In this study, seismic interferometry is used to analyze dynamic processes in the Earth’s shallow subsurface caused by environmental processes and ground shaking. In the first part of the thesis, the feasibility of a passive monitoring with ambient seismic noise at the pilot site for CO2 injection in Ketzin is investigated. Monitoring the expansion of the CO2 plume is essential for the characterization of the reservoir as well as the detection of potential leakage. From June 2008 until August 2013, more than 67000 tons of CO2 were injected into a saline aquifer at a depth of about 650 m. Passive seismic data recorded at a seismic network around the injection site was cross-correlated in a frequency range of 0.5-4.5 Hz over a period of 4 years. The frequency band of 0.5-0.9 Hz, in which surface waves exhibit a high sensitivity at the depth of the reservoir, is not suitable for monitoring purposes as it is only weakly excited. In a frequency range of 1.5-3 Hz, periodic velocity variations with a period of approximately one year are found that cannot be caused by the CO2 injection. The prominent propagation direction of the noise wave field indicates a wind farm as the dominant source providing the temporally stable noise field. This spacial stability excludes variations of the noise source distribution as a spurious cause of velocity variations. Based on an amplitude decrease associated with time windows towards later parts of the coda, the variations must be generated in the shallow subsurface. A comparison to groundwater level data reveals a direct correlation between depth of the groundwater level and the seismic velocity. The influence of ground frost on the seismic velocities is documented by a sharp increase of velocity when the maximum daily temperature stays below 0 C. Although the observed periodic changes and the changes due to ground frost affect only the shallow subsurface, they mask potential signals of material changes from the reservoir depths. To investigate temporal seismic velocity changes due to earthquake-related processes and environmental forcing in northern Chile, 8 years of ambient seismic noise recorded by the Integrated Plate Boundary Observatory Chile (IPOC) are analyzed. By autocorrelating the ambient seismic noise field, approximations of the Green’s functions are retrieved and velocity changes are measured with Coda Wave Interferometry. At station PATCX, seasonal changes of seismic velocity caused by thermal stress as well as transient velocity reductions are observed in the frequency range of 4-6 Hz. Sudden velocity drops occur at times of mostly earthquake-induced ground describing the seismic velocity variations based on continuous observations of the local ground acceleration. The model assumes that not only the shaking of large earthquakes causes velocity drops, but any small vibrations continuously induce minor velocity variations that are immediately compensated by healing in the steady state. The shaking effect is accumulated over time and best described by the integrated envelope of the ground acceleration over one day, which is the temporal resolution of the velocity measurements. In the model, the amplitude of the velocity reduction as well as the recovery time are proportional to the strength of the excitation. The increase of coseismic velocity change and recovery time with increasing excitation is confirmed by laboratory tests with ultrasound. Despite having only two free scaling parameters, the model fits the data of the shaking-induced velocity variation in remarkable detail. Additionally, a linear trend is observed that might be related to a recovery process from one or more earthquakes before the measurement period. A clear relationship between ground shaking and induced velocity reductions is not visible at other stations. The outstanding sensitivity of PATCX to ground shaking and thermal stress can be attributed to the special geological setting of the station, where the subsurface material consists of a relatively loose conglomerate with high pore volume leading to stronger nonlinearity compared to the other IPOC stations. / In dieser Studie werden mit Hilfe von seismischer Interferometrie kleinste dynamische Prozesse in der Erdkruste beobachtet, welche beispielsweise durch umweltbedingte oder anthropogene Einflüsse sowie Bodenerschütterungen hervorgerufen werden können. Im ersten Teil der Arbeit werden Änderungen in der seismischen Geschwindigkeit am