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Related Experiment Videos

Resistance distribution in the hopping percolation model.

Yakov M Strelniker1, Shlomo Havlin, Richard Berkovits

  • 1Minerva Center, Jack and Pearl Resnick Institute of Advanced Technology, and Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
Summary

We analyzed effective resistance in disordered resistor networks. The distribution of resistance follows a log-normal function, depending on disorder strength and network size.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Network Science

Background:

  • Random resistor networks are crucial for understanding conductivity in disordered materials.
  • Percolation models describe the formation of conducting paths in such systems.
  • Disorder in bond conductivity significantly impacts network properties.

Purpose of the Study:

  • To investigate the distribution function of effective resistance in 2D and 3D random resistor networks.
  • To analyze the behavior of resistance distribution under varying degrees of disorder.
  • To determine the functional form and scaling of the resistance distribution.

Main Methods:

  • Simulating random resistor networks with bond conductivity following an exponential distribution.
  • Analyzing the distribution function P(rho) of effective resistance (rho).

Related Experiment Videos

  • Examining networks in both strong-disorder (L/kappa(nu) > 1) and extreme-disorder (L/kappa(nu) < 1) regimes.

    • Main Results:

    • The distribution function P(rho) depends only on the ratio L/kappa(nu), a measure of disorder relative to network size.
    • P(rho) can be accurately approximated by a log-normal distribution.
    • The dispersion of the log-normal distribution is proportional to kappa(nu)/L.

    Conclusions:

    • The effective resistance distribution in disordered resistor networks is robust across different disorder regimes.
    • A log-normal distribution provides a universal description for resistance distribution, dependent on disorder and size.
    • The findings offer insights into the statistical properties of conductivity in complex disordered systems.