Related papers: Heterogeneous anomalous diffusion in view of super…
Fractional transport of particles on a comb structure in the presence of an inhomogeneous convection flow is studied. The large scale asymptotics is considered. It is shown that a contaminant spreads superdiffusively in the direction…
We present a model of anomalous diffusion consisting of an ensemble of particles undergoing homogeneous Brownian motion except for confinement by randomly placed reflecting boundaries. For power-law distributed compartment sizes, we…
We study the causes of anomalous dispersion in Darcy-scale porous media characterized by spatially heterogeneous hydraulic properties. Spatial variability in hydraulic conductivity leads to spatial variability in the flow properties through…
The physical approach of a small particle (virus, medical drug) to the cell membrane represents the crucial first step before active internalization and is governed by thermal diffusion. Using a fully analytical theory we show that the…
We introduce a homogenization approach to characterize the dynamical response of a generic dispersive spacetime crystal in the long-wavelength limit. The theory is applied to dispersive spacetime platforms with a travelling-wave modulation.…
Models of biological processes are often subject to different sources of noise. Developing an understanding of the combined effects of different types of uncertainty is an open challenge. In this paper, we study a variant of the…
In this paper Gaussian models of retarded and accelerated anomalous diffusion are considered. Stochastic differential equations of fractional order driven by single or multiple fractional Gaussian noise terms are introduced to describe…
The two--dimensional diffusive dynamics of test particles in a random electromagnetic field is studied. The synthetic electromagnetic fluctuations are generated through randomly placed magnetised ``clouds'' oscillating with a frequency…
At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…
We show through intensive simulations that the paradigmatic features of anomalous diffusion are indeed the features of a (continuous-time) random walk driven by two different Markovian hopping-trap mechanisms. If $p \in (0,1/2)$ and $1-p$…
For every $\alpha < \frac13$, we construct an explicit divergence-free vector field $\mathbf{b}(t,x)$ which is periodic in space and time and belongs to $C^0_t C^{\alpha}_x \cap C^{\alpha}_t C^0_x$ such that the corresponding scalar…
A living cell's interior is one of the most complex and intrinsically dynamic systems, providing an elaborate interplay between cytosolic crowding and ATP-driven motion, which controls cellular functionality. Here, we investigated two…
We study the biased diffusion of particles moving in one direction under the action of a constant force in the presence of a piecewise linear random potential. Using the overdamped equation of motion, we represent the first and second…
We demonstrate that standard delay systems with a linear instantaneous and a delayed nonlinear term show weak chaos, asymptotically subdiffusive behavior, and weak ergodicity breaking if the nonlinearity is chosen from a specific class of…
A model for anomalous transport of tracer particles diffusing in complex media in two dimensions is proposed. The model takes into account the characteristics of persistent motion that active bath transfer to the tracer, thus the model…
The comb model is a simplified description for anomalous diffusion under geometric constraints. It represents particles spreading out in a two-dimensional space where the motions in the x-direction are allowed only when the y coordinate of…
Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems.…
We explore the nature of anomalous diffusion of wave packets in disorder-free incommensurate multi-walled carbon nanotubes. The spectrum-averaged diffusion exponent is obtained by calculating the multifractal dimension of the energy…
A simple model of an active colloid consisting of dumbbell-shaped particles that cyclically change their length without propelling themselves is proposed and analyzed. At nanoscales, it represents an idealization for bacterial cytoplasm or…
A generalized persistent random walk (GPRW) model to study anomalous particle diffusion influenced by angular heterogeneity is presented. Consider the motion of a particle is composed of many consecutive straight line segments. At the end…