Pilotstandort für CO2-Speicherung in Ketzin untersucht. In einer Tiefe von 650m wurden dort zwischen Juni 2008 und August 2013 über 67000 Tonnen CO2 eingelagert. In einem Frequenzbereich vom 0,05-4,5 Hz wurden Kreuzkorrelationen des seismischen Hintergrundrauschens an einem kleinräumigen Netzwerk über einen Zeitraum von 4 Jahren berechnet. Der Frequenzbereich zwischen 0,5 und 0,9 Hz weist eine hohe Sensitivität von Oberflächenwellen in der Tiefe des Reservoirs auf, ist aber nur sehr schwach angeregt und eignet sich deswegen nicht für die Analyse. In einem Frequenzbereich von 1,5-3 Hz zeigen sich periodische Geschwindigkeitsänderungen mit einer Periode von einem Jahr, welche nicht durch die Einlagerung von CO2 erzeugt werden können. Eine Analyse des seismischen Hintergrundrauschens zeigt, dass dieses über den gesamten Zeitraum hinweg hauptsächlich aus der Richtung eines Windparks kommt. Durch die Stabilität des Wellenfeldes können Änderungen in den Quellpositionen, welche sich in scheinbaren Geschwindigkeitsänderungen zeigen können, ausgeschlossen werden. Eine Amplitudenabnahme der Geschwindigkeitsänderungen hin zu späteren Zeitfenstern in der Coda lässt auf oberflächennahe Prozesse als Ursache schließen. Ein Vergleich zwischen den jährlichen Geschwindigkeitsänderungen mit Schwankungen im Grundwasserspiegel zeigt eine direkte Korrelation. Ein sprunghafter Anstieg in der Geschwindigkeit zeigt sich im Winter, wenn die Tageshöchsttemperaturen unter den Gefrierpunkt sinken und der Boden zufriert. Obwohl Bodenfrost und Änderungen im Grundwasserspiegel nur einen sehr oberflächennahen Bereich betreffen, so überdecken sie dennoch mögliche Signale durch die Einlagerung von CO2. Im zweiten Teil der Arbeit werden Geschwindigkeitsänderungen in Nordchile untersucht, welche durch erdbebeninduzierte Prozesse und umweltbedingte Einflüsse hervorgerufen werden. Dazu wurden über einen Zeitraum von 8 Jahren Autokorrelationen des seismischen Hintergrundrauschens des IPOC Netzwerkes (Integrated Plate Boundary Observatory Chile) berechnet und mit seismischer Interferometrie ausgewertet. An der Station PATCX können in einem Frequenzbereich von 4-6 Hz periodische Geschwindigkeitsänderungen beobachet werden, welche durch thermisch induzierte Dehnung hervorgerufen werden. Außerdem treten transiente Geschwindigkeitsabnamen nach Bodenerschütterungen auf, welche hauptsächlich von Erdbeben verursacht werden. Die seismische Geschwindigkeit kehrt daraufhin langsam wieder auf ihr vorheriges Niveau zurück. Für die Geschwindigkeitsänderungen wurde ein empirisches Modell entwickelt, welches auf Messungen der lokalen Bodenerschütterung basiert. Dabei wird angenommen, dass nicht nur große erdbebeninduzierte, sondern auch kleinste Bodenerschütterungen einen Abfall der Geschwindigkeit erzeugen, welche wiederum innerhalb kürzester Zeit durch Heilung in den Gleichgewichtszustand zurückkehrt. Dabei summieren sich die Effekte durch die Bodenerschütterungen mit der Zeit auf und werden am besten mit dem Integral der lokalen Bodenbeschleunigung über die Messwerte eines Tages beschrieben. Die Diskretisierung von einem Tag entspricht der zeitlichen Auflösung in der Messung der Geschwindigkeitsänderungen. Sowohl die Amplitude der Geschwindigkeitsabnahme als auch die Zeit bis der Gleichgewichtszustand wieder erreicht ist (Heilungszeit) werden im Modell als proportinal zur Größe der Anregung angenommen. Eine Korrelation der Heilungszeit und der Amplitude der koseismischen Geschwindigkeitsabnahme mit der Größe der Anregung konnte mit Hilfe von Laboruntersuchungen mit Ultraschall bestätigt werden. Mit nur zwei Parametern beschreibt das Modell die transienten Geschwindigkeitsänderungen in bemerkenswerter Genauigkeit. Desweiteren beinhaltet das Modell einen linearen Verlauf in den Geschwindigkeitsänderungen, welcher vermutlich durch einen Heilungsprozess hervorgerufen wird, der auf ein oder mehrere Erdbeben vor dem Messzeitraum folgte. Eine Beziehung zwischen Bodenerschütterung und Geschwindigkeitsänderung ist an anderen Stationen des IPOC Netzwerkes nicht erkennbar. Die herausragende Sensitivität von PATCX im Hinblick auf Bodenerschütterung und thermische Dehnung kann den speziellen geologischen Gegebenheiten an der Station zugeschrieben werden. Bei dem dort vorliegenden Material handelt es sich um ein relativ loses Konglomerat mit großem Porenvolumen, welches ein starkes nichtlineares Verhalten aufweist, was an anderen IPOC Stationen nicht zu erwarten ist.

