Dissertations / Theses on the topic 'Asymptotic Analysis'
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Churchman, Christopher M. "Asymptotic analysis of complete contacts." Thesis, University of Oxford, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.441071.
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Lladser, Manuel Eugenio. "Asymptotic enumeration via singularity analysis." Connect to this title online, 2003. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1060976912.
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Thesis (Ph. D.)--Ohio State University, 2003.Title from first page of PDF file. Document formatted into pages; contains x, 227 p.; also includes graphics Includes bibliographical references (p. 224-227). Available online via OhioLINK's ETD Center
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PEREIRA, LUIS CLAUDIO PALMA. "ASYMPTOTIC ANALYSIS OF SHAPED REFLECTOR ANTENNAS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1988. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=8374@1.
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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOEste trabalho apresenta uma nova técnica para aproximação de uma superfície refletora definida numericamente, i.e., por pontos fornecidos pelo processo de síntese da antena. As limitações inerentes às técnicas usuais são aqui eliminadas pela utilização de Pseudo-Splines Quínticas que interpolam uma distribuição arbitrária de pontos por uma superfície suave, com derivadas primeiras e segundas contínuas, assegurando uma representação única para o domínio de interesse. O procedimento é, então, aplicado ao subrefletor modelado de uma antena Cassegrain, com subseqüente cálculo do campo eletromagnético espalhado, permitindo uma análise detalhada de sua aplicabilidade. Uma teoria assintótica uniforme de difração é, também, aqui desenvolvida de modo a acomodar o espalhamento de feixes Gaussianos, descritivos, em freqüências altas, do diagrama de irradiação de alimentadores comumente empregados em sistemas refletores, por superfícies condutoras, através do rastreamento do campo eletromagnético ao longo de raios no espaço complexo. A análise do problema canônico (difração por semi-plano) estabelece as particularidades do método e a comparação com a solução rigorosa existente comprova sua acurácia, permitindo a extensão a problemas tridimensionais vetorais. A teoria Complexa da Difração, assim formulada, é, então aplicada ao cálculo do campo espalhado por diferentes geometrias de antenas refletoras, ilustrando a versatilidade do método bem como suas limitações.
In order to evaluate the electromagnetic field scattered by shaped reflector antennas, one has to fit a surface to a set of points furnished by a synthesis technique. A new method, capable of interpolating arbitrarily located data points by a smooth surface is here presented. The interpolating function, called Quintic Pseudo-Spline, has continuous first and seconde order derivatives and yields a unique representation for the entire domain. The method is tested on the shaped subreflector of a Cassegrain antenna providing a thorough investigation of its applicability. Also, an uniform asymptotic theory of diffraction is derived in order to analyse the scattering of Gaussin beams, descriptive of the high-frequency radiation pattern of feed horns commonly employed in reflector systems, by conducting surfaces with edges. The constraints inherent to usual methods of analysis are hereby avoided by tracking these beam-type fields along straight rays in a complex coordinate space. Investigation of the canonical problem of scattering of a Gaussian beam by a conducting half-plane establishes the characteristics of the complex ray diffraction process. Comparison of the results thus obtained with the rigorous solution reveals the accuracy of the proposed theory and permits its extension to the three-dimensional vector problem. The resulting Complex Theory of Diffraction is then applied to the evaluation of the scattered field for several reflector antenna geometries, illustrating the versatility of the method as well as its limitation.
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Chu, Kevin Taylor. "Asymptotic analysis of extreme electrochemical transport." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/33669.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.Includes bibliographical references (p. 237-244).
In the study of electrochemical transport processes, experimental exploration currently outpaces theoretical understanding of new phenomena. Classical electrochemical transport theory is not equipped to explain the behavior of electrochemical systems in the extreme operating conditions required by modern devices. In this thesis, we extend the classical theory to examine the response of two electrochemical systems that form the basis for novel electrochemical devices. We first examine the DC response of an electrochemical thin film, such as the separator in a micro-battery, driven by current applied through reactive electrodes. The model system consists of a binary electrolyte between parallel-plate electrodes, each possessing a compact Stern layer which mediates Faradaic reactions with Butler-Volmer kinetics. Our analysis differs from previous studies in two significant ways. First, we impose the full nonlinear, reactive boundary conditions appropriate for electrolytic/galvanic cells.
(cont.) Since surface effects become important for physically small systems, the use of reactive boundary conditions is critical in order to gain insight into the behavior of actual electrochemical thin films that are sandwiched between reactive electrodes, especially at high current densities. For instance, our analysis shows that reaction rate constants and the Stern-layer capacitance have a strong influence on the response of the thin film. Second, we analyze the system at high current densities (far beyond the classical diffusion-limited current) which may be important for high power-density applications. At high currents, we obtain previously unknown characterizations of two interesting features at the cathode end of the cell: (i) a nested boundary layer structure and (ii) an extended space charge region. Next, we study the response of a metal (i.e., polarizable) colloid sphere in an electrolyte solution over a range of applied electric fields.
(cont.) This problem, which underlies novel electrokinetically driven microfluidic devices, has traditionally been analyzed using circuit models which neglect bulk concentration variations that arise due to double layer charging. Our analysis, in contrast, is based on the Nernst-Planck equations which explicitly allow for bulk concentration gradients. A key feature of our analysis is the use of surface conservation laws to provide effective boundary conditions that couple the double layer charging dynamics, surface transport processes, and bulk transport processes. The formulation and derivation of these surface conservation laws via boundary layer analysis is one of the main contributions of this thesis. For steady applied fields, our analysis shows that bulk concentrations gradients become significant at high applied fields and affect both bulk and double layer transport processes. We also find that surface transport becomes important for strong applied fields as a result of enhanced absorption of ions by the double layer.
(cont.) Unlike existing theoretical studies which focus on weak applied fields (so that both of these effects remain weak), we explore the response of the system to strong applied fields where both bulk concentration gradients and surface transport contribute at leading order. For the unsteady problem at applied fields that are not too strong, we find that diffusion processes, which are necessary for the system to relax to steady-state, are suppressed at leading-order but appear as higher-order corrections. This result is derived in a novel way using time-dependent matched asymptotic analysis. Unfortunately, the dynamic response of the system to large applied fields seems to introduce several complications that make the analysis (both mathematical and numerical) quite challenging; the resolution of these challenges is left for future work. Both of these problems require the use of novel techniques of asymptotic analysis (e.g., multiple parameter asymptotic expansions, surface conservation laws, and time-dependent asymptotic matching) and advanced numerical methods (e.g., pseudospectral methods, Newton-Kantorovich method, and direct matrix calculation of Jacobians) which may be applicable elsewhere.
by Kevin Taylor Chu.
Ph.D.
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Maling, Ben. "Asymptotic analysis of array-guided waves." Thesis, Imperial College London, 2016. http://hdl.handle.net/10044/1/44725.
