Jammed systems of oriented needles always percolate on square lattices.

Random sequential adsorption (RSA) is a standard method of modeling adsorption of large molecules at the liquid-solid interface. Several studies have recently conjectured that in the RSA of rectangular needles, or k-mers, on a square lattice, percolation is impossible if the needles are sufficiently long (k of order of several thousand). We refute these claims and present rigorous proof that in any jammed configuration of nonoverlapping, fixed-length, horizontal, or vertical needles on a square lattice, all clusters are percolating clusters.

Percolation framework in Ising-spin relaxation.

We introduce a framework based on the percolation idea to investigate the relaxation under zero-temperature Glauber and outflow dynamics on L x L square and triangular lattices. This helps us to understand the appearance of a double time regime in the survival probability. We show that the first, short-time, regime corresponds to relaxation through droplets and the second, long-time, regime corresponds to relaxation through stripes.

Impact of composition of extended objects on percolation on a lattice.

We consider the percolation aspect of random sequential adsorption of extended particles onto a two-dimensional lattice using computer Monte Carlo simulations. We investigate how the composition of the particles influences the value of the percolation threshold. Two regimes can be distinguished: one for almost linear particles (with the composition of straight segments reaching 85-100 %) and the second one for more bent (flexible) ones.

Three types of outflow dynamics on square and triangular lattices and universal scaling.

In this paper we propose a generalization of the one-dimensional outflow dynamics (KD). The rule is introduced as a simplification of Galam dynamics (GD) proposed in an earlier paper. We simulate three types of outflow dynamics, GD, Stauffer dynamics, and KD, both on the square and triangular lattices and show whether the outflow dynamics is sensitive to the lattice structure.

The effect of impurities on jamming in random sequential adsorption of elongated objects.

We consider the jamming aspect of random sequential adsorption of extended particles onto two-dimensional lattice by computer Monte Carlo simulations. The initial presence of impurities on the substrate disturbs this phenomenon significantly and we study here how the size and density of impurity particles affect the resulting jamming threshold. We present the formula for jamming threshold as a closed function of all important parameters (the size of primary particles, the size of impurity particles, and the final density of impurities).

The study of percolation with the presence of impurities.

We consider the process of percolation cluster formation for point-like conductors subjected to random sequential adsorption onto two-dimensional lattice by computer Monte Carlo simulations. The initial presence of impurities disturbs this phenomenon significantly and we study here how the size and density of impurity particles affect the resulting percolation threshold. Some unexpected features such as the nonmonotonicity of the percolation threshold as a function of impurity concentration are discussed.