Pareto and Boltzmann-Gibbs behaviors in a deterministic multi-agent system

A deterministic system of interacting agents is considered as a model for economic dynamics. The dynamics of the system is described by a coupled map lattice with nearest neighbor interactions. The evolution of each agent results from the competition between two factors: the agent’s own tendency to grow and the environmental influence that moderates this growth. Depending on the values of the parameters that control these factors, the system can display Pareto or Boltzmann-Gibbs statistical behaviors in its asymptotic dynamical regime. The regions where these behaviors appear are calculated on the space of parameters of the system. Other statistical properties, such as the mean wealth, the standard deviation, and the Gini coefficient characterizing the degree of equity in the wealth distribution are also calculated.     

Quasi-one-dimensional In atomic chains on Si(1 1 1) at low temperature studied by reflection high-energy positron diffraction and scanning tunneling microscopy

We have investigated a quasi-one-dimensional structure of Si(1 1 1)-8 × 2-In surface using reflection high-energy positron diffraction (RHEPD) and scanning tunneling microscopy (STM). From the RHEPD rocking curve analyses, we confirmed the formation of the In hexagon structure proposed by González et al. [C. González, F. Flores, J. Ortega, Phys. Rev. Lett. 96 (2006) 136101]. Furthermore, we found that the empty-state STM image at 44 K is consistent with that calculated with the optimum hexagon structure by the RHEPD analyses.     

Theoretical model for study of the voltage-current curve of a Langmuir-probe used in the hot region of the ECR plasma

In the last years the ATOMKI-ECRIS group started a local plasma diagnostics research project, to adapt the probe to the ECR plasma conditions. Until now we made progress in the study of the cold plasma region. The results has been reported in e.g. [L. Kenéz, S. Biri, J. Karácsony, A. Valek, Nucl. Instrum. Methods Phys. Res. B 187 (2) (2002) 249; L. Kenéz, S. Biri, J. Karácsony, A. Valek, T. Nakagawa, K.E. Stiebing, V. Mironov, Rev. Sci. Instrum. 73 (2) (2002) 617]. In this Letter we make a step further report the first experiments carried out in the hot ECR plasma. We used a simple probe inserted in the hot resonant plasma. We point out that this probe works as emitting probe. We developed a theoretical model to explain the unusual shaped voltage-current characteristics and tested its validity using computational study of the presented theory.     

Cooperation in N-person evolutionary snowdrift game in scale-free Barabási-Albert networks

Cooperation in the N-person evolutionary snowdrift game (NESG) is studied in scale-free Barabási-Albert (BA) networks. Due to the inhomogeneity of the network, two versions of NESG are proposed and studied. In a model where the size of the competing group varies from agent to agent, the fraction of cooperators drops as a function of the payoff parameter. The networking effect is studied via the fraction of cooperative agents for nodes with a particular degree. For small payoff parameters, it is found that the small-k agents are dominantly cooperators, while large-k agents are of non-cooperators. Studying the spatial correlation reveals that cooperative agents will avoid to be nearest neighbors and the correlation disappears beyond the next-nearest neighbors. The behavior can be explained in terms of the networking effect and payoffs. In another model with a fixed size of competing groups, the fraction of cooperators could show a non-monotonic behavior in the regime of small payoff parameters. This non-trivial behavior is found to be a combined effect of the many agents with the smallest degree in the BA network and the increasing fraction of cooperators among these agents with the payoff for small payoffs.     

Statistical mechanics of money

In a closed economic system, money is conserved. Thus, by analogy with energy, the equilibrium probability distribution of money must follow the exponential Boltzmann-Gibbs law characterized by an effective temperature equal to the average amount of money per economic agent. We demonstrate how the Boltzmann-Gibbs distribution emerges in computer simulations of economic models. Then we consider a thermal machine, in which the difference of temperatures allows one to extract a monetary profit. We also discuss the role of debt, and models with broken time-reversal symmetry for which the Boltzmann-Gibbs law does not hold. The instantaneous distribution of money among the agents of a system should not be confused with the distribution of wealth. The latter also includes material wealth, which is not conserved, and thus may have a different (e.g. power-law) distribution. Received 22 June 2000     

Metal-insulator transition in the In/Si(1 1 1) surface

The metal-insulator transition observed in the In/Si(1 1 1)-4 × 1 reconstruction is studied by means of ab initio calculations of a simplified model of the surface. Different surface bands are identified and classified according to their origin and their response to several structural distortions. We support the, recently proposed [C. González, J. Ortega, F. Flores, New J. Phys. 7 (2005) 100], combination of a shear and a Peierls distortions as the origin of the metal-insulator transition. Our results also seem to favor an electronic driving force for the transition.     

