Conductivity of a periodic two-component system of rhombic type
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The conductivity and the distribution of electric field, current, and charge density in a periodic two-component system composed of rhombs with an arbitrary vertex angle of 2α are investigated. The effective conductivity of such a medium is represented by a tensor with components σ eff 11 (α) and σ eff 22 (α) in the principal axes that satisfy the Dykhne relation σ eff 11 (α) σ eff 22 (α)=σ 1σ2, where σ1, σ2 are the isotropic conductivities of media 1 and 2. In addition, the relation σ eff 22 (α)=σ eff 11 (π/2−α) is satisfied. The principal axes are directed along the diagonals of the rhombs. It is shown that there are three lines in the rectangle 0<α ≤π/2,−1<Z<1((Z=σ1−σ2)/(σ 1+σ2)) on which the charge density is expressed in terms elliptic functions. An explicit expression is obtained for all physical quantities on these lines.
KeywordsSpectroscopy State Physics Field Theory Elementary Particle Quantum Field Theory
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