Anomalous dielectric relaxation with multispecies linear reaction dynamics

Tao Hong, Shu Peng, Yu Peng, Zhengming Tang and Kama Huang

Physica A: Statistical Mechanics and its Applications, 2023, vol. 613, issue C

Abstract: Anomalous dielectric relaxation in complex reactions is difficult to specify, since there is no classic model for the reacting species with anomalous subdiffusion in the presence of an external electric field. In this paper, the anomalous dielectric relaxation of a multispecies system with linear reaction dynamics is studied based on the biased continuous time random walks. Different reaction–subdiffusion equations are derived via the mathematical random subordination time and the deterministic physical time. The mathematical random subordination time is based on the assumption that the jumping probabilities are determined at the end of the waiting times, while the deterministic physical time is based on the assumption that the jumping probabilities are independent of time and evaluated at the start of the waiting times. The force fields are operated by the Riemann–Liouville fractional derivative in the reaction–subdiffusion equations with the deterministic physical time, while the opposite results are found in the reaction–subdiffusion equations with the mathematical random subordination time. The explicit expressions for the anomalous dielectric relaxation of a reversible reaction are further derived according to the two reaction–subdiffusion equations in the presence of space- and time-dependent electric fields. The numerical calculations are carried to validate the reliability of the different expressions for the anomalous dielectric relaxation, and the reaction–subdiffusion equation with the deterministic physical time is proved to be suitable for describing the anomalous dielectric relaxation.

Keywords: Biased continuous time random walk; Anomalous dielectric relaxation; Multispecies reaction; Stochastic process (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:613:y:2023:i:c:s0378437123000663

DOI: 10.1016/j.physa.2023.128511

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