3,176 research outputs found
Exact Solutions of Integrable 2D Contour Dynamics
A class of exact solutions of the dispersionless Toda hierarchy constrained
by a string equation is obtained. These solutions represent deformations of
analytic curves with a finite number of nonzero harmonic moments. The
corresponding tau-functions are determined and the emergence of cusps is
studied.Comment: 13 pages, 3 figure
Genus-zero Whitham hierarchies in conformal-map dynamics
A scheme for solving quasiclassical string equations is developped to prove
that genus-zero Whitham hierarchies describe the deformations of planar domains
determined by rational conformal maps. This property is applied in normal
matrix models to show that deformations of simply-connected supports of
eigenvalues under changes of coupling constants are governed by genus-zero
Whitham hierarchies.Comment: 12 pages, 3 figure
Phase transitions in multi-cut matrix models and matched solutions of Whitham hierarchies
We present a method to study phase transitions in the large N limit of matrix
models using matched solutions of Whitham hierarchies. The endpoints of the
eigenvalue spectrum as functions of the temperature are characterized both as
solutions of hodograph equations and as solutions of a system of ordinary
differential equations. In particular we show that the free energy of the
matrix model is the quasiclassical tau-function of the associated hierarchy,
and that critical processes in which the number of cuts changes in one unit are
third-order phase transitions described by C1 matched solutions of Whitham
hierarchies. The method is illustrated with the Bleher-Eynard model for the
merging of two cuts. We show that this model involves also a birth of a cut
Fine structure in the large n limit of the non-hermitian Penner matrix model
In this paper we apply results on the asymptotic zero distribution of the
Laguerre polynomials to discuss generalizations of the standard large limit
in the non-hermitian Penner matrix model. In these generalizations , but the product is not necessarily fixed to the value of the 't
Hooft coupling . If and the limit exists, then the large limit is well-defined but
depends both on and on . This result implies that for the standard
large limit with fixed is not well-defined. The parameter
determines a fine structure of the asymptotic eigenvalue support: for
the support consists of an interval on the real axis with charge fraction
and an -dependent oval around the origin with charge fraction
. For these two components meet, and for the oval collapses to
the origin. We also calculate the total electrostatic energy ,
which turns out to be independent of , and the free energy
, which does depend of the fine structure
parameter . The existence of large asymptotic expansions of
beyond the planar limit as well as the double-scaling limit are
also discussed
Spectral curves in gauge/string dualities: integrability, singular sectors and regularization
We study the moduli space of the spectral curves which
characterize the vacua of U(n) supersymmetric gauge theories
with an adjoint Higgs field and a polynomial tree level potential . It is
shown that there is a direct way to associate a spectral density and a
prepotential functional to these spectral curves. The integrable structure of
the Whitham equations is used to determine the spectral curves from their
moduli. An alternative characterization of the spectral curves in terms of
critical points of a family of polynomial solutions to
Euler-Poisson-Darboux equations is provided. The equations for these critical
points are a generalization of the planar limit equations for one-cut random
matrix models. Moreover, singular spectral curves with higher order branch
points turn out to be described by degenerate critical points of .
As a consequence we propose a multiple scaling limit method of regularization
and show that, in the simplest cases, it leads to the Painlev\`{e}-I equation
and its multi-component generalizations.Comment: 29 pages, 4 figure
Novas tendências em marketing por causa do auge da Internet
The use of Internet has changed considerably the marketing practice. In this article the
authors carry on a literature review to analyse the factors involved in the process and also
the advantages, challenges and opportunities of this technology from a marketing
perspective.El uso de Internet ha traído cambios considerables para la práctica del Marketing. Este
artículo lleva a cabo una revisión bibliográfica donde se analizan los factores que están
relacionados con el proceso de cambio así como las ventajas, desafíos y oportunidades
que ofrece esta nueva tecnología desde una perspectiva del Marketing.O uso da Internet trouxe mudanças consideráveis para a prática do Marketing. Este artigo
realiza uma revisão bibliográfica onde se analisam os fatores que estão relacionados com
o processo de mudança assim como as vantagens, desafios e oportunidades oferecidas por
esta nova tecnologia a partir de uma perspectiva de Marketing
Climate change mitigation, a carbon tax or an emissions trading scheme? : an analysis of the Norwegian perspective
Climate Changes are a latent issue which has to be addressed in a correct way in order to mitigate it; to have a Climate policy is important to work against the effects of climate change which have been caused by mankind.
The objective of this Master’s thesis is to contribute to the analysis of emissions trading and emissions taxation as climate policy instruments. Hence, the regulations of the European Union emissions trading system (EU-ETS) are presented and analyzed, and then applied to the Norwegian system
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