A. Jurlewicz

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Keywords: Fractional calculus Anomalous diffusion Continuous time random walk Central limit theory Operator stable law a b s t r a c t In a continuous time random walk (CTRW), a random waiting time precedes each random jump. The CTRW is coupled if the waiting time and the subsequent jump are dependent random variables. The CTRW is used in physics to model(More)
In this paper, we propose a transparent subordination approach to anomalous diffusion processes underlying the nonexponential relaxation. We investigate properties of a coupled continuous-time random walk that follows from modeling the occurrence of jumps with compound counting processes. As a result, two different diffusion processes corresponding to over-(More)
A stochastic generalization of renormalization-group transformation for continuous-time random walk processes is proposed. The renormalization consists in replacing the jump events from a randomly sized cluster by a single renormalized (i.e., overall) jump. The clustering of the jumps, followed by the corresponding transformation of the interjump time(More)
We present a class of continuous-time random walks (CTRWs), in which random jumps are separated by random waiting times. The novel feature of these CTRWs is that the jumps are clustered. This introduces a coupled effect, with longer waiting times separating larger jump clusters. We show that the CTRW scaling limits are time-changed processes. Their(More)
In the frame of a new probabilistic approach to relaxation, the scenario of relaxation leading to the Havriliak– Negami and Kohlrausch–Williams–Watts responses of complex systems is presented. In this approach the macroscopic laws are related to the micro/mesoscopic stochastic characteristics of the relaxing systems. This provides a rigorous formulation of(More)
Empirical evidence accumulated over the years shows that the time-dependent change of macroscopic properties of physical systems evolving to equilibrium exhibits a great degree of universality. We address the question of the origins of the universal relaxation laws in terms of probabilistic approach based on the multichannel parallel relaxation mechanism.(More)
Unlike the classical exponential relaxation law, the widely prevailing universal law with its fractional power-law dependence of susceptibility on frequency cannot be explained in the framework of any intuitively simple physical concept. The resulting constancy of the ratio of the imaginary to the real parts of the complex susceptibility, known as the(More)
Charge transport processes in disordered complex media are accompanied by anomalously slow relaxation for which usually a broad distribution of relaxation times is adopted. To account for those properties of the environment, a standard kinetic approach in description of the system is addressed either in the framework of continuous-time random walks (CTRWs)(More)
In this paper the complex dielectric permittivity of gallium doped Cd(0.99)Mn(0.01)Te mixed crystals is studied at different temperatures. We observe a two-power-law relaxation pattern with m and n, the low- and high-frequency power-law exponents respectively, satisfying the relation m < 1-n. To interpret the empirical result we propose a correlated-cluster(More)
We present dielectric spectroscopy data obtained for gallium-doped Cd(0.99)Mn(0.01)Te:Ga mixed crystals, which exhibit a very special case of the two-power-law relaxation pattern with the high-frequency power-law exponent equal to 1. We explain this behavior, which cannot be fitted by any of the well-known empirical relaxation functions, in a subordinated(More)
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