No description available.

No description available.

With over 830,000 km of operating pipeline in Canada alone, their safe and continued functioning underpins much of daily life. A key type of risk associated with pipelines is third-party damage, damage caused by actions not associated with the pipelines normal operation. The question of whether the pressurized structure like pipeline or pressure vessel would undergo “unzipping” due to the third-party impact is crucial for the safety of pipelines or pressure vessels in service needs to be answered. Thus, we endeavour to develop a methodology for assessment of design solutions effectiveness to prevent a pipeline or pressure vessel failure in an abrupt explosion-like fashion due to third-party damage. Model of crack propagation determining whether the “unzipping” rupture will occur is viewed as a key element in the safety-driven design procedure providing significant effect on the safety of operation. The crack propagation modeling is achieved through the use of nonlinear fracture mechanics technique. The method of singular integral equations is used to calculate the critical stress required for the catastrophic failure of pipeline or pressure vessel damaged due to third-party interference. The model was implemented as a FORTRAN program. Testing of the developed numerical tool was performed using experimental data available in the literature, with the results showing promising agreement. / February 2016

Estimation of the Radar Cross Section of large inhomogeneous scattering objects such as composite aircrafts, ships and biological bodies at high frequencies has posed large computational challenge. The detection of scattering from wake vortex leading to detection and possible identification of low observable aircrafts also demand the development of computationally efficient and rigorous numerical techniques. Amongst the various methods deployed in Computational Electromagnetics, the Method of Moments predicts the electromagnetic characteristics accurately. Method of Moments is a rigorous method, combined with an array of modeling techniques such as triangular patch, cubical cell and tetrahedral modeling. Method of Moments has become an accurate technique for solving electromagnetic problems from complex shaped homogeneous and inhomogeneous objects. One of the drawbacks of Method of Moments is the fact that it results into a dense matrix, the inversion of which is a computationally complex both in terms of physical memory and compute power. This has been the prime reason for the Method of Moments hitherto remaining as a low frequency method. With recent advances in supercomputing, it is possible to extend the range of Method of Moments for Radar Cross Section computation of aircraft like structures and radiation characteristic of antennas mounted on complex shaped bodies at realistic frequencies of practical interest. This thesis is a contribution in this direction. The main focus of this thesis is development of parallel Method of Moments solvers, applied to solve real world electromagnetic wave scattering and radiation problems from inhomogeneous objects. While the methods developed in this thesis are applicable to a variety of problems in Computational Electromagnetics as shown by illustrative examples, in specific, it has been applied to compute the Radar Cross Section enhancement due to acoustic disturbances and flow inhomogeneities from the wake vortex of an aircraft, thus exploring the possibility of detecting stealth aircraft. Illustrative examples also include the analysis of antenna mounted on an aircraft. In this thesis, first the RWG basis functions have been used in Method of Moments procedure, for solving scattering problems from complex conducting structures such as aircraft and antenna(s) mounted on airborne vehicles, of electrically large size of about 45 and 0.76 million unknowns. Next, the solver using SWG basis functions with tetrahedral and pulse basis functions with cubical modeling have been developed to solve scattering from 3D inhomogeneous bodies. The developed codes are validated by computing the Radar Cross Section of spherical homogeneous and inhomogeneous layered scatterers, lossy dielectric cylinder with region wise inhomogeneity and high contrast dielectric objects. Aerodynamic flow solver ANSYS FLUENT, based on Finite Volume Method is used to solve inviscid compressible flow problem around the aircraft. The gradients of pressure/density are converted to dielectric constant variation in the wake region by using empirical relation and interpolation techniques. Then the Radar Cross Section is computed from the flow inhomogeneities in the vicinity of a model aircraft and beyond (wake zone) using the developed parallel Volume Surface Integral Equation using Method of Moments and investigated more rigorously. Radar Cross Section enhancement is demonstrated in the presence of the flow inhomogeneities and detectability is discussed. The Bragg scattering that occurs when electromagnetic and acoustic waves interact is also discussed and the results are interpreted in this light. The possibility of using the scattering from wake vortex to detect low visible aircraft is discussed. This thesis also explores the possibility of observing the Bragg scattering phenomenon from the acoustic disturbances, caused by the wake vortex. The latter sets the direction for use of radars for target identification and beyond target detection. The codes are parallelized using the ScaLAPACK and BiCG iterative method on shared and distributed memory machines, and tested on variety of High Performance Computing platforms such as Blue Gene/L (22.4TF), Tyrone cluster, CSIR-4PI HP Proliant 3000 BL460c (360TF) and CRAY XC40 machines. The parallelization speedup and efficiency of all the codes has also been shown.

