Le problème d’oscillation de fluides dans un conteneur est un problème classique d’hydrodynamique qui est etudié par des mathématiciens et ingénieurs depuis plus de 150 ans. Le présent travail est lié à l’étude de l’alternance des fonctions propres paires et impaires du problème de Steklov-Neumann pour les domaines à deux dimensions ayant une forme symétrique. On obtient des résultats sur la parité de deuxième et troisième fonctions propres d’un tel problème pour les trois premiers modes, dans le cas de domaines symétriques arbitraires. On étudie aussi la simplicité de deux premières valeurs propres non nulles d’un tel problème. Il existe nombre d’hypothèses voulant que pour le cas des domaines symétriques, toutes les valeurs propres sont simples. Il y a des résultats de Kozlov, Kuznetsov et Motygin [1] sur la simplicité de la première valeur propre non nulle obtenue pour les domaines satisfaisants la condition de John. Dans ce travail, il est montré que pour les domaines symétriques, la deuxième valeur propre non-nulle du problème de Steklov-Neumann est aussi simple. / The study of liquid sloshing in a container is a classical problem of hydrodynamics that has been actively investigated by mathematicians and engineers over the past 150 years. The present thesis is concerned with the properties of eigenfunctions of the two-dimensional sloshing problem on axially symmetric planar domains. Here the axis of symmetry is assumed to be orthogonal to the free surface of the fluid. In particular, we show that the second and the third eigenfunctions of such a problem are, respectively, odd and even with respect to the axial symmetry. There is a well-known conjecture that all eigenvalues of the two-dimensional sloshing problem are simple. Kozlov, Kuznetsov and Motygin [1] proved the simplicity of the first non-zero eigenvalue for domains satisfying the John's condition. In the thesis we show that for axially symmetric planar domains, the first two non-zero eigenvalues of the sloshing problem are simple.

Thesis (Ph. D.)--University of Alabama at Birmingham, 2007. / Additional advisors: Richard Brown, Ioulia Karpechina, Ryoichi Kawai, Boris Kunin. Description based on contents viewed Feb. 5, 2008; title from title screen. Includes bibliographical references (p. 73-75).

We present, extend, and apply a method to extract the contribution of a subregion of a data set to the global flow. To isolate this contribution, we decompose the flow in the subregion into a potential flow that is induced by the original flow on the boundary and a localized flow. The localized flow is obtained by subtracting the potential flow from the original flow. Since the potential flow is free of both divergence and rotation, the localized flow retains the original features and captures the region-specific flow that contains the local contribution of the considered subdomain to the global flow. In the remainder of the paper, we describe an implementation on unstructured grids in both two and three dimensions for steady and unsteady flow fields. We discuss the application of some widely used feature extraction methods on the localized flow and describe applications like reverse-flow detection using the potential flow. Finally, we show that our algorithm is robust and scalable by applying it to various flow data sets and giving performance figures.