<p>Doktorska disertacija posve&para;cena je re&middot;savanju nelinearnih hiperboli&middot;cnih skalarnih zakona odr&middot;zanja u heterogenim sredinama, prou&middot;cavanjem osobina kompaktnosti re&middot;senja familija aproksimativnih jedna&middot;cina. Ta&middot;cnije, u cilju dobijanja re&middot;senja u = u(t; x) problema @ t u + divx f (t; x; u) = 0;uj t=0 = u 0(x); gde su promenljive x 2 R d i t 2 R+<br />, posmatramo familije problema koji na neki na&middot;cin aproksimiraju po&middot;cetni problem, a koje znamo da re&middot;simo, i ispitujemo familije dobijenih re&middot;senja koja zovemo aproksimativna re&middot;senja. Cilj nam je da poka&middot;zemo da je dobijena familija u nekom smislu prekompaktna,<br />tj. da ima konvergentan podniz &middot;cija granica re&middot;sava po&middot;cetni problem.</p> / <p>Doctoral theses is dedicated to solving nonlinear hyperbolic scalar conservation laws in heterogeneous media, by studying compactness properties of the family of solutions to approximate problems. More precise, in order to obtain solution u = u(t; x) to the problem @ t u + divx f (t; x; u) = 0; uj t=0 = u 0 (x); (4.18) where x 2 R d and t 2 R+<br />, we study the solutions of the families of problems that, in some way, approximate previously mentioned problem, which we know how to solve. We call those solutions approximate solutions. The aim is to show that the obtained family is in some sense precompact, i.e. has convergent subsequence that solves the problem (4.18).</p>

TM-(transverse magnetic)guided waves, propagating in a lossless, nonmagnetic three-layer structure (substrate-film-cladding) are studied. Two types of the dielectric permittivities (I and II) are analyzed. All three media of the waveguide with the permittivity of type I are assumed to exhibit a local Kerr-like tensorial nonlinearity. Maxwell's equations in this case are reduced to an exact differential equation leading to a first integral, relating two electric field components so that one component can be eliminated. The other one can be found by integration. Combination of the first integral with the boundary conditions leads to an exact analytical dispersion relations (expressed in terms of integrals) establishing a link between the parameters of the problem (in particular, thickness of the film, the propagation constant of the travelling wave, the electric field components at the interface substrate-film). The film thickness and the propagation constant satisfying the dispersion relation (by given electric field component at the boundary substrate-film)are associated to the possible modes travelling through the waveguide. Numerical evaluation of the corresponding power flow derived using of Maxwell' equations and the first integral processes straightforwardly, without known wave solutions at first. The waveguide with the permittivity of type II consists of the film with the dielectric function depending on the field intensity (Kerr-type nonlinearity) as well as on the transverse coordinate (spatially varying permittivity) situated between the linear, isotropic substrate and cladding. The problem in this case is reduced to a system of two integral equations. Using the Banach fixed-point theorem it is shown that the solutions of Maxwell's equations exist in form of a uniformly convergent sequence of iterations. The conditions of the Banach fixed-point theorem are derived and used to estimate the quality of the approximation. The exact dispersion relation is derived. Results of numerical evaluation of the dispersion relation and field solutions are presented in the first approximation. Solutions of the dispersion relation, the field components and the power flow obtained using the method for the permittivity I are compared with these found using an integral equation approach (the permittivity II but without the coordinate dependence) - the consistency is remarkably good. The proposed methods seem to be applicable to permittivities more general as considered.

