28 citations · 32 across the 10 of their papers we have counts for
12 papers
Riemann boundary value problem with piecewise constant matrix
Vladimir V. Mityushev
The vector-matrix Riemann boundary value problem for the unit disk with piecewise constant matrix is constructively solved by a method of functional equations. By functional equati…
Effective conductivity of a random suspension of highly conducting spherical particles
Vladimir Mityushev, Wojciech Nawalaniec
Randomly distributed non-overlapping perfectly conducting spheres are embedded in a conducting matrix with the concentration of inclusions . Jeffrey (1973) suggested an analytic…
Lattice sums for polyanalytic functions
Piotr Drygas, Vladimir Mityushev
In 1892, Lord Rayleigh estimated the effective conductivity of rectangular arrays of disks and proved, by means of the Eisenstein summation, that the lattice sum is equal to…
Exact and "exact" formulae in the theory of composites
Igor Andrianov, Vladimir Mityushev
The effective properties of composites and review literature on the methods of Rayleigh, Natanzon--Filshtinsky, functional equations and asymptotic approaches are outlined. In conn…
A relation on the effective conductivity of composites
Vladimir Mityushev
Consider a 2D composites with non-overlapping equal inclusions imbedded in a host material of the normalized unit conductivity. The conductivity of inclusions takes two values $σ_1…
Closed-form evaluation of 2D static lattice sums
Semyon Yakubovich, Piotr Drygas, Vladimir Mityushev
In the present paper, employing properties of the complete elliptic integrals of the first and second kind, we deduce closed-form formulae for the lattice sums and other new formul…
Pattern formations and optimal packing
Vladimir Mityushev
Patterns of different symmetries may arise after solution to reaction-diffusion equations. Hexagonal arrays, layers and their perturbations are observed in different models after n…
Effective Conductivity and Critical Properties of a Hexagonal Array of Superconducting Cylinders
Simon Gluzman, Vladimir Mityushev, Wojciech Nawalaniec +1
Effective conductivity of a 2D composite corresponding to the regular hexagonal arrangement of superconducting disks is expressed in the form of a long series in the volume fractio…
Composites with invisible inclusions: eigenvalues of R-linear problem
Vladimir Mityushev
An new eigenvalue -linear problem arisen in the theory of metamaterials is stated and constructively investigated for circular non-overlapping inclusions. An asymptotic…
Random composites and the generalized method of Schwarz I. Conductivity problems
Vladimir Mityushev
Two-phase composites with non-overlapping inclusions randomly embedded in matrix are investigated. A straight forward approach is applied to estimate the effective properties of ra…
Optimal packing of spheres in and extremal effective conductivity
Vladimir Mityushev
Optimal packing of spheres in is studied by optimization of the energy (effective conductivity) of composites with ideally conducting spherical inclusions. It is…
Series, Index and Threshold for Random 2D Composite
Simon Gluzman, Vladimir Mityushev
Effective conductivity of a 2D random composite is expressed in the form of long series in the volume fraction of ideally conducting disks. The problem of a {\it direct} reconstruc…