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We develop and apply computational and analytical techniques to study wave-like propagation and resonant effects in periodic and quasi-periodic systems. Two themes that unify the content herein are the guidance and confinement of energy using periodic structures, and the utility of asymptotic analysis to aid computation and produce results that lend physical insight to the problems in question. In the first research chapter, we develop the method of high-frequency homogenisation (HFH) for electromagnetic waves in dielectric media, and apply this to the example of a planar array of dielectric spheres. The theory conveniently describes a range of dynamic effects, including effectively anisotropic behaviour in certain frequency regimes. In the second research chapter, we apply the HFH method to a cylindrical Bragg fibre, and use this to set up an effective eigenvalue problem in which the quasi-periodic system representing the fibre cladding is represented by a single continuous Bessel-like equation. We compare the results with those of direct numerical simulations and discuss how the theory could be developed to aid the study of photonic crystal cavities or fibres. In the remaining chapters, we consider the complex resonances of structures with angular periodicity. We demonstrate the emergence of quasi-normal modes with high Q-factors for the Helmholtz equation in such domains, and explore some of their properties using multiple scale analysis. In the final two chapters, we focus on a particular subset of these domains, and using matched asymptotic expansions show that the Q-factors for certain solutions depend exponentially on the number of inclusions arranged in a circular ring. Finally, we extend this analysis to flexural waves in thin elastic plates, and discuss the possibility of structured-ring resonators based on these solutions.
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Dew, N. "Asymptotic structure of Banach spaces." Thesis, University of Oxford, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.270612.
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The notion of asymptotic structure of an infinite dimensional Banach space was introduced by Maurey, Milman and Tomczak-Jaegermann. The asymptotic structure consists of those finite dimensional spaces which can be found everywhere `at infinity'. These are defined as the spaces for which there is a winning strategy in a certain vector game. The above authors introduced the class of asymptotic $\ell_p$ spaces, which are the spaces having simplest possible asymptotic structure. Key examples of such spaces are Tsirelson's space and James' space. We prove some new properties of general asymptotic $\ell_p$ spaces and also compare the notion of asymptotic $\ell_2$ with other notions of asymptotic Hilbert space behaviour such as weak Hilbert and asymptotically Hilbertian. We study some properties of smooth functions defined on subsets of asymptotic $\ell_\infty$ spaces. Using these results we show that that an asymptotic $\ell_\infty$ space which has a suitably smooth norm is isomorphically polyhedral, and therefore admits an equivalent analytic norm. We give a sufficient condition for a generalized Orlicz space to be a stabilized asymptotic $\ell_\infty$ space, and hence obtain some new examples of asymptotic $\ell_\infty$ spaces. We also show that every generalized Orlicz space which is stabilized asymptotic $\ell_\infty$ is isomorphically polyhedral. In 1991 Gowers and Maurey constructed the first example of a space which did not contain an unconditional basic sequence. In fact their example had a stronger property, namely that it was hereditarily indecomposable. The space they constructed was `$\ell_1$-like' in the sense that for any $n$ successive vectors $x_1 < \ldots < x_n$, $\frac{1}{f(n)} \sum_{i=1}^n \| x_i \| \leq \| \sum_{i=1}^n x_i \| \leq \sum_{i=1}^n \| x_i \|,$ where $ f(n) = \log_2 (n+1) $. We present an adaptation of this construction to obtain, for each $ p \in (1, \infty)$, an hereditarily indecomposable Banach space, which is `$\ell_p$-like' in the sense described above. We give some sufficient conditions on the set of types, $\mathscr{T}(X)$, for a Banach space $X$ to contain almost isometric copies of $\ell_p$ (for some $p \in [1, \infty)$) or of $c_0$. These conditions involve compactness of certain subsets of $\mathscr{T}(X)$ in the strong topology. The proof of these results relies heavily on spreading model techniques. We give two examples of classes of spaces which satisfy these conditions. The first class of examples were introduced by Kalton, and have a structural property known as Property (M). The second class of examples are certain generalized Tsirelson spaces. We introduce the class of stopping time Banach spaces which generalize a space introduced by Rosenthal and first studied by Bang and Odell. We look at subspaces of these spaces which are generated by sequences of independent random variables and we show that they are isomorphic to (generalized) Orlicz spaces. We deduce also that every Orlicz space, $h_\phi$, embeds isomorphically in the stopping time Banach space of Rosenthal. We show also, by using a suitable independence condition, that stopping time Banach spaces also contain subspaces isomorphic to mixtures of Orlicz spaces.
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Kong, Fanhui. "Asymptotic distributions of Buckley-James estimator." Online access via UMI:, 2005.
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Åslund, Jan. "Asymptotic analysis of junctions in multi-structures /." Linköping : Univ, 2002. http://www.bibl.liu.se/liupubl/disp/disp2002/tek739s.pdf.
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Lu, Yulong. "Asymptotic analysis and computations of probability measures." Thesis, University of Warwick, 2017. http://wrap.warwick.ac.uk/94863/.
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This thesis is devoted to asymptotic analysis and computations of probability measures. We are concerned with the probability measures arising from two classes of problems: Bayesian inverse problems and rare events in molecular dynamics. In the former we are interested in the concentration phenomenon of the posterior measures such as posterior consistency, and the computational methods for sampling the posterior, such as the Markov Chain Monte Carlo (MCMC). In the latter we want to describe the most probable transition paths on molecular energy landscapes in the small temperature regime. First, we examine the asymptotic normality of a general family of finite dimensional probability measures indexed by a small parameter. We begin this by studying the best Gaussian approximation to the target measure with respect to the Kullback-Leibler divergence, and then analyse the asymptotic behaviour of such approximation via Γ-convergence. This abstract theory is employed to study the posterior consistency of a finite dimensional Bayesian inverse problem. Next, we are concerned with a Bayesian inverse problem arising from barcode denoising, namely reconstructing a binary signal from finite many noisy pointwise evaluations. By choosing the prior appropriately, we show that in the small noise limit the resulting posterior concentrates on a manifold which consists of a family of parametrized binary profiles. Furthermore, we extend the use of Gaussian approximation in the context of the (infinite dimensional) transition path problem. In particular, we characterize the most probable paths as an ensemble of paths which fluctuates within an optimal Gaussian tube. The low temperature limit of these optimal paths is also identified via the Γ-convergence of some relevant variational problem. Finally, we introduce, analyze and implement a novel Bayesian level set method for solving geometric inverse problems. This Bayesian approach not only removes some draw- backs of classical level set methods but also enables quantifying geometric uncertainties induced by noisy measurements.
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Shi, Fangwei. "Asymptotic analysis of new stochastic volatility models." Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/60648.
