Dissertations / Theses on the topic 'Spectral asymptotic'
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Zabroda, Olga Nikolaievna. "Generalized convolution operators and asymptotic spectral theory." Doctoral thesis, Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200602061.
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The dissertation contributes to the further advancement of the theory of various classes of discrete and continuous (integral) convolution operators. The thesis is devoted to the study of sequences of matrices or operators which are built up in special ways from generalized discrete or continuous convolution operators. The generating functions depend on three variables and this leads to considerably more complicated approximation sequences. The aim was to obtain for each case a result analogous to the first Szegö limit theorem providing the first order asymptotic formula for the spectra of regular convolutions.
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Mascarenhas, Helena. "Convolution type operators on cones and asymptotic spectral theory." Doctoral thesis, [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=970638809.
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Rosenberger, Elke. "Asymptotic spectral analysis and tunnelling for a class of difference operators." Phd thesis, [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=98050368X.
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Jacq, Thomas Soler. "Asymptotic spectral analysis of growing graphs and orthogonal matrix-valued polynomials." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2016. http://hdl.handle.net/10183/143939.
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Neste trabalho abordaremos a an alise espectral de grafos por dois estudos: técnicas de probabilidade quântica e por polinômios ortogonais com valores em matrizes. No Capítulo 1, consideraremos a matriz de adjacência do grafo tal como um operador linear e sua decomposição quântica permitir a uma an alise espectral que produzir a um teorema do limite central para tal grafo. No Capítulo 2, consideraremos uma medida com valores em matrizes induzida por polinômios ortogonais com valores em matrizes. Sob certas condições, e possível exibir explicitamente uma expressão de tal medida. Algumas aplicações em teoria dos grafos são dadas quando nos restringimos as matrizes estoc asticas e com valores em 0-1. Do nosso conhecimento, os cálculos e exemplos obtidos nas seçõoes 0.3.2, 0.3.3, 2.4 e 2.5 são novos.In this work we focus on the spectral analysis of graphs via two studies: quantum probabilistic techniques and by orthogonal matrix-valued polynomials. In Chapter 1 we consider the adjacency matrix of a graph as a linear operator, and its quantum decomposition will allow a spectral analysis that will produce a central limit theorem for such graph. In Chapter 2, we consider a matrix-valued measure induced by orthogonal matrix-valued polynomials. Under certain conditions, it is possible to display an explicit expression for such measure. Some applications to combinatorics and graph theory are given when we restrict to the stochastic and 0-1 matrices. Up to our knowledge, the calculations and examples obtained in sections 0.3.2, 0.3.3, 2.4 and 2.5 are new.
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Hudson, Richard James Frederick. "Long memory spectral regression : an approach using generalised least squares." Thesis, Queensland University of Technology, 2002.
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Cherdantsev, Mikhail. "Asymptotic analysis of some spectral problems in high contrast homogenisation and in thin domains." Thesis, University of Bath, 2008. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.501494.
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We study the spectral properties of two problems involving small parameters. The first one is an eigenvalue problem for a divergence form elliptic operator Aε with high contrast periodic coefficients of period ε in each coordinate, where ε is a small parameter. The coefficients are perturbed on a bounded domain of 'order one' size. The local perturbation of coefficients for such operator could result in emergence of localised waves in the gaps of the Floquet-Bloch spectrum. We prove that, for the so-called double porosity type scaling, the eigenfunctions decay exponentially at in infinity, uniformly in ε. Then, using the tools of twoscale convergence for high contrast homogenisation, we prove the strong twoscale convergence of the eigenfunctions of Aε to the eigenfunctions of a two-scale limit homogenised operator A₀ , consequently establishing 'asymptotic one-to-one correspondence' between the eigenvalues and the eigenfunctions of these two operators. We also prove by direct means the stability of the essential spectrum of the homogenised operator with respect to the local perturbation of its coefficients. That allows us to establish not only the strong two-scale resolvent convergence of Aε to A₀ but also the Hausdor convergence of the spectra of Aε to the spectrum of A₀ , preserving the multiplicity of the isolated eigenvalues. As the second problem we consider the eigenvalue problem for the Laplacian in a network of thin domains with Dirichlet boundary conditions. We construct an asymptotic solution to the problem using the method of matched asymptotic expansions to obtain appropriate boundary conditions for the terms of the asymptotics near the junctions of thin domains. We justify the asymptotics and prove the error bound of order h3=2 , where h is the width of thin domains.
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Pielaszkiewicz, Jolanta Maria. "On the asymptotic spectral distribution of random matrices : closed form solutions using free independence." Licentiate thesis, Linköping University, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-58181.
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The spectral distribution function of random matrices is an information-carrying object widely studied within Random matrix theory. In this thesis we combine the results of the theory together with the idea of free independence introduced by Voiculescu (1985). Important theoretical part of the thesis consists of the introduction to Free probability theory, which justifies use of asymptotic freeness with respect to particular matrices as well as the use of Stieltjes and R-transform. Both transforms are presented together with their properties. The aim of thesis is to point out characterizations of those classes of the matrices, which have closed form expressions for the asymptotic spectral distribution function. We consider all matrices which can be decomposed to the sum of asymptotically free independent summands. In particular, explicit calculations are performed in order to illustrate the use of asymptotic free independence to obtain the asymptotic spectral distribution for a matrix Q and generalize Marcenko and Pastur (1967) theorem. The matrix Q is defined as
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Pielaszkiewicz, Jolanta. "On the asymptotic spectral distribution of random matrices : Closed form solutions using free independence." Licentiate thesis, Linköpings universitet, Matematisk statistik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-92637.
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The spectral distribution function of random matrices is an information-carrying object widely studied within Random matrix theory. In this thesis we combine the results of the theory together with the idea of free independence introduced by Voiculescu (1985). Important theoretical part of the thesis consists of the introduction to Free probability theory, which justifies use of asymptotic freeness with respect to particular matrices as well as the use of Stieltjes and R-transform. Both transforms are presented together with their properties. The aim of thesis is to point out characterizations of those classes of the matrices, which have closed form expressions for the asymptotic spectral distribution function. We consider all matrices which can be decomposed to the sum of asymptotically free independent summands. In particular, explicit calculations are performed in order to illustrate the use of asymptotic free independence to obtain the asymptotic spectral distribution for a matrix Q and generalize Marcenko and Pastur (1967) theorem. The matrix Q is defined as
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Södergren, Anders. "Asymptotic Problems on Homogeneous Spaces." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-132645.
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This PhD thesis consists of a summary and five papers which all deal with asymptotic problems on certain homogeneous spaces. In Paper I we prove asymptotic equidistribution results for pieces of large closed horospheres in cofinite hyperbolic manifolds of arbitrary dimension. All our results are given with precise estimates on the rates of convergence to equidistribution. Papers II and III are concerned with statistical problems on the space of n-dimensional lattices of covolume one. In Paper II we study the distribution of lengths of non-zero lattice vectors in a random lattice of large dimension. We prove that these lengths, when properly normalized, determine a stochastic process that, as the dimension n tends to infinity, converges weakly to a Poisson process on the positive real line with intensity 1/2. In Paper III we complement this result by proving that the asymptotic distribution of the angles between the shortest non-zero vectors in a random lattice is that of a family of independent Gaussians. In Papers IV and V we investigate the value distribution of the Epstein zeta function along the real axis. In Paper IV we determine the asymptotic value distribution and moments of the Epstein zeta function to the right of the critical strip as the dimension of the underlying space of lattices tends to infinity. In Paper V we determine the asymptotic value distribution of the Epstein zeta function also in the critical strip. As a special case we deduce a result on the asymptotic value distribution of the height function for flat tori. Furthermore, applying our results we discuss a question posed by Sarnak and Strömbergsson as to whether there in large dimensions exist lattices for which the Epstein zeta function has no zeros on the positive real line.
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Ferreira, Rita Alexandra Gonçalves. "Spectral and homogenization problems." Doctoral thesis, Faculdade de Ciências e Tecnologia, 2011. http://hdl.handle.net/10362/7856.
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Dissertation for the Degree of Doctor of Philosophy in MathematicsFundação para a Ciência e a Tecnologia through the Carnegie Mellon | Portugal Program under Grant SFRH/BD/35695/2007, the Financiamento Base 20010 ISFL–1–297, PTDC/MAT/109973/2009 and UTA
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Rand, Peter. "Asymptotic analysis of solutions to elliptic and parabolic problems." Doctoral thesis, Linköping : Matematiska institutionen, Linköpings universitet, 2006. http://www.bibl.liu.se/liupubl/disp/disp2006/tek1044s.pdf.
