Optimal Path in Strong Disorder and Shortest Path in Invasion Percolation with Trapping

Markus Porto; Shlomo Havlin; Stefan Schwarzer; Armin Bunde

doi:10.1103/PhysRevLett.79.4060

Optimal Path in Strong Disorder and Shortest Path in Invasion Percolation with Trapping

Markus Porto, Shlomo Havlin, Stefan Schwarzer, and Armin Bunde

Phys. Rev. Lett. 79, 4060 – Published 24 November 1997

Abstract

We present analytical and numerical results suggesting that the optimal path in an energy landscape in the strong disorder limit is in the universality class of the shortest path in invasion percolation with trapping. Our results imply that, in contrast to common belief, invasion percolation with trapping and regular percolation in $d = 3$ are in different universality classes.

Received 17 July 1997

DOI:https://doi.org/10.1103/PhysRevLett.79.4060

Authors & Affiliations

Markus Porto^1,2, Shlomo Havlin^1,2, Stefan Schwarzer³, and Armin Bunde¹

¹Institut für Theoretische Physik III, Justus-Liebig-Universität Giessen, Heinrich-Buff-Ring 16, 35392 Giessen, Germany
²Minerva Center and Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel
³Institut für Computeranwendungen 1, Universität Stuttgart, 70569 Stuttgart, Germany