ANOMALIES IN CURVED SPACETIME AT FINITE TEMPERATURE

We discuss the problem of the breakdown of conformal and gauge symmetries at finite temperature in curved-spacetime background, when the changes in the background are gradual, in order to have a well-defined quantum field theory at finite temperature. We obtain the expressions for Seeley's coefficients and the heat-kernel expansion in this regime. As applications, we consider the self-interacting lambdaphi4 and chiral Schwinger models in curved backgrounds at finite temperature.

Análise e estimativa dos componentes do balanço de energia em ecossistema de manguezal amazônico

As medições e estimativas dos componentes do balanço de energia foram feitos acima da copa das árvores no ecossistema de manguezal natural, localizada a 30 km da cidade de Bragança-PA, entre novembro de 2002 e agosto de 2003. Os dados foram utilizados para a análise das variações sazonais e horárias do fluxo de calor sensível e calor latente, bem como a avaliação da partição de energia. Os dados meteorológicos foram coletados pela estação meteorológica automática (EMA) e os fluxos foram calculados utilizando-se a técnica de covariância de vórtices turbulentos. Os modelos de Penman-Monteith e Shuttleworth foram usados para estimar o fluxo de calor sensível e calor latente. O objetivo deste estudo foi analisar o equilíbrio e a partição de energia no manguezal, assim como fazer uma avaliação do comportamento de modelos empíricos para estimar os fluxos de energia. O saldo de radiação apresentou valores mais elevados no período menos chuvoso. A razão de Bowen mostrou valor geralmente baixo, o que indica que uma proporção maior de energia foi utilizada sob a forma de calor latente. O modelo Shuttleworth é mais eficiente na estimativa de fluxos de calor sensível. Para estimar o fluxo de calor latente do modelo de Penman-Monteith foi mais eficiente durante a estação seca e o modelo Shuttleworth durante a estação chuvosa.

Anomalous gauge couplings from composite Higgs and warped extra dimensions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Técnicas de análise de dados distribuídos em áreas

Pós-graduação em Biometria - IBB

Mesonic chiral perturbation theory - odd intrinsic parity sector

In der vorliegenden Dissertation werden zwei verschiedene Aspekte des Sektors ungerader innerer Parität der mesonischen chiralen Störungstheorie (mesonische ChPT) untersucht. Als erstes wird die Ein-Schleifen-Renormierung des führenden Terms, der sog. Wess-Zumino-Witten-Wirkung, durchgeführt. Dazu muß zunächst der gesamte Ein-Schleifen-Anteil der Theorie mittels Sattelpunkt-Methode extrahiert werden. Im Anschluß isoliert man alle singulären Ein-Schleifen-Strukturen im Rahmen der Heat-Kernel-Technik. Zu guter Letzt müssen diese divergenten Anteile absorbiert werden. Dazu benötigt man eine allgemeinste anomale Lagrange-Dichte der Ordnung O(p^6), welche systematisch entwickelt wird. Erweitert man die chirale Gruppe SU(n)_L x SU(n)_R auf SU(n)_L x SU(n)_R x U(1)_V, so kommen zusätzliche Monome ins Spiel. Die renormierten Koeffizienten dieser Lagrange-Dichte, die Niederenergiekonstanten (LECs), sind zunächst freie Parameter der Theorie, die individuell fixiert werden müssen. Unter Betrachtung eines komplementären vektormesonischen Modells können die Amplituden geeigneter Prozesse bestimmt und durch Vergleich mit den Ergebnissen der mesonischen ChPT eine numerische Abschätzung einiger LECs vorgenommen werden. Im zweiten Teil wird eine konsistente Ein-Schleifen-Rechnung für den anomalen Prozeß (virtuelles) Photon + geladenes Kaon -> geladenes Kaon + neutrales Pion durchgeführt. Zur Kontrolle unserer Resultate wird eine bereits vorhandene Rechnung zur Reaktion (virtuelles) Photon + geladenes Pion -> geladenes Pion + neutrales Pion reproduziert. Unter Einbeziehung der abgeschätzten Werte der jeweiligen LECs können die zugehörigen hadronischen Strukturfunktionen numerisch bestimmt und diskutiert werden.

