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 $n$ limit in the non-hermitian Penner matrix model. In these generalizations $g_n n\to t$, but the product $g_n n$ is not necessarily fixed to the value of the 't Hooft coupling $t$. If $t>1$ and the limit $l = \lim_{n\rightarrow \infty} |\sin(\pi/g_n)|^{1/n}$ exists, then the large $n$ limit is well-defined but depends both on $t$ and on $l$. This result implies that for $t>1$ the standard large $n$ limit with $g_n n=t$ fixed is not well-defined. The parameter $l$ determines a fine structure of the asymptotic eigenvalue support: for $l\neq 0$ the support consists of an interval on the real axis with charge fraction $Q=1-1/t$ and an $l$-dependent oval around the origin with charge fraction $1/t$. For $l=1$ these two components meet, and for $l=0$ the oval collapses to the origin. We also calculate the total electrostatic energy $\mathcal{E}$, which turns out to be independent of $l$, and the free energy $\mathcal{F}=\mathcal{E}-Q\ln l$, which does depend of the fine structure parameter $l$. The existence of large $n$ asymptotic expansions of $\mathcal{F}$ 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 $y^2=W'(z)^2+f(z)$ which characterize the vacua of $\mathcal{N}=1$ U(n) supersymmetric gauge theories with an adjoint Higgs field and a polynomial tree level potential $W(z)$. 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 $\mathbb{W}$ 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 $\mathbb{W}$. 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

Biomolecules and interstellar molecules: structure, interactions and spectroscopic characterization

El trabajo de investigación de la presente Memoria, realizado con técnicas espectroscópicas de alta resolución en las regiones de microondas y milimétricas, presenta dos grandes vertientes: el estudio de moléculas y biomoléculas en fase gas y el de moléculas candidatas a estar presentes en el medio interestelar. En el estudio de moléculas y biomoléculas en fase gas, el objetivo es intentar establecer una conexión entre su estructura y las propiedades que dichas poseen, en un entorno libre de interacciones intermoleculares y con el medio, mediante el uso de la espectroscopia de microondas en jet supersónicos y en combinación con técnicas de ablación láser (LA-CP-FTMW y LA-MB-FTMW espectrómetros). Se han abordado con este fin: el estudio de edulcorantes artificiales como el D-sorbitol y la sacarina para intentar esclarecer el origen del dulzor; el efecto exo-anomérico ha sido puesto en evidencia por primera vez mediante el estudio de la methyl-β-D-xylopyranose; el primer estudio estructural en fase gas de los dos ácidos fenólicos más importantes, trans-cinámico y trans-p-cumárico,, y el estudio del dipéptido Ac-Val-NH2 para ver los efectos conformacionales que puede tener una cadena lateral apolar.Departamento de Química Física y Química InorgánicaDoctorado en Químic

Una aproximación al matrimonio en la Edad Moderna, desde los Discursos del padre Pedro de Calatayud

El objeto de este trabajo es el estudio del matrimonio en Castilla durante la Edad Moderna. Entendemos que este tema tiene un gran interés por varias razones. De hecho, en las últimas décadas ha sido estudiado desde diversas perspectivas, en el marco de la Demografía Histórica, de la Historia Social, religiosa y cultural. El matrimonio ha sido punto de partida para los numerosos trabajos y monografías que se han elaborado para el caso peninsular en torno al estudio de la familia, y más recientemente del estudios de Historia de Género, al analizar especialmente el papel de la mujer en el estado de casada. Afrontandolo desde una ángulo concreto; a través de una fuente -impresa- de la época, una obra de literatura moral y religiosa, publicada en Castilla en el siglo XVIIIDepartamento de Historia Moderna, Contemporánea y de América, Periodismo y Comunicación Audiovisual y PublicidadGrado en Histori

Trace Metal and Speciation Analysis using Ion-Exchange and Energy Dispersive X-ray Fluorescence Spectrometry

Studies have been carried out on specific ion-exchange (Dowex 50W-X8 and Dowex 1-X8) and chelation (Chelex-100) resins, in order to determine their physical and chemical characteristics, to understand and explain their limits of function and to optimise their use as substrates in trace metal and speciation measurement by EDXRF. Structural information was obtained by scanning electron microscopy and x-ray microanalysis showing a homogeneous distribution of functional groups and retained ions on both sectioned and whole resins. Particle size experiments performed on Dowex 50W-X8 (38 - 840 µm) showed that this parameter has no effect on the relationship between intensity of fluorescence and concentration or mass of resin. Inter-element effects were not observed in the analysis of multielemental specimens prepared on ion-exchange / chelation media by EDXRF. This indicates that the proposed method has a significant advantage when compared with other methodologies. A theoretical ‘model’, based on the formation of thin films on the surface of the resin beads, has been proposed in order to link and explain the effects observed in these experiments. The use of a batch retention system has shown distinct advantages over using columns in terms of linearity, accuracy, precision, rapidity and simplicity. Parameters such as pH and ionic strength of the solution, concentration of competing ions and volume of the sample have been proven to be critical. The maximum retention capacity has been determined as 3.2, 1.1 and 0.67 mEq/g for Dowex 50W-X8, Dowex 1-X8 and Chelex-100 respectively. The optimum mass of resin for XRF analysis was found to be 0.5 g, for all resins tested. The linear range covered 4 to 5 orders of magnitude. These findings show the potential of the investigated media to overcome instrumental and sample limitations. Based on the physico-chemical information found, methodologies for three different applications of the resins to EDXRF determinations have been developed and their analytical possibilities explored. The multi-elemental determination of metals in sewage sludge digests was achieved by retaining the metals on Dowex 50W-X8 at pH 2 and Chelex-100 at pH 4. Chelex-100 allows quantitative recoveries for Cu and Zn. A wider range of elements was determined on Dowex 50W-X8, although with poorer recoveries (60 - 90%). The limits of detection were 10 - 21 µg when Dowex 50W-X8 was used and 8 - 49 µg for Chelex-100. The method was validated by the analysis of a certified material. The determination of Kβ/Kα intensity ratios for Cr and Mn species and its potential as a tool for direct elemental speciation has also been studied. A difference in Kβ/Kα between the oxidation states of the analytes was only observed during the analysis of solutions of the metal species by EDXRF at the 98% level of confidence. Finally, the speciation and preconcentration of Cr(III) and Cr(VI) in waters has been performed by retention on Dowex 50W-X8 and Dowex 1-X8 followed by EDXRF determination. Efficient recoveries and preconcentration factors of up to 500 were achieved, leading to limits of detection of 30 µg/L for Cr(VI) and 40 µg/L for Cr(III). This method is simple, fast and inexpensive, allowing quantitative recoveries in the speciation of chromium in waste waters