Dissertations / Theses on the topic 'Integral Equation Approach'
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Chapman, Geoffrey John Douglas. "A weakly singular integral equation approach for water wave problems." Thesis, University of Bristol, 2005. http://hdl.handle.net/1983/54f56a00-8496-4990-8410-d2c677839095.
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Messali, Nouari. "An integral equation approach to continuous system identification and model reduction." Thesis, Loughborough University, 1988. https://dspace.lboro.ac.uk/2134/33193.
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An integral equation description for linear systems is developed and used as the basis for the development of various system identification, model reduction and order determination methods. The system integral equation is utilized in the problem of parameter identification in continuous linear single-input single-output, multi-input multi-output and linear in parameters nonlinear systems. The approach is developed in the time domain where the effect of non-zero initial conditions and additive disturbances occurs naturally. Parameter estimates are deduced using several weighted residual concepts which have previously been used to produce approximate solutions to differential equations.
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Chamberlain, Peter George. "Wave propagation on water of uneven depth : an integral equation approach." Thesis, University of Reading, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.304583.
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Menotti, Enrico. "Time-dependent and three-dimensional phenomena in free-electron laser amplifiers within the integral-equation approach." Doctoral thesis, Università degli studi di Trieste, 2011. http://hdl.handle.net/10077/4485.
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O'Donoghue, Padraic Eimear. "Boundary integral equation approach to nonlinear response control of large space structures : alternating technique applied to multiple flaws in three dimensional bodies." Diss., Georgia Institute of Technology, 1985. http://hdl.handle.net/1853/20685.
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Kulkarni, Shashank D. "Development and validation of a Method of Moments approach for modeling planar antenna structures." Worcester, Mass. : Worcester Polytechnic Institute, 2007. http://www.wpi.edu/Pubs/ETD/Available/etd-042007-151741/.
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Dissertation (Ph.D.)--Worcester Polytechnic Institute.Keywords: patch antennas; volume integral equation (VIE); method of moments (MoM); low order basis functions; convergence. Includes bibliographical references (leaves 169-186 ).
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Pipis, Konstantinos. "Eddy-current testing modeling of axisymmetric pieces with discontinuities along the axis by means of an integral equation approach." Thesis, Université Paris-Saclay (ComUE), 2015. http://www.theses.fr/2015SACLS176/document.
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Le contrôle non destructif (CND) de pièces pour des applications dans l'industrie a mené au besoin de modèles rapides et précises. Tels modèles servent au développement des méthodes d'inspection, à l'optimisation des capteurs utilisés aux essais, à l'évaluation des courbes de Probabilité de Detection (POD) ainsi qu'à la caractérisation de défauts. Cette thèse se focalise au CND par Courants de Foucault (CF) de pièces cylindriques avec des discontinuités selon z et contenant un défaut fin. Un modèle pour l'inspection de telles pièces a été développé afin de traiter des applications comme l'inspection des pièces alésées trouvées en aéronautique et des tubes des générateurs de vapeur utilisés dans l'industrie nucléaire. Ce modèle est basé sur une formulation d'équation intégrale. Plus précisément, la variation de l'impédance du capteur, dit signal CF, est calculée à partir d'une équation intégrale sur la surface du défaut. La formulation suivie est basée sur la méthode d'intégration surfacique (SIM). Cette formulation nécessite, d'un côté, le calcul du champ électrique en absence du défaut et, de l'autre côté, l'expression d'une fonction de Green qui correspond à la géométrie de la pièce sans défaut. Les deux problèmes électromagnétiques sont résolus en utilisant la méthode Truncation Region Eigenfunction Expansion (TREE). La méthode TREE est un outil performant pour la résolution des problèmes électromagnétiques qui prend en compte la décroissance rapide de l'intensité du champ afin de tronquer le domaine d'intérêt à une distance, où le champ est négligeable.Le modèle est validé en comparant le signal CF calculé avec des résultats obtenues par une approche combinant la méthode d'intégration volumique (VIM) et SIM, dite l'approche VIM-SIM (implémentée dans la plateforme CIVA) ainsi qu'avec le modèle d'éléments finis (FEM). Nous avons traité trois configurations différentes : un demi-espace conducteur alésé avec un défaut fin, une plaque conductrice avec un alésage et un défaut, et un tube semi-infini avec un défaut fin à la proximité de son bord. La comparaison des résultats montre un très bon accord entre les trois modèles. Le temps de calcul avec le modèle SIM est considérablement inférieur aux temps de calcul des autres modèles. En outre, le modèle SIM donne la possibilité d'effectuer le balayage du capteur dans le tube ou l'alésage dans le cas des pièces aléséesNondestructive Testing (NDT) of parts for industrial applications such as in nuclear and aeronautical industry has led to the need for fast and precise models. Such models are useful for the development of the inspection methods, the optimisation of probes, the evaluation of the Probability of Detection (POD) curves or for the flaw characterisation.This PhD thesis focuses on the eddy-current NDT of layered cylindrical pieces with discontinuities in the z direction and containing a narrow crack. A model for the inspection of such pieces is developed in order to be applied on the inspection of fastener holes met in aeronautics and of steam generator tubes in nuclear sector.The model is based on an integral equation formalism. More precisely, for the calculation of the impedance change one needs to solve an integral equation over the surface of the narrow crack, which is represented by a surface electric dipole distribution. This is the method known as surface integration method (SIM). This formulation requires, on the one hand, the calculation of the electric field in the absence of the flaw, the so-called primary field, and, on the other hand, the Green's function expression corresponding to the geometry of the flawless piece. Both electromagnetic problems are solved by means of the Truncation Region Eigenfunction Expansion (TREE) method. The TREE method is a powerful tool for the solution of electromagnetic problems which uses the rapid decrease of the field in order to truncate the region of interest at a distance where the field is negligible.The model is validated by comparing the results of the coil impedance variation with those obtained by an approach that combines the volume integral method (VIM) with SIM, known as VIM-SIM method, implemented in the commercial software CIVA and the finite element method (FEM) implementation in COMSOL software. Three different configurations have treated. The more general geometry of a conducting half-space with a borehole, a conducting plate with a borehole and a crack and a conducting semi-infinite tube with a crack near the edge. The results of the three models show good agreement between them. The computational time of the SIM model is significantly lower compared to previous models. Furthermore, another advantage of the SIM model is that it provides the possibility of a scan inside the borehole
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Murakami, Shota. "Theoretical Prediction of Changes in Protein Structural Stability upon Cosolvent or Salt Addition and Amino-acid Mutation." 京都大学 (Kyoto University), 2017. http://hdl.handle.net/2433/225706.
