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K. Kulakowski

Publications and source records attributed to K. Kulakowski.

At least 37 records · Page 2Linked to original sources
arXiv2006

Stable states of systems of bistable magnetostrictive wires against applied field, applied stress and spatial geometry

Long-range magnetostatic interaction between wires strongly depends on their spatial position. This interaction, combined with applied tensile stress, influences the hysteresis loop of the system of wires through the stress dependence of their coercive fields. As a result, we obtain a set of stable magnetic states of the system, dependent on the applied field, applied stress and mutual positions of the wires. These states can be used to encode the system history.

cond-mat.mtrl-sci↗
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

Avalanches in complex spin networks

We investigate the magnetization reversal processes on classes of complex spin networks with antiferromagnetic interaction along the network links. With slow field ramping the hysteresis loop and avalanches of spin flips occur due to topological inhomogeneity of the network, even without any disorder of the magnetic interaction [B. Tadic, et al., Phys. Rev. Lett. 94 (2005) 137204]. Here we study in detail properties of the magnetization avalanches, hysteresis curves and density of domain walls and show how they can be related to the structural inhomogeneity of the network. The probability distribution of the avalanche size, N_s(s), displays the power-law behaviour for small s, i.e. N_s(s)\propto s^{-α}. For the scale-free networks, grown with preferential attachment, αincreases with the connectivity parameter M from 1.38 for M=1 (trees) to 1.52 for M=25. For the exponential networks, αis close to 1.0 in the whole range of M.

cond-mat.dis-nn↗
arXiv2005

Bonabeau model on a fully connected graph

Numerical simulations are reported on the Bonabeau model on a fully connected graph, where spatial degrees of freedom are absent. The control parameter is the memory factor f. The phase transition is observed at the dispersion of the agents power h_i. The critical value f_C shows a hysteretic behavior with respect to the initial distribution of h_i. f_C decreases with the system size; this decrease can be compensated by a greater number of fights between a global reduction of the distribution width of h_i. The latter step is equivalent to a partial forgetting.

physics.soc-ph↗
arXiv2005

How to distinguish between stick-slip and pure slip oscillations

Numerical simulations are performed for the stick-slip motion in the Burridge-Knopoff model of one block. Calculated amplitude increases with the driving velocity. We argue that this effect can be a criterion to distinguish between the stick-slip and pure slip oscillations.

cond-mat.other↗
arXiv2005

How to count trees?

We propose a new topological invariant of unlabeled trees of N nodes. The invariant is a set of Nx2 matrices of integers, with sum_j k^{d_{i,j}} and v_i as the matrix elements, where d_{i,j} are the elements of the distance matrix and v_i denotes i-th node's degree and k in N. To compare the invariant calculated for possibly different graphs, the matrix rows are ordered with respect to first column, and -- if necessary -- with respect to the second one. We use the new invariant to evaluate from below the number of topologically different unlabeled trees up to N=17. The results slightly exceed the asymptotic evaluation of Otter.

cond-mat.stat-mech↗
arXiv2005

Heider Balance in Human Networks

Recently, a continuous dynamics was proposed to simulate dynamics of interpersonal relations in a society represented by a fully connected graph. Final state of such a society was found to be identical with the so-called Heider balance (HB), where the society is divided into two mutually hostile groups. In the continuous model, a polarization of opinions was found in HB. Here we demonstrate that the polarization occurs also in Barabasi-Albert networks, where the Heider balance is not necessarily present. In the second part of this work we demonstrate the results of our formalism, when applied to reference examples: the Southern women and the Zachary club.

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↗
arXiv2005

Matrix representation of evolving networks

We present the distance matrix evolution for different types of networks: exponential, scale-free and classical random ones. Statistical properties of these matrices are discussed as well as topological features of the networks. Numerical data on the degree and distance distributions are compared with theoretical predictions.

cond-mat.stat-mech↗
arXiv2004

Spin glass properties of an Ising antiferromagnet on the Archimedean (3,12^2) lattice

We investigate magnetic properties of a two-dimensional periodic structure with Ising spins and antiferromagnetic nearest neighbor interaction. The structure is topologically equivalent to the Archimedean (3,12^2) lattice. The ground state energy is degenerate. In some ground states, the spin structure is translationally invariant, with the same configuration in each unit cell. Numerical results are reported on specific heat and static magnetic usceptibility against temperature. Both quantities show maxima at temperature T>0. They reveal some sensitivity on the initial state in temperatures where the Edwards--Anderson order parameter is positive. For zero temperature and low frequency of the applied field, the magnetic losses are negligible. However, the magnetization curve displays some erratic behavior due to the metastable states.

