Morphology of Laplacian random walks
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
Accepted: 22 October 2010
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.
PACS: 62.20.M- – Structural failure of materials / 46.50.+a – Fracture mechanics, fatigue and cracks / 05.40.Fb – Random walks and Levy flights
© EPLA, 2010