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A good options pricing model should be able to fit the market volatility surface with high accuracy. While the standard continuous stochastic volatility models can generate volatility smiles consistent with market data for relatively larger maturities, these models cannot reproduce market smiles for small maturities, which have the well-observed 'small-time explosion' feature. In this thesis we propose three new types of stochastic volatility models, and we focus on the small-time asymptotic behaviour of the implied volatility in these models. We show that these models can generate implied volatilities with explosion, hence they can theoretically provide a better fit to the market data. The thesis is organised as follows. Chapter 0 is the introduction. We briefly discuss the development and performance of standard continuous stochastic volatility models, and raise the small-time fitness issue of these traditional models. In Chapter 1 we propose the randomised Heston model and analyse its small and large time asymptotic behaviours. In particular, we show that any small-time explosion rate in between of [0, 1/2] for the implied variance can be captured by a suitable choice of the initial randomisation. In Chapter 2 we propose a fractional version of the Heston model and detail the small-time asymptotic behaviour of the implied volatility in this setting. We precise the link between the explosion rate and the Hurst parameter. Finally, in Chapter 3 we propose a new stochastic volatility model based on the recent work by Conus and Wildman in which the stock price can have past dependency. We show that in the case of a CIR variance process this model has similar behaviours to a fractional Heston environment.
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Graner, Johannes. "On Asymptotic Properties of Principal Component Analysis." Thesis, Uppsala universitet, Tillämpad matematik och statistik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-420649.
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Robbins, Michael. "Change -point analysis asymptotic theory and applications /." Connect to this title online, 2009. http://etd.lib.clemson.edu/documents/1252423918/.
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Wang, Qi. "Asymptotic Multiphysics Modeling of Composite Beams." DigitalCommons@USU, 2011. https://digitalcommons.usu.edu/etd/1066.
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A series of composite beam models are constructed for efficient high-fidelity beam analysis based on the variational-asymptotic method (VAM). Without invoking any a priori kinematic assumptions, the original three-dimensional, geometrically nonlinear beam problem is rigorously split into a two-dimensional cross-sectional analysis and a one-dimensional global beam analysis, taking advantage of the geometric small parameter that is an inherent property of the structure.
The thermal problem of composite beams is studied first. According to the quasisteady theory of thermoelasticity, two beam models are proposed: one for heat conduction analysis and the other for thermoelastic analysis. For heat conduction analysis, two different types of thermal loads are modeled: with and without prescribed temperatures over the crosssections. Then a thermoelastic beam model is constructed under the previously solved thermal field. This model is also extended for composite materials, which removed the restriction on temperature variations and added the dependence of material properties with respect to temperature based on Kovalenoko’s small-strain thermoelasticity theory.
Next the VAM is applied to model the multiphysics behavior of beam structure. A multiphysics beam model is proposed to capture the piezoelectric, piezomagnetic, pyroelectric, pyromagnetic, and hygrothermal effects. For the zeroth-order approximation, the classical models are in the form of Euler-Bernoulli beam theory. In the refined theory, generalized Timoshenko models have been developed, including two transverse shear strain measures. In order to avoid ill-conditioned matrices, a scaling method for multiphysics modeling is also presented. Three-dimensional field quantities are recovered from the one-dimensional variables obtained from the global beam analysis.
A number of numerical examples of different beams are given to demonstrate the application and accuracy of the present theory. Excellent agreements between the results obtained by the current models and those obtained by three-dimensional finite element analysis, analytical solutions, and those available in the literature can be observed for all the cross-sectional variables. The present beam theory has been implemented into the computer program VABS (Variational Asymptotic Beam Sectional Analysis).
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Baligh, Mohammadhadi. "Analysis of the Asymptotic Performance of Turbo Codes." Thesis, University of Waterloo, 2006. http://hdl.handle.net/10012/883.
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Battail [1989] shows that an appropriate criterion for the design of long block codes is the closeness of the normalized weight distribution to a Gaussian distribution. A subsequent work shows that iterated product of single parity check codes satisfy this criterion [1994]. Motivated by these earlier works, in this thesis, we study the effect of the interleaver on the performance of turbo codes for large block lengths, $N\rightarrow\infty$. A parallel concatenated turbo code that consists of two or more component codes is considered. We demonstrate that for $N\rightarrow\infty$, the normalized weight of the systematic $\widehat{w_1}=\displaystyle\frac{w_1}{\sqrt{N}}$, and the parity check sequences $\widehat{w_2}=\displaystyle\frac{w_2}{\sqrt{N}}$ and $\widehat{w_3}=\displaystyle\frac{w_3}{\sqrt{N}}$ become a set of jointly Gaussian distributions for the typical values of $\widehat{w_i},i=1,2,3$, where the typical values of $\widehat{w_i}$ are defined as $\displaystyle\lim_{N\rightarrow\infty}\frac{\widehat{w_i}}{\sqrt{N}}\neq 0,1$ for $i=1,2,3$. To optimize the turbo code performance in the waterfall region which is dominated by high-weight codewords, it is desirable to reduce $\rho_{ij}$, $i,j=1,2,3$ as much as possible, where $\rho_{ij}$ is the correlation coefficient between $\widehat{w_i}$ and $\widehat{w_j}$. It is shown that: (i)~$\rho_{ij}>0$, $i,j=1,2,3$, (ii)~$\rho_{12},\rho_{13}\rightarrow 0$ as $N\rightarrow\infty$, and (iii)~$\rho_{23}\rightarrow 0$ as $N\rightarrow\infty$ for "almost" any random interleaver. This indicates that for $N\rightarrow\infty$, the optimization of the interleaver has a diminishing effect on the distribution of high-weight error events, and consequently, on the error performance in the waterfall region. We show that for the typical weights, this weight distribution approaches the average spectrum defined by Poltyrev [1994]. We also apply the tangential sphere bound (TSB) on the Gaussian distribution in AWGN channel with BPSK signalling and show that it performs very close to the capacity for code rates of interest. We also study the statistical properties of the low-weight codeword structures. We prove that for large block lengths, the number of low-weight codewords of these structures are some Poisson random variables. These random variables can be used to evaluate the asymptotic probability mass function of the minimum distance of the turbo code among all the possible interleavers. We show that the number of indecomposable low-weight codewords of different types tend to a set of independent Poisson random variables. We find the mean and the variance of the union bound in the error floor region and study the effect of expurgating low-weight codewords on the performance. We show that the weight distribution in the transition region between Poisson and Gaussian follows a negative binomial distribution. We also calculate the interleaver gain for multi-component turbo codes based on these Poisson random variables. We show that the asymptotic error performance for multi-component codes in different weight regions converges to zero either exponentially (in the Gaussian region) or polynomially (in the Poisson and negative binomial regions) with respect to the block length, with the code-rate and energy values close to the channel capacity.
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Moyles, Iain. "Hybrid asymptotic-numerical analysis of pattern formation problems." Thesis, University of British Columbia, 2015. http://hdl.handle.net/2429/53715.
