Abstract
The percolation properties of random networks containing resistors (two-way streets) and/or diodes (one-way streets) are considered. The directionality constraints of the diodes are found to lead to novel geometrical behavior. As a simple example, various random cluster models with a preferred direction, such as directed random walks or directed lattice animals, are shown to be anisotropic in character. The critical behavior of directed percolation is then treated and its connection with branching Markov processes is explained. A closely related "reverse" percolation problem, a transition from one-way percolation to isotropic percolation, is introduced. Finally, the geometrical properties of a network containing arbitrarily oriented diodes are treated. Symmetry and duality arguments are applied to yield exact results for certain aspects of its critical behavior.
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Redner, S. (1983). Directionality effects in percolation. In: Hughes, B.D., Ninham, B.W. (eds) The Mathematics and Physics of Disordered Media: Percolation, Random Walk, Modeling, and Simulation. Lecture Notes in Mathematics, vol 1035. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073262
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DOI: https://doi.org/10.1007/BFb0073262
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