arXiv subjects

Yuri Yu. Tarasevich

Publications and source records attributed to Yuri Yu. Tarasevich.

At least 37 records · Page 2Linked to original sources

arXiv2022

Exact percolation probabilities for a square lattice: Site percolation on a plane, cylinder, and torus

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 extremely cumbersome, they are presented as separate files in Supplemental material. The system sizes for which this was feasible varied up to $L=17$ for a plane, up to $L=16$ for a cylinder, and up to $L=12$ for a torus. To obtain a percolation probability polynomial, all possible combinations of occupied and empty sites have to be taken into account. However, using dynamic programming along with some ideas related to the topology, we offer an algorithm which allows a significant reduction in the number of configurations requiring consideration. A rigorous formal description of the algorithm is presented. Divisibility properties of the polynomials have been rigorously proved. Reliability of the polynomials obtained have been confirmed by the divisibility tests. The wrapping probability polynomials on a torus provide a better estimate of the percolation threshold than that from the spanning probability polynomials. Surprisingly, even a naive finite size scaling analysis allows an estimate to be obtained of the percolation threshold $p_c = 0.59269$.

cond-mat.stat-mech↗

arXiv2022

Electrical conductivity of random metallic nanowire networks: An analytical consideration along with computer simulation

We have proposed an analytical model for the electrical conductivity in random, metallic, nanowire networks. We have mimicked such random nanowire networks as random resistor networks (RRN) produced by the homogeneous, isotropic, and random deposition of conductive zero-width sticks onto an insulating substrate. We studied the electrical conductivity of these RRNs using a mean-field approximation. An analytical dependency of the electrical conductivity on the main physical parameters (the number density and electrical resistances of these wires and of the junctions between them) has been derived. Computer simulations have been performed to validate our theoretical predictions. We computed the electrical conductivity of the RRNs against the number density of the conductive fillers for the junction-resistance-dominated case and for the case where the wire resistance and the junction resistance were equal. The results of the computations were compared with this mean-field approximation. Our computations demonstrated that our analytical expression correctly predicts the electrical conductivity across a wide range of number densities.

cond-mat.stat-mech↗

arXiv2021

Electrical conductivity of nanoring-based transparent conductive films: A mean-field approach

We have studied the electrical conductivity of nanoring-based, transparent conductive films, these being promising elements for flexible electronic devices. Both the wire resistance and the junction resistance were taken into account. We have calculated the dependency of the electrical conductivity on the number density of the rings. We have proposed a mean-field approach to estimate the dependency of the electrical conductivity on the main parameters. Comparison of direct computations of the electrical conductivity and the estimates provided by the mean-field approach evidenced the applicability of this approach for those cases where the wire resistance dominates over the junction resistance and where both resistances are of the same order. For these two cases, both the direct computations and the mean-field approach evidenced a linear dependence of the electrical conductivity of the films on the number density of the conductive rings. By contrast, the dependence of the electrical conductivity on the number density of the conductive rings is a quadratic when the junction resistance dominates over the wire resistance. In this case, the mean-field approach significantly overestimates the electrical conductivity, since the main assumptions underlying this approach are no longer fulfilled.

cond-mat.stat-mech↗

arXiv2021

Electrical conductivity of nanorod-based transparent electrodes: Comparison of mean-field approaches

We mimic nanorod-based transparent electrodes as random resistor networks (RRN) produced by the homogeneous, isotropic, and random deposition of conductive zero-width sticks onto an insulating substrate. We suppose that the number density (the number of objects per unit area of the surface) of these sticks exceeds the percolation threshold, i.e., the system under consideration is a conductor. We computed the electrical conductivity of random resistor networks vs the number density of conductive fillers for the wire-resistance-dominated case, for the junction-resistance-dominated case, and for an intermediate case. We also offer a consistent continuous variant of the mean-field approach. The results of the RRN computations were compared with this mean-field approach. Our computations suggest that, for a qualitative description of the behavior of the electrical conductivity in relation to the number density of conductive wires, the mean-field approximation can be successfully applied when the number density of the fillers $n > 2n_c$, where $n_c$ is the percolation threshold. However, note the mean-field approach slightly overestimates the electrical conductivity. We demonstrate that this overestimate is caused by the junction potential distribution.

cond-mat.dis-nn↗

arXiv2021

Relaxation of saturated random sequential adsorption packings of discorectangles aligned on a line

Relaxation of the packing of elongated particles (discorectangles) aligned on a line was studied numerically. The aspect ratio (length-to-width ratio) for the discorectangles was varied within the range $\varepsilon \in [1;50]$. The initial jamming (saturated) state was produced using the basic variant of the random sequential adsorption (RSA) model with random positions and orientations of particles. The relaxation was performed by allowing rotational and translational diffusion motions of the particles wile their centers remained located on the line. The effects of the aspect ratio $\varepsilon$ on the kinetics of relaxation, the orientation order parameter and the distribution function of the distances between nearest-neighbor discorectangles were analyzed. The transport properties of the resulting 1D systems were also analyzed by using the diffusion of a tracer particle (random walker) between the nearest-neighbor discorectangles. In the relaxed states the anomalous diffusion was observed having a hopping exponent $d_w>2$ dependent upon $\varepsilon$.