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In this thesis we present an analysis of the Gierer-Meinhardt model with saturation (GMS) on various curve geometries in ℝ². We derive a boundary fitted coordinate framework which translates an asymptotic two-component differential equation into a single component reaction diffusion equation with singular interface conditions. We create a numerical method that generalizes the solution of such a system to arbitrary two-dimensional curves and show how it extends to other models with singularity properties that are related to the Laplace operator. This numerical method is based on integrating logarithmic singularities which we handle by the method of product integration where logarithmic singularities are handled analytically with numerically interpolated densities. In parallel with the generalized numerical method, we present some analytical solutions to the GMS model on a circular and slightly perturbed circular curve geometry. We see that for the regular circle, saturation leads to a hysteresis effect for two dynamically stable branches of equilibrium radii. For the near circle we show that there are two distinct perturbations, one resulting from the introduction of a angular dependent radius, and one caused by Fourier mode interactions which causes a vertical shift to the solution. We perform a linear stability analysis to the true circle solution and show that there are two classes of eigenvalues leading to breakup or zigzag instabilities. For the breakup instabilities we show that the saturation parameter can completely stabilize perturbations that we show are always unstable without saturation and for the zigzag instabilities we show that the eigenvalues are given by the near circle curve normal velocity. The breakup analysis is based on the reduction of an implicit non-local eigenvalue problem (NLEP) to a root finding problem. We derive conditions for which this eigenvalue problem can be made explicit and use it to analyze a stripe and ring geometry. This formulation allows us to classify certain technical properties of NLEPs such as instability bands and a Hopf bifurcation condition analytically.Science, Faculty of
Mathematics, Department of
Graduate
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Landman, Irina M. "Asymptotic analysis of vibrations of thin cylindrical shells." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape4/PQDD_0016/MQ54326.pdf.
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Yaobin, Wen. "Asymptotic Analysis of Interference in Cognitive Radio Networks." Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/23997.
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The aggregate interference distribution in cognitive radio networks is studied in a rigorous and analytical way using the popular Poisson point process model. While a number of results are available for this model for non-cognitive radio networks, cognitive radio networks present extra levels of difficulties for the analysis, mainly due to the exclusion region around the primary receiver, which are typically addressed via various ad-hoc approximations (e.g., based on the interference cumulants) or via the large-deviation analysis. Unlike the previous studies, we do not use here ad-hoc approximations but rather obtain the asymptotic interference distribution in a systematic and rigorous way, which also has a guaranteed level of accuracy at the distribution tail. This is in contrast to the large deviation analysis, which provides only the (exponential) order of scaling but not the outage probability itself. Unlike the cumulant-based analysis, our approach provides a guaranteed level of accuracy at the distribution tail. Additionally, our analysis provides a number of novel insights. In particular, we demonstrate that there is a critical transition point below which the outage probability decays only polynomially but above which it decays super-exponentially. This provides a solid analytical foundation to the earlier empirical observations in the literature and also reveals what are the typical ways outage events occur in different regimes. The analysis is further extended to include interference cancelation and fading (from a broad class of distributions). The outage probability is shown to scale down exponentially in the number of canceled nearest interferers in the below-critical region and does not change significantly in the above-critical one. The proposed asymptotic expressions are shown to be accurate in the non-asymptotic regimes as well.
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Vanel, Alice. "Asymptotic analysis of discrete and continuous periodic media." Thesis, Imperial College London, 2018. http://hdl.handle.net/10044/1/64911.
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Mechanical mass-spring networks have long acted to motivate, and gain qualitative intuition, in solid-state physics, continuous media containing periodic arrays of inclu- sions such as phononic crystals, and more recently in metamaterials. While in some cases an exact or approximate analogy between the continuous model and its discrete representation can be systematically drawn, more often such analogies are introduced heuristically to aid interpretation with the lumped parameters estimated and accepted as qualitative. This thesis builds towards making the analogy exact; we first look at the discrete masses and springs lattices and apply multiple-scales methods directly to Green’s function integrals to extract the behaviour near critical frequencies. The features we uncover, and the asymptotics, are generic for many lattice structures. We then identify and study a new class of materials, two- and three- dimensional phononic crystals formed by closely spaced rigid cylinders or interconnected perforated boxes, respectively, and show that such materials constitute a versatile and tuneable family of subwavelength metamaterials. Intuitively, the voids and narrow gaps that characterise the crystals form an interconnected network of Helmholtz-like resonators. We use this intuition to argue that these continuous phononic crystals are in fact asymptotically equivalent, at low frequencies, to discrete mass-spring networks whose lumped param- eters we derive explicitly. The crystals are tantamount to metamaterials as their entire acoustic branch is squeezed into a subwavelength regime where the ratio of wavelength to period scales like the ratio of period to gap width raised to the power 1/4 in two dimensions and 1/2 in three dimensions; at yet larger wavelengths we accordingly find a comparably large effective refractive index. The fully analytical dispersion relations predicted by the discrete models yield dispersion curves that agree with those from finite-element simulations of the continuous crystals.
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Rao, Chaitanya Kumar Hassibi Babak Hassibi Babak. "Asymptotic analysis of wireless systems with Rayleigh fading /." Diss., Pasadena, Calif. : Caltech, 2007. http://resolver.caltech.edu/CaltechETD:etd-04252007-122857.
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Shekar, Bharath Chandra. "Modeling, evaluation, and asymptotic analysis of attenuation anisotropy." Thesis, Colorado School of Mines, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3609531.
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Seismic attenuation is sensitive to the physical properties of the subsurface, which makes attenuation analysis a useful tool for reservoir characterization. In this thesis, I present algorithms for estimating directionally dependent attenuation coefficients and perform asymptotic and numerical analysis of wave propagation in attenuative anisotropic media.
First, I introduce a methodology to estimate the S-wave interval attenuation coefficient by extending the layer-stripping method of Behura and Tsvankin (2009) to mode-converted (PS) waves. Kinematic reconstruction of pure shear (SS) events in the target layer and the overburden is performed by combining velocity-independent layer stripping with the PP+PS=SS method. Then, application of the spectral-ratio method and the dynamic version of velocity-independent layer stripping to the constructed SS reflections yields the S-wave interval attenuation coefficient in the target layer. The attenuation coefficient estimated for a range of source-receiver offsets can be inverted for the interval attenuation-anisotropy parameters. The method is tested on synthetic data generated with the anisotropic reflectivity method for layered VTI (transversely isotropic with a vertical symmetry axis) media and vertical symmetry planes of orthorhombic media.
Then, I analyze a cross-hole data set generated by perforation shots set off in a horizontal borehole to induce hydraulic fracturing in a tight gas reservoir. The spectral-ratio method is applied to pairs of traces to set up a system of equations for directionally-dependent effective attenuation. Although the inversion provides clear evidence of attenuation anisotropy, the narrow range of propagation directions impairs the accuracy of anisotropy analysis. The observed variations of the attenuation coefficient between different perforation stages appear to be related to changes in the medium due to hydraulic fracturing and stimulation.
Important insights into point-source radiation in attenuative anisotropic media can be gained by applying asymptotic methods. I derive the asymptotic Green's function in homogeneous, attenuative, arbitrarily anisotropic media using the steepest-descent method. The saddle-point condition helps describe the behavior of the far field slowness and group-velocity vectors and evaluate the inhomogeneity angle (the angle between the real and imaginary parts of the slowness vector). The results from the asymptotic analysis are compared with those from the ray-perturbation method for P-waves in TI media.
