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Elago, David. "Robust computational methods for two-parameter singular perturbation problems." Thesis, University of the Western Cape, 2010. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_1693_1308039217.
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This thesis is concerned with singularly perturbed two-parameter problems. We study a tted nite difference method as applied on two different meshes namely a piecewise mesh (of Shishkin type) and a graded mesh (of Bakhvalov type) as well as a tted operator nite di erence method. We notice that results on Bakhvalov mesh are better than those on Shishkin mesh. However, piecewise uniform meshes provide a simpler platform for analysis and computations. Fitted operator methods are even simpler in these regards due to the ease of operating on uniform meshes. Richardson extrapolation is applied on one of the tted mesh nite di erence method (those based on Shishkin mesh) as well as on the tted operator nite di erence method in order to improve the accuracy and/or the order of convergence. This is our main contribution to this eld and in fact we have achieved very good results after extrapolation on the tted operator finitete difference method. Extensive numerical computations are carried out on to confirm the theoretical results.
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Young, Caroline Jane. "Methods of geographical perturbation for disclosure control." Thesis, University of Southampton, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.486433.
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Disclosure control methods are used to protect the confidentiality of individuals and households in aggregate census data. With growth in computational power, the disclosure control problem has been rapidly transformed. Increased analytical power has stimulated user demand for more detailed information for smaller geographic areas and to customized geographical boundaries. However, the possibility of allowing census users to create their own aggregates from census microdata, and for small areas, can lead to problems of disclosure by differencing. Traditionally, methods of statistical disclosure control have been aspatial in nature. This thesis describes a new framework of geographical perturbation methods designed to deal with the spatial nature of disclosure risk. The research offers several new contributions, specifically; . (1) Aframework of new geographical perturbation methods is defined, based on creating uncertainty around geographical location. Zone-independent methods are designed for protection in a flexibletabulation scenario'and to account for the spatial dimension of risk. • (2) Techniques for implementation of t~ese methods are tested on a synthetic census dataset which· show comparable risk-utility outcomes to RRS (an existing method used for the US and UK Censuses). The advantages and disadvantages of the proposed methods are discussed with regard to ease of implementation and flexibility of parameter values. (3) One of these new methods; LOS, is then explored in more detail showing a significant improvement over RRS in terms of the risk-utility outcome. Risk reduction is illustrated in a geographical differencing scenario and distortion to utility explored in a spatial context of typical census users' analyses.
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Munyakazi, Justin Bazimaziki. "Higher Order Numerical Methods for Singular Perturbation Problems." Thesis, Online Access, 2009. http://etd.uwc.ac.za/usrfiles/modules/etd/docs/etd_gen8Srv25Nme4_6335_1277251056.pdf.
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Kateregga, Michael. "Perturbation methods in derivatives pricing under stochastic volatility." Thesis, Stellenbosch : Stellenbosch University, 2012. http://hdl.handle.net/10019.1/71708.
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Thesis (MSc)--Stellenbosch University, 2012.ENGLISH ABSTRACT: This work employs perturbation techniques to price and hedge financial derivatives in a stochastic volatility framework. Fouque et al. [44] model volatility as a function of two processes operating on different time-scales. One process is responsible for the fast-fluctuating feature of volatility and corresponds to the slow time-scale and the second is for slowfluctuations or fast time-scale. The former is an Ergodic Markov process and the latter is a strong solution to a Lipschitz stochastic differential equation. This work mainly involves modelling, analysis and estimation techniques, exploiting the concept of mean reversion of volatility. The approach used is robust in the sense that it does not assume a specific volatility model. Using singular and regular perturbation techniques on the resulting PDE a first-order price correction to Black-Scholes option pricing model is derived. Vital groupings of market parameters are identified and their estimation from market data is extremely efficient and stable. The implied volatility is expressed as a linear (affine) function of log-moneyness-tomaturity ratio, and can be easily calibrated by estimating the grouped market parameters from the observed implied volatility surface. Importantly, the same grouped parameters can be used to price other complex derivatives beyond the European and American options, which include Barrier, Asian, Basket and Forward options. However, this semi-analytic perturbative approach is effective for longer maturities and unstable when pricing is done close to maturity. As a result a more accurate technique, the decomposition pricing approach that gives explicit analytic first- and second-order pricing and implied volatility formulae is discussed as one of the current alternatives. Here, the method is only employed for European options but an extension to other options could be an idea for further research. The only requirements for this method are integrability and regularity of the stochastic volatility process. Corrections to [3] remarkable work are discussed here.
AFRIKAANSE OPSOMMING: Hierdie werk gebruik steuringstegnieke om finansiële afgeleide instrumente in ’n stogastiese wisselvalligheid raamwerk te prys en te verskans. Fouque et al. [44] gemodelleer wisselvalligheid as ’n funksie van twee prosesse wat op verskillende tyd-skale werk. Een proses is verantwoordelik vir die vinnig-wisselende eienskap van die wisselvalligheid en stem ooreen met die stadiger tyd-skaal en die tweede is vir stadig-wisselende fluktuasies of ’n vinniger tyd-skaal. Die voormalige is ’n Ergodiese-Markov-proses en die laasgenoemde is ’n sterk oplossing vir ’n Lipschitz stogastiese differensiaalvergelyking. Hierdie werk behels hoofsaaklik modellering, analise en skattingstegnieke, wat die konsep van terugkeer to die gemiddelde van die wisseling gebruik. Die benadering wat gebruik word is rubuust in die sin dat dit nie ’n aanname van ’n spesifieke wisselvalligheid model maak nie. Deur singulêre en reëlmatige steuringstegnieke te gebruik op die PDV kan ’n eerste-orde pryskorreksie aan die Black-Scholes opsie-waardasiemodel afgelei word. Belangrike groeperings van mark parameters is geïdentifiseer en hul geskatte waardes van mark data is uiters doeltreffend en stabiel. Die geïmpliseerde onbestendigheid word uitgedruk as ’n lineêre (affiene) funksie van die log-geldkarakter-tot-verval verhouding, en kan maklik gekalibreer word deur gegroepeerde mark parameters te beraam van die waargenome geïmpliseerde wisselvalligheids vlak. Wat belangrik is, is dat dieselfde gegroepeerde parameters gebruik kan word om ander komplekse afgeleide instrumente buite die Europese en Amerikaanse opsies te prys, dié sluit in Barrier, Asiatiese, Basket en Stuur opsies. Hierdie semi-analitiese steurings benadering is effektief vir langer termyne en onstabiel wanneer pryse naby aan die vervaldatum beraam word. As gevolg hiervan is ’n meer akkurate tegniek, die ontbinding prys benadering wat eksplisiete analitiese eerste- en tweede-orde pryse en geïmpliseerde wisselvalligheid formules gee as een van die huidige alternatiewe bespreek. Hier word slegs die metode vir Europese opsies gebruik, maar ’n uitbreiding na ander opsies kan’n idee vir verdere navorsing wees. Die enigste vereistes vir hierdie metode is integreerbaarheid en reëlmatigheid van die stogastiese wisselvalligheid proses. Korreksies tot [3] se noemenswaardige werk word ook hier bespreek.
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Ahmed, Samah. "Perturbation field theory methods for calculating expectation values." Thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/26214.
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Tronko, Natalia. "Hamiltonian Perturbation Methods for Magnetically Confined Fusion Plasmas." Thesis, Aix-Marseille 2, 2010. http://www.theses.fr/2010AIX22088/document.
