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A Pekalski

Publications and source records attributed to A Pekalski.

8 recordsLinked to original sources
PubMed2001

Percolation and jamming in random bond deposition.

A model is presented in which on the bonds of a square lattice linear segments ("needles") of a constant length a are randomly placed. We investigate the dependence of the percolation and jamming thresholds on the length of the needles. The difference from the standard site deposition problem is demonstrated. We show that the system undergoes a transition at a=6. When shorter needles are used, the system first becomes percolating before becoming jammed. For longer needles the lattice becomes jammed but there is no percolation. We present evidence that the transition is due to different clustering of the short and long needles. We also determine the Fisher exponent, obtaining the same value as for standard two-dimensional percolation.

Journal Article↗
PubMed2001

Ising model on a small world network.

A one-dimensional Ising model is studied, via Monte Carlo simulations, on a small world network, where each site has, apart from couplings to its two nearest neighbors, a certain probability to be linked to one of its farther neighbors. It is demonstrated that even a small fraction of such links enables the system to order at finite temperatures. The critical exponent beta is smaller than the two-dimensional value, and seems to be independent of the concentration of the extra links. The dependence of the magnetization and the critical temperature on the concentration of the small world links is also presented.

Journal Article↗
PubMed2001

Coexistence in a predator-prey system.

We propose a lattice model of two populations, predators and prey. The model is solved via Monte Carlo simulations. Each species moves randomly on the lattice and can live only a certain time without eating. The lattice cells are either grass (eaten by prey) or tree (giving cover for prey). Each animal has a reserve of food that is increased by eating (prey or grass) and decreased after each Monte Carlo step. To breed, a pair of animals must be adjacent and have a certain minimum of food supply. The number of offspring produced depends on the number of available empty sites. We show that such a predator-prey system may finally reach one of the following three steady states: coexisting, with predators and prey; pure prey; or an empty one, in which both populations become extinct. We demonstrate that the probability of arriving at one of the above states depends on the initial densities of the prey and predator populations, the amount of cover, and the way it is spatially distributed.

Animals↗
PubMed2001

Percolation and jamming in random sequential adsorption of linear segments on a square lattice.

We present the results of a study of random sequential adsorption of linear segments (needles) on sites of a square lattice. We show that the percolation threshold is a nonmonotonic function of the length of the adsorbed needle, showing a minimum for a certain length of the needles, while the jamming threshold decreases to a constant with a power law. The ratio of the two thresholds is also nonmonotonic and it remains constant only in a restricted range of the needles length. We determine the values of the correlation length exponent for percolation, jamming, and their ratio.

Journal Article↗
PubMed2001

Population dynamics with and without selection.

A model describing population dynamics is presented. We study the effect of selection pressure and inbreeding on the time evolution of the population and the chances of survival. We find that the selection is in general beneficial, enabling survival of a population whose size is declining. Inbreeding reduces the survival chances since it leads to clustering of individuals. We have also found, in agreement with biological data, that there is a threshold value of the initial size of the population, as well as of the habitat, below which the population will almost certainly become extinct. We present analytical and computer simulation approaches.

Biological Evolution↗