The presented master’s thesis deals with the application of the gradient elasticity in fracture mechanics problems. Specifically, the displacement and stress field around the crack tip is a matter of interest. The influence of a material microstructure is considered. Introductory chapters are devoted to a brief historical overview of gradient models and definition of basic equations of dipolar gradient elasticity derived from Mindlin gradient theory form II. For comparison, relations of classical elasticity are introduced. Then a derivation of asymptotic displacement field using the Williams asymptotic technique follows. In the case of gradient elasticity, also the calculation of the J-integral is included. The mathematical formulation is reduced due to the singular nature of the problem to singular integral equations. The methods for solving integral equations in Cauchy principal value and Hadamard finite part sense are briefly introduced. For the evaluation of regular kernel, a Gauss-Chebyshev quadrature is used. There also mentioned approximate methods for solving systems of integral equations such as the weighted residual method, especially the least square method with collocation points. In the main part of the thesis the system of integral equations is derived using the Fourier transform for straight crack in an infinite body. This system is then solved numerically in the software Mathematica and the results are compared with the finite element model of ceramic foam.

Cette thèse s'intéresse à l'étude des stratégies d'introduction de populations dans l'environnement. Les deux principaux contextes présentés sont la lutte biologique et la réintroduction d'espèces. Si ces deux types d'introduction diffèrent, des processus biotiques et abiotiques les influencent de manière similaire. En particulier les populations introduites, souvent de petite taille, peuvent être sensibles à diverses formes de stochasticité, voire subir une baisse de leur taux de croissance à faible effectif, ce qu'on appelle « effet Allee ». Ces processus peuvent interagir avec les stratégies d'introduction des organismes et moduler leur efficacité. Dans un premier temps, nous modélisons le processus d'introduction à l'aide de systèmes dynamiques impulsionnels : la dynamique de la population est décrite par des équations différentielles ordinaires qui, à des instants donnés, sont perturbées par des augmentations soudaines de la taille de la population. Cette approche se concentre sur l'influence des effets Allee sur les populations isolées (réintroduction) ou dans un cadre proie-prédateur (lutte biologique). Dans un second temps, en nous concentrant sur l'aspect réintroduction, nous étendons ce cadre de modélisation pour prendre en compte des aspects stochastiques liés à l'environnement ou aux introductions elles-mêmes. Finalement, nous considérons un modèle individu centré pour étudier l'effet de la stochasticité démographique inhérente aux petites populations. Ces différentes approches permettent d'analyser l'influence de la distribution temporelle des introductions et ainsi déterminer les stratégies qui maximisent les chances de succès des introductions. / This thesis investigates introduction strategies of populations in the environment. Two main situations are considered: biological control and species reintroduction. Although these two kinds of introductions are different, many biotic and abiotic processes influence them in a similar way. Introduced populations are often small and may be sensitive to various stochastic factors. Further, small populations may suffer from a decrease of their growth rate when the population is small, a feature called "Allee effect". These processes may interact with introduction strategies and modulate their efficiency. First, we represent the introduction process using impulsive dynamical systems: population dynamics are described by ordinary differential equations that are disrupted at some instants by instantaneous increases of the population size. This approach focuses on the influence of Allee effects on single-species (reintroduction) or predator-prey interactions (biological control). Then, we concentrate on the reintroduction approach and extend the previous deterministic framework to take into consideration stochastic factors arising from the environment or from introductions themselves. Finally, we consider an individual-based model to study the effects of demographic stochasticity which is inherent to small populations. These different approaches allow to investigate the temporal distribution of introductions and determine which introduction strategies maximize the probability of success of introductions.