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Goncalves-Ferreira, Rita Alexandria. "Spectral and Homogenization Problems." Research Showcase @ CMU, 2011. http://repository.cmu.edu/dissertations/83.
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In this dissertation we will address two types of homogenization problems. The first one is a spectral problem in the realm of lower dimensional theories, whose physical motivation is the study of waves propagation in a domain of very small thickness and where it is introduced a very thin net of heterogeneities. Precisely, we consider an elliptic operator with "ε-periodic coefficients and the corresponding Dirichlet spectral problem in a three-dimensional bounded domain of small thickness δ. We study the asymptotic behavior of the spectrum as ε and δ tend to zero. This asymptotic behavior depends crucially on whether ε and δ are of the same order (δ ≈ ε), or ε is of order smaller than that of δ (δ = ετ , τ < 1), or ε is of order greater than that of δ (δ = ετ , τ > 1). We consider all three cases.
The second problem concerns the study of multiscale homogenization problems with linear growth, aimed at the identification of effective energies for composite materials in the presence of fracture or cracks. Precisely, we characterize (n+1)-scale limit pairs (u,U) of sequences {(uεLN⌊Ω,Duε⌊Ω)}ε>0 ⊂ M(Ω;ℝd) × M(Ω;ℝd×N) whenever {uε}ε>0 is a bounded sequence in BV (Ω;ℝd). Using this characterization, we study the asymptotic behavior of periodically oscillating functionals with linear growth, defined in the space BV of functions of bounded variation and described by n ∈ ℕ microscales
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Xia, Xiaoyue. "New asymptotic methods for the global analysis of ordinary differential equations and for non-selfadjoint spectral problems." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1437062908.
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Kley, Tobias [Verfasser], Holger [Gutachter] Dette, Herold [Gutachter] Dehling, and Marc [Gutachter] Hallin. "Quantile-based spectral analysis : asymptotic theory and computation / Tobias Kley ; Gutachter: Holger Dette, Herold Dehling, Marc Hallin ; Fakultät für Mathematik." Bochum : Ruhr-Universität Bochum, 2014. http://d-nb.info/1228624046/34.
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Vasilevskaya, Elizaveta. "Open periodic waveguides : Theory and computation." Thesis, Sorbonne Paris Cité, 2016. http://www.theses.fr/2016USPCD008/document.
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Cette thèse porte sur la propagation des ondes acoustiques dans des milieux périodiques.Ces milieux ont des propriétés remarquables car le spectre associée à l’opérateur d’ondesdans ces milieux a une structure de bandes : il existe des plages de fréquences danslesquelles les ondes monochromatiques ne se propagent pas. Plus intéressant encore, enintroduisant des défauts linéiques dans ce type de milieux, on peut créer des modes guidésà l’intérieur de ces bandes de fréquences interdites. Dans ce manuscrit nous montrons qu’ilest possible de créer de tels modes guidés dans le cas de milieux périodiques particuliersde type quadrillage : plus précisément, le domaine périodique considéré est constitué duplan R2 privé d’un ensemble infini d’obstacles rectangulaires régulièrement espacés (d’unedistance ") dans deux directions orthogonales du plan, que l’on perturbe localement endiminuant la distance entre deux colonnes d’obstacles. Les résultats sont ensuite étendusau cas 3D.Ce travail comporte un aspect théorique et un aspect numérique. Du point de vue théoriquel’analyse repose sur le fait que, comme " est petit, le spectre de l’opérateur associé ànotre problème est "proche" du spectre d’un problème posé sur le graphe obtenu commela limite géométrique du domaine quand " tend vers 0. Or, pour le graphe limite, il estpossible de calculer explicitement le spectre. Ensuite, en utilisant des méthodes d’analyseasymptotique on étudie le spectre de l’opérateur non-limite. On illustre les résultats théoriquespar des résultats numériques obtenus à l’aide d’une méthode numérique spécialementdédiée aux milieux périodiques : cette dernière est basée sur la réduction du problèmede valeurs propres initial (linéaire) posé dans un domaine non-borné à un problème nonlinéaireposé dans un domaine borné (en utilisant l’opérateur de Dirichlet-to-Neumannexact)The present work deals with propagation of acoustic waves in periodic media. Thesemedia have particularly interesting properties since the spectrum associated with theunderlying wave operator in such media has a band-gap structure: there exist intervals offrequences for which monochromatic waves do not propagate. Moreover, by introducinglinear defects in this kind of media, one can create guided modes inside the bands offorbidden frequences. In this work we show that it is possible to create such guidedmodes in the case of particular periodic media of grid type: more precisely, the periodicdomain in question is R2 minus an infinite set of rectangular obstacles periodically spacedin two orthogonal directions (the distance between two neighbour obstacles being "),which is locally perturbed by diminishing the distance between two columns of obstacles.The results are extended to the 3D case.This work has a theoretical and a numerical aspect. From the theoretical point of view theanalysis is based on the fact that, " being small, the spectrum of the operator associatedwith our problem is "close" to the spectrum of a problem posed on a graph which is ageometric limit of the domain as " tends to 0. However, for the limit graph the spectrumcan be computed explicitly. Then, we study the spectrum of the non-limit operatorusing asymptotic analysis. Theoretical results are illustrated by numerical computationsobtained with a numerical method developed for study of periodic media: this method isbased on the reduction of the initial (linear) eigenvalue problem posed in an unboundeddomain to a non-linear problem posed in a bounded domain (using the exact Dirichletto-Neumann operator)
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Suleymanova, Asilya. "On the spectral geometry of manifolds with conic singularities." Doctoral thesis, Humboldt-Universität zu Berlin, 2017. http://dx.doi.org/10.18452/18420.
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Wir beginnen mit der Herleitung der asymptotischen Entwicklung der Spur des Wärmeleitungskernes, $\tr e^{-t\Delta}$, für $t\to0+$, wobei $\Delta$ der Laplace-Beltrami-Operator auf einer Mannigfaltigkeit mit Kegel-Singularitäten ist; dabei folgen wir der Arbeit von Brüning und Seeley. Dann untersuchen wir, wie die Koeffizienten der Entwicklung mit der Geometrie der Mannigfaltigkeit zusammenhängen, insbesondere fragen wir, ob die (mögliche) Singularität der Mannigfaltigkeit aus den Koeffizienten - und damit aus dem Spektrum des Laplace-Beltrami-Operators - abgelesen werden kann. In wurde gezeigt, dass im zweidimensionalen Fall ein logarithmischer Term und ein nicht lokaler Term im konstanten Glied genau dann verschwinden, wenn die Kegelbasis ein Kreis der Länge $2\pi$ ist, die Mannigfaltigkeit also geschlossen ist. Dann untersuchen wir wir höhere Dimensionen. Im vier-dimensionalen Fall zeigen wir, dass der logarithmische Term genau dann verschwindet, wenn die Kegelbasis eine
sphärische Raumform ist. Wir vermuten, dass das Verschwinden eines nicht lokalen Beitrags zum konstanten Term äquivalent ist dazu, dass die Kegelbasis die runde Sphäre ist; das kann aber bisher nur im zyklischen Fall gezeigt werden. Für geraddimensionale Mannigfaltigkeiten höherer Dimension und mit Kegelbasis von konstanter Krümmung zeigen wir weiter, dass der logarithmische Term ein Polynom in der Krümmung ist, das Wurzeln ungleich 1 haben kann, so dass erst das Verschwinden von mehreren Termen - die derzeit noch nicht explizit behandelt werden können - die Geschlossenheit der Mannigfaltigkeit zur Folge haben könnte.We derive a detailed asymptotic expansion of the heat trace for the Laplace-Beltrami operator on functions on manifolds with one conic singularity, using the Singular Asymptotics Lemma of Jochen Bruening and Robert T. Seeley. Then we investigate how the terms in the expansion reflect the geometry of the manifold. Since the general expansion contains a logarithmic term, its vanishing is a necessary condition for smoothness of the manifold. It is shown in the paper by Bruening and Seeley that in the two-dimensional case this implies that the constant term of the expansion contains a non-local term that determines the length of the (circular) cross section and vanishes precisely if this length equals $2\pi$, that is, in the smooth case. We proceed to the study of higher dimensions. In the four-dimensional case, the logarithmic term in the expansion vanishes precisely when the cross section is a spherical space form, and we expect that the vanishing of a further singular term will imply again smoothness, but this is not yet clear beyond the case of cyclic space forms. In higher dimensions the situation is naturally more difficult. We illustrate this in the case of cross sections with constant curvature. Then the logarithmic term becomes a polynomial in the curvature with roots that are different from 1, which necessitates more vanishing of other terms, not isolated so far.
