arXiv subjects

K. Malarz

Publications and source records attributed to K. Malarz.

At least 19 recordsLinked to original sources

arXiv2026

Bak--Tang--Wiesenfeld model for various topologies and ranges of interaction

In this paper, the Bak--Tang--Wiesenfeld model for various substrate topologies and a variety of neighborhoods is reconsidered. With computer simulation, we study the distribution of avalanche sizes. Using the Z-score we confirm that independently of the substrate topology and the range of neighborhood, the exponent that governs the power law of the probability distribution of the size of avalanches is the same and approximately equal 1.208(39). However, this requires a smartly chosen number of deposited grains in relation to the linear size of the system.

cond-mat.stat-mech↗

arXiv2021

Percolation thresholds on triangular lattice for neighbourhoods containing sites up-to the fifth coordination zone

We determine thresholds $p_c$ for random-site percolation on a triangular lattice for all available neighborhoods containing sites from the first to the fifth coordination zones, including their complex combinations. There are 31 distinct neighbourhoods. The dependence of the value of the percolation thresholds $p_c$ on the coordination number $z$ are tested against various theoretical predictions. The newly proposed single scalar index $ξ=\sum_i z_ir_i^2/i$ (depending on the coordination zone number $i$, the neighbourhood coordination number $z$ and the square-distance $r^2$ to sites in $i$-th coordination zone from the central site) allows to differentiate among various neighbourhoods and relate $p_c$ to $ξ$. The thresholds roughly follow a power law $p_c\proptoξ^{-γ}$ with $γ\approx 0.710(19)$.

cond-mat.stat-mech↗

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↗

arXiv2019

Paradox of integration -- Dynamics of two-dimensional status

According to Peter M. Blau [Exchange and Power in Social Life, Wiley and Sons, p. 43], the process of integration of a newly formed group has a paradoxical aspect: most attractive individuals are rejected because they raise fear of rejection. Often, their solution is to apply a self-deprecating strategy, which artificially raises the social statuses of their opponents. Here we introduce a two-dimensional space of status, and we demonstrate that with this setup, the self-deprecating strategy efficiently can prevent the rejection. Examples of application of this strategy in the scale of a society are provided.

physics.soc-ph↗

arXiv2015

Game of collusions

A new model of collusions in an organization is proposed. Each actor $a_{i=1,\cdots,N}$ disposes one unique good $g_{j=1,\cdots,N}$. Each actor $a_i$ has also a list of other goods which he/she needs, in order from desired most to those desired less. Finally, each actor $a_i$ has also a list of other agents, initially ordered at random. The order in the last list means the order of the access of the actors to the good $g_j$. A pair after a pair of agents tries to make a transaction. This transaction is possible if each of two actors can be shifted upwards in the list of actors possessed by the partner. Our numerical results indicate, that the average time of evolution scales with the number $N$ of actors approximately as $N^{2.9}$. For each actor, we calculate the Kendall's rank correlation between the order of desired goods and actor's place at the lists of the good's possessors. We also calculate individual utility funcions $η_i$, where goods are weighted according to how strongly they are desired by an actor $a_i$, and how easily they can be accessed by $a_i$. Although the individual utility functions can increase or decrease in the time course, its value averaged over actors and independent simulations does increase in time. This means that the system of collusions is profitable for the members of the organization.

physics.soc-ph↗

arXiv2015

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

In the paper random-site percolation thresholds for simple cubic lattice with sites' 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 $p_C(\text{4NN})=0.31160(12)$, $p_C(\text{4NN+NN})=0.15040(12)$, $p_C(\text{4NN+2NN})=0.15950(12)$, $p_C(\text{4NN+3NN})=0.20490(12)$, $p_C(\text{4NN+2NN+NN})=0.11440(12)$, $p_C(\text{4NN+3NN+NN})=0.11920(12)$, $p_C(\text{4NN+3NN+2NN})=0.11330(12)$, $p_C(\text{4NN+3NN+2NN+NN})=0.10000(12)$, where 3NN, 2NN, NN stands 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 two times larger lattice constant the percolation threshold $p_C$(4NN) is exactly equal to $p_C$(NN). The simplified Bastas et al. method allows for reaching uncertainty of the percolation threshold value $p_C$ similar to those obtained with classical method but ten times faster.

