Related papers: Pattern formation in a two-dimensional two-species…
We consider heat transfer in an infinite two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a heat source. The basic equations for the particles of the lattice are stated in the form of a system…
A family of novel models of liquid on a 2D lattice (2D lattice liquid models) have been proposed as primitive models of soft-material membrane. As a first step, we have formulated them as single-component, single-layered, classical particle…
The short-range attraction and long-range repulsion (SALR) between nanoparticles or macromolecules can lead to spontaneous pattern formation on solid surfaces, fluid interfaces or membranes. In order to study the self-assembly in such…
Many modern production and measurement facilities incorporate multiphase systems at low pressures. In this region of flows at small, non-zero Knudsen- and low Mach numbers the classical mesoscopic Monte Carlo methods become increasingly…
Using an analytically tractable lattice model for reaction-diffusion processes of hard-core particles we demonstrate that under nonequilibrium conditions phase coexistence may arise even if the system is effectively one-dimensional as e.g.…
Numerical simulations and finite-size scaling analysis have been carried out to study standard and inverse percolation of straight rigid rods on triangular lattices. In the case of standard (inverse) percolation, the lattice is initially…
We numerically examine a binary system of particles with repulsive interactions, where one species is driven by a rotating drive and the other is subjected either to a constant drive in a fixed direction or to a rotating drive that is out…
We analyze diffusion of small particles in a solid polymeric medium taking into account a short range particle-polymer interaction. The system is modeled by a particle diffusion on a ternary lattice where the sites occupied by polymer…
We present an extended microcanonical Lanczos method (MCLM) for a direct evaluation of the diffusion constant and its frequency dependence within the disordered Anderson model of noninteracting particles. The method allows to study systems…
Using Monte Carlo simulations and finite-size scaling analysis, the critical behavior of attractive rigid rods of length k (k-mers) on square lattices at intermediate density has been studied. A nematic phase, characterized by a big domain…
In this short note, we review a recently developed method for analysing multi-component driven diffusive systems with open boundaries. The approach generalises the extremal-current principle known for single-component models and is based on…
L\"uscher has suggested a method to determine phase shifts from the finite volume dependence of the two-particle energy spectrum. We apply this to two models in d=2: (a) the Ising model, (b) a system of two Ising fields with different mass…
The problem of the lattice diffusion of two particles coupled by a contact repulsive interaction is solved by finding analytical expressions of the two-body probability characteristic function. The interaction induces anomalous drift with a…
We study the diffusion process through an ideal polymer network, using numerical methods. Polymers are modeled by random walks on the bonds of a two-dimensional square lattice. Molecules occupy the lattice cells and may jump to the…
In this work, we investigate the dynamics of interacting particle systems subjected to repulsive forces, such as lattices of magnetized particles. To this end, we first develop a general model capable of capturing the complete dynamical…
Traditionally, time-development of the mean square displacement has been employed to determine the diffusion coefficient from the trajectories of single particles. However, this approach is sensitive to the noise and the motion blur upon…
A theoretical model of shape-anisometric particles embedded in a cubic lattice is formulated for binary mixtures combining rod-like, plate-like and spherical particles. The model aims at providing a tool for the prediction and…
The generalized Lin-Taylor model defined on the hexagonal lattice is used to investigate the phase separation in an asymmetric binary liquid mixture consisting of large A (hexagons) and small B (triangles) particles. By considering…
A mesoscopic continuum model is employed to analyse the transport mechanisms and structure formation during the redistribution stage of deposition experiments where organic molecules are deposited on a solid substrate with periodic…
When two molecular species with mutual affinity are mixed together, various self-assembled phases can arise at low temperature, depending on the shape of like and unlike interactions. Among them, stripes -- where layers of one type are…