Heating and cooling needs have been highly demanded as the extreme weathers become increasingly frequent and global warming becomes well-founded. Because ground temperature keeps relatively constant at 20-30 feet below the surface, using the earth as a thermal mass for temperature conditioning and thermal management creates an energy-efficient and environmentally beneficial approach to surface heating and cooling, which has been used in self-heated pavement, greenhouse, and building integrated photovoltaic thermal systems. Inspired by the human body wherein a blood circulation system keeps skin nearly at a constant temperature under environmental changes, a thermal fluid circulation system is introduced to the geothermal well system. Through bi-directional heat exchange between surface space with the ground, heat harvested at high temperatures can be stored underground for utilization at low temperatures, so that the surface temperature variations can be significantly reduced for daily and yearly cycles minimizing the heating/cooling needs. Understanding the heat transfer under the ground and thermal stress of the heat exchange systems induced by the temperature changes is critical for system design, performance prediction and optimization, and system control and operation. This dissertation studies heat transfer and thermomechanical problems for different geothermal systems. The temperature field of the earth can be calculated given the heat source and ambient temperature. Due to nonuniform thermal expansion caused by temperature differences or material mismatches, thermal stress will be induced. Its interaction with surface mechanical load and displacement constraint will be investigated for the design and failure analysis of the fluid circulation and heat exchange system. In the theoretical study, the earth is approximated as a semi-infinite domain. Green's function technique has been used in the analysis of heat conduction, elastic, and thermoelastic problems respectively. The semi-infinite domain with a surface boundary condition can be considered a special case of two semi-infinite domains with a perfectly bonded interface, which forms an infinite bi-material domain. For a Dirichlet boundary value problem with a constant temperature or displacement, the top semi-infinite domain can be considered with infinitely large conductivity or stiffness, respectively; for a Neumann boundary value problem with zero flux or traction, the top semi-infinite domain can be considered with a zero conductivity or stiffness, respectively. The general Green's functions of an infinite bi-material domain can recover the classic solutions for Boussinesq's problem, Mindlin's problem, Kelvin's problem, etc. The three-dimensional (3D) problems can be used to recover the corresponding two-dimensional (2D) problems by an integral of Green's function in one dimension through the Hadamard regularization. Firstly, the heat transfer problem in an infinite bi-material is introduced and the Green's function is formulated for the temperature change caused by a point heat source in the material. It is used to simulate heat transfer for a spherical heat exchanger embedded underground in geothermal energy applications. The temperature field of the spherical inhomogeneity embedded in an infinite bi-material subjected to a uniform far-field steady-state or sinusoidal heat flux is determined by solving the boundary value problem. Eshelby’s equivalent inclusion method (EIM) is used to consider the mismatch of the thermal conductivities of the particle from the matrix, which is simulated by a prescribed temperature gradient. When the material of one semi-infinite domain exhibits zero or infinite thermal conductivity, the above solution can be used for a semi-infinite domain containing a heat source with heat insulation or constant temperature on the boundary, respectively. The analytical solution has been verified with the finite element method. The formulation is used to simulate a spherical heat source embedded in a semi-infinite domain. The method can be immediately applied to the design of geothermal energy systems for heat storage and harvesting. When the heat exchanger is a long horizontal pipe, a similar procedure can be conducted for the corresponding 2D problem. If the temperature exhibits a cyclic change, such as daily variation, the formulation is extended to the harmonic transient heat conduction problems. Secondly, a similar formulation has been introduced for the elastic problem of an infinite bi-material. The Green's function is formulated for the displacement caused by a point force in the bi-material. It is used to simulate the stress transfer for a spherical heat exchanger embedded underground in geothermal energy applications. The formulation of the heat transfer problem is extended to the corresponding elastic problem. How a surface mechanical load is transferred to the underground heat exchanger is illustrated. The interactions between a heat exchanger and the surface load are investigated. Finally, the thermoelastic problem of an infinite bi-material is introduced and the Green's function is formulated for the displacement field caused by a point heat source in the material. It can be straightforwardly used to derive the thermoelastic stress caused by a distributed heat source by volume integrals. However, when the thermal conductivity and elasticity of the heat exchanger are different from the earth in actual geothermal energy applications, the Green's function cannot be directly used. By analogy to Eshelby's equivalent inclusion method, a dual equivalent inclusion method (DEIM) is introduced to address the dual material mismatch in thermal and elastic properties. The fundamental solutions of a bi-material for thermal, elastic, and thermoelastic problems are versatile and recover the ones of the single material domain for both 2D and 3D problems. The equivalent inclusion method is successfully extended to the thermoelastic problems to simulate the material mismatch. The formulation can be used in designing a geothermal heat exchanger for heat storage and supply for energy-efficient buildings as well as other geothermal applications. Future work will extend the fundamental solutions to time-dependent thermomechanical load and investigate the daily and seasonal heat exchange with the ground using different configurations of the pipelines. The algorithms will be integrated into the inclusion-based boundary element method (iBEM) for geothermal system design and analysis.

