Random 2D Composites and the Generalized Method of Schwarz
Author
Source
Advances in Mathematical Physics
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-12-21
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
Two-phase composites with nonoverlapping inclusions randomly embedded in matrix are investigated.
A straightforward approach is applied to estimate the effective properties of random 2D composites.
First, deterministic boundary value problems are solved for all locations of inclusions, that is, for all events of the considered probabilistic space C by the generalized method of Schwarz.
Second, the effective properties are calculated in analytical form and averaged over C .
This method is related to the traditional method based on the average probabilistic values involving the n -point correlation functions.
However, we avoid computation of the correlation functions and compute their weighted moments of high orders by an indirect method which does not address the correlation functions.
The effective properties are exactly expressed through these moments.
It is proved that the generalized method of Schwarz converges for an arbitrary multiply connected doubly periodic domain and for an arbitrary contrast parameter.
The proposed method yields an algorithm which can be applied with symbolic computations.
The Torquato-Milton parameter ζ 1 is exactly written for circular inclusions.
American Psychological Association (APA)
Mityushev, Vladimir. 2015. Random 2D Composites and the Generalized Method of Schwarz. Advances in Mathematical Physics،Vol. 2015, no. 2015, pp.1-15.
https://search.emarefa.net/detail/BIM-1052990
Modern Language Association (MLA)
Mityushev, Vladimir. Random 2D Composites and the Generalized Method of Schwarz. Advances in Mathematical Physics No. 2015 (2015), pp.1-15.
https://search.emarefa.net/detail/BIM-1052990
American Medical Association (AMA)
Mityushev, Vladimir. Random 2D Composites and the Generalized Method of Schwarz. Advances in Mathematical Physics. 2015. Vol. 2015, no. 2015, pp.1-15.
https://search.emarefa.net/detail/BIM-1052990
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1052990