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Dahlen, Anders. "Identification of stochastic systems : Subspace methods and covariance extension." Doctoral thesis, KTH, Mathematics, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3178.
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Durugo, Samuel O. "Higher-order airy functions of the first kind and spectral properties of the massless relativistic quartic anharmonic oscillator." Thesis, Loughborough University, 2014. https://dspace.lboro.ac.uk/2134/16497.
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This thesis consists of two parts. In the first part, we study a class of special functions Aik (y), k = 2, 4, 6, ··· generalising the classical Airy function Ai(y) to higher orders and in the second part, we apply expressions and properties of Ai4(y) to spectral problem of a specific operator. The first part is however motivated by latter part. We establish regularity properties of Aik (y) and particularly show that Aik (y) is smooth, bounded, and extends to the complex plane as an entire function, and obtain pointwise bounds on Aik (y) for all k. Some analytic properties of Aik (y) are also derived allowing one to express Aik (y) as a finite sum of certain generalised hypergeometric functions. We further obtain full asymptotic expansions of Aik (y) and their first derivative Ai'(y) both for y > 0 and for y < 0. Using these expansions, we derive expressions for the negative real zeroes of Aik (y) and Ai'(y). Using expressions and properties of Ai4(y), we extensively study spectral properties of a non-local operator H whose physical interpretation is the massless relativistic quartic anharmonic oscillator in one dimension. Various spectral results for H are derived including estimates of eigenvalues, spectral gaps and trace formula, and a Weyl-type asymptotic relation. We study asymptotic behaviour, analyticity, and uniform boundedness properties of the eigenfunctions Ψn(x) of H. The Fourier transforms of these eigenfunctions are expressed in two terms, one involving Ai4(y) and another term derived from Ai4(y) denoted by Āi4(y). By investigating the small effect generated by Āi4(y) this work shows that eigenvalues λn of H are exponentially close, with increasing n Ε N, to the negative real zeroes of Ai4(y) and those of its first derivative Ai'4(y) arranged in alternating and increasing order of magnitude. The eigenfunctions Ψ(x) are also shown to be exponentially well-approximated by the inverse Fourier transform of Ai4(|y| - λn) in its normalised form.
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Bejjani, Nadine. "Wave propagation in multilayered plates : the Bending-Gradient model and the asymptotic expansion method." Thesis, Paris Est, 2019. http://www.theses.fr/2019PESC1025.
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Cette thèse est consacrée à la modélisation de la propagation des ondes planes dans les plaques multicouches infinies, dans le cadre de l'élasticité linéaire. L’objet du travail est de trouver une approximation analytique ou semi-analytique des relations de dispersion des ondes lorsque le rapport de l'épaisseur de la plaque sur la longueur d'onde est petit. Ces relations de dispersion, liant la fréquence angulaire et le nombre d'onde, fournissent des informations clés sur les caractéristiques de propagation des différents modes. On propose dans cette thèse deux modélisations : le modèle du Bending-Gradient et la méthode des développements asymptotiques. La pertinence de ces méthodes est testée en comparant leurs prédictions à celles des théories de plaques bien connues, et à des résultats de référence obtenus par la méthode des éléments finis. Au préalable, dans la première partie de la thèse, une justification mathématique de la théorie du Bending-Gradient dans le cadre statique est réalisée à l’aide des méthodes variationnelles. Il s'agit d'abord d'identifier les espaces mathématiques dans lesquels les problèmes variationnels du Bending-Gradient sont bien posés. Puis, des théorèmes d'existence et d'unicité des solutions correspondantes sont ensuite formulés et prouvés. La deuxième partie est consacrée à la formulation des équations du mouvement du Bending-Gradient. Des simulations numériques sont effectuées pour plusieurs types d'empilements, permettant ainsi de tester la validité du modèle pour la modélisation de la propagation des ondes de flexion. La troisième partie est dédiée à l'analyse asymptotique des équations tridimensionnelles du mouvement, menée à bien grâce à la méthode des développements asymptotiques, le petit paramètre étant le rapport de l'épaisseur sur la longueur d'onde. En supposant que les champs tridimensionnels s'écrivent comme des séries en puissance du petit paramètre, on obtient une succession de problèmes à résoudre en cascade. La validité de cette méthode est évaluée par comparaison avec la méthode des éléments finisThis thesis is dedicated to the modelling of plane wave propagation in infinite multilayered plates, in the context of linear elasticity. The aim of this work is to find an analytical or semi-analytical approximation of the wave dispersion relations when the ratio of the thickness to the wavelength is small. The dispersion relations, linking the angular frequency and the wave number, provide key information about the propagation characteristics of the wave modes. Two methods are proposed in this thesis: the Bending-Gradient model and the asymptotic expansion method. The relevance of these methods is tested by comparing their predictions to those of well-known plate theories, and to reference results computed using the finite element method. Preliminarily, the first part of the thesis is devoted to the mathematical justification of the Bending-Gradient theory in the static framework using variational methods. The first step is to identify the mathematical spaces in which the variational problems of the Bending-Gradient are well posed. A series of existence and uniqueness theorems of the corresponding solutions are then formulated and proved. The second part is dedicated to the formulation of the equations of motion of the Bending-Gradient theory. Numerical simulations are realized for different types of layer stacks to assess the ability of this model to correctly predict the propagation of flexural waves. The third part is concerned with the asymptotic analysis of the three-dimensional equations of motion, carried out using the asymptotic expansion method, the small parameter being the ratio of the thickness to the wavelength. Assuming that the three-dimensional fields can be written as expansions in power of the small parameter, a series of problems which can be solved recursively is obtained. The validity of this method is evaluated by comparison with the finite element method
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Khalile, Magda. "Problèmes spectraux avec conditions de Robin sur des domaines à coins du plan." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS235/document.
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Dans cette thèse, nous étudions les propriétés spectrales du Laplacien avec la condition de bord de Robin attractive sur des domaines du plan à coins. Notre but est de comprendre l’influence des coins convexes sur l’asymptotique des valeurs propres de cet opérateur lorsque le paramètre de Robin est grand. Nous montrons en particulier que l’asymptotique des premières valeurs propres de Robin sur des polygones curvilignes est déterminée par des opérateurs modèles : les Laplaciens agissant sur les secteurs tangents au domaine. Pour une certaine classe de polygones droits, nous montrons l’existence d’un opérateur effectif sur le bord du domaine qui détermine l’asymptotique des valeurs propres suivantes. Enfin, des asymptotiques de Weyl pour différents seuils dépendant du paramètre de Robin sont obtenuesIn this thesis, we are interested in the spectral properties of the Laplacian with the attractive Robin boundary condition on planar domains with corners. The aim is to understand the influence of the convex corners on the spectral properties of this operator when the Robin parameter is large. In particular, we show that the asymptotics of the first Robin eigenvalues on curvilinear polygons is determined by model operators: the Robin Laplacians acting on infinite sectors. For a particular class of polygons with straight edges, we prove the existence of an effective operator acting on the boundary of the domain and determining the asymptotics of the further eigenvalues. Finally, some Weyl-type asymptotics for different thresholds depending on the Robin parameter are obtained
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LANGELLA, BEATRICE. "NORMAL FORM AND KAM METHODS FOR HIGHER DIMENSIONAL LINEAR PDES." Doctoral thesis, Università degli Studi di Milano, 2020. http://hdl.handle.net/2434/798372.
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In this thesis an approach to linear PDEs on higher dimensional spatial domains is proposed. I prove two kinds of results: first I develop an algorithm which enables to obtain reducibility for linear PDEs which depend quasi-periodically on time, and I apply it to a quasilinear transport equation of the form
∂_t u= ν•∇u+ ε P (ωt)u on the d-dimensional torus T^d, where ε is a small parameter, ν and ω are Diophantine vectors, P (ωt)=V(x,ωt)•∇+W(ωt), V is a smooth function on T^(d+n) and W(ωt) is an unbounded pseudo-differential operator of order strictly less than 1. The strategy is an extension of the methods originally developed in the context of quasilinear one dimensional equations. It consists in first using quantum normal form techniques in order to conjugate the original system to a new one with a smoothing perturbation, and then exploiting the smoothing nature of the new perturbation in order to balance the effects of the small denominators, which in this problem accumulate very fast to 0.