by Chu Lap-foo. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 68-69). / Introduction --- p.iii / Chapter 1 --- Basic Properties of Singular Solutions --- p.1 / Chapter 1.1 --- An Asymptotic Radial Result --- p.2 / Chapter 1.2 --- Local Uniqueness of Radial Solutions --- p.8 / Chapter 2 --- Dirichlet Problem : Existence Theory I --- p.11 / Chapter 2.1 --- Formulation --- p.12 / Chapter 2.2 --- Explicit Solutions on Balls --- p.14 / Chapter 2.3 --- The Moser Inequality --- p.19 / Chapter 2.4 --- Existence of Solutions in General Domains --- p.24 / Chapter 2.5 --- Spectrum of the Problem --- p.26 / Chapter 3 --- Dirichlet Problem : Existence Theory II --- p.29 / Chapter 3.1 --- Mountain Pass Lemma --- p.29 / Chapter 3.2 --- Existence of Second Solution --- p.31 / Chapter 4 --- Dirichlet Problem : Non-Existence Theory --- p.36 / Chapter 4.1 --- Upper Bound of λ* in Star-Shaped Domains --- p.36 / Chapter 4.2 --- Numerical Values --- p.41 / Chapter 5 --- The Neumann Problem --- p.42 / Chapter 5.1 --- Existence Theory I --- p.43 / Chapter 5.2 --- Existence Theory II --- p.47 / Chapter 6 --- The Schwarz Symmetrization --- p.49 / Chapter 6.1 --- Definitions and Basic Properties --- p.49 / Chapter 6.2 --- Inequalities Related to Symmetrization --- p.58 / Chapter 6.3 --- An Application to P.D.E --- p.63 / Bibliography --- p.68

Orientadores: Marcelo da Silva Montenegro, Massimo Grossi / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-20T13:53:15Z (GMT). No. of bitstreams: 1 Neves_SergioLeandroNascimento_D.pdf: 694748 bytes, checksum: 52d4109b562640e98c9a0a6098d9cb46 (MD5) Previous issue date: 2012 / Resumo: Neste trabalho, consideramos uma classe de problemas de Neumann com perturbação singular e fazemos um estudo do número de soluções do tipo "single peak" que se concentram em um mesmo ponto. Estudamos casos de concentração no interior e na fronteira do domínio. Obtemos um resultado de multiplicidade exata que relaciona o número de tais soluções com o número de zeros estáveis de um campo vetorial associado / Abstract: In this work, we consider a class of Neumann problems with singular perturbation and we study the number of single peak solutions which concentrate at the same point. We study concentration in the interior and at the boundary of the domain. We obtain an exact multiplicity result which relates the number of such solutions with the number of stable zeros of an associated vector field. / Doutorado / Matematica / Doutor em Matemática

This thesis consists of three self-contained parts, each with its own abstract, body, references and page numbering. Part I, 'Potential theory, path integrals and the Laplacian of the indicator', finds the transition density of absorbed or reflected Brownian motion in a d-dimensional domain as a Feynman-Kac functional involving the Laplacian of the indicator, thereby relating the hitherto unrelated fields of classical potential theory and path integrals. Part II, 'The problem of alternatives', considers parallel investment in alternative technologies or drugs developed over time, where there can be only one winner. Parallel investment accelerates the search for the winner, and increases the winner's expected performance, but is also costly. To determine which candidates show sufficient performance and/or promise, we find an integral equation for the boundary of the optimal continuation region. Part III, 'Optimal support for renewable deployment', considers the role of government subsidies for renewable technologies. Rapidly diminishing subsidies are cheaper for taxpayers, but could prematurely kill otherwise successful technologies. By contrast, high subsidies are not only expensive but can also prop up uneconomical technologies. To analyse this trade-off we present a new model for technology learning that makes capacity expansion endogenous. There are two reasons for this standalone structure. First, the target readership is divergent. Part I concerns mathematical physics, Part II operations research, and Part III policy. Readers interested in specific parts can thus read these in isolation. Those interested in the thesis as a whole may prefer to read the three introductions first. Second, the separate parts are only partially interconnected. Each uses some theory from the preceding part, but not all of it; e.g. Part II uses only a subset of the theory from Part I. The quickest route to Part III is therefore not through the entirety of the preceding parts. Furthermore, those instances where results from previous parts are used are clearly indicated.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-05-11T15:47:00Z No. of bitstreams: 1 samueloliveiradealmeida.pdf: 770018 bytes, checksum: 7270cb9d1478f3f95d8316be0a0c13aa (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-06-27T18:35:32Z (GMT) No. of bitstreams: 1 samueloliveiradealmeida.pdf: 770018 bytes, checksum: 7270cb9d1478f3f95d8316be0a0c13aa (MD5) / Made available in DSpace on 2016-06-27T18:35:32Z (GMT). No. of bitstreams: 1 samueloliveiradealmeida.pdf: 770018 bytes, checksum: 7270cb9d1478f3f95d8316be0a0c13aa (MD5) Previous issue date: 2013-04-05 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho estudamos a existência de soluções para problemas elípticos envolvendo o expoente crítico de Sobolev. Primeiramente, investigamos a existência de soluções para um problema superlinear do tipo Ambrosetti-Prodi com ressonância em 1, onde 1 é o primeiro autovalor de (−Δ,1 0 (Ω)). Além disso, estudamos resultados de multiplicidade para uma classe de equações elípticas críticas relacionadas com o problema de Brézis-Nirenberg, com condição de contorno de Neumann sobre a bola. / In this work we study the existence of solutions for elliptic problems involving critical Sobolev exponent. Firstly we investigate the existence of solutions for an Ambrosetti-Prodi type superlinear problem with resonance at 1 , where 1 is the first eigenvalue of (−Δ,1 0 (Ω)). Besides, we study multiplicity results for a class of critical elliptic equations related to the Brézis-Nirenberg problem with Neumann boundary condition on a ball.