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Les effets auto-consistantes sont omniprésents dans les plasmas de fusion. Ils sont dus au fait que les équations de Maxwell qui décrivent l’évolution des champs électromagnétiques contiennent la densité de charge et de courant des particules.D’autre côté à son tour les trajectoires des particules sont influencés par les champs à travers les équations de mouvement ( où l’équation de Vlasov). Le résultat decette interaction auto-consistente se résume dans un effet cumulatif qui peut causer le déconfinement de plasma à l’intérieur d’une machine de fusion. Ce travail de thèse traite les problèmes liés à l’amélioration de confinement de plasma de fusion dans le cadre des approches hamiltonienne et lagrangien par le contrôle de transport turbulent et la création des barrières de transport. Les fluctuations auto-consistantes de champs électromagnétiques et de densités des particules sont à l’origine de l’apparition des instabilités de plasma qui sont à son tour liés aux phénomènes de transport. Dans la perspective de comprendre les mécanismes de la turbulence sousjacente,on considère ici l’application des méthodes hamiltoniennes pour des plasmasnon-collisionnellesThis thesis deals with dynamicla investigation of magnetically confined fusion plasmas by using Lagrangian and Hamilton formalisms. It consists of three parts. The first part is devoted to the investigation of barrier formation for the EXB drift model by means of the Hamiltonian control method. The strong magnetic field approach is relevant for magnetically confined fusion plasmas ; this is why at the first approximation one can consider the dynamics of particles driven by constant and uniform magnetic field. In this case only the electrostatic turbulence is taken into account. During this study the expressions for the control term (quadratic in perturbation amplitude) additive to the electrostatic potential, has been obtained. The effeciency of such a control for stopping turbulent diffusion has been shown analytically abd numerically. The second and the third parts of this thesis are devoted to study of self consistent phenomena in magnetized plasmas through the Maxwell-Vlasov model. In particular, the second part of this thesis treats the problem of the monumentum transport by derivation of its conservation law. the Euler-Poincare variational principle (with constrained variations) as well as Noether's theorem is apllied here. this derivation is realized in two cases : first, in electromagnetic turbulence case for the full Maxwell-Vlasov system, and then in electrostatic turbulence case for the gyrokinetic Maxwell-Vlasov system. Then the intrinsic mechanisms reponsible for the intrinsic plama rotation, that can give an important in plasma stabilization, are identified. The last part of this thesis deals with dynamicla reduction for the Maxwell-Vlaslov model. More particularly; the intrisic formulation for the guiding center model is derived. Here the term 'intrinsis" means that no fixed frame was used during its construction. Due to that not any problem related to the gyrogauge dependence of dynamics appears. The study of orbits of trapped particles is considered as one of the possible for illustration of the first step of such a dynamical reduction
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Hwang, Ho-yon. "Identification methods for physical parameters in structures." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/15652.
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Pulya, Ravishankar Sandheep. "Device Modelling of Perovskite Solar Cells using Small Perturbation Methods." Doctoral thesis, Universitat Jaume I, 2019. http://hdl.handle.net/10803/667627.
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Perovskite solar cells (PSC) have emerged as an important player in the search for producing c1ean and renewable energy at
high efficiencies. However, there exist several bottlenecks to maximise their efficiency and stability. This thesis explores the
physical mechanisms related to these limitations in operation and provides a deeper understanding as to how to overcome
them. Through systematic experiments based on the small perturbation methods of Impedance Spectroscopy (IS) and
Intensity Modulated Photocurrent Spectroscopy (IMPS), the perovskite/selective contact interfaces are identified as a critical
factor that controls charge accumulation, recombination ando extraction. Therefore, these interfaces require to be carefully
tuned in order to gain control over the device operation. Based on these insights, a robust equivalent circuit of the PSC is
developed that provides a strong foundation for further development of these solar cells.Las células solares de perovskite (PSC) se han convertido en un jugador importante en la búsqueda de producir energía limpia y renovable con altas eficiencias. Sin embargo, existen varios cuellos de botella para maximizar su eficiencia y estabilidad. Esta tesis explora los mecanismos físicos relacionados con estas limitaciones en la operación y proporciona una comprensión más profunda de cómo superarlas. A través de experimentos sistemáticos basados en los pequeños métodos de perturbación de la espectroscopia de impedancia (IS) y la espectroscopia de fotocorriente modulada de intensidad (IMPS), las interfaces de contacto perovskita / selectiva se identifican como un factor crítico que controla la acumulación de carga, la recombinación y la extracción. Por lo tanto, estas interfaces deben ajustarse con cuidado para poder controlar el funcionamiento del dispositivo. Sobre la base de estas ideas, se desarrolla un sólido circuito equivalente del PSC que proporciona una base sólida para el desarrollo posterior de estas células solares.
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Fung, Jimmy Jr. "Parameter Identification of Nonlinear Systems Using Perturbation Methods and Higher-Order Statistics." Thesis, Virginia Tech, 1998. http://hdl.handle.net/10919/36921.
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A parametric identification procedure is proposed that combines
the method of multiple scales and higher-order statistics to
efficiently and accurately model nonlinear
systems. A theoretical background for the method of
multiple scales and higher-order
statistics is given.
Validation of the procedure is performed
through applying it to numerical simulations of two
nonlinear systems. The results show how the procedure can
successfully characterize the system damping and nonlinearities and
determine the corresponding parameters.
The procedure is then applied to experimental measurements from
two structural systems, a
cantilevered beam and a three-beam frame. The results show that
quadratic damping should be accounted for in both systems.
Moreover, for the three-beam frame, the parametric excitation is
much more important than the direct excitation.
To show the flexibility of the
procedure, numerical simulations of ship motion under parametric
excitation are used to determine nonlinear parameters govening the
relation between pitch, heave, and roll motions. The results show
a high level of agreement between the numerical simulation and the
mathematical model with the identified parameters.Master of Science
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Sabouri, Pouya. "Application of perturbation theory methods to nuclear data uncertainty propagation using the collision probability method." Thesis, Grenoble, 2013. http://www.theses.fr/2013GRENI071/document.
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Dans cette thèse, nous présentons une étude rigoureuse des barres d'erreurs et des sensibilités de paramètres neutroniques (tels le keff) aux données nucléaires de base utilisées pour les calculer. Notre étude commence au niveau fondamental, i.e. les fichiers de données ENDF et leurs incertitudes, fournies sous la forme de matrices de variance/covariance, et leur traitement. Lorsqu'un calcul méthodique et consistant des sensibilités est consenti, nous montrons qu'une approche déterministe utilisant des formalismes bien connus est suffisante pour propager les incertitudes des bases de données avec un niveau de précision équivalent à celui des meilleurs outils disponibles sur le marché, comme les codes Monte-Carlo de référence. En appliquant notre méthodologie à trois exercices proposés par l'OCDE, dans le cadre des Benchmarks UACSA, nous donnons des informations, que nous espérons utiles, sur les processus physiques et les hypothèses sous-jacents aux formalismes déterministes utilisés dans cette étudeThis dissertation presents a comprehensive study of sensitivity/uncertainty analysis for reactor performance parameters (e.g. the k-effective) to the base nuclear data from which they are computed. The analysis starts at the fundamental step, the Evaluated Nuclear Data File and the uncertainties inherently associated with the data they contain, available in the form of variance/covariance matrices. We show that when a methodical and consistent computation of sensitivity is performed, conventional deterministic formalisms can be sufficient to propagate nuclear data uncertainties with the level of accuracy obtained by the most advanced tools, such as state-of-the-art Monte Carlo codes. By applying our developed methodology to three exercises proposed by the OECD (UACSA Benchmarks), we provide insights of the underlying physical phenomena associated with the used formalisms
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Donner, Ralf. "Numerical methods of resonant dynamics for the Galaxy." Thesis, University of Oxford, 2005. http://ora.ox.ac.uk/objects/uuid:136ae026-e3d4-4153-b124-edc8256c14c9.
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Numerical methods of resonant dynamics with applications to the Galaxy are considered in this thesis. We derive generating functions for first-order perturbation theory and the associated orbital frequencies by matrix calculus. For two action-angle spaces (J,θ) and (i,φ) related by a canonical map I·φ+s, we show that J can be averaged over ergodic orbits φ to provide an estimator of I to within O(|s|2). We provide examples in one and two dimensions and compare the technique to calculations of actions by numerical line integration in Poincaré sections. We then use spectral dynamics and the Laskar frequency map (Laskar, 1993) to identify the dynamically important resonances of the 'flattened' axisymmetric isochrone potential. We simulate resonant capture in a low-order resonance by populating representative tori of a spherical isochrone Hamiltonian and integrating the orbits while adiabatically introducing axisymmetry. We use the averaging technique described above to observe the fraction of orbits captured, and we compare the result to a theoretical prediction. We return to first-order perturbation theory to analyse its strengths and weaknesses, in particular near orbital pericentre, and when one action is significantly smaller than another. We also reproduce the expected pendulum dynamics in the resonant action-angle plane for orbits in our capture simulation. We develop the concept of adaptive dynamics: we vary the initial orbital energy of the particles in the capture simulations and show that resonant and non-resonant orbits can be identified as clusters in the perturbed action plane. For a given Hamiltonian, we use the perturbed frequencies and a linear regression fit in the action plane as diagnostics of a set of model Hamiltonians on a grid in a suitable parameter space. We find we are able to constrain the parameters of a model Hamiltonian by this method. Finally, we reject the null hypothesis that resonant structures in phase space can be found by traditional methods of density estimation.
