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Dietz, Otto. "Linear and non-linear properties of light." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2016. http://dx.doi.org/10.18452/17474.
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Alle optischen Systeme haben den gleichen Zweck: Sie manipulieren Eigenschaften des Lichts, durch Interaktion mit Materie. In dieser Arbeit werden zwei wichtige Teilaspekte aus diesem Kontext untersucht, im linearen und im nicht-linearen Bereich. In Teil I werden die bekannten Bragg-Reflexionen in neuem Licht betrachtet. Bragg Reflexion findet statt, wenn Licht mit einem periodischen Medium interagiert. Die Bragg-Bedingung verknüpft den Gitterabstand in einem Kristall mit der Wellenlänge, die von ihm reflektiert wird. In dieser Arbeit werden die Bragg Reflexionen in gewellten Wellenleitern untersucht. Es wird gezeigt, dass die Bragg-Bedingung nicht ausreicht, um die Streuung in diesen Wellenleitern zu verstehen. Es wird numerisch und analytisch demonstriert, dass unebene Ränder eine neue Reflexionsbedingung schaffen, die über das einfache Bragg-Bild hinausgeht. Dieser Streueffekt, der Square Gradient Bragg-Mechanismus ist aus statistischen Streuansätzen bekannt. Er hängt mit der Krüummung des Randes zusammen und hat einen starken Einfluss auf die Wellenleitung in diesen Systemen. In dieser Arbeit wird die erste allgemeine Theorie für den Square Gradient Bragg Streumechanismus vorgestellt, die es ermöglicht, Voraussagen für einzelne Wellenleiter mit beliebig deformierten Rändern zu treffen. Eine weitere wichtige Eigenschaft des Lichts wird in Teil II dieser Arbeit untersucht: Die Verschränkung zwischen zwei Photonen. Verschränkung ist ein intuitiv nicht verständliches Phänomen, weil es in der uns umgebenden klassischen Welt kein Analogon hat. Insbesondere verletzt es unsere implizite Annahme eines lokalen Realismus, weil voneinander entfernte Teilchen scheinbar instantan miteinander wechselwirken können. In dieser Arbeit wird eine neue und verstimmbare Quelle für verschränkte Photonen entworfen. Die Photonenpaare werden in nicht-linearen Kristallen erzeugt, aber ihre Verschränkung wird rein geometrisch erzwungen. Dieser geometrische Ansatz erlaubt es, die Frequenz der Photonen einzustellen. Hier übertrifft diese neue Quelle ihre Vorgänger, die ausführlich besprochen werden. Die Verschränkung der erzeugten Photonen wird experimentell nachgewiesen.Any optical experiment, any optical technology is only about one thing: Manipulating the properties of light through interaction with matter. This thesis will address two important issues in this broad context, in the linear and in the non-linear regime. In Part I, the well-known Bragg reflection is revised. Bragg reflection takes place whenever light interacts with a periodic structure. The famous Bragg condition relates the lattice spacing in a crystal to the wavelength which is effectively reflected by that lattice. In this thesis the Bragg reflection in dielectric waveguides is investigated. It is shown that the Bragg condition is not sufficient to describe the scattering situation in waveguides with corrugated boundaries. It is demonstrated, analytically and numerically, that corrugated boundaries cause a new type of reflection condition, which goes beyond the Bragg picture. This scattering mechanism, the Square Gradient Bragg Scattering, is known from statistical scattering approaches. It is connected to the curvature of the boundary and has a strong influence on the wave propagation in these systems. Here the first general theory for Square Gradient Bragg Scattering is presented, which allows for making predictions for single corrugated waveguides with arbitrary boundaries. Another important property of light is investigated in Part II of this thesis: The entanglement of two photons. Entanglement is a counter-intuitive phenomenon, because it has no classical analogy. It especially violates our assumption of local realism, because distant particles seemingly act on each other instantaneously. In this thesis a new tunable and portable source of photon pairs is designed. The photon pairs are created in non-linear crystals, but their entanglement is enforced in a purely geometrical manner. This geometrical approach makes the setup tunable. This is where the new design supersedes its predecessor, which will be discussed in detail. The entanglement of the generated photons is demonstrated experimentally.
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Trussell, Christine. "The works of Cy Twombly : non-linear language and non-linear consciousness." Thesis, Oxford Brookes University, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.325293.
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Shabat, Mohammed Musa Ramadan. "Linear and non-linear electromagnetic waves at magnetic and non-magnetic interfaces." Thesis, University of Salford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.277642.
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Chia, John. "Non-linear contextual bandits." Thesis, University of British Columbia, 2012. http://hdl.handle.net/2429/42191.
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The multi-armed bandit framework can be motivated by any problem where there is an abundance of choice and the utility of trying something new must be balanced with that of going with the status quo. This is a trade-off that is present in the everyday problem of where and what to eat: should I try a new restaurant or go to that Chinese place on the corner? In this work, a multi-armed bandit algorithm is presented which uses a non-parametric non-linear data model (a Gaussian process) to solve problems of this sort. The advantages of this method over existing work is highlighted through experiments. The method is also capable of modelling correlations between separate instances of problems, e.g., between similar dishes at similar restaurants. To demonstrate this, a few experiments are performed. The first, a synthetic example where the reward function is actually sampled from a Gaussian process, begs the question but helps pin down the properties of the algorithm in a controlled environment. The second, a problem where the objective is to aim a cannon at a distant target, shows how a well-defined objective, i.e., hit the target, can be used to speed up convergence. Finally, the third, an experiment with photographic post-processing, shows how the algorithm can learn from experience. The experiments demonstrate both the flexibility and the computational complexity of the model. This complexity means that problems such as the aforementioned restaurant problem, among others, are still future work.
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Alberte, Lāsma. "Non-linear massive gravity." Diss., Ludwig-Maximilians-Universität München, 2013. http://nbn-resolving.de/urn:nbn:de:bvb:19-159425.
