Related papers: Active L\'evy Matter: Anomalous Diffusion, Hydrody…

Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…

Levy flights and subdiffusive processes and their properties are discussed. We derive the space- and time-fractional transport equations, and consider their solutions in external potentials. An extensive list of references is included.

Probing the anomalous nanoscale intermixing using molecular dynamics (MD) simulations in Pt/Ti bilayer we reveal the superdiffusive nature of interfacial atomic transport. It is shown that the Pt atoms undergo anomalous atomic transport…

The phenomenon of group motion is common in nature, ranging from the schools of fish, birds and insects, to avalanches, landslides and sand drift. If we treat objects as collectively moving particles, such phenomena can be studied from a…

We present evidence that the concurrent existence of two populations of particles with different effective diameters is not a prerequisite for the occurrence of anomalous phase behaviors in systems of particles interacting through…

Anomalous diffusion occurs in a wide range of systems, including protein transport within cells, animal movement in complex habitats, pollutant dispersion in groundwater, and nanoparticle motion in synthetic materials. Accurately estimating…

The evolution of infinitesimal, localized perturbations is investigated in a one-dimensional diatomic gas of hard-point particles (HPG) and thereby connected to energy diffusion. As a result, a Levy walk description, which was so far…

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…

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.…

Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of…

Dry active matter in an anisotropic medium is of experimental relevance, and the interplay between anisotropy and the dynamics of the active matter remains under-explored. Here, we derive the hydrodynamic equations of a generic dry polar…

The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by "viscoelastic" anomalous diffusion, in which the increments of the motion feature…

Collective motion is a phenomenon observed across length scales in nature, from bacterial swarming and tissue migration to the flocking of animals. The mechanisms underlying this behavior vary significantly depending on the biological…

In the Heliosphere, power-law particle distributions are observed e.g. upstream of interplanetary shocks, which can result from superdiffusive transport. This non-Gaussian transport regime may result from intermittent magnetic field…

Anomalous diffusion, process in which the mean-squared displacement of system states is a non-linear function of time, is usually identified in real stochastic processes by comparing experimental and theoretical displacements at relatively…

Levy walk (LW) process has been used as a simple model for describing anomalous diffusion in which the mean squared displacement of the walker grows non-linearly with time in contrast to the diffusive motion described by simple random walks…

Chaotic transitions in inertial fluids typically proceed through a direct energy cascade from large to small scales. In contrast, active systems, composed of self propelled units, inject energy at microscopic scales and therefore exhibit an…

Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in…

Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. The resulting time series are usually evaluated in terms of time averages. Often anomalous diffusion is…

Many natural and industrial processes rely on constrained transport, such as proteins moving through cells, particles confined in nanocomposite materials or gels, individuals in highly dense collec- tives and vehicular traffic conditions.…