Es erfolgt eine Darstellung der theoretischen Grundlagen, die für die Berechnung von optimal wachsenden Störungen nötig sind. Bei Anwendung des Projektionsoperators ist es möglich, die Anfangsstörung zu berechnen, welche die größtmögliche kinetische Energie nach Ablauf eines Optimierungsintervalls in einem vorher spezifizierten Gebiet erlangt. Die Berechnung dieser sogenannten lokalen optimalen Vektoren erfolgt für ein barotropes Modell, das um zeitunabhängige Grundströme linearisiert ist. Die lokalen optimalen Vektoren sind für Grundströme ermittelt worden, die aus einem gleitenden 10-Tages Mittel bestehen. Als Zielgebiet kam dabei der Nordatlantik-Europa Bereich zur Anwendung. Auf diese Weise war es möglich, zu untersuchen, welche Gebiete einen Einfluss auf das Störungswachstum besitzen. Dabei stellte sich heraus, dass für Optimierungszeiten größer 96 Stunden vier verschiedene Startgebiete existieren. Besonderes Interesse galt dem Transport von kinetischer Energie aus diesen Startgebieten in das Zielgebiet. Teilweise zeigte sich, dass die Energie über PNA ähnliche Strukturen in das Zielgebiet getragen wird. / Under the use of a projection operator it is possible to calculate perturbations with maximal energy growth during optimization time at some pre-chosen geographical area. The so called local optimal perturbations are computed for a barotropic model, linarized about time independent basic states. The optimal perturbations are determined for basic states consisting of 10-day running means of the daily streamfunctions. The chosen target area was the North Atlantic-European sector. In this way it was possible to find relevant \"starting regions\" leading to optimal energy growth in the target area. We found four such regions for long optimization times (> 96 hours). Thereby, the mechanisms responsible for the transport of the perturbations from the starting regions into the target area was thereby of special interest. In particular cases we found that structures similar to Pacific North America (PNA) patterns are involved in the energy transfer.

The chemical master equation (CME) represents the accepted stochastic description of chemical reaction kinetics in mesoscopic systems. As its exact solution – which gives the corresponding probability density function – is possible only in very simple cases, there is a clear need for approximation techniques. Here, we propose a novel perturbative three-step approach which draws heavily on graph theory: (i) we expand the eigenvalues of the transition state matrix in the CME as a series in a non-dimensional parameter that depends on the reaction rates and the reaction volume; (ii) we derive an analogous series for the corresponding eigenvectors via a graph-based algorithm; (iii) we combine the resulting expansions into an approximate solution to the CME. We illustrate our approach by applying it to a reversible dimerization reaction; then, we formulate a set of conditions, which ensure its applicability to more general reaction networks. We follow attempting to apply the results to a more complicated system, namely push-pull, but the problem reveals too complex for a complete solution. Finally, we discuss the limitations of the methodology.

