Wealth redistribution with finite resources

We present a simplified model for the exploitation of finite resources by interacting agents, where each agent receives a random fraction of the available resources. An extremal dynamics ensures that the poorest agent has a chance to change its economic welfare. After a long transient, the system self-organizes into a critical state that maximizes the average performance of each participant. Our model exhibits a new kind of wealth condensation, where very few extremely rich agents are stable in time and the rest stays in the middle class.Comment: 4 pages, 3 figures, RevTeX 4 styl

Randmoness and Step-like Distribution of Pile Heights in Avalanche Models

The paper develops one-parametric family of the sand-piles dealing with the grains' local losses on the fixed amount. The family exhibits the crossover between the models with deterministic and stochastic relaxation. The mean height of the pile is destined to describe the crossover. The height's densities corresponding to the models with relaxation of the both types tend one to another as the parameter increases. These densities follow a step-like behaviour in contrast to the peaked shape found in the models with the local loss of the grains down to the fixed level [S. Lubeck, Phys. Rev. E, 62, 6149, (2000)]. A spectral approach based on the long-run properties of the pile height considers the models with deterministic and random relaxation more accurately and distinguishes the both cases up to admissible parameter values.Comment: 5 pages, 5 figure

Corrections to Universal Fluctuations in Correlated Systems: the 2D XY-model

Generalized universality, as recently proposed, postulates a universal non-Gaussian form of the probability density function (PDF) of certain global observables for a wide class of highly correlated systems of finite volume N. Studying the 2D XY -model, we link its validity to renormalization group properties. It would be valid if there were a single dimension 0 operator, but the actual existence of several such operators leads to T-dependent corrections. The PDF is the Fourier transform of the partition function Z(q) of an auxiliary theory which differs by a dimension 0 perturbation with a very small imaginary coefficient iq/N from a theory which is asymptotically free in the infrared. We compute the PDF from a systematic loop expansion of ln Z(q).Comment: To be published in Phys. Rev.

d_c=4 is the upper critical dimension for the Bak-Sneppen model

Numerical results are presented indicating d_c=4 as the upper critical dimension for the Bak-Sneppen evolution model. This finding agrees with previous theoretical arguments, but contradicts a recent Letter [Phys. Rev. Lett. 80, 5746-5749 (1998)] that placed d_c as high as d=8. In particular, we find that avalanches are compact for all dimensions d<=4, and are fractal for d>4. Under those conditions, scaling arguments predict a d_c=4, where hyperscaling relations hold for d<=4. Other properties of avalanches, studied for 1<=d<=6, corroborate this result. To this end, an improved numerical algorithm is presented that is based on the equivalent branching process.Comment: 4 pages, RevTex4, as to appear in Phys. Rev. Lett., related papers available at http://userwww.service.emory.edu/~sboettc

Unified Scaling Law for Earthquakes

We show that the distribution of waiting times between earthquakes occurring in California obeys a simple unified scaling law valid from tens of seconds to tens of years, see Eq. (1) and Fig. 4. The short time clustering, commonly referred to as aftershocks, is nothing but the short time limit of the general hierarchical properties of earthquakes. There is no unique operational way of distinguishing between main shocks and aftershocks. In the unified law, the Gutenberg-Richter b-value, the exponent -1 of the Omori law for aftershocks, and the fractal dimension d_f of earthquakes appear as critical indices.Comment: 4 pages, 4 figure

The origin of power-law distributions in self-organized criticality

The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk process in a one-dimensional lattice. Power law distributions of the lifetime and spatial size are found when the random walk is unbiased with equal probability to move in opposite directions. This shows that power-law distributions in self-organized criticality may be caused by the balance of competitive interactions. At the mean time, the mean spatial size for avalanches with the same lifetime is found to increase in a power law with the lifetime.Comment: 4 pages in RevTeX, 3 eps figures. To appear in J.Phys.G. To appear in J. Phys.

Spatial-temporal correlations in the process to self-organized criticality

A new type of spatial-temporal correlation in the process approaching to the self-organized criticality is investigated for the two simple models for biological evolution. The change behaviors of the position with minimum barrier are shown to be quantitatively different in the two models. Different results of the correlation are given for the two models. We argue that the correlation can be used, together with the power-law distributions, as criteria for self-organized criticality.Comment: 3 pages in RevTeX, 3 eps figure

Condensation of Tubular D2-branes in Magnetic Field Background

It is known that in the Minkowski vacuum a bunch of IIA superstrings with D0-branes can be blown-up to a supersymmetric tubular D2-brane, which is supported against collapse by the angular momentum generated by crossed electric and magnetic Born-Infeld (BI) fields. In this paper we show how the multiple, smaller tubes with relative angular momentum could condense to a single, larger tube to stabilize the system. Such a phenomena could also be shown in the systems under the Melvin magnetic tube or uniform magnetic field background. However, depending on the magnitude of field strength, a tube in the uniform magnetic field background may split into multiple, smaller tubes with relative angular momentum to stabilize the system.Comment: Latex 10 pages, mention the dynamical joining of the tubes, modify figure

The Moduli Space of Noncommutative Vortices

The abelian Higgs model on the noncommutative plane admits both BPS vortices and non-BPS fluxons. After reviewing the properties of these solitons, we discuss several new aspects of the former. We solve the Bogomoln'yi equations perturbatively, to all orders in the inverse noncommutivity parameter, and show that the metric on the moduli space of k vortices reduces to the computation of the trace of a k-dimensional matrix. In the limit of large noncommutivity, we present an explicit expression for this metric.Comment: Invited contribution to special issue of J.Math.Phys. on "Integrability, Topological Solitons and Beyond"; 10 Pages, 1 Figure. v2: revision of history in introductio