arXiv subjects

Agata Fronczak

Publications and source records attributed to Agata Fronczak.

At least 55 records · Page 3Linked to original sources

arXiv2012

The microscopic meaning of grand potential: cluster properties of the one-dimensional lattice gas

We demonstrate, with a concrete example, how the combinatorial approach to a general system of particles, which was introduced in detail in the earlier paper arXiv:1205.4986, works and where it enters to provide a genuine extension of results obtainable by more traditional methods of statistical mechanics. To this end, an effort is made to study cluster properties of the one-dimensional lattice gas with nearest neighbor interactions. Three cases: the infinite temperature limit, the range of finite temperatures, and the zero temperature limit are discussed separately, yielding some new results and providing alternative proofs of known results. In particular, the closed-form expression for the grand partition function in the zero temperature limit is obtained, which results in the non-analytic behavior of the grand potential, in accordance with the Yang-Lee theory.

physics.gen-ph↗

arXiv2012

Statistical mechanics of the international trade network

Analyzing real data on international trade covering the time interval 1950-2000, we show that in each year over the analyzed period the network is a typical representative of the ensemble of maximally random weighted networks, whose directed connections (bilateral trade volumes) are only characterized by the product of the trading countries' GDPs. It means that time evolution of this network may be considered as a continuous sequence of equilibrium states, i.e. quasi-static process. This, in turn, allows one to apply the linear response theory to make (and also verify) simple predictions about the network. In particular, we show that bilateral trade fulfills fluctuation-response theorem, which states that the average relative change in import (export) between two countries is a sum of relative changes in their GDPs. Yearly changes in trade volumes prove that the theorem is valid.

q-fin.GN↗

arXiv2012

General, combinatorial formula for the density of states: insights into the energy equipartition principle and the theory of phase transitions

A completely new approach to the problem of energy distribution in statistical mechanics is developed that results in a general, combinatorial formula for the density of states. Relying on the approach the energy equipartition principle is reexamined and a new perspective on the theory of phase transitions (as resulting from nontrivial patterns of energy distribution characterized by the well-defined classes of forbidden microstates) is given.

cond-mat.stat-mech↗

arXiv2012

Structural Hamiltonian of the international trade network

It is common wisdom that no nation is an isolated economic island. All nations participate in the global economy and are linked together through trade and finance. Here we analyze international trade network (ITN), being the network of import-export relationships between countries. We show that in each year over the analyzed period of 50 years (since 1950) the network is a typical representative of the ensemble of maximally random networks. Structural Hamiltonians characterizing binary and weighted versions of ITN are formulated and discussed. In particular, given binary representation of ITN (i.e. binary network of trade channels) we show that the network of partnership in trade is well described by the configuration model. We also show that in the weighted version of ITN, bilateral trade volumes (i.e. directed connections which represent trade/money flows between countries) are only characterized by the product of the trading countries' GDPs, like in the famous gravity model of trade.

q-fin.GN↗

arXiv2012

The microscopic meaning of grand potential resulting from combinatorial approach to a general system of particles

We present a completely new approach to the problem of interacting fluids, which we believe may provide important insights into microscopic mechanisms that lead to the occurrence of phase transitions. The approach exploits enumerative properties and combinatorial meaning of Bell polynomials. We derive the exact formula for probability of a general system of N particles at temperature T to consist of k weakly coupled clusters of various sizes. We also show that the grand potential of the system may be considered as the exponential generating function for the number of internal states (thermodynamic probability) of these clusters. The microscopic interpretation of the grand potential is novel and surprising, especially if one recalls that until now the only thermodynamic meaning of this free energy was known. We also derive an approximated expression for the density of states.

