Wealth distributions in asset exchange models

A model for the evolution of the wealth distribution in an economically interacting population is introduced, in which a specified amount of assets are exchanged between two individuals when they interact. The resulting wealth distributions are determined for a variety of exchange rules. For “random” exchange, either individual is equally likely to gain in a trade, while “greedy” exchange, the richer individual gains. When the amount of asset traded is fixed, random exchange leads to a Gaussian wealth distribution, while greedy exchange gives a Fermi-like scaled wealth distribution in the long-time limit. Multiplicative processes are also investigated, where the amount of asset exchanged is a finite fraction of the wealth of one of the traders. For random multiplicative exchange, a steady state occurs, while in greedy multiplicative exchange a continuously evolving power law wealth distribution arises. Received: 13 August 1997 / Revised: 31 December 1997 / Accepted: 26 January 1998     

Class formation in a social network with asset exchange

We study two kinds of economic exchanges, additive and multiplicative, in a system of N agents. The work is divided into two parts. In the first one, the agents are free to interact with each other. The system evolves to a Boltzmann-Gibbs distribution with additive exchange and condenses with a multiplicative one. If bankruptcy is introduced, both types of exchange lead to condensation. Condensation times have been studied. In the second part, the agents are placed in a social network. We analyze the behavior of wealth distributions in time, and the formation of economic classes is observed for certain values of network connectivity.     

Search for signatures of phase transition and critical point in heavy-ion collisions

The general concepts in the critical phenomena related with the notions of “scaling” and “universality” are considered. Behavior of various systems near a phase transition is displayed. Search for clear signatures of the phase transition of the nuclear matter and location of the critical point in heavy-ion collisions (HIC) is discussed. The experimental data on inclusive spectra measured in HIC at RHIC and SPS over a wide range of energies s _{N N} ^1/2 = 9–200 GeV are analyzed in the framework of z-scaling. A microscopic scenario of the constituent interactions is presented. Dependence of the energy loss on the momentum of the produced hadron, energy and centrality of the collision is studied. Self-similarity of the constituent interactions described in terms of momentum fractions is used to characterize the nuclear medium by “specific heat” and colliding nuclei by fractal dimensions. Preferable kinematical regions to search for signatures of the phase transition of the nuclear matter produced in HIC are discussed. Discontinuity of the “specific heat” is assumed to be a signature of the phase transition and the critical point.     

Extended theories of gravity and their cosmological and astrophysical applications

Astrophysical observations are pointing out huge amounts of “dark matter” and “dark energy” needed to explain the observed large scale structure and cosmic dynamics. The emerging picture is a spatially flat, homogeneous Universe undergoing the today observed accelerated phase. Despite of the good quality of astrophysical surveys, commonly addressed as Precision Cosmology, the nature and the nurture of dark energy and dark matter, which should constitute the bulk of cosmological matter-energy, are still unknown. Furthermore, up to now, no experimental evidence has been found, at fundamental level, to explain such mysterious components. The problem could be completely reversed considering dark matter and dark energy as “shortcomings” of General Relativity in its simplest formulation (a linear theory in the Ricci scalar R, minimally coupled to the standard perfect fluid matter) and claiming for the “correct” theory of gravity as that derived by matching the largest number of observational data, without imposing any theory a priori. As a working hypothesis, accelerating behavior of cosmic fluid, large scale structure, potential of galaxy clusters, rotation curves of spiral galaxies could be reproduced by means of extending the standard theory of General Relativity. In other words, gravity could acts in different ways at different scales and the above “shortcomings” could be due to incorrect extrapolations of the Einstein gravity, actually tested at short scales and low energy regimes. After a survey of what is intended for Extended Theories of Gravity in the so called “metric” and “Palatini” approaches, we discuss some cosmological and astrophysical applications where the issues related to the dark components are addressed by enlarging the Einstein theory to more general f (R) Lagrangians, where f (R) is a generic function of Ricci scalar R, not assumed simply linear. Obviously, this is not the final answer to the problem of “dark-components” but it can be considered as an operative scheme whose aim is to avoid the addition of unknown exotic ingredients to the cosmic pie.     

