Prof. Krzysztof Malarz

Faculty of Physics and Applied Computer Science, AGH University of Krakow, Kraków, Małopolskie, Poland

Prof. Krzysztof Malarz

Faculty of Physics and Applied Computer Science, AGH University of Krakow, Kraków, Małopolskie, Poland

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Academic Career Length

29Years (1998-Present)

(Calculated once Scilit publication data is synced: current year − year of first publication + 1)

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18 January 2005 in Physical Review E

Journal Article

Square-lattice site percolation at increasing ranges of neighbor bonds

Krzysztof Malarz

Serge Galam

We report site percolation thresholds for square lattice with neighbor bonds at various increasing ranges. Using Monte Carlo techniques we found that nearest neighbors (NN), next-nearest neighbors (NNN), next-next-nearest neighbors (4N), and fifth-nearest neighbors (6N) yield the same

p_{c} = 0.592 \dots

. The fourth-nearest neighbors (5N) give

p_{c} = 0.298 \dots

. This equality is proved to be mathematically exact using symmetry argument. We then consider combinations of various kinds of neighborhoods with

(NN + NNN)

(NN + 4 N)

(NN + NNN + 4 N)

, and

(NN + 5 N)

. The calculated associated thresholds are respectively

p_{c} = 0.407 \dots

, 0.337…, 0.288…, and 0.234…. The existing Galam-Mauger universal formula for percolation thresholds does not reproduce the data showing dimension and coordination number are not sufficient to build a universal law which extends to complex lattices.

1 October 2012 in Reports on Mathematical Physics

Journal Article

Simple Cubic Random-Site Percolation Thresholds for Complex Neighbourhoods

ŁK

Łukasz Kurzawski

Krzysztof Malarz

7 April 2015 in Physical Review E

Journal Article

Simple cubic random-site percolation thresholds for neighborhoods containing fourth-nearest neighbors

Krzysztof Malarz

In this paper, random-site percolation thresholds for a simple cubic (SC) lattice with site neighborhoods containing next-next-next-nearest neighbors (4NN) are evaluated with Monte Carlo simulations. A recently proposed algorithm with low sampling for percolation thresholds estimation (Bastas et al., arXiv:1411.5834) is implemented for the studies of the top-bottom wrapping probability. The obtained percolation thresholds are

p_{C} (4 NN) = 0.311 60 (12), p_{C} (4 NN + NN) = 0.150 40 (12), p_{C} (4 NN + 2 NN) = 0.159 50 (12), p_{C} (4 NN + 3 NN) = 0.204 90 (12), p_{C} (4 NN + 2 NN + NN) = 0.114 40 (12), p_{C} (4 NN + 3 NN + NN) = 0.119 20 (12), p_{C} (4 NN + 3 NN + 2 NN) = 0.113 30 (12)

, and

p_{C} (4 NN + 3 NN + 2 NN + NN) = 0.100 00 (12)

, where 3NN, 2NN, and NN stand for next-next-nearest neighbors, next-nearest neighbors, and nearest neighbors, respectively. As an SC lattice with 4NN neighbors may be mapped onto two independent interpenetrated SC lattices but with a lattice constant that is twice as large, the percolation threshold

p_{C}

(4NN) is exactly equal to

p_{C}

(NN). The simplified method of Bastas et al. allows for uncertainty of the percolation threshold value

p_{C}

to be reached, similar to that obtained with the classical method but ten times faster.

1 September 2006 in International Journal of Modern Physics C

Journal Article

MAJORITY-VOTE MODEL ON (3, 4, 6, 4) AND (3⁴, 6) ARCHIMEDEAN LATTICES

F. W. S. Lima

Krzysztof Malarz

6 April 2005 in Physical Review Letters

Journal Article

Magnetization Reversal in Spin Patterns with Complex Geometry

Bosiljka Tadic

Krzysztof Malarz

Krzysztof Kułakowski

We study field-driven dynamics of spins with antiferromagnetic interactions along the links of a complex substrate geometry, which is modeled by graphs of a controlled connectivity distribution. The magnetization reversal occurs in avalanches of spin flips, which are pinned by the topological constraints of the underlying graph. The hysteresis loop and avalanche sizes are analyzed and classified in terms of the graph’s connectivity and clustering. The results are relevant for magnets with a hierarchical spatial inhomogeneity and for design of nanoscale magnetic devices.

26 August 2019 in International Journal of Modern Physics C

Journal Article

Efficient space virtualization for the Hoshen–Kopelman algorithm

M. Kotwica

P. Gronek

Krzysztof Malarz

About Me

Graduated from Faculty of Physics and Nuclear Techniques, University of Mining and Metallurgy, Kraków in 1996. PhD in computational and theoretical physics at Faculty of Physics and Nuclear Techniques, University of Mining and Metallurgy in 2000. DSc (habilitation) in complex systems, computational and theoretical physics at Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Kraków in 2016. His scientific interests cover studies of the complex systems (sociophysics, population aging and evolution and modelling of the magnetic interactions) by means of computer simulations (including cellular automata technique). He wrote over seventy journal papers. He has positions of associate professor and deputy dean at the Faculty of Physics and Applied Computer Science AGH-UST in Kraków. He serves as senior editor for “Open Physics”, topic editor for “Entropy” and review editor for “Frontiers in Physics”.

Prof. Krzysztof Malarz

Prof. Krzysztof Malarz

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