Related papers: Persistent Sinai type diffusion in Gaussian random…
We investigate superdiffusion for stochastic processes generated by nonuniformly hyperbolic system models, in terms of the convergence of rescaled distributions to the normal distribution following the abnormal central limit theorem, which…
Brownian yet non-Gaussian diffusion has recently been observed in numerous biological and active matter system. The cause of the non-Gaussian distribution have been elaborately studied in the idea of a superstatistical dynamics or a…
In recent years, several experiments highlighted a new type of diffusion anomaly, which was called Brownian yet non-Gaussian diffusion. In systems displaying this behavior, the mean squared displacement of the diffusing particles grows…
We demonstrate that continuous time random walks in which successive waiting times are correlated by Gaussian statistics lead to anomalous diffusion with mean squared displacement <r^2(t)>~t^{2/3}. Long-ranged correlations of the waiting…
A relation between the effective diffusion coefficient in a lattice with random site energies and random trasition rates and the macroscopic conductivity in a random resistor network allows for elucidating possible sources of anomalous…
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…
Refraction of a Longuet-Higgins Gaussian sea by random ocean currents creates persistent local variations in average energy and wave action. These variations take the form of lumps or streaks, and they explicitly survive dispersion over…
This paper presents new findings concerning the dynamics of the slow height variations in surfaces produced by the two-dimensional isotropic Kuramoto-Sivashinsky equation with an additional nonlinear term. In addition to the disordered…
We establish an unexpected phenomenon of strong regularization along normal convergence on Wiener chaoses. For every sequence of chaotic random variables, convergence in law to the Gaussian distribution is upgraded to superconvergence: the…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
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…
A one-dimensional model of classical diffusion in a random force field with a weak concentration $\rho$ of absorbers is studied. The force field is taken as a Gaussian white noise with $\mean{\phi(x)}=0$ and $\mean{\phi(x)\phi(x')}=g…
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…
The emerging diffusive dynamics in many complex systems shows a characteristic crossover behaviour from anomalous to normal diffusion which is otherwise fitted by two independent power-laws. A prominent example for a subdiffusive-diffusive…
Fluctuation scaling (FS) and anomalous diffusion have been discussed in different contexts, even though both are often observed in complex systems. To clarify the relationship between these concepts, we investigated approximately three…
We survey recent results of normal and anomalous diffusion of two types of random motions with long memory in ${\Bbb R}^d$ or ${\Bbb Z}^d$. The first class consists of random walks on ${\Bbb Z}^d$ in divergence-free random drift field,…
We study the generalized Langevin equation approach to anomalous diffusion for a harmonic oscillator and a free particle driven by different forms of internal noises, such as power-law-correlated and distributed-order noises that fulfil…
A generalized logarithmic law for high-order moments of passive scalars is proposed for turbulent boundary layers. This law is analogous to the generalized log law that has been proposed for high-order moments of the turbulent longitudinal…
We study out of equilibrium dynamics and aging for a particle diffusing in one dimensional environments, such as the random force Sinai model, as a toy model for low dimensional systems. We study fluctuations of two times $(t_w, t)$…
We consider the Newtonian dynamics of a massive particle in a one dimemsional random potential which is a Brownian motion in space. This is the zero temperature nondamped Sinai model. As there is no dissipation the particle oscillates…