Transport and Percolation Theory in Weighted Networks (original) (raw)
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Current Flow in Random Resistor Networks: The Role of Percolation in Weak and Strong Disorder
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Journal of Statistical Physics, 1994
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Anomalous Conductance and Diffusion in Complex Networks
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Physical Review B, 1986
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Physical Review Letters, 1984
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Investigation of the conductivity of random networks
Physica A: Statistical Mechanics and its Applications, 1999
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Scaling Law of Resistance Fluctuations in Stationary Random Resistor Networks
Physical Review Letters, 2000
In a random resistor network we consider the simultaneous evolution of two competing random processes consisting in breaking and recovering the elementary resistors with probabilities W D and W R . The condition W R . W D ͑͞1 1 W D ͒ leads to a stationary state, while in the opposite case, the broken resistor fraction reaches the percolation threshold p c . We study the resistance noise of this system under stationary conditions by Monte Carlo simulations. The variance of resistance fluctuations ͗dR 2 ͘ is found to follow a scaling law j p 2 p c j 2k0 with k 0 5.5. The proposed model relates quantitatively the defectiveness of a disordered media with its electrical and excess-noise characteristics. PACS numbers: 85.40.Qx, 05.40.Ca, 68.35.Rh, 72.70.+m Random resistor networks (RRN) have proven to be a useful model of electronic transport through disordered media . To this purpose, several percolation approaches have been applied to RRNs to investigate complex interactions where structural or electronic rearrangements modify the properties of the system under investigation. Examples include biological systems [2], electronic transport in composite materials , amorphous and crystalline semiconductors , or breakdown of electrical properties . Recently, degradation toward failure has been addressed successfully with standard and biased percolation models .
Journal de Physique Lettres, 1983
2014 Pour des barreaux de taille n x n x L, avec L ~ n et n ~ 18, nous calculons la conductivité d'un réseau aléatoire de conducteurs et d'isolants. Au seuil de percolation sur un réseau cubique simple, nos résultats Monte Carlo donnent une conductivité qui décroît comme n-2,1 quand la largeur n du barreau augmente pour la percolation de sites et celle de liens. Quand on tient compte des corrections au scaling avec un exposant de correction 03C9 d'ordre 1, notre meilleure estimation pour l'exposant t de la conductivité est t/v = 2,2 ± 0,1 à la fois pour le cas des liens et celui des sites. Ces résultats sont en accord avec la conjecture de Alexander-Orbach t/v ~ 2,26 pour l'exposant de la conductivité en dimension 3. Abstract. 2014 For very long bars of size n x n x L, with L ~ n, and n up to 18, we calculate the conductivity of a random network of resistors and insulators. At the percolation threshold in a simple cubic lattice our Monte Carlo data give a conductivity decreasing with bar diameter n as n-2.1 for site and bond percolation. Taking into account corrections to scaling with a correction exponent 03C9
Physical Review E, 2009
In this study we investigate electrical conduction in finite rectangular random resistor networks in quasione and two dimensions far away from the percolation threshold p c by the use of a bond percolation model. Various topologies such as parallel linear chains in one dimension, as well as square and triangular lattices in two dimensions, are compared as a function of the geometrical aspect ratio. In particular we propose a linear approximation for conduction in two-dimensional systems far from p c , which is useful for engineering purposes. We find that the same scaling function, which can be used for finite-size scaling of percolation thresholds, also applies to describe conduction away from p c . This is in contrast to the quasi-one-dimensional case, which is highly nonlinear. The qualitative analysis of the range within which the linear approximation is legitimate is given. A brief link to real applications is made by taking into account a statistical distribution of the resistors in the network. Our results are of potential interest in fields such as nanostructured or composite materials and sensing applications.