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Michelis, Katina. "A sequential eigenfunction expansion approach for certain nonlinear integral equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0006/MQ44221.pdf.
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Michelis, Katina. "A sequential eigenfunction expansion approach for certain nonlinear integral equations /." Thesis, McGill University, 1997. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=20588.
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In the numerical solution of nonlinear integral equations, classic finite difference and series methods lead to systems of nonlinear algebraic or transcendental equations which are solved by iterative schemes such as the Newton method. The present work develops a sequential eigenfunction expansion for the numerical solution of certain nonlinear integral equations. The nonlinear term provides constraints for the amplitudes of the eigenfunctions and a subsequent iteration is used to refine these coefficients. A comparative study of the present method with the Broyden method is conducted. It is shown that the expansion procedure provides an early indication about the multiplicity of solutions which is not present when using the classic methods of solution. Numerical examples are presented which demonstrate the robustness of the expansion method in determining multiple solutions.
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HENRY, CLEMENT BERNARD PIERRE. "Volume Integral Equation Methods for Forward and Inverse Bioelectromagnetic Approaches." Doctoral thesis, Politecnico di Torino, 2021. http://hdl.handle.net/11583/2914544.
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Guernsey, Bryan James. "A locally corrected Nyström method for surface integral equations an object oriented approach /." Lexington, Ky. : [University of Kentucky Libraries], 2007. http://lib.uky.edu/ETD/ukyelen2007t00623/BJG_Thesis.pdf.
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Thesis (M.S.)--University of Kentucky, 2007.Title from document title page (viewed on September 4, 2007). Document formatted into pages; contains: iv, 67 p., [3] : ill. (some col.). Includes abstract and vita. Includes bibliographical references (p. [68]-[69]).
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Guernsey, Bryan James. "A LOCALLY CORRECTED NYSTRM METHOD FOR SURFACE INTEGRAL EQUATIONS: AN OBJECT ORIENTED APPROACH." UKnowledge, 2007. http://uknowledge.uky.edu/gradschool_theses/460.
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Classically, researchers in Computational Physics and specifically in Computational Electromagnetics have sought to find numerical solutions to complex physical problems. Several techniques have been developed to accomplish such tasks, each of which having advantages over their counterparts. Typically, each solution method has been developed separately despite having numerous commonalities with other methods. This fact motivates a unified software tool to house each solution method to avoid duplicating previous efforts. Subsequently, these solution methods can be used alone or in conjunction with one another in a straightforward manner. The aforementioned goals can be accomplished by using an Object Oriented software approach. Thus, the goal of the presented research was to incorporate a specific solution technique, an Integral Equation Nystrm method, into a general, Object Oriented software framework.
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Dyrssen, Hannah. "Valuation and Optimal Strategies in Markets Experiencing Shocks." Doctoral thesis, Uppsala universitet, Tillämpad matematik och statistik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-316578.
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This thesis treats a range of stochastic methods with various applications, most notably in finance. It is comprised of five articles, and a summary of the key concepts and results these are built on. The first two papers consider a jump-to-default model, which is a model where some quantity, e.g. the price of a financial asset, is represented by a stochastic process which has continuous sample paths except for the possibility of a sudden drop to zero. In Paper I prices of European-type options in this model are studied together with the partial integro-differential equation that characterizes the price. In Paper II the price of a perpetual American put option in the same model is found in terms of explicit formulas. Both papers also study the parameter monotonicity and convexity properties of the option prices. The third and fourth articles both deal with valuation problems in a jump-diffusion model. Paper III concerns the optimal level at which to exercise an American put option with finite time horizon. More specifically, the integral equation that characterizes the optimal boundary is studied. In Paper IV we consider a stochastic game between two players and determine the optimal value and exercise strategy using an iterative technique. Paper V employs a similar iterative method to solve the statistical problem of determining the unknown drift of a stochastic process, where not only running time but also each observation of the process is costly.
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Mountfort, Francesca Helen. "A path integral approach to the coupled-mode equations with specific reference to optical waveguides." Thesis, Stellenbosch : University of Stellenbosch, 2009. http://hdl.handle.net/10019.1/2536.
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MScThesis (MSc (Physics))--University of Stellenbosch, 2009.
The propagation of electromagnetic radiation in homogeneous or periodically modulated media can be described by the coupled mode equations. The aim of this study was to derive analytical expressions modeling the solutions of the coupled-mode equations, as alternative to the generally used numerical and transfer-matrix methods. The path integral formalism was applied to the coupled-mode equations. This approach involved deriving a path integral from which a generating functional was obtained. From the generating functional a Green’s function, or propagator, describing the nature of mode propagation was extracted. Initially a Green’s function was derived for the propagation of modes having position independent coupling coefficients. This corresponds to modes propagating in a homogeneous medium or in a uniform grating formed by a periodic variation of the index of refraction along the direction of propagation. This was followed by the derivation of a Green’s function for the propagation of modes having position dependent coupling coefficients with the aid of perturbation theory. This models propagation through a nonuniform inhomogeneous medium, specifically a modulated grating. The propagator method was initially tested for the case of propagation in an arbitrary homogeneous medium. In doing so three separate cases were considered namely the copropagation of two modes in the forward and backward directions followed by the counter propagation of the two modes. These more trivial cases were used as examples to develop a rigorous mathematical formalism for this approach. The results were favourable in that the propagator’s results compared well with analytical and numerical solutions. The propagator method was then tested for mode propagation in a periodically perturbed waveguide. This corresponds to the relevant application of mode propagation in uniform gratings in optical fibres. Here two case were investigated. The first scenario was that of the copropagation of two modes in a long period transmission grating. The results achieved compared well with numerical results and analytical solutions. The second scenario was the counter propagation of two modes in a short period reflection grating, specifically a Bragg grating. The results compared well with numerical results and analytical solutions. In both cases it was shown that the propagator accurately predicts many of the spectral properties of these uniform gratings. Finally the propagator method was applied to a nonuniform grating, that is a grating for which the uniform periodicity is modulated - in this case by a raised-cosine function. The result of this modulation is position dependent coupling coefficients necessitating the use of the Green’s function derived using perturbation theory. The results, although physically sensible and qualitatively correct, did not compare well to the numerical solution or the well established transfer-matrix method on a quantitative level at wavelengths approaching the design wavelength of the grating. This can be explained by the breakdown of the assumptions of first order perturbation theory under these conditions.