Finally, I address the problem of efficient viscoelastic modeling in heterogeneous anisotropic media. The Kirchhoff scattering integral is employed to generate reflected P-waves, with the required Green's functions computed by summation of Gaussian beams. The influence of attenuation on the Gaussian beams is incorporated using ray-perturbation theory. The method is applied to generate synthetic data from a highly attenuative VTI medium above a horizontal reflector and a structurally complex acoustic model with a salt body.
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Espinola, Rocha Jesus Adrian. "Short-time Asymptotic Analysis of the Manakov System." Diss., The University of Arizona, 2006. http://hdl.handle.net/10150/195734.
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The Manakov system appears in the physics of optical fibers, as well as in quantum mechanics, as multi-component versions of the Nonlinear Schr\"odinger and the Gross-Pitaevskii equations.Although the Manakov system is completely integrable its solutions are far from being explicit in most cases. However, the Inverse Scattering Transform (IST) can be exploited to obtain asymptotic information about solutions.This thesis will describe the IST of the Manakov system, and its asymptotic behavior at short times. I will compare the focusing and defocusing behavior, numerically and analytically, for squared barrier initial potentials. Finally, I will show that the continuous spectrum gives the dominant contribution at short-times.
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Alkhamisi, Mahdi. "Asymptotic analysis of the one-way random effects models." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ50063.pdf.
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Rand, Peter. "Asymptotic analysis of solutions to elliptic and parabolic problems." Doctoral thesis, Linköping : Matematiska institutionen, Linköpings universitet, 2006. http://www.bibl.liu.se/liupubl/disp/disp2006/tek1044s.pdf.
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FIGUEROA, HUGO HENRIQUE HERNANDEZ. "UNIFORM ASYMPTOTIC ANALYSIS OF DIFFRACTION BY CONVEX CONDUCTOR SURFACES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1987. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=14584@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIORINSTITUTO MILITAR DE ENGENHARIA
TELECOMUNICAÇÕES BRASILEIRAS S/A
Esta dissertação tem por objetivo desenvolver, a partir do estudo do problema canônico de espalhamento eletromagnético por um cilindro circular perfeitamente condutor, uma formulação assintótica uniforme para a difração por superfícies condutoras convexas. A solução obtida é então aplicada à análise de desempenho de refletores parabólicos com borda espessa visando fornecer subsídios ao projeto de antenas com nível de lobos secundários controlado.
It is the purpose of this dissertation to develop an uniform asymptotic formulation for the diffraction by convex conducting surfaces, starting from the study of the canonical problem of electromagnetic scattering by perfectly conducting circular cylinders. The solution thus obtained in then applied to the analysis of parabolic reflectors with a curved surface section attached to the outside of the aperture edges, in order to provide with an insight into designing antennas with controlled sidelobe patterns.
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Visram, Abeed. "Asymptotic limit analysis for numerical models of atmospheric frontogenesis." Thesis, Imperial College London, 2014. http://hdl.handle.net/10044/1/23219.
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Accurate prediction of the future state of the atmosphere is important throughout society, ranging from the weather forecast in a few days time to modelling the effects of a changing climate over decades and generations. The equations which govern how the atmosphere evolves have long been known; these are the Navier-Stokes equations, the laws of thermodynamics and the equation of state. Unfortunately the nonlinearity of the equations prohibits analytic solutions, so simplified models of particular flow phenomena have historically been, and continue to be, used alongside numerical models of the full equations. In this thesis, the two-dimensional Eady model of shear-driven frontogenesis (the creation of atmospheric fronts) was used to investigate how errors made in a localised region can affect the global solution. Atmospheric fronts are the boundary of two different air masses, typically characterised by a sharp change in air temperature and wind direction. This occurs across a small length of O(10 km), whereas the extent of the front itself can be O(1000 km). Fronts are a prominent feature of mid-latitude weather systems and, despite their narrow width, are part of the large-scale, global solution. Any errors made locally in the treatment of fronts will therefore affect the global solution. This thesis uses the convergence of the Euler equations to the semigeostrophic equations, a simplified model which is representative of the large-scale flow, including fronts. The Euler equations were solved numerically using current operational techniques. It was shown that highly predictable solutions could be obtained, and the theoretical convergence rate maintained, even with the presence of near-discontinuous solutions given by intense fronts. Numerical solutions with successively increased resolution showed that the potential vorticity, which is a fundamental quantity in determining the large-scale, balanced flow, approached the semigeostrophic limit solution. Regions of negative potential vorticity, indicative of local areas of instability, were reduced at high resolution. In all cases, the width of the front reduced to the grid-scale. While qualitative features of the limit solution were reproduced, a stark contrast in amplitude was found. The results of this thesis were approximately half in amplitude of the limit solution. Some attempts were made at increasing the intensity of the front through spatial- and temporal-averaging. A scheme was proposed that conserves the potential vorticity within the Eady model.
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Janicki, William D. (William Daniel). "Asymptotic analysis of hypersonic vehicle dynamics along entry trajectory." Thesis, Massachusetts Institute of Technology, 1991. http://hdl.handle.net/1721.1/42502.
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Genovese, de Oliveira Andrea. "Asymptotic and stability analysis of a tumour growth model." Thesis, University of Nottingham, 2017. http://eprints.nottingham.ac.uk/40473/.
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We investigate avascular tumour growth as a two-phase process consisting of cells and liquid. Initially, we simulate a continuum moving-boundary model formulated by Byrne, King, McElwain, Preziosi, (Applied Mathematics Letters, 2003, 16, 567-573) in one dimension and analyse the dependence of the tumour growth on the natural nutrient and cell concentration levels outside of the tumour along with its ability to model known biological dynamics of tumour growth. We investigate linear stability of time-dependent solution profiles in the moving-boundary formulation of a limit case (with negligible nutrient consumption and cell drag) and compare analytical predictions of their saturation, growth and exponential decay against numerical simulations of the full one dimensional model formulated in the article cited above. With this limit case and its time-dependent solution, we analytically obtained a critical nutrient concentration that determines whether a tumour will grow or decay. Then, we formulated the analogous model and boundary conditions for tumour growth in two dimensions. By considering the same limit case and its time-dependent solutions in two dimensions, we obtain an asymptotic limit of the two-dimensional perturbations for large time in the case where the tumour is growing by using the method of matched asymptotic approximations. Having characterised an asymptotic limit of the perturbations, we compare it to its numerical counterpart and to the time-dependent solution profiles in order to analytically obtain a condition for instability.
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Xu, Xingbai Xu. "Asymptotic Analysis for Nonlinear Spatial and Network Econometric Models." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1461249529.
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Pasik, Michael Francis. "An asymptotic analysis of a leaky parallel-plate waveguide." Diss., The University of Arizona, 1993. http://hdl.handle.net/10150/186163.
