Oriented Percolation Model
المؤلف:
Grimmett, G.
المصدر:
Percolation, 2nd ed. Berlin: Springer-Verlag, 1999.
الجزء والصفحة:
...
15-5-2022
1989
Oriented Percolation Model
A 
-dimensional discrete percolation model on a regular point lattice 
is said to be oriented if 
is an oriented lattice. One common such model takes place on the so-called north-east oriented lattice 
obtained by orienting each edge of an arbitrary (perhaps unoriented) point lattice 
in the direction of increasing coordinate-value.
The above figure shows an example of a subset of a 2-dimensional oriented percolation model on the north-east lattice. Here, each edge has been deleted with probability 
for some 
, independently of all other edges.
Oriented percolation models are especially common in several areas of physics including astrophysics, solid state physics, and particle physics. Worth noting is that, while obvious parallels exist between oriented and unoriented percolation models, the proofs of results in the presence of orientation offer differ greatly from those of their unoriented analogues; indeed, the existence of so-called "one-way streets" restricts the degree of spatial freedom possessed by the flowing fluid (Grimmett 1999).
REFERENCES
Grimmett, G. Percolation, 2nd ed. Berlin: Springer-Verlag, 1999.
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