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Introduction
Publications
Publications (40)
Motivated by a wonderful paper [7] where a powerful method was introduced, we prove a criterion for a vector α∈Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec...
We have found analytical expressions (polynomials) of the percolation probability for site percolation on a square lattice of size $L \times L$ sites when considering a plane (the crossing probability in a given direction), a cylinder (spanning probability), and a torus (wrapping probability along one direction). Since some polynomials are extremel...
We have found analytical expressions (polynomials) of the percolation probability for site percolation on a square lattice of size $L \times L$ sites when considering a plane (the crossing probability in a given direction), a cylinder (spanning probability), and a torus (wrapping probability along one direction). Since some polynomials are extremel...
We found analytical expressions (polynomial) of percolation probability for site percolation on a square lattice of size L × L sites considering a torus (wrapping probability along one direction). The system size is L = 12. To obtain a percolation probability polynomial, all possible combination of occupied and empty sites have to be accounted. We...
We found analytical expressions (polynomials) of percolation probability for site percolation on a square lattice of size L × L sites considering a torus (wrapping probability along one direction). The system size varied up to L = 11. To obtain a percolation probability polynomial, all possible combination of occupied and empty sites have to be acc...
We have found analytical expressions (polynomials) of the percolation probability for site percolation on a square lattice of size L × L sites when considering a cylinder (spanning probability). The system sizes for which this was feasible varied up to L = 16. To obtain a percolation probability polynomial, all possible combinations of occupied and...
We have found analytical expressions (polynomials) of the percolation probability for site percolation on a square lattice of size × sites when considering a plane (the crossing probability in a given direction), a cylinder (spanning probability), and a torus (wrapping probability along one direction). The system sizes for which this was feasible v...
We prove a result related to Dirichlet spectrum for simultaneous approximation to two real numbers in Euclidean norm and badly or very well approximability.
We mimic random nanowire networks by the homogeneous, isotropic, and random deposition of conductive zero-width sticks onto an insulating substrate. The number density (the number of objects per unit area of the surface) of these sticks is supposed to exceed the percolation threshold, i.e., the system under consideration is a conductor. To identify...
Connectedness percolation phenomena in the two-dimensional packing of elongated particles (discorectangles) were studied numerically. The packings were produced using random sequential adsorption off-lattice models with preferential orientations of the particles along a given direction. The partial ordering was characterized by the order parameter...
We mimic nanorod-based transparent electrodes as random resistor networks produced by the homogeneous, isotropic, and random deposition of conductive zero-width sticks onto an insulating substrate. The number density (the number of objects per unit area of the surface) of these sticks is supposed to exceed the percolation threshold, i.e., the syste...
We have proposed and implemented a modification of the well-known wall follower algorithm to identify a backbone (a current-carrying part) of the percolation cluster. The advantage of the modified algorithm is identification of the whole backbone without visiting all edges. The algorithm has been applied to backbone identification in networks produ...
We have proposed and implemented a modification of the well-known wall follower algorithm to identify a backbone (a current-carrying part) of the percolation cluster. The advantage of the modified algorithm is identification of the whole backbone without visiting all edges. The algorithm has been applied to backbone identification in networks produ...
We consider $N$ circles of equal radii, $r$, having their centers randomly placed within a square domain $\mathcal{D}$ of size $L \times L$ with periodic boundary conditions ($\mathcal{D} \in \mathbb{R}^2$). When two or more circles intersect each other, each circle is divided by the intersection points into several arcs. We found the exact length...
Motivated by a wonderful paper by Ngoc Ai Van Nguyen, Anthony Po\"els and Damien Roy, where a powerful method was introduced, we prove a criterion for a vector $\pmb{\alpha}\in \mathbb{R}^d$ to be a badly approximable vector. Moreover we construct certain examples which show that a more general version of our criterion is not valid.
We have studied the electrical conductivity of two-dimensional nanowire networks. An analytical evaluation of the contribution of tunneling to their electrical conductivity suggests that it is proportional to the square of the wire concentration. Using computer simulation, three kinds of resistance were taken into account, viz., (i) the resistance...