Cette thèse s'inscrit dans le sujet des opérateurs intégraux de frontière définis sur le disque unitaire en trois dimensions, leurs relations avec les problèmes externes de Laplace et Helmholtz, et leurs applications au préconditionnement des systèmes linéaires obtenus en utilisant la méthode des éléments finis de frontière.On décrit d'abord les méthodes intégrales pour résoudre les problèmes de Laplace et de Helmholtz en dehors des objets à frontière régulière lipschitzienne, et en dehors des surfaces bidimensionnelles ouvertes dans un espace tridimensionnel. La formulation intégrale des problèmes de Laplace et de Helmholtz pour ces cas est décrite formellement. La mise en oeuvre d'une méthode numérique utilisant la méthode des éléments finis de frontière est également décrite. Les avantages et les défis inhérents à la méthode sont abordés : la complexité du calcul numérique (de mémoire et algorithmique) et le mal conditionnement inhérentes à des systèmes linéaires associés.Dans une deuxième partie on expose une technique optimale de préconditionnement (indépendante de la discrétisation) sur la base des opérateurs intégraux de frontière. On montre comment cette technique est facilement réalisable dans le cas de problèmes définis en dehors d'un objet régulier à frontière lipschitzienne, mais qu'elle pose des problèmes quand ils sont définis en dehors d'une surface ouverte dans un espace tridimensionnel. On montre que les opérateurs intégraux de frontière associés à la résolution des problèmes de Dirichlet et Neumann définis en dehors des surfaces ont des inverses bien définis. On montre également que ceux-ci pourraient conduire à des techniques de préconditionnement optimales, mais que ses formes explicites ne sont pas faciles à obtenir. Ensuite, on montre une méthode pour obtenir de tels opérateurs inverses de façon explicite lorsque la surface sur laquelle ils sont définis est un disque unitaire dans un espace tridimensionnel. Ces opérateurs inverses explicites seront, cependant, en forme des séries, et n'auront pas une adaptation immédiate pour leur utilisation dans des méthodes des éléments finis de frontière.Dans une troisième partie on montre comment certaines modifications aux opérateurs inverses mentionnés permettent d'obtenir des expressions variationnelles explicites et fermées, non plus sous la forme des séries, en conservant certaines caractéristiques importantes pour l'effet de préconditionnement cherché. Ces formes explicites sont en effet applicables aux méthodes des éléments finis frontière. On obtient des expressions variationnelles précises et on propose des calculs numériques pour leur utilisation avec des éléments finis frontière. Ces méthodes numériques sont testées en utilisant différentes identités obtenues dans la théorie développée, et sont ensuite utilisées pour produire des matrices préconditionnantes. Leur performance en tant que préconditionneurs de systèmes linéaires associés à des problèmes de Laplace et Helmholtz à l'extérieur du disque est testée. Enfin, on propose extension de cette méthode pour couvrir les cas de surfaces diverses. Ceci est illustré et étudié dans les cas précis des problèmes extérieurs à des surfaces en forme de carré et en forme de L dans un espace tridimensionnel. / This thesis is about some boundary integral operators defined on the unit disk in a three-dimensional spaces, their relation with the exterior Laplace and Helmholtz problems, and their application to the preconditioning of the systems arising when solving these problems using the boundary element method.We begin by describing the so-called integral method for the solution of the exterior Laplace and Helmholtz problems defined on the exterior of objects with Lipschitz-regular boundaries, or on the exterior of open two-dimensional surfaces in a three-dimensional space. We describe the integral formulation for the Laplace and Helmholtz problem in these cases, their numerical implementation using the boundary element method, and we discuss its advantages and challenges: its computational complexity (both algorithmic and memory complexity) and the inherent ill-conditioning of the associated linear systems.In the second part we show an optimal preconditioning technique (independent of the chosen discretization) based on operator preconditioning. We show that this technique is easily applicable in the case of problems defined on the exterior of objects with Lipschitz-regular boundary surfaces, but that its application fails for problems defined on the exterior of open surfaces in three-dimensional spaces. We show that the boundary integral operators associated with the resolution of the Dirichlet and Neumann problems defined on the exterior of open surfaces have inverse operators, and that these operators would provide optimal preconditioners, but that they are not easily obtainable. Then we show a technique to explicitly obtain such inverse operators for the particular case when the open surface is the unit disk in a three-dimensional space. Their explicit inverse operators will be given, however, in the form of series, and will not be immediately applicable in the use of boundary element methods.In the third part we show how some modifications to these inverse operators allow us to obtain variational explicit and closed form expressions, no longer expressed as series, but also conserve nonetheless some characteristics that are relevant for their preconditioning effect. These explicit and closed forms expressions are applicable in boundary element methods. We obtain precise variational expressions for them and propose numerical schemes to compute the integrals needed for their use with boundary elements. The proposed numerical methods are tested using identities available within the developed theory and then used to build preconditioning matrices. Their performance as preconditioners for linear systems is tested for the case of the Laplace and Helmholtz problems for the unit disk. Finally, we propose an extension of this method that allows for the treatment of cases of open surfaces other that the disk. We exemplify and study this extension in its use on a square-shaped and an L-shaped surface screen in a three-dimensional space.