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Massive gravity is a particular theoretical model that modifies gravity on cosmological scales and therefore could provide a dynamical explanation for the observed accelerated expansion of our Universe. In this thesis we investigate various theoretical problems of massive gravity, important for its consistency and phenomenological viability. It is known that the predictions from the linearized massive gravity contradict the predictions of General Relativity. It is, however, an artifact due to the breakdown of the perturbative expansion in the massless limit. In our work we investigate this problem in the diffeomorphism invariant formulation of massive gravity in which the graviton mass term is written in terms of four scalar fields. We determine the so-called Vainshtein scale below which the scalar modes of the massive graviton enter the non-perturbative regime for a wide class of non-linear mass terms. We find the asymptotic solutions of the spherically symmetric gravitational field below and above the Vainshtein radius, and show that massive gravity goes smoothly to the General Relativity below this scale. We also determine the corresponding corrections to the Newton potential. In general, any non-linear extension of the quadratic graviton mass term propagates the Boulware-Deser ghost. The only theory in which the ghost is not propagating in the high energy decoupling limit, is the de Rham-Gabadadze-Tolley theory. Here we show that the ghost arises in the fourth order of perturbations in this theory away from the decoupling limit. However, we further argue that the ghost can be avoided in the full non-linear theory if not all four scalar fields propagate independent degrees of freedom. In particular, we investigate the simple example of (1+1)-dimensional massive gravity and find that the theory exhibits a gauge symmetry, which reduces the number of degrees of freedom. We also generalize the diffeomorphism invariant formalism of massive gravity to arbitrary curved backgrounds. We find that, given a specific background metric, the resulting generally covariant massive gravity exhibits an internal symmetry in the configuration space of the scalar fields. The symmetry transformations of the scalar fields are given by the isometries of the reference metric. In particular, we investigate massive gravity on de Sitter space in this formalism. We confirm the known result that, in the case when the graviton mass is related to the cosmological constant as m^2=2\Lambda/3, the theory is partially massless and propagates only four degrees of freedom.Massive Gravitation ist ein theoretisches Modell, welches Gravitation auf kosmologischen Längenskalen modifiziert, und das so eine dynamische Erklärung für die beobachtete Beschleunigung der Expansion des Universums liefern könnte. In dieser Arbeit untersuchen wir verschiedene theoretische Probleme der massiven Gravitation, die wichtig bezüglich der Konsistenz und phänomenologischen Viabilität der Theorie sind. Es ist bekannt, dass die Vorhersagen der massiven Gravitation auf linearer Ordnung den Vorhersagen der allgemeinen Relativitätstheorie widersprechen. Dies ist jedoch ein Artefakt, das vom Zusammenbruch der perturbativen Entwicklung im masselosen Limes verursacht wird. In unserer Arbeit untersuchen wir dieses Problem in der Diffeomorphismen-invarianten Formulierung der massiven Gravitation, in der der Graviton-Massenterm mit vier skalare Feldern ausgedrückt wird. Wir bestimmen die sogenannte Vainshtein-Skala, unterhalb derer sich die skalaren Moden des massiven Gravitons nichtperturbativ verhalten, für eine große Klasse möglicher Massenterme. Wir finden die asymptotischen Lösungen des sphärisch symmetrischen Gravitationsfeldes inner- und außerhalb des Vainshtein-Radiuses und zeigen, dass massive Gravitation sich unterhalb dieser Skala kontinuierlich der Allgemeinen Relativitätstheorie annähert. Außerdem bestimmen wir die resultierenden Korrekturen zum Newton-Potential. Im Allgemeinen propagiert in jeder Theorie mit einer nichtlinearen Erweiterung des quadratischen Graviton-Massenterms ein Boulware-Deser Geist. Die einzige solche Theorie, in der der Geist im Hochenergie-Entkopplungslimes nicht propagiert, ist das de Rham-Gabadadze-Tolley Modell. Hier zeigen wir, dass der Geist selbst in dieser Theorie außerhalb des Entkopplungslimes in vierter Ordnung Störungstheorie erscheint. Wir argumentieren dann jedoch, dass der Geist in der voll nichtlinearen Theorie vermeiden werden kann, wenn nicht alle Skalarfelder unabhängige Freiheitsgrade darstellen. In dieser Hinsicht untersuchen wir das einfache Beispiel (1+1)-dimensionaler massiver Gravitation und finden, dass diese Theorie eine Eichsymmetrie enthält, die die Anzahl der Freiheitsgrade reduziert. Schließlich verallgemeinern wir den Diffeomorphismen-invarianten Formalismus massiver Gravitation auf allgemeine gekrümmte Hintergründe. Wir finden, dass auf bestimmten Hintergründen die resultierende allgemein kovariante massive Gravitation eine Symmetrie im Konfigurationsraum der skalaren Felder aufweist. Die Symmetrietransformationen der skalaren Felder sind durch die Isometrien der Referenzmetrik gegeben. Insbesondere untersuchen wir massive Gravitation auf de Sitter-Raum in diesem Formalismus. Wir bestätigen das bekannte Ergebnis, dass, im Falle einer Gravitonmasse im Verhältnis zur kosmologischen Konstante von m^2=2\Lambda/3, die Theorie teilweise masselos ist. Dadurch propagieren in diesem Fall nur vier Freiheitsgrade.
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Bosher, Simon Henry Bruce. "Non-linear elasticity theory." Thesis, Queen Mary, University of London, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.407883.
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Assadullahi, Hooshyar. "Non-Linear Cosmological Perturbations." Thesis, University of Portsmouth, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.523623.
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Bowtell, Philip. "Non-linear functional relationships." Thesis, University of Reading, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.284183.
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Lamb, Richard Hubbert. "Parametric non-linear filtering." Thesis, Massachusetts Institute of Technology, 1987. http://hdl.handle.net/1721.1/14463.
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Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1987.Vita.
Includes bibliographical references (p. 183-184).
by Richard H. Lamb, Jr.
Sc.D.
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Rigopoulos, Gerasimos I. "Non-linear inflationary perturbations." Thesis, University of Cambridge, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.614830.
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Sun, Yi. "Non-linear hierarchical visualisation." Thesis, Aston University, 2002. http://publications.aston.ac.uk/13263/.
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This thesis applies a hierarchical latent trait model system to a large quantity of data. The motivation for it was lack of viable approaches to analyse High Throughput Screening datasets which maybe include thousands of data points with high dimensions. We believe that a latent variable model (LTM) with a non-linear mapping from the latent space to the data space is a preferred choice for visualising a complex high-dimensional data set. As a type of latent variable model, the latent trait model can deal with either continuous data or discrete data, which makes it particularly useful in this domain. In addition, with the aid of differential geometry, we can imagine that distribution of data from magnification factor and curvature plots. Rather than obtaining the useful information just from a single plot, a hierarchical LTM arranges a set of LTMs and their corresponding plots in a tree structure. We model the whole data set with a LTM at the top level, which is broken down into clusters at deeper levels of the hierarchy. In this manner, the refined visualisation plots can be displayed in deeper levels and sub-clusters may be found. Hierarchy of LTMs is trained using expectation-maximisation (EM) algorithm to maximise its likelihood with respect to the data sample. Training proceeds interactively in a recursive fashion (top-down). The user subjectively identifies interesting regions on the visualisation plot that they would like to model in a greater detail. At each stage of hierarchical LTM construction, the EM algorithm alternates between the E - and M - step. Another problem that can occur when visualising a large data set is that there may be significant overlaps of data clusters. It is very difficult for the user to judge where centres of regions of interest should be put. We address this problem by employing the minimum message length technique, which can help the user to decide the optimal structure of the model.
