Diffusion on random clusters and the parasite problem

S. Wilke; Y. Gefen; V. Ilkovic; A. Aharony; D. Stauffer

doi:10.1088/0305-4470/17/3/026

Diffusion on random clusters and the parasite problem

S. Wilke
, Y. Gefen
, V. Ilkovic
, A. Aharony
, D. Stauffer

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

In the parasite problem, a particle ('ant') diffuses randomly on a random percolation cluster in the limit of concentration to 0 ('lattice animal'). Monte Carlo simulations and scaling arguments show that for large animals the distance r travelled by this parasite increases as t(1/z_A) with time t. The authors find z_A approximately=3.4 on the simple cubic lattice and z_A approximately=2.6 on the square lattice. This anomalous diffusion is in rough agreement with a generalisation of a suggestion by Alexander and Orbach (1982). Heuristic arguments in favour of this suggestion are given. Also, they look at corrections to scaling for concentrations equal to the percolation threshold.

Original language	English
Pages (from-to)	647-656
Number of pages	10
Journal	Journal of Physics A: Mathematical and General
Volume	17
Issue number	3
DOIs	https://doi.org/10.1088/0305-4470/17/3/026
State	Published - 21 Feb 1984
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy

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10.1088/0305-4470/17/3/026

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abstract = "In the parasite problem, a particle ('ant') diffuses randomly on a random percolation cluster in the limit of concentration to 0 ('lattice animal'). Monte Carlo simulations and scaling arguments show that for large animals the distance r travelled by this parasite increases as t(1/zA) with time t. The authors find zA approximately=3.4 on the simple cubic lattice and zA approximately=2.6 on the square lattice. This anomalous diffusion is in rough agreement with a generalisation of a suggestion by Alexander and Orbach (1982). Heuristic arguments in favour of this suggestion are given. Also, they look at corrections to scaling for concentrations equal to the percolation threshold.",

author = "S. Wilke and Y. Gefen and V. Ilkovic and A. Aharony and D. Stauffer",

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AU - Wilke, S.

AU - Gefen, Y.

AU - Ilkovic, V.

AU - Aharony, A.

AU - Stauffer, D.

PY - 1984/2/21

Y1 - 1984/2/21

N2 - In the parasite problem, a particle ('ant') diffuses randomly on a random percolation cluster in the limit of concentration to 0 ('lattice animal'). Monte Carlo simulations and scaling arguments show that for large animals the distance r travelled by this parasite increases as t(1/zA) with time t. The authors find zA approximately=3.4 on the simple cubic lattice and zA approximately=2.6 on the square lattice. This anomalous diffusion is in rough agreement with a generalisation of a suggestion by Alexander and Orbach (1982). Heuristic arguments in favour of this suggestion are given. Also, they look at corrections to scaling for concentrations equal to the percolation threshold.

AB - In the parasite problem, a particle ('ant') diffuses randomly on a random percolation cluster in the limit of concentration to 0 ('lattice animal'). Monte Carlo simulations and scaling arguments show that for large animals the distance r travelled by this parasite increases as t(1/zA) with time t. The authors find zA approximately=3.4 on the simple cubic lattice and zA approximately=2.6 on the square lattice. This anomalous diffusion is in rough agreement with a generalisation of a suggestion by Alexander and Orbach (1982). Heuristic arguments in favour of this suggestion are given. Also, they look at corrections to scaling for concentrations equal to the percolation threshold.

UR - https://www.scopus.com/pages/publications/0009367246

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EP - 656

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 3

ER -

Diffusion on random clusters and the parasite problem

Abstract

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