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Analytic study of a model of biased diffusion on a random comblike structure

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  • Pottier, N.

Abstract

An analytic study of a model of biased diffusion on a random comblike structure in which a bias field exists along the backbone is presented. The asymptotic behaviour at large time of the average probability of presence of the particle at its initial site is calculated directly in an exact manner. As for the particle position and dispersion, they are first computed in a periodized system of arbitrary period N. The corresponding quantities for the random system are then obtained by taking the limit N → ∞. The general features of the results strongly depend on the distribution of the lengths of the branches. While for an exponential distribution transport properties are normal, anomalous drift and diffusion may take place for a power law distribution when long branches are present with sufficiently high weights.

Suggested Citation

  • Pottier, N., 1994. "Analytic study of a model of biased diffusion on a random comblike structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 208(1), pages 91-123.
    • Handle: RePEc:eee:phsmap:v:208:y:1994:i:1:p:91-123
    DOI: 10.1016/0378-4371(94)90535-5
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    1. Aslangul, C. & Pottier, N. & Chvosta, P., 1994. "Analytic study of a model of diffusion on a random comblike structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 203(3), pages 533-565.
    2. Weiss, George H. & Havlin, Shlomo, 1986. "Some properties of a random walk on a comb structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 134(2), pages 474-482.
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    1. Kotak, Jesal D. & Barma, Mustansir, 2022. "Bias induced drift and trapping on random combs and the Bethe lattice: Fluctuation regime and first order phase transitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).

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