3,945 research outputs found
Different hierarchy of avalanches observed in the Bak-Sneppen evolution model
We introduce a new quantity, average fitness, into the Bak-Sneppen evolution
model. Through the new quantity, a different hierarchy of avalanches is
observed. The gap equation, in terms of the average fitness, is presented to
describe the self-organization of the model. It is found that the critical
value of the average fitness can be exactly obtained. Based on the simulations,
two critical exponents, avalanche distribution and avalanche dimension, of the
new avalanches are given.Comment: 5 pages, 3 figure
Noncommutative Vortex Solitons
We consider the noncommutative Abelian-Higgs theory and investigate general
static vortex configurations including recently found exact multi-vortex
solutions. In particular, we prove that the self-dual BPS solutions cease to
exist once the noncommutativity scale exceeds a critical value. We then study
the fluctuation spectra about the static configuration and show that the exact
non BPS solutions are unstable below the critical value. We have identified the
tachyonic degrees as well as massless moduli degrees. We then discuss the
physical meaning of the moduli degrees and construct exact time-dependent
vortex configurations where each vortex moves independently. We finally give
the moduli description of the vortices and show that the matrix nature of
moduli coordinates naturally emerges.Comment: 22 pages, 1 figure, typos corrected, a comment on the soliton size is
adde
Solitons in the one-dimensional forest fire model
Fires in the one-dimensional Bak-Chen-Tang forest fire model propagate as
solitons, resembling shocks in Burgers turbulence. The branching of solitons,
creating new fires, is balanced by the pair-wise annihilation of oppositely
moving solitons. Two distinct, diverging length scales appear in the limit
where the growth rate of trees, , vanishes. The width of the solitons, ,
diverges as a power law, , while the average distance between solitons
diverges much faster as .Comment: 4 pages with 2 figures include
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
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
Self-organized Networks of Competing Boolean Agents
A model of Boolean agents competing in a market is presented where each agent
bases his action on information obtained from a small group of other agents.
The agents play a competitive game that rewards those in the minority. After a
long time interval, the poorest player's strategy is changed randomly, and the
process is repeated. Eventually the network evolves to a stationary but
intermittent state where random mutation of the worst strategy can change the
behavior of the entire network, often causing a switch in the dynamics between
attractors of vastly different lengths.Comment: 4 pages, 3 included figures. Some text revision and one new figure
added. To appear in PR
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
Elliptic supertube and a Bogomol'nyi-Prasad-Sommerfield D2-brane--anti-D2-brane Pair
An exact solution, in which a D2-brane and an anti-D2-brane are connected by
an elliptically tubular D2-brane, is obtained without any junction condition.
The solution is shown to preserve one quarter of the supersymmetries of the
type-IIA Minkowski vacuum. We show that the configuration cannot be obtained by
"blowing-up" from some inhomogeneously D0-charged superstrings. The BPS bound
tells us that it is rather composed of D0-charged D2-brane-anti-D2-brane pair
and a strip of superstrings connecting them. We obtain the correction to the
charges of the string end points in the constant magnetic background.Comment: v3. 12 pages, journal version; title changed, length trimmed to fit
for Rapid Communication forma
Renormalization group approach to the critical behavior of the forest fire model
We introduce a Renormalization scheme for the one and two dimensional
Forest-Fire models in order to characterize the nature of the critical state
and its scale invariant dynamics. We show the existence of a relevant scaling
field associated with a repulsive fixed point. This model is therefore critical
in the usual sense because the control parameter has to be tuned to its
critical value in order to get criticality. It turns out that this is not just
the condition for a time scale separation. The critical exponents are computed
analytically and we obtain , and ,
respectively for the one and two dimensional case, in very good agreement with
numerical simulations.Comment: 4 pages, 3 uuencoded Postcript figure
Dynamics of BPS States in the Dirac-Born-Infeld Theory
The Dirac-Born-Infeld action with transverse scalar fields is considered to
study the dynamics of various BPS states. We first describe the characteristic
properties of the so-called 1/2 and 1/4 BPS states on the D3 brane, which can
be interpreted as F/D-strings ending on a D3-brane in Type IIB string theory
picture. We then study the response of the BPS states to low energy excitations
of massless fields on the brane, the scalar fields representing the shape
fluctuation of the brane and U(1) gauge fields describing the open string
excitations on the D-brane. This leads to an identification of interactions
between BPS states including the static potentials and the kinetic
interactions.Comment: 19 pages, 4 figures References added, Typographical errors are
correcte
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