The quantum normal form procedure developed in order to obtain reducibility for the above transport equation is global in phase space. In order to overcome such a limitation, the second problem I tackle in this thesis is that of developing a local quantum normal form procedure, which could be applied to much more general systems. As the simplest relevant model containing all the difficulties of the general case, I consider the operator H=-∆+V(x) with Floquet boundary conditions on the flat torus T^d_Γ, where T^d_Γ is the manifold obtained as quotient between the d-dimensional space R^d and an arbitrary d-dimensional lattice Γ, with the purpose of adapting the quantum normal form procedure to deal with this operator. As a result, I prove for the operator H a Structure Theorem à la Nekhoroshev, and I characterize the asymptotic behavior of all its eigenvalues. The asymptotic expansion is in |λ|^{-δ}, with δ ∊ (0, 1) for most of the eigenvalues λ (stable eigenvalues), while it is a "directional expansion" for the remaining eigenvalues (unstable eigenvalues).
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Khosravi, Mahta. "Spectral asymptotics of Heisenberg manifolds." Thesis, McGill University, 2005. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=85924.
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Let R(t) be the error term in Weyl's law for (2 n + 1)-dimensional Heisenberg manifolds. We prove that in the 'rational' case, R(lambda) is of order O(tn -7/41). In the 'irrational' case, for generic (2n + 1)-dimensional Heisenberg manifolds with n > 1, we prove that the error term is of the order Odtn-1/4+8 for every positive delta. The polynomial growth is optimal. We also prove that for arithmetic Heisenberg metrics, 1T&vbm0;Rt &vbm0;2dt=cT2n+1 2+Od T2n+14+d where c is a specific nonzero constant and delta is an arbitrary small positive number. In the three dimensional case, this is consistent with the conjecture of Petridis and Toth [PT] stating that R(t) = Odt34 +d .
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Savale, Nikhil Jr (Nikhil A. ). "Spectral asymptotics for coupled Dirac operators." Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/77804.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.Cataloged from PDF version of thesis.
Includes bibliographical references (p. 137-139).
In this thesis, we study the problem of asymptotic spectral flow for a family of coupled Dirac operators. We prove that the leading order term in the spectral flow on an n dimensional manifold is of order r n+1/2 followed by a remainder of O(r n/2). We perform computations of spectral flow on the sphere which show that O(r n-1/2) is the best possible estimate on the remainder. To obtain the sharp remainder we study a semiclassical Dirac operator and show that its odd functional trace exhibits cancellations in its first n+3/2 terms. A normal form result for this Dirac operator and a bound on its counting function are also obtained.
by Nikhil Savale.
Ph.D.
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Oliveira, Juliano Ribeiro de. "Comportamento assintótico para soluções de certas equações diferenciais funcionais periódicas." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-12052008-095753/.
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Estamos interessados em estudar o comportamento assintótico das soluções de uma classe de Equações Diferenciais Funcionais (EDF) lineares e autônomas do tipo neutro, onde os coeficientes, na parte não neutra, são funções periódicas de período comum w! e os retardamentos são múltiplos de w. Para isto, utilizamo-nos da teoria espectral de operadores aplicada ao chamado operador monodrômico \'PI\' : C \'SETA\' C, cuja ação é evoluir um dado estado um passo de tamanho w. Calculamos o resolvente deste operador, donde inferimos todas as propriedades espectrais que nos permitem determinar o comportamento assintótico das soluções. Mostramos a importância de se determinar autovalores dominantes para a obtenção das estimativas, e mostramos resultados neste sentido. Estudamos em detalhe três exemplos que ilustram a teoria e demonstram sua aplicabilidadeWe are interested in the study of the asymptotic behavior of the solutions of a class of linear autonomous Functional Differential Equations (FDE) of neutral type, where the coeficients of the non neutral part are periodic functions with common period w and the time delays are multiples of w. We employ the spectral theory for linear operators applied to the so called monodromic operator \'PI\' : C \'ARROW\'! C, whose action is to evolve a given state one step of size w. We compute the resolvent of this operator, from where we infer the spectral properties that allows us to determine the asymptotic behavior of the solutions. We show the importance to determine whether an eigenvalue is dominant, in order to obtain the estimates for the correspondet solution, and we show results in this direction. Finally we study in detail three examples that illustrate the theory and demonstrate its applicability
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Mampitiya, M. A. Upali. "Spectral asymptotics for polar vector Sturm-Liouville problems." Thesis, University of Ottawa (Canada), 1985. http://hdl.handle.net/10393/4690.
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Mampitiya, M. A. Upali. "Spectral asymptotics for left-definite vector Sturm-Liouville problems." Thesis, University of Ottawa (Canada), 1988. http://hdl.handle.net/10393/5425.
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Al-Naggar, Ibtesam M. Abu-Sulayman. "Asymptotics for the solution of the Schrödinger equation." Thesis, University of Hull, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.262439.
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Dechaume, Antoine. "Analyse asymptotique et numérique des équations de Navier-Stokes : cas du canal indenté." Toulouse 3, 2006. http://www.theses.fr/2006TOU30023.
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Ce travail à pour sujet la problématique de la modélisation de la couche limite dans le cadre d'écoulements incompressibles. Cela nécessite de prendre en compte l'interaction forte entre la couche limite et le reste de l'écoulement, qui mène au couplage fort de ces deux modèles. Avec les méthodes classiques d'analyse asymptotique des problèmes de perturbation singulière, telle que la Méthode des Développements Asymptotiques Raccordés (MDAR), de tels modèles peuvent être construits. La forme et mise en oeuvre complexes de ces modèles, le cadre restreint pour lequel ils peuvent s'appliquer, et la difficulté d'exprimer l'approximation globale en assemblant les solutions locales, sont autant d'inconvénients que l'on souhaite dépasser. C'est pour cela qu'une autre méthode d'analyse asymptotique est ici utilisée, la Méthode des Approximations Successives Complémentaires (MASC), qui permet de s'affranchir de ces inconvénients. Elle met en avant l'existence d'une approximation globale du problème, d'où en découle la méthode qui permet de la construire. L'emploi de développements asymptotiques généralisés, contrairement à la MDAR qui est basée sur des développements réguliers, donne aux modèles obtenus une portée plus générale et une forme plus simple. Grâce à la MASC, selon la situation physique, deux types de modèles peuvent être obtenus. Les premiers sont similaires dans leur résolution à ceux obtenus classiquement. Cela consiste à résoudre un système d'équations parabolique couplé à un système elliptique. Le second type de modèle est complètement elliptique, et conduit à l'approche Navier-Stokes Réduit (NSR). Du fait du traitement implicite de l'ellipticité propre à ce type de modèle, on peut espérer avoir la possibilité d'étudier des écoulements décollés présentant des interactions amont plus importantes. Notamment, dans le cadre de l'écoulement en canal bi-dimensionnel, le modèle obtenu est exactement celui de NSR. Aucune justification basée sur une analyse asymptotique ne permettait jusqu'alors d'assurer la validité d'une telle approche. .This work deals with the problems of incompressible boundary layer modeling. The strong interaction between the boundary layer and external flow is to be accounted for, which leads to the coupling of these two models. Such models can be obtained with the classical methods of singular perturbation asymptotic analysis, such as the Method of Matched Asymptotic Expansions (MMAE). The complex shape and implementation of these models, the restricted cases for which they apply, and the difficulty to obtain global approximations from local ones, are many of the drawbacks we wish to transcend. This is the reason why a new asymptotic method is used, the Successive Complementary Expansions Method (SCEM), which avoids these limitations. The SCEM is based on the assumption of the structure of a global approximation, and then infers a method of constructing this approximation. The use of generalized asymptotic expansions, contrary to the MMAE which is based on regular expansions, leads to more general and simpler models. Thanks to the SCEM, according to the physical situation, two types of models can be obtained. .
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Male, Camille. "Forte et fausse libertés asymptotiques de grandes matrices aléatoires." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2011. http://tel.archives-ouvertes.fr/tel-00673551.