physics.gen-ph↗

arXiv2010

Origins of Taylor's power law for fluctuation scaling in complex systems

Taylor's fluctuation scaling (FS) has been observed in many natural and man-made systems revealing an amazing universality of the law. Here we give strong theoretical foundations for the origins and abundance of Taylor's FS in different complex systems. The universality of our approach is validated against real world data ranging from bird and insect populations through human chromosomes and traffic intensity in transportation networks to stock market dynamics. Using fundamental principles of statistical physics (both equilibrium and non-equilibrium) we prove that Taylor's law results from the well-defined density of states (DOS) function of a system that gives the number of states characterized by the same value of a macroscopic parameter (i.e., the number of birds observed in a given area, traffic intensity measured as a number of cars passing trough a given observation point or daily activity in the stock market measured in millions of dollars).

physics.soc-ph↗

arXiv2009

Taylor's power law for fluctuation scaling in traffic

In this article, we study transportation network in Minnesota. We show that the system is characterized by Taylor's power law for fluctuation scaling with nontrivial values of the scaling exponent. We also show that the characteristic exponent does not unequivocally characterize a given road network, as it may differ within the same network if one takes into account location of observation points, season, period of day, or traffic intensity. The results are set against Taylor's fluctuation scaling in the Nagel-Schreckenberg cellular automaton model for traffic. It is shown that Taylor's law may serve, beside the fundamental diagram, as an indicator of different traffic phases (free flow, traffic jam etc.).

physics.soc-ph↗

arXiv2007

Critical line in undirected Kauffman boolean networks - the role of percolation

We show that to correctly describe the position of the critical line in the Kauffman random boolean networks one must take into account percolation phenomena underlying the process of damage spreading. For this reason, since the issue of percolation transition is much simpler in random undirected networks, than in the directed ones, we study the Kauffman model in undirected networks. We derive the mean field formula for the critical line in the giant component of these networks, and show that the critical line characterizing the whole network results from the fact that the ordered behavior of small clusters shields the chaotic behavior of the giant component. We also show a possible attitude towards the analytical description of the shielding effect. The theoretical derivations given in this paper quite tally with numerical simulations done for classical random graphs.

cond-mat.dis-nn↗

arXiv2007

Biased random walks on complex networks: the role of local navigation rules

We study the biased random walk process in random uncorrelated networks with arbitrary degree distributions. In our model, the bias is defined by the preferential transition probability, which, in recent years, has been commonly used to study efficiency of different routing protocols in communication networks. We derive exact expressions for the stationary occupation probability, and for the mean transit time between two nodes. The effect of the cyclic search on transit times is also explored. Results presented in this paper give the basis for theoretical treatment of the transport-related problems on complex networks, including quantitative estimation of the critical value of the packet generation rate.

cond-mat.dis-nn↗

arXiv2007

Kauffman Boolean model in undirected scale free networks

We investigate analytically and numerically the critical line in undirected random Boolean networks with arbitrary degree distributions, including scale-free topology of connections $P(k)\sim k^{-γ}$. We show that in infinite scale-free networks the transition between frozen and chaotic phase occurs for $3<γ< 3.5$. The observation is interesting for two reasons. First, since most of critical phenomena in scale-free networks reveal their non-trivial character for $γ<3$, the position of the critical line in Kauffman model seems to be an important exception from the rule. Second, since gene regulatory networks are characterized by scale-free topology with $γ<3$, the observation that in finite-size networks the mentioned transition moves towards smaller $γ$ is an argument for Kauffman model as a good starting point to model real systems. We also explain that the unattainability of the critical line in numerical simulations of classical random graphs is due to percolation phenomena.

cond-mat.dis-nn↗

arXiv2007

Thermodynamic forces, flows, and Onsager coefficients in complex networks

We present Onsager formalism applied to random networks with arbitrary degree distribution. Using the well-known methods of non-equilibrium thermodynamics we identify thermodynamic forces and their conjugated flows induced in networks as a result of single node degree perturbation. The forces and the flows can be understood as a response of the system to events, such as random removal of nodes or intentional attacks on them. Finally, we show that cross effects (such as thermodiffusion, or thermoelectric phenomena), in which one force may not only give rise to its own corresponding flow, but to many other flows, can be observed also in complex networks.