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Morad, Farhad. "Non-linear Curve Fitting." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-43600.
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The work done in this thesis is to examine various methods for curve fitting. Linear least squares and non-linear least squares will be described and compared, and the Newton method, Gauss--Newton method and Levenberg--Marquardt method will be applied to example problems.Syftet med denna uppsats är att beskriva och använda olika metoder för kurvanpassning, det vill säga att passa matematiska funktioner till data. De metoder som undersöks är Newtons metod, Gauss--Newton metoden och Levenberg--Marquardt metoden. Även skillnaden mellan linjär minsta kvadrat anpassning och olinjär minsta kvadrat anpassning. Till sist tillämpas Newton, Gauss Newton och Levenberg--Marquardt metoderna på olika exempel.
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Persson, Jonas. "Linear models of non-linear power system components." Licentiate thesis, KTH, Electrical Systems, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-1415.
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Milillo, Irene. "Linear and non-linear effects in structure formation." Thesis, University of Portsmouth, 2010. https://researchportal.port.ac.uk/portal/en/theses/linear-and-nonlinear-effects-in-structure-formation(a5115b9e-d7af-4255-83bd-ddb7913c1e31).html.
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The subject matter of this thesis is the formation of large-scale structure in the universe. Most of the study has dealt with the non-linear evolution of cosmological uctuations, focusing on the scalar sector of perturbation theory. The period of transition between the radiation era and the matter era has been largely examined, extending the already known linear results to a nonstandard matter model and to a non-linear analysis. The obtained second order solutions for the matter uctuations variables have been used to find the skewness of the density and velocity distributions, an important statistical estimator measuring the level of non-Gaussianity of a distribution. In the context of cosmological perturbations, a complete Post-Newtonian (1PN) treatment is presented with the aim of obtaining a set of equations suitable in particular for the intermediate scales. The final result agrees with both the non linear Newtonian theory of small scales and the linear general relativistic theory of large scales. Analyzing the limiting cases of our approach to 1PN cosmology, we have clarified the link between the Newtonian theory of gravity and General Relativity. This work is the result of the agreement signed by the Department of Physics, University of Roma Tor Vergata and the Institute of Cosmology and Gravitation, University of Portsmouth, United Kingdom in the formal context of the co-tutela project. The chapters 5, 6 and 7 are the themes of two articles in preparation, that will be shortly submitted: "How the universe got its skewness" - M. Bruni, I.Milillo, K.Koyama; "Post-Newtonian Cosmology" - I. Milillo, D.Bertacca, M. Bruni
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Strandell, Gustaf. "Linear and Non-linear Deformations of Stochastic Processes." Doctoral thesis, Uppsala : Matematiska institutionen, Univ. [distributr], 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3689.
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Koch, Frank. "Linear and non-linear measurements in optical fibres." Thesis, Imperial College London, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.399244.
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Lampietti, Dario Giovanni. "Foreign exchange markets linear vs. non-linear models /." [Zürich] : [Citibank], 1993. http://www.ub.unibe.ch/content/bibliotheken_sammlungen/sondersammlungen/dissen_bestellformular/index_ger.html.
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MILILLO, IRENE. "Linear and non-linear effects in structure formation." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2010. http://hdl.handle.net/2108/1246.
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La tesi riguarda la formazione di strutture a larga scala nell'universo, cioè l'origine degli addensamenti di materia che hanno portato alla formazione dei cluster di galassie. La maggior parte del lavoro ha riguardato aspetti non lineari della Teoria delle Perturbazioni Cosmologiche, trattando in particolare il periodo di transizione tra epoca della radiazione e epoca della materia. In questo contesto si è considerato un modello non-standard di materia, analizzando il ruolo dell'indice barotropico nell'evoluzione del contrasto di densità .
La nota approssimazione Meszaros è stata generalizzata ad una analisi non lineare che ha permesso di trovare la skewness della distribzione di materia, un importante indice di non-Gaussianità rilevabile dai dati osservativi.
Nel contesto delle perturbazioni cosmologiche è stata formulata la teoria Post-Newtoniana (1PN) con lo scopo di ottenere un set di equazioni valido per ogni range di distanze, in particolare per le scale intermedie. I risultati finali coincidono sia con la teoria lineare relativistica per grandi scale sia con la teoria non lineare Newtoniana per piccole scale; quest'ultima connessione fornisce una chiara visione della relazione fra Relatività Generale e teoria Newtoniana.The subject matter of this thesis is the formation of large-scale structure in the universe, describing the clustering of matter in galaxies and clusters of galax- ies. Most of the study has dealt with the non-linear evolution of cosmological fluctuations, focusing on the scalar sector of perturbation theory. The period of transition between the radiation era and the matter era has been largely examined, extending the already known linear results to a non-standard matter model and to a non-linear analysis. The obtained second order solutions for the matter fluctuations variables have been used to find the skewness of the density and velocity distributions, an important statistic estimator measuring the level of non-Gaussianity of a statistic ensamble. In the contest of cosmological perturbations a complete Post-Newtonian (1PN) treatment is presented with the aim of obtain a set of equations suitable in particular for the intermediate scales. The final result agrees with both the non linear Newtonian theory of small scales and the linear general relativistic theory of large scales. Analyzing the limit cases of our approach to 1PN cosmology, we have clarified the link between the Newtonian theory of gravity and General Relativity.
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Schittenkopf, Christian, Georg Dorffner, and Engelbert J. Dockner. "Non-linear versus non-gaussian volatility models." SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, 1999. http://epub.wu.ac.at/724/1/document.pdf.
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One of the most challenging topics in financial time series analysis is the modeling of conditional variances of asset returns. Although conditional variances are not directly observable there are numerous approaches in the literature to overcome this problem and to predict volatilities on the basis of historical asset returns. The most prominent approach is the class of GARCH models where conditional variances are governed by a linear autoregressive process of past squared returns and variances. Recent research in this field, however, has focused on modeling asymmetries of conditional variances by means of non-linear models. While there is evidence that such an approach improves the fit to empirical asset returns, most non-linear specifications assume conditional normal distributions and ignore the importance of alternative models. Concentrating on the distributional assumptions is, however, essential since asset returns are characterized by excess kurtosis and hence fat tails that cannot be explained by models with suffcient heteroskedasticity. In this paper we take up the issue of returns' distributions and contrast it with the specification of non-linear GARCH models. We use daily returns for the Dow Jones Industrial Average over a large period of time and evaluate the predictive power of different linear and non-linear volatility specifications under alternative distributional assumptions. Our empirical analysis suggests that while non-linearities do play a role in explaining the dynamics of conditional variances, the predictive power of the models does also depend on the distributional assumptions. (author's abstract)Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"
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Neff, Andrew. "Linear and non-linear control of a quadrotor UAV." Connect to this title online, 2007. http://etd.lib.clemson.edu/documents/1181251774/.
