相关论文: Enhancement, slow relaxation, ergodicity and rejuv…

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…

Stochastic interactions generically enhance self-diffusivity in living and biological systems, e.g. optimizing navigation strategies and controlling material properties of cellular tissues and bacterial aggregates. Despite this, the…

We find a general formula for the distribution of time-averaged observables for systems modeled according to the sub-diffusive continuous time random walk. For Gaussian random walks coupled to a thermal bath we recover ergodicity and…

Burstiness, the tendency of interaction events to be heterogeneously distributed in time, is critical to information diffusion in physical and social systems. However, an analytical framework capturing the effect of burstiness on generic…

Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of…

This paper uses dynamical invariants to describe the evolution of collisionless systems subject to time-dependent gravitational forces without resorting to maximum-entropy probabilities. We show that collisionless relaxation can be viewed…

In many situations, the combined effect of advection and diffusion greatly increases the rate of convergence to equilibrium -- a phenomenon known as enhanced dissipation. Here we study the situation where the advecting velocity field…

This work develops asymptotic properties of a class of switching jump diffusion processes. The processes under consideration may be viewed as a number of jump diffusion processes modulated by a random switching mechanism. The underlying…

We calculate the diffusion coefficients of persistent random walks on cubic and hypercubic lattices, where the direction of a walker at a given step depends on the memory of one or two previous steps. These results are then applied to study…

Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…

Starting from a simple animal-biology example, a general, somewhat counter-intuitive property of diffusion random walks is presented. It is shown that for any (non-homogeneous) purely diffusing system, under any isotropic uniform incidence,…

Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. The resulting time series are usually evaluated in terms of time averages. Often anomalous diffusion is…

We prove an invariance principle for continuous-time random walks in a dynamically averaging environment on $\mathbb Z$. In the beginning, the conductances may fluctuate substantially, but we assume that as time proceeds, the fluctuations…

Explicit examples of scalar enhanced diffusion due to resonances between different transport mechanisms are presented. Their signature is provided by the sharp and narrow peaks observed in the effective diffusivity coefficients and, in the…

We consider three kinds of discrete-time arrival processes: transient, intermediate and recurrent, characterized by a finite, possibly finite and infinite number of events, respectively. In this context, we study renewal processes which are…

We investigate the detailed dynamics of gains and losses made by agents in some kinetic models of wealth exchange. The concept of a walk in an abstract gain-loss space for the agents had been introduced in an earlier work. For models in…

Diffusion models proved to be powerful models for generative speech enhancement. In recent SGMSE+ approaches, training involves a stochastic differential equation for the diffusion process, adding both Gaussian and environmental noise to…

We derive the probability density of a diffusion process generated by nonergodic velocity fluctuations in presence of a weak potential, using the Liouville equation approach. The velocity of the diffusing particle undergoes dichotomic…

This work focuses on recurrence and ergodicity of switching diffusions consisting of continuous and discrete components, in which the discrete component takes values in a countably infinite set and the rates of switching at current time…

Here we study the long time behavior of an advection-diffusion equation with a general time varying (including random) shear flow imposing no-flux boundary conditions on channel walls. We derive the asymptotic approximation of the scalar…