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Lang, Simon [Verfasser], and Jones S. [Akademischer Betreuer] C. "Perturbation Dynamics and Impact of Different Perturbation Methods in Tropical Cyclone Ensemble Forecasting / Simon Lang. Betreuer: S. C. Jones." Karlsruhe : KIT-Bibliothek, 2011. http://d-nb.info/1017797110/34.
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ZHOU, XIANWEN. "Application of Perturbation Methods to Modeling Correlated Defaults in Financial Markets." NCSU, 2006. http://www.lib.ncsu.edu/theses/available/etd-03022006-170911/.
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In recent years people have seen a rapidly growing market for credit derivatives. Among these traded credit derivatives, a growing interest has been shown on multi-name credit derivatives, whose underlying assets are a pool of defaultable securities. For a multi-name credit derivative, the key is the default dependency structure among the underlying portfolio of reference entities, instead of the individual term structure of default probabilities for each single reference entity as in the case of single-name derivative. So far, however, default dependency modeling is still the most demanding open problem in the pricing of credit derivatives. The research in this dissertation is trying to model the default dependency with aid of perturbation method, which was first proposed by Fouque, Papanicolaou and Sircar (2000) as a powerful tool to pricing options under stochastic volatility. Specifically, after a theoretic result regarding the approximation accuracy of the perturbation method and an application of this method to pricing American options under stochastic volatility by Monte Carlo approach, a multi-dimensional Merton model under stochastic volatility is studied first, and then the multi-dimensional generalization of the first-passage model under stochastic volatility comes next, which is then followed by a copula perturbed from the standard Gaussian copula.
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McKinley, Michael Scott. "Higher-order boundary condition perturbation methods in transport and diffusion theory." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/16034.
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Karlgaard, Christopher David. "Second-Order Relative Motion Equations." Thesis, Virginia Tech, 2001. http://hdl.handle.net/10919/34025.
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This thesis presents an approximate solution of second order
relative motion equations. The equations of motion for a Keplerian
orbit in spherical coordinates are expanded in Taylor series form
using reference conditions consistent with that of a circular
orbit. Only terms that are linear or quadratic in state variables
are kept in the expansion. A perturbation method is employed to
obtain an approximate solution of the resulting nonlinear
differential equations. This new solution is compared with the
previously known solution of the linear case to show improvement,
and with numerical integration of the quadratic differential
equation to understand the error incurred by the approximation. In
all cases, the comparison is made by computing the difference of
the approximate state (analytical or numerical) from numerical
integration of the full nonlinear Keplerian equations of motion.Master of Science
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Dalla, Riva Matteo. "Potential theoretic methods for the analysis of singularly perturbed problems in linearized elasticity." Doctoral thesis, Università degli studi di Padova, 2008. http://hdl.handle.net/11577/3426270.
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The dissertation is made of two chapters. The first chapter is dedicated to the investigation of some properties of the layer potentials of a constant coefficient elliptic partial differential operator. In the second chapter, we focus our attention to the Lamè equations, which are related to the physic of an isotropic homogeneous elastic body.
In particular, in the first chapter, we investigate the dependence of the single layer potential upon perturbation of the density, the support and the coefficients of the corresponding operator. Under some more restrictive assumptions on the operator, we prove a real analyticity theorem for the single layer potential and its derivatives.
As a first step, we introduce a particular fundamental solution of a given constant coefficient partial differential operator. For this purpose, we exploite the construction of a fundamental solution given by John (1955). We have verified that, if the coefficients of the operator are constrained to a bounded set, then there exist a particular fundamental solution which is a sum of functions which depend real analytically on the coefficients of the operator. Such a result resembles the results of Mantlik (1991, 1992) (see also Tréves (1962)), where more general assumptions on the operator are considered. We observe that it is not a corollary. Indeed, we need a suitably detailed expression for the fundamental solution, which cannot be deduced by Mantlik's results.
The next step is to introduce the support of our single layer potentials. It will be a compact sub-manifold of the the n-dimensional euclidean space parametrized by a suitable diffeomorphism defined on the boundary of a fixed domain.
Then, we will be ready to state in Theorem 1.7 the main result of this chapter, which is a real analyticity result in the frame of Shauder spaces. The main idea of the proof stems from the papers of Lanza de Cristoforis & Preciso (1999) and by Lanza de Cristoforis & Rossi (2004, 2005) and exploits the Implicit Mapping Theorem for real analytic functions. Indeed, our main Theorem 1.7 is in some sense a natural extension of theorems obtained by Lanza de Cristoforis & Preciso (1999) and by Lanza de Cristoforis & Rossi (2004, 2005), for the Cauchy integral and for the Laplace and Helmholtz operators, respectively. Here we confine our attention to elliptic operators which can be factorized with operators of order 2.
In the last section of the first chapter, we consider some applications of Theorem 1.7. In particular, we deduce a real analyticity theorem for the single and double layer potential which arise in the analysis of the boundary value problems for the Lamè equations and for the Stokes system.
In the second chapter, we focus our attention to the Lamè equations. We consider some boundary value problems defined in a domain with a small hole. For each of them, we investigate the behavior of the solution and of the corresponding energy integral as the hole shrinks to a point.
This kind of problem is not new at all and has been long investigated by the techniques of asymptotic analysis. It is perhaps difficult to give a complete list of contributions. Here we mention the work of Keller, Kozlov, Movchan, Maz'ya, Nazarov, Plamenewskii, Ozawa and Ward. The results that we present are in accordance with the behavior one would expect by looking at the above mentioned literature, but we adopt a different approach proposed by Lanza de Cristoforis (2001, 2002, 2005, 2007.) To do so, we exploit the real analyticity results for the elastic layer potentials obtained in the first chapter.
We now briefly outline the main difference between our approach and the one of asymptotic analysis. Let d>0 be a parameter which is proportional to the diameter of the hole, so that the singularity of the domain appears when d=0. By the approach of the asymptotic analysis, we can expect to obtain results which are expressed by means of known functions of d plus an unknown term which is smaller than a positive power of d. Whereas, our results are expressed by means of real analytic functions of d defined in a whole open neighborhood of d=0 and by, possibly singular, but completely known functions of d, such as d^(2-n) or log d.
Moreover, not only we can consider the dependence upon d, we can also investigate the dependence of the solution and the corresponding energy integral upon perturbations of the coefficients of the operator, and of the point where the hole is situated, and of the shape of the hole, and of the shape of the outer domain, and of the boundary data on the boundary of the hole, and of the boundary data on the boundary of the outer domain, and of the interior data. Also in this case we obtain results expressed by means of real analytic functions and completely known functions such as d^(2-n) and log d.
The first boundary value problem we have studied is a Dirichlet boundary value problem with homogeneous data in the interior. Then, we turned to investigate a Robin boundary value problem with homogeneous data in the interior. In this case we have also described the behavior of the solution and the corresponding energy integral when both the domain and the boundary data display a singularity for d=0. Finally, we have studied a Dirichlet boundary value problem with non-homogeneous data in the interior.
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Eriksson, Daniel. "Perturbative Methods in General Relativity." Doctoral thesis, Umeå : Department of Physics, Umeå University, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-1488.
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Lowis, D. R. "Application of theoretical methods to the study of small molecules in solution." Thesis, University of Oxford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.240696.
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Lang, Lucas [Verfasser]. "Development of New Multistate Multireference Perturbation Theory Methods and Their Application / Lucas Lang." Bonn : Universitäts- und Landesbibliothek Bonn, 2020. http://d-nb.info/121913984X/34.
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Sultanov, Oskar, Leonid Kalyakin, and Nikolai Tarkhanov. "Elliptic perturbations of dynamical systems with a proper node." Universität Potsdam, 2014. http://opus.kobv.de/ubp/volltexte/2014/7046/.
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The paper is devoted to asymptotic analysis of the Dirichlet problem for a second order partial differential equation containing a small parameter multiplying the highest order derivatives. It corresponds to a small perturbation of a dynamical system having a stationary solution in the domain.