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Goomanee, Salvish. "Rigorous Approach to Quantum Integrable Models at Finite Temperature." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSEN039/document.
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Cette thèse développe un cadre rigoureux qui permet de démontrer des représentations exactes associées à divers observables de la chaîne XXZ de Heisenberg de spin 1/2 à température finie. Il a était argumenté dans la littérature que l’énergie libre par site ou les longueurs de corrélations admettent des représentations intégrales où les intégrandes sont exprimées en termes de solutions d’équations intégrales non-linéaires. Les dérivations de ces représentations reposaient sur divers conjectures telles que l’existence d’une valeur propre de la matrice de transfert quantique, real, non-dégénérée, de module maximale, de l’échangeabilitée de la limite du volume infinie et du nombre de Trotter à l’infinie, de l’existence et de l’unicité des solutions des equation intégrales non-linéaires auxiliaires et finalement de l’identification des valeurs propers de la matrice de transfert quantiques avec les solutions de l’équations intégrales non-linéaires. Nous démontrons toutes ces conjectures dans le regime de haute température. Nôtre analyse nous permet aussi de démontrer que pour ces température suffisamment élevées, il est possible d’avoir une description d’un certain sous-ensemble de valeurs propres sous-dominante de la matrice de transfert quantique décrite en terme de solutions d’une chaîne de spin-1 de taille finieThis thesis develops a rigorous framework allowing one to prove the exact representations for various observables in the XXZ Heisenberg spin-1/2 chain at finite temperature. Previously it has been argued in the literature that the per-site free energy or the correlation lengths admit integral representations whose integrands are expressed in terms of solutions of non-linear integral equations. The derivations of such representations relied on various conjectures such as the existence of a real, non-degenerate, maximal in modulus Eigenvalue of the quantum transfer matrix, the exchangeability of the infinite volume limit and the Trotter number limits, the existence and uniqueness of the solutions to the auxiliary non-linear integral equations and finally the identification of the quantum transfer matrix’s Eigenvalues with solutions to the non-linear integral equation. We rigorously prove all these conjectures in the high temperature regime. Our analysis also allows us to prove that for temperatures high enough, one may describe a certain subset of sub-dominant Eigenvalues of the quantum transfer matrix described in terms of solutions to a spin-1 chain of finite length
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Welack, Sven. "Counting statistics and waiting time distributions in nanoscale electron transport : from path integral to rate equation approaches /." View abstract or full-text, 2009. http://library.ust.hk/cgi/db/thesis.pl?CHEM%202009%20WELACK.
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Matsumura, Yoshihiro. "Theoretical Approaches to Self-Assembly of Metal Complex and Fundamental Properties of Molecules in Solution Phase." Kyoto University, 2017. http://hdl.handle.net/2433/226786.
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LY, KIM HA. "ON TWO APPROACHES FOR PARTIAL DIFFERENTIAL EQUATIONS IN SEVERAL COMPLEX VARIABLES." Doctoral thesis, Università degli studi di Padova, 2014. http://hdl.handle.net/11577/3423534.
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The aim of this thesis is to present influence of notations of ''type" on partial differential equations in several complex variables. The notations of "type" here include the finite and the infinite type in the sense of Hormander, and D'Angelo. In particular, in the first part, under the finite type condition, we will consider the existence and uniqueness of solutions for the initial value problem associated to the heat operator δs+□b on CR manifolds. The finite type m is the critical condition to provide pointwise estimates of the heat kernel via theory of singular integral operators developed by E. Stein and A. Nagel, D.H. Phong and E. Stein. Next, in the second part, we will introduce a new method to investigate the Cauchy-Riemann equations δu = φ. The solutions are constructed via the integral representation method. Moreover, we will show that the new method here is also applied well to the complex Monge-Ampère operator (ddc)n inCn. The main point is that our method can pass some well-known results from the case of finite type to infinite type.Lo scopo di questa tesi è quello di presentare l'influenza di notazioni di " tipo'' su equazioni differenziali alle derivate parziali in più variabili complesse. Le notazioni di "tipo" qui includono il finito e il tipo di infinito, nel senso di Hormander, e D'Angelo. In particolare, nella prima parte, a condizione tipo finito, prenderemo in considerazione l'esistenza e l'unicità delle soluzioni per il problema del valore iniziale associato ai operatore calore δs+□b su varietà CR. Il tipo finito m è la condizione fondamentale per fornire stime puntuali del nucleo del calore attraverso la teoria degli operatori integrali singolari sviluppate da E. Stein e A. Nagel, D.H. Phong e E. Stein. Prossimo, nella seconda parte, introdurremo un nuovo metodo per indagare la equazioni Cauchy-Riemann δu = φ. Le soluzioni sono costruite con via metodo rappresentazione integrale. Inoltre, mostreremo che il nuovo metodo qui viene applicato anche ben al complesso operatore Monge-Ampère (ddc)n inCn. Il punto principale è che il nostro metodo può passare alcuni risultati noti dal caso di tipo finito al tipo di infinito.
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Fnaiech, Emna Amira. "Développement d’un outil de simulation du procédé de contrôle non destructif des tubes ferromagnétiques par un capteur à flux de fuite." Thesis, Paris 11, 2012. http://www.theses.fr/2012PA112311/document.