We have studied the electrical conductivity of two-dimensional nanowire networks. An analytical evaluation of the contribution of tunneling to their electrical conductivity suggests that it is proportional to the square of the wire concentration. Using computer simulation, three kinds of resistance were taken into account, viz., (i) the resistance...
We consider $N$ circles of equal radii, $r$, having their centers randomly placed within a square domain $\mathcal{D}$ of size $L \times L$ with periodic boundary conditions ($\mathcal{D} \in \mathbb{R}^2$). When two or more circles intersect each other, each circle is divided by the intersection points into several arcs. We found the exact length...
Using Monte Carlo simulation, we studied the electrical conductance of two-dimensional films. The films consisted of a poorly conductive host matrix and highly conductive rodlike fillers (rods). The rods were of various lengths, obeying a log-normal distribution. They were allowed to be aligned along a given direction. The impacts of the length dis...
Using Monte Carlo simulation, we studied the electrical conductance of two-dimensional films. The films consisted of a poorly conductive host matrix and highly conductive rodlike fillers (rods). The rods were of various lengths, obeying a log-normal distribution. They were allowed to be aligned along a given direction. The impacts of length dispers...
Numerical simulations by means of the Monte Carlo method have been performed to study the electrical properties of a two-dimensional composite filled with rodlike particles. The main goal was to study the effect of the alignment of such rods on the anisotropy of its electrical conductivity. A continuous model was used. In this model, the rods have...
Numerical simulations by means of the Monte Carlo method have been performed to study the electrical properties of a two-dimensional composite filled with rodlike particles. The main goal was to study the effect of the alignment of such rods on the anisotropy of its electrical conductivity. A continuous model was used. In this model, the rods have...
We define two-dimensional Dirichlet spectrum (with respect to Euclidean norm)
as
D_2=\lambda\in\mathbf{R} | \exists \mathbf{v}=(v_1,v_2)\in \mathbf {R}^2:
\limsup\limits_{t\rightarrow\infty} {t\cdot\psi_{v}^2(t)}=\lambda, where
\psi_{v}(t)=\min\limits_{1\leqslant q\leqslant t}\sqrt{|q v_1|^2+|q v_2|^2} is
the two-dimensional "irrationality measure...
We prove the existence of a family of vectors with continuum many elements v is an element of R-s admitting infinitely many simultaneous (phi(p)/p(1/s))(1 + B . phi(1+ 1/s) (p))-approximations and admitting no simultaneous (phi(p)/p(1/s))(1 - B . phi(1+1/s)(p))-approximation. We prove that for 0 < t <= T the closed interval [t, t(1 + 16B . t(1+1/s)...
We prove the existence of real numbers badly approximated by rational fractions whose denominators form a sublacunar sequence. For example, for the ascending sequence s(n), n = 1, 2, 3,..., generated by the ordered numbers of the form 2(i)3(j), i, j = 1, 2, 3,..., we prove that the set of real numbers a such that inf(n is an element of N) n paralle...
New quantitative results on the intersection of winning sets and the Hausdorff dimension of this intersection are obtained. An application to the problem on fractional parts of the sequence
{ 2n 3m a}\{ 2^n 3^m \alpha \}
is given.
In the reference work of I. Ruzsa, Zs. Tuza, M. Voigt it was proved that χd=supχ(CR(D)) is a finite number (χ(CR(D)) - graph's chromatic number) and the estimates are obtained: d≤χd≤exp(γd) (1), were γ - some positive constant. Now it is proved that at d≥3 valid are the following inequalities: d≤χd≤27·d2. Thus the exponential estimate superior (1)...
Projects
Projects (2)
The current interest in the study of the 2D systems of randomly deposited metallic nanowires is inspired by a combination of their high electrical conductivity with excellent optical transparency. Another kind of the transparent electrodes is junction-free networks, e.g., crack-template-based.
Transparent electrodes show great potential for use in numerous technological applications.
The electrical conductivity of a monolayer produced by the random sequential adsorption (RSA) of linear k-mers (particles occupying k adjacent adsorption sites) onto a square lattice is studied by means of computer simulation. Some defects or impurities may be imbedded in the substrate, i.e. a fraction of lattice sites may be forbidden for deposition. In our study, electrical properties may vary along k-mers, i.e. some sites of k-mers may be nonconducting or conducting.
