percolation$59044$ - ορισμός. Τι είναι το percolation$59044$
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Τι (ποιος) είναι percolation$59044$ - ορισμός

MATHEMATICAL THEORY CONCERNING THE BEHAVIOR OF CONNECTED CLUSTERS IN A RANDOM GRAPH
2D percolation cluster; 2D Percolation cluster; Percolative; Site percolation; Bond percolation
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  • Zoom in a critical percolation cluster (Click to animate)
  • Bond percolation in a square lattice from p=0.3 to p=0.52
  • A 3D tube network percolation determination

Percolation theory         
In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected clusters merge into significantly larger connected, so-called spanning clusters.
Percolation threshold         
  • (1+1)D Kagome Lattice
  • (1+1)D Square Lattice
  • (1+1)D Triangular Lattice
  • (2+1)D BCC Lattice
  • (2+1)D SC Lattice
  • 2D continuum percolation with disks
  • 2D continuum percolation with ellipses of aspect ratio 2
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  • 2-uniform lattice #37
  • Uniform tilings]], in which all polygons are regular and each vertex is surrounded by the same sequence of polygons. The notation "(3<sup>4</sup>, 6)", for example, means that every vertex is surrounded by four triangles and one hexagon. Some common names that have been given to these lattices are listed in the table below.
  • Example image caption
  • Delaunay triangulation
  • Example image caption
  • The Gabriel Graph, a subgraph of the Delaunay triangulation in which the circle surrounding each edge does not enclose any other points of the graph
  • Depiction of the non-planar Hanoi network HN-NP<ref name="ZiffBoettcherCook09"/>
  • Example image caption
  • Long-range bond percolation model. The lines represent the possible bonds with width decreasing as the connection probability decreases (left panel). An instance of the model together with the clusters generated (right panel).
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  • Example image caption
  • The Relative Neighborhood Graph (black lines)<ref name="Melchert13"/> superimposed on the Delaunay triangulation (black plus grey lines).
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  • Uniform Infinite Planar Triangulation, showing bond clusters.  From<ref name = "BernardiCurienMiermont17"/>
  • The Voronoi covering or line graph (dotted red lines) and the Voronoi diagram (black lines)
  • Voronoi diagram (solid lines) and its dual, the Delaunay triangulation (dotted lines), for a [[Poisson distribution]] of points
THRESHOLD OF PERCOLATION THEORY MODELS
Percolation thresholds; Thresholds in networks
The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in random systems. Below the threshold a giant connected component does not exist; while above it, there exists a giant component of the order of system size.
Percolation test         
MEASURE OF THE ABSORPTION RATE OF SOIL
Perk test; Percolation testing; Perc test
A percolation test (colloquially called a perc test) is a test to determine the water absorption rate of soil (that is, its capacity for percolation) in preparation for the building of a septic drain field (leach field) or infiltration basin. The results of a percolation test are required to properly design a septic system.

Βικιπαίδεια

Percolation theory

In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected clusters merge into significantly larger connected, so-called spanning clusters. The applications of percolation theory to materials science and in many other disciplines are discussed here and in the articles network theory and percolation.