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Le principe du contrôle par flux de fuite magnétique (Magnetic Flux Leakage MFL) consiste à aimanter la pièce à contrôler par un champ magnétique et à détecter à l'aide d'un capteur magnétique les fuites des lignes du champ qui résultent de la présence d'un défaut dans la pièce. Dans le but d'améliorer les performances d'un dispositif de détection, le CEA et la société Vallourec collaborent pour développer un modèle numérique dédié au contrôle virtuel des défauts longitudinaux dans les tubes ferromagnétiques. Le dispositif expérimental comprend un circuit magnétique tournant à une vitesse constante autour du tube qui défile. Dans le cadre de cette thèse, on débute le problème de la modélisation sans tenir compte des effets de la vitesse de rotation, il s'agit donc de résoudre un problème d'électromagnétisme en régime magnétostatique.Pour résoudre ce problème, on propose de comparer une approche semi-analytique basée sur le formalisme des équations intégrales (EI) et une approche purement numérique utilisant les éléments finis (EF).Dans la première partie de cette thèse, après avoir établi le formalisme théorique par EI, un premier modèle considérant des matériaux ferromagnétiques à perméabilité magnétique constante (régime linéaire) a été mis en œuvre en 2D. Ce modèle a été appliqué pour un exemple de système extrait de la littérature et validé numériquement par une comparaison des résultats EI/EF. Pour une meilleure détection, il est opportun de saturer magnétiquement la pièce. Le matériau ferromagnétique est alors caractérisé par une courbe B(H) non-linéaire. Par conséquent, la deuxième partie de la thèse a été consacrée à la mise en œuvre du modèle en régime non linéaire qui tient compte de cette caractéristique.Différentes méthodes de discrétisation ont été étudiées afin de réduire le nombre d'inconnues et le temps de calcul. L'originalité de la thèse réside dans l'utilisation des fonctions d'interpolation d'ordre élevé (polynôme de Legendre) pour une discrétisation des équations intégrales par une approche de type Galerkin. Les premiers essais de validation numérique de ce modèle ont été effectués sur un système MFL simplifié. Des premiers essais de validation expérimentale pour des données obtenues par EF ont été effectués en deux phases : La première a consisté à vérifier le distribution du champ magnétique pour un tube sain et en régime magnétostatique. La deuxième phase a consisté à calculer la réponse d'un défaut dans le tube ferromagnétique en tenant en compte les effets éventuels de la rotation du circuit magnétique par rapport au tubeThe principle of the non destructive testing by magnetic flux leakage (MFL) is to magnetize the part to be inspected by a magnetic field and to detect a flaw thanks to magnetic leakage field lines due to the strong decreasing of the magnetic permeability in the flawed region. In order to improve the performance of detection, the CEA and the Vallourec society collaborate to develop a numerical model dedicated to the virtual NDT of longitudinal defects in ferromagnetic tubes. The experimental system includes a magnetic circuit rotating at a constant speed around the tube to be inspected. The modeling task is started without considering the effects of the rotational speed, so the magnetostatic regime is considered to solve the modeling problem. In the framework of this thesis, we propose to compare a semi-analytical approach based on the formalism of integral equations method (IEM) and a purely numerical approach using finite element method (FEM).In the first part of this thesis, the theoretical formalism was established. A first simple discretization scheme is been implemented in the linear regime considering a constant magnetic permeability. This first numerical model has been validated for a simplified MFL configuration extracted and modified from the literature.For better detection, it is wishable to magnetically saturate the piece under-test. The ferromagnetic material is then characterized by a B(H) curve. Therefore, the second part of the thesis was devoted to the implementation of the model in the non-linear regime that takes into account this non-linear characteristic. Different discretization schemes have been studied in order to reduce the number of unknowns and the computational time. The originality of the thesis lies in the use of basis function of high order (Legendre polynomials) associated to a Galerkin approach for the discretization of integral equations. The first numerical result has been validated on a simplified MFL system. The first results of the experimental validation based on simulated data obtain by FEM have been performed in two steps. The first one consists to verify the distribution of the magnetic field for a ferromagnetic tube without any defect and in the magnetostatic regime. The objective of the second one was to compute the response of the flaw and to evaluate the effects of the rotational speed of the magnetic circuit around the tube
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Patier, Laurent. "Etude de techniques de calculs multi-domaines appliqués à la compatibilité électromagnétique." Phd thesis, Université Blaise Pascal - Clermont-Ferrand II, 2010. http://tel.archives-ouvertes.fr/tel-00834164.
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Le contexte d'étude est celui de la Compatibilité ÉlectroMagnétique (CEM). L'objectif de la CEM est, comme son nom l'indique, d'assurer la compatibilité entre une source de perturbation électromagnétique et un système électronique victime. Or, la prédiction de ces niveaux de perturbation ne peut pas s'effectuer à l'aide d'un simple calcul analytique, en raison de la géométrie qui est généralement complexe pour le système que l'on étudie, tel que le champ à l'intérieur d'un cockpit d'avion par exemple. En conséquence, nous sommes contraints d'employer des méthodes numériques, dans le but de prédire ce niveau de couplage entre les sources et les victimes. Parmi les nombreuses méthodes numériques existantes à ce jour, les méthodes Multi-Domaines (MD) sont très prisées. En effet, elles offrent la liberté aux utilisateurs de choisir la méthode numérique la plus adaptée, en fonction de la zone géométrique à calculer. Au sein de ces méthodes MD, la " Domain Decomposition Method " (DDM) présente l'avantage supplémentaire de découpler chacun de ces domaines. En conséquence, la DDM est particulièrement intéressante, vis-à-vis des méthodes concurrentes, en particulier sur l'aspect du coût numérique. Pour preuve, l'ONERA continue de développer cette méthode qui ne cesse de montrer son efficacité depuis plusieurs années, notamment pour le domaine des Surfaces Équivalentes Radar (SER) et des antennes. L'objectif de l'étude est de tirer profit des avantages de cette méthode pour des problématiques de CEM. Jusqu'à maintenant, de nombreuses applications de CEM, traitées par le code DDM, fournissaient des résultats fortement bruités. Même pour des problématiques électromagnétiques très simples, des problèmes subsistaient, sans explication convaincante. Ceci justifie cette étude. Le but de cette thèse est de pouvoir appliquer ce formalisme DDM à des problématiques de CEM. Dans cette optique, nous avons été amenés à redéfinir un certain nombre de conventions, qui interviennent au sein de la DDM. Par ailleurs, nous avons développé un modèle spécifique pour les ouvertures, qui sont des voies de couplage privilégiées par les ondes, à l'intérieur des cavités que représentent les blindages. Comme les ouvertures sont, en pratique, de petites dimensions devant la longueur d'onde, on s'est intéressé à un modèle quasi-statique. Nous proposons alors un modèle, qui a été implémenté, puis validé. Suite à ce modèle, nous avons développé une méthode originale, basée sur un calcul en deux étapes, permettant de ne plus discrétiser le support des ouvertures dans les calculs 3D.
