4,969 research outputs found
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
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
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.
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
- …