cond-mat.stat-mech↗
arXiv2004

Off-lattice simulation of the solid phase DNA amplification

Recent simulations of the solid phase DNA amplification (SPA) by J.-F. Mercier et al (Biophys. J. 85 (2003) 2075) are generalized to include two kinds of primers and the off-lattice character of the primer distribution on the surface. The sigmoidal character of the primer occupation by DNA, observed experimentally, is reproduced in the simulation. We discuss an influence of two parameters on the efficience of the amplification process: the initial density p_0 of the occupied primers from the interfacial amplification and the ratio r of the molecule length to the average distance between primers. The number of cycles till the saturation decreases with p_0 roughly as p_0^{-0.26}. For r=1.5, the number of occupied primers is reduced by a factor two, when compared to the case of longer molecules. Below r=1.4, the effectivity of SPA is reduced by a factor 100.

q-bio.BM↗
arXiv2004

Magnetization reversal in spin patterns with complex geometry

We study field-driven dynamics of spins with antiferromagnetic interaction 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 graph's connectivity and clustering. The results are relevant for magnets with a hierarchical spatial inhomogeneity and for design of nanoscale magnetic devices.

cond-mat.stat-mech↗
arXiv2004

Dependence of the average to-node distance on the node degree for random graphs and growing networks

In a graph, nodes can be characterized locally (with their degree $k$) or globally (e.g. with their average length path $ξ$ to other nodes). Here we investigate how $ξ$ depends on $k$. Our earlier algorithm of the construction of the distance matrix is applied to the random graphs. Numerical calculations are performed for the random graphs and the growing networks: the scale-free ones and the exponential ones. The results are relevant for search strategies in different networks.

cond-mat.stat-mech↗
arXiv2004

Memory effect in growing trees

We show that the structure of a growing tree preserves an information on the shape of an initial graph. For the exponential trees, evidence of this kind of memory is provided by means of the iterative equations, derived for the moments of the node-node distance distribution. Numerical calculations confirm the result and allow to extend the conclusion to the Barabasi--Albert scale-free trees. The memory effect almost disappears, if subsequent nodes are connected to the network with more than one link.

cond-mat.dis-nn↗
arXiv2004

How pairs of partners emerge in an initially fully connected society

A social group is represented by a graph, where each pair of nodes is connected by two oppositely directed links. At the beginning, a given amount $p(i)$ of resources is assigned randomly to each node $i$. Also, each link $r(i,j)$ is initially represented by a random positive value, which means the percentage of resources of node $i$ which is offered to node $j$. Initially then, the graph is fully connected, i.e. all non-diagonal matrix elements $r(i,j)$ are different from zero. During the simulation, the amounts of resources $p(i)$ change according to the balance equation. Also, nodes reorganise their activity with time, going to give more resources to those which give them more. This is the rule of varying the coefficients $r(i,j)$. The result is that after some transient time, only some pairs $(m,n)$ of nodes survive with non-zero $p(m)$ and $p(n)$, each pair with symmetric and positive $r(m,n)=r(n,m)$. Other coefficients $r(m,i\ne n)$ vanish. Unpaired nodes remain with no resources, i.e. their $p(i)=0$, and they cease to be active, as they have nothing to offer. The percentage of survivors (i.e. those with with $p(i)$ positive) increases with the velocity of varying the numbers $r(i,j)$, and it slightly decreases with the size of the group. The picture and the results can be interpreted as a description of a social algorithm leading to marriages.

cond-mat.other↗
arXiv2004

Node-node distance distribution for growing networks

We present the simulation of the time evolution of the distance matrix. The result is the node-node distance distribution for various kinds of networks. For the exponential trees, analytical formulas are derived for the moments of the distance distribution.

cond-mat.stat-mech↗
arXiv2003

History-dependent synchronization in the Burridge-Knopoff model

A three-blocks Burridge-Knopoff model is investigated. The dimensionless velocity-dependent friction force $F(v)\propto (1+av)^{-1}$ is linearized around $a=0$. In this way, the model is transformed into a six-dimensional mapping $\mathbf{x}(t_{n})\to \mathbf{x}(t_{n+1})$, where $t_n$ are time moments when a block starts to move or stops. Between these moments, the equations of motion are integrable. For $a<0.1$, the motion is quasiperiodic or periodic, depending on the initial conditions. For the periodic solution, we observe a synchronization of the motion of the lateral blocks. For $a>0.1$, the motion becomes chaotic. These results are true for the linearized mapping, linearized numerical and non-linearized numerical solutions.

nlin.AO↗