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An asymptotic analysis of a leaky parallel-plate waveguide is presented. The walls of the waveguide consist of bonded wire meshes which are modeled using a sheet impedance boundary condition. The fields are excited by magnetic line sources exterior to the waveguide. The wire meshes allow for coupling between the interior of the waveguide and the exterior region. In addition, each mesh can support a surface wave. We employ Fourier transform techniques to derive an integral representation for the magnetic field. We present various interpretations of the integral representation and evaluate the integral asymptotically using the method of steepest descents. The case of a pole near the saddle point is considered in detail. The integral is also evaluated numerically to determine the accuracy of the asymptotic results. The contributions to the radiation pattern of the structure from the surface-wave and leaky-wave poles, as well as the saddle point, are considered individually. The parameters of the structure are adjusted to exploit the contributions from the poles in the near far zone. The transient response of the structure to a double exponential pulse is also investigated. An alternative representation which is computationally efficient for computing the transient response in early time is derived. The use of the alternative representation for dense distributions of leaky-wave poles is also considered.
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Serkov, S. K. "Asymptotic analysis of mathematical models for elastic composite media." Thesis, University of Bath, 1998. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.390311.
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Sachs, Matthias Ernst. "The Generalised Langevin Equation : asymptotic properties and numerical analysis." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/29566.
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In this thesis we concentrate on instances of the GLE which can be represented in a Markovian form in an extended phase space. We extend previous results on the geometric ergodicity of this class of GLEs using Lyapunov techniques, which allows us to conclude ergodicity for a large class of GLEs relevant to molecular dynamics applications. The main body of this thesis concerns the numerical discretisation of the GLE in the extended phase space representation. We generalise numerical discretisation schemes which have been previously proposed for the underdamped Langevin equation and which are based on a decomposition of the vector field into a Hamiltonian part and a linear SDE. Certain desirable properties regarding the accuracy of configurational averages of these schemes are inherited in the GLE context. We also rigorously prove geometric ergodicity on bounded domains by showing that a uniform minorisation condition and a uniform Lyapunov condition are satisfied for sufficiently small timestep size. We show that the discretisation schemes which we propose behave consistently in the white noise and overdamped limits, hence we provide a family of universal integrators for Langevin dynamics. Finally, we consider multiple-time stepping schemes making use of a decomposition of the fluctuation-dissipation term into a reversible and non-reversible part. These schemes are designed to efficiently integrate instances of the GLE whose Markovian representation involves a high number of auxiliary variables or a configuration dependent fluctuation-dissipation term. We also consider an application of dynamics based on the GLE in the context of large scale Bayesian inference as an extension of previously proposed adaptive thermostat methods. In these methods the gradient of the log posterior density is only evaluated on a subset (minibatch) of the whole dataset, which is randomly selected at each timestep. Incorporating a memory kernel in the adaptive thermostat formulation ensures that time-correlated gradient noise is dissipated in accordance with the fluctuation-dissipation theorem. This allows us to relax the requirement of using i.i.d. minibatches, and explore a variety of minibatch sampling approaches.
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Elsawi, Mohamed Abdel Halim. "Asymptotic analysis of the spatial weights of the arbitrarily high order transport method." Access restricted to users with UT Austin EID Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3031048.
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Södergren, Anders. "Asymptotic Problems on Homogeneous Spaces." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-132645.
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This PhD thesis consists of a summary and five papers which all deal with asymptotic problems on certain homogeneous spaces. In Paper I we prove asymptotic equidistribution results for pieces of large closed horospheres in cofinite hyperbolic manifolds of arbitrary dimension. All our results are given with precise estimates on the rates of convergence to equidistribution. Papers II and III are concerned with statistical problems on the space of n-dimensional lattices of covolume one. In Paper II we study the distribution of lengths of non-zero lattice vectors in a random lattice of large dimension. We prove that these lengths, when properly normalized, determine a stochastic process that, as the dimension n tends to infinity, converges weakly to a Poisson process on the positive real line with intensity 1/2. In Paper III we complement this result by proving that the asymptotic distribution of the angles between the shortest non-zero vectors in a random lattice is that of a family of independent Gaussians. In Papers IV and V we investigate the value distribution of the Epstein zeta function along the real axis. In Paper IV we determine the asymptotic value distribution and moments of the Epstein zeta function to the right of the critical strip as the dimension of the underlying space of lattices tends to infinity. In Paper V we determine the asymptotic value distribution of the Epstein zeta function also in the critical strip. As a special case we deduce a result on the asymptotic value distribution of the height function for flat tori. Furthermore, applying our results we discuss a question posed by Sarnak and Strömbergsson as to whether there in large dimensions exist lattices for which the Epstein zeta function has no zeros on the positive real line.
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Guo, Shiyan. "Asymptotic Analysis of Wave Propagation through Periodic Arrays and Layers." Thesis, Loughborough University, 2011. https://dspace.lboro.ac.uk/2134/8886.
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In this thesis, we use asymptotic methods to solve problems of wave propagation through infinite and finite (only consider those that are finite in one direction) arrays of scatterers. Both two- and three-dimensional arrays are considered. We always assume the scatterer size is much smaller than both the wavelength and array periodicity. Therefore a small parameter is involved and then the method of matched asymptotic expansions is applicable. When the array is infinite, the elastic wave scattering in doubly-periodic arrays of cavity cylinders and acoustic wave scattering in triply-periodic arrays of arbitrary shape rigid scatterers are considered. In both cases, eigenvalue problems are obtained to give perturbed dispersion approximations explicitly. With the help of the computer-algebra package Mathematica, examples of explicit approximations to the dispersion relation for perturbed waves are given. In the case of finite arrays, we consider the multiple resonant wave scattering problems for both acoustic and elastic waves. We use the methods of multiple scales and matched asymptotic expansions to obtain envelope equations for infinite arrays and then apply them to a strip of doubly or triply periodic arrays of scatterers. Numerical results are given to compare the transmission wave intensity for different shape scatterers for acoustic case. For elastic case, where the strip is an elastic medium with arrays of cavity cylinders bounded by acoustic media on both sides, we first give numerical results when there is one dilatational and one shear wave in the array and then compare the transmission coefficients when one dilatational wave is resonated in the array for normal incidence. Key words: matched asymptotic expansions, multiple scales, acoustic scattering, elastic scattering, periodic structures, dispersion relation.
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Duba, Chuene Thama. "Asymptotic analysis of the parametrically driven damped nonlinear evolution equation." Master's thesis, University of Cape Town, 1997. http://hdl.handle.net/11427/22076.
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Bibliography: pages 179-184.Singular perturbation methods are used to obtain amplitude equations for the parametrically driven damped linear and nonlinear oscillator, the linear and nonlinear Klein-Gordon equations in the small-amplitude limit in various frequency regimes. In the case of the parametrically driven linear oscillator, we apply the Lindstedt-Poincare method and the multiple-scales technique to obtain the amplitude equation for the driving frequencies Wdr ~ 2ω₀,ω₀, (2/3)ω₀ and (1/2)ω₀. The Lindstedt-Poincare method is modified to cater for solutions with slowly varying amplitudes; its predictions coincide with those obtained by the multiple-scales technique. The scaling exponent for the damping coefficient and the correct time scale for the parametric resonance are obtained. We further employ the multiple-scales technique to derive the amplitude equation for the parametrically driven pendulum for the driving frequencies Wdr ~ 2ω₀, ω₀, (2/3)ω₀, (1/2)ω₀ and 4ω₀. We obtain the correct scaling exponent for the amplitude of the solution in each of these frequency regimes.
