Related papers: Effective conductivities of some multi-color, isot…
We present a tiling of more than 99.985698% of the Euclidean plane with six colors, reducing the previous record for uncovered fraction of the plane by about 12.8%. We also present a tiling of more than 95.99% of the plane with five colors.…
Surface conductance measurements on p-type doped germanium show a small but systematic change to the surface conductivity at different length scales. This effect is independent of the structure of the surface states. We interpret this…
Let $\cal T$ be a tiling of the plane with equilateral triangles no two of which share a side. We prove that if the side lengths of the triangles are bounded from below by a positive constant, then $\cal T$ is periodic and it consists of…
Recent experiments on amorphous materials have established the existence of surface states similar to those of crystalline three-dimensional topological insulators (TIs). Amorphous topological insulators are also independently of interest…
In this article we prove that, restricted to the row-constrained case, effective sets of colourings in the $2$-fold horocyclic tessellations of the hyperbolic plane $\mathbb{H}^2$ are sofic.
Positive bi-linear maps between matrix algebras play important roles to detect tri-partite entanglement by the duality between bi-linear maps and tri-tensor products. We exhibit indecomposable positive bi-linear maps between $2\times 2$…
A projective rectangle is like a projective plane that may have different lengths in two directions. We develop properties of the graph of lines, in which adjacency means having a common point, especially its strong regularity and clique…
The optical conductivity and the relevant electronic excitation processes are investigated in topologically-nontrivial MXenes, Mo$_2$HfC$_2$O$_2$ and W$_2$HfC$_2$O$_2$, utilizing first-principles calculation and effective model analysis.…
The viscosity and thermal conductivity of binary, ternary and quaternary mixtures of helium, neon, argon, and krypton at low density are computed for wide ranges of temperature and molar fractions, applying the Chapman-Enskog method. Ab…
Partially molten materials resist shearing and compaction. This resistance is described by a fourth-rank effective viscosity tensor. When the tensor is isotropic, two scalars determine the resistance: an effective shear and an effective…
We propose a model of transport in thick-film resistors which naturally explains the observed nonuniversal values of the conductance exponent t extracted in the vicinity of the percolation transition. Essential ingredients of the model are…
The quantum theory of conductivity of semiconductor objects, to which the quantum wells, wires and dots concern, is constructed. Average values of current and charge densities, induced by a weak electromagnetic field, are calculated. It is…
We obtained the analytical expression for the effective thermoelectric properties and dimensionless figure of merit of a composite with interfacial electrical and thermal resistances using a micromechanics-based homogenisation. For the…
In conductor-insulator nanocomposites in which conducting fillers are dispersed in an insulating matrix the electrical connectedness is established by interparticle tunneling or hopping processes. These systems are intrinsically…
In [B.Gruenbaum, G.C. Shephard, Spherical tilings with transitivity properties, in: The geometric vein, Springer, New York, 1981, pp. 65-98], they proved "for every spherical normal tiling by congruent tiles, if it is isohedral, then the…
A rigorous mathematical proof is given of a class of vector identities that provide a way to separate an arbitrary vector field (over a linear space) into the sum of a radial (i.e., pointing toward the radial unit vector) vector field,…
A thin conducting sheet - graphene, for example - transmits, absorbs, and reflects radiation. A sheet that is very thin, even vanishingly so, can still produce 50% absorption at normal incidence if it has conductivity corresponding to half…
Regular colored graphs are dual representations of pure colored D-dimensional complexes. These graphs can be classified with respect to an integer, their degree, much like maps are characterized by the genus. We analyse the structure of…
The periodic tiling conjecture asserts that if a region $\Sigma\subset \mathbb R^d$ tiles $\mathbb R^d$ by translations then it admits at least one fully periodic tiling. This conjecture is known to hold in $\mathbb R$, and recently it was…
Disordered hyperuniform dispersions are exotic amorphous two-phase materials characterized by an anomalous suppression of long-wavelength volume-fraction fluctuations, endowing them with novel physical properties. While such unusual…