arXiv subjects

Nikolai I. Lebovka

Publications and source records attributed to Nikolai I. Lebovka.

24 records · Page 2Linked to original sources

arXiv2015

Jamming and percolation in generalized models of random sequential adsorption of linear $k$-mers on a square lattice

The jamming and percolation for two generalized models of random sequential adsorption (RSA) of linear $k$-mers (particles occupying $k$ adjacent sites) on a square lattice are studied by means of Monte Carlo simulation. The classical random sequential adsorption (RSA) model assumes the absence of overlapping of the new incoming particle with the previously deposited ones. The first model LK$_d$ is a generalized variant of the RSA model for both $k$-mers and a lattice with defects. Some of the occupying $k$ adjacent sites are considered as insulating and some of the lattice sites are occupied by defects (impurities). For this model even a small concentration of defects can inhibit percolation for relatively long $k$-mers. The second model is the cooperative sequential adsorption (CSA) one, where, for each new $k$-mer, only a restricted number of lateral contacts $z$ with previously deposited $k$-mers is allowed. Deposition occurs in the case when $z\leq (1-d)z_m$ where $z_m=2(k+1)$ is the maximum numbers of the contacts of $k$-mer, and $d$ is the fraction of forbidden NN contacts. Percolation is observed only at some interval $k_{min}\leq k\leq k_{max}$ where the values $k_{min}$ and $k_{max}$ depend upon the fraction of forbidden contacts $d$. The value $k_{max}$ decreases as $d$ increases. A logarithmic dependence of the type $\log(k_{max})=a+bd$, where $a=-4.03 \pm 0.22$, $b=4.93 \pm 0.57 $, is obtained.

cond-mat.stat-mech↗

arXiv2014

Impact of defects on percolation in random sequential adsorption of linear k-mers on square lattice

The effect of defects on the percolation of linear $k$-mers (particles occupying $k$ adjacent sites) on a square lattice is studied by means of Monte Carlo simulation. The $k$-mers are deposited using a random sequential adsorption mechanism. Two models, $L_d$ and $K_d$, are analyzed. In the $L_d$ model, it is assumed that the initial square lattice is non-ideal and some fraction of sites, $d$, is occupied by non-conducting point defects (impurities). In the $K_d$ model, the initial square lattice is perfect. However, it is assumed that some fraction of the sites in the $k$-mers, $d$, consists of defects, i.e., are non-conducting. The length of the $k$-mers, $k$, varies from 2 to 256. Periodic boundary conditions are applied to the square lattice. The dependencies of the percolation threshold concentration of the conducting sites, $p_c$, vs the concentration of defects, $d$, were analyzed for different values of $k$. Above some critical concentration of defects, $d_m$, percolation is blocked in both models, even at the jamming concentration of $k$-mers. For long $k$-mers, the values of $d_m$ are well fitted by the functions $d_m \propto k_m^{-α}-k^{-α}$ ($α= 1.28 \pm 0.01$, $k_m = 5900 \pm 500$) and $d_m \propto \log (k_m/k)$ ($k_m = 4700 \pm 1000$ ), for the $L_d$ and $K_d$ models, respectively. Thus, our estimation indicates that the percolation of $k$-mers on a square lattice is impossible even for a lattice without any defects if $k\gtrapprox 6 \times 10^3$.

cond-mat.stat-mech↗

arXiv2013

Fine topological structure of coherent complex light created by carbon nanocomposites in LC