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Ottobre, Michela. "Asymptotic analysis for Markovian models in non-equilibrium statistical mechanics." Thesis, Imperial College London, 2012. http://hdl.handle.net/10044/1/9797.
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This thesis is mainly concerned with the problem of exponential convergence to equilibrium for open classical systems. We consider a model of a small Hamiltonian system coupled to a heat reservoir, which is described by the Generalized Langevin Equation (GLE) and we focus on a class of Markovian approximations to the GLE. The generator of these Markovian dynamics is an hypoelliptic non-selfadjoint operator. We look at the problem of exponential convergence to equilibrium by using and comparing three different approaches: classic ergodic theory, hypocoercivity theory and semiclassical analysis (singular space theory). In particular, we describe a technique to easily determine the spectrum of quadratic hypoelliptic operators (which are in general non-selfadjoint) and hence obtain the exact rate of convergence to equilibrium.
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MARZIANI, ROBERTA. "Asymptotic analysis of nonlinear models for line defects in materials." Doctoral thesis, Gran Sasso Science Institute, 2020. http://hdl.handle.net/20.500.12571/10041.
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The thesis is devoted to the study of the elastic behavior of solid crystals in the presence of dislocation defects by a variational point of view. In the first part we consider a Geometrically nonlinear elastic model in the three-dimensional setting, that allows for large rotations. Adopting a core approach, which consists in regularizing the problem at scale epsilon>0 around the dislocation lines, we perform the asymptotic analysis of the regularized energy as epsilon tends to 0. We focus in particular on the leading order regime and prove that the energy rescaled by $eps^2|logeps|$ Gamma converges to the line-tension for a dislocation density derived by Conti, Garroni and Ortiz in a three-dimensional linear framework.
The analysis is performed under the assumption that the dislocations are well separated at intermediate scale, this in fact will allow to treat individually each dislocation by means of a suitable cell formula.
The nonlinear nature of the energy requires that in the characterization of the cell formula we take into account that the deformation gradient is close to a fixed rotation.
In the second part we obtain the same Gamma-limit but starting from a nonlinear elastic model with mixed growth, that is we consider an elastic energy which is substantially quadratic far from the dislocations and sub-quadratic in the core region. This can be seen as another way of regularising the problem and allow us to slightly relax the diluteness condition of the admissible dislocation density and improve the compactness result obtained in the previous case.
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Matsui, Kazunori. "Asymptotic analysis of an ε-Stokes problem with Dirichlet boundary conditions." Thesis, Karlstads universitet, Institutionen för matematik och datavetenskap (from 2013), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-71938.
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In this thesis, we propose an ε-Stokes problem connecting the Stokes problem and the corresponding pressure-Poisson equation using one pa- rameter ε > 0. We prove that the solution to the ε-Stokes problem, converges as ε tends to 0 or ∞ to the Stokes and pressure-Poisson prob- lem, respectively. Most of these results are new. The precise statements of the new results are given in Proposition 3.5, Theorem 4.1, Theorem 5.2, and Theorem 5.3. Numerical results illustrating our mathematical results are also presented.STINT (DD2017-6936) "Mathematics Bachelor Program for Efficient Computations"
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Thim, Johan. "Simple Layer Potentials on Lipschitz Surfaces: An Asymptotic Approach." Doctoral thesis, Linköpings universitet, Tillämpad matematik, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-16280.
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This work is devoted to the equation
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Barwari, Bala Farhad. "Asymptotic and numerical solutions of a two-component reaction diffusion system." Thesis, University of Nottingham, 2016. http://eprints.nottingham.ac.uk/37231/.
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In this thesis, we study a two-component reaction diffusion system in one and two spatial dimensions, both numerically and asymptotically. The system is related to a nonlocal reaction diffusion equation which has been proposed as a model for a single species that competes with itself for a common resource. In one spatial dimension, we find that this system admits traveling wave solutions that connect the two homogeneous steady states. We also analyse the long-time behaviour of the solutions. Although there exists a lower bound on the speed of travelling wave solutions, we observe that numerical solutions in some regions of parameter space exhibit travelling waves that propagate for an asymptotically long time with speeds below this lower bound. We use asymptotic methods to both verify these numerical results and explain the dynamics of the problem, which include steady, unsteady, spike-periodic travelling and gap-periodic travelling waves. In two spatial dimensions, the numerical solutions of the axisymmetric form of the system are presented. We also establish the existence of a steady axisymmetric solution which takes a form of a circular patch. We then carry out a linear stability analysis of the system. Finally, we perform bifurcation analysis of these patch solutions via a numerical continuation technique and show how these solutions change with respect to variation of one bifurcation parameter.
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AMAR-SERVAT, Emmanuelle. "Asymptotic solutions and resonances for Klein-Gordon and Schrödinger operators." Phd thesis, Université Paris-Nord - Paris XIII, 2002. http://tel.archives-ouvertes.fr/tel-00002342.
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Mon travail de thèse se situe dans le cadre de l'analyse semi-classique. Il se divise en trois parties. Dans la première, j'ai étudié l'opérateur de Klein-Gordon semi-classique en dimension un. Dans la zone où le potentiel reste sous le niveau d'énergie, il existe pour cet opérateur des constructions de solutions WKB, similaires à celles développées pour l'opérateur de Schrödinger. Sous certaines hypothèses, on a prolongé ces solutions hors de cette zone, grâce aux méthodes utilisées près des points tournants pour l'opérateur de Schrödinger. On a ensuite étudié un exemple pour lequel on peut faire des calculs explicites. Enfin, en dimension quelconque, on a obtenu une nouvelle majoration des fonctions propres, lorsque la distance d'Agmon associée à cet opérateur a un gradient lipschitzien. La deuxième partie concerne l'opérateur de Schrödinger et l'étude des résonances en dimension un. Lorsque le potentiel présente deux puits et une mer pour les niveaux d'énergies considérés, on a obtenu des conditions de non croisement des résonances ainsi que leur graphe, grâce à la construction de modes. En présence d'un nombre quelconque de puits, cela permet également de calculer une estimation de la partie imaginaire des résonances dans le cas d'une interaction simple. Enfin, dans la troisième partie, on considère un opérateur de Schrödinger dont le potentiel présente un maximum non dégénéré. On a étudié les résonances générées par une courbe homocline qui passe par ce maximum. En dimension un, on a obtenu une condition de quantification, et par suite les résonances recherchées. En dimension quelconque, on a construit une solution asymptotique sortante le long de cette courbe, en adaptant la méthode de B. Helffer et J. Sjöstrand pour le fond de puits non résonnant. Une transformation FBI permet ensuite de conjecturer un premier niveau de résonances.
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Yu, Wenbin. "Variational asymptotic modeling of composite dimensionally reducible structures." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/12225.
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Li, Bo. "An analysis of Texas rainfall data and asymptotic properties of space-time covariance estimators." [College Station, Tex. : Texas A&M University, 2006. http://hdl.handle.net/1969.1/ETD-TAMU-1868.
