20 citations · 77 across the 11 of their papers we have counts for
11 papers
Exact percolation probabilities for a square lattice: Site percolation on a plane, cylinder, and torus
Renat K. Akhunzhanov, Andrei V. Eserkepov, Yuri Yu. Tarasevich
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…
A note on Dirichlet spectrum
Renat K. Akhunzhanov, Nikolay G. Moshchevitin
We prove a result related to Dirichlet spectrum for simultaneous approximation to two real numbers in Euclidean norm and badly or very well approximability.
Random nanowire networks: Identification of a current-carrying subset of wires using a modified wall follower algorithm
Yuri Yu. Tarasevich, Andrei V. Eserkepov, Renat K. Akhunzhanov +1
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…
Connectedness percolation in the random sequential adsorption packings of elongated particles
Nikolai I. Lebovka, Mykhailo O. Tatochenko, Nikolai V. Vygornitskii +3
Connectedness percolation phenomena in two-dimensional packings of elongated particles (discorectangles) were studied numerically. The packings were produced using random sequentia…
Identification of a current-carrying subset of a percolation cluster using a modified wall follower algorithm
Renat K. Akhunzhanov, Andrei V. Eserkepov, Yuri Yu. Tarasevich
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…
On badly approximable numbers
Renat Akhunzhanov, Nikolay Moshchevitin
Motivated by a wonderful paper by Ngoc Ai Van Nguyen, Anthony Poëls and Damien Roy, where a powerful method was introduced, we prove a criterion for a vector $\pmbα\in \mathbb{R}^d…
Effect of tunneling on the electrical conductivity of nanowire-based films: computer simulation within a core--shell model
Irina V. Vodolazskaya, Andrei V. Eserkepov, Renat K. Akhunzhanov +1
We have studied the electrical conductivity of two-dimensional nanowire networks. An analytical evaluation of the contribution of tunneling to their electrical conductivity suggest…
Circles of equal radii randomly placed on a plane: some rigorous results, asymptotic behavior, and application to transparent electrodes
Renat K. Akhunzhanov, Yuri Yu. Tarasevich, Irina V. Vodolazskaya
We consider circles of equal radii, , having their centers randomly placed within a square domain of size with periodic boundary conditions ($\mat…
Electrical conductance of two-dimensional composites with embedded rodlike fillers: an analytical consideration and comparison of two computational approaches
Yuri Yu. Tarasevich, Irina V. Vodolazskaya, Andrei V. Eserkepov +1
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 f…
Anisotropy in electrical conductivity and transparency of films of aligned conducting rods
Nikolai I. Lebovka, Yuri Yu. Tarasevich, Nikolai V. Vygornitskii +2
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 ma…
On two-dimensional Dirichlet spectrum
Renat Akhunzhanov, Denis Shatskov
We define two-dimensional Dirichlet spectrum (with respect to Euclidean norm) as D_2=λ\in\mathbf{R} | \exists \mathbf{v}=(v_1,v_2)\in \mathbf {R}^2: \limsup\limits_{t\rightarrow\in…