Fine complex light structure, optical singularities and electroconductivty of nematic 5CB doped by multi-walled carbon nanotubes (MWCNTs) were investigated. MWCNTs gather spontaneously to system of micro scale clusters with random fractal borders at small enough concentration. They are surrounded by the striped micro scale cladding which creates optical singularities in propagating laser beam. Applied transverse electric field above the Freedericksz initiates homeotropic arrangement of 5CB and the striped inversion walls between nanotubes clusters what diminishes free energy of a composite. Theory of their appearance and properties was built. Simultaneously the striped cladding disappears what can be treated as new mechanism of structure orientation nonlinearity in nonlinear photonics. Polarization singularities (circular C points) were measured firstly. Percolation of clusters enhances strongly electrical conductivity of the system and creates inversion walls even without applied field. Carbon nanotubes composites in LC form bridge between nano dopants and micro/macro system and are promising for applications. Elaborated protocol of singular optics inspection and characterization of LC nanocomposites is promising tool for applications in modern nanosience and technique.

cond-mat.soft↗

arXiv2012

Percolation of linear $k$-mers on square lattice: from isotropic through partially ordered to completely aligned state

Numerical simulations by means of Monte Carlo method and finite-size scaling analysis have been performed to study the percolation behavior of linear $k$-mers (also denoted in the literature as rigid rods, needles, sticks) on two-dimensional square lattices $L \times L$ with periodic boundary conditions. Percolation phenomena are investigated for anisotropic relaxation random sequential adsorption of linear $k$-mers. Especially, effect of anisotropic placement of the objects on the percolation threshold has been investigated. Moreover, the behavior of percolation probability $R_L(p)$ that a lattice of size $L$ percolates at concentration $p$ has been studied in details in dependence on $k$, anisotropy and lattice size $L$. A nonmonotonic size dependence for the percolation threshold has been confirmed in isotropic case. We propose a fitting formula for percolation threshold $p_c = a/k^α+b\log_{10} k+ c$, where $a$, $b$, $c$, $α$ are the fitting parameters varying with anisotropy. We predict that for large $k$-mers ($k\gtrapprox 1.2\times10^4$) isotropic placed at the lattice, percolation cannot occur even at jamming concentration.

cond-mat.dis-nn↗

arXiv2011

Random sequential adsorption of partially oriented linear $k$-mers on square lattice

Jamming phenomena on a square lattice are investigated for two different models of anisotropic random sequential adsorption (RSA) of linear $k$-mers (particles occupying $k$ adjacent adsorption sites along a line). The length of a $k$-mer varies from 2 to 128. Effect of $k$-mer alignment on the jamming threshold is examined. For completely ordered systems where all the $k$-mers are aligned along one direction (e.g., vertical), the obtained simulation data are very close to the known analytical results for 1d systems. In particular, the jamming threshold tends to the R{é}nyi's Parking Constant for large $k$. In the other extreme case, when $k$-mers are fully disordered, our results correspond to the published results for short $k$-mers. It was observed that for partially oriented systems the jamming configurations consist of the blocks of vertically and horizontally oriented $k$-mers ($v$- and $h$-blocks, respectively) and large voids between them. The relative areas of different blocks and voids depend on the order parameter $s$, $k$-mer length and type of the model. For small $k$-mers ($k\leqslant 4$), denser configurations are observed in disordered systems as compared to those of completely ordered systems. However, longer $k$-mers exhibit the opposite behavior.

cond-mat.dis-nn↗

arXiv2011

Dispersions of multi-walled carbon nanotubes in liquid crystals: new challenges to molecular theories of anisotropic soft matter

Aggregation of carbon nanotubes dispersed in nematic liquid crystalline medium is discussed. A model is proposed, which assumes that the aggregates consist of a "skeleton" formed by stochastically arranged nanotubes and a "shell" ("coat") of incorporated and adjacent nematic molecules. The aggregates of this type can be considered as large quasi-macroscopic particles in the nematic matrix. The resulting composite system represents a new type of complex molecular liquids involving self-organization of particles in anisotropic medium. Many essential features and implications of the theoretical model (e.g., effects of concentration of the nanotubes, their aspect ratio and orientational order parameter on the size and fractal dimensionality of the aggregates formed, as well as on the rate of aggregation) are in good agreement with experimental data obtained by various physical methods.

cond-mat.mes-hall↗