Histogram Distribution Function for Relaxation Rates as Zipf’s Power Law for Universal Dielectric Relaxation - A Case Study for a Complex Disordered System| Chapter 7 | New Frontiers in Physical Science Research Vol. 4

 This stage gives a new treatment of analytical approach to catch an insight of a non-Debye Complex-Disordered entertainment especially to the Universal Dielectric Relaxation (UDR) law. The chaste power standard for dielectric relaxation, is current as inverse of capacity of time that is  i(t) ∼ t−n for a step-voltage excitation to dielectric This is UDR and commonly known as Curie-von Schweidler society This law is empirically derivative and is observed in various relaxation experiments on various dielectrics studies because late  19th Century. This UDR law is a singular capacity law. There maybe non-singular non-Debye relaxation societies too. We will concisely mention the results of a non-singular relaxation standard especially by Mittag Leffler function In this affiliate, we give simple numerical treatment to receive the distribution of relaxation rates (λ -in part of per second) of this Curie-von Schweidler standard, and show that the relaxation rate follows Zipf’s capacity law distribution. We further show the method grown here in this episode give Zipfian capacity law distribution for diminishing time continuous (τ) and discuss its tangible contradiction. In this episode, we develop possible reason that as to why Zipfian classification of relaxation rates performs for UDR i.e. Curie-von Schweidler Law, and relate this standard to time variant and scale helpless rate of relaxation. In this chapter, we assume appearance of partial derivative while using Zipfian power regulation distribution for Curie-von Schweidler entertainment phenomena. We also describe the Curie-von Schweidler relaxation i(t) ∼ t−n as concurrent multi-body relaxations which have a allocation/histogram for relaxation rates as right-distorted one. That is the graph resembling pie with large number of relaxations accompanying lower value of rate (slow rates) understood with long tail of small number of relaxations accompanying faster relaxation rates, diminishing simultaneously. The chapter gives a likely foundation for further studies in gettv the rate relaxation distribution functions for different non-Debye type relaxation functions, and a new type of clarification regarding reasons of Zipfian distributions.

Author(s) Details: Shantanu Das, Bhabha Atomic Research Center (BARC), Mumbai, India. Please see the link here: https://stm.bookpi.org/NFPSR-V4/article/view/8752