The stability criteria for single-mode standing-wave laser oscillators in the strongly homogeneously broadened limit are reported for the first time. Two types of stability criteria are presented. The first type, called type 1, corresponds to the minimum value of threshold parameter for which an infinitesimal perturbation away from steady state grows into an oscillatory solution. Another type of stability criteria, called type 2, corresponds to the minimum value of threshold parameter for which large amplitude oscillatory solutions do not decay to the steady state solution. Undamped pulsations in single mode strongly homogeneously broadened standing-wave laser oscillators are found to occur at a much higher excitation level than that of ring-laser oscillators with the same type of line broadening. The effect of detuning on stability criteria is also investigated. We discovered that detuning tends to raise the type 1 instability threshold and to decrease the type 2 instability threshold.

Ho, Tak Ngai = 中子星在絶熱冷卻下的不穩定性 : 數值模擬和簡單類比 / 何德藝. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 101-102). / Abstracts in English and Chinese. / Ho, Tak Ngai = Zhong zi xing zai jue re leng que xia de bu wen ding xing : shu zhi mo ni he jian dan lei bi / He Deyi. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- The astrophysical problem --- p.2 / Chapter 2.1 --- Neutron stars --- p.2 / Chapter 2.2 --- Equations --- p.4 / Chapter 2.3 --- EOS --- p.6 / Chapter 2.4 --- Equilibrium configurations --- p.8 / Chapter 2.5 --- Stability --- p.9 / Chapter 2.6 --- The key equilibrium properties --- p.10 / Chapter 2.7 --- Adiabatic cooling --- p.11 / Chapter 2.8 --- Modeling adiabatic cooling by varying T --- p.13 / Chapter 3 --- Numerical Simulations in GR --- p.17 / Chapter 3.1 --- Introduction --- p.17 / Chapter 3.2 --- The equations and the EOS --- p.17 / Chapter 3.3 --- Evolution of a stellar system in GR --- p.20 / Chapter 3.4 --- Results --- p.22 / Chapter 4 --- Newtonian model --- p.27 / Chapter 4.1 --- Introduction --- p.27 / Chapter 4.2 --- Newtonian fluid equations --- p.28 / Chapter 4.3 --- Polytropes --- p.28 / Chapter 4.4 --- Model EOS --- p.31 / Chapter 4.5 --- Equilibrium solutions --- p.33 / Chapter 4.6 --- Stability --- p.35 / Chapter 4.7 --- Dynamics --- p.38 / Chapter 4.8 --- Adiabatic changes --- p.42 / Chapter 4.9 --- Results --- p.46 / Chapter 5 --- Model of instability --- p.52 / Chapter 5.1 --- Introduction . --- p.52 / Chapter 5.2 --- Analytical study of the model --- p.54 / Chapter 5.3 --- Numerical verification --- p.55 / Chapter 5.4 --- Summary --- p.59 / Chapter 6 --- Model of criticality --- p.62 / Chapter 6.1 --- Introduction --- p.62 / Chapter 6.2 --- General discussion of equilibrium properties --- p.63 / Chapter 6.3 --- Construction of model --- p.67 / Chapter 6.4 --- Study of the model --- p.75 / Chapter 6.5 --- Conclusion --- p.82 / Chapter 7 --- Conclusion --- p.85 / Appendix --- p.87 / Chapter A --- Neutron stars cooling due to neutrinos emission --- p.87 / Chapter B --- Determining how r change --- p.89 / Chapter C --- Basic equations in the GR context --- p.91 / Chapter C.1 --- ADM formulation of the field equations --- p.91 / Chapter C.2 --- Explicit form of the hyperbolic equation --- p.93 / Chapter D --- One-zone model --- p.95 / Chapter E --- Numerical scheme of getting the EOS --- p.98 / Bibliography --- p.101

School of Engineering Includes bibliographical references (leaves 248-256)

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Includes bibliographical references / xii, [291] leaves : ill. (some col.) ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Civil Engineering, 1992

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published_or_final_version / abstract / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

In this work, we investigate input-to-state stability (ISS) and other related stability properties for control systems with time-delays. To overcome the complexity caused by the presence of the delays, we adopt a Razumikhin approach. The underlying idea of this approach is to treat the delayed variables as system uncertainties. The advantage of this approach is that one works in the more familiar territory of stability analysis for delay-free systems in the context of ISS instead of carrying out stability analysis on systems of functional differential equations. Our first step is to provide criteria on ISS and input-to-input stability properties based on the Razumikhin approach. We then turn our attention to large-scale interconnected systems. It has been well recognized that the small-gain theory is a powerful tool for stability analysis of interconnected systems. Using the Razumikhin approach, we develop small-gain theorems for interconnected systems consisting of two or more subs ystems with time-delays present either in the interconnection channels or within the subsystems themselves. As an interesting application, we apply our results to an existing model for hematopoesis, a blood cell production process,and improve the previous results derived by linear methods. Another important stability notion in the framework of ISS is the integral ISS (iISS) property. This is a weaker property than ISS, so it supplies to a larger class of systems. As in the case of ISS, we provide Razumikhin criteria on iISS for systems with delays. An example is presented to illustrate that though very useful in practice, the Razumikhin approach only provides sufficient conditions, not equivalent conditions. Finally, we address stability of time-varying systems with delays in the framework of ISS. / In particular, we consider Lyapunov-Razumikhin functions whose decay rates are affected by time-varying functions that can be zero or even negative on some sets of non-zero measure. Our motivation is that it is often less demanding to find or construct such a Lyapunov function than one with a uniform decay rate. We also extend our small-gain theorems to the time-varying case by treating the time-varying system as an auxiliary time-invariant system. / Shanaz Tiwari. / Thesis (Ph.D.)--Florida Atlantic University, 2012. / Includes bibliography and index. / Electronic reproduction. Boca Raton, Fla., 2012. Mode of access: World Wide Web.