Thermoplastic materials have significant nonlinear behaviour. The nonlinear behaviour is described by creep curves. The curves of creep modules are dependent on stress, temperature and time. The dissertation thesis deals with the approximation of the creep modules by Prony series. Subsequently three procedures are proposed to take account of creep modules. The proposed procedures are used in two applications. The first application deals with the ring stiffness value of a corrugated sewage pipe. The ring stiffness value is influenced by the creep modulus. The other one deals with a thermoplastic flange connection. The clamping force is dependent on the creep modulus of thermoplastics. The problems were solved by ANSYS program system.

No / This paper presents a circuit model which is used to calibrate the performance of nonlinear RF energy conversion inside a high quality factor resonant cavity with a known nonlinear loading device. The nonlinear radiofrequency energy conversion can be detected by exciting the fundamental operating frequency and observing the second harmonic resonant frequency within a doubly resonant cavity. By implementing the proposed mathematical model, the required input power can be estimated to maximise the chance of detecting the weak second harmonic signal prior to carry out the measurement.

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The present thesis employs fuzzy-polynomial control techniques in order to improve the stability analysis and control of nonlinear systems. Initially, it reviews the more extended techniques in the field of Takagi-Sugeno fuzzy systems, such as the more relevant results about polynomial and fuzzy polynomial systems. The basic framework uses fuzzy polynomial models by Taylor series and sum-of-squares techniques (semidefinite programming) in order to obtain stability guarantees. The contributions of the thesis are: ¿ Improved domain of attraction estimation of nonlinear systems for both continuous-time and discrete-time cases. An iterative methodology based on invariant-set results is presented for obtaining polynomial boundaries of such domain of attraction. ¿ Extension of the above problem to the case with bounded persistent disturbances acting. Different characterizations of inescapable sets with polynomial boundaries are determined. ¿ State estimation: extension of the previous results in literature to the case of fuzzy observers with polynomial gains, guaranteeing stability of the estimation error and inescapability in a subset of the zone where the model is valid. ¿ Proposal of a polynomial Lyapunov function with discrete delay in order to improve some polynomial control designs from literature. Preliminary extension to the fuzzy polynomial case. Last chapters present a preliminary experimental work in order to check and validate the theoretical results on real platforms in the future. / Pitarch Pérez, JL. (2013). Contributions to fuzzy polynomial techniques for stability analysis and control [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/34773

[ES] Dentro del campo del Análisis Numérico, la resolución de ecuaciones y sistemas de ecuaciones no lineales es uno de los aspectos más relevantes y estudiados. Esto se debe a que gran cantidad de problemas de Matemática Aplicada, como la resolución de ecuaciones diferenciales, ecuaciones en derivadas parciales o ecuaciones integrales entre muchos otros, pueden reducirse a buscar la solución de un sistema no lineal. Generalmente, es muy difícil obtener la solución analítica de este tipo de problemas y, en muchos casos, aunque es posible llegar a encontrar la solución exacta, es muy complicado trabajar con dicha expresión por su complejidad. Además, con el desarrollo de las nuevas tecnologías, se han hecho grandes avances en el uso de herramientas computacionales, por lo que las dimensiones de algunos de los problemas que se plantean en campos como la Economía, la Ingeniería, la Ciencia de datos, etc. han crecido considerablemente, dando lugar a problemas de grandes dimensiones. Por estos motivos, es de gran utilidad y, en muchos casos, resulta necesario resolver estos problemas no lineales de forma aproximada, por supuesto, con técnicas matemáticamente rigurosas dentro del campo del Análisis Numérico. Por las razones expuestas, los métodos iterativos para aproximar la solución de ecuaciones y sistemas de ecuaciones no lineales han constituido a lo largo de los últimos años un importante campo de investigación. La implementación