Modelling fluctuations of financial time series: from cascade process to stochastic volatility model

In this paper, we provide a simple, “generic” interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that in this context 1/f power spectra, as recently observed in reference [23], naturally emerge. We then propose a simple solvable “stochastic volatility” model for return fluctuations. This model is able to reproduce most of recent empirical findings concerning financial time series: no correlation between price variations, long-range volatility correlations and multifractal statistics. Moreover, its extension to a multivariate context, in order to model portfolio behavior, is very natural. Comparisons to real data and other models proposed elsewhere are provided. Received 22 May 2000     

Magnetostatics dualism in a one-dimensional chain of classical magnetic moments

Magnetostatic interaction in polycrystalline nanowires manifests itself in two competing ways, providing the existence of a stable domain structure even in the absence of exchange interaction between crystals. It has been found that not only the domain structure but also the block magnetization structure of the nanowire consisting of exchange-noninteracting crystallites are of magnetostatic nature. The average domain wall width and magnetization correlation length have been calculated analytically and validated by simulation. The feasibility of the “easy axis” and “easy plane” phases of the effective anisotropy for different crystallite shapes has been demonstrated.     

On some features of the phase diagram of a ferroic with the cubic paraphase

The phase diagram of a ferroic with the paraphase of symmetry O _h has been studied for a three-dimensional order parameter. In the simplest model, which allows for the existence of a phase of the general position, i.e., the triclinic phase, the region of its existence has been investigated analytically. The invariance of the shape of this region is shown. The conditions providing the formation of a “swallowtail”-type feature in the region of existence of the monoclinic phase are considered. A convenient parametrization is proposed for the representation of the phase diagram, including all possible phases.     

Spurious character of singularities associated with phase transitions in cylindrical pores

Phase transitions of simple fluids and binary fluid mixtures confined into long cylindrical pores are re-examined, such as capillary condensation/evaporation and wetting transitions. While a large part of the literature ignores the fact that due to the quasi-one-dimensional character of these systems a singular behavior associated with a sharp phase transition cannot occur, we pay attention to the extent in which these phase transitions are smoothed out (in relation to the magnitude of the pore cross-sectional area). We argue that the finiteness of the pore length is an important parameter which controls the physical phenomena that are observed in simulations (and presumably also experiments explaining the distinction between the apparent “pore critical temperature” and the “hysteresis critical temperature”). We illustrate our arguments with recent findings from simulations of a lattice gas/Ising system and of the Asakura-Oosawa model of colloid-polymer mixtures.     

Switching of banana liquid crystal mesophases under field

Taking advantage of the great number of bent-core or “banana" compounds synthesized and studied in the laboratory, we describe their behaviour under the application of an external electric field. If the field were a static one, we would work within the frame of an equilibrium phase diagram in a (field E, temperature T) space where some phases would be simple dielectrics and others ferroelectric ones with a macroscopic polarization, either spontaneous or induced by the field. In this paper, we deal with the basic responses of “banana” liquid crystals under the application of a low frequency (1 to 100 Hz) AC field. Firstly square-wave voltages allow us to locate the phase boundary between dielectric (at lower field) and ferroelectric phases (higher field) at a given temperature and field threshold. Then we apply slowly varying AC voltages with shapes like triangle or “triple-plateau” to check out the stability of the induced ferroelectric phase versus field removal. Three behaviours are encountered, the unstable one (short lifetime of the high-field ferroelectric phase) where the macroscopic polarization is destroyed and then rebuilt in the opposite direction during each half period and usually called “antiferroelectric”; the stable one (long lifetime) with a polarization that rotates at constant modulus which is labeled as “ferroelectric” and a new one where the macroscopic polarization is proportional to the applied fied, we named this behaviour as “superparaelectric”. Let us stress that these observations apply to the ferroelectric phases of the (E, T) phase diagram not to the zero field (0,T) phases observed in the usual phase characterization experiments except for an eventual spontaneous ferroelectric phase. Received 18 April 2002 and Received in final form 17 January 2003 Published online: 16 April 2003 RID="a" ID="a"e-mail: marcerou@crpp.u-bordeaux.fr RID="b" ID="b"URL: http://www.crpp-bordeaux.cnrs.fr     