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Cette thèse s'inscrit dans la théorie des matrices aléatoires, à l'intersection avec la théorie des probabilités libres et des algèbres d'opérateurs. Elle s'insère dans une démarche générale qui a fait ses preuves ces dernières décennies : importer les techniques et les concepts de la théorie des probabilités non commutatives pour l'étude du spectre de grandes matrices aléatoires. On s'intéresse ici à des généralisations du théorème de liberté asymptotique de Voiculescu. Dans les Chapitres 1 et 2, nous montrons des résultats de liberté asymptotique forte pour des matrices gaussiennes, unitaires aléatoires et déterministes. Dans les Chapitres 3 et 4, nous introduisons la notion de fausse liberté asymptotique pour des matrices déterministes et certaines matrices hermitiennes à entrées sous diagonales indépendantes, interpolant les modèles de matrices de Wigner et de Lévy.
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Watson, Simon P. "On the asymptotics of the Dirichlet Laplacian : cones, corners and conduction." Thesis, University of Bristol, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.246266.
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Kobeissi, Hussein. "Eigenvalue Based Detector in Finite and Asymptotic Multi-antenna Cognitive Radio Systems." Thesis, CentraleSupélec, 2016. http://www.theses.fr/2016SUPL0011/document.
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La thèse aborde le problème de la détection d’un signal dans une bande de fréquences donnée sans aucune connaissance à priori sur la source (détection aveugle) dans le contexte de la radio intelligente. Le détecteur proposé dans la thèse est basé sur l’estimation des valeurs propres de la matrice de corrélation du signal reçu. A partir de ces valeurs propres, plusieurs critères ont été développés théoriquement (Standard Condition Number, Scaled Largest Eigenvalue, Largest Eigenvalue) en prenant pour hypothèse majeure un nombre fini d’éléments, contrairement aux hypothèses courantes de la théorie des matrices aléatoires qui considère un comportement asymptotique de ces critères. Les paramètres clés des détecteurs ont été formulés mathématiquement (probabilité de fausse alarme, densité de probabilité) et une correspondance avec la densité GEV a été explicitée. Enfin, ce travail a été étendu au cas multi-antennes (MIMO) pour les détecteurs SLE et SCNIn Cognitive Radio, Spectrum Sensing (SS) is the task of obtaining awareness about the spectrum usage. Mainly it concerns two scenarios of detection: (i) detecting the absence of the Primary User (PU) in a licensed spectrum in order to use it and (ii) detecting the presence of the PU to avoid interference. Several SS techniques were proposed in the literature. Among these, Eigenvalue Based Detector (EBD) has been proposed as a precious totally-blind detector that exploits the spacial diversity, overcome noise uncertainty challenges and performs adequately even in low SNR conditions. The first part of this study concerns the Standard Condition Number (SCN) detector and the Scaled Largest Eigenvalue (SLE) detector. We derived exact expressions for the Probability Density Function (PDF) and the Cumulative Distribution Function (CDF) of the SCN using results from finite Random Matrix Theory; In addition, we derived exact expressions for the moments of the SCN and we proposed a new approximation based on the Generalized Extreme Value (GEV) distribution. Moreover, using results from the asymptotic RMT we further provided a simple forms for the central moments of the SCN and we end up with a simple and accurate expression for the CDF, PDF, Probability of False-Alarm, Probability of Detection, of Miss-Detection and the decision threshold that could be computed and hence provide a dynamic SCN detector that could dynamically change the threshold value depending on target performance and environmental conditions. The second part of this study concerns the massive MIMO technology and how to exploit the large number of antennas for SS and CRs. Two antenna exploitation scenarios are studied: (i) Full antenna exploitation and (ii) Partial antenna exploitation in which we have two options: (i) Fixed use or (ii) Dynamic use of the antennas. We considered the Largest Eigenvalue (LE) detector if noise power is perfectly known and the SCN and SLE detectors when noise uncertainty exists
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Hauser, Elias [Verfasser], and Uta Renata [Akademischer Betreuer] Freiberg. "Spectral asymptotics for stretched fractals / Elias Hauser ; Betreuer: Uta Renata Freiberg." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2019. http://d-nb.info/1192305221/34.
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Yeates, Stephen. "Non-quasianalytic representations of semigroups : their spectra and asymptotics." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.297366.
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Alias, Azwani B. "Mathematical modelling of nonlinear internal waves in a rotating fluid." Thesis, Loughborough University, 2014. https://dspace.lboro.ac.uk/2134/15861.
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Large amplitude internal solitary waves in the coastal ocean are commonly modelled with the Korteweg-de Vries (KdV) equation or a closely related evolution equation. The characteristic feature of these models is the solitary wave solution, and it is well documented that these provide the basic paradigm for the interpretation of oceanic observations. However, often internal waves in the ocean survive for several inertial periods, and in that case, the KdV equation is supplemented with a linear non-local term representing the effects of background rotation, commonly called the Ostrovsky equation. This equation does not support solitary wave solutions, and instead a solitary-like initial condition collapses due to radiation of inertia-gravity waves, with instead the long-time outcome typically being an unsteady nonlinear wave packet. The KdV equation and the Ostrovsky equation are formulated on the assumption that only a single vertical mode is used. In this thesis we consider the situation when two vertical modes are used, due to a near-resonance between their respective linear long wave phase speeds. This phenomenon can be described by a pair of coupled Ostrovsky equations, which is derived asymptotically from the full set of Euler equations and solved numerically using a pseudo-spectral method. The derivation of a system of coupled Ostrovsky equations is an important extension of coupled KdV equations on the one hand, and a single Ostrovsky equation on the other hand. The analytic structure and dynamical behaviour of the system have been elucidated in two main cases. The first case is when there is no background shear flow, while the second case is when the background state contains current shear, and both cases lead to new solution types with rich dynamical behaviour. We demonstrate that solitary-like initial conditions typically collapse into two unsteady nonlinear wave packets, propagating with distinct speeds corresponding to the extremum value in the group velocities. However, a background shear flow allows for several types of dynamical behaviour, supporting both unsteady and steady nonlinear wave packets, propagating with the speeds which can be predicted from the linear dispersion relation. In addition, in some cases secondary wave packets are formed associated with certain resonances which also can be identified from the linear dispersion relation. Finally, as a by-product of this study it was shown that a background shear flow can lead to the anomalous version of the single Ostrovsky equation, which supports a steady wave packet.
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Li, Liangpan. "Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators." Thesis, Loughborough University, 2016. https://dspace.lboro.ac.uk/2134/23004.
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In this dissertation we study non-negative self-adjoint Laplace type operators acting on smooth sections of a vector bundle. First, we assume base manifolds are compact, boundaryless, and Riemannian. We start from the Fourier integral operator representation of half-wave operators, continue with spectral zeta functions, heat and resolvent trace asymptotic expansions, and end with the quantitative Wodzicki residue method. In particular, all of the asymptotic coefficients of the microlocalized spectral counting function can be explicitly given and clearly interpreted. With the auxiliary pseudo-differential operators ranging all smooth endomorphisms of the given bundle, we obtain certain asymptotic estimates about the integral kernel of heat operators. As applications, we study spectral asymptotics of Dirac type operators such as characterizing those for which the second coefficient vanishes. Next, we assume vector bundles are trivial and base manifolds are Euclidean domains, and study non-negative self-adjoint extensions of the Laplace operator which acts component-wise on compactly supported smooth functions. Using finite propagation speed estimates for wave equations and explicit Fourier Tauberian theorems obtained by Yuri Safarov, we establish the principle of not feeling the boundary estimates for the heat kernel of these operators. In particular, the implied constants are independent of self-adjoint extensions. As a by-product, we affirmatively answer a question about upper estimate for the Neumann heat kernel. Finally, we study some specific values of the spectral zeta function of two-dimensional Dirichlet Laplacians such as spectral determinant and Casimir energy. For numerical purposes we substantially improve the short-time Dirichlet heat trace asymptotics for polygons. This could be used to measure the spectral determinant and Casimir energy of polygons whenever the first several hundred or one thousand Dirichlet eigenvalues are known with high precision by other means.
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Rey, Thomas. "Quelques contributions à l'analyse mathématique et numérique d'équations cinétiques collisionnelles." Phd thesis, Université Claude Bernard - Lyon I, 2012. http://tel.archives-ouvertes.fr/tel-00738709.