computacional de estos métodos es una importante herramienta dentro de las Ciencias Aplicadas ya que dan solución a problemas que antiguamente eran difíciles de resolver. La investigación que se lleva a cabo en esta Tesis Doctoral se centra en estudiar, diseñar y aplicar métodos iterativos que mejoren en ciertos aspectos a los esquemas clásicos, como por ejemplo: la velocidad de convergencia, la aplicabilidad a problemas no diferenciales, la accesibilidad o la eficiencia. Buena parte del trabajo desarrollado en esta memoria se centra en el estudio de métodos iterativos para problemas multidimensionales, en especial, nos hemos centrado en el estudio de esquemas libres de derivadas. Además, uno de los ejes centrales de la presente Tesis Doctoral se enfoca en el estudio de la convergencia local y semilocal de métodos ya desarrollados en la literatura reciente o de nuevos métodos iterativos diseñados en este mismo trabajo. Este estudio garantiza para los métodos analizados la existencia de solución dado un punto de partida, el dominio de convergencia de las soluciones del problema y la unicidad de éstas bajo ciertas condiciones. Para complementar el estudio de convergencia de los métodos, en algunos capítulos también se realiza un estudio dinámico de los métodos aplicados a ecuaciones no lineales para, posteriormente, extrapolar los resultados al caso multidimensional. Además, como parte de algunos experimentos numéricos, se ha comparado la accesibilidad de distintos métodos numéricos a través de las cuencas de atracción representadas en diferentes planos dinámicos, tanto para el caso unidimensional como el multidimensional. Finalmente, en la mayor parte de los Capítulos de esta tesis se aplican los métodos iterativos estudiados a la resolución de problemas no lineales de Matemática Aplicada. Estos problemas pueden estar preparados para poner a prueba los algoritmos diseñados o ser problemas reales presentes en algunas Ciencias Aplicadas como la Ingeniería, la Física, la Química, etc. Los resultados anteriormente descritos forman parte de la presente Tesis Doctoral para la obtención del título de Doctora en Matemáticas. / [CA] Dins del camp de l'Anàlisi Numèrica, la resolució d'equacions i sistemes d'equacions no lineals és un dels aspectes més rellevants i estudiats. Això és pel fet de que gran quantitat de problemes de Matemàtica Aplicada, com la resolució d'equacions diferencials, equacions en derivades parcials o equacions integrals entre molts altres, poden reduir-se a buscar la solució d'un sistema no lineal. Generalment, és molt difícil obtindre la solució analítica d'estos problemes i, en molts casos, encara que és possible arribar a trobar la solució exacta, és molt complicat treballar amb aquesta expressió per la seua complexitat. A més, amb el desenvolupament de les tecnologies, s'han fet grans avanços en l'ús d'eines computacionals, per la qual cosa les dimensions d'alguns dels problemes que es plantegen en camps com l'Economia, l'Enginyeria, la Ciència de dades, etc. han crescut considerablement, donant lloc a problemes de grans dimensions. Per aquestos motius, és de gran utilitat i, en molts casos, resulta necessari resoldre estos problemes no lineals de manera aproximada, per descomptat, amb tècniques matemàticament riguroses dins del camp de l'Anàlisi Numèrica. Per les raons exposades, els mètodes iteratius per a aproximar la solució d'equacions i sistemes d'equacions no lineals han constituït al llarg dels últims anys un important camp d'investigació. La implementació computacional d'estos mètodes és una eina important dins de les Ciències Aplicades ja que donen solució a problemes que antigament eren difícils de resoldre. La investigació que es porta a terme en esta Tesi Doctoral es centra en estudiar, dissenyar i aplicar mètodes iteratius que milloren en certs aspectes als esquemes clàssics com són: la velocitat de convergència, l'aplicabilitat a problemes no diferencials, l'accessibilitat o l'eficiència. Bona part del treball desenvolupat en esta memòria es centra en l'estudi de mètodes iteratius per a problemes multidimensionals, especialment, ens hem centrar en l'estudi d'esquemes lliures de derivades. A més, part de la present Tesi Doctoral està centrada en l'estudi de la convergència local i semilocal de mètodes ja desenvolupats en la literatura recent o de nous mètodes iteratius dissenyats en aquest mateix text. Este estudi garanteix per als mètodes l'existència de solució donat un punt de partida, el domini de