相关论文: Random walks on fractals and stretched exponential…
We study random walks on the dilute hypercube using an exact enumeration Master equation technique, which is much more efficient than Monte Carlo methods for this problem. For each dilution $p$ the form of the relaxation of the memory…
Stretched exponential relaxation of a quantity n versus time t according to n = n_0 exp[-(lambda* t)^beta] is ubiquitous in many research fields, where lambda* is a characteristic relaxation rate and the stretching exponent beta is in the…
We attempt to give a bird's eye view of the physical mechanisms leading to anomalous relaxation, and the relation of this phenomenon with anomalous diffusion and transport. Whereas in some cases these two notions are indeed deeply related,…
Relaxation in glasses is often approximated by a stretched-exponential form: $f(t) = A \exp [-(t/\tau)^{\beta}]$. Here, we show that the relaxation in a model of sheared non-Brownian suspensions developed by Cort\'e et al. [Nature Phys. 4,…
Diffusion on a diluted hypercube has been proposed as a model for glassy relaxation and is an example of the more general class of stochastic processes on graphs. In this article we determine numerically through large scale simulations the…
Amorphous solids or glasses are known to exhibit stretched-exponential decay over broad time intervals in several of their macroscopic observables: intermediate scattering function, dielectric relaxation modulus, time-elastic modulus etc.…
Stretched-exponential relaxation is a widely observed phenomenon found in ordered ferromagnets as well as glassy systems. One modeling approach connects this behavior to a droplet dynamics described by an effective Langevin equation for the…
Simulations of a stochastic fixed-energy sandpile in one and two dimensions reveal slow relaxation of the order parameter, even far from the critical point. The decay of the activity is best described by a stretched-exponential form. The…
The question of whether glass continues to relax at low temperature is of fundamental and practical interest. Here, we report a novel atomistic simulation method allowing us to directly access the long-term dynamics of glass relaxation at…
This short report details the mathematical properties of the stretched exponential function and some of its applications in materials science. G(tau) distributions for different values of the stretching parameter beta are provided.
The relaxation of the specific heat and the entropy to their equilibrium values is investigated numerically for the three-dimensional Coulomb glass at very low temperatures. The long time relaxation follows a stretched exponential function,…
This paper is concerned with the connection between the properties of dielectric relaxation and ac (alternating-current) conduction in disordered dielectrics. The discussion is divided between the classical linear-response theory and a…
A new master equation to mimic the dynamics of a collection of interacting random walkers in an open system is proposed and solved numerically.In this model, the random walkers interact through excluded volume interaction (single-file…
There are many materials whose dielectric properties are described by a stretched exponential, the so-called Kohlrausch-Williams-Watts (KWW) relaxation function. Its physical origin and statistical-mechanical foundation have been a matter…
We have analytically obtained the non-exponential relaxation function for disordered complex systems applying the multi-level jumping formalism to the fluctuation quantity which makes diffusive motion stochastically in the disordered…
We identify a link between the glass transition and percolation of mobile regions in configuration space. We find that many hallmarks of glassy dynamics, for example stretched-exponential response functions and a diverging structural…
The relaxation dynamics of glass-forming systems shows a multitude of features that are absent in normal liquids, such as non-exponential relaxation and a strong temperature-dependence of the relaxation time. Connecting these dynamic…
The origin of stretched exponential relaxation in supercooled glass-forming liquids is one of the central questions regarding the anomalous dynamics of these fluids. The dominant explanation for this phenomenon has long been the proposition…
We consider the non--equilibrium dynamics of a chain of classical rotators coupled at its edges to an external reservoir at zero temperature. We find that the energy is released in a strongly discontinuous fashion, with sudden jumps…
We consider relaxation processes that exhibit a stretched exponential behavior. We find that in those systems, where the relaxation arises from two competing exponential processes, the size of the system may play a dominant role. Above a…