77,201 research outputs found
On the rooted Tutte polynomial
The Tutte polynomial is a generalization of the chromatic polynomial of graph
colorings. Here we present an extension called the rooted Tutte polynomial,
which is defined on a graph where one or more vertices are colored with
prescribed colors. We establish a number of results pertaining to the rooted
Tutte polynomial, including a duality relation in the case that all roots
reside around a single face of a planar graph. The connection with the Potts
model is also reviewed.Comment: plain latex, 14 pages, 2 figs., to appear in Annales de l'Institut
Fourier (1999
A Generic Dynamical Model of Gamma-ray Burst Remnants
The conventional generic model is deemed to explain the dynamics of
-ray burst remnants very well, no matter whether they are adiabatic or
highly radiative. However, we find that for adiabatic expansion, the model
could not reproduce the Sedov solution in the non-relativistic phase, thus the
model needs to be revised. In the present paper, a new differential equation is
derived. The generic model based on this equation has been shown to be correct
for both radiative and adiabatic fireballs, and in both ultra-relativistic and
non-relativistic phase.Comment: 10 pages, LaTeX, 4 postscript figures, accepted for publication in
MNRA
GRB 060206: hints of precession of the central engine?
Aims. The high-redshift (z=4.048) gamma-ray burst GRB 060206 showed unusual behavior, with a significant rebrightening by a factor of ~4 at about 3000 s after the burst. We argue that this rebrightening implies that the central engine became active again after the main burst produced by the first ejecta, then drove another more collimated jet-like ejecta with a larger viewing angle. The two ejecta both interacted with the ambient medium, giving rise to forward shocks that propagated into the ambient medium and reverse shocks that penetrated into the ejecta. The total emission was a combination of the emissions from the reverse- and forward- shocked regions. We discuss how this combined emission accounts for the observed rebrightening.
Methods. We apply numerical models to calculate the light curves from the shocked regions, which include a forward shock originating in the first ejecta and a forward-reverse shock for the second ejecta.
Results. We find evidence that the central engine became active again 2000 s after the main burst. The combined emission produced by interactions of these two ejecta with the ambient medium can describe the properties of the afterglow of this burst. We argue that the rapid rise in brightness at ~3000 s in the afterglow is due to the off-axis emission from the second ejecta. The precession of the torus or accretion disk of the central engine is a natural explanation for the departure of the second ejecta from the line of sight
GRB afterglows: deep Newtonian phase and its application
Gamma-ray burst afterglows have been observed for months or even years in a
few cases. It deserves noting that at such late stages, the remnants should
have entered the deep Newtonian phase, during which the majority of
shock-accelerated electrons will no longer be highly relativistic. To calculate
the afterglows, we must assume that the electrons obey a power-law distribution
according to their kinetic energy, not simply the Lorentz factor.Comment: Poster at the 4th workshop "Gamma-Ray Bursts in the Afterglow Era"
(Rome, 2004), accepted for publication in the proceedings. 4 pages, with 3
figures inserte
Soluble kagome Ising model in a magnetic field
An Ising model on the kagome lattice with super-exchange interactions is
solved exactly under the presence of a nonzero external magnetic field. The
model generalizes the super-exchange model introduced by Fisher in 1960 and is
analyzed in light of a free-fermion model. We deduce the critical condition and
present detailed analyses of its thermodynamic and magnetic properties. The
system is found to exhibit a second-order transition with logarithmic
singularities at criticality.Comment: 8 pages, 8 figures, references adde
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