相关论文: Weak Non Self-Averaging Behaviour for Diffusion in…

We study the scaling laws of diffusion in two-dimensional media with long-range correlated disorder through exact enumeration of random walks. The disordered medium is modelled by percolation clusters with correlations decaying with the…

A brief review of our recent studies aiming at a better understanding of the scaling behaviour of polymers in disordered environments is given. The main emphasis is on a simple generic model where the polymers are represented by…

We study a scenario under which variable step random walks give anomalous statistics. We begin by analyzing the Martingale Central Limit Theorem to find a sufficient condition for the limit distribution to be non-Gaussian. We note that the…

We study a one dimensional generalization of the exponential trap model using both numerical simulations and analytical approximations. We obtain the asymptotic shape of the average diffusion front in the sub-diffusive phase. Our central…

Folklore has, that the universal scaling properties of linear polymers in disordered media are well described by the statistics of self-avoiding walks Folklore has, that the universal scaling properties of linear polymers in disordered…

In two dimensions polymer collapse has been shown to be complex with multiple low temperature states and multi-critical points. Recently, strong numerical evidence has been provided for a long-standing prediction of universal scaling of…

We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times, but anomalous…

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…

In this work we investigate the dynamics of random walk processes on scale-free networks in a short to moderate time scale. We perform extensive simulations for the calculation of the mean squared displacement, the network coverage and the…

We study asymptotic properties of diffusion and other transport processes (including self-avoiding walks and electrical conduction) on large randomly branched polymers using renormalized dynamical field theory. We focus on the swollen phase…

We introduce a new self-interacting random walk on the integers in a dynamic random environment and show that it converges to a pure diffusion in the scaling limit. We also find a lower bound on the diffusion coefficient in some special…

We consider random walks (RWs) and self-avoiding walks (SAWs) on disordered lattices directly at the percolation threshold. Applying numerical simulations, we study the scaling behavior of the models on the incipient percolation cluster in…

The behavior of the maximal displacement of a supercritical branching random walk has been a subject of intense studies for a long time. But only recently the case of time-inhomogeneous branching has gained focus. The contribution of this…

Experimental studies of the diffusion of biomolecules in the environment of biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule…

We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…

Daily, are reported systems in nature that present anomalous diffusion phenomena due to irregularities of medium, traps or reactions process. In this scenario, the diffusion with traps or localised--reactions emerge through various…

The effect of the correlations in the diluteness pattern in the systems with non-integral dimensionality, on $\nu=\frac{4}{5}$ superdiffusion process is considered in this paper. These spatial correlations have proved to be very effective…

We investigate both analytically and numerically the ensemble of minimum-weight loops and paths in the negative-weight percolation model on random graphs with fixed connectivity and bimodal weight distribution. This allows us to study the…

The scaling behavior of linear polymers in disordered media, modelled by self-avoiding walks (SAWs) on the backbone of percolation clusters in two, three and four dimensions is studied by numerical simulations. We apply the pruned-enriched…

We investigate the diffusion limited aggregation of particles executing persistent random walks. The scaling properties of both random walks and large aggregates are presented. The aggregates exhibit a crossover between ballistic and…