cond-mat.stat-mech↗

arXiv2021

Confinement effects on the random sequential adsorption packings of elongated particles in a slit

The behavior of a system of two-dimensional elongated particles (discorectangles) packed into a slit between two parallel walls was analyzed using a simulation approach. The packings were produced using the random sequential adsorption model with continuous positional and orientational degrees of freedom. The aspect ratio (length-to-width ratio, $\varepsilon=l/d$) of the particles was varied within the range $\varepsilon \in [1;32]$ while the distance between the walls was varied within the range $h/d\in [1;80]$. The properties of the deposits when in the jammed state (the coverage, the order parameter, and the long-range (percolation) connectivity between particles) were studied numerically. The values of $\varepsilon$ and $h$ significantly affected the structure of the packings and the percolation connectivity. In particular, the observed nontrivial dependencies of the jamming coverage $φ(\varepsilon)$ or $φ(h)$ were explained by the interplay of the different geometrical factors related to confinement, particle orientation degrees of freedom and excluded volume effects.

cond-mat.soft↗

arXiv2021

Random nanowire networks: Identification of a current-carrying subset of wires using a modified wall follower algorithm

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 any current-carrying part (the backbone) of the percolation cluster, we have proposed and implemented a modification of the well-known wall follower algorithm -- one type of maze solving algorithm. The advantage of the modified algorithm is its identification of the whole backbone without visiting all the edges. The complexity of the algorithm depends significantly on the structure of the graph and varies from $O\left(\sqrt{N_\text{V}}\right)$ to $Θ(N_\text{V})$. The algorithm has been applied to backbone identification in networks with different number densities of conducting sticks. We have found that (i) for number densities of sticks above the percolation threshold, the strength of the percolation cluster quickly approaches unity as the number density of the sticks increases; (ii) simultaneously, the percolation cluster becomes identical to its backbone plus simplest dead ends, i.e., edges that are incident to vertices of degree 1. This behavior is consistent with the presented analytical evaluations.

cond-mat.stat-mech↗

arXiv2021

Connectedness percolation in the random sequential adsorption packings of elongated particles

Connectedness percolation phenomena in two-dimensional packings of elongated particles (discorectangles) were studied numerically. The packings were produced using random sequential adsorption (RSA) off-lattice model with preferential orientations of particles along a given direction. The partial ordering was characterized by order parameter $S$, with $S=0$ for completely disordered films (random orientation of particles) and $S=1$ for completely aligned particles along the horizontal direction $x$. The aspect ratio (length-to-width ratio) for the particles was varied within the range $\varepsilon \in [1;100]$. Analysis of connectivity was performed assuming a core-shell structure of particles. The value of $S$ affected the structure of packings, formation of long-range connectivity and electrical conductivity behavior. The effects were explained accounting for the competition between the particles' orientational degrees of freedom and the excluded volume effects. For aligned deposition, the anisotropy in electrical conductivity was observed and the values along alignment direction, $σ_x$, were larger than the values in perpendicular direction, $σ_y$. The anisotropy in localization of percolation threshold was also observed in finite sized packings, but it disappeared in the limit of infinitely large systems.

cond-mat.dis-nn↗

arXiv2020

Identification of a current-carrying subset of a percolation cluster using a modified wall follower algorithm

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 produced by random deposition of conductive sticks onto an insulating substrate. We have found that (i) for concentrations of sticks above the percolation threshold, the strength of the percolating cluster quickly approaches unity; (ii) simultaneously, the percolation cluster is identical to its backbone plus simplest dead ends, i.e., edges that are incident to vertices of unit degree.

cond-mat.dis-nn↗

arXiv2020

Characterization of domain formation during random sequential adsorption of stiff linear $k$-mers onto a square lattice

Using computer simulation, we have studied the random sequential adsorption of stiff linear $k$-mers onto a square lattice. Each such particle occupies $k$ adjacent lattice sites. During deposition, the two mutually perpendicular orientations of the particles are equiprobable, hence, a macroscopically isotropic monolayer is formed. However, this monolayer is locally anisotropic, since the deposited particles tend to form domains of particles with the same orientation. Using the "excluded area" concept, we have classified lattice sites into several types and examined how the fraction of each type of lattice site varies as the number of deposited particles increases. The behaviors of these quantities have allowed us to identify the following stages of domain formation (i) the emergence of domain seeds; (ii) the filling of domains; (iii) densification of the domains.