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Hagan, Richard Peter. "Linear and Non-Linear Aspects of the Multifocal-Electroretinogram." Thesis, University of Liverpool, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.507506.
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Naruko, Atsushi. "Non-linear Cosmological Perturbation Theory." 京都大学 (Kyoto University), 2012. http://hdl.handle.net/2433/157769.
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Liangrocapart, Sompong. "Non-linear spectral mixing models." Thesis, University of Surrey, 2001. http://epubs.surrey.ac.uk/842807/.
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In this research study, non-linear spectral mixing models have been developed and employed to achieve unmixing the proportions of components accurately and retrieving the physical parameters of the mixture. The first focus is on a comparative study of linear and non-linear spectral mixing models. A carefully-controlled experiment was conducted in the laboratory. The aim is to test both models to unmix ternary powdered-chalk mixtures by using the directional reflectance data. The results demonstrated the superiority of the non-linear model over the linear model. However, there was at least one case when the linear model produced more accurate results than the non-linear model. As a consequence, a hypothesis was made that the directional reflectance data obtained from certain measurement geometries may not contain useful information for deriving surface parameters. In order to investigate this, an error analysis was employed to observe the sensitivity to error of a physical parameter, which is needed in the non-linear unmixing, when estimated from directional reflectance data at certain measurement geometries. This theoretical investigation was tested against reflectance data of mineral mixtures obtained from a laboratory experiment. The results showed that the unmixing could be improved when the angular measurements were carefully chosen. Information contained in each surface measurement can be useful or damaging depending on the measurement geometry and the brightness of the surface itself. The next focus is on the utilisation of non-linear spectral mixing model to retrieve the biophysical properties of vegetation canopies by means of a canopy reflectance modelling. A two-layer model of the bidirectional reflectance of homogeneous vegetation canopies was proposed in this study. The anisotropic scatterings of both the vegetation canopy and the background were taken into account. This new model was validated against simulated and field-measurement data. The results showed that this model can be used to model the bidirectional reflectance and to retrieve the optical properties of canopy elements (leaves) and background of a homogeneous canopy. Finally, a simple non-linear spectral mixing model was developed. The second order interaction between vegetation and soil was taken into account. Results from the experiments showed that the vegetation cover and leaf area index of moderate density canopies can be retrieved by using this model.
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Berg, Joris van den. "Non-linear sand wave evolution." Enschede : University of Twente [Host], 2007. http://doc.utwente.nl/57884.
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Baldock, Thomas Edward. "Non-linear transient water waves." Thesis, Imperial College London, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.432369.
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Price, C. J. "Non-linear semi-infinite programming." Thesis, University of Canterbury. Mathematics and Statistics, 1992. http://hdl.handle.net/10092/7920.
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Optimisation problems occur in many branches of science, engineering, and economics, as well as in other areas. The diversity of the various types of optimisation problems is extremely large, and so a unified approach is not attempted here. This thesis concentrates on a specific type of problem: non-linear semi-infinite programming.
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Moni, Jacob Ngilla. "Non linear two layer flows." Thesis, Keele University, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.240022.
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Townsend, Shane Martin Joseph. "Non-linear model predictive control." Thesis, Queen's University Belfast, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.301061.
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Minne, Andreas. "Non-linear Free Boundary Problems." Doctoral thesis, KTH, Matematik (Avd.), 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-178110.
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This thesis consists of an introduction and four research papers related to free boundary problems and systems of fully non-linear elliptic equations. Paper A and Paper B prove optimal regularity of solutions to general elliptic and parabolic free boundary problems, where the operators are fully non-linear and convex. Furthermore, it is proven that the free boundary is continuously differentiable around so called "thick" points, and that the free boundary touches the fixed boundary tangentially in two dimensions. Paper C analyzes singular points of solutions to perturbations of the unstable obstacle problem, in three dimensions. Blow-up limits are characterized and shown to be unique. The free boundary is proven to lie close to the zero-level set of the corresponding blow-up limit. Finally, the structure of the singular set is analyzed. Paper D discusses an idea on how existence and uniqueness theorems concerning quasi-monotone fully non-linear elliptic systems can be extended to systems that are not quasi-monotone.QC 20151210
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Ganapathy, Annadurai Shathiyakkumar. "Non-Linear Electromechanical System Dynamics." ScholarWorks@UNO, 2014. http://scholarworks.uno.edu/td/1799.
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Electromechanical systems dynamics analysis is approached through nonlinear differential equations and further creating a state space model for the system. There are three modules analyzed and validated, first module consists two magnet coupled with a mass spring damper system as a band-pass system, Low-pass equivalent system and Low-pass equivalent system through perturbation analysis. Initially Band Pass frameworks for the systems are formulated considering the relation between the mechanical forcing and current. Using Mathematical tools such as Hilbert transforms, Low-Pass equivalent of the systems are derived. The state equations of the systems are then used to design a working model in MATLAB and simulations investigated completely. The scope of the modules discussed for further development of tools various applications.
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Wokiyi, Dennis. "Non-linear inverse geothermal problems." Licentiate thesis, Linköpings universitet, Matematik och tillämpad matematik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-143031.
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The inverse geothermal problem consist of estimating the temperature distribution below the earth’s surface using temperature and heat-flux measurements on the earth’s surface. The problem is important since temperature governs a variety of the geological processes including formation of magmas, minerals, fosil fuels and also deformation of rocks. Mathematical this problem is formulated as a Cauchy problem for an non-linear elliptic equation and since the thermal properties of the rocks depend strongly on the temperature, the problem is non-linear. This problem is ill-posed in the sense that it does not satisfy atleast one of Hadamard’s definition of well-posedness. We formulated the problem as an ill-posed non-linear operator equation which is defined in terms of solving a well-posed boundary problem. We demonstrate existence of a unique solution to this well-posed problem and give stability estimates in appropriate function spaces. We show that the operator equation is well-defined in appropriate function spaces. Since the problem is ill-posed, regularization is needed to stabilize computations. We demostrate that Tikhonov regularization can be implemented efficiently for solving the operator equation. The algorithm is based on having a code for solving a well- posed problem related to the operator equation. In this study we demostrate that the algorithm works efficiently for 2D calculations but can also be modified to work for 3D calculations.