We focus on the case where the trajectories of the system go into the domain and the stationary solution is a proper node.
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Khabir, Mohmed Hassan Mohmed. "Numerical singular perturbation approaches based on spline approximation methods for solving problems in computational finance." Thesis, University of the Western Cape, 2011. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_7416_1320395978.
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Options are a special type of derivative securities because their values are derived from the value of some underlying security. Most options can be grouped into either of the two categories: European options which can be exercised only on the expiration date, and American options which can be exercised on or before the expiration date. American options are much harder to deal with than European ones. The reason being the optimal exercise policy of these options which led to free boundary problems. Ever since the seminal work of Black and Scholes [J. Pol. Econ. 81(3) (1973), 637-659], the differential equation approach in pricing options has attracted many researchers. Recently, numerical singular perturbation techniques have been used extensively for solving many differential equation models of sciences and engineering. In this thesis, we explore some of those methods which are based on spline approximations to solve the option pricing problems. We show a systematic construction and analysis of these methods to solve some European option problems and then extend the approach to solve problems of pricing American options as well as some exotic options. Proposed methods are analyzed for stability and convergence. Thorough numerical results are presented and compared with those seen in the literature.
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Patel, Dipak. "Development of density perturbation methods for separating cells on the basis of their immunological identity." Thesis, University of Essex, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.307860.
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Sudbery, Ian Martin. "Methods for genome-scale gene perturbation studies of the TRAIL-induced apoptosis pathway in mammalian cell culture." Thesis, University of Cambridge, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.612450.
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Ramos, Quoirin Humberto. "Indefinite problems for a homogeneous perturbation of the p-laplacian." Doctoral thesis, Universite Libre de Bruxelles, 2009. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210198.
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Note de l'administrateur du service :le résumé de cette thèse est disponible dans le fichier déposé par l'auteur. Il ne peut techniquement pas être placé sous cette rubrique, dans la mesure où il contient des formules mathématiques avec des caractères grecs.Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Nyamayaro, Takura T. A. "On the design and implementation of a hybrid numerical method for singularly perturbed two-point boundary value problems." University of the Western Cape, 2014. http://hdl.handle.net/11394/4326.
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>Magister Scientiae - MScWith the development of technology seen in the last few decades, numerous solvers have been developed to provide adequate solutions to the problems that model different aspects of science and engineering. Quite often, these solvers are tailor-made for specific classes of problems. Therefore, more of such must be developed to accompany the growing need for mathematical models that help in the understanding of the contemporary world. This thesis treats two point boundary value singularly perturbed problems. The solution to this type of problem undergoes steep changes in narrow regions (called boundary or internal layer regions) thus rendering the classical numerical procedures inappropriate. To this end, robust numerical methods such as finite difference methods, in particular fitted mesh and fitted operator methods have extensively been used. While the former consists of transforming the continuous problem into a discrete one on a non-uniform mesh, the latter involves a special discretisation of the problem on a uniform mesh and are known to be more accurate. Both classes of methods are suitably designed to accommodate the rapid change(s) in the solution. Quite often, finite difference methods on piece-wise uniform meshes (of Shishkin-type) are adopted. However, methods based on such non-uniform meshes, though layer-resolving, are not easily extendable to higher dimensions. This work aims at investigating the possibility of capitalising on the advantages of both fitted mesh and fitted operator methods. Theoretical results are confirmed by extensive numerical simulations.
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Heunen, Guido Willem Jozef Christiaan. "New experimental methods for perturbation crystallography single-crystal X-ray diffraction on piezoelectric crystals in quasi-static electric fields /." [S.l. : Amsterdam : s.n.] ; Universiteit van Amsterdam [Host], 2000. http://dare.uva.nl/document/83423.
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Trac, Steven Cy. "Robust Explicit Construction of 3D Configuration Spaces Using Controlled Linear Perturbation." Scholarly Repository, 2008. http://scholarlyrepository.miami.edu/oa_dissertations/189.
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We present robust explicit construction of 3D configuration spaces using controlled linear perturbation. The input is two planar parts: a fixed set and a moving set, where each set is bounded by circle segments. The configuration space is the three-dimensional space of Euclidean transformation (translations plus rotations) of the moving set relative to the fixed set. The goal of constructing the 3D configuration space is to determine the boundary representation of the free space where the intersection of the moving set and fixed set is empty. To construct the configuration space, we use the controlled linear perturbation algorithm. The controlled linear perturbation algorithm assigns function signs that are correct for a nearly minimal input perturbation. The output of the algorithm is a consistent set of function signs. This approach is algorithm-independent, and the overhead over traditional floating point methods is reasonable. If the fixed and moving sets are computer representations of physical objects, then computing the configuration space greatly aids in many computational geometry problems. The main focus of computing the configuration space is for the path planning problem. We must find if a path exists from the start to the goal, where the fixed set is the obstacle, and the moving set is the object trying to reach the goal.
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Stein, Martin. "C0-Semigroup Methods for Delay Equations." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1225964082538-00880.
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In der Dissertation werden Werkzeuge zur Analyse von Wohlgestelltheit und Asymptotik von Integro-Differential- und Verzögerungsgleichungen entwickelt. Im ersten Teil der Arbeit (Kapitel 1 und 2) werden Methoden zur Bestimmung der Modulhalbgruppe (kleinste dominierende C0-Halbgruppe) einer C0-Halbgruppe zur Verfügung gestellt, die unter anderem auf Volterra-Halbgruppen (die aus Integro-Differentialgleichungen hervorgehen) und Evolutionshalbgruppen (Rückkopplungsgleichungen mit Zeitverzögerung, Transport in Netzwerken) angewendet werden. Im Mittelpunkt des zweiten Teils (Kapitel 3 und 4) steht ein Integro-Differentialgleichungstyp, der Schwingungsphänomene von Tragswerksflächen im Unterschallbereich beschreibt. Das besondere dieser Gleichung ist das Auftreten der Zeitableitung der gesuchten Funktion im Integralterm. Es werden eine Reihe von Wohlgestelltheitskriterien hergeleitet, welche Wohlgestelltheit der Gleichung liefern, ohne das es möglich ist, durch partielle Integration die Zeitableitung im Integralterm zu beseitigen und dadurch die Gleichung auf einen bekannten Integro-Differentialgleichungstyp zurückzuführen. Die entwickelten Methoden eignen sich auch für die Herleitung neuer Wohlgestelltheitskriterien für andere Verzögerungsgleichungen. Entsprechende Resultate werden in Kapitel 4 hergeleitetIn the dissertation tools for the analysis of well-posedness and asymptotic behaviour of integro-differential equations and delay equations are developed. In the first part (chapter 1 and 2) methods for the determination of the modulus semigroup (smallest dominating C0-semigroup) of a C0-semigroup are provided and applied to various examples such as Volterra semigroups and evolution semigroups and transport evolution equations in networks. The main interest of the second part (chapter 3 and 4) is a type of an integro-differential equation which occurs in the modelling of the flutter of airfoils at subsonic speed. The remarkable property of the equation is the time derivative of the sought function in the integral term. A number of well-posedness criteria are proved for which integration by parts is not possible. The developed methods are also suitable for the derivation of new well-posedness results for other delay semigroups. Corresponding criteria are presented in chapter 4
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Maurer, Marina [Verfasser], and Christian [Akademischer Betreuer] Ochsenfeld. "Efficient quantum-chemical methods for calculating NMR shieldings in second-order Møller-Plesset perturbation theory / Marina Maurer ; Betreuer: Christian Ochsenfeld." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2014. http://d-nb.info/1125883987/34.
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Goubinat, Damien. "Contrôle géométrique et méthodes numériques : application au problème de montée d'un avion." Phd thesis, Toulouse, INPT, 2017. http://oatao.univ-toulouse.fr/18608/7/Goubinat.pdf.
