26 research outputs found
A comparative modeling of supernova 1993J
The light curve of Supernova (SN) 1993J is calculated using two approaches to
radiation transport as exemplified by the two computer codes, STELLA and
EDDINGTON. Particular attention is paid to shock breakout and the photometry in
the U, B, and V bands during the first 120 days. The hydrodynamical model, the
explosion of a 13 Msun star which had lost most of its hydrogenic envelope to a
companion, is the same in each calculation. The comparison elucidates
differences between the approaches and also serves to validate the results of
both. STELLA includes implicit hydrodynamics and is able to model supernova
evolution at early times, before the expansion is homologous. STELLA also
employs multi-group photonics and is able to follow the radiation as it
decouples from the matter. EDDINGTON uses a different algorithm for integrating
the transport equation, assumes homologous expansion, and uses a finer
frequency resolution. Good agreement is achieved between the two codes only
when compatible physical assumptions are made about the opacity. A new result
for SN 1993J is a prediction of the continuum spectrum near the shock breakout
(calculated by STELLA) which is superior to the results of other standard
single energy group hydrocodes such as VISPHOT or TITAN. Based on the results
of our independent codes, we discuss the uncertainties involved in the current
time dependent models of supernova light curves.Comment: 43 pages with 22 eps figures, aaspp4.sty + epsf.sty, Accepted by ApJ,
to appear in March 20, 1998 issue, Vol. 49
Resolvents and Seiberg-Witten representation for Gaussian beta-ensemble
The exact free energy of matrix model always obeys the Seiberg-Witten (SW)
equations on a complex curve defined by singularities of the quasiclassical
resolvent. The role of SW differential is played by the exact one-point
resolvent. We show that these properties are preserved in generalization of
matrix models to beta-ensembles. However, since the integrability and
Harer-Zagier topological recursion are still unavailable for beta-ensembles, we
need to rely upon the ordinary AMM/EO recursion to evaluate the first terms of
the genus expansion. Consideration in this paper is restricted to the Gaussian
model.Comment: 15 page
Challenges of beta-deformation
A brief review of problems, arising in the study of the beta-deformation,
also known as "refinement", which appears as a central difficult element in a
number of related modern subjects: beta \neq 1 is responsible for deviation
from free fermions in 2d conformal theories, from symmetric omega-backgrounds
with epsilon_2 = - epsilon_1 in instanton sums in 4d SYM theories, from
eigenvalue matrix models to beta-ensembles, from HOMFLY to super-polynomials in
Chern-Simons theory, from quantum groups to elliptic and hyperbolic algebras
etc. The main attention is paid to the context of AGT relation and its possible
generalizations.Comment: 20 page