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Chen, Hua, Wei-Xi Li, and Chao-Jiang Xu. "Gevrey hypoellipticity for linear and non-linear Fokker-Planck equations." Universität Potsdam, 2007. http://opus.kobv.de/ubp/volltexte/2009/3028/.
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Häggström, Lundevaller Erling. "Tests of random effects in linear and non-linear models." Doctoral thesis, Umeå universitet, Statistik, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-15.
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Häggström, Lundevaller Erling. "Tests of random effects in linear and non-linear models /." Umeå : Department of Statistics, University of Umeå, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-15.
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Miao, Quan. "Nuclear Dynamics in Linear and Non-linear X-ray Processes." Doctoral thesis, KTH, Teoretisk kemi och biologi, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-133432.
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New generations of brilliant synchrotron radiation sources and intense X-ray and optical lasers have opened unprecedent opportunities in linear and non-linear spectroscopies of molecules. This together with new instrumentation calls for further development of theory to explain observations and suggest new experiments. These two goals are the main objectives of the present thesis. In the first part of the thesis we study resonant inelastic X-ray scattering of the oxygen molecule. Recent experimental data of O2 show the dependence of the vibrational profile on the polarization of the X-rays. This vibrational scattering anisotropy is explained by the interference of the resonant and nonresonant inelastic scattering channels in O2. The second part of the thesis explores X-ray lasing caused by ultrafast dissociation of the HCl molecule in a repulsive core-excited state pumped by an X-ray free-electron laser. We show that the lasing efficiency is drastically enhanced due to the self-trapping of the amplified pulse into the ridge of the gain. The third part of the thesis is devoted to another non-linear phenomenon - optical limiting. Our time-dependent simulations are in agreement with the experimental data and show that phthalocyanines with heavy central metals exhibit good optical limiting properties for nanosecond pulses. Symmetry and the symmetry breaking are important fundamental concepts in physics, chemistry and biology. In the next part of the thesis we study theoretically the novel symmetry breaking mechanism in resonant Auger scattering. Both theory and electron-ion coincidence measurements for the oxygen molecule evidence the symmetry breaking of the oxygen cation caused by momentum exchange between the fast Auger electron and counter propagating dissociating oxygen atoms. The last part of the thesis is devoted to the role of the rotational degrees of freedom in X- ray ionization of molecules. We present here new results related to the rotational Doppler and angular recoil effects in X-ray ionization using the N2 and HCl molecules as illustrating examples. The dependence of the ionization cross section on the direction of ejection of fast electrons explains the sensitivity of the rotational broadening to the final state and to the polarization of X-rays observed recently for the N2 molecule. The theory reveals the novel effect of site-selectivity of X-ray valence ionization caused by the excitation of the rotational degrees of freedom which is different for different ionization sites. Large recoil angular momentum related to the ejection of an electron from the light hydrogen atom results in a red shifted broad pedestal in the X-ray photoelectron spectrum of HCl.QC 20131108
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Pechev, Alexandre Nikolov. "Robust linear and non-linear control of magnetically levitated systems." Thesis, Cardiff University, 2004. http://orca.cf.ac.uk/55944/.
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The two most advanced applications of contactless magnetic levitation are high-speed magnetic bearings and magnetically levitated vehicles (Maglev) for ground transportation using superconducting magnets and controlled d.c. electromagnets. The repulsion force from superconducting magnets provide stable levitation with low damping, while the suspension force generated by electromagnets is inherently unstable. This instability, due to the in verse force-distance relationship, requires the addition of feedback controllers to sustain stable suspension. The problem of controlling magnetically levitated systems using d.c. electromagnets under different operating conditions has been studied in this thesis with a design process primarily driven by experimental results from a representative single-magnet test rig and a multi-magnet vehicle. The controller-design stages are presented in detail and close relationships have been constructed between selection of performance criteria for the derivation process and desired suspension characteristics. Both linear and nonlinear stabilising compensators have been developed. Simulation and experimental results have been studied in parallel to assess operational stability and the main emphasis has been given to assessing performance under different operational conditions. For the experimental work, a new digital signal processor-based hardware platform has been designed, built with interface to Matlab/Simulink. The controller design methods and algorithmic work presented in this thesis can be divided into: non-adaptive, adaptive, optimal linear and nonlinear. Adaptive algorithms based on model reference control have been developed to improve the performance of the suspension system in the presence of considerable variations in external payload and force disturbances. New design methods for Maglev suspension have been developed using robust control theory (%oo and fi synthesis). Single- and multi-magnet control problems have been treated using the same framework. A solution to the Hoo controller-optimisation problem has been derived and applied to Maglev control. The sensitivity to robustness has been discussed and tools for assessing the robustness of the closed-loop system in terms of sustaining stability and performance in the presence of uncertainties in the suspension model have been presented. Multivariable controllers based on %00 and /i synthesis have been developed for a laboratory scale experimental vehicle weighing 88 kg with four suspension magnets, and experimental results have been derived to show superiority of the proposed design methods in terms of ability to deal with external disturbances. The concept of Hoo control has been extended to the nonlinear setting using the concepts of energy and dissipativity, and nonlinear state-feedback and out put-feed back controllers for Maglev have been developed and reported. Simulation and experimental results have been presented to show the improved performance of these controllers to attenuate guideway-induced disturbances while maintaining acceptable suspension qualities and larger operational bandwidth.
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Rahimzadeh, Behzad. "Linear and non-linear viscoelastic behaviour of binders and asphalts." Thesis, University of Nottingham, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.246403.
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Womersley, Martin Nigel. "Linear and non-linear optical properties of electro-optic crystals." Thesis, University of Warwick, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.263787.
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Wilcox, Samuel L. "Constructing quasi-linear oxygen uptake responses from non-linear parameters." Thesis, Kansas State University, 2014. http://hdl.handle.net/2097/18706.