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Ce travail s’intéresse à la phase de montée d’un aéronef civil. Les trajectoires minimisant le temps de montée ainsi que que celles minimisant la consommation de carburant sont étudiées au travers du contrôle optimal géométrique. La dynamique associée à la phase de montée possède un phénomène dit de perturbation singulière. Ce phénomène, présent dans les systèmes multi-échelle, rend difficile la résolution numérique du problème de contrôle associé. La réduction desystème hamiltonien, permettant de s’affranchir de la difficulté numérique introduite par la perturbation singulière, est étudiée d’un point de vue théorique puis numérique. Dans un second temps, le système réduit est étudié géométriquement. L’utilisation des outils du contrôle géométrique combinée à celui des synthèses à temps court permet de déterminer des familles de trajectoires localement temps-optimales pour des temps courts. Cette étude est complétée par une étude des trajectoires temps-optimales en présence de contraintes d’état. D’un point de vue plus numérique, les méthodes directes et indirectes sont utilisées pour résoudre les différents problèmes. Une synthèse locale est alors réalisée en partant des familles de trajectoires déterminées pour des temps courts. Une étude des trajectoires minimisant la consommation de carburant est également réalisée.
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Stein, Martin. "C0-Semigroup Methods for Delay Equations." Doctoral thesis, Technische Universität Dresden, 2007. https://tud.qucosa.de/id/qucosa%3A23902.
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In der Dissertation werden Werkzeuge zur Analyse von Wohlgestelltheit und Asymptotik von Integro-Differential- und Verzögerungsgleichungen entwickelt. Im ersten Teil der Arbeit (Kapitel 1 und 2) werden Methoden zur Bestimmung der Modulhalbgruppe (kleinste dominierende C0-Halbgruppe) einer C0-Halbgruppe zur Verfügung gestellt, die unter anderem auf Volterra-Halbgruppen (die aus Integro-Differentialgleichungen hervorgehen) und Evolutionshalbgruppen (Rückkopplungsgleichungen mit Zeitverzögerung, Transport in Netzwerken) angewendet werden. Im Mittelpunkt des zweiten Teils (Kapitel 3 und 4) steht ein Integro-Differentialgleichungstyp, der Schwingungsphänomene von Tragswerksflächen im Unterschallbereich beschreibt. Das besondere dieser Gleichung ist das Auftreten der Zeitableitung der gesuchten Funktion im Integralterm. Es werden eine Reihe von Wohlgestelltheitskriterien hergeleitet, welche Wohlgestelltheit der Gleichung liefern, ohne das es möglich ist, durch partielle Integration die Zeitableitung im Integralterm zu beseitigen und dadurch die Gleichung auf einen bekannten Integro-Differentialgleichungstyp zurückzuführen. Die entwickelten Methoden eignen sich auch für die Herleitung neuer Wohlgestelltheitskriterien für andere Verzögerungsgleichungen. Entsprechende Resultate werden in Kapitel 4 hergeleitet.In the dissertation tools for the analysis of well-posedness and asymptotic behaviour of integro-differential equations and delay equations are developed. In the first part (chapter 1 and 2) methods for the determination of the modulus semigroup (smallest dominating C0-semigroup) of a C0-semigroup are provided and applied to various examples such as Volterra semigroups and evolution semigroups and transport evolution equations in networks. The main interest of the second part (chapter 3 and 4) is a type of an integro-differential equation which occurs in the modelling of the flutter of airfoils at subsonic speed. The remarkable property of the equation is the time derivative of the sought function in the integral term. A number of well-posedness criteria are proved for which integration by parts is not possible. The developed methods are also suitable for the derivation of new well-posedness results for other delay semigroups. Corresponding criteria are presented in chapter 4.
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Krauss, Ryan. "Experimental Identification of Nonlinear Systems." Thesis, Virginia Tech, 1998. http://hdl.handle.net/10919/36912.
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A procedure is presented for using a primary resonance excitation in
experimentally identifying the nonlinear parameters of a model approximating the
response of a cantilevered beam by a single mode. The model accounts for cubic
inertia and stiffness nonlinearities and quadratic damping. The method of
multiple scales is used to determine the frequency-response function for the
system. Experimental frequency- and amplitude-sweep data are compared with the
prediction of the frequency-response function in a least-squares curve-fitting
algorithm. The algorithm is improved by making use of experimentally known
information about the location of the bifurcation points. The method is
validated by using the parameters extracted to predict the force-response curves
at other nearby frequencies.
We then compare this technique with two other techniques that have been presented in the literature. In addition to the amplitude- and frequency-sweep technique presented, we apply a second frequency-domain technique and a time-domain technique to the second mode of a cantilevered beam. We apply the restoring-force surface method assuming no a priori knowledge of the system and use the shape of the surface to guide us in assuming a form for the equation of motion. This equation is used in applying the frequency-domain techniques: a backbone curve-fitting technique based on the describing-function method and the amplitude- and frequency-sweep technique based on the method of multiple scales. We derive the equation of motion from a Lagrangian and discover that the form assumed based on the restoring-force surface is incorrect. All of the methods are reapplied with the new form for the equation of motion. Differences in the parameter estimates are discussed. We conclude by discussing the limitations encountered for each technique. These include the inability to separate the nonlinear curvature and inertia effects and problems in estimating the coefficients of small terms with the time-domain technique.
Master of Science
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Baù, Giulio. "Techniques for simulation and control of innovative aerospace systems: numerical models for attitude and orbital dynamics." Doctoral thesis, Università degli studi di Padova, 2012. http://hdl.handle.net/11577/3422105.
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The PhD thesis deals mainly with special and general perturbation techniques. The main results are the development of a new regularized method for propagating the motion of a particle around an attractive central body and the derivation of accurate analytical formulas to predict the motion in the particular case of constant tangential thrustLa tesi di dottorato tratta principalmente tecniche speciali e generali di perturbazione. I risultati più significativi sono lo sviluppo di un nuovo metodo regolarizzato per la propagazione del moto di una particella intorno ad un corpo centrale di attrazione e la derivazione di formule analitiche accurate per predire il moto nel caso particolare di accelerazione tangenziale costante
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Sinnokrot, Mutasem Omar. "Theoretical Investigations of pi-pi Interactions and Their Role in Molecular Recognition." Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/5019.
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Noncovalent interactions are of pivotal importance in many areas of chemistry, biology, and materials science, and the intermolecular interactions involving aromatic rings in particular, are fundamental to molecular organization and recognition processes. The work detailed in this thesis involves the application of state-of-the-art ab initio electronic structure theory methods to elucidate the nature of pi-pi interactions. The binding energies, and geometrical and orientational preferences of the simplest prototype of aromatic pi-pi interactions, the benzene dimer, are explored. We obtain the first converged values of the binding energies using highly accurate methods and large basis sets. Results from this study predict the T-shaped and parallel-displaced configurations of benzene dimer to be nearly isoenergetic.
The role of substituents in tuning pi-pi interaction is investigated. By studying dimers of benzene with various monosubstituted benzenes (in the sandwich and two T-shaped configurations), we surprisingly find that all of the substituted sandwich dimers considered bind more strongly than benzene dimer. We also find that these interactions can be tuned by a modest degree of substitution. Energy decomposition analysis using symmetry-adapted perturbation theory (SAPT) reveals that models based solely on electrostatic effects will have difficulty in reliably predicting substituent effects in pi-pi interactions.
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長家, 康展. "確率論的手法による炉心解析に関する研究." 京都大学 (Kyoto University), 2012. http://hdl.handle.net/2433/165032.
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Fukasaku, Kotaro. "Explorative study for stochastic failure analysis of a roughened bi-material interface: implementation of the size sensitivity based perturbation method." Thesis, Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/41114.
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In our age in which the use of electronic devices is expanding all over the world, their reliability and miniaturization have become very crucial. The thesis is based on the study of one of the most frequent failure mechanisms in semiconductor packages, the delamination of interface or the separation of two bonded materials, in order to improve their adhesion and a fortiori the reliability of microelectronic devices. It focuses on the metal (-oxide) / polymer interfaces because they cover 95% of all existing interfaces.
Since several years, research activities at mesoscopic scale (1-10µm) have proved that the more roughened the surface of the interface, i.e., presenting sharp asperities, the better the adhesion between these two materials. Because roughness exhibits extremely complex shapes, it is difficult to find a description that can be used for reliability analysis of interfaces. In order to investigate quantitatively the effect of roughness variation on adhesion properties, studies have been carried out involving analytical fracture mechanics; then numerical studies were conducted with Finite Element Analysis. Both were done in a deterministic way by assuming an ideal profile which is repeated periodically.