convergència de les solucions del problema i la unicitat d'estes sota unes certes condicions. Per a complementar l'estudi de convergència dels mètodes, en alguns capítols també es realitza un estudi dinàmic dels mètodes aplicats a equacions no lineals per a, posteriorment, extrapolar els resultats al cas multidimensional. A més, com a part d'alguns experiments numèrics, s'ha comparat l'accessibilitat de diferents mètodes numèrics a través de les conques d'atracció representades en diferents plans dinàmics, tant per al cas unidimensional com el multidimensional. Finalment, en la major part dels Capítols d'esta tesi s'apliquen els mètodes iteratius estudiats a la resolució de problemes no lineals de Matemàtica Aplicada. Estos problemes poden estar preparats per a probar la funcionalitat dels algorismes dissenyats o ser problemes reals presents en algunes Ciències Aplicades com l'Enginyeria, la Física, la Química, etc. Els resultats anteriorment descrits formen part de la present Tesi Doctoral per a l'obtenció del títol de Doctora en Matemàtiques. / [EN] Within the field of Numerical Analysis, the resolution of equations and systems of nonlinear equations is one of the most relevant and studied aspects. This is due to the fact that a large number of problems in Applied Mathematics, such as the solution of differential equations, partial differential equations or integral equations among many others, can be reduced to the solution of a non-linear system. Generally, it is very difficult to obtain the analytical solution of this type of problems and, in many cases, although it is possible to find the exact solution, it is very complicated to work with this expression due to its complexity. Moreover, with the development of technologies, great advances have been made in the use of computational tools, so that the dimensions of some of the problems that arise in fields such as Economics, Engineering, Data Science, etc. have grown considerably, giving rise to problems of large dimensions. For these reasons, it is very useful and, in many cases, necessary to solve these non linear problems in an approximate way, of course, with mathematically rigorous techniques within the field of Numerical Analysis. For these reasons, iterative methods for approximating the solution of nonlinear equations and systems of equations have been an important field of research in recent years. The computational implementation of these methods is an important tool in the Applied Sciences as they provide solutions to problems that were difficult to solve in the past. The research carried out in this Doctoral Thesis focuses on the study, design and application of iterative methods that improve certain aspects of classical schemes such as: speed of convergence, applicability to non differential problems, accessibility or efficiency. A large part of the work developed in this thesis focuses on the study of iterative methods for multidimensional problems, in particular, we have specialised on derivative-free schemes. In addition, part of this Doctoral Thesis is centred on the study of the local and semilocal convergence of methods already developed in the recent literature or of new iterative methods designed in this work. This study guarantees the existence of a solution given a starting point, the convergence domain of the solutions of the problem and their uniqueness under certain conditions. To complement the study of the convergence of the methods, in some chapters a dynamical study of the methods applied to nonlinear equations is also carried out in order to extrapolate the results to the multidimensional case. In addition, as part of some numerical experiments, the accessibility of different numerical methods has been compared across the basins of attraction represented in different dynamical planes, both for the unidimensional and the multidimensional case. Finally, in most of the chapters of this thesis, the iterative methods studied are applied to the resolution of non-linear problems in Applied Mathematics. These problems can be prepared to taste the designed algorithms or be real problems present in some Applied Sciences such as Engineering, Physics, Chemistry, etc. The results described above form part of this Doctoral Thesis to obtain the title of Doctor in Mathematics. / García Villalba, E. (2024). Métodos iterativos libres de derivadas para la resolución de ecuaciones y sistemas de ecuaciones no lineales [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/204853