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Master of ScienceDepartment of Kinesiology
Thomas J. Barstow
Purpose: Oxygen uptake (VO2) has been shown to be controlled by a nonlinear system, yet the VO2 response to ramp style exercise appears linear. We tested the hypothesis that an integrative model incorporating nonlinear parameter values could accurately estimate actual VO2 responses to ramp style exercise. Methods: Six healthy, men completed three bouts of varying ramp rate exercise (slow ramp (SR): 15 W/min, regular ramp (RR) 30 W/min, fast ramp (FR) 60W/min) and four bouts of extended-step incremental exercise, where each step lasted 5-15 min or until volitional fatigue on a cycle ergometer on separate days. The step-responses were then fit with a simple monoexponential starting at time zero (MONO) or allowing a time delay and using only the first 5 min of data (5TD). The resulting VO2 parameters from the step protocol were incorporated into an integrative model for the estimation of the VO2 response to each of the rates of ramp incremental exercise. The parameters from the actual and model ramp protocols were compared with 2 way repeated-measures ANOVAs. Results: Both Gain (G) and Mean Response Time (MRT) (or time constant) values increased significantly across work rate transitions (mean±SD; Gain:10.0±0.9, 11.6±1.1, 13.1±1.3, 17.6±3.3 ml O2/min/W; MRT:39.4±7.7, 54.0±5.4, 79.6±15.0, 180.1±56.2 s). Up to maximalVO2 the models over-estimated the actual VO2 response for FR (Gain: ACT 8.7±1.0, MONO 9.9±0.4, 5TD 10.3±0.3 ml O2/min/W). Up to 80% maximal VO2 the models accurately predicted the actual VO2 response across all ramp rates (Gain: ACT 10.7±1.1, 10.2±0.5, 9.2±1.0; MONO 11.0±0.8, 10.3±0.6, 9.2±0.5; 5TD 10.4±0.4, 10.2±0.3, 9.8±0.2 ml O2/min/W, values are listed SR,RR,FR). Conclusions: When variable parameter values (G and either MRT or time constant and time delay) were utilized by an integrative model, accurate estimations of the VO2 response to ramp incremental exercise were possible regardless of ramp rate (up to 80% maximal VO2). The increases in both G and MRT (or time constant) appear to balance each other to produce the quasi-linear VO2 responses.
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Escobar-Ruiz, Edwill Alejandro. "Linear and non-linear ultrasonic NDE of titanium diffusion bonds." Thesis, Imperial College London, 2014. http://hdl.handle.net/10044/1/28681.
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Diffusion bonding is an attractive solid-state welding technique that promises weight reduction and improved performance in the aerospace industry. However, its adoption in fracture critical titanium components has been limited by the complications that macroscopic anisotropy introduces to typical ultrasonic NDE. Two strands of ultrasonic NDE, linear and non-linear acoustics, have been studied with the aim of overcoming these complications. A promising linear technique that uses the phase of reflected diffusion-bond signals to extract otherwise hidden interface information was selected for further development. The principal parameters that affect the phase analysis of ultrasonic signals were investigated and their optimisation resulted in up to an order of magnitude improvement in phase measurement reliability, even at low signal-to-noise ratios. The application of these optimised parameters without a priori knowledge of the signal arrival time was illustrated, and the sensitivity of the approach to ambient temperature and annealing effects was also explored. The original technique was susceptible to measurement error and proved impractical for typical aerospace component geometries, but these shortcomings have been overcome by the improvements and adaptations proposed here. However, it was shown that the efficacy of the technique depends on the relative acoustic impedances of the bonded media and, coupled with the sensitivity limit intrinsic to linear acoustic methods, this dependence acted to curtail the benefits of the approach and prompted the exploration of alternative techniques. Non-linear ultrasonic methods are significantly more sensitive than their linear counterparts to the imperfections likely to be present at diffusion-bonded interfaces, but suppressing extraneous contributions to the non-linear response of the interface is not trivial. An approach that succeeds in suppressing such contributions was studied and developed here. The technique, which is based on the non-collinear mixing of ultrasonic waves to generate a spectrally, modally and spatially dissociable third wave, was used to reliably characterise a set of samples whose bond quality was indeterminable using linear ultrasonic methods. Application of the technique to diffusion-bonded titanium aerospace components has been demonstrated and a significant improvement in ultrasonic NDE capability was achieved.
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Croft, Lance Calloway. "Interpolating Beach Profile Data Using Linear and Non-linear Functions." Scholar Commons, 2014. https://scholarcommons.usf.edu/etd/5206.
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ABSTRACT
Beach and nearshore surveys are conducted in a variety of ways, the most commonly used being the level-and-transit method; because it is inexpensive, time conducive and highly accurate. Specifically, beach surveys are conducted to better understand cross-shore, long-shore sediment transport processes, as well as to quantify volume changes, which are used to evaluate beach performance. In this study, a section of the beach on Sand Key, FL was surveyed using rod-and-transit. In addition to the commonly used linear data analysis, a non-linear analysis was conducted using NURBS (Non-Uniform Rational B-Splines).
Survey data was collected within a short time window to ensure minimal environmental changes associated with waves and anthropological factors. Beach profiles were surveyed using two spatial resolutions, including 1) a typical variable resolution determined by the rodman based on observed morphology changes, and 2) a uniform, high resolution of 25 centimeters per point. The results indicate that variable resolution survey with careful observation by the rodman provided adequate accuracy as compared to the very high-resolution survey.
The goal of this study is to create a realistic surface between the beach profiles that are spaced relatively far apart. The commonly used contouring method (a linear method) may create mismatch among major morphology units, .e.g., bar crest, if they have different elevations alongshore. Here a non-linear method is developed by 1) identifying major morphological units, in this case dune top, berm crest, trough bottom, and bar crest 2) linking the units using a cubic spline, and 3) generating a surface using a NURBS sweep2 function. Bisector profiles are sliced from the surface generated using linear and non-linear methods, and compared with surveyed profiles at the same location. The profiles generated using the non-linear method matched more closely to the measured profile than that from the linear method. The non-linear NURBS surface resulted in a consistently greater beach volume between the surveyed profiles than the linear method of volume calculation.
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Mancinelli, Mattia. "Linear and non linear coupling effects in sequence of microresonators." Doctoral thesis, Università degli studi di Trento, 2013. https://hdl.handle.net/11572/369276.
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My work was carried out with the aim of devising and characterize novel integrated devices for signal routing in optical networks on chip. Several type of optical microresonators, both in a single and coupled configuration (CROW, SCISSOR), are discussed starting from the fundamental theory till dealing with novel configurations. The coupling between a Mach-Zehnder interferometer and such configuration of microresonators is also investigated. Since the used material platform is the silicon on insulator (SOI), an in depth study of the microresonators behaviour has demanded an investigation in both in the linear and non-linear regime.
All devices were fabricated through a standard CMOS facility by using deep UV lithography in order to verify the reliability of resolution and throughput similar to those required for commercial applications. Particular attention has been paid in the study of structures robust with respect to manufacturing defects.
All the steps necessary to develop a device for integrated optics are studied in deep: device conception, device simulations through analytic and FEM simulations, GDS mask design, experimental characterizations.
