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P. Gronek

Publications and source records attributed to P. Gronek.

4 recordsLinked to original sources
arXiv2019

Efficient space virtualisation for Hoshen--Kopelman algorithm

In this paper the efficient space virtualisation for Hoshen--Kopelman algorithm is presented. We observe minimal parallel overhead during computations, due to negligible communication costs. The proposed algorithm is applied for computation of random-site percolation thresholds for four dimensional simple cubic lattice with sites' neighbourhoods containing next-next-nearest neighbours (3NN). The obtained percolation thresholds are $p_C(\text{NN})=0.19680(23)$, $p_C(\text{2NN})=0.08410(23)$, $p_C(\text{3NN})=0.04540(23)$, $p_C(\text{2NN+NN})=0.06180(23)$, $p_C(\text{3NN+NN})=0.04000(23)$, $p_C(\text{3NN+2NN})=0.03310(23)$, $p_C(\text{3NN+2NN+NN})=0.03190(23)$, where 2NN and NN stand for next-nearest neighbours and nearest neighbours, respectively.

physics.comp-ph↗
arXiv2014

If others jump to the queue front, how long I will wait?

Two models of a queue are proposed: a human queue and two lines of vehicles before a narrowing. In both models, a queuer tries to evaluate his waiting time, taking into account the delay caused by intruders who jump to the queue front. As the collected statistics of such events is very limited, the evaluation can give very long times. The results provide an example, when direct observations should be supplemented by an inference from the context.

physics.soc-ph↗
arXiv2005

The Heider balance and social distance

The Heider balance is a state of a group of people with established mutual relations between them. These relations, friendly or hostile, can be measured in the Bogardus scale of the social distance. In previous works on the Heider balance, these relations have been described with integers 0 and $\pm1$. Recently we have proposed real numbers instead. Also, differential equations have been used to simulate the time evolution of the relations, which were allowed to vary within a given range. In this work, we investigate an influence of this allowed range on the system dynamics. As a result, we have found that a narrowing of the range of relations leads to a large delay in achieving the Heider balance. Another point is that a slight shift of the initial distribution of the social distance towards friendship can lead to a total elimination of hostility.

physics.soc-ph↗