483 citations · 1.4k across the 27 of their papers we have counts for
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Percolation in a triangle on a square lattice
Zbigniew Koza
Percolation on a plane is usually associated with clusters spanning two opposite sides of a rectangular system. Here we investigate three-leg clusters generated on a square lattice…
Jammed systems of oriented dimers always percolate on hypercubic lattices
Zbigniew Koza, Grzegorz Kondrat
Random sequential adsorption (RSA) is a standard method of modeling adsorption of large molecules at the liquid-solid interface. Here we consider jammed states of the RSA process o…
Critical p=1/2 in percolation on semi-infinite strips
Zbigniew Koza
We study site percolation on lattices confined to a semi-infinite strip. For triangular and square lattices we find that the probability that a cluster touches the three sides of s…
Jammed systems of oriented needles always percolate on square lattices
Grzegorz Kondrat, Zbigniew Koza, Piotr Brzeski
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 t…
Percolation of overlapping squares or cubes on a lattice
Zbigniew Koza, Grzegorz Kondrat, Karol Suszczyński
Porous media are often modelled as systems of overlapping obstacles, which leads to the problem of two percolation thresholds in such systems, one for the porous matrix and the oth…
From discrete to continuous percolation in dimensions 3 to 7
Zbigniew Koza, Jakub Poła
We propose a method of studying the continuous percolation of aligned objects as a limit of a corresponding discrete model. We show that the convergence of a discrete model to its…
The dual model for an Ising model with nearest and next-nearest neighbors
Adam Strycharski, Zbigniew Koza
We construct and analyse a dual model to the Ising model with the nearest and next-nearest neighbors on the rectangular lattice (NNNI model). The Hamiltonian of the dual model turn…
The Ising model in a Bak-Tang-Wiesenfeld sandpile
Zbigniew Koza, Marcel Ausloos
We study the spin-1 Ising model with non-local constraints imposed by the Bak-Tang-Wiesenfeld sandpile model of self-organized criticality (SOC). The model is constructed as if the…
Numerical analysis of reversible A + B <-> C reaction-diffusion systems
Zbigniew Koza
We develop an effective numerical method of studying large-time properties of reversible reaction-diffusion systems of type A + B <-> C with initially separated reactants. Using it…
General relation between drift velocity and dispersion of a molecular motor
Zbigniew Koza
We model a processive linear molecular motor as a particle diffusing in a one-dimensional periodic lattice with arbitrary transition rates between its sites. We present a relativel…
Asymptotic expansion for reversible A + B <-> C reaction-diffusion process
Zbigniew Koza
We study long-time properties of reversible reaction-diffusion systems of type A + B <-> C by means of perturbation expansion in powers of 1/t (inverse of time). For the case of eq…
General technique of calculating drift velocity and diffusion coefficient in arbitrary periodic systems
Zbigniew Koza
We develop a practical method of computing the stationary drift velocity V and the diffusion coefficient D of a particle (or a few particles) in a periodic system with arbitrary tr…
The asymptotic behaviour of the initially separated A + B(static) -> 0 reaction-diffusion systems
Zbigniew Koza
We examine the long-time behaviour of A+B \to 0 reaction-diffusion systems with initially separated species A and B. All of our analysis is carried out for arbitrary (positive) val…