cond-mat.dis-nn↗

arXiv2007

Phase transitions in social networks

We study a model of network with clustering and desired node degree. The original purpose of the model was to describe optimal structures of scientific collaboration in the European Union. The model belongs to the family of exponential random graphs. We show by numerical simulations and analytical considerations how a very simple Hamiltonian can lead to surprisingly complicated and eventful phase diagram.

physics.soc-ph↗

arXiv2006

Publish or perish: analysis of scientific productivity using maximum entropy principle and fluctuation-dissipation theorem

Using data retrieved from the INSPEC database we have quantitatively discussed a few syndromes of the publish-or-perish phenomenon, including continuous growth of rate of scientific productivity, and continuously decreasing percentage of those scientists who stay in science for a long time. Making use of the maximum entropy principle and fluctuation-dissipation theorem, we have shown that the observed fat-tailed distributions of the total number of papers x authored by scientists may result from the density of states function g(x;τ) underlying scientific community. Although different generations of scientists are characterized by different productivity patterns, the function g(x;τ) is inherent to researchers of a given seniority τ, whereas the publish-or-perish phenomenon is caused only by an external field θinfluencing researchers.

physics.soc-ph↗

arXiv2006

Ferromagnetic fluid as a model of social impact

The paper proposes a new model of spin dynamics which can be treated as a model of sociological coupling between individuals. Our approach takes into account two different human features: gregariousness and individuality. We will show how they affect a psychological distance between individuals and how the distance changes the opinion formation in a social group. Apart from its sociological aplications the model displays the variety of other interesting phenomena like self-organizing ferromagnetic state or a second order phase transition and can be studied from different points of view, e.g. as a model of ferromagnetic fluid, complex evolving network or multiplicative random process.

physics.soc-ph↗

arXiv2005

Microscopic explanation of non-Debye relaxation for heat transfer

We give a microscopic explanation of both Debye and non-Debye thermalization processes that have been recently reported by Gall and Kutner (Physica A 352, 347 (2005)). Due to reduction of the problem to first passage phenomena we argue that relaxation functions f(t) introduced by the authors directly correspond to survival probabilities S(t) of particles in the considered systems. We show that in the case of broken ergodicity (i.e. in the case of mirror collisions) the survival probability decays as a power law S(t)=τ/t.

cond-mat.stat-mech↗

arXiv2005

Universal scaling of distances in complex networks

Universal scaling of distances between vertices of Erdos-Renyi random graphs, scale-free Barabasi-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks are observed. A mean distance between two nodes of degrees k_i and k_j equals to =A-B log(k_i k_j). The scaling is valid over several decades. A simple theory for the appearance of this scaling is presented. Parameters A and B depend on the mean value of a node degree _nn calculated for the nearest neighbors and on network clustering coefficients.

cond-mat.dis-nn↗

arXiv2005

Fluctuation-dissipation relations for complex networks

In the paper, we study fluctuations over several ensembles of maximum-entropy random networks. We derive several fluctuation-dissipation relations characterizing susceptibilities of different networks to changes in external fields. In the case of networks with a given degree sequence, we argue that the scale-free topologies of real-world networks may arise as a result of self-organization of real systems into sparse structures with low susceptibility to random external perturbations. We also show that the ensembles of networks with noninteracting links (both uncorrelated and with two-point correlations) are equivalent to random networks with hidden variables.

cond-mat.dis-nn↗

arXiv2005

Interplay between network structure and self-organized criticality

We investigate, by numerical simulations, how the avalanche dynamics of the Bak-Tang-Wiesenfeld (BTW) sandpile model can induce emergence of scale-free (SF) networks and how this emerging structure affects dynamics of the system. We also discuss how the observed phenomenon can be used to explain evolution of scientific collaboration.

cond-mat.other↗