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 $\gamma$.

<p>Among computational electromagnetic methods, Integral Equation (IE) solvers have a great capability in solving open-region problems such as scattering and radiation, due to no truncation boundary condition required. Volume Integral Equation (VIE) solvers are especially capable of handling arbitrarily shaped geometries and inhomogeneous materials. However, the numerical system resulting from a VIE analysis is a dense system, having $N^2$ nonzero elements for a problem of $ N $ unknowns. The dense numerical system in conjunction with the large number of unknowns resulting from a volume discretization prevents a practical use of the VIE for solving large-scale problems.</p> <p>In this work, two fast algorithms of $ O(N \log N) $ complexity to generate an rank-minimized $ H^2 $-representation for electrically large VIEs are developed. The algorithms systematically compress the off-diagonal admissible blocks of full VIE matrix into low-rank forms of total storage of $O(N)$. Both algorithms are based on nested cross approximation, which are purely algebraic. The first one is a two-stage algorithm. The second one is optimized to only use one-stage, and has a significant speedup. Numerical experiments on electrically large examples with over 33 million unknowns demonstrate the efficiency and accuracy of the proposed algorithms. </p> <p>Important applications of VIEs in thermal and quantum engineering have also been explored in this work. Creating spin(circularly)-polarized infrared thermal radiation source without an external magnetic field is important in science and engineering. Here we study two materials, magnetic Weyl semimetals and manganese-bismuth(MnBi), which both have permittivity tensors of large gyrotropy, and can emit circularly-polarized thermal radiations without an external magnetic field. We also design symmetry-broken metasurfaces, which show strong circularly-polarized radiations in simulations and experiments. In spin qubit quantum computing systems, metallic gates and antennas are necessary for quantum gate operations. But their existence greatly enhances evanescent wave Johnson noise (EWJN), which induces the decay of spin qubits and limits the quantum gate operation fidelity. Here we first use VIE to accurately simulate realistic quantum gate designs and quantify the influence on gate fidelity due to this noise.</p>