cond-mat.stat-mech↗

arXiv2015

Heavy context dependence---decisions of underground soldiers

An attempt is made to simulate the disclosure of underground soldiers in terms of theory of networks. The coupling mechanism between the network nodes is the possibility that a disclosed soldier is going to disclose also his acquaintances. We calculate the fraction of disclosed soldiers as dependent on the fraction of those who, once disclosed, reveal also their colleagues. The simulation is immersed in the historical context of the Polish Home Army under the communist rule in 1946-49.

physics.soc-ph↗

arXiv2013

Influence of long-range interactions on strategy selection in crowd

An order--disorder phase transition is observed for Ising-like systems even for arbitrarily chosen probabilities of spins flips [K. Malarz et al, Int. J. Mod. Phys. C 22, 719 (2011)]. For such athermal dynamics one must define $(z+1)$ spin flips probabilities $w(n)$, where $z$ is a number of the nearest-neighbours for given regular lattice and $n=0,\cdots,z$ indicates the number of nearest spins with the same value as the considered spin. Recently, such dynamics has been successfully applied for the simulation of a cooperative and competitive strategy selection by pedestrians in crowd [P. Gawroński et al, Acta Phys. Pol. A 123, 522 (2013)]. For the triangular lattice ($z=6$) and flips probabilities dependence on a single control parameter $x$ chosen as $w(0)=1$, $w(1)=3x$, $w(2)=2x$, $w(3)=x$, $w(4)=x/2$, $w(5)=x/4$, $w(6)=x/6$ the ordered phase (where most of pedestrians adopt the same strategy) vanishes for $x>x_C\approx 0.429$. In order to introduce long-range interactions between pedestrians the bonds of triangular lattice are randomly rewired with the probability $p$. The amount of rewired bonds can be interpreted as the probability of communicating by mobile phones. The critical value of control parameter $x_C$ increases monotonically with the number of rewired links $M=pzN/2$ from $x_C(p=0)\approx 0.429$ to $x_C(p=1)\approx 0.81$.

physics.soc-ph↗

arXiv2012

Strategies in crowd and crowd structure

In an emergency situation, imitation of strategies of neighbours can lead to an order-disorder phase transition, where spatial clusters of pedestrians adopt the same strategy. We assume that there are two strategies, cooperating and competitive, which correspond to a smaller or larger desired velocity. The results of our simulations within the Social Force Model indicate that the ordered phase can be detected as an increase of spatial order of positions of the pedestrians in the crowd.

physics.soc-ph↗

arXiv2010

Majority-vote model on triangular, honeycomb and Kagome lattices

On Archimedean lattices, the Ising model exhibits spontaneous ordering. Three examples of these lattices of the majority-vote model with noise are considered and studied through extensive Monte Carlo simulations. The order/disorder phase transition is observed in this system. The calculated values of the critical noise parameter are q_c=0.089(5), q_c=0.078(3), and q_c=0.114(2) for honeycomb, Kagome and triangular lattices, respectively. The critical exponents beta/nu, gamma/nu and 1/nu for this model are 0.15(5), 1.64(5), and 0.87(5); 0.14(3), 1.64(3), and 0.86(6); 0.12(4), 1.59(5), and 1.08(6) for honeycomb, Kagome and triangular lattices, respectively. These results differs from the usual Ising model results and the majority-vote model on so-far studied regular lattices or complex networks. The effective dimensionalities of the system D_{eff}= 1.96(5) (honeycomb), D_{eff} =1.92(4) (Kagome), and D_{eff}= 1.83(5) (triangular) for these networks are just compatible to the embedding dimension two.

cond-mat.stat-mech↗

arXiv2010

Communication and trust in the bounded confidence model

The communication process in a situation of emergency is discussed within the Scheff theory of shame and pride. The communication involves messages from media and from other persons. Three strategies are considered: selfish (to contact friends), collective (to join other people) and passive (to do nothing). We show that the pure selfish strategy cannot be evolutionarily stable. The main result is that the community structure is statistically meaningful only if the interpersonal communication is weak.

physics.soc-ph↗

arXiv2010

Critical behaviour of the Ising S=1/2 and S=1 model on (3,4,6,4) and (3,3,3,3,6) Archimedean lattices