Pathway model,superstatistics, Tsallis statistics,and a generalized measure of entropy

The pathway model of Mathai [A pathway to matrix-variate gamma and normal densities, Linear Algebra Appl. 396 (2005) 317–328] is shown to be inferable from the maximization of a certain generalized entropy measure. This entropy is a variant of the generalized entropy of order α$\alpha$, considered in Mathai and Rathie [Basic Concepts in Information Theory and Statistics: Axiomatic Foundations and Applications, Wiley Halsted, New York and Wiley Eastern, New Delhi, 1975], and it is also associated with Shannon, Boltzmann–Gibbs, Rényi, Tsallis, and Havrda–Charvát entropies. The generalized entropy measure introduced here is also shown to have interesting statistical properties and it can be given probabilistic interpretations in terms of inaccuracy measure, expected value, and information content in a scheme. Particular cases of the pathway model are shown to be Tsallis statistics [C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys. 52 (1988) 479–487] and superstatistics introduced by Beck and Cohen [Superstatistics, Physica A 322 (2003) 267–275]. The pathway model's connection to fractional calculus is illustrated by considering a fractional reaction equation.     

Frustration and quantum phase transitions in an anisotropic antiferromagnet on a square lattice

We study the effect of frustration between nearest and next-nearest neighbors of the quantum S=1 anisotropic Heisenberg model on a square lattice using the bond operator technique. A single-site anisotropy term induces a quantum phase transition in the system. We calculate the effect of zero-temperature quantum fluctuations on the magnetization for the Néel and collinear antiferromagnetic phases.     

Measuring the self-similarity exponent in Lévy stable processes of financial time series

Geometric method-based procedures, which will be called GM algorithms herein, were introduced in [M.A. Sánchez Granero, J.E. Trinidad Segovia, J. García Pérez, Some comments on Hurst exponent and the long memory processes on capital markets, Phys. A 387 (2008) 5543-5551], to efficiently calculate the self-similarity exponent of a time series. In that paper, the authors showed empirically that these algorithms, based on a geometrical approach, are more accurate than the classical algorithms, especially with short length time series. The authors checked that GM algorithms are good when working with (fractional) Brownian motions. Moreover, in [J.E. Trinidad Segovia, M. Fernández-Martínez, M.A. Sánchez-Granero, A note on geometric method-based procedures to calculate the Hurst exponent, Phys. A 391 (2012) 2209-2214], a mathematical background for the validity of such procedures to estimate the self-similarity index of any random process with stationary and self-affine increments was provided. In particular, they proved theoretically that GM algorithms are also valid to explore long-memory in (fractional) Lévy stable motions.     

Considerations on “Harmonic balancing approach to nonlinear oscillations of a punctual charge in the electric field of charged ring”

In a previous short communication [A. Beléndez, E. Fernández, J.J. Rodes, R. Fuentes, I. Pascual, Phys. Lett. A 373 (2009) 735] the nonlinear oscillations of a punctual charge in the electric field of a charged ring were analyzed. Approximate frequency-amplitude relations and periodic solutions were obtained using the harmonic balance method. Now we clarify an important aspect about of this oscillation charge. Taking into account Earnshaw's theorem, this punctual charge cannot be a free charge and so it must be confined, for example, on a finite conducting wire placed along the axis of the ring. Then, the oscillatory system may consist of a punctual charge on a conducting wire placed along the axis of the uniformly charged ring.     

Formal equivalence between Tsallis and extended Boltzmann-Gibbs statistics

A formal correspondence between the q-distribution obtained from the Tsallis entropy and non-Maxwellian distributions obtained from the Boltzmann-Gibbs (BG) entropy is obtained. This formal correspondence is obtained by imposing an infinite number of constraints when one maximizes the BG entropy. Different from the approach of Tsallis, Prato and Plastino [C. Tsallis, D. Prato, A.R. Plastino, Astrophys. Space Sci., 290 (2004) 259-274], we relate the constraints to the central moments, providing a natural meaning to the q-parameter.     

Evolutionary games on scale-free networks with a preferential selection mechanism

Considering the heterogeneity of individuals’ influence in the real world, we introduce a preferential selection mechanism to evolutionary games (the Prisoner’s Dilemma Game and the Snowdrift Game) on scale-free networks and focus on the cooperative behavior of the system. In every step, each agent chooses an individual from all its neighbors with a probability proportional to k^α indicating the influence of the neighbor, where k is the degree. Simulation results show that the cooperation level has a non-trivial dependence on α. To understand the effect of preferential selection mechanism on the evolution of the system, we investigate the time series of the cooperator frequency in detail. It is found that the cooperator frequency is greatly influenced by the initial strategy of hub nodes when α>0. This observation is confirmed by investigating the system behavior when some hub nodes’ strategies are fixed.     

Digital applications of the planar Hall effect in ferromagnetic thin films

The planar Hall effect in ferromagnetic thin films has been optimized with respect to composition dependence and geometric structure. Various devices can be realized with this effect, using the output voltage or the output current in a short circuited loop.This work was sponsored by Délégation Générate á la Recherche Scientifique et Technique.The authors thank R. Morille for the preparation of thin films.     