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Bennett, James Cameron, and james bennett@student rmit edu au. "Mathematical Analysis of Film Blowing." RMIT University. Mathematical and Geospatial Sciences, 2008. http://adt.lib.rmit.edu.au/adt/public/adt-VIT20081128.115021.
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Film blowing is a highly complex industrial process used to manufacture thin plastic films for uses in a wide range of applications; for example, plastic bags. The mathematical modelling of this process involves the analysis of highly nonlinear differential equations describing the complex phenomena arising in the film blowing process, and requires a sophisticated mathematical approach. This dissertation applies an innovative combination of tools, namely analytic, numerical and heuristic mathematical techniques to the analysis of the film blowing process. The research undertaken examines, in particular, a two-point boundary value problem arising from the modelling of the radial profile of the polymer film. For even the simplest modelling of this process, namely the isothermal Newtonian model, the resulting differential equation is a highly nonlinear, second order one, with an extra degree of difficulty due to the presence of a small parameter multiplying the highest derivative. Thus, the problem falls into the category of a nonlinear singular perturbation problem. Analytic techniques are applied to the isothermal Newtonian blown film model to obtain a closed form explicit approximation to the film bubble radius. This is then used as a base approximation for an iterative numerical scheme to obtain an improved numerical solution of the problem. The process is extended to include temperature variations, varying viscosity (Power law model) and viscoelastic effects (Maxwell model). As before, closed form approximations are constructed for these models which are used to launch numerical schemes, whose solutions display good accuracy. The results compare well with results obtained by purely numerical solutions in the literature.
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Yuan, Zhongyi. "Quantitative analysis of extreme risks in insurance and finance." Diss., University of Iowa, 2013. https://ir.uiowa.edu/etd/2422.
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In this thesis, we aim at a quantitative understanding of extreme risks. We use heavy-tailed distribution functions to model extreme risks, and use various tools, such as copulas and MRV, to model dependence structures. We focus on modeling as well as quantitatively estimating certain measurements of extreme risks.
We start with a credit risk management problem. More specifically, we consider a credit portfolio of multiple obligors subject to possible default. We propose a new structural model for the loss given default, which takes into account the severity of default. Then we study the tail behavior of the loss given default under the assumption that the losses of the obligors jointly follow an MRV structure. This structure provides an ideal framework for modeling both heavy tails and asymptotic dependence. Using HRV, we also accommodate the asymptotically independent case. Multivariate models involving Archimedean copulas, mixtures and linear transforms are revisited.
We then derive asymptotic estimates for the Value at Risk and Conditional Tail Expectation of the loss given default and compare them with the traditional empirical estimates.
Next, we consider an investor who invests in multiple lines of business and study a capital allocation problem. A randomly weighted sum structure is proposed, which can capture both the heavy-tailedness of losses and the dependence among them, while at the same time separates the magnitudes from dependence. To pursue as much generality as possible, we do not impose any requirement on the dependence structure of the random weights. We first study the tail behavior of the total loss and obtain asymptotic formulas under various sets of conditions. Then we derive asymptotic formulas for capital allocation and further refine them to be explicit for some cases.
Finally, we conduct extreme risk analysis for an insurer who makes investments. We consider a discrete-time risk model in which the insurer is allowed to invest a proportion of its wealth in a risky stock and keep the rest in a risk-free bond. Assume that the claim amounts within individual periods follow an autoregressive process with heavy-tailed innovations and that the log-returns of the stock follow another autoregressive process, independent of the former one. We derive an asymptotic formula for the finite-time ruin probability and propose a hybrid method, combining simulation with asymptotics, to compute this ruin probability more efficiently. As an application, we consider a portfolio optimization problem in which we determine the proportion invested in the risky stock that maximizes the expected terminal wealth subject to a constraint on the ruin probability.
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Zarroug, Moundheur. "Asymptotic methods applied to some oceanography-related problems." Doctoral thesis, Stockholm : Department of Meteorology, Stockholm University, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-37763.
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Diss. (sammanfattning) Stockholm : Stockholms universitet, 2010.At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript.
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Rosenberger, Elke. "Asymptotic spectral analysis and tunnelling for a class of difference operators." Phd thesis, [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=98050368X.
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Lindsay, Alan Euan. "Topics in the asymptotic analysis of linear and nonlinear eigenvalue problems." Thesis, University of British Columbia, 2010. http://hdl.handle.net/2429/26271.
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In Applied Mathematics, linear and nonlinear eigenvalue problems arise frequently when characterizing the equilibria of various physical systems. In this thesis, two specific problems are studied, the first of which has its roots in micro engineering and concerns Micro-Electro Mechanical Systems (MEMS).
A MEMS device consists of an elastic beam deflecting in the presence of an electric field. Modelling such devices leads to nonlinear eigenvalue problems of second and fourth order whose solution properties are investigated by a variety of asymptotic and numerical techniques.
The second problem studied in this thesis considers the optimal strategy for distributing a fixed quantity of resources in a bounded two dimensional domain so as to minimize the probability of extinction of some species evolving in the domain. Mathematically, this involves the study of an indefinite weight eigenvalue problem on an arbitrary two dimensional domain with homogeneous Neumann boundary conditions, and the optimization of the principal eigenvalue of this problem. Under the assumption that resources are placed on small patches whose area relative to that of the entire domain is small, the underlying eigenvalue problem is solved explicitly using the method of matched asymptotic expansions and several important qualitative results are established.
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Venu, Kurella. "Asymptotic analysis of first passage processes : with applications to animal movement." Thesis, University of British Columbia, 2011. http://hdl.handle.net/2429/36961.
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Understanding the dependence of animal behaviour on resource distribution is a central problem in mathematical ecology. In a habitat, the distribution of food resources and their accessibility from an animal's location together with the search time involved in foraging, all govern the survival of a species. In this work, we
investigate various scenarios that affect foraging habits of animals in a landscape. The work, unlike previous studies, analyzes the first passage quantities on complex prey-predator distributions in a given domain in order to derive simple analytical problems that can readily be solved numerically. We use standard stochastic models such as the Kolmogorov equations of first passage times and splitting probability, to model both the foraging time of a predator and the chances of
survival of prey on a landscape with prey and predator patches. We obtain an asymptotic solution to these Kolmogorov equations using a hybrid asymptotic-numerical singular perturbation technique that utilizes the fact that the ratio of the size of prey patches is small in comparison to the overall landscape. Results from this hybrid approach are then verified by undertaking full numerical simulations of the governing partial differential equations of the first passage processes. By using this hybrid formulation we identify the underlying parameters that affect
the search time of a predator and splitting probability of prey, which are otherwise difficult to ascertain using only numerical tools. This
analytical understanding of how parameters influence the first passage processes is a key step in quantifying foraging behavior in model ecological systems.
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Totzeck, Claudia [Verfasser]. "Asymptotic Analysis of Optimal Control Problems and Global Optimization / Claudia Totzeck." München : Verlag Dr. Hut, 2017. http://d-nb.info/1126295876/34.
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