3,194 research outputs found
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
Gamma-Ray Bursts from Up-Scattered Self-Absorbed Synchrotron Emission
We calculate the synchrotron self-Compton emission from internal shocks
occurring in relativistic winds as a source of gamma-ray bursts, with allowance
for self-absorption. For plausible model parameters most pulses within a
Gamma-Ray Burst (GRB) are optically thick to synchrotron self-absorption at the
frequency at which most electrons radiate. Up-scattering of photon number
spectra harder than (such as the self-absorbed emission) yields inverse
Compton photon number spectra that are flat, therefore our model has the
potential of explaining the low-energy indices harder than (the
optically thin synchrotron limit) that have been observed in some bursts. The
optical counterparts of the model bursts are sufficiently bright to be detected
by such experiments as LOTIS, unless the magnetic field is well below
equipartition.Comment: to be published in ApJL, 5 pages, 3 color figure
Extremal Optimization at the Phase Transition of the 3-Coloring Problem
We investigate the phase transition of the 3-coloring problem on random
graphs, using the extremal optimization heuristic. 3-coloring is among the
hardest combinatorial optimization problems and is closely related to a 3-state
anti-ferromagnetic Potts model. Like many other such optimization problems, it
has been shown to exhibit a phase transition in its ground state behavior under
variation of a system parameter: the graph's mean vertex degree. This phase
transition is often associated with the instances of highest complexity. We use
extremal optimization to measure the ground state cost and the ``backbone'', an
order parameter related to ground state overlap, averaged over a large number
of instances near the transition for random graphs of size up to 512. For
graphs up to this size, benchmarks show that extremal optimization reaches
ground states and explores a sufficient number of them to give the correct
backbone value after about update steps. Finite size scaling gives
a critical mean degree value . Furthermore, the
exploration of the degenerate ground states indicates that the backbone order
parameter, measuring the constrainedness of the problem, exhibits a first-order
phase transition.Comment: RevTex4, 8 pages, 4 postscript figures, related information available
at http://www.physics.emory.edu/faculty/boettcher
GRB990123: The Case for Saturated Comptonization
The recent simultaneous detection of optical, X-ray and gamma-ray photons
from GRB990123 during the burst provides the first broadband multi-wavelength
characterization of the burst spectrum and evolution. Here we show that a
direct correlation exists between the time-varying gamma-ray spectral shape and
the prompt optical emission. This combined with the unique signatures of the
time-resolved spectra of GRB990123 convincingly supports earlier predictions of
the saturated Comptonization model. Contrary to other suggestions, we find that
the entire continuum from optical to gamma-rays can be generated from a single
source of leptons (electrons and pairs). The optical flux only appears to lag
the gamma-ray flux due to the high initial Thomson depth of the plasma. Once
the plasma has completely thinned out, the late time afterglow behavior of our
model is the same as in standard models based on the Blandford-McKee (1976)
solution.Comment: 10 pages, including 3 figures and 1 table, submitted to The
Astrophysical Journal Letter
Aging in Dense Colloids as Diffusion in the Logarithm of Time
The far-from-equilibrium dynamics of glassy systems share important
phenomenological traits. A transition is generally observed from a
time-homogeneous dynamical regime to an aging regime where physical changes
occur intermittently and, on average, at a decreasing rate. It has been
suggested that a global change of the independent time variable to its
logarithm may render the aging dynamics homogeneous: for colloids, this entails
diffusion but on a logarithmic time scale. Our novel analysis of experimental
colloid data confirms that the mean square displacement grows linearly in time
at low densities and shows that it grows linearly in the logarithm of time at
high densities. Correspondingly, pairs of particles initially in close contact
survive as pairs with a probability which decays exponentially in either time
or its logarithm. The form of the Probability Density Function of the
displacements shows that long-ranged spatial correlations are very long-lived
in dense colloids. A phenomenological stochastic model is then introduced which
relies on the growth and collapse of strongly correlated clusters ("dynamic
heterogeneity"), and which reproduces the full spectrum of observed colloidal
behaviors depending on the form assumed for the probability that a cluster
collapses during a Monte Carlo update. In the limit where large clusters
dominate, the collapse rate is ~1/t, implying a homogeneous, log-Poissonian
process that qualitatively reproduces the experimental results for dense
colloids. Finally an analytical toy-model is discussed to elucidate the strong
dependence of the simulation results on the integrability (or lack thereof) of
the cluster collapse probability function.Comment: 6 pages, extensively revised, final version; for related work, see
http://www.physics.emory.edu/faculty/boettcher/ or
http://www.fysik.sdu.dk/staff/staff-vip/pas-personal.htm
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