We investigate the critical properties of the Ising S=1/2 and S=1 model on (3,4,6,4) and (3,3,3,3,6) Archimedean lattices. The system is studied through the extensive Monte Carlo simulations. We calculate the critical temperature as well as the critical point exponents gamma/nu, beta/nu and nu basing on finite size scaling analysis. The calculated values of the critical temperature for S=1 are k_BT_C/J=1.590(3) and k_BT_C/J=2.100(4) for (3,4,6,4) and (3,3,3,3,6) Archimedean lattices, respectively. The critical exponents beta/nu, gamma/nu and 1/nu for S=1 are beta/nu=0.180(20), gamma/nu=1.46(8) and 1/nu=0.83(5) for (3,4,6,4) and 0.103(8), 1.44(8) and 0.94(5) for (3,3,3,3,6) Archimedean lattices. Obtained results differ from the Ising S=1/2 model on (3,4,6,4), (3,3,3,3,6) and square lattice. The evaluated effective dimensionality of the system for S=1 are D_{eff}=1.82(4) for (3,4,6,4) and D_{eff}=1.64(5) for (3,3,3,3,6).

cond-mat.stat-mech↗

arXiv2008

Spectral properties of adjacency and distance matrices for various networks

The spectral properties of the adjacency (connectivity) and distance matrix for various types of networks: exponential, scale-free (Albert--Barabasi) and classical random ones (Erdos--Renyi) are evaluated. The graph spectra for dense graph in the Erdos-Renyi model are derived analytically.

cond-mat.dis-nn↗

arXiv2007

The Sznajd dynamics on a directed clustered network

The Sznajd model is investigated in the directed Erdos--Renyi network with the clusterization coefficient enhanced to 0.3 by the method of Holme and Kim (Phys. Rev. E65 (2002) 026107). Within additional triangles, all six links are present. In this network, some nodes preserve the minority opinion. The time tau of getting equilibrium is found to follow the log-normal distribution and it increases linearly with the system size. Its dependence on the initial opinion distribution is different from the analytical results for fully connected networks.

physics.soc-ph↗

arXiv2007

Square lattice site percolation thresholds for complex neighbourhoods

In this paper we compute the square lattice random sites percolation thresholds in case when sites from the 4th and the 5th coordination shells are included for neighbourhood. The obtained results support earlier claims, that (a) the coordination number and the space dimension are insufficient for building universal formulae for percolation thresholds and (b) that percolation threshold may not decrease monotonically with lattice site coordination number.

cond-mat.stat-mech↗

arXiv2006

Gossip in random networks

We consider the average probability X of being informed on a gossip in a given social network. The network is modeled within the random graph theory of Erdos and Renyi. In this theory, a network is characterized by two parameters: the size N and the link probability p. Our experimental data suggest three levels of social inclusion of friendship. The critical value p_c, for which half of agents are informed, scales with the system size as N^{-γ} with γ\approx 0.68. Computer simulations show that the probability X varies with p as a sigmoidal curve. Influence of the correlations between neighbors is also evaluated: with increasing clustering coefficient C, X decreases.

physics.soc-ph↗

arXiv2006

Majority-vote model on (3,4,6,4) and (3^4,6) Archimedean lattices

On Archimedean lattices, the Ising model exhibits spontaneous ordering. Two examples of these lattices of the majority-vote model with noise are considered and studied through extensive Monte Carlo simulations. The order/disorder phase transition is observed in this system. The calculated values of the critical noise parameter are q_c=0.091(2) and q_c=0.134(3) for (3,4,6,4) and (3^4,6) Archimedean lattices, respectively. The critical exponents beta/nu, gamma/nu and 1/nu for this model are 0.103(6), 1.596(54), 0.872(85) for (3,4,6,4) and 0.114(3), 1.632(35), 0.978(104) for (3^4,6) Archimedean lattices. These results differs from the usual Ising model results and the majority-vote model on so-far studied regular lattices or complex networks. The effective dimensionality of the system [D_{eff}(3,4,6,4)=1.802(55) and D_{eff}(3^4,6)=1.860(34)] for these networks are reasonably close to the embedding dimension two.

cond-mat.stat-mech↗

arXiv2006

Truth seekers in opinion dynamics models

We modify the model of Deffuant et al. to distinguish true opinion among others in the fashion of Hegselmann and Krause . The basic features of both models modified to account for truth seekers are qualitatively the same.

physics.soc-ph↗