The conductivity of the two component system of the chessboard type
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The effective conductivity of the sample with a chessboard structure is found. The corner points are singular for the electric field and charge density. The effective conductivity, charge density and electric potential are expressed in terms of a Weierstrass elliptic function. The results are valid for films and for cylindrical samples with the same cross-section structure. We confirm the conjecture of Dykhne about the value of the effective conductivity for the chessboard structure.
KeywordsSpectroscopy State Physics Field Theory Elementary Particle Quantum Field Theory
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- 1.A. M. Dykhne, Zh. Éksp. Teor. Fiz. 59, 110 (1970) [Sov. Phys. JETP 32, 63 (1971)].Google Scholar
- 2.A. L. Efros and B. I. Shklovskii, Phys. Status Solidi B 76, 475 (1976).Google Scholar
- 5.Yu. A. Drezin and A. M. Dykhne, Zh. Éksp. Teor. Fiz. 84, 1756 (1983) [Sov. Phys. JETP 57, 1024 (1983)].Google Scholar
- 6.I. M. Khalatnikov and A. Kamenshik, submitted to Zh. Éksp. Teor. Fiz. [submitted to JETP].Google Scholar
- 7.M. A. Lavrent’ev and B. V. Shabat, Methods of Theory of Function of Complex Variables (Fizmatgiz, Moscow, 1958).Google Scholar
- 8.Handbook of Mathematical Functions, Ed. by M. Abramowitz and I. A. Stegun (Dover, New York, 1971; Nauka, Moscow, 1979).Google Scholar
- 9.I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Nauka, Moscow, 1971; Academic, New York, 1980).Google Scholar