Related papers: Anomalous diffusion as a stochastic component in t…
We investigate the dynamics of a single tracer exploring a course of fixed obstacles in the vicinity of the percolation transition for particles confined to the infinite cluster. The mean-square displacement displays anomalous transport,…
Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a…
We consider a model system in which anomalous diffusion is generated by superposition of underlying linear modes with a broad range of relaxation times. In the language of Gaussian polymers, our model corresponds to Rouse (Fourier) modes…
This paper presents a simple tool for characterising the timescale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in…
We study the distribution of first passage time (FPT) in Levy type of anomalous diffusion. Using recently formulated fractional Fokker-Planck equation we obtain three results. (1) We derive an explicit expression for the FPT distribution in…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
Starting with Arnold's pioneering work, the term "Arnold diffusion" has been used to describe the slow diffusion taking place in the space of the actions in Hamiltonian nonlinear dynamical systems with three or more degrees of freedom. The…
According to a traditional point of view Boltzmann entropy is intimately related to linear Fokker-Planck equations (Smoluchowski, Klein-Kramers, and Rayleigh equations) that describe a well-known nonequilibrium phenomenon: (normal) Brownian…
In a recent paper, Michael J. Saxton proposes to interpret as anomalous diffusion the occurrence of apparent transient sub-diffusive regimes in mean-squared displacements (MSD) plots, calculated from experimental trajectories of molecules…
We present a methodology for the study of the dispersion of trajectories of stochastic processes in reconstructed phase spaces from observed data. The methodology allows to find ensembles of analog states, i.e. states that are close in the…
Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. In this work we introduce a new fractional operator…
Modern single-particle-tracking techniques produce extensive time-series of diffusive motion in a wide variety of systems, from single-molecule motion in living-cells to movement ecology. The quest is to decipher the physical mechanisms…
The purpose of this tutorial is to introduce the main concepts behind normal and anomalous diffusion. Starting from simple, but well known experiments, a series of mathematical modeling tools are introduced, and the relation between them is…
We demonstrate the existence of an anomalous structure in the data on the diffractive elastic scattering of hadrons at high energies and small momentum transfer. We analyze five sets of experimental data on $p(\overline{p})-p $ scattering…
We demonstrate and analyze anomalous diffusion properties of point-like particles in a two-dimensional system with circular scatterers arranged in a square lattice and governed by smooth potentials, referred to as the square soft Lorentz…
We introduce a novel way to extract information from turbulent datasets by applying an ARMA statistical analysis. Such analysis goes well beyond the analysis of the mean flow and of the fluctuations and links the behavior of the recorded…
We are discussing long-time, scaling limit for the anomalous diffusion composed of the subordinated L\'evy-Wiener process. The limiting anomalous diffusion is in general non-Markov, even in the regime, where ensemble averages of a…
We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti-)persistence. We present an…
An anomalous diffusion model for ion channel gating is put forward. This scheme is able to describe non-exponential, power-law like distributions of residence time intervals in several types of ion channels. Our method presents a…
Anomalous diffusion and L\'evy flights, which are characterized by the occurrence of random discrete jumps of all scales, have been observed in a plethora of natural and engineered systems, ranging from the motion of molecules to climate…