Local influence (LI) analysis is an important statistical method for studying the sensitivity of a proposed model to model inputs. However, arbitrarily perturbing a model may result in misleading inference about the influential aspects in the model. Hence, an important issue of local influence analysis is to select an appropriate perturbation vector. In this thesis, we develop a general method to select an appropriate perturbation vector as well as second-order local influence measures to address this issue in the context of latent variable models (LVMs). The proposed methodologies are applied to nonlinear structural equation models (NSEMs), generalized linear mixed models (GLMMs), and two-level structural equation models (SEMs) with continuous and ordered categorical data. For nonlinear structural equation models, some perturbation schemes are investigated, including three schemes where simultaneous perturbations are made on components of latent vectors to assess the influence of these components and pinpoint the causal influential ones. In generalized linear mixed models, perturbation schemes are designed such that the influence of the observations in the clusters can be assessed under some schemes and the influence assessment of the clusters can be obtained under the other schemes. In two-level structural equation models, some perturbation schemes are considered to obtain the influence assessment of the clusters. The proposed procedures are illustrated by simulation studies and real examples. / Chen, Fei. / Adviser: Sik-Yum Lee. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3584. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 73-77). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Yeung Yuk Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 82-85). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivations --- p.1 / Chapter 1.2 --- Historical background --- p.2 / Chapter 1.3 --- Outline of this thesis --- p.3 / Chapter 2 --- Mode classifications --- p.5 / Chapter 2.1 --- Fluid modes --- p.6 / Chapter 2.1.1 --- f mode (fundamental mode) --- p.6 / Chapter 2.1.2 --- p mode (pressure mode) --- p.7 / Chapter 2.1.3 --- g mode (gravity mode) --- p.7 / Chapter 2.2 --- w mode (spacetime mode) --- p.8 / Chapter 3 --- Oscillations of neutron stars --- p.10 / Chapter 3.1 --- The equilibrium configurations of neutron star models --- p.10 / Chapter 3.1.1 --- Newtonian stars --- p.10 / Chapter 3.1.2 --- Relativistic stars --- p.11 / Chapter 3.2 --- Perturbation of the star's equilibrium --- p.14 / Chapter 3.2.1 --- Axial perturbation equation --- p.15 / Chapter 3.2.2 --- Boundary conditions --- p.16 / Chapter 3.2.3 --- Numerical techniques --- p.16 / Chapter 3.2.4 --- The Quasinormal modes of stars --- p.18 / Chapter 4 --- Excitation and detection of QNMs --- p.20 / Chapter 4.1 --- Studies of excitation of stellar QNMs --- p.20 / Chapter 4.2 --- Detection of QNM ringing --- p.21 / Chapter 4.3 --- Parameter estimation --- p.23 / Chapter 5 --- Oscillations of realistic neutron stars --- p.28 / Chapter 5.1 --- Motivations of study --- p.28 / Chapter 5.2 --- Realistic equations of state --- p.29 / Chapter 5.3 --- Axial QNM --- p.36 / Chapter 6 --- Logarithmic perturbation method --- p.38 / Chapter 6.1 --- Introduction --- p.38 / Chapter 6.2 --- Logarithmic perturbation theory --- p.39 / Chapter 6.3 --- Evaluation of perturbation formulae --- p.42 / Chapter 6.3.1 --- The first-order perturbation --- p.42 / Chapter 6.3.2 --- The second-order perturbation --- p.47 / Chapter 6.4 --- Comparison of LPT calculations with exact results --- p.47 / Chapter 6.5 --- Discussion --- p.51 / Chapter 7 --- Scaled coordinate logarithmic perturbation method --- p.53 / Chapter 7.1 --- Rescaling of the axial perturbation equations --- p.54 / Chapter 7.1.1 --- The original axial perturbation equations --- p.55 / Chapter 7.1.2 --- The rescaled axial perturbation equations --- p.56 / Chapter 7.2 --- The formalism of SCLPT --- p.57 / Chapter 7.2.1 --- Logarithmic perturbation theory --- p.59 / Chapter 7.2.2 --- First-order perturbation --- p.63 / Chapter 7.2.3 --- Second-order perturbation --- p.65 / Chapter 7.3 --- Comparison of the perturbation calculation with the exact result --- p.67 / Chapter 7.4 --- Discussion --- p.70 / Chapter 8 --- Conclusion --- p.73 / Chapter 8.1 --- Summary --- p.73 / Chapter 8.2 --- Outlook --- p.74 / Chapter A --- Units conventions --- p.76 / Chapter B --- Numerical technique in Leaver's series --- p.77 / Chapter C --- Method of numerical derivatives --- p.80 / Bibliography --- p.82

In this thesis we present research into linear perturbations in Lemaître-Tolman-Bondi (LTB) and Assisted Coupled Quintessence (ACQ) Cosmologies. First we give a brief overview of the standard model of cosmology. We then introduce Cosmological Perturbation Theory (CPT) at linear order for a at Friedmann-Robertson-Walker (FRW) cosmology. Next we study linear perturbations to a Lemaître-Tolman-Bondi (LTB) background spacetime. Studying the transformation behaviour of the perturbations under gauge transformations, we construct gauge invariant quantities in LTB. We show, using the perturbed energy conservation equation, that there is a conserved quantitiy in LTB which is conserved on all scales. We then briefly extend our discussion to the Lemaître spacetime, and construct gauge-invariant perturbations in this extension of LTB spacetime. We also study the behaviour of linear perturbations in assisted coupled quintessence models in a FRW background. We provide the full set of governing equations for this class of models, and solve the system numerically. The code written for this purpose is then used to evolve growth functions for various models and parameter values, and we compare these both to the standard CDM model and to current and future observational bounds. We also examine the applicability of the "small scale approximation", often used to calculate growth functions in quintessence models, in light of upcoming experiments such as SKA and Euclid. We nd the results of the full equations deviates from the approximation by more than the experimental uncertainty for these future surveys. The construction of the numerical code, Pyessence, written in Python to solve the system of background and perturbed evolution equations for assisted coupled quintessence, is also discussed.

