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Possible connection between the optimal path and flow in percolation clusters.

Eduardo López1, Sergey V Buldyrev, Lidia A Braunstein

  • 1Center for Polymer Studies, Boston University, Boston, Massachusetts 02215, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2005
PubMed
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Researchers investigated optimal paths in disordered lattices. They found distinct behaviors compared to percolation clusters, but similarities emerge when optimal paths are confined within these clusters.

Area of Science:

  • Statistical physics
  • Complex systems

Background:

  • Optimal path problems are crucial in various scientific fields.
  • Understanding behavior in disordered systems is a key challenge.

Purpose of the Study:

  • To analyze the optimal path length distribution in a d-dimensional lattice under strong disorder.
  • To compare the universality class of optimal paths with that of flow in percolation clusters.

Main Methods:

  • Calculated the probability distribution of optimal path length (l opt).
  • Investigated scaling forms in 2D and 3D lattices.
  • Studied tracer path length (l tr) in percolation clusters.

Main Results:

  • Identified a power-law decay in optimal path length distribution for r << L.

Related Experiment Videos

  • Found that unconstrained optimal paths differ from percolation tracers.
  • Observed similar scaling properties when optimal paths are confined to percolation clusters.

    • Conclusions:

    • Optimal paths in strong disorder and percolation flow are not universally the same.
    • Confinement of optimal paths to percolation clusters reveals shared scaling behaviors.