Quantum field theory of (p,0)-forms on kaehler manifolds

In questa tesi abbiamo studiato la quantizzazione di una teoria di gauge di forme differenziali su spazi complessi dotati di una metrica di Kaehler. La particolarità di queste teorie risiede nel fatto che esse presentano invarianze di gauge riducibili, in altre parole non indipendenti tra loro. L'invarianza sotto trasformazioni di gauge rappresenta uno dei pilastri della moderna comprensione del mondo fisico. La caratteristica principale di tali teorie è che non tutte le variabili sono effettivamente presenti nella dinamica e alcune risultano essere ausiliarie. Il motivo per cui si preferisce adottare questo punto di vista è spesso il fatto che tali teorie risultano essere manifestamente covarianti sotto importanti gruppi di simmetria come il gruppo di Lorentz. Uno dei metodi più usati nella quantizzazione delle teorie di campo con simmetrie di gauge, richiede l'introduzione di campi non fisici detti ghosts e di una simmetria globale e fermionica che sostituisce l'iniziale invarianza locale di gauge, la simmetria BRST. Nella presente tesi abbiamo scelto di utilizzare uno dei più moderni formalismi per il trattamento delle teorie di gauge: il formalismo BRST Lagrangiano di Batalin-Vilkovisky. Questo metodo prevede l'introduzione di ghosts per ogni grado di riducibilità delle trasformazioni di gauge e di opportuni “antifields" associati a ogni campo precedentemente introdotto. Questo formalismo ci ha permesso di arrivare direttamente a una completa formulazione in termini di path integral della teoria quantistica delle (p,0)-forme. In particolare esso permette di dedurre correttamente la struttura dei ghost della teoria e la simmetria BRST associata. Per ottenere questa struttura è richiesta necessariamente una procedura di gauge fixing per eliminare completamente l'invarianza sotto trasformazioni di gauge. Tale procedura prevede l'eliminazione degli antifields in favore dei campi originali e dei ghosts e permette di implementare, direttamente nel path integral condizioni di gauge fixing covarianti necessari per definire correttamente i propagatori della teoria. Nell'ultima parte abbiamo presentato un’espansione dell’azione efficace (euclidea) che permette di studiare le divergenze della teoria. In particolare abbiamo calcolato i primi coefficienti di tale espansione (coefficienti di Seeley-DeWitt) tramite la tecnica dell'heat kernel. Questo calcolo ha tenuto conto dell'eventuale accoppiamento a una metrica di background cosi come di un possibile ulteriore accoppiamento alla traccia della connessione associata alla metrica.

Upper-ocean microstructure data from the tropical Atlantic

SST variability within the Atlantic cold tongue (ACT) region is of climatic relevance for the surrounding continents. A multi cruise data set of microstructure observations is used to infer regional as well as seasonal variability of upper ocean mixing and diapycnal heat flux within the ACT region. The variability in mixing intensity is related to the variability in large scale background conditions, which were additionally observed during the cruises. The observations indicate fundamental differences in background conditions in terms of shear and stratification below the mixed layer (ML) for the western and eastern equatorial ACT region causing critical Froude numbers (Fr) to be more frequently observed in the western equatorial ACT. The distribution of critical Fr occurrence below the ML reflects the regional and seasonal variability of mixing intensity. Turbulent dissipation rates (?) at the equator (2°N-2°S) are strongly increased in the upper thermocline compared to off-equatorial locations. In addition, ? is elevated in the western equatorial ACT compared to the east from May to November, whereas boreal summer appears as the season of highest mixing intensities throughout the equatorial ACT region, coinciding with ACT development. Diapycnal heat fluxes at the base of the ML in the western equatorial ACT region inferred from ? and stratification range from a maximum of 90 Wm-2 in boreal summer to 55 Wm-2 in September and 40 Wm-2 in November. In the eastern equatorial ACT region maximum values of about 25 Wm-2 were estimated during boreal summer reducing to about 5 Wm-2 towards the end of the year. Outside the equatorial region, inferred diapycnal heat fluxes are comparably low rarely exceeding 10 Wm-2. Integrating the obtained heat flux estimates in the ML heat budget at 10°W on the equator accentuates the diapycnal heat flux as the largest ML cooling term during boreal summer and early autumn. In the western equatorial ACT elevated meridional velocity shear in the upper thermocline contributes to the enhanced diapycnal heat flux within this region during boreal summer and autumn. The elevated meridional velocity shear appears to be associated with intra-seasonal wave activity.

