Related papers: On the strong anomalous diffusion
We investigate the bounds between normal or anomalous effective diffusion for inertial particles transported by parallel flows. The infrared behavior of the fluid kinetic-energy spectrum, i.e. the possible presence of long-range…
The stochastic dynamics of colloidal particles with surface activity--in the form of catalytic reaction or particle release--and self-phoretic effects is studied analytically. Three different time scales corresponding to inertial effects,…
Anomalous diffusion is the fundamental ansatz of phenomenological theories of passive scalar turbulence, and has been confirmed numerically and experimentally to an extraordinary extent. The purpose of this survey is to discuss our recent…
We discuss the diffusion phenomenon in the parabolic and hyperbolic regimes. New effects related to the finite velocity of the diffusion process are predicted, that can partially explain the strange behavior associated to adsorption…
Anomalous diffusion occurs at very different scales in nature, from atomic systems to motions in cell organelles, biological tissues or ecology, and also in artificial materials, such as cement. Being able to accurately measure the…
We investigate statistical properties of several classes of periodic billiard models which are diffusive. An introductory chapter gives motivation, and then a review of statistical properties of dynamical systems is given in chapter 2. In…
Models of one-dimensional driven diffusive systems sometimes exhibit an abrupt increase of the correlation length to an anomalously large but finite value as the parameters of the model are varied. This behavior may be misinterpreted as a…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…
Quantum walks are known to propagate quadratically faster than their classical counterparts and are used to model dynamics in various quantum systems. The spread of the quantum walk in position space shows anomalous diffusion behavior. By…
Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…
Uchaikin suggested a mathematical model of an anomalous diffusion in a space was suggested. This model origins in an investigation of processes in complex systems with variable structure: glasses, liquid crystals, biopolymers, proteins and…
Sub-diffusion in biological systems is conventionally treated as anomalous, requiring fractional derivatives, heavy-tailed waiting times, or fitted memory kernels. We argue that this anomaly is an artifact of an incomplete phase space.…
We demonstrate that 2D Fermi liquids can support peculiar excitations that are not subject to Landau's $T^2$ dissipation. The long-lived excitations relax through correlated angular dynamics involving "lock-step" angular displacements along…
Diffusion at solid-liquid interfaces is crucial in many technological and biophysical processes. Although its behavior seems deceivingly simple, recent studies showing passive superdiffusive transport suggest diffusion on surfaces may hide…
In classical diffusion, particle step-sizes have a Gaussian distribution. However, in superdiffusion, they have power-law tails, with transport dominated by rare, long L\'evy flights. Similarly, if the time interval between scattering…
We present computer simulations of anomalous diffusion, $< r^2(t) > \sim a t^{1-\delta}$, in two dimensions. The Monte Carlo calculations are in excellent agreement with previous renormalization group calculations. Interestingly, use of a…
Superdiffusion is an anomalous transport behavior. Recently, a new mechanism, termed the ``nodal mechanism," has been proposed to induce superdiffusion in quantum models. However, existing realizations of the nodal mechanism have so far…
We study anomalous heat conduction and anomalous diffusion in low dimensional systems ranging from nonlinear lattices, single walled carbon nanotubes, to billiard gas channels. We find that in all discussed systems, the anomalous heat…
A generalization of the Drude model is studied. On the one hand, the free motion of the particles is allowed to be sub- or superdiffusive; on the other hand, the distribution of the time delay between collisions is allowed to have a long…