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Pattern formation in a two-dimensional system of rod-like particles has been simulated using a lattice approach. Rod-like particles were modelled as linear $k$-mers of two mutually perpendicular orientations ($k_x$- and $k_y$-mers) on a square lattice with periodic boundary conditions (torus). Two kinds of random sequential adsorption model were used to produce the initial homogeneous and isotropic distribution of $k$-mers with different values of packing fraction. By means of the Monte Carlo technique, translational diffusion of the $k$-mers was simulated as a random walk, while rotational diffusion was ignored, so, $k_x$- and $k_y$-mers were considered as individual species. The system tends toward a well-organized nonequilibrium steady state in the form of diagonal stripes for the relatively long $k$-mer ($k \geq 6$) and moderate packing densities (in the interval $p_{down} < p < p_{up}$, where both the critical packing fractions $p_{down}$ and $p_{up}$ are depended on $k$)., 10 pages, 10 figures, 20 references; XXIX IUPAP Conference in Computational Physics (CCP2017) https://ccp2017.sciencesconf.org/; submitted to J.Phys.Conf.Ser

The processes of formation of electrically conductive films filled by aligned elongated nanoparticles, i.e. nanotubes, nanowires or fibers attract great attention in nanotecnological applications. The alignment can be controlled by external electric fields, evaporation-driven self-assembly and assisted by different other techniques. This work studies the impact of defects on electrical connectivity of ideally aligned monolayer of rods (k-mers). By means of Monte Carlo simulation the problem of percolation for conductive rods on a discrete insulating substrate (square lattice) is analyzed. The aspect ratio of the particles changes within the interval 1-64, the insulating defects were distributed both on the lattice and on the particles. We found that even a very small amount of the insulating defects on the particles can destroy the electrical connectivity. The critical concentration of the defects decreases as the aspect ratio of the particles increases.

We simulated the spread of an activity in a virtual group using the model of excitable medium. We assumed that the structure of the virtual group corresponds to a scale- free network. In our simulation, the network consists of 100 nodes, the average degree of the nodes is 1.98. We considered the propagation of excitation both in a homogeneous and an inhomogeneous excitable medium. The simulation showed that the initial conditions have a little effect on the behaviour of the model. In inhomogeneous medium, fraction of the excited nodes increases, when permanent excited elements ('active' centres) appear in the network. The fraction of the excited nodes increases, when we increase the number of the permanent excited elements. Locations of the active centres do not affect at the level of excitation. External source of activator increases the fraction of the excited nodes in the scale-free network with distribution of parameters.

By means of the Monte Carlo simulation, we study the layers produced by the random sequential adsorption of the linear rigid objects (k-mers also known as rigid or stiff rods, sticks, needles) onto the square lattice with defects in the presence of an external field. The value of k varies from 2 to 32. The point defects randomly and uniformly placed on the substrate hinder adsorption of the elongated objects. The external field affects isotropic deposition of the particles, consequently the deposited layers are anisotropic. We study the influence of the defect concentration, the length of the objects, and the external field on the percolation threshold and the jamming concentration. Our main findings are (i) the critical defect concentration at which the percolation never occurs even at jammed state decreases for short k-mers (k 16) as anisotropy increases, (ii) the corresponding critical k-mer concentration decreases with anisotropy growth, (iii) the jamming concentration decreases drastically with growth of k-mer length for any anisotropy, (iv) for short k-mers, the percolation threshold is almost insensitive to the defect concentration for any anisotropy.