All the devices parameters are carefully reported to allow the reproduction of the experimental results. Where it was possible, suggestions on how to improve the fabricated devices performance were given.
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Mancinelli, Mattia Mancinelli. "Linear and non linear coupling effects in sequence of microresonators." Doctoral thesis, University of Trento, 2013. http://eprints-phd.biblio.unitn.it/1050/1/Doctoral_thesis_Mattia_Mancinelli_2013.pdf.
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My work was carried out with the aim of devising and characterize novel integrated devices for signal routing in optical networks on chip. Several type of optical microresonators, both in a single and coupled configuration (CROW, SCISSOR), are discussed starting from the fundamental theory till dealing with novel configurations. The coupling between a Mach-Zehnder interferometer and such configuration of microresonators is also investigated. Since the used material platform is the silicon on insulator (SOI), an in depth study of the microresonators behaviour has demanded an investigation in both in the linear and non-linear regime.
All devices were fabricated through a standard CMOS facility by using deep UV lithography in order to verify the reliability of resolution and throughput similar to those required for commercial applications. Particular attention has been paid in the study of structures robust with respect to manufacturing defects.
All the steps necessary to develop a device for integrated optics are studied in deep: device conception, device simulations through analytic and FEM simulations, GDS mask design, experimental characterizations.
All the devices parameters are carefully reported to allow the reproduction of the experimental results. Where it was possible, suggestions on how to improve the fabricated devices performance were given.
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Torres, Ledesma César Enrique. "Non linear ellipter equations with non-local regional operators." Tesis, Universidad de Chile, 2013. http://www.repositorio.uchile.cl/handle/2250/115927.
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Doctor en Ciencias de la Ingeniería, Mención Modelación MatemáticaEsta tesis consiste de cinco partes. En la primera parte se considera el problema de Dirichlet lineal y no lineal con una difusi\'on no local regional definido implicitamente por \!\!donde $0< \alpha < 1$, $\rho \in C(\overline)$ y $\lambda dist(x,\partial \Omega) \leq \rho (x) \leq dist(x, \partial \Omega)$ con $\lambda \in (0,1]$, $x\in \Omega$. Haciendo uso del teorema de Lax-Milgran y el Teorema del paso de la monta\~na se demuestra la existencia de soluciones d\'ebiles. En la segunda parte, se considera la ecuaci\'on de Schr\"odinger no lineal con difusi\'on no local regional {\small \begin{eqnarray}\label{Aeq04-} \epsilon^{2\alpha} (-\Delta)_{\rho}^{\alpha}u + u = f(u) \quad \mbox{in}\quad \mathbb{R}^{n},\quad u \in H^{\alpha}(\mathbb{R}^{n}), \end{eqnarray}} \!\!donde $0< \alpha <1$, $\epsilon>0$, $n\geq 2$ y $f:\mathbb{R} \to \mathbb{R}$ es super-lineal y tiene un crecimiento sub-critico. El operador $(-\Delta)_{\rho}^{\alpha}$ es el laplaciano no local regional, con rango de alcance determinado por una funci\'on positiva $\rho \in C(\mathbb{R}^{n}, \mathbb{R}^{+})$ y definido por {\small \begin{eqnarray}\label{Aeq05-} \int_{\mathbb{R}^{n}} \!\!\!\!(-\Delta)_{\rho}^{\alpha} uvdx = \int_{\mathbb{R}^{n}}\!\!\int_{B(0,\rho (x))} \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\frac{[u(x+z) - u(x)][v(x+z) - v(x)]}{|z|^{n+2\alpha}}dzdx. \end{eqnarray}} \!\!Se prueba la existencia de soluci\'on d\'ebil para (\ref{Aeq04-}) aplicando el Teorema del paso de la monta\~na al funcional $I_{\rho}$ definido en $H_{\rho}^{\alpha}(\mathbb{R}^{n})$, combinado con un argumento de comparaci\'on creado por Rabinowitz. El objetivo principal de la tercera parte es estudiar el comportamiento de concentraci\'on de la soluci\'on d\'ebil de la ecuaci\'on (\ref{Aeq04-}) con $f(s) = s^{p}$, cuando $\epsilon \to 0$. En la cuarta parte se estudia el resultado de simetr\'ia para las soluciones ground state de (\ref{Aeq04-}). Para tal prop\'osito, se combina los rearreglos de funciones con los m\'etodos variacionales. Finalmente, se considera un sistema Hamiltoniano fraccionario {\small \begin{eqnarray}\label{Aeq08-} _{t}D_{\infty}^{\alpha}(_{-\infty}D_{t}^{\alpha}u(t)) + L(t)u(t) = & \nabla W(t,u(t)) \end{eqnarray}} \!\!donde $\alpha \in (1/2,1)$, $t\in \mathbb{R}$, $u\in \mathbb{R}^{n}$, $L\in C(\mathbb{R}, \mathbb{R}^{n\times n})$ es una matriz sim\'etrica positiva definida para todo $t\in \mathbb{R}$, $W\in C^{1}(\mathbb{R} \times \mathbb{R}^{n}, \mathbb{R})$ y $\nabla W (t,u)$ es el gradiente de $W$ en $u$. Se demuestra que (\ref{Aeq08-}) posee al menos una soluci\'on no trivial via el Teorema del paso de la monta\~na.
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Nabti, Abderrazak. "Non linear, non-local evolution equations : theory and application." Thesis, La Rochelle, 2015. http://www.theses.fr/2015LAROS032.