With the development of statistical and stochastic roughness representation on the one hand, and with the emergence of probabilistic fracture mechanics on the other, the present work adds a stochastic framework to the previous studies. In fact, one of the Stochastic Finite Element Methods, the Perturbation method is chosen for implementation, because it can investigate the effect of the geometric variations on the mechanical response such as displacement field. In addition, it can carry out at once what traditional Finite Element Analysis does with numerous simulations which require changing geometric parameters each time.
This method is developed analytically, then numerically by implementing a module in a Finite Element package MSc. Marc/Mentat. In order to get acquainted and to validate the implementation, the Perturbation method is applied analytically and numerically to the 3 point bending test on a beam problem, because the input of the Perturbation method in terms of roughness parameters is still being studied. The capabilities and limitations of the implementation are outlined.
Finally, recommendations for using the implementation and for furture work on roughness representation are discussed.
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Voliotis, Dimitrios. "Contribution à l’étude des chaînes de spin quantique avec une perturbation aléatoire ou apériodique." Thesis, Université de Lorraine, 2016. http://www.theses.fr/2016LORR0253/document.
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Au cours de cette thèse, nous avons étudié le comportement critique de chaînes de spins quantiques en présence de couplages désordonnés ou répartis de manière apériodique. Il est bien établi que le comportement critique des chaînes de spins quantiques d’Ising et de Potts est gouverné par le même point fixe de désordre infini. Nous avons implémenté́ une version numérique de la technique de renormalisation de désordre infini (SDRG) afin de tester cette prédiction. Dans un second temps, nous avons étudié la chaîne quantique d’Ashkin-Teller désordonnée par renormalisation de la matrice densité́ (DMRG). Nous confirmons le diagramme de phase précédemment proposé en déterminant la position des pics du temps d’autocorrélation intégré des corrélations spin-spin et polarisation-polarisation ainsi que ceux des fluctuations de l’aimantation et de la polarisation. Enfin, l’existence d’une double phase de Griffiths est confirmée par une étude détaillée de la décroissance des fonctions d’autocorrélation en dehors des lignes critiques. Comme attendu, l’exposant dynamique diverge à l’approche de ces lignes. Dans le cas apériodique, nous avons étudié les chaînes quantiques d’Ising et de Potts. En utilisant la méthode SDRG, nous avons confirmé les résultats connus pour la chaîne d’Ising et proposé des estimations de la dimension d’échelle magnétique. Dans le cas du modèle de Potts à q états, nous avons estimé l’exposant magnétique et observé qu’il était indépendant du nombre d’états q pour toutes les séquences dont l’exposant de divagation est nul. Toutefois, nous montrons que l’exposant dynamique est fini et augmente avec le nombre d’états q. En revanche, pour la séquence de Rudin-Shapiro, les résultats sont compatibles avec un point fixe de désordre infini et donc un exposant dynamique infiniIn the present thesis, the critical and off-critical behaviors of quantum spin chains in presence of a random or an aperiodic perturbation of the couplings is studied. The critical behavior of the Ising and Potts random quantum chains is known to be governed by the same Infinite-Disorder Fixed Point. We have implemented a numerical version of the Strong-Disorder Renormalization Group (SDRG) to test this prediction. We then studied the quantum random Ashkin-Teller chain by Density Matrix Renormalization Group. The phase diagram, previously obtained by SDRG, is confirmed by estimating the location of the peaks of the integrated autocorrelation times of both the spin-spin and polarization-polarization autocorrelation functions and of the disorder fluctuations of magnetization and polarization. Finally, the existence of a double-Griffiths phase is shown by a detailed study of the decay of the off-critical autocorrelation functions. As expected, a divergence of the dynamical exponent is observed along the two transition lines. In the aperiodic case, we studied both the Ising and Potts quantum chains. Using numerical SDRG, we confirmed the known analytical results for the Ising chains and proposed a new estimate of the magnetic scaling dimension.For the quantum q-state Potts chain, we estimated the magnetic scaling dimension for various aperiodic sequences and showed that it is independent of q for all sequences with a vanishing wandering exponent. However, we observed that the dynamical exponent is finite and increases with the number of states q. In contrast, for the Rudin-Shapiro sequence, the results are compatible with an Infinite-Disorder Fixed Point with a diverging dynamical exponent, equipe de renormalization
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Graf, Daniel [Verfasser], and Christian [Akademischer Betreuer] Ochsenfeld. "Development of efficient electronic-structure methods based on the adiabatic-connection fluctuation-dissipation theorem and Møller–Plesset perturbation theory / Daniel Graf ; Betreuer: Christian Ochsenfeld." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2021. http://d-nb.info/123217629X/34.
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Filippini, Gaëlle. "Simulation moléculaire de monocouches auto-assemblées sur l'or." Phd thesis, Université Blaise Pascal - Clermont-Ferrand II, 2013. http://tel.archives-ouvertes.fr/tel-00905250.
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Ce travail concerne l'étude de monocouches auto-assemblées (SAMs) sur l'or par simulation moléculaire. Des SAMs électroactives formées de chaines ferrocenylalcanethiols et alcanethiols et des SAMs constituées de β-cyclodextrines immobilisées sur des surfaces pouvant donner lieu à la formation de complexes d'inclusion à l'interface ont été étudiées. L'objectif était d'obtenir des grandeurs macroscopiques qui soient directement comparables aux grandeurs expérimentales. Pour cela, des simulations de dynamique moléculaire ont été couplées à des calculs de perturbation thermodynamique afin d'obtenir des grandeurs rédox et des propriétés thermodynamiques d'association. La reproduction de grandeurs expérimentales a dans un premier temps permis de valider les méthodologies de simulation et les champs de forces utilisés. Ceci a ensuite conduit à envisager la simulation moléculaire comme une technique prédictive pour l'étude de nouveaux systèmes. Les grandeurs macroscopiques obtenues ont pu être interprétées grâce à une caractérisation structurale et énergétique des processus mis en jeu.
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Claude, Bertille. "Calcul des vibrations non linéaires d’une structure composite en contact avec un fluide par la Méthode Asymptotique Numérique : application à la vibroacoustique." Thesis, Lorient, 2018. http://www.theses.fr/2018LORIS516/document.
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La maîtrise du bruit et des vibrations est un objectif fréquemment rencontré dans le domaine industriel. Qu’il s’agisse de questions de confort ou de sécurité, les domaines d’applications sont nombreux et variés : transport, BTP, ingénierie civile et militaire… Dans cette thèse, un problème de vibroacoustique interne avec couplage fluide-structure est étudié. Il s’agit d’une cavité remplie de fluide dont les parois sont constituées d’une structure sandwich viscoélastique. Les difficultés numériques associées à ce modèle portent sur la non linéarité du matériau et sur les propriétés des opérateurs matriciels manipulés (conditionnement, non symétrie). Le calcul des vibrations du système dissipatif couplé nécessite une valeur initiale, choisie comme la solution du problème conservatif. Cette solution n’étant pas aisée à déterminer, deux solveurs aux valeurs propres basés sur la Méthode Asymptotique Numérique (MAN) sont proposés pour résoudre le problème des vibrations libres du système conservatif. Associant des techniques de perturbation d'ordre élevé et de continuation, la MAN permet de transformer le problème non linéaire de départ en une suite de problèmes linéaires, plus simples à résoudre. Les solutions obtenues sont ensuite utilisées comme point initial pour déterminer la réponse libre du système dissipatif. Un solveur de Newton d’ordre élevé, basé sur les techniques d’homotopie et de perturbation est développé pour résoudre ce problème. Enfin, le régime forcé est étudié. Pour toutes les configurations envisagées, les résultats obtenus mettent en évidence des performances numériques améliorées par rapport aux méthodes classiquement utilisées (Arpack, Newton…)Noises and vibrations control is a common objective in the industrial field. Whether it is a question of comfort or safety, the fields of application are numerous and varied: transport, building, civil and military engineering… In this thesis, a vibroacoustics interior problem with fluid-structure coupling is studied. A cavity filled of fluid whose walls are made of a sandwich viscoelastic structure is considered. The numerical difficulties associated with this model relate to the non-linearity of the viscoelastic material and the properties of the matrix operators used (conditioning, non-symmetry). The calculation of the vibrations of the coupled dissipative system requires an initial value, chosen as the solution to the conservative problem. Since this solution is difficult to determine, two eigenvalue algorithms based on the Asymptotic Numerical Method (ANM) are proposed to solve the problem of free vibrations of the conservative system. Combining high order perturbation and continuation techniques, ANM transforms the initial non-linear problem into a set of linear problems that are easier to solve. The solutions obtained are then used as the initial point to determine the free vibrations of the dissipative problem. A high order Newton solver, based on homotopy and perturbation techniques, is developed to solve this problem. Finally, the forced harmonic response of the damped system is computed. For all the configurations tested, the results obtained show improved numerical performance compared to the methods conventionally used (Arpack solver, Newton algorithm…)
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Sayi, Mbani T. "High Accuracy Fitted Operator Methods for Solving Interior Layer Problems." University of the Western Cape, 2020. http://hdl.handle.net/11394/7320.