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Cette thèse est dédiée à l'étude mathématique et numérique d'une classe d'équations cinétiques collisionnelles, de type équation de Boltzmann. Nous avons porté un intérêt tout particulier à l'équation des milieux (ou gaz) granulaires, initialement introduite dans la littérature physique pour décrire le comportement hors équilibre de matériaux composés d'un grand nombre de grains, ou particules, non nécessairement microscopiques, et interagissant par des collisions dissipant l'énergie cinétique. Ces modèles se sont révélés avoir une structure mathématique très riche. Cette thèse se structure en trois partie pouvant être lues de manière indépendante, mais néanmoins en rapport avec des équations cinétiques collisionnelles en général, et l'équation des milieux granulaires en particulier. La première partie est dédiée à l'étude mathématique du comportement asymptotique de certaines équations cinétiques collisionnelles dans un cadre homogène en espace. Nous y montrons des résultats de type explosion et convergence vers la solution autosimilaire avec calcul explicite des taux, pour des opérateurs de type Boltzmann, grâce à l'utilisation (entre autre) d'une nouvelle méthode de changement de variables dépendant directement de la solution de l'équation considérée. En particulier, nous démontrons que pour un modèle de gaz granulaire - dit anormal - il est possible d'observer une explosion en temps fini. Dans la deuxième partie, orientée analyse numérique et calcul scientifique, nous nous intéressons développement et à l'étude de méthodes spectrales pour la résolution de problèmes multi-échelles, issus de la théorie des équations cinétiques collisionnelles. Les méthodes de changement de variables tiennent aussi une place importante dans cette partie, et permettent d'observer numériquement des phénomènes non triviaux qui apparaissent lors de l'étude de gaz granulaires, comme la création d'amas de matière ou la caractérisation précise du retour vers l'équilibre. La troisième et dernière partie est dédiée à l'étude spectrale de l'opérateur des milieux granulaires avec bain thermique, linéarisé au voisinage d'un équilibre homogène en espace, afin d'établir des résultats de type stabilité et convergence vers une limite hydrodynamique. Ce travail est en fait la généralisation d'un résultat célèbre dans la théorie de l'équation de Boltzmann, dû à R. Ellis et M. Pinsky, et établissant rigoureusement la première limite hydrodynamique vers les équations d'Euler compressibles linéaires puis Navier-Stokes de cette équation.
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Caron, Emmanuel. "Comportement des estimateurs des moindres carrés du modèle linéaire dans un contexte dépendant : Étude asymptotique, implémentation, exemples." Thesis, Ecole centrale de Nantes, 2019. http://www.theses.fr/2019ECDN0036.
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Dans cette thèse, nous nous intéressons au modèle de régression linéaire usuel dans le cas où les erreurs sont supposées strictement stationnaires. Nous utilisons un résultat de Hannan (1973) qui a prouvé un Théorème Limite Central pour l’estimateur des moindres carrés sous des conditions très générales sur le design et le processus des erreurs. Pour un design et un processus d’erreurs vérifiant les conditions d’Hannan, nous définissons un estimateur de la matrice de covariance asymptotique de l’estimateur des moindres carrés et nous prouvons sa consistance sous des conditions très générales. Ensuite nous montrons comment modifier les tests usuels sur le paramètre du modèle linéaire dans ce contexte dépendant. Nous proposons différentes approches pour estimer la matrice de covariance afin de corriger l’erreur de première espèce des tests. Le paquet R slm que nous avons développé contient l’ensemble de ces méthodes statistiques. Les procédures sont évaluées à travers différents ensembles de simulations et deux exemples particuliers de jeux de données sont étudiés. Enfin, dans le dernier chapitre, nous proposons une méthode non-paramétrique par pénalisation pour estimer la fonction de régression dans le cas où les erreurs sont gaussiennes et corréléesIn this thesis, we consider the usual linear regression model in the case where the error process is assumed strictly stationary.We use a result from Hannan (1973) who proved a Central Limit Theorem for the usual least squares estimator under general conditions on the design and on the error process. Whatever the design and the error process satisfying Hannan’s conditions, we define an estimator of the asymptotic covariance matrix of the least squares estimator and we prove its consistency under very mild conditions. Then we show how to modify the usual tests on the parameter of the linear model in this dependent context. We propose various methods to estimate the covariance matrix in order to correct the type I error rate of the tests. The R package slm that we have developed contains all of these statistical methods. The procedures are evaluated through different sets of simulations and two particular examples of datasets are studied. Finally, in the last chapter, we propose a non-parametric method by penalization to estimate the regression function in the case where the errors are Gaussian and correlated
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Singh, Pranav. "High accuracy computational methods for the semiclassical Schrödinger equation." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/274913.
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The computation of Schrödinger equations in the semiclassical regime presents several enduring challenges due to the presence of the small semiclassical parameter. Standard approaches for solving these equations commence with spatial discretisation followed by exponentiation of the discretised Hamiltonian via exponential splittings. In this thesis we follow an alternative strategy${-}$we develop a new technique, called the symmetric Zassenhaus splitting procedure, which involves directly splitting the exponential of the undiscretised Hamiltonian. This technique allows us to design methods that are highly efficient in the semiclassical regime. Our analysis takes place in the Lie algebra generated by multiplicative operators and polynomials of the differential operator. This Lie algebra is completely characterised by Jordan polynomials in the differential operator, which constitute naturally symmetrised differential operators. Combined with the $\mathbb{Z}_2$-graded structure of this Lie algebra, the symmetry results in skew-Hermiticity of the exponents for Zassenhaus-style splittings, resulting in unitary evolution and numerical stability. The properties of commutator simplification and height reduction in these Lie algebras result in a highly effective form of $\textit{asymptotic splitting:} $exponential splittings where consecutive terms are scaled by increasing powers of the small semiclassical parameter. This leads to high accuracy methods whose costs grow quadratically with higher orders of accuracy. Time-dependent potentials are tackled by developing commutator-free Magnus expansions in our Lie algebra, which are subsequently split using the Zassenhaus algorithm. We present two approaches for developing arbitrarily high-order Magnus--Zassenhaus schemes${-}$one where the integrals are discretised using Gauss--Legendre quadrature at the outset and another where integrals are preserved throughout. These schemes feature high accuracy, allow large time steps, and the quadratic growth of their costs is found to be superior to traditional approaches such as Magnus--Lanczos methods and Yoshida splittings based on traditional Magnus expansions that feature nested commutators of matrices. An analysis of these operatorial splittings and expansions is carried out by characterising the highly oscillatory behaviour of the solution.
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at, Andreas Cap@esi ac. "Smoothness and High Energy Asymptotics of the Spectral Shift Function in Many--Body Scattering." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1048.ps.
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DePew, Kyle David. "On the astromineralogy of the 13 [mu]m feature in the spectra of oxygen-rich AGB stars." Diss., Columbia, Mo. : University of Missouri-Columbia, 2006. http://hdl.handle.net/10355/4562.
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Thesis (M.S.)--University of Missouri-Columbia, 2006.The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (February 6, 2007) Includes bibliographical references.
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Geisinger, Leander [Verfasser], and Timo [Akademischer Betreuer] Weidl. "On the semiclassical limit of the Dirichlet Laplace operator : two-term spectral asymptotics and sharp spectral estimates / Leander Geisinger. Betreuer: Timo Weidl." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2011. http://d-nb.info/1017972613/34.
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Norgren, Ofelia. "Pulsation Properties in Asymptotic Giant Branch Stars." Thesis, Uppsala universitet, Teoretisk astrofysik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-388388.
