Related papers: Different effects of external force fields on agin…
One of the most important scaling laws of time dependent fracture is Basquin's law of fatigue, namely, that the lifetime of the system increases as a power law with decreasing external load amplitude, $t_f\sim \sigma_0^{-\alpha}$, where the…
Growing experimental evidence shows that cell monolayers can induce long-lived perturbations to their environment, akin to footprints, which in turn influence the global dynamics of the system. Inspired by these observations, we propose a…
Physical aging is one of the non-equilibrium phenomena where physical properties change over time due to structural relaxation. Aging in spin glass systems has been explained by a trap model on the temperature-independent energy landscape.…
Levy walks define a fundamental concept in random walk theory which allows one to model diffusive spreading that is faster than Brownian motion. They have many applications across different disciplines. However, so far the derivation of a…
Brownian yet non-Gaussian processes have recently been observed in numerous biological systems and the corresponding theories have been built based on random diffusivity models. Considering the particularity of random diffusivity, this…
We consider the linear response of systems modelled by continuous-time random walks (CTRW) and by fractional Fokker-Planck equations under the influence of time-dependent external fields. We calculate the corresponding response functions…
Sinai's model of diffusion in one-dimension with random local bias is studied by a real space renormalization group which yields asymptotically exact long time results. The distribution of the position of a particle and the probability of…
The statistics of records for a time series generated by a continuous time random walk is studied, and found to be independent of the details of the jump length distribution, as long as the latter is continuous and symmetric. However, the…
The purpose of this paper is to implement a random death process into a persistent random walk model which produces subballistic superdiffusion (L\'{e}vy walk). We develop a Markovian model of cell motility with the extra residence variable…
In this article, we present a mathematical model that answers a classical question concerning how much force, which is generally called static friction force, will it require to initiate the motion of a soft solid block such as gel, rubber…
Molecular dynamics simulations are used to investigate the connection between thermal history and physical aging in polymer glasses, in particular the effects of a temperature square step. Measurements of two-time correlation functions show…
Intriguing phenomena such as subrecoil laser cooling of atoms, or aging phenomenon in glasses, have in common that the systems considered do not reach a steady-state during the experiments, although the experimental time scales are very…
Recent experiments (G. Ariel, et al., Nature Comm. 6, 8396 (2015)) revealed an intriguing behavior of swarming bacteria: they fundamentally change their collective motion from simple diffusion into a superdiffusive L\'{e}vy walk dynamics.…
Once the problem of ensemble averaging is removed, correlations between the response of a single molecule to an external driving field $F$, with the history of fluctuations of the particle, become detectable. Exact analytical theory for the…
We study a method for detecting the origins of anomalous diffusion, when it is observed in an ensemble of times-series, generated experimentally or numerically, without having knowledge about the exact underlying dynamics. The reasons for…
Time dependent entropy of constant force motion is investigated. Their joint entropy so called Leipnik's entropy is obtained. The main purpose of this work is to calculate Leipnik's entropy by using time dependent wave function which is…
We study the linear response to an external perturbation of a renewal process, in an aging condition that, with no perturbation, would yield super-diffusion. We use the phenomenological approach to the linear response adopted in earlier…
We present a detailed study of simple `tree' models for off equilibrium dynamics and aging in glassy systems. The simplest tree describes the landscape of a random energy model, whereas multifurcating trees occur in the solution of the…
Different methods are used to determine the scaling exponents associated with a time series describing a complex dynamical process, such as those observed in geophysical systems. Many of these methods are based on the numerical evaluation…
The effect of a constant applied external force, induced for instance by an electric or gravitational field, on the dispersion of Brownian particles in periodic media with spatially varying diffusivity, and thus mobility, is studied. We…