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Philosophiae Doctor - PhDFitted operator finite difference methods (FOFDMs) for singularly perturbed problems have been explored for the last three decades. The construction of these numerical schemes is based on introducing a fitting factor along with the diffusion coefficient or by using principles of the non-standard finite difference methods. The FOFDMs based on the latter idea, are easy to construct and they are extendible to solve partial differential equations (PDEs) and their systems. Noting this flexible feature of the FOFDMs, this thesis deals with extension of these methods to solve interior layer problems, something that was still outstanding. The idea is then extended to solve singularly perturbed time-dependent PDEs whose solutions possess interior layers. The second aspect of this work is to improve accuracy of these approximation methods via methods like Richardson extrapolation. Having met these three objectives, we then extended our approach to solve singularly perturbed two-point boundary value problems with variable diffusion coefficients and analogous time-dependent PDEs. Careful analyses followed by extensive numerical simulations supporting theoretical findings are presented where necessary.
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Venkatachalapathy, Muthukumaran [Verfasser], Leif [Akademischer Betreuer] Dehmelt, and Jan Georg [Gutachter] Hengstler. "Development and application of methods for spatio-temporal perturbation and analysis of protein interactions via intracellular protein microarrays / Muthukumaran Venkatachalapathy. Betreuer: Leif Dehmelt. Gutachter: Jan Georg Hengstler." Dortmund : Universitätsbibliothek Dortmund, 2016. http://d-nb.info/1112560777/34.
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Lindholm, Johan. "Development and Validation of HPLC Methods for Analytical and Preparative Purposes." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis, Univ.-bibl. [distributör], 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4442.
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Fischer, André. "Advanced Cluster Methods for Correlated-Electron Systems." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-191382.
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In this thesis, quantum cluster methods are used to calculate electronic properties of correlated-electron systems. A special focus lies in the determination of the ground state properties of a 3/4 filled triangular lattice within the one-band Hubbard model. At this filling, the electronic density of states exhibits a so-called van Hove singularity and the Fermi surface becomes perfectly nested, causing an instability towards a variety of spin-density-wave (SDW) and superconducting states. While chiral d+id-wave superconductivity has been proposed as the ground state in the weak coupling limit, the situation towards strong interactions is unclear.
Additionally, quantum cluster methods are used here to investigate the interplay of Coulomb interactions and symmetry-breaking mechanisms within the nematic phase of iron-pnictide superconductors. The transition from a tetragonal to an orthorhombic phase is accompanied by a significant change in electronic properties, while long-range magnetic order is not established yet. The driving force of this transition may not only be phonons but also magnetic or orbital fluctuations. The signatures of these scenarios are studied with quantum cluster methods to identify the most important effects.
Here, cluster perturbation theory (CPT) and its variational extention, the variational cluster approach (VCA) are used to treat the respective systems on a level beyond mean-field theory. Short-range correlations are incorporated numerically exactly by exact diagonalization (ED). In the VCA, long-range interactions are included by variational optimization of a fictitious symmetry-breaking field based on a self-energy functional approach. Due to limitations of ED, cluster sizes are limited to a small number of degrees of freedom.
For the 3/4 filled triangular lattice, the VCA is performed for different cluster symmetries. A strong symmetry dependence and finite-size effects make a comparison of the results from different clusters difficult. The ground state in the weak-coupling limit is superconducting with chiral d+id-wave symmetry, in accordance to previous renormalization group approaches. In the regime of strong interactions SDW states are preferred over superconductivity and a collinaer SDW state with nonuniform spin moments on a quadrupled unit cell has the lowest grand potential. At strong coupling, inclusion of short-range quantum fluctuations turns out to favor this collinear state over the chiral phase predicted by mean-field theory. At intermediate interactions, no robust conclusion can be drawn from the results.
Symmetry-breaking mechanisms within the nematic phase of the iron-pnictides are studied using a three-band model for the iron planes on a 4-site cluster. CPT allows a local breaking of the symmetry within the cluster without imposing long-range magnetic order. This is a crucial step beyond mean-field approaches to the magnetically ordered state, where such a nematic phase cannot easily be investigated. Three mechanisms are included to break the fourfold lattice symmetry down to a twofold symmetry. The effects of anisotropic magnetic couplings are compared to an orbital ordering field and anisotropic hoppings. All three mechanisms lead to similar features in the spectral density. Since the anisotropy of the hopping parameters has to be very large to obtain similar results as observed in ARPES, a phonon-driven transition is unlikely.
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Nunez, Manuel A., and Robert M. Freund. "Condition-Measure Bounds on the Behavior of the Central Trajectory of a Semi-Definete Program." Massachusetts Institute of Technology, Operations Research Center, 1999. http://hdl.handle.net/1721.1/5132.
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We present bounds on various quantities of interest regarding the central trajectory of a semi-definite program (SDP), where the bounds are functions of Renegar's condition number C(d) and other naturally-occurring quantities such as the dimensions n and m. The condition number C(d) is defined in terms of the data instance d = (A, b, C) for SDP; it is the inverse of a relative measure of the distance of the data instance to the set of ill-posed data instances, that is, data instances for which arbitrary perturbations would make the corresponding SDP either feasible or infeasible. We provide upper and lower bounds on the solutions along the central trajectory, and upper bounds on changes in solutions and objective function values along the central trajectory when the data instance is perturbed and/or when the path parameter defining the central trajectory is changed. Based on these bounds, we prove that the solutions along the central trajectory grow at most linearly and at a rate proportional to the inverse of the distance to ill-posedness, and grow at least linearly and at a rate proportional to the inverse of C(d)2 , as the trajectory approaches an optimal solution to the SDP. Furthermore, the change in solutions and in objective function values along the central trajectory is at most linear in the size of the changes in the data. All such bounds involve polynomial functions of C(d), the size of the data, the distance to ill-posedness of the data, and the dimensions n and m of the SDP.
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Elsheikh, Sara Mohamed Ahmed Suleiman. "Analysis and implementation of robust numerical methods to solve mathematical models of HIV and Malaria co-infection." Thesis, University of the Western Cape, 2011. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_2221_1319804516.
Full textAbstract:
There is a growing interest in the dynamics of the co-infection of these two diseases. In this thesis, firstly we focus on studying the effect of a distributed delay representing the incubation period for the malaria parasite in the mosquito vector to possibly reduce the initial transmission and prevalence of malaria. This model can be regarded as a generalization of SEI models (with a class for the latently infected mosquitoes) and SI models with a discrete delay for the incubation period in mosquitoes. We study the possibility of occurrence of backward bifurcation. We then extend these ideas to study a full model of HIV and malaria co-infection. To get further inside into the dynamics of the model, we use the geometric singular perturbation theory to couple the fast and slow models from the full model. Finally, since the governing models are very complex, they cannot be solved analytically and hence we develop and analyze a special class of numerical methods to solve them.
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Yoffe, Samuel Robert. "Investigation of the transfer and dissipation of energy in isotropic turbulence." Thesis, University of Edinburgh, 2012. http://hdl.handle.net/1842/7541.