Similarity of Co-Species in Co and CoMo-sulfide catalysts supported on carbon and alumina. A Mössbauer emission spectroscopic study

It is shown that, irrespective of the application of carbon or alumina as a support, the local structure of the “Co-sulfide” phase formed during sulfidation of Co-and CoMo-catalysts is the same. A relation is found between the quadrupole splitting (Q.S. value) of the “Co-sulfide” phase and its dispersion. The higher the dispersion, the larger the Q.S. value. The so-called “Co-Mo-S” doublet is observed in all cases and it turns out to be related to a highly dispersed “Co-sulfide” phase instead of a Co, Mo and S containing phase.     

Microscopic mechanisms of spin-dependent electric polarization in 3d oxides

We present a short critical overview of different microscopic models for nonrelativistic and relativistic magnetoelectric coupling including the so-called “spin current scenario”, ab-initio calculations, and several recent microscopic approaches to a spin-dependent electric polarization in 3d oxides.     

Features of the melting dynamics of a vortex lattice in a high-T c superconductor in the presence of pinning centers

The phase transition “triangular lattice-vortex liquid” in layered high-T _c superconductors in the presence of pinning centers is studied. A two-dimensional system of vortices simulating the superconducting layers in a high-T _c Shubnikov phase is calculated by the Monte Carlo method. It was found that in the presence of defects the melting of the vortex lattice proceeds in two stages: First, the ideal triangular lattice transforms at low temperature (≃3 K)into islands which are pinned to the pinning centers and rotate around them and then, at a higher temperature (≃8 K for T _c 584 K), the boundaries of the “islands” become smeared and the system transforms into a vortex liquid. As the pinning force increases, the temperatures of both phase transitions shift: The temperature of the point “triangular lattice-rotating lattice” decreases slightly (to ≃2 K)and the temperature of the phase transition “rotating lattice-vortex liquid” increases substantially (≃70 K). Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 269–274 (25 August 1997)     

Wealth condensation in a Barabasi-Albert network

We study the flow of money among agents in a Barabasi-Albert (BA) scale free network, where each network node represents an agent and money exchange interactions are established through links. The system allows money trade between two agents at a time, betting a fraction f of the poorer’s agent wealth. We also allow for the bet to be biased, giving the poorer agent a winning probability p. In the no network case there is a phase transition involving a relationship between p and f. In the networked case, we also found a condensation interface, however, this is not a complete condensation due to the presence of clusters in the network and its topology. As can be expected, the winner is always a well-connected agent, but we also found that the mean wealth decreases with the agents’ connectivity.     

Moment coupling in the interaction of atoms and their ions with a 3<Emphasis Type="Italic">d</Emphasis>-electron shell

The moment coupling of an interacting ion and an atom with a 3d-electron shell is analyzed for the ground state of identical atoms and ions where resonant charge exchange proceeds with transition of a 4s-electron. The interaction of the ion charge with the atom quadrupole moment is important for this system along with the exchange interactions and spin-orbit interactions inside an isolated atom and an ion. The quadrupole moment for 3d-atoms in the ground states is evaluated. The hierarchy of interactions in a molecular ion is analyzed depending on ion-atom distances and is compared with the standard Hund scheme. The resonant charge exchange proceeds effectively at separations corresponding to an intermediate case between cases “a” and “c” of the Hund coupling scheme.     