cond-mat.stat-mech↗

arXiv2020

"Paris car parking problem" for partially ordered discorectangles on a line

The random sequential adsorption (RSA) of identical elongated particles (discorectangles) on a line ("Paris car parking problem") was studied numerically. An off-lattice model with continuous positional and orientational degrees of freedom was considered. The possible orientations of the discorectanles were restricted between $θ\in [-θ_\text{m}; θ_\text{m}]$ while the aspect ratio (length-to-width ratio) for the discorectangles was varied within the range $\varepsilon \in [1;100]$. Additionally, the limiting case $\varepsilon=\infty$ (i.e., widthless sticks) was considered. We observed, that the RSA deposition for the problem under consideration was governed by the formation of rarefied holes (containing particles oriented along a line) surrounded by comparatively dense stacks (filled with almost parallel particles oriented in the vertical direction). The kinetics of the changes of the order parameter, and the packing density are discussed. Partial ordering of the discorectangles significantly affected the packing density at the jamming state, $φ_\text{j}$, and shifted the cusps in the $φ_\text{j}(\varepsilon)$ dependencies. This can be explained by the effects on the competition between the particles' orientational degrees of freedom and the excluded volume effects.

cond-mat.dis-nn↗

arXiv2020

Random sequential adsorption of partially ordered discorectangles onto a continuous plane

Computer simulation was used to study the random sequential adsorption of identical discorectangles onto a continuous plane . The problem was analyzed for a wide range of discorectangle aspect ratios ($\varepsilon \in [1;100]$). We studied anisotropic deposition, i.e., the orientations of the deposited particles were uniformly distributed within some interval such that the particles were preferentially aligned along a given direction. The kinetics of the changes in the packing density $φ$ found at different values of $S_0$ are discussed. Partial ordering of the discorectangles significantly affected the packing density at the jamming state, $φ_\text{j}$, and shifted the cusps in the $φ_\text{j}(\varepsilon)$ dependencies. The structure of the jammed state was analyzed using the adsorption of disks of different diameters into the porous space between the deposited discorectangles. The analysis of the connectivity between the discorectangles was performed assuming a core---shell structure of particles.

cond-mat.soft↗

arXiv2019

Two-dimensional systems of elongated particles: From diluted to dense

This chapter is devoted to the analysis of jamming and percolation behavior of two-dimensional systems of elongated particles. We consider both continuous and discrete spaces (with the special attention to the square lattice), as well the systems with isotropically deposited and aligned particles. Overviews of different analytical and computational methods and main results are presented.

cond-mat.dis-nn↗

arXiv2019

Percolation thresholds for discorectangles: numerical estimation for a range of aspect ratios

Using Monte Carlo simulation, we have studied the percolation of discorectangles. Also known as stadiums or two-dimensional spherocylinders, a discorectangle is a rectangle with semicircles at a pair of opposite sides. Scaling analysis was performed to obtain the percolation thresholds in the thermodynamic limits. We found: (i) for the two marginal aspect ratios $\varepsilon = 1$ (disc) and $\varepsilon \to \infty$ (stick) the percolation thresholds coincide with known values within the statistical error; (ii) for intermediate values of $\varepsilon$ the percolation threshold lies between the percolation thresholds for ellipses and rectangles and approaches the latter as the aspect ratio increases.

cond-mat.dis-nn↗

arXiv2019

Effect of tunneling on the electrical conductivity of nanowire-based films: computer simulation within a core--shell model

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 of the wires, (ii) the wire---wire junction resistance, and (iii) the tunnel resistance between wires. We found that the percolation threshold decreased due to tunneling. However, tunneling had negligible effect on the electrical conductance of dense nanowire networks.

cond-mat.mes-hall↗

arXiv2019

Circles of equal radii randomly placed on a plane: some rigorous results, asymptotic behavior, and application to transparent electrodes

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 distribution of the arcs. In the limiting case of dense systems and large size of the domain $\mathcal{D}$ ($L \to \infty$ in such a way that the number of circle per unit area, $n=N/L^2$, is constant), the arc distribution approaches the probability density function (PDF) $f(ψ) = 4 n r^2\exp(-4 n r^2 ψ)$, where $ψ$ is the central angle subtended by the arc. This PDF is then used to estimate the sheet resistance of transparent electrodes based on conductive rings randomly placed onto a transparent insulating film.

cond-mat.stat-mech↗

arXiv2019

Aging in two dimensional suspensions of rods as driven by Brownian diffusion

Aging in a two dimensional suspension containing rods was studied by means of kinetic Monte Carlo simulations. An off-lattice model with continuous positional and orientational degrees of freedom was considered. The initial state was produced using a random sequential adsorption model. During the aging, the rods underwent translational and rotational Brownian motions. The simulations were run at different values of number density (the number of rods per unit area), $ρ$, and of the initial orientation order parameter, $S_i$. The rods were assumed to have core---shell structures. The evolutions of both the connectivity and the order parameter in the course of the aging were examined.

cond-mat.stat-mech↗

arXiv2019

Transparent electrodes with nanorings: a computational point of view

Four samples of transparent conductive films with different numbers of silver nanorings per unit area were produced. The sheet resistance, transparency, and haze were measured for each sample. Using Monte Carlo simulation, we studied the electrical conductivity of random resistor networks produced by the random deposition of the conducting rings onto the substrate. Both systems of equal-sized rings, and systems with rings of different sizes were simulated. Our simulations demonstrated the linear dependence of the electrical conductivity on the number of rings per unit area. Size dispersity decreased the percolation threshold, but without having any other significant effect on the behavior of the electrical conductance. Analytical estimations obtained for dense systems of equal-sized conductive rings were consistent with the simulations.

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