TY - JOUR A1 - Chechkin, Aleksei V. A1 - Seno, Flavio A1 - Metzler, Ralf A1 - Sokolov, Igor M. T1 - Brownian yet Non-Gaussian Diffusion: From Superstatistics to Subordination of Diffusing Diffusivities JF - Physical review : X, Expanding access N2 - A growing number of biological, soft, and active matter systems are observed to exhibit normal diffusive dynamics with a linear growth of the mean-squared displacement, yet with a non-Gaussian distribution of increments. Based on the Chubinsky-Slater idea of a diffusing diffusivity, we here establish and analyze a minimal model framework of diffusion processes with fluctuating diffusivity. In particular, we demonstrate the equivalence of the diffusing diffusivity process with a superstatistical approach with a distribution of diffusivities, at times shorter than the diffusivity correlation time. At longer times, a crossover to a Gaussian distribution with an effective diffusivity emerges. Specifically, we establish a subordination picture of Brownian but non-Gaussian diffusion processes, which can be used for a wide class of diffusivity fluctuation statistics. Our results are shown to be in excellent agreement with simulations and numerical evaluations. Y1 - 2017 U6 - https://doi.org/10.1103/PhysRevX.7.021002 SN - 2160-3308 VL - 7 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Dzhanoev, Arsen R. A1 - Sokolov, Igor M. T1 - The effect of the junction model on the anomalous diffusion in the 3D comb structure JF - Chaos, solitons & fractals : applications in science and engineering ; an interdisciplinary journal of nonlinear science N2 - The diffusion in the comb structures is a popular model of geometrically induced anomalous diffusion. In the present work we concentrate on the diffusion along the backbone in a system where sidebranches are planes, and the diffusion thereon is anomalous and described by continuous time random walks (CTRW). We show that the mean squared displacement (MSD) in the backbone of the comb behaves differently depending on whether the waiting time periods in the sidebranches are reset after the step in the backbone is done (a rejuvenating junction model), or not (a non-rejuvenating junction model). In the rejuvenating case the subdiffusion in the sidebranches only changes the prefactor in the ultra-slow (logarithmic) diffusion along the backbone, while in the non-rejuvenating case the ultraslow, logarithmic subdiffusion is changed to a much faster power-law subdiffusion (with a logarithmic correction) as it was found earlier by Iomin and Mendez [25]. Moreover, in the first case the result does not change if the diffusion in the backbone is itself anomalous, while in the second case it does. Two of the special cases of the considered models (the non-rejuvenating junction under normal diffusion in the backbone, and rejuvenating junction for the same waiting time distribution in the sidebranches and in junction points) were also investigated within the approach based on the corresponding generalized Fokker-Planck equations. (c) 2017 Elsevier Ltd. All rights reserved. KW - Comb model KW - Comb-lattice model KW - Cylindrical comb KW - Junction model KW - Anomalous diffusion Y1 - 2017 U6 - https://doi.org/10.1016/j.chaos.2017.12.001 SN - 0960-0779 SN - 1873-2887 VL - 106 SP - 330 EP - 336 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Sandev, Trifce A1 - Sokolov, Igor M. A1 - Metzler, Ralf A1 - Chechkin, Aleksei V. T1 - Beyond monofractional kinetics JF - Chaos, solitons & fractals : applications in science and engineering ; an interdisciplinary journal of nonlinear science N2 - We discuss generalized integro-differential diffusion equations whose integral kernels are not of a simple power law form, and thus these equations themselves do not belong to the family of fractional diffusion equations exhibiting a monoscaling behavior. They instead generate a broad class of anomalous nonscaling patterns, which correspond either to crossovers between different power laws, or to a non-power-law behavior as exemplified by the logarithmic growth of the width of the distribution. We consider normal and modified forms of these generalized diffusion equations and provide a brief discussion of three generic types of integral kernels for each form, namely, distributed order, truncated power law and truncated distributed order kernels. For each of the cases considered we prove the non-negativity of the solution of the corresponding generalized diffusion equation and calculate the mean squared displacement. (C) 2017 Elsevier Ltd. All rights reserved. KW - Distributed order diffusion-wave equations KW - Complete Bernstein function KW - Completely monotone function Y1 - 2017 U6 - https://doi.org/10.1016/j.chaos.2017.05.001 SN - 0960-0779 SN - 1873-2887 VL - 102 SP - 210 EP - 217 PB - Elsevier CY - Oxford ER -