Full textAbstract:
Numerical simulation is becoming increasingly used to support theoretical effort into understanding the turbulence problem. We develop theoretical ideas related to the transfer and dissipation of energy, which clarify long-standing issues with the energy balance in isotropic turbulence. These ideas are supported by results from large scale numerical simulations. Due to the large number of degrees of freedom required to capture all the interacting scales of motion, the increase in computational power available has only recently allowed flows of interest to be realised. A parallel pseudo-spectral code for the direct numerical simulation (DNS) of isotropic turbulence has been developed. Some discussion is given on the challenges and choices involved. The DNS code has been extensively benchmarked by reproducing well established results from literature. The DNS code has been used to conduct a series of runs for freely-decaying turbulence. Decay was performed from a Gaussian random field as well as an evolved velocity field obtained from forced simulation. Since the initial condition does not describe developed turbulence, we are required to determine when the field can be considered to be evolved and measurements are characteristic of decaying turbulence. We explore the use of power-law decay of the total energy and compare with the use of dynamic quantities such as the peak dissipation rate, maximum transport power and velocity derivative skewness. We then show how this choice of evolved time affects the measurement of statistics. In doing so, it is found that the Taylor dissipation surrogate, u^3 / L, is a better surrogate for the maximum inertial flux than dissipation. Stationary turbulence has also been investigated, where we ensure that the energy input rate remains constant for all runs and variation is only introduced by modifying the fluid viscosity (and lattice size). We present results for Reynolds numbers up to Rλ = 335 on a 1024^3 lattice. Using different methods of vortex identification, the persistence of intermittent structure in an ensemble average is considered and shown to be reduced as the ensemble size increases. The longitudinal structure functions are computed for smaller lattices directly from an ensemble of realisations of the real-space velocity field. From these, we consider the generalised structure functions and investigate their scaling exponents using direct analysis and extended self-similarity (ESS), finding results consistent with the literature. An exploitation of the pseudo-spectral technique is used to calculate second- and third-order structure functions from the energy and transfer spectra, with a comparison presented to the real-space calculation. An alternative to ESS is discussed, with the second-order exponent found to approach 2/3. The dissipation anomaly is then considered for both forced and free-decay. Using different choices of the evolved time for a decaying simulation, we show how the behaviour of the dimensionless dissipation coefficient is affected. The Karman-Howarth equation (KHE) is studied and a derivation of a work term presented using a transformation of the Lin equation. The balance of energy represented by the KHE is then investigated using the pseudo-spectral method mentioned above. The consequences of this new input term for the structure functions are discussed. Based on the KHE, we develop a model for the behaviour of the dimensionless dissipation coefficient that predicts Cɛ= Cɛ(∞)+CL/RL. DNS data is used to fit the model. We find Cɛ(∞) = 0.47 and CL = 19.1 for forced turbulence, with excellent agreement to the data. Theoretical methods based on the renormalization group and statistical closures are still being developed to study turbulence. The dynamic RG procedure used by Forster, Nelson and Stephen (FNS) is considered in some detail and a disagreement in the literature over the method and results is resolved here. An additional constraint on the loop momentum is shown to cause a correction to the viscosity increment such that all methods of evaluation lead to the original result found by FNS. The application of statistical closure and renormalized perturbation theory is discussed and a new two-time model probability density functional presented. This has been shown to be self-consistent to second order and to reproduce the two-time covariance equation of the local energy transfer (LET) theory. Future direction of this work is discussed.
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Shamsudin, Khan Yasmin. "Non-Steroidal Anti-Inflammatory Drugs in Cyclooxygenases 1 and 2 : Binding modes and mechanisms from computational methods and free energy calculations." Doctoral thesis, Uppsala universitet, Beräkningsbiologi och bioinformatik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-328478.
Full textAbstract:
Non-steroidal anti-inflammatory drugs (NSAIDs) are one of the most commonly used classes of drugs. They target the cyclooxygenases (COX) 1 and 2 to reduce the physiological responses of pain, fever, and inflammation. Due to their role in inducing angiogenesis, COX proteins have also been identified as targets in cancer therapies. In this thesis, I describe computational protocols of molecular docking, molecular dynamics simulations and free energy calculations. These methods were used in this thesis to determine structure-activity relationships of a diverse set of NSAIDs in binding to their target proteins COX-1 and 2. Binding affinities were calculated and used to predict the binding modes. Based on combinations of molecular dynamics simulations and free energy calculations, binding mechanisms of sub-classes of NSAIDs were also proposed. Two stable conformations of COX were probed to understand how they affect inhibitor affinities. Finally, a brief discussion on selectivity towards either COX isoform is discussed. These results will be useful in future de novo design and testing of third-generation NSAIDs.
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Fégeant, Olivier. "Noise from wind turbines." Doctoral thesis, KTH, Byggnader och installationer, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3100.
Full textAbstract:
A rapid growth of installed wind power capacity is expectedin the next few years. However, the siting of wind turbines ona large scale raises concerns about their environmental impact,notably with respect to noise. To this end, variable speed windturbines offer a promising solution for applications in denselypopulated areas like the European countries, as this designwould enable an efficient utilisation of the masking effect dueto ambient noise. In rural and recreational areas where windturbines are sited, the ambient noise originates from theaction of wind on the vegetation and about the listener's ear(pseudo-noise). It shows a wind speed dependence similar tothat of the noise from a variable speed wind turbine and cantherefore mask the latter for a wide range of conditions.However, a problem inherent to the design of these machines istheir proclivity to pure tone generation, because of theenhanced difficulty of avoiding structural resonances in themechanical parts. Pure tones are deemed highly annoying and areseverely regulated by most noise policies. In relation to thisproblem, the vibration transmission of structure-borne sound tothe tower of the turbine is investigated, in particular whenthe tower is stiffened at its upper end. Furthermore, sincenoise annoyance due to wind turbine is mostly a masking issue,the wind-related sources of ambient noise are studied and theirmasking potentials assessed. With this aim, prediction modelsfor wind-induced vegetation noise and pseudo-noise have beendeveloped. Finally, closely related to the effect of masking,is the difficulty, regularly encountered by local authoritiesand wind farm developers, to measure noise immission from windturbines. A new measurement technique has thus been developedin the course of this work. Through improving thesignal-to-noise ratio between wind turbine noise and ambientnoise, the new technique yields more accurate measurementresults. Keywords: Masking, vibration transmission, diffraction,ambient noise, pseudo-noise, cylindrical shell, perturbationmethods, structural mobility, acoustic outdoor measurement.QC 20100616
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Meesala, Vamsi Chandra. "Modeling and Analysis of a Cantilever Beam Tip Mass System." Thesis, Virginia Tech, 2018. http://hdl.handle.net/10919/83378.
Full textAbstract:
We model the nonlinear dynamics of a cantilever beam with tip mass system subjected to different excitation and exploit the nonlinear behavior to perform sensitivity analysis and propose a parameter identification scheme for nonlinear piezoelectric coefficients.
First, the distributed parameter governing equations taking into consideration the nonlinear boundary conditions of a cantilever beam with a tip mass subjected to principal parametric excitation are developed using generalized Hamilton's principle. Using a Galerkin's discretization scheme, the discretized equation for the first mode is developed for simpler representation assuming linear and nonlinear boundary conditions. We solve the distributed parameter and discretized equations separately using the method of multiple scales. We determine that the cantilever beam tip mass system subjected to parametric excitation is highly sensitive to the detuning. Finally, we show that assuming linearized boundary conditions yields the wrong type of bifurcation.
Noting the highly sensitive nature of a cantilever beam with tip mass system subjected to parametric excitation to detuning, we perform sensitivity of the response to small variations in elasticity (stiffness), and the tip mass. The governing equation of the first mode is derived, and the method of multiple scales is used to determine the approximate solution based on the order of the expected variations. We demonstrate that the system can be designed so that small variations in either stiffness or tip mass can alter the type of bifurcation. Notably, we show that the response of a system designed for a supercritical bifurcation can change to yield a subcritical bifurcation with small variations in the parameters. Although such a trend is usually undesired, we argue that it can be used to detect small variations induced by fatigue or small mass depositions in sensing applications.
Finally, we consider a cantilever beam with tip mass and piezoelectric layer and propose a parameter identification scheme that exploits the vibration response to estimate the nonlinear piezoelectric coefficients. We develop the governing equations of a cantilever beam with tip mass and piezoelectric layer by considering an enthalpy that accounts for quadratic and cubic material nonlinearities. We then use the method of multiple scales to determine the approximate solution of the response to direct excitation. We show that approximate solution and amplitude and phase modulation equations obtained from the method of multiple scales analysis can be matched with numerical simulation of the response to estimate the nonlinear piezoelectric coefficients.Master of Science