相关论文: L\'{e}vy flights in random environments
The L\'evy walk process with rests is discussed. The jumping time is governed by an $\alpha$-stable distribution with $\alpha>1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a…
The paper is devoted to the relationship between the continuous Markovian description of Levy flights developed previously and their equivalent representation in terms of discrete steps of a wandering particle, a certain generalization of…
We study a random walk on a point process given by an ordered array of points $(\omega_k, \, k \in \mathbb{Z})$ on the real line. The distances $\omega_{k+1} - \omega_k$ are i.i.d. random variables in the domain of attraction of a…
We consider the A + A --> emptyset reaction, where the transport of the particles is given by Levy flights in a quenched random potential. With a common literature model of the disorder, the random potential can only increase the rate of…
Rayleigh-L\'evy flights are simplified cosmological tools which capture certain essential statistical properties of the cosmic density field, including hierarchical structures in higher-order correlations, making them a valuable reference…
This paper describes the stochastic Levy--Lorentz gas driven by general long-range reference random walk on correlated and entangled random medium. Further consideration has been laid on the stochastic reinforcement of the underlying random…
We study the statistics of encounters of L\'evy flights by introducing the concept of vicious L\'evy flights - distinct groups of walkers performing independent L\'evy flights with the process terminating upon the first encounter between…
We study the long time asymptotics of probability density functions (pdfs) of L\'{e}vy flights in different confining potentials. For that we use two models: Langevin - driven and (L\'{e}vy - Schr\"odinger) semigroup - driven dynamics. It…
We obtain the dynamic correlation function of two-dimensional lattice gas with nearest-neighbor repulsion in ordered c(2$\times$2) phase (antiferromagnetic ordering) under the condition of low concentration of structural defects. It is…
Using dynamic renormalization group we study the transport in driven diffusive systems in the presence of quenched random drift velocity with long-range correlations along the transport direction. In dimensions $d\mathopen< 4$ we find fixed…
We study the effect of quenched disorder on nonequilibrium systems of interacting particles, specifically, driven diffusive lattice gases with spatially disordered jump rates. The exact steady-state measure is found for a class of models…
We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…
We investigate the dynamic impact of heterogeneous environments on superdiffusive random walks known as L\'evy flights. We devote particular attention to the relative weight of source and target locations on the rates for spatial…
The random-field Ising model shows extreme critical slowdown that has been described by activated dynamic scaling: the characteristic time for the relaxation to equilibrium diverges exponentially with the correlation length, $\ln \tau\sim…
We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight…
It is well established that the phase transition between survival and extinction in spreading models with short-range interactions is generically associated with the directed percolation (DP) universality class. In many realistic spreading…
L\'evy Flights are paradigmatic generalised random walk processes, in which the independent stationary increments---the "jump lengths"---are drawn from an $\alpha$-stable jump length distribution with long-tailed, power-law asymptote. As a…
The effect of quenched disorder on non-equilibrium phase transitions in the directed percolation universality class is studied by a strong disorder renormalization group approach and by density matrix renormalization group calculations. We…
We study the critical dynamics of a real scalar field in two dimensions near a continuous phase transition. We have built up and solved Dynamical Renormalization Group equations at one-loop approximation. We have found that, different form…
A combined dynamics consisting of Brownian motion and L\'evy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of…