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Arens, Tilo [Verfasser]. "Scattering by biperiodic layered media : the integral equation approach / Tilo Arens." 2010. http://d-nb.info/1004958242/34.
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Shia, Run-Lie. "Partially Coherent Wave Scattering and Radiative Transfer: An Integral Equation Approach." Thesis, 1986. https://thesis.library.caltech.edu/11414/1/Shia_RL_1986.pdf.
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This thesis consists of two parts. The first one is "Scattering of Waves in a Random Medium," and the second one is "Radiative Transfer in a Sphere Illuminated by a Parallel Beam: An Integral Equation Approach."
In the first part, a new formalism tor partially coherent wave scattering in a random medium is developed. In this formalism the coherent wave is the solution of a phenomenological wave equation, and the mutual coherence function of the wave field satisfies a simple integral equation. Using this formalism, the Peierls equation can be readily derived. Also, an improved version of the Peierls equation is derived in which the intensity of the wave field and the first order derivative of the mutual coherence function are calculated at the same time. A simple problem is solved to find the mutual coherence function produced by a laser beam in the atmosphere. The similarity between the mutual coherence function and the density matrix or quantum mechanics is explored and a measure of the randomness is defined for the partially coherent wave field.
In the second part of this work, the problem of multiple scattering of non-polarized light in a planetary body of arbitrary shape illuminated by a parallel beam is formulated using the integral equation approach. There exists a simple functional whose stationarity condition is equivalent to solving the equation of radiative transfer and whose value at the stationary point is proportional to the differential cross section. Our analysis reveals a direct relation between the microscopic symmetry of the. Phase function for each scattering event and the macroscopic symmetry of the differential cross section for the entire planetary body, and the intimate connection between these symmetry relations and the variational principle. The case of a homogeneous sphere containing isotropic scatterers is investigated in detail. It is shown that the solution can be expanded in a multipole series such that the general spherical problem is reduced to solving a set of decoupled integral equations in one dimension. Computations have been performed for a range of parameters of interest, and illustrative examples of applications to planetary problems are provided.
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"An efficient volume integral equation approach for characterization of lossy dielectric materials." 2004. http://library.cuhk.edu.hk/record=b6073666.
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Lui Man Leung."May 2004."
Thesis (Ph.D.)--Chinese University of Hong Kong, 2004.
Includes bibliographical references.
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Mode of access: World Wide Web.
Abstracts in English and Chinese.
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Chen, Po-Yuan, and 陳柏源. "Null-field Integral Equation Approach for Solving Stress Concentration Problems with Circular Boundaries." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/23472398222930790589.
Full textAbstract:
碩士國立臺灣海洋大學
河海工程學系
94
In the thesis, boundary value problems with circular boundaries are formulated in a unified manner by using null-field integral equation in conjunction with degenerate kernels and Fourier series expansions. Laplace problems of circular holes as well as Helmholtz problem of SH-wave impinging on circular cavities and/or inclusions were studied. The fundamental solution is expanded to degenerate form by separating the source point and field point in the polar coordinate. The main gain of using degenerate kernels for interior and exterior expansions is free of calculating the principal values. In order to fully describe the circular boundary, the present method employs the Fourier series to approximate the boundary potential. By collocating the null-field points on the real boundary with the same number of Fourier coefficients, the unknown coefficients in the algebraic system can be easily determined. The present method is treated as a “semi-analytical” solution since error only attributes to the truncation of Fourier series. Four advantages, well-posed model, principal value free, elimination of boundary-layer effect and exponential convergence, are achieved. Besides, the null-field approach in conjunction with degenerate kernels and Fourier series expansions is also employed to derive the Green’s function for boundary value problems stated for annular problems of Laplace equations and the generalized Poisson integral formula is obtained. Finally, several examples involving torsion, bending, and infinite domain with cavity and half-plane with alluvial valleys and inclusions problem were given to demonstrate the validity of the proposed method. Also, the numerical results agree well after comparing with available solutions in the literature. A general-purpose program for multiple circular cavities and/or inclusions of various radii and arbitrary positions was developed.
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Chen, Chia-Tsung, and 陳佳聰. "Null-field integral equation approach for Helmholtz (interior and exterior acoustic) problems with circular boundaries." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/32886338890663734577.
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碩士國立臺灣海洋大學
河海工程學系
93
In this thesis, the Helmholtz (interior and exterior acoustic) problems with circular boundaries are studied by using the null-field integral equations in conjunction with degenerate kernels and Fourier series to avoid calculating the Cauchy and Hadamard principal values. Adaptive observer system of polar coordinate is considered to fully employ the property of degenerate kernels. For the hypersingular equation, vector decomposition for the radial and tangential gradient of potential is carefully considered. In interior acoustic problems, direct-searching scheme is employed to detect the eigenvalues by using the singular value decomposition (SVD) technique. It is analytically verified that an inner circle results in the spurious eigenvalue which are demonstrated in the numerical experiments. Both the singular and hypersingular equations result in spurious eigenvalues which are the associated interior Dirichlet and Neumann problems of interior circular domain of inner circle, respectively. Two approaches to overcome spurious eigenvalus, SVD updating technique and Burton & Miller methods are employed to suppress the appearance of spurious eigenvalue. Several examples are demonstrated to see the validity of the present formulation and numerical results indicate the better accuracy than BEM in predicting the spurious eigenvalues. In exterior acoustic problems, the radiation and scattering problems with multiple circular cylinders as well as single one are also examined successfully. The analytical solution of semi-circular canyon subject to the incident SH wave was derived by using the present formulation and it is not only more concise but also easier computation than that of Trifunac’s solution. The extension to multiple semi-circular canyons is also addressed.
