Morphology of Laplacian random walks

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Published 26 November 2010 Europhysics Letters Association
, , Citation J. Ø. H. Bakke et al 2010 EPL 92 36004 DOI 10.1209/0295-5075/92/36004

0295-5075/92/3/36004

Abstract

Roughness of random walks in the presence of a Laplacian field is studied in two dimensions for various strengths of the field parametrized by η. We find an ηc∼4.5±0.3 at which a transition occurs from a tortuous fractal structure to a one-dimensional profile of the walk. At ηc, the walks are self-affine with a roughness exponent ζ=0.80±0.05. For increasing η-values, the roughness exponent increases.

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10.1209/0295-5075/92/36004