Microstructure of two‐phase random media. III. The n‐point matrix probability functions for fully penetrable spheres

1983 ◽  
Vol 79 (3) ◽  
pp. 1505-1510 ◽  
Author(s):  
S. Torquato ◽  
G. Stell
Keyword(s):  
Random Media ◽  
Two Phase ◽  
Probability Functions ◽  
Penetrable Spheres

scholarly journals Rock-soil slope stability analysis by two-phase random media and finite elements

2018 ◽  
Vol 9 (6) ◽  
pp. 1649-1655 ◽  
Author(s):  
Yong Liu ◽  
Huawen Xiao ◽  
Kai Yao ◽  
Jun Hu ◽  
Hong Wei
Keyword(s):  
Stability Analysis ◽  
Finite Elements ◽  
Slope Stability ◽  
Random Media ◽  
Slope Stability Analysis ◽  
Soil Slope ◽  
Two Phase

Necessary and sufficient conditions for the two-point phase probability function of two-phase random media

2008 ◽  
Vol 464 (2095) ◽  
pp. 1761-1779 ◽  
Author(s):  
John A Quintanilla
Keyword(s):  
Random Media ◽  
Probability Function ◽  
Recent Literature ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Condition ◽  
Two Phase ◽  
Decomposition Formula ◽  
Positive Matrices ◽  
Necessary And Sufficient

Constructing realizations of random media with a specified two-point phase probability function S 2 has attracted considerable attention in the recent literature. However, little is known about conditions under which a prescribed S 2 is realizable. The only known necessary and sufficient condition, due to McMillan, involves a class of square matrices, called corner-positive matrices, about which almost nothing is known except their definition. As a result, McMillan's theorem has gone mostly unused in the literature for over 50 years. In this paper, we present a general decomposition formula for corner-positive matrices, which allows McMillan's theorem to be written in a significantly more tractable and testable form. We also connect McMillan's theorem with many known but heretofore unrelated necessary conditions on S 2 , extending many of these conditions.

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