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Autor Medina Reus, Elena |
Documentos disponibles escritos por este autor (35)
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Álvarez Galindo, Gabriel ; Martínez Alonso, Luis ; Medina Reus, Elena | Elsevier Science BV | 2011-07-11We present a method to compute the genus expansion of the free energy of Hermitian matrix models from the large N expansion of the recurrence coefficients of the associated family of orthogonal polynomials. The method is based on the Bleher-Its [...]![]()
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In this work we use Riemann-Hilbert problems for multiple orthogonal polynomials in order to derive string equations associated to Lax-Orlov pairs operators. These string equations provide us with a useful tool to analyze the large n-limit of th[...]![]()
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A previously introduced scheme for describing integrable deformations of algebraic curves is completed. Lenard relations are used to characterize and classify these deformations in terms of hydrodynamic-type systems. A general solution of the co[...]![]()
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It is proved that the system of string equations of the dispersionless 2-Toda hierarchy which arises in the planar limit of the hermitian matrix model also underlies certain processes in HeleShaw flows.![]()
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Álvarez Galindo, Gabriel ; Martínez Alonso, Luis ; Medina Reus, Elena | 2013-06This paper deals with the determination of the S-curves in the theory of non-hermitian orthogonal polynomials with respect to exponential weights along suitable paths in the complex plane. It is known that the corresponding complex equilibrium p[...]![]()
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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-funct[...]![]()
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Wide classes of explicit solutions of the Manin-Radul and Jacobian supersymmetric KP hierarchies are constructed by using line bundles over complex supercurves based on the Riemann sphere. Their construction extends several ideas of the standard[...]![]()
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Álvarez, Gabriel ; Martínez Alonso, Luis ; Medina Reus, Elena | Academic Press Inc Elsevier Science | 2015-10In this paper we apply results on the asymptotic zero distribution of the Laguerre polynomials to discuss generalizations of the standard large n limit in the non-hermitian Penner matrix model. In these generalizations g_(n)n ? t, but the produ[...]![]()
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We consider the following system: [GRAPHICS] which has been used as a model for various phenomena, including motion of species by chemotaxis and equilibrium of self-attracting clusters. We show that, in space dimension N = 3, (S) possess radial [...]![]()
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A scheme for solving quasiclassical-string equations is developed to prove that genus-zero hitham hierarchies describe the deformations of planar domains determined by rational conformal-maps. This property is applied in normal matrix models to[...]![]()
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We propose to use eigenvalue densities of unitary random matrix ensembles as mass distributions in gravitational lensing. The corresponding lens equations reduce to algebraic equations in the complex plane which can be treated analytically. We p[...]![]()
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Kodama, Y. ; Konopelchenko, Boris ; Martínez Alonso, Luis ; Medina Reus, Elena | American Institute of Physics | 2005-11A general scheme for determining and studying hydrodynamic type systems describing integrable deformations of algebraic curves is applied to cubic curves. Lagrange resolvents of the theory of cubic equations are used to derive and characterize t[...]![]()
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Single-field inflaton models in the kinetic dominance period admit formal solutions given by generalized asymptotic expansions called psi series. We present a method for computing psi series for the Hubble parameter as a function of the inflaton[...]![]()
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Álvarez Galindo, Gabriel ; Martínez Alonso, Luis ; Medina Reus, Elena | IOP publishing ltd | 2011-07-15We present a method to characterize and compute the large N formal asymptotics of regular and critical Hermitian matrix models with general even potentials in the one-cut and two-cut cases. Our analysis is based on a method to solve continuum li[...]![]()
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The DaveyStewartson equation is considered from the point of view of the bilinear formalism of the Kyoto school. Multidromion solutions are constructed in terms of free fermions and their asymptotic properties are characterized. The dynamical pr[...]![]()
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Fasano, A. ; Herrero, Miguel A. ; López, J. M. ; Medina Reus, Elena | Italian Society for Applied and Industrial Mathematics (SIMAI) | 2010A mathematical model to describe the process of formation of bone tissue by replacement of cartilage tissue is presented and discussed. This model is based on an absorption-diffusion system which describes the interaction of two key signalling m[...]![]()
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The Riemann-Hilbert problems for multiple orthogonal polynomials of types I and II are used to derive string equations associated with pairs of Lax-Orlov operators. A method for determining the quasiclassical limit of string equations in the pha[...]![]()
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In this work a mathematical model for the interaction of two key signalling molecules in rat tibia ossification is presented and discussed. The molecules under consideration are Indian hedgehog (Ihh) and parathyroid hormone-related peptide (PTHr[...]![]()
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The one-cut case of the Hermitian random matrix model in the large N limit is considered. Its singular sector in the space of coupling constants is analyzed from the point of view of the hodograph equations of the underlying dispersionless Toda [...]![]()
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Álvarez Galindo, Gabriel ; Martínez Alonso, Luis ; Medina Reus, Elena | IOP publishing ltd | 2017-03-24The partition function of the Penner matrix model for both positive and negative values of the coupling constant can be explicitly written in terms of the Barnes G function. In this paper we show that for negative values of the coupling constant[...]![]()
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Álvarez Galindo, Gabriel ; Martínez Alonso, Luis ; Medina Reus, Elena | Elsevier Science BV | 2015-08-15We apply the method we have described in a previous paper (2013) to determine the phase structure of asymptotic zero densities of the standard cubic model of non-Hermitian orthogonal polynomials. We provide a complete description of the two phas[...]![]()
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We present a method for studying 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[...]![]()
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A ?¯formalism for studying dispersionless integrable hierarchies is applied to the dispersionless KP (dKP) hierarchy. We relate this formalism to the theory of quasiconformal mappings on the plane and present some classes of explicit solutions o[...]![]()
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Critical processes of ideal integrable models of Hele-Shaw flows are considered. A regularization method based on multiscaling expansions of solutions of the KdV and Toda hierarchies characterized by string equations is proposed. Examples are ex[...]