The Theory of Characteristic Modes is being adopted by many research groups around the world in the last decade. This topic and their use in different metallic antenna design is growing very fast. However, most of the applications has been only concentrated on conducting surfaces without any physical knowledge about its limitations and its physical interpretation. As far as dielectric bodies are concerned, there have not been so many published articles. The reason is that there are different integro-differential formulations and the interpretation of their solutions is not as obvious as in conducting bodies. Here, a theoretical interpretation considering loss-less conducting and dielectric bodies is presented. The conclusions drawn in this thesis will allow us to better understand the solutions of the Theory of Characteristic Modes and their limitations. This is important for antenna engineering. In addition, this analysis will allow to develop a novel method for the design of antennas based on dielectric resonators, DRA. This method is called Substructure based-PMCHWT method, and is based on the implementation of the Schur complements of the method of moments matrix operator. This study permits to optimize the radiation bandwidth in the same analysis process for both, the dielectric and the feed, e.g. slot. Moreover, it allows to understand how the slot behaves in the presence of the dielectric resonator and vice versa. This method can also be used to design DRA using low permittivities. This is important in the design of DRA because the feed perturbs the system and produces a shift in the resonances of the characteristic modes. So, therefore, by considering the feed system in the characteristic modes analysis a more realistic results than a conventional analysis is obtained. On the other hand, the resonances of the characteristic modes at low permittivities are displaced from what are the natural resonances of the dielectric resonator and also the corresponding S11 resonance. Thus, designing with this new method it can draw new conclusions about the design of DRA using the Theory of Characteristic Modes. / En la última década, la teoría de los modos característicos está siendo utilizada por muchos grupos de investigación en todo el mundo. Este tema y su uso en diferentes diseños de antenas metálicas está creciendo muy rápido. Sin embargo, la mayoría de las aplicaciones se han concentrado únicamente en antenas metálicas sin ningún conocimiento físico acerca de sus limitaciones y su interpretación física. En lo que se refiere a cuerpos dieléctricos, no han habido tantos artículos publicados como en metales. La razón es que existen diferentes formulaciones integro-diferenciales y la interpretación de sus soluciones no es tan obvia como en cuerpos metálicos. En esta tesis se presenta una interpretación física de las soluciones de la Teoría de Modos Característicos al considerar cuerpos metálicos y dieléctricos sin pérdidas. Las conclusiones de esta tesis nos permitirán comprender mejor las soluciones de la Teoría de Modos Característicos y sus limitaciones. Esto es importante en ingeniería de antenas. Además, este análisis permitirá desarrollar un nuevo método para el diseño de antenas basadas en resonadores dieléctricos, DRA. Este método está basado en la formulación PMCHWT y la función de Green multicapa utilizada en el método de los momentos (MoM). A este nuevo método se le ha denominado "Substructure Characteristic Mode method", y está basado en la implementación de los complementos Schur sobre las submatrices del operador del MoM. Este estudio permite optimizar el ancho de banda de radiación de un DRA en el mismo proceso de análisis tanto para el dieléctrico como para la alimentación, como por ejemplo una ranura. Además, este método permite comprender como se comporta la ranura en presencia del resonador dieléctrico y viceversa. Este método también puede usarse para diseñar DRA usando permitividades bajas. Esto es importante en el diseño de DRA porque la alimentación perturba el sistema y produce un cambio en las resonancias de los modos característicos. Por lo tanto, al considerar la alimentación en el análisis de modos característicos se obtienen resultados más realistas comparándolos con los obtenidos mediante un análisis convencional. Así, diseñando con el "Substructure Characteristic Mode method" se pueden extraer nuevas conclusiones sobre el diseño de DRA mediante la Teoría de Modos Característicos. / En l'última dècada, la teoria dels modes característics està sent utilitzada per molts grups d'investigació en tot el món. Este tema i el seu ús en diferents dissenys d'antenes metàl·liques està creixent molt ràpid. No obstant això, la majoria de les aplicacions s'han concentrat únicament en superfícies conductores sense cap coneixement físic sobre les seues limitacions i la seua interpretació física. Pel que fa a cossos dielèctrics, no hi ha hagut tants articles publicats com en metalls. La raó és que hi ha diferents formulacions integro- diferencials i la interpretació de les seues solucions no és tan òbvia com en cossos conductors. En esta tesi es presenta una interpretació teòrica considerant cossos conductors i dielèctrics sense pèrdues. Les conclusions d'esta tesi ens permetran comprendre millor les solucions de la Teoria de Modes Característics i les seues limitacions. Açò és important en enginyeria d'antenes. Açò és important en enginyeria d'antenes. A més, esta anàlisi permetrà desenrotllar un nou mètode per al disseny d'antenes basades en ressonadors dielèctrics, DRA. Este mètode està basat en la formulació PMCHWT i la funció de Green multicapa utilitzada en el mètode dels moments (MoM) . A este nou mètode se li ha denominat "Substructure Characteristic Mode method", i està basat en la implementació dels complements Schur sobre les submatrius de l'operador del MoM. Este estudi permet optimitzar l'amplada de banda de radiació d'un DRA en el mateix procés d'anàlisi tant per al dielèctric com per a l'alimentació, com per exemple una ranura. A més, este mètode permet comprendre com es comporta la ranura en presència del ressonador dielèctric i viceversa. Este mètode també pot usar-se per a dissenyar DRA usant baixes permitivitats. Açò és important en el disseny de DRA perquè l'alimentació pertorba el sistema i produïx un canvi en les ressonàncies dels modes característics. Per tant, al considerar l'alimentació en l'anàlisi de modes característics s'obtenen resultats més realistes comparant-los amb els obtinguts per mitjà d'una anàlisi convencional. Així, dissenyant amb el "Substructure Characteristic Mode method" es poden extraure noves conclusions sobre el disseny de DRA per mitjà de la Teoria de Modes Característics. / Bernabeu Jiménez, T. (2017). Contribution to the physical interpretation of characteristic mode resonances. Application to dielectric resonator antennas [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/86177