1/fnoise in percolation and percolationlike systems

Abstract

The behavior of 1/f noise effective intensity in two-phase percolation systems and percolationlike systems with an exponentially wide distribution of bond resistances is reviewed. Monte Carlo simulations on random resistor networks are performed. For a two-phase system the numerical values of noise critical exponents ϭ1.54Ϯ0.025, Јϭ0.61Ϯ0.02, wϭ6.31Ϯ0.25, and wЈϭ6.9Ϯ0.25 are found in agreement with theoretical analysis performed with the help of a hierarchical model of a two-phase percolation system. For a system with an exponentially wide spectrum of bond resistances, i.e., a system in which bonds take on resistances rϭr 0 exp͑Ϫx͒, where ӷ1 and x is a random variable, it is assumed that in the individual resistors the noise generating mechanism obeys the form ͕␦r 2 ͖ϳr 2ϩ . In this case the effective noise intensity C e ϵS⍀, where S is the relative power spectral density of system resistance fluctuations and ⍀ is the system volume, is given by C e ϳ m exp͑Ϫx c ͒, where 1Ϫx c is the percolation threshold. The exponent m is ''double universal,'' i.e., it is independent of lattice geometry and of the microscopic noise generating mechanism. Numerical simulations performed for ϭ1 and 0 give approximately mХ2.3 and confirm this ''double universality'' of the exponent m. The connections between 1/f noise effective intensity and effective susceptibility in a two-phase weakly nonlinear percolation system are also established. ͓S1063-651X͑96͒04405-4͔ PACS number͑s͒: 64.60.Ak, 64.60.Ht * Electronic address: snar@carrier.kiev.ua

Evaluation of Permeability of Microporous Media, Using the Modified Random-Trajectory Approach

“…Calculations performed using Eqs. [7]- [11] are in accordance with this general suggestion. Figure 2 presents the influence of the coordination number n 0 on the permeability at the same porosity and variation of the parameter ϕ defined below.…”

“…This suggestion is confirmed by results of calculations performed with using Eqs. [7]- [11] and is presented in Fig. 1.…”

“…Another option in the use of Monte Carlo regards its combination with a nonstochastic approach, for example, thermodynamics (5). The Monte Carlo method is applicable to absolutely disordered systems, in which structural changes are possible with the same probability (6,7). In studies of percolation and permeability, the Monte Carlo method is, in most cases, combined with other methods like the percolation cluster approach.…”

Resistance Noise Near to Electrical Breakdown: Steady State of Random Networks as a Function of the Bias

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“…In particular, by focusing on electrical breakdown, a large attention has been devoted to the determination, by both theory 1-3 , 6,7,20 , 36-42 and experiments 1-3 , 13-18 of the critical exponents describing the resistance and the variance of resistance fluctuations in terms of the conducting particle (or defect) concentration 36,37 . In fact, it is well known that the study of the resistance fluctuations is a fundamental tool to extract information about the system stability 1-4 , 27-29 , [39][40][41][42][43][44][45][46][47][48] . In spite of the wide literature on the subject few attempts have been made so far 21,22 to describe the behavior of a disordered medium over the full range of the applied stress, i.e.…”