Related papers: Effective conductivities of some multi-color, isot…
In the work, a modified effective medium theory is constructed for calculating the effective properties of thermoelectric composites with different values of percolation thresholds. It is shown that even at concentrations beyond the…
The effective conductivity of the infinite checkerboard (chessboard) and analogous higher-dimensional checkered structures, are considered. An algebraic expression is derived by accounting for the symmetries of the structures.
We determine the effective conductivity of a two-dimensional composite consisting of a doubly periodic array of identical circular cylinders within a homogeneous matrix. We obtain an exact analytic expression for the effective conductivity…
A tessellation or tiling is a collection of sets, called tiles, that cover a plane without gaps and overlaps. The present note is an invitation to get to know the beauty and majesty of tessellations and triangulation of orientable surfaces.
The perturbation theory for calculation of the effective conductivity of the plane consisting of pieces of different conductivities is constructed and the convenient diagram technique for this perturbation theory is elaborated. It is shown…
In the framework of the perturbation theory an expression suitable for calculation of the effective conductivity of 3-D inhomogeneous metals is derived. Formally, the final expression is an exact result, however, a function written as a…
A method is presented for approximating the effective conductivity of composite media with thin interphase regions, which is exact to first order in the interphase thickness. The approximations are computationally efficient in the sense the…
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 $\sigma_1$ and $\sigma_2$ with the probabilities $p$ and $1-p$,…
The electrical conductivity is calculated for regular inhomogeneous two component isotropic medium in which droplets of one phase with conductivity sigma_2 are embedded in another, with conductivity sigma_1. An expression is formulated…
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 fraction of ideally conducting disks. According to our calculations…
Connections are found between the two-component percolation problem and the conductor/insulator percolation problem. These produce relations between critical exponents, and suggest formulae connecting the conductivity exponents in different…
Assemblies of circular inclusions with spiraling laminate structure inside them are studied, such as spirals with inner inclusions, spirals with shells, assemblies of "wheels" - structures from laminates with radially dependent volume…
The finite-size scaling behaviour for percolation and conduction is studied in two-dimensional triangular-shaped random resistor networks at the percolation threshold. The numerical simulations are performed using an efficient star-triangle…
We consider the dynamics of light rays in the trihexagonal tiling where triangles and hexagons are transparent and have equal but opposite indices of refraction. We find that almost every ray of light is dense in a region of a particular…
A first step in investigating colour symmetries of periodic and nonperiodic patterns is determining the number of colours which allow perfect colourings of the pattern under consideration. A perfect colouring is one where each symmetry of…
It has been common knowledge since 1950 that seven colours can be assigned to tiles of an infinite honeycomb with cells of unit diameter such that no two tiles of the same colour are closer than $d(7)=\frac{\sqrt{7}}{2}$ apart. Various…
The heterogeneity of composite leads to the extra charge concentration at the boundaries of different phases that results essentially nonzero effective electric susceptability. The relation between tensors of effective electric…
An integral equation based scheme is presented for the fast and accurate computation of effective conductivities of two-component checkerboard-like composites with complicated unit cells at very high contrast ratios. The scheme extends…
This paper deals with iteration stable (STIT) tessellations, and, more generally, with a certain class of tessellations that are infinitely divisible with respect to iteration. They form a new, rich and flexible class of spatio-temporal…
A new Sesame-type table for the electrical conductivity of aluminum is described. The table is based on density functional theory calculations and ranges from 0.001 to 1 times solid density (2.7 g/cm^3 ), and from 0.01 to 1000 eV in…