相关论文: Comment on "Anomalous heat conduction and anomalou…

We study the scale dependence of effective diffusion of fluid tracers, specifically, its dependence on the P\'{e}clet number, a dimensionless parameter of the ratio between advection and molecular diffusion. Here, we address the case that…

We study by means of numerical simulations the velocity reversal model, a one-dimensional mechanical model of heat transport introduced in 1985 by Ianiro and Lebowitz. Our numerical results indicate that this model, although it does not…

We show that the criticism of our paper [Phys. Rev. B 65, 125109 (2002)] by Wang, Millis, and Das Sarma [cond-mat/0206203] is based on a trivial mathematical mistake they have committed.

Numerical studies of some unidimensional systems suggest that Fourier law is satisfied, where theory predicts a divergence of heat conductivity with the system size. Here, I revisit some such models, finding that in all cases a divergence…

A type-I model of non-isothermal multicomponent systems of gases describing mass diffusive and heat conductive phenomena is presented. The derivation of the model and a convergence result among thermomechanical theories in the smooth regime…

The crossing probability in the time direction is defined for an off-equilibrium reaction-diffusion system as the probability that the system of size L is still active at time t, in the finite-size scaling limit. Exact results are obtained…

The long wavelength diffusion coefficient of a critical fluid confined between two parallel plates separated by a distance L is strongly affected by the finite size. Finite size scaling leads us to expect that the vanishing of the diffusion…

We experimentally study anomalous diffusion of ultra-cold atoms in a one dimensional polarization optical lattice. The atomic spatial distribution is recorded at different times and its dynamics and shape are analyzed. We find that the…

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 anomalous mean square fluctuations are shown to arise naturally from the ordinary diffusion equation interpreted scale invariantly in a formalism endowing real numbers with a nonarchimedean multiplicative structure. A variable $t$…

Contrary to what is asserted in a recent paper by Kostadt and Liu ("Causality and stability of the relativistic diffusion equation"), experiments can tell apart (and in fact do) hyperbolic theories from parabolic theories of dissipation. It…

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…

The mechanisms leading to a seemingly superluminal propagation of light in dispersive media are examined. The anomalous dispersion near an absorption line, involved in the first experiments displaying negative group velocity propagation, is…

According to the classical theory of Brownian motion, the mean squared displacement of diffusing particles evolves linearly with time whereas the distribution of their displacements is Gaussian. However, recent experiments on mesoscopic…

We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle / functional central limit theorem) to hold for observables of compact group extensions of nonuniformly…

We provide a concise PDE-based proof of anomalous diffusion in the Kraichan model -- a stochastic, white-in-time model of passive scalar turbulence. That is, we show an exponential rate of $L^2$ decay in expectation of a passive scalar…

This review article aims to stress and reunite some of the analytic formalism of the anomalous diffusive processes that have succeeded in their description. Also, it has the objective to discuss which of the new directions they have taken…

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…

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…

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…