Microscopic theory of the electro-acoustic echo in order-disorder antiferroelectrics

A microscopic theory of the electro-acoustic echo (EAE) is proposed for the case in which two pulses of a variable electric field act on an antiferroelectric. This theory augments the phenomenological theory proposed for the purpose of interpreting experiments on the main regularities of the electro-acoustic echo in order-disorder antiferroelectrics. The deuterization effect and “pre-polarization” effect are explained. The shape of the echo signal is derived analytically and it is shown that this shape depends on the time interval between pump pulses. Fiz. Tverd. Tela (St. Petersburg) 40, 118–121 (January 1998)     

Unparticles in gauge theory

A field model for a quark and an antiquark binding is described. Quarks interact via a gauge unparticle (“ungluon”). The model is formulated in terms of Lagrangian which features the source field S(x) which becomes a local pseudo-Goldstone field of conformal symmetry — the pseudodilaton mode and from which the gauge non-primary unparticle field is derived by B _μ(x) ∼ ∂_μ S(x). Because the conformal sector is strongly coupled, the mode S(x) may be one of new states accessible at high energies. We have carried out an analysis of the important quantity that enters in the “ungluon” exchange pattern — the “ungluon” propagator.     

The σK coupling in the chiral unitary approach and the isoscalar ¯N , ¯A interaction

We evaluate the “σ " exchange contribution to the ˉN → ˉN scattering within a chiral unitary approach. We show that the chiral transition potentials for ππ → Kˉ in the t -channel lead to a “σ " contribution that vanishes in the ˉ forward direction and, hence, would produce a null “σ " exchange contribution to the K^- optical potential in nuclear matter in a simple impulse approximation. This is a consequence of the fact that the leading-order chiral Lagrangian gives an I = 0 ππ → Kˉ amplitude proportional to the squared momentum transfer, q². This finding poses questions on the meaning or the origin of “σ " exchange potentials used in relativistic mean-field approaches to the K^- nuclear self-energy. This elementary “σ ” exchange potential in ˉN → ˉN is compared to the Weinberg-Tomozawa term and is found to be smaller than the present theoretical uncertainties but will be relevant in the future when aiming at fitting increasingly more accurate data.     

Phase diagram and isotope effect in cobaltites with spin-state transitions

The oxygen isotope effect was investigated in cobalt oxides (Pr_{1 − y} Eu _y )_0.7Ca_0.3CoO₃ (0.12 < y < 0.26). The measurements of magnetization, electric resistivity, differential magnetic susceptibility, thermal expansion, and specific heat show that as the Eu concentration increases, a transition from “ferromagnetic metal” to “weakly magnetic insulator” is observed at y ≈ 0.18. In the insulating ground state, the transition occurs with a Co spin-state change that is suppressed in the ferromagnetic (FM) metallic phase. The spin-state transition at y > 0.18 is accompanied by a substantial oxygen isotope effect that is virtually absent in the FM phase (y < 0.18).     

Ground-state instability in systems of strongly interacting fermions

The stability of a fermion system is analyzed for a model repulsive pair interaction potential. The possibility of different types of restructuring of the Fermi ground state (at sufficiently great coupling constant) is related to the analyticity properties of such potential. In particular, for the screened Coulomb law it is shown that the restructuring cannot be of the Fermi condensation type, known earlier for some exactly solvable models, but instead belongs to the class of topological transitions. A phase diagram constructed for this model in the variables “screening parameter-coupling constant” displays two kinds of topological transitions: a “5/2” kind, similar to the known Lifshitz transitions in metals, and a “2” kind, characteristic for a uniform strongly interacting system. Pis'ma Zh. éksp. Teor. Fiz. 68, No. 12, 893–899 (25 December 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Self-Similarity of Volume Measures for Laplacians¶on P. C. F. Self-Similar Fractals

Our main goal in this paper is to obtain a precise analogue of Weyl's asymptotic formula for the eigenvalue distribution of Laplacians on a certain class of “finitely ramified” (or p.c.f.) self-similar fractals, building, in particular, on the work of [7, 9, 22, 24]. Our main result consists in precisely identifying (for the class of “decimable fractals”) the volume measures constructed by the second author in [24] for general p.c.f. fractals and showing that they are self-similar. From a physical point of view, our results should be relevant to the study of the density of states for diffusions and wave propagation in fractal media. Received: 6 September 1999 / Accepted: 7 October 2000