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Sung, I.-Cheng, and 宋易澄. "Null-field integral equation approach for solving torsion problems of a circular bar with coated fibers or cracks." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/03633984710584678311.
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碩士國立臺灣海洋大學
河海工程學系
104
In this thesis, the null-field integral equation approach in conjunction with the degenerate kernel is used to solve the torsion problems of a circular bar with coated fibers or cracks. The degenerate kernel is employed to substitute the closed-form fundamental solution in the integral equations. In order to fully capture the geometry property, the boundary densities are expanding by Fourier series and eigenfunction expansion for circular boundary and elliptical boundary, respectively. For a circular bar with coated fibers, there are some difficulties on directly analyzing the bar since it has different materials in the bar. By using the technique of taking free body, the bar could be decomposed into three parts. One is a circular bar with circular holes, another is multiple individual circular-ring coatings, and the other is multiple circular fibers. After collocating points on each boundary and satisfying the continuity of displacement and equilibrium of force between interfaces, the unknown coefficients of Fourier series or eigenfunction can be determined by a linear algebraic system. For the problem of cracks in a bar, we adopt the limiting process of approaching the semi-minor axis of elliptical hole to be zero to simulate cracks. Finally, several numerical examples are employed to verify the feasibility and validity of the proposed approach. Besides, the partially and totally neutral behaviors for the composite bars are numerically analyzed.
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Jiang, Rui-En, and 江瑞恩. "Scattering of flexural wave in thin plate with multiple circular inclusions by using the null-field integral equation approach." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/39001510930257373739.
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碩士中華技術學院
機電光工程研究所在職專班
97
Abstract In this thesis, a semi-analytical approach is proposed to solve the scattering problem of flexural waves in an infinite thin plate with multiple circular inclusions subject to the incident flexural wave by using the null-field integral equation in conjunction with Fourier series. By using the addition theorem, all dynamic kernels of the plate are expanded into degenerate forms. Furthermore, the rotated degenerate kernels are derived to consider the cases of multiple circular inclusions by using tensor transformation. The scattering plate problem with multiple circular inclusions can be solved by decomposing it into several internal inclusion problems and an external plate problem subject to the incident wave. The intensity of radiation fields, including the internal inclusions and the external plate, can be solved by using the continuity conditions and the proposed method. The dynamic moment concentration factor (DMCF) around the circular inclusions, as well as the far field scattering pattern is determined. The numerical results for an infinite plate with one inclusion are compared with the available analytical solutions to verify the validity of the proposed method. For the cases of small wave number, the proposed quasi-static results of multiple circular inclusions are compared with static data of finite element method (FEM) using ABAQUS. The numerical convergence analysis shows that the required number of terms for the Fourier series depends on both the incident wave number and space between inclusions. As the incident wave number increases, the DMCF distributions along the inclusion become dramatically fluctuated. Numerical results indicate that the DMCF of two inclusions is apparently larger than that of one inclusion when two inclusions are close to each other. Fictitious frequency appearing in the external problem can be suppressed by using the more number of Fourier series terms. The effects of space between inclusions on both the DMCF and the far scattering pattern are also investigated in this thesis. It shows that the space between scatters has the opposite effect on the near field DMCF in comparison with the far field scattering pattern. Keywords: scattering, flexural wave, dynamic moment concentration factor, far field scattering pattern, thin plate, inclusion, null-field integral equation, degenerate kernel, Fourier series
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Nie, Xiaochun, and Le-Wei Li. "Electromagnetic Scattering by Open-Ended Cavities: An Analysis Using Precorrected-FFT Approach." 2002. http://hdl.handle.net/1721.1/4001.
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In this paper, the precorrected-FFT method is used to solve the electromagnetic scattering from two-dimensional cavities of arbitrary shape. The integral equation is discretized by the method of moments and the resultant matrix equation is solved iteratively by the generalized conjugate residual method. Instead of directly computing the matrix-vector multiplication, which requires N² operations, this approach reduces the computation complexity to O(N log N) as well as avoids the storage of large matrices. At the same time, a technique known as the complexifying k is applied to accelerate the convergence of the iterative method in solving this resonance problem. Some examples are considered and excellent agreements of radar cross sections between these computed using the present method and those from the direct solution are observed, demonstrating the feasibility and efficiency of the present method.Singapore-MIT Alliance (SMA)
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Ke, Jia-Nan, and 柯佳男. "Derivation of the Green's function for Laplace and Helmholtz problems with circular boundaries by using the null-field integral equation approach." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/43681454379916338619.
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碩士國立臺灣海洋大學
河海工程學系
95
In this thesis, we derive the Green’s function for Laplace and Helmholtz problems with circular apertures and/or inclusions subjected to the Dirichlet, Neumann, mixed and imperfect-interface boundary conditions by using the null-field integral equation approach in conjunction with degenerate kernels, Fourier series and the adaptive observer system. After exactly collocating points on each real circular boundary to satisfy the boundary conditions, a linear algebraic system is obtained. Then unknown coefficients can be easily determined. Five advantages: (1) mesh-free generation (2) well-posed model, (3) principal value free (4) elimination of boundary-layer effect (5) exponential convergence, are achieved. Finally, several examples, including the eccentric case, half-plane Laplace problems with circular apertures and inclusions, and anti-plane dynamic Green’s function for several circular inclusions problems, were demonstrated to see the validity of the present formulation and match well with available solutions in the literature. Besides, parameter study of wave number and interface constant is done. Special cases of cavity and ideal bonding are also examined. A general-purpose program for deriving the Green’s function of Laplace or Helmholtz problems with arbitrary number of circular apertures and/or inclusions of arbitrary radii and various positions involving the Dirichlet or the Neumann or mixed boundary condition was developed.
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Svetogorova, Elena. "Integral equation approach to reflection and transmission of a plane TE-wave at a (linear/nonlinear) dielectric film with spatially varying permittivity." Doctoral thesis, 2004. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2004110212.