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Asymptotic Giant Branch (AGB) stars are stars with low- to intermediate mass in a late stage in their stellar evolution. An important feature of stellar evolution is the ongoing nucleosynthesis, the creation of heavier elements. Unlike main sequence stars, the AGB stars have a thick convective envelope which makes it possible to dredge-up the heavier fused elements from the stellar core to its surface. AGB stars are also pulsating variable stars, meaning the interior expands and contracts, causing the brightness to fluctuate. These pulsations will also play a major role in the mass loss observed in these stars. The mass loss is caused by stellar winds that accelerate gas and dust from the surface of these stars and thereby chemical enrich the interstellar medium. It is important to understand the properties of these pulsations since they play a key role in how stellar winds are produced and then enrich the galaxy with heavier synthesized elements. These pulsation periods can be observed with their corresponding Light-Curves, where the periodic motion of the brightness can be clearly seen. The main goal with this project is to calculate these pulsation periods for different AGB stars and compare these values with the periods listed in the General Catalogue of Variable Stars (GCVS). The comparison between these values gives a better understanding of methods of determining these periods and the uncertainties that follow.Asymptotiska jättegrenen är en del av slutstadiet för låg- till medelmassiva stjärnor (AGB stjärnor). Ett viktigt kännetecken hos stjärnutvecklingen är den pågående nukleosyntesen, sammanslagningen av tyngre ämnen i stjärnans inre. Till skillnad mot stjärnor på huvudserien har AGB stjärnor ett tjockt konvektivt lager som gör det möjligt att dra upp dessa nybildade ämnen till stjärnans yta. AGB stjärnor är pulserande variabla stjärnor där variationer i stjärnans radie gör att ljusstyrkan varierar. Dessa pulsationer kommer även att spela en viktig roll för den massförlust som observeras hos dessa stjärnor. Massförlusten orsakas av stjärnvindar som accelererar gas och stoft från stjärnans yta och därmed kemiskt berikar det interstellära mediet. Det är viktigt att förstå dessa pulsationer eftersom de är en viktig komponent för hur stjärnvindar uppstår och sedan berikar galaxer med tyngre ämnen. Dessa pulsationsperioder kan studeras genom att observera stjärnornas ljuskurvor, där man tydligt ser det periodiska beteendet hos ljusstyrkan. Det huvudsakliga målet med detta projekt är att beräkna dessa perioder för olika AGB stjärnor och att sedan jämföra dem med värden från General Catalogue of Variable Stars (GCVS). Jämförelsen mellan dessa värden ger en bättre förståelse för metoderna som används för att bestämma dessa perioder och hur osäkra dessa värden är.
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Harrat, Ayoub. "Problème de moments avec applications et estimations du spectre discret des opérateurs définis par des matrices infinies non bornées THE QUINTIC COMPLEX MOMENT PROBLEM ASYMPTOTIC EXPANSION OF LARGE EIGENVALUES FOR A CLASS OF UNBOUNDED JACOBI MATRICES." Thesis, Littoral, 2020. http://www.theses.fr/2020DUNK0563.
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Dans cette thèse on donne d'abord une solution concrète pour presque tous les scénarios qu'on peut avoir dans le problème de moments complexe quintique et en particulier dans le cas d'une mesure à support minimal. On présente aussi de nombreux exemples pour illustrer chaque cas. La seconde partie présente une approche qui permet de passer du problème de moments tronqué au problème complet à l'aide des idempotents. Il s'agit d'une approche très différente de celle utilisée dans la première partie.Plus précisément, au lieu d'appliquer les méthodes de R. Curto et L. Fialkow où l'objet central est la matrice de moments, on utilise l'approche de F. Vasilescu dont l'objet central est la fonctionnelle de Riesz. Cette fonctionnelle fait associer à chaque monôme tᵅ la valeur γ∝ et elle satisfait trois conditions naturelles dans le cas où la suite (γ∝)∝∈ℕᵈ est donnée par les intégrales de tᵅ par rapport à une mesure. La troisième partie est consacrée à l'asymptotique du spectre pour une classe de matrices hermitiennes tridiagonales infinies. Le but est d'obtenir le comportement asymptotique précis des valeurs propres y associées à partir du comportement asymptotique de ces coefficients. Le résultat est obtenu par une approche nouvelle qui est une adaptation de la théorie de perturbations de Schrieffer-Wolff utilisée en physique de la matière condensée. Cette méthode marche également pour des matrices 'bande', mais le cas des matrices tridiagonales est le plus important pour des applications et encore les expressions explicites des premières corrections dans la formule asymptotique sont plus simples pour les matrices tridiagonalesIn this thesis, we first provide a concrete solution to the, almost all, quintic TCMP (that is, when m = 5). We also study the cardinality of the minimal representing measure. Based on the bi-variate recurrence sequence properties with some Curto-Fialkow's results. Our method intended to be useful for all odd-degree moment problems. Second, we investigate the full moment problem for discrete measures using Vasilescu's idempotent approach based on Λ-multiplicative elements with respect to the associated square positive Riesz functional. We give a sufficient condition for the existence of a discrete integral representation for the associated Riesz functional, which turns to be necessary in bounded shift space case. A particular attention is given to Λ-multiplicative elements, where a total description, for the cases where they are a single point indicator functions, is given. Lastly, We investigate a class of infinite Jacobi matrices which define unbounded self-adjoint operators with discrete spectrum. Our purpose is to establish the asymptotic expansion of large eigenvalues and to compute two correction terms explicitly. This method works in general for band matrices but Jacobi matrices case still much interesting due to applications and explicit expressions obtained for the first correction terms in the asymptotic formula
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Ourmières-Bonafos, Thomas. "Quelques asymptotiques spectrales pour le Laplacien de Dirichlet : triangles, cônes et couches coniques." Thesis, Rennes 1, 2014. http://www.theses.fr/2014REN1S143/document.
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Cette thèse est consacrée à l'étude du spectre de l'opérateur de Laplace avec conditions de Dirichlet dans différents domaines du plan ou de l'espace. Dans un premier temps on s'intéresse à des triangles asymptotiquement plats et des cônes de petite ouverture. Ces problèmes admettent une reformulation semi-classique et nous donnons des développements asymptotiques à tout ordre des premières valeurs et fonctions propres. Ce type de résultat est déjà connu pour des domaines minces à profil régulier. Pour les triangles et les cônes, on prouve que le problème admet maintenant deux échelles. Dans un second temps, on étudie une famille de couches coniques indexées par leur ouverture. Là encore, on s'intéresse à la limite semi-classique quand l'ouverture tend vers zéro: on donne un développement asymptotique à deux termes des premières valeurs propres et on démontre un résultat de localisation des fonctions propres associées. Nous donnons également, à ouverture fixée, un équivalent du nombre de valeurs propres sous le seuil du spectre essentielThis thesis deals with the spectrum of the Dirichlet Laplacian in various two or three dimensional domains. First, we consider asymptotically flat triangles and cones with small aperture. These problems admit a semi-classical formulation and we provide asymptotic expansions at any order for the first eigenvalues and the associated eigenfunctions. These type of results is already known for thin domains with smooth profiles. For triangles and cones, we show that the problem admits now two different scales. Second, we study a family of conical layers parametrized by their aperture. Again, we consider the semi-classical limit when the aperture tends to zero: We provide a two-term asymptotics of the first eigenvalues and we prove a localization result about the associated eigenfunctions. We also estimate, for each chosen aperture, the number of eigenvalues below the threshold of the essential spectrum
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Ho, Xuan Hieu. "On multifractality, Schwarzian derivative and asymptotic variance of whole-plane SLE." Thesis, Orléans, 2016. http://www.theses.fr/2016ORLE2060/document.
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Soit f une instance du whole-plane $\SLE_\kappa$ : on sait que pour certaines valeurs de κ, p les moments dérivés $\mathbb{E}(\vert f'(z) \vert^p)$ peuvent être écrits sous une forme fermée, étude qui a permis de mettre au jour une nouvelle phase du spectre des moyennes intégrales. Le but de cette thèse est une étude des moments généralisés $\frac{\vert f'(z) \vert^p}{\vert f(z) \vert^q}$ : cette étude permet de confirmer la structure algébrique riche du whole-plane SLE. On montre que les formes fermées des moments mixtes $\mathbb{E}\big(\frac{\vert f'(z) \vert^p}{\vert f(z) \vert^q}\big)$ apparaissent sur une famille dénombrable de paraboles du plan (p, q), en étendant les équations de Beliaev-Smirnov à ce cas. Nous introduisons également le spectre généralisé β(p, q; κ), correspondant au comportement asymptotiques des moyennes intégrales mixtes. Le spectre généralisé moyen du whole-plane SLE prend quatre formes possibles, séparés par cinq séparatrices dans $\R^2$. Nous proposons également une approche semblable pour la dérivée Schwarziene S(f)(z) de l’application de SLE. Les calculs sur les équations de Beliaev-Smirnov d’une certaine générale forme de moment mène à une formulation explicite de $\mathbb{E}(S(f)(z))$ . Nous étudions finalement la variance asymptotique de McMullen et démontrons une relation entre la croissance infinitésimale du spectre de la moyenne intégrale et la variance asymptotique pour SLE₂Let f an instance of the whole-plane $\SLE_\kappa$ conformal map from the unit disk D to the slit plane: We know that for certain values of κ, p the derivative moments $\mathbb{E}(\vert f'(z) \vert^p)$ can be written in a closed form, study that has updated a new phase of the integral means spectrum. The goal of this thesis is a study on generalized moments $\frac{\vert f'(z) \vert^p}{\vert f(z) \vert^q}$ : ΒββThis study permit confirm the rich algebraic structure of the whole-plane version of SLE. It will be showed that closed forms of the mixed moments E mixtes $\mathbb{E}\big(\frac{\vert f'(z) \vert^p}{\vert f(z) \vert^q}\big)$ can be obtained on a countable family of parabolas in the moment plane (p, q), by extending the so-called Beliaev–Smirnov equation to this case. We also introduce the generalized integral means spectrum, β(p, q; κ), corresponding to the singular behavior of the mixed moments. The average generalized spectrum of whole-plane SLE takes four possible forms, separated by five phase transition lines in $\R^2$. We also propose a similar approach for the Schwarzian derivative S(f)(z) of SLE maps. Computations on the Beliaev–Smirnov equation of a certain general form of moment lead to an explicit formula of $\mathbb{E}(S(f)(z))$ . We finally study the McMullen asymptotic variance and prove a relation between the infinitesimal growth of the integral mean spectrum and the asymptotic variance in an expectation sense for SLE₂
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Di, Gesù Giacomo. "Semiclassical spectral analysis of discrete Witten Laplacians." Phd thesis, Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2013/6528/.