A non-linear dynamic lumped-parameter model of a rectangular plate

A lumped-parameter model of a rectangular plate is developed by assuming fundamental mode solutions and using Hamilton's Principle and the Euler equations to set up the differential equation of motion for the system. The plate theory used may be described as the dynamic analogue of the von Kármán large-deflection theory. Four sets of symmetrical boundary conditions are considered with the restriction of uniform pressure dynamic loads. The model takes the form of a mass on a cubic-hardening spring with each term defined by algebraic expressions of the plate parameters. The results for some specific problems are compared with two previous solutions. This method is less accurate but simpler to develop and apply.     

Optical properties of GeO2 in the ultraviolet region

The optical constants of amorphous and crystalline GeO₂ were determined by measurements of reflectivity in the region of phonon energy 0·5–25 eV and subsequent use of Kramers-Kronig analysis. The differences between the spectra of GeO₂ and those of SiO₂ are shown and discussed.The author would like to express her gratitude to Prof. J. Tauc for his interest in this work, to Dr. Z. Trousil, J. Charvát, Dr. S. Koc, Mrs. V. Míková and Dr. Németh-Sallay for the preparation of the samples, to Dr. L. ervinka and Dr. M. Rozsival for the test of their structure and to Dr. M. Závtová and Dr. I. Gregora for kind cooperation in the index-of-refraction measurements. Very useful comments by Dr, J. Sak are gratefully acknowledged.It is also a pleasure to thank Dr. R. P. Madden for discussion on the later stage of this work.     

Boltzmann-Gibbs thermal equilibrium distribution for classical systems and Newton law: a computational discussion

We implement a general numerical calculation that allows for a direct comparison between nonlinear Hamiltonian dynamics and the Boltzmann-Gibbs canonical distribution in Gibbs Γ-space. Using paradigmatic first-neighbor models, namely, the inertial XY ferromagnet and the Fermi-Pasta-Ulam β-model, we show that at intermediate energies the Boltzmann-Gibbs equilibrium distribution is a consequence of Newton second law (F=ma). At higher energies we discuss partial agreement between time and ensemble averages.     

SIR model of epidemic spread with accumulated exposure

We study an extended and modified SIR model of epidemic spread in which susceptible agents during interactions with infectious neighbors are exposed to the disease and can consequently become infectious. The studied model is extended to include heterogeneity of interactions which is modelled assuming random character of the dose accumulated by susceptible agents in every interaction with infectious neighbors. When the accumulated exposure is larger than the individual’s resistance, an agent becomes infectious and consequently introduces a new source of an epidemic which is capable of passing the disease further. We study statistical properties characterizing the course of an epidemic. The examination of the modified SIR model reveals a possible “resonant activation”-like behavior of the system in the duration of the epidemic outbreak and a possible bistable behavior of the model with accumulated exposure. Furthermore, the linear scaling of the duration of the epidemic with the system size for a wide range of the model parameters is recorded.     

Weighted self-similar networks under preferential attachment

We introduce an abstract evolutionary formalism that generates weighted networks whose growth under stochastic preferential attachment triggers unrestricted weight rearrangements in existing links. The class of resulting algorithms for different parameter values includes the Barabási-Albert and Barrat-Barthélemy-Vespignani models as special cases. We solve the recursions that describe the average growth to derive exact solutions for the expected degree and strength distribution, the individual strength and weight development and the joint distribution of neighboring degrees. We find that the network exhibits a particular form of self-similarity, namely every sufficiently interconnected node has on average the same constitution of small-degree neighbors as any other node of large degree. Finally we suggest potential applications in several fields of interest.     

A quenched study of the Schrödinger functional with chirally rotated boundary conditions: Applications

In a previous paper (González López, et al., 2013) [1], we have discussed the non-perturbative tuning of the chirally rotated Schrödinger functional (χSF$\chi \text{SF}$). This tuning is required to eliminate bulk O(a) cutoff effects in physical correlation functions. Using our tuning results obtained in González López et al. (2013) [1] we perform scaling and universality tests analyzing the residual O(a  ) cutoff effects of several step-scaling functions and we compute renormalization factors at the matching scale. As an example of possible application of the χSF$\chi \text{SF}$ we compute the renormalized strange quark mass using large volume data obtained from Wilson twisted mass fermions at maximal twist.     

Anisotropic ac dissipation at the surface of mesoscopic superconductors

In this work we study the ac dissipation of mesoscopic superconductors at microwave frequencies using the time dependent Ginzburg-Landau equations. Our numerical simulations show that the ac dissipation is strongly dependent on the orientation of the ac magnetic field (h_ac) relative to the dc magnetic field (H_dc). When h_ac is parallel to H_dc we observe that each vortex penetration event produces a significant suppression of the ac losses because the imaginary part of the ac susceptibility as a function of H_dc increases before the penetration of vortices, and then it decreases abruptly after vortices have entered into the sample. In the second case, when h_ac is perpendicular to H_dc, we observe that the jumps in dissipation occur at the same values of H_dc but are much smaller than in the parallel configuration. The behavior of the dissipation in the perpendicular configuration is similar to previous results obtained in recent microwave experiments using mesoscopic lithographed squares of Pb [A.D. Hernández, O. Arés, C. Hart, D. Domínguez, H. Pastoriza, A. Butera, J. Low Temp. Phys. 135 (2004) 119].