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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Pseudospectra and Linearization Techniques of Rational Eigenvalue Problems

Torshage, Axel January 2013 (has links)
This thesis concerns the analysis and sensitivity of nonlinear eigenvalue problems for matrices and linear operators. The first part illustrates that lack of normality may result in catastrophic ill-conditioned eigenvalue problem. Linearization of rational eigenvalue problems for both operators over finite and infinite dimensional spaces are considered. The standard approach is to multiply by the least common denominator in the rational term and apply a well known linearization technique to the polynomial eigenvalue problem. However, the symmetry of the original problem is lost, which may result in a more ill-conditioned problem. In this thesis, an alternative linearization method is used and the sensitivity of the two different linearizations are studied. Moreover, this work contains numerically solved rational eigenvalue problems with applications in photonic crystals. For these examples the pseudospectra is used to show how well-conditioned the problems are which indicates whether the solutions are reliable or not.
2

Nonmodal Analysis of Temporal Transverse Shear Instabilities in Shallow Flows

Tun, Yarzar January 2017 (has links)
Shallow flows are those whose width is significantly larger than their depth. In these types of flows, two dimensional coherent structures can be generated and can influence the flow greatly by the lateral transfer of mass and momentum. The development of coherent structures as a result of flow instabilities has been a topic of interest for environmental fluid mechanics for decades. Studies on the use of linear modal stability analysis is commonly found in literature. However, the relatively recent development in the field of hydrodynamic stability suggests that the traditional linear modal stability analysis does not describe the behaviour of the perturbations in finite time. The discrepancy between asymptotic behaviour and finite time behaviour is particularly large in shear driven flows and it is most likely to be the case for shallow flows. This study aims to provide a better understanding of finite time growth of perturbation energy in shallow flows. The three cases of shallow flows evaluated are the mixing layer, jet and wake. The critical cases are obtained through the linear modal analysis and nonmodal analysis was conducted to show the transient behaviour in finite time for what is so-called marginally stable. Finally, the thesis concludes by generalizing the finite time energy growth in the S-k space.
3

Novi indikatori stabilnosti za empirijske trofičke mreže / New stability indicators for the empirical food webs

Cvetković Dragana 31 October 2017 (has links)
<p>Ova doktorska disertacija uvodi nov pristup ispitivanju stabilnosti dinamičkih<br />sistema, korišćenjem teorije pseudospektra. Na taj način se postojeći pojam<br />stabilnosti profinjuje pojmom robusne stabilnosti, koji mnogo adekvatnije<br />opisuje realnu ekološku stabilnost. Razvijen je nov matematički alat za<br />izračunavanje indikatora stabilnosti, koji je zatim ilustrovan na primeru dva<br />ekosistema tla, sa po četiri uzorka, u četiri različita stadijuma razvoja.</p> / <p>This doctoral dissertation establishes a novel approach to the stability analysis of<br />dynamical systems, in terms of matrix pseudospectrum. In that manner, the existing<br />concept of stability has undergone essential refinement so as to give birth to the<br />concept of robust stability, which has the ability to capture the ecological stability at a<br />more adequate level. Additionally, within the framework of the dissertation, a new<br />mathematical tool for the stability indicators computation has been developed, which<br />has then been used to illustrate theoretical results in form of two soil ecosystems,<br />each of them sampled four times, all of them observed in four distinct stages of<br />evolution.</p>

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