Porosity and specific surface for interpenetrable‐sphere models of two‐phase random media

1985 ◽  
Vol 82 (2) ◽  
pp. 1014-1020 ◽  
Author(s):  
Per Arne Rikvold ◽  
George Stell
Keyword(s):  
Specific Surface ◽  
Random Media ◽  
Two Phase

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.

Effective equations of two-phase flow in random media

1995 ◽  
Vol 3 (3) ◽  
pp. 385-406 ◽  
Author(s):  
A. Bourgeat ◽  
S. M. Kozlov ◽  
A. Mikelić
Keyword(s):  
Random Media ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase

Effective equations of two-phase flow in random media

1995 ◽  
Vol 3 (3) ◽  
pp. 385-406 ◽  
Author(s):  
A. Bourgeat ◽  
S.M. Kozlov ◽  
A. Mikelic
Keyword(s):  
Random Media ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase

scholarly journals Photocatalytic activity of spectro-pure titanium dioxide: Effects of crystalline structure, specific surface area and sorption properties

2003 ◽  
Vol 5 (3) ◽  
pp. 159-166 ◽  
Author(s):  
Evgeny I. Kapinus ◽  
Tatyana A. Khalyavka ◽  
Valentina V. Shimanovskaya ◽  
Tatyana I. Viktorova ◽  
Vladimir V. Strelko
Keyword(s):  
Titanium Dioxide ◽  
Photocatalytic Activity ◽  
Specific Surface ◽  
Surface Area ◽  
Specific Surface Area ◽  
Pure Titanium ◽  
Specific Rate ◽  
Two Phase ◽  
Photocatalytic Reactions ◽  
Optically Pure

Dispersed optically pure anatase, rutile and two-phase samples of titanium dioxide were prepared using a sol-gel technique. In particle of two-phase samples, the anatase nuclei are surrounded by a rutile envelope. Content of anatase in the two-phase particles varied between 20 and 80%. Particles of all theTiO2samples had a globular shape of diameter between 10 and 30μm. When compared to the corresponding technical-grade samples, the optically pure anatase and rutile demonstrated higher photocatalytic activity in the destruction of tetradecylpyridinium chloride, Methylene Blue and tetrachlorofluorescein as well as in reduction ofCr2O7,MnO4,[Fe(CN)6]3−and[Fe(CN)6]4−. The photocatalytic reactions bring about the reduction of the inorganic anions to yield water insoluble substances and mineralization of the organic compounds. Rate constant of the all above processes do not depend on specific surface area ofTiO2and adsorption of the substrates on theTiO2samples. The rutile calcined at 1027K exhibits the highest specific rate constants. Exposure toγ-radiation increases photocatalytic activity of the dispersedTiO2. The influence ofTiO2and substrate on the photocatalytic reactions is caused by the influence of these factors on the formation of reactive electron hole pair and on the efficiency of the interfacial electron transfer.

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