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A discrete analogue of the Witten Laplacian on the n-dimensional integer
lattice is considered. After rescaling of the operator and the lattice size we
analyze the tunnel effect between different wells, providing sharp asymptotics
of the low-lying spectrum. Our proof, inspired by work of B. Helffer,
M. Klein and F. Nier in continuous setting, is based on the construction of
a discrete Witten complex and a semiclassical analysis of the corresponding
discrete Witten Laplacian on 1-forms. The result can be reformulated in
terms of metastable Markov processes on the lattice.In dieser Arbeit wird auf dem n-dimensionalen Gitter der ganzen Zahlen ein Analogon des Witten-Laplace-Operatoren eingeführt. Nach geeigneter Skalierung des Gitters und des Operatoren analysieren wir den Tunneleffekt zwischen verschiedenen Potentialtöpfen und erhalten vollständige Aymptotiken für das tiefliegende Spektrum. Der Beweis (nach Methoden, die von B. Helffer, M. Klein und F. Nier im Falle des kontinuierlichen Witten-Laplace-Operatoren entwickelt wurden) basiert auf der Konstruktion eines diskreten Witten-Komplexes und der Analyse des zugehörigen Witten-Laplace-Operatoren auf 1-Formen. Das Resultat kann im Kontext von metastabilen Markov Prozessen auf dem Gitter reformuliert werden und ermöglicht scharfe Aussagen über metastabile Austrittszeiten.
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Sugiura, Shiro. "Asymptomatic C-reactive protein elevation in neutropenic children." Kyoto University, 2017. http://hdl.handle.net/2433/226006.
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GuimarÃes, Francisco Rafael Vasconcelos. "Node Selection Techniques in Spectrum Sharing Cooperative Cognitive Networks." Universidade Federal do CearÃ, 2013. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=10885.
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In this dissertation, the performance of cooperative cognitive systems with spectrum sharing is investigated. A low-complexity and high performance node selection strategy is proposed for two different of cooperative cognitive
systems models. In the first model, the secondary network is composed by one source node that communicates with one among L destinations through a direct link and also assisted by one among N AF or DF relays nodes. The selected secondary destination employs a selection combining technique for choosing the best link (direct or dual-hop link) from the secondary source. Considering an underlay spectrum sharing approach, the secondary communication is performed taking into account an interference constraint, where the overall transmit power is limited by the interference at the primary receiver as well as by the maximum transmission power available at the respective nodes. An asymptotic analysis is carried out, revealing that the diversity order of the considered system is not affected by the interference, and equals to L + N. In the second model, by its turn, the secondary network is composed by one source, N AF or DF relays, and one destination. However, it is assumed the presence of M primary receivers. A relay selection strategy is proposed with the aim of maximing the end-to-end signal-to-noise ratio and, at the same time, to satisfy the interference constraints imposed by these primary receivers. After the relay selection procedure is performed, the secondary destination chooses the best path (direct link or relaying link) by employing a selection combining scheme. An asymptotic analysis is carried out, revealing that the system diversity order equals to N + 1, and showing that it is not affected neither by the number of primary receivers nor by the interference threshold. A close-form expression and an approximation for the outage probability is derived for the DF and AF protocols, respectively.Nesta dissertaÃÃo, o desempenho de sistemas cooperativos cognitivos com compartilhamento espectral à investigado. Uma estratÃgia de seleÃÃo de nÃs de baixa complexidade e alto desempenho à proposta para dois modelos distintos de redes cooperativas cognitivas. No primeiro modelo, a rede secundÃria à composta por um nà fonte que comunica-se com um dentre L nÃs destinos atravÃs de um link direto e atravÃs de um dentre N nÃs relays decodifica-e-encaminha (DF) ou amplifica-e-encaminha (AF). O nà destino secundÃrio selecionado emprega uma tÃcnica de combinaÃÃo por seleÃÃo para selecionar o melhor link (direto ou auxiliar) a partir da fonte secundÃria. Considerando um ambiente com compartilhamento espectral, tem-se que a comunicaÃÃo secundÃria à realizada levando em consideraÃÃo uma restriÃÃo de interferÃncia, na qual a potÃncia de transmissÃo à governada pela interferÃncia no receptor primÃrio bem como pela mÃxima potÃncia de transmissÃo dos respectivos nÃs secundÃrios. Uma anÃlise assintÃtica à realizada, revelando que a ordem de diversidade do sistema nÃo à afetada pela interferÃncia, sendo igual a L + N. Jà no segundo modelo, a rede secundÃria à composta por uma fonte, N relays DF ou AF e um nà destino, no entanto assume-se a presenÃa de M receptores primÃrios. A seleÃÃo do relay deve satisfazer as restriÃÃes de interferÃncia impostas por estes Ãltimos. ApÃs a seleÃÃo de relay ser realizada, o nà destino seleciona o melhor caminho (link direto ou link via relay) proveniente da fonte utilizando um combinador por seleÃÃo. Uma anÃlise assintÃtica à realizada, revelando que a ordem de diversidade do esquema proposto iguala a N + 1, o que mostra que a mesma nÃo à afetada nem pelo nÃmero de receptores primÃrios nem pelo limiar de interferÃncia. Uma expressÃo em forma fechada para a probabilidade de outage à obtida para ambos protocolos cooperativos. SimulaÃÃes Monte Carlo sÃo apresentadas com o intuito de validar as anÃlises propostas.
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Weich, Tobias [Verfasser], and Pablo [Akademischer Betreuer] Ramacher. "Singular Equivariant Spectral Asymptotics of Schrödinger Operators in Rn and Resonances of Schottky Surfaces / Tobias Weich. Betreuer: Pablo Ramacher." Marburg : Philipps-Universität Marburg, 2014. http://d-nb.info/1052994938/34.
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Pankratova, Iryna. "L'homogénéisation d'équations de convection-diffusion singulières et de problèmes spectraux à poids indéfini." Phd thesis, Ecole Polytechnique X, 2011. http://pastel.archives-ouvertes.fr/pastel-00593511.
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Le but de la thèse est d'étudier l'homogénéisation d'équations de convection-diffusion singulières et de problèmes spectraux à poids indéfini. La thèse se compose de deux parties. La première partie contient des résultats qualitatifs et asymptotiques pour les solutions d'équations de type convection-diffusion stationnaires et instationnaires, qui sont définies dans des domaines bornés ou nonbornés. Les problèmes examinés comprennent des études qualitatives pour une équation elliptique avec des termes du premier ordre dans un cylindre semi-infini, l'homogénéisation de modèles de convection-diffusion dans des cylindres minces et une analyse asymptotique d'équations de convection-diffusion instationnaires avec un grand terme du premier ordre, posées dans un domaine borné. La deuxième partie de la thèse porte sur l'homogénéisation de problèmes spectraux à poids indéfini, pouvant changer de signe. On montre que le comportement asymptotique dépend essentiellement de la moyenne du poids, notamment si la moyenne est nulle ou non nulle. On construit alors le développement asymptotique du spectre dans les deux cas.