Orientador: Francisco Odair Vieira de Paiva / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-21T19:28:36Z (GMT). No. of bitstreams: 1 Malavazi_MazilioCoronel_D.pdf: 1741221 bytes, checksum: becbc428943851a9a63bba6d406db3ca (MD5) Previous issue date: 2013 / Resumo: O resumo poderá ser visualizado no texto completo da tese digital / Abstract: The abstract is available with the full electronic document / Doutorado / Matematica / Doutor em Matemática

Η παρούσα διατριβή ερευνητικά εντάσσεται στην περιοχή της Μη Γραμμικής Ανάλυσης και ειδικότερα στην επίλυση Μη Γραμμικών Ελλειπτικών Μερικών Διαφορικών Εξισώσεων (Μ.Δ.Ε.) με υπερκρίσιμο εκθέτη. Η μη γραμμικότητα δεν επιτρέπει την επίλυση των εξισώσεων αυτών χρησιμοποιώντας τις συμπαγείς εμφυτεύσεις. Αξιοποιώντας τις ιδιότητες συμμετρίας που παρουσιάζει η πολλαπλότητα, αφενός παρακάμπτουμε το εμπόδιο αυτό και αφετέρου επιτυγχάνουμε να επιλύσουμε εξισώσεις αυτού του τύπου με υπερκρίσιμο εκθέτη. Στο πρώτο μέρος της Διατριβής υπολογίζουμε την πρώτη βέλτιστη σταθερά στη γενική ανισότητα Sobolev και στη γενική ανισότητα Sobolev με σύνορο στον στερεό τόρο, μελετάμε το φαινόμενο της συμπύκνωσης και επιλύουμε τα προβλήματα (P1) και (P2). Στο δεύτερο μέρος υπολογίζουμε την πρώτη βέλτιστη σταθερά στη γενική ανισότητα Sobolev και στη γενική ανισότητα Sobolev με σύνορο σε μια λεία, συμπαγή, n-διάστατη, n\geq 3, πολλαπλότητα Riemann (M,g) με σύνορο, που είναι αναλλοίωτη από τη δράση μιας οποιασδήποτε συμπαγούς υποομάδας G της ομάδας των ισομετριών Is(M,g) της Μ και της οποίας όλες οι G-τροχιές έχουν άπειρο πληθάριθμο και κάνουμε μια σύντομη παρουσίαση των λύσεων των προβλημάτων (P3) και (P4). / The present Thesis is incorporated in the research area of Nonlinear Analysis, especially solvability of Nonlinear Elliptic PDE’s with supercritical exponent.The nonlinear nature of the equations makes it impossible to be solved by means of compact imbeddings. Taking advantage of the symmetry properties of the manifold we overcome the obstacle as well as we succeed in solving equations of this type possessing supercritical exponent. In the first part of the Thesis we calculate the first best constant in the general Sobolev inequality and in the general Sobolev trace inequality on the solid torus, we study the phenomenon of concentration and solve problems (P1) and (P2).In the second part we calculate the first best constant in the general Sobolev inequality and in the general Sobolev trace inequality on a smooth, compact, n−dimensional Riemannian manifold (M, g), n _ 3, with boundary, which is invariant under the action of a subgroup G of the isometry group Is(M, g) of M, the orbits of which have infinity cardinality. We also present brief solutions of problems (P3) and (P4).