Random composite: stirred or shaken?

• Autorzy: Gluzman S. , Mityushev V. , Nawalaniec W. , Sokal G.
• Języki publikacji: EN

Abstrakty

EN

A James Bond’s (JB) catchphrase “shaken, not stirred" is explored for the problem of effective conductivity of composites. The superconductivity critical index s for the conductivity of random non-overlapping disks turns out to be distinctly different for shaking and stirring protocols. In the case of stirring modeled by random walks the formula s(τ) = 0.5 + 0.8 3√τ is deduced for evolution of the critical index with the normalized time 0 ≤ τ ≤ 1, which is proportional to the number of random walks and serving as the disorder measure. Strikingly, the coefficient 0.8 is very close to the critical index for shaking protocol and 0.5 is the critical index for regular lattices. The obtained formula for s is based on the analytical solution to the 2D conductivity problem of randomly distributed disks up to O(x19), where x denotes the concentration of inclusions and its extension to special 3D composites.

Słowa kluczowe

EN

effective conductivity of composites; superconductivity critical index; shaking and stirring protocols; random composites

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2016
• Tom: Vol. 68, nr 3
• Strony: 229--241
• Opis fizyczny: Bibliogr. 50 poz., rys.

Twórcy

autor

Gluzman S.

• Ekayna Vihara Bathurst 3000, Apt 606 Toronto ON, M6B 3B4, Canada

autor

Mityushev V.

• Department of Computer Sciences and Computer Methods Pedagogical University Podchorążych 2 30-084 Kraków, Poland

autor

Nawalaniec W.

• Department of Computer Sciences and Computer Methods Pedagogical University Podchorążych 2 30-084 Kraków, Poland

autor

Sokal G.

• Department of Computer Sciences and Computer Methods Pedagogical University Podchorążych 2 30-084 Kraków, Poland

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