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The reflection and transmission of an electromagnetic TE-polarized plane wave at a dielectric film between two linear semi-infinite media (substrate and cladding) is considered. All media are assumed to be homogeneous in x- and z- direction, isotropic, and non-magnetic. The permittivity of the film is assumed to be characterized by a continuously differentiable function of the transverse coordinate and the field. To obtain solutions of Maxwell´s equations that satisfy the boundary conditions the problem is reduced to a Helmholtz equation, which is transformed to a Volterra integral equation for the field intensity inside the film. The Volterra equation is solved by iteration subject to the appropriate boundary conditions. The (iteration) solutions for the linear case and for the nonlinear case are expressed in terms of a uniformly convergent series and a uniformly convergent sequence, respectively. The uniform convergence is proved using the Banach Fixed-Point Theorem. The condition for its applicability leads to a condition for the parameters of the problem. By iterating the Volterra equation an approximate solution for the intensity inside the film is presented. The mathematical basis of the procedure is outlined in detail. Using an approximate solution, the phase function,the phase shifts on reflection and transmission, the reflectivity and the absorptance are determined.Further iterations of the Volterra equation are possible.Semianalytical and numerical examples illustrate the main features of the approach. The method is succesfully applied to different permittivity functions (real, complex, Kerr-like and saturable nonlinear). The agreement between the approximate analytical solutions and numerical solutions is satisfactory. It seems that the method proposed can serve as a means to optimize certain parameters of the problem (material and/or geometrical) for particular purposes.
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Fan, Yu, and 范羽. "Null-field boundary integral equation approach for scattering problem of canyon or hill containing circular or elliptic boundary subject to SH-wave." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/41429751772225064576.
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碩士國立臺灣海洋大學
河海工程學系
100
Scattering problem of seismic wave is an important issue for studying earthquake in seismology. In this thesis, we employed the null-field boundary integral equation approach in conjunction with degenerate kernels and Fourier series (eigenfunction expansion) to solve the SH-wave scattering problems containing circular (elliptic) boundary. By expanding the fundamental solution to degenerate kernels in the polar coordinates (elliptic coordinates), the collocation points could located on the real boundary of problem, and the boundary densities for circular (elliptic) boundaries were expanded by using Fourier series (eigenfunction expansion) in the polar coordinates (elliptic coordinates). The advantages of null-field boundary integral equation approach were (1) free from calculating the principal value, (2) well-posed system, (3) exponential convergence, (4) no boundary-layer effect and (5) meshless. This approach was also a semi-analytical approach since the error came from the number of truncation terms of the Fourier series (eigenfunction expansion). After imbedding the original problem to an infinite domain, the scattering problem could be decomposed to multi-regions for creating complete circular (elliptic) boundary. Therefore, the null-field boundary integral equation could fully use for the scattering problem, and a linear algebraic system could be constructed. In this thesis, the problems of circular-arc canyon, elliptic-arc canyon, circular-arc hill and elliptic-arc hill were considered. The parameter studies of different incident angles of SH-wave and dimensionless frequency were investigated, and the focusing effect was also observed in the case of hill.
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Svetogorova, Elena [Verfasser]. "Integral equation approach to reflection and transmission of a plane TE-wave at a (linear-nonlinear) dielectric film with spatially varying permittivity / von Elena Svetogorova." 2004. http://d-nb.info/973198524/34.
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Hsu, Yin-Hsiang, and 徐胤祥. "Scattering problems of semi-circular canyon or hill containing a circular hole or inclusion subject to SH wave by using the null-field boundary integral equation approach." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/48266825868674321916.
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碩士國立臺灣海洋大學
河海工程學系
99
The influence of a canyon or hill on the ground motion due to earthquake is an important issue for engineers. The amplification factor is a key for structural safety. In the thesis, we employ the null-field boundary integral equation method (BIEM) to deal with the canyon problem and hill problem subject SH-waves. To fully utilize the analytical property of the null-field boundary integral equations in conjunction with the degenerate kernels for solving the canyon problem and hill problem, the first one is a half-plane problem that can be imbedded to an infinite domain with an artificial boundary of a full circle. The other problem can be divided into two subdomains by using the concept of taking free body. One is a semi-circular hill containing tunnels and the other is a half-plane problem containing a semi-circular cut. The half-plane problem can be imbedded to an infinite domain with an artificial boundary of a full circle such that the degenerate kernel can be fully adopted. Next, the fundamental solution is expanded to the degenerate kernel in the polar coordinates for the problem containing circular boundaries. Boundary densities are expanded by using the natural base of the Fourier series. By this way, the field point can be exactly located on the real boundary and is free from calculating Cauchy and Hadamard principal values. Then, we will consider the displacement continuity and equilibrium of force on the artificial interface. Finally, the semi-analytical formulation of the null-field BIE in companion with matching boundary conditions can yield six constraint equations. Moreover, we attempt to solve the problem of semi-circular hills containing a circular tunnel or a circular inclusion. We also provide semi-analytical solutions for a benchmark example. The Parameters study of the tunnel size, wave number and incident angle of SH wave are investigated.
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Huang, Zheng Wen, and 黃政文. "A new generalized green''s impedance space-domain integral equation approach and its application to the characterization and design of a new class of dielectric-line-loaed coplanar strips." Thesis, 1994. http://ndltd.ncl.edu.tw/handle/88377884401648515027.
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Altundag, Ahmet. "On a Two Dimensional Inverse Scattering Problem for a Dielectric." Doctoral thesis, 2012. http://hdl.handle.net/11858/00-1735-0000-0006-B3F7-6.
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Schmidt, Friedemann [Verfasser]. "Fast computational treatment of molecular complexation in solution : hybrid integral equation approaches / vorgelegt von Friedemann Schmidt." 2001. http://d-nb.info/963639013/34.
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Lee, Jia-Wei, and 李家瑋. "Null-field boundary integral equations approach for solving Helmholtz problems of free vibration and water wave containing circular and elliptical boundaries." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/23613276688349156796.
