182 leaves : ill. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Mawson Institute for Antarctic Research, 1972

Thesis (Ph.D.) -- University of Adelaide, Mawson Institute for Antarctic Research, 1972.

Thesis (Ph.D.)--Dept. of Applied Mathematics, University of Adelaide, 1971.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 117-120). Also available via the Internet.

Thesis (M.S.)--University of Michigan, 1964.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1964. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

The effects of small random fluctuations on deterministic systems are studied. The deterministic systems of interest have multiple steady states. As parameters vary, two or three of the steady states coalesce. This work is concerned with the long time behavior of the system, when the system starts near an unstable steady state. The deterministic separatrix is surrounded by a tube that contains up to two stable steady states. The quantity of basic interest is the probability of first exit from the tube through a specified boundary, conditioned on initial position. In the diffusion approximation this probability satisfies a backward diffusion equation. Formal asymptotic solutions of the backward equation are constructed. The solutions are obtained by a generalized "ray method" and are given in terms of various incomplete special functions. As an example, the effects of fluctuations on a substrate inhibited reaction in an open vessel are analyzed. The theory is compared with exact solutions, for a one dimensional model; and Monte Carlo experiments, for a two dimensional model. / Science, Faculty of / Mathematics, Department of / Unknown

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Systems that operate in airborne environments and rely on the resolution provided by optical sensors require a stabilization system to isolate the line-of-sight (LOS) from the operating environment. For systems employing television sensors, stabilization accuracy is of prime importance in maintaining sufficient picture resolution to allow target identification and recognition at maximum ranges. The development of system models that accurately predict stabilization performance is important both in design trade-offs and in the system design and testing [l]. Two basic concepts are available for achieving LOS stabilization; momentum stabilization which employs a spinning mass and rate stabilization which utilizes inertial rate sensors. Previously rate stabilized platforms have been employed for high performance laser designator systems mounted in aircraft while momentum stabilized platforms have been used on tactical missiles. Rate stabilized platforms have not been used often in tactical missiles due to their higher cost and the lack of high performance stabilization requirements over large field-of-regards on the missile seekers. This paper develops the system models necessary to evaluate the LOS stabilization performance for either concept. To demonstrate the validity of the models derived, a case study is presented covering both momentum and rate stabilized systems which is verified with simulation results.