Morphology of Laplacian random walks

¹ Department of Physics, Norwegian University of Science and Technology - N-7496 Trondheim, Norway
² Schlumberger Stavanger Research - N-4068 Stavanger, Norway
³ Institute of Mathematical Sciences - Chennai 600 113, India

^a alex.hansen@ntnu.no

Received: 12 April 2010
Accepted: 22 October 2010

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 η_c∼4.5±0.3 at which a transition occurs from a tortuous fractal structure to a one-dimensional profile of the walk. At η_c, the walks are self-affine with a roughness exponent ζ = 0.80±0.05. For increasing η-values, the roughness exponent increases.