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碩士國立臺灣海洋大學
河海工程學系
98
Following the success of five advantages of the null-field boundary integral equation method (BIEM), the Helmholtz problems containing elliptical boundaries are solved by using the null-field BIEM in conjunction degenerate kernels and eigenfunction expansion in this thesis. Not only problems of interior free vibration and exterior water wave problems are considered. To fully utilize the property of ellipse for solving the Helmholtz problems, the elliptic coordinates and the associated Mathieu functions are adopted. The closed-form fundamental solution is expressed in terms of the degenerate kernel in the elliptic coordinates. Besides, the boundary densities are expanded by using the eigenfunction expansion. A Jacobian term may exist in the degenerate kernel, boundary density or boundary contour integration and they can cancel each other out. By scaling the boundary flux using a Jacobian term, the orthogonal relations can be reserved in the boundary contour integral and contour integration along elliptical boundaries can be analytically determined. By this way, the unknown coefficients can be easily determined through a linear algebraic system after matching boundary conditions. This approach is one kind of semi-analytical methods since errors only occur from the truncation of the number of the eigenfunction expansion terms in the real implementation. Although spurious eigenvalues of interior eigenproblem as well as fictitious frequencies for the exterior problem for elliptical boundaries may appear in the BIEM, it is interesting to find that those of them happen to be zeros of the modified Mathieu functions of the first kind or their derivatives. The appearances of spurious eigenvalues and fictitious frequencies are effectively suppressed by using three alternatives including the Combined Helmholtz Interior integral Equation Formulation (CHIEF) method, Burton & Miller approach and the singular value decomposition (SVD) updating technique. Besides, the near-trapped mode for an array of four elliptical cylinders is also observed. To avoid the addition theorem by translating the Bessel and Mathieu functions, the adaptive observer system is employed to solve the Helmholtz problems containing circular and elliptical boundaries at the same time in a semi-analytical manner. Finally, a general-purpose program was developed for solving eigenproblems or water wave problems containing arbitrary number, different sizes and various locations of circular and elliptical boundaries.
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(10669023), Fukeng Huang. "A new scalar auxiliary variable approach for general dissipative systems." Thesis, 2021.
Find full textAbstract:
In this thesis, we first propose a new scalar auxiliary variable (SAV) approach for general dissipative nonlinear systems. This new approach is half computational cost of the original SAV approach, can be extended to high order unconditionally energy stable backward differentiation formula (BDF) schemes and not restricted to the gradient flow structure. Rigorous error estimates for this new SAV approach are conducted for the Allen-Cahn and Cahn-Hilliard type equations from the BDF1 to the BDF5 schemes in a unified form. As an application of this new approach, we construct high order unconditionally stable, fully discrete schemes for the incompressible Navier-Stokes equation with periodic boundary condition. The corresponding error estimates for the fully discrete schemes are also reported. Secondly, by combining the new SAV approach with functional transformation, we propose a new method to construct high-order, linear, positivity/bound preserving and unconditionally energy stable schemes for general dissipative systems whose solutions are positivity/bound preserving. We apply this new method to second order equations: the Allen-Cahn equation with logarithm potential, the Poisson-Nernst-Planck equation and the Keller-Segel equations and fourth order equations: the thin film equation and the Cahn-Hilliard equation with logarithm potential. Ample numerical examples are provided to demonstrate the improved efficiency and accuracy of the proposed method.
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Bothner, Thomas Joachim. "Asymptotics of the Fredholm determinant corresponding to the first bulk critical universality class in random matrix models." 2013. http://hdl.handle.net/1805/3655.
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Indiana University-Purdue University Indianapolis (IUPUI)We study the one-parameter family of determinants $det(I-\gamma K_{PII}),\gamma\in\mathbb{R}$ of an integrable Fredholm operator $K_{PII}$ acting on the interval $(-s,s)$ whose kernel is constructed out of the $\Psi$-function associated with the Hastings-McLeod solution of the second Painlev\'e equation. In case $\gamma=1$, this Fredholm determinant describes the critical behavior of the eigenvalue gap probabilities of a random Hermitian matrix chosen from the Unitary Ensemble in the bulk double scaling limit near a quadratic zero of the limiting mean eigenvalue density. Using the Riemann-Hilbert method, we evaluate the large $s$-asymptotics of $\det(I-\gamma K_)$ for all values of the real parameter $\gamma$.
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Suri, Ratneesh. "Optimal harvesting strategies for fisheries : a differential equations approach : a thesis presented in partial fulfillment of the requirement for the degree of Doctor of Philosophy in Mathematics at Massey University, Albany, New Zealand." 2008. http://hdl.handle.net/10179/765.
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The purpose of fisheries management is to achieve a sustainable development of the activity, so that future generations can also benefit from the resource. However, the optimal harvesting strategy usually maximizes an economically important objective function formed by the harvester which can lead to the extinction of the resource population. Therefore, sustainability has been far more difficult to achieve than is commonly thought; fish populations are becoming increasingly limited and catches are declining due to overexploitation. The aim of this research is to determine an optimal harvesting strategy which fulfills the economic objective of the harvester while maintaining the population density over a pre-specified minimum viable level throughout the harvest. We develop and investigate the harvesting model in both deterministic and stochastic settings. We first employ the Expected Net Present Value approach and determine the optimal harvesting policy using various optimization techniques including optimal control theory and dynamic programming. Next we use real options theory, model fish harvesting as a real option, and compute the value of the harvesting opportunity which also yields the optimal harvesting strategy. We further extend the stochastic problem to include price elasticity of demand and present results for di¤erent values of the coefficient of elasticity.
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Sovič, Pavel. "Didaktické situace pro výuku matematiky ve francouzštině." Master's thesis, 2019. http://www.nusl.cz/ntk/nusl-408416.
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The diploma thesis focuses on learning Maths through French language using the CLIL method at a secondary vocational school. The acronym CLIL (Content and Language Integrated Learning), EMILE (Enseignement de Matières par Intégration d'une Langue Etrangère) or e.g. AICL (Apprentissage Intégré d'un Contenu et d'une Langue) refers to integrated learning of a content-based subject through an additional language. There are always two aims of such tuition. The first aim is the content goal (e.g. to gain particular specialized knowledge or skill in mathematics); the second aim is the language goal (e.g. to learn essential vocabulary and sentence structures in order to lead a discussion concerning the solution of a quadratic equation in the French language). Based on a literary research, analysis of educational CLIL materials, and especially in connection with theoretical grounds of the method (constructivism, problem-solving, critical thinking, active and communicative approach) there was established a study plan focusing on the topic of quadratic equations. The experimental tuition was put into practice with the 1st year students of a secondary school, where the French language is taught as the second foreign language. The main objective, apart from the tuition itself and its analysis, was to assess the...