We propose and construct a two-parameter expansion around a Friedmann-Lemaitre- Robertson-Walker geometry which uses both large-scale and small-scale perturbations analogous to cosmological perturbation theory and post-Newtonian gravity. We justify this observationally, derive a set of field equations valid on a fraction of the horizon size and perform a detailed investigation of the associated gauge problem. We find only the Newtonian gauge, out of the standard gauges used in cosmological perturbation theory, is applicable to post-Newtonian perturbations; we can identify a consistent set of perturbed quantities in the matter and gravity sectors and construct corresponding gauge-invariant quantities. The field equations, written in terms of these quantities, takes on a simpler form, and allows the effects of small-scale structure on the large-scale properties of the Universe to be clearly identified and discussed for different physical scenarios. With a definition of statistical homogeneity, we find that the cosmological constant and the average energy density, of radiation and dust, source the Friedmann equation, whereas only the inhomogeneous part of the Newtonian energy density sources the Newton-Poisson equation { even though both originate from the same equation. There exists field equations at new orders in our formalism, such as a frame-dragging field equation a hundred times larger than expected from using cosmological perturbation theory alone. Moreover, we find non-linear gravity, mode-mixing and a mixing-of-scales at orders one would not expect from intuition based on cosmological perturbation theory. By recasting the field equations as an effective fluid we observe that these non-linearities lead to, for example, a large-scale effective pressure and anisotropic stress. We expect our formalism to be useful for accurately modelling our Universe, and for investigating the effects of non-linear gravity in the era of ultra-large-scale surveys.

Perturbation techniques are useful in the design of low complexity adaptive antenna arrays for estimating the gradient required in stochastic descent algorithms. Implementing projected perturbation sequences in an adaptive array allows the simultaneous reception of signals and the adaptation of the array weights while preserving the constraints imposed on the array weights.This thesis quantifies the performance of narrowband adaptive array processors that employ projected perturbation techniques. For different perturbation receiver structures the performance is determined under idealised conditions and importantly also when practical implementation issues are taken into account.The arrays performance is characterised by analysing the transient performance of the weight covariance matrix and by determining the misadjustment. By drawing similarities between two established analysis techniques a new misadjustment analysis technique is introduced.Practical implementation can impact on the arrays performance such that the benefit of the projected perturbation approach is lost. By characterising the array's sensitivity to perturbation noise additional projections which counteract some implementation effects are identified. The level of loss of performance due to weight quantisation and the limited dynamic range of the array weights is determined.

Dans cette thèse on considère le prolongement méromorphe fini de la résolvante du laplacien libre sur une variété riemannienne connexe non compacte de dimension supérieure ou égale à 2. Ses pôles sont appelés résonances. On suppose que la variété possède certaines symétries comme S^1, (S^1)^m ou encore SO(n). Avec cette hypothèse, on construit des potentiels V dits isorésonants c'est-à-dire tels que le laplacien plus V ait les mêmes résonances que le laplacien libre avec les mêmes multiplicités. Au passage on est amené à estimer le bas du spectre du laplacien agissant sur les fonctions S^1 homogènes à support compact. On montre également que ces potentiels isorésonants peuvent modifier l'ordre des résonances. Enfin, les résonances sont parfois définies comme pôles de l'opérateur de diffusion : on montre que dans ce cadre on a aussi l'isorésonance de nos potentiels.

Dans cette these, il s'agit d'etudier le comportement du spectre d'operateurs non-autoadjoints sous de tres petites perturbations. Nous montrons d'abord une loi de Weyl bidimensionelle pour les valeurs propres dans un certain domaine d'un operateur modele perturbe par une somme de noyaux oscillatoires. Ensuite nous montrons que ce resultat est aussi vrai avec une tres grande probabilite pour des perturbations multiplicatives aleatoires de l'operateur de Schroedinger non-autoadjoint. Enfin, nous completons ces resultats par une majoration du nombre de valeurs propres dans une region ou ceux-cis ne s'appliquent pas.

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