, memory effects in the velocity relaxation of an isolated dust particle exposed to…
Reaction-diffusion equations deliver a versatile tool for the description of reactions in inhomogeneous systems under the assumption that the characteristic reaction scales and the scales of the inhomogeneities in the reactant…
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…
We study the first passage time (FPT) problem in Levy type of anomalous diffusion. Using the recently formulated fractional Fokker-Planck equation, we obtain an analytic expression for the FPT distribution which, in the large passage time…
We prove optimal estimates for the decay in time of solutions to a rather general class of non-local in time subdiffusion equations in $\mathbb{R}^d$. An important special case is the time-fractional diffusion equation, which has seen much…
Fractional diffusion equations imply non-Gaussian distributions that generalise the standard diffusive process. Recent advances in fractional calculus lead to a class of new fractional operators defined by non-singular memory kernels,…
Deriving evolution equations accounting for both anomalous diffusion and reactions is notoriously difficult, even in the simplest cases. In contrast to normal diffusion, reaction kinetics cannot be incorporated into evolution equations…
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…
We study diffusion of a particle in a system composed of K parallel channels, where the transition rates within the channels are quenched random variables whereas the inter-channel transition rate v is homogeneous. A variant of the strong…
We study the relaxation of a diffusive particle confined in an arbitrary external potential and subject to a non-Markovian resetting protocol. With a constant rate $r$, a previous time $\tau$ between the initial time and the present time…
Several classes of physical systems exhibit ultraslow diffusion for which the mean squared displacement at long times grows as a power of the logarithm of time ("strong anomaly") and share the interesting property that the probability…
Two models of binary fragmentation are introduced in which a time dependent transition size produces two regions of fragment sizes above and below the transition size. In the models we consider a fixed rate of fragmentation for the largest…
Anomalous diffusion phenomena have been observed in many complex physical and biological systems. One significant advance recently is the physical extension of particle's motion in static medium to uniformly (and even nonuniformly)…
Understanding the properties of response time distributions is a long-standing problem in cognitive science. We provide a tutorial overview of several contemporary models that assume power law scaling is a plausible description of the…
The unified description of diffusion processes that cross over from a ballistic behavior at short times to normal or anomalous diffusion (sub- or superdiffusion) at longer times is constructed on the basis of a non-Markovian generalization…