7,075 research outputs found
A Simple Explanation for Taxon Abundance Patterns
For taxonomic levels higher than species, the abundance distributions of
number of subtaxa per taxon tend to approximate power laws, but often show
strong deviationns from such a law. Previously, these deviations were
attributed to finite-time effects in a continuous time branching process at the
generic level. Instead, we describe here a simple discrete branching process
which generates the observed distributions and find that the distribution's
deviation from power-law form is not caused by disequilibration, but rather
that it is time-independent and determined by the evolutionary properties of
the taxa of interest. Our model predicts-with no free parameters-the
rank-frequency distribution of number of families in fossil marine animal
orders obtained from the fossil record. We find that near power-law
distributions are statistically almost inevitable for taxa higher than species.
The branching model also sheds light on species abundance patterns, as well as
on links between evolutionary processes, self-organized criticality and
fractals.Comment: 10 pages, 4 Fig
Word Processors with Line-Wrap: Cascading, Self-Organized Criticality, Random Walks, Diffusion, Predictability
We examine the line-wrap feature of text processors and show that adding
characters to previously formatted lines leads to the cascading of words to
subsequent lines and forms a state of self-organized criticality. We show the
connection to one-dimensional random walks and diffusion problems, and we
examine the predictability of catastrophic cascades.Comment: 6 pages, LaTeX with RevTeX package, 4 postscript figures appende
Dual of Big-bang and Big-crunch
Starting from the Janus solution and its gauge theory dual, we obtain the
dual gauge theory description of the cosmological solution by procedure of the
double anaytic continuation. The coupling is driven either to zero or to
infinity at the big-bang and big-crunch singularities, which are shown to be
related by the S-duality symmetry. In the dual Yang-Mills theory description,
these are non singular at all as the coupling goes to zero in the N=4 Super
Yang-Mills theory. The cosmological singularities simply signal the failure of
the supergravity description of the full type IIB superstring theory.Comment: 18 pages, 5 figures, references added, minor corrections, further
minor corrections, v4: some clarification and more details adde
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
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
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
Conformal field theory correlations in the Abelian sandpile mode
We calculate all multipoint correlation functions of all local bond
modifications in the two-dimensional Abelian sandpile model, both at the
critical point, and in the model with dissipation. The set of local bond
modifications includes, as the most physically interesting case, all weakly
allowed cluster variables. The correlation functions show that all local bond
modifications have scaling dimension two, and can be written as linear
combinations of operators in the central charge -2 logarithmic conformal field
theory, in agreement with a form conjectured earlier by Mahieu and Ruelle in
Phys. Rev. E 64, 066130 (2001). We find closed form expressions for the
coefficients of the operators, and describe methods that allow their rapid
calculation. We determine the fields associated with adding or removing bonds,
both in the bulk, and along open and closed boundaries; some bond defects have
scaling dimension two, while others have scaling dimension four. We also
determine the corrections to bulk probabilities for local bond modifications
near open and closed boundaries.Comment: 13 pages, 5 figures; referee comments incorporated; Accepted by Phys.
Rev.
Exact equqations and scaling relations for f-avalanche in the Bak-Sneppen evolution model
Infinite hierarchy of exact equations are derived for the newly-observed
f-avalanche in the Bak-Sneppen evolution model. By solving the first order
exact equation, we found that the critical exponent which governs the
divergence of the average avalanche size, is exactly 1 (for all dimensions),
confirmed by the simulations. Solution of the gap equation yields another
universal exponent, denoting the the relaxation to the attractor, is exactly 1.
We also establish some scaling relations among the critical exponents of the
new avalanche.Comment: 5 pages, 1 figur
Breakdown of self-organized criticality
We introduce two sandpile models which show the same behavior of real
sandpiles, that is, an almost self-organized critical behavior for small
systems and the dominance of large avalanches as the system size increases. The
systems become fully self-organized critical, with the critical exponents of
the Bak, Tang and Wiesenfeld model, as the system parameters are changed,
showing that these systems can make a bridge between the well known theoretical
and numerical results and what is observed in real experiments. We find that a
simple mechanism determines the boundary where self-organized can or cannot
exist, which is the presence of local chaos.Comment: 3 pages, 4 figure
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