Geometry of Dirac Operators

Thesis (Master, Mathematics & Statistics) -- Queen's University, 2016-07-04 20:27:20.386

An Analogue of Beurling-Hörmander’s Theorem for the Dunkl-Bessel Transform

Mathematics Subject Classification: Primary 35R10, Secondary 44A15

Geometry of Dirac Operators

Let $M$ be a compact, oriented, even dimensional Riemannian manifold and let $S$ be a Clifford bundle over $M$ with Dirac operator $D$. Then \[ \textsc{Atiyah Singer: } \quad \text{Ind } \mathsf{D}= \int_M \hat{\mathcal{A}}(TM)\wedge \text{ch}(\mathcal{V}) \] where $\mathcal{V} =\text{Hom}_{\mathbb{C}l(TM)}(\slashed{\mathsf{S}},S)$. We prove the above statement with the means of the heat kernel of the heat semigroup $e^{-tD^2}$. The first outstanding result is the McKean-Singer theorem that describes the index in terms of the supertrace of the heat kernel. The trace of heat kernel is obtained from local geometric information. Moreover, if we use the asymptotic expansion of the kernel we will see that in the computation of the index only one term matters. The Berezin formula tells us that the supertrace is nothing but the coefficient of the Clifford top part, and at the end, Getzler calculus enables us to find the integral of these top parts in terms of characteristic classes.

The average mixing matrix signature

Laplacian-based descriptors, such as the Heat Kernel Signature and the Wave Kernel Signature, allow one to embed the vertices of a graph onto a vectorial space, and have been successfully used to find the optimal matching between a pair of input graphs. While the HKS uses a heat di↵usion process to probe the local structure of a graph, the WKS attempts to do the same through wave propagation. In this paper, we propose an alternative structural descriptor that is based on continuoustime quantum walks. More specifically, we characterise the structure of a graph using its average mixing matrix. The average mixing matrix is a doubly-stochastic matrix that encodes the time-averaged behaviour of a continuous-time quantum walk on the graph. We propose to use the rows of the average mixing matrix for increasing stopping times to develop a novel signature, the Average Mixing Matrix Signature (AMMS). We perform an extensive range of experiments and we show that the proposed signature is robust under structural perturbations of the original graphs and it outperforms both the HKS and WKS when used as a node descriptor in a graph matching task.

Estimates of the surface heat fluxes in Antarctic waters

The authors have attempted to compute the heat balance terms on the basis of formulas by Budyoko (1974). Some of the meteorological and oceanographic data were collected during the Trans Antarctic Expedition (1989-90). These data were supplemented by the data (1956-1988) made available by the national climatic center of NOAA (National Oceanic and Atmospheric Administration). Monthly means of sea surface temperature in Antarctic waters and meteorological data at a station (77°51'S; 166°39'E) 33m above sea level are given.

Approximate solutions and error estimates for a Stokes boundary value problem

The aim of this paper is the numerical treatment of a boundary value problem for the system of Stokes' equations. For this we extend the method of approximate approximations to boundary value problems. This method was introduced by V. Maz'ya in 1991 and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present paper we develop an approximation procedure for the solution of the interior Dirichlet problem for the system of Stokes' equations in two dimensions. The procedure is based on potential theoretical considerations in connection with a boundary integral equations method and consists of three approximation steps as follows. In a first step the unknown source density in the potential representation of the solution is replaced by approximate approximations. In a second step the decay behavior of the generating functions is used to gain a suitable approximation for the potential kernel, and in a third step Nyström's method leads to a linear algebraic system for the approximate source density. For every step a convergence analysis is established and corresponding error estimates are given.

Estimates for the Poisson kernel and Hardy spaces on compact manifolds

We study Hardy spaces on the boundary of a smooth open subset or R-n and prove that they can be defined either through the intrinsic maximal function or through Poisson integrals, yielding identical spaces. This extends to any smooth open subset of R-n results already known for the unit ball. As an application, a characterization of the weak boundary values of functions that belong to holomorphic Hardy spaces is given, which implies an F. and M. Riesz type theorem. (C) 2004 Elsevier B.V. All rights reserved.

Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.