Optimal paths in disordered media: Scaling of the crossover from self-similar to self-affine behavior

Markus Porto, Nehemia Schwartz, Shlomo Havlin, Armin Bunde

Research output: Contribution to journalArticlepeer-review

46 Scopus citations

Abstract

We study optimal paths in disordered energy landscapes using energy distributions of the type [Formula Presented] that lead to the strong disorder limit. If we truncate the distribution, so that [Formula Presented] only for [Formula Presented] and [Formula Presented] otherwise, we obtain a crossover from self-similar (strong disorder) to self-affine (moderate disorder) behavior at a path length [Formula Presented] We find that [Formula Presented] where the exponent [Formula Presented] has the value [Formula Presented] both in [Formula Presented] and [Formula Presented] We show how the crossover can be understood from the distribution of local energies on the optimal paths.

Original languageEnglish
Pages (from-to)R2448-R2451
JournalPhysical Review E
Volume60
Issue number3
DOIs
StatePublished - Sep 1999

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