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Cette thèse concerne l’étude qualitative (existence locale, existence globale, explosion en temps fini) de quelques équations de Schrödinger non-linéaires non-locales. Dans le cas où les solutions explosent en temps fini, l’estimation du temps maximal d’existence des solutions sera présentée. Le chapitre 1 concerne l’étude d’une équation de Schrödinger non-linéaire sur RN. On s’intéresse à l’existence locale d’une solution pour toute condition initiale donnée dans L2(RN). De plus, on montre que la norme-L2 de la solution explose en temps fini T < 1. Les démonstrations reposent essentiellement sur le théorème de point fixe de Banach et les estimations de Strichartz, et aussi sur le choix convenable de la fonction test dans la formulation faible du problème. Dans le chapitre 2, on considère une équation de Schrödinger non-linéaire non-locale en temps, et on démontre que les solutions de notre problème explosent en temps fini ; ensuite on obtient des conditions nécessaires d’existence globale. Finalement, on obtient une borne inférieure du temps maximal d’existence de la solution. Le chapitre 3 porte sur la non-existence de solutions d’une équation de Schrödinger non-linéaire posée dans RN. Dans un premier temps, sous certaines conditions sur la donnée initiale, on montre qu’il n’existe pas de solution faible globale ; puis on donne une estimation du temps maximal d’existence de la solution. Enfin, on établit des conditions d’existence locale, ou globale de l’équation considérée. En plus, on généralise les résultats précédents au cas d’un système 2 _ 2. Le dernier chapitre traite une équation de Schrödinger non-linéaire non-locale en temps sur le groupe de Heisenberg H. En utilisant la méthode de la fonction test, on démontre que l’équation n’admet pas de solution faible globale. De plus, on obtient, sous certaines conditions sur les données initiales, une estimation inférieure du temps maximal d’existence de la solutionOur objective in this thesis is to study the existence of local solutions, existence global and blow up of solutions at a finite time to some nonlinear nonlocal Schrödinger equations. In the case when a solution blows-up at a finite time T < 1, we obtain an upper estimate of the life span of solutions. In the first chapter, we consider a nonlinear Schrödinger equation on RN. We first prove local existence of solution for any initial condition in L2 space. Then we prove nonexistence of a nontrivial global weak solution. Furthermore, we prove that the L2-norm of the local intime L2-solution blows up at a finite time. The second chapter is dedicated to study an initial value problem for the nonlocal intime nonlinear Schrödinger equation. Using the test function method, we derive a blow-up result. Then based on integral inequalities, we estimate the life span of blowing-up solutions. In the chapter 3, we prove nonexistence result of a space higher-order nonlinear Schrödinger equation. Then, we obtain an upper bound of the life span of solutions. Furthermore, the necessary conditions for the existence of local or global solutions are provided. Next, we extend our results to the 2 _ 2-system. Our method of proof rests on a judicious choice of the test function in the weak formulation of the equation. Finally, we consider a nonlinear nonlocal in time Schrödinger equation on the Heisenberg group. We prove nonexistence of non-trivial global weak solution of our problem. Furthermore, we give an upper bound of the life span of blowing up solutions
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Edlund, Ove. "Solution of linear programming and non-linear regression problems using linear M-estimation methods /." Luleå, 1999. http://epubl.luth.se/1402-1544/1999/17/index.html.
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Camacho, Alonso Máximo Cosme. "Three essays in non-linear macroeconometrics." Doctoral thesis, Universitat Autònoma de Barcelona, 2001. http://hdl.handle.net/10803/4028.
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Esta tesis trata de ser una contribución a la literatura en predicción con modelos no lineales en diversas vías. En el primer capítulo, se extienden a un contexto multivariante los modelos STAR para investigar las relaciones no lineales que aparecen entre la producción de la economía americana y el Composite index of Leading Indicators (CLI). Usando la estimación máximo verosímil, se extienden al contexto VAR los test de linealidad, selección de modelos y adecuación de modelos. Se encuentra evidencia empírica en favor del uso de modelos logísticos para identificar los estados de la economía. En el segundo capítulo, se encuentra que el filtro óptimo para convertir los datos del CLI en una probabilidad de recesión es la combinación de un modelo Markov-switching y de una especificación no-paramétrica. Usando este filtro, se muestra como una tasa de crecimiento del indicador igual a cero no es nada en sí misma sino que se debe usar el filtro apropiado para que, teniendo en cuenta el estado de la economía, convierta este dato en una apropiada probabilidad de recesión. Finalmente, en el tercer capítulo se estudian relaciones de cointegración en las cuales, incluso aunque el atractor a largo plazo se asuma lineal, la fuerza con la que los errores de cointegración se desvanecen depende del estado del ciclo económico con un modelo Markoz-switching. Se muestra como este hecho conecta con la idea de tendencias estocásticas comunes no lineales. Así mismo, se estudia la repercusión sobre las funciones de respuesta al impulso y la descomposición de la varianza.This dissertation, is an attempt to contribute to the literature on nonlinear forecasting in several ways. In the first chapter, I extend to a multiple equation framework the STAR models in order to investigate the nonlinear interactions between US output (GDP) and the Composite index of Leading Indicators (CLI). Using maximum likelihood as the base for estimation, I extend to the VAR case linearity tests, model selection tests, and model adequacy tests. Additionally, I find empirical evidence in favor of using logistic models for capturing the business cycles phases. In the second chapter, I find that the optimal filter to convert the CLI releases into a probability of recession is a combination of the forecasts from a Markov-switching model and a nonparametric specification. Using this filter, I show how a release of zero rate of growth for the CLI must be interpreted carefully since it implies different probabilities of recession depending on the actual state of the economy. Finally, in the third chapter, I study cointegrating relationships such that, even though the long-run attractor is linear, the strength with which the equilibrium errors vanishes is assumed to follow a Markov-switching dynamics. I show that this assumption connect with the idea of nonlinear common stochastic trends. In addition, I study its implication for asymmetric impulse responses and variance decomposition.
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Ahmadian, Saieni Hooman. "Non-linear vibrations of tensegrity structures." Thesis, KTH, Mekanik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-109453.
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A study has been done on different methods to solve the linear and non-linear problems with single or multi degrees of freedom structures. To do that direct time integration methods are used to solve the dynamic equilibrium equations. It has been tried to perform general methods to apply in most structures. In this thesis structures are made of cables and bars but the solution methods which is presented can be applied for any structure, and to utilize those implicit and explicit methods for all structures it is needed to know the tangent stiffness matrix and mass matrix for the structure. Then, it would be possible to analyze the dynamic response of structures under general loads and by general it can be understood that by application of arbitrary forces on different nodes of structure, the method generates result based on applied forces. It is crucial to get the right tangent stiffness matrix and mass matrix to know the dynamic equation in each node. Hence, the method will then work correctly to solve the dynamic problems. More, a parametric study has been done to see the effects of times step, stiffness of elements, length of elements, and other mechanical properties of elements, and this parametric study enables one to produce new results by changing every parameter. Also, continuation of the study on x-frame tensegrity has been done by solving them to check out dynamic response of structure with proposed methods of this thesis. Moreover, a method is presented to use the codes of solver methods of current thesis to apply them for other structures. Hence, as a future work, one can combine the codes of structures and solver codes of this thesis for dynamic response of structure. In fact the main effort of this thesis is on presenting different methods to solve various structures.
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Jeang, Fure Lin. "Non-linear analysis of concrete fracture /." Thesis, Connect to this title online; UW restricted, 1985. http://hdl.handle.net/1773/10133.
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Hagerud, Gustaf E. "A new non-linear GARCH model." Doctoral thesis, Stockholm : Economic Research Institute, Stockholm School of Economics [Ekonomiska forskningsinstitutet vid Handelshögsk.] (EFI), 1997. http://www.hhs.se/efi/summary/444.htm.
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