We consider a general class of finite dimensional deterministic dynamical systems with finitely many local attractors each of which supports a unique ergodic probability measure, which includes in particular the class of Morse–Smale systems in any finite dimension. The dynamical system is perturbed by a multiplicative non-Gaussian heavytailed Lévy type noise of small intensity ε > 0. Specifically we consider perturbations leading to a Itô, Stratonovich and canonical (Marcus) stochastic differential equation. The respective asymptotic first exit time and location problem from each of the domains of attractions in case of inward pointing vector fields in the limit of ε-> 0 has been investigated by the authors. We extend these results to domains with characteristic boundaries and show that the perturbed system exhibits a metastable behavior in the sense that there exits a unique ε-dependent time scale on which the random system converges to a continuous time Markov chain switching between the invariant measures. As examples we consider α-stable perturbations of the Duffing equation and a chemical system exhibiting a birhythmic behavior.

The ascent of liquids with low dielectric constant on straight cylinders are obtained.

We consider the problem of estimating the reliability of bundles constructed of several fibres, given a particular kind of censored data. The bundles consist of several fibres which have their own independent identically dis-tributed failure stresses (i.e.the forces that destroy the fibres). The force applied to a bundle is distributed between the fibres in the bundle, accord-ing to a load-sharing model. A bundle with these properties is an example of a load-sharing system. Ropes constructed of twisted threads, compos-ite materials constructed of parallel carbon fibres, and suspension cables constructed of steel wires are all examples of load-sharing systems. In par-ticular, we consider bundles where load-sharing is described by either the Equal load-sharing model or the more general Local load-sharing model. In order to estimate the cumulative distribution function of failure stresses of bundles, we need some observed data. This data is obtained either by testing bundles or by testing individual fibres. In this thesis, we develop several theoretical testing methods for both fibres and bundles, and related methods of statistical inference. Non-parametric and parametric estimators of the cumulative distribu-tion functions of failure stresses of fibres and bundles are obtained from different kinds of observed data. It is proved that most of these estimators are consistent, and that some are strongly consistent estimators. We show that resampling, in this case random sampling with replacement from sta-tistically independent portions of data, can be used to assess the accuracy of these estimators. Several numerical examples illustrate the behavior of the obtained estimators. These examples suggest that the obtained estimators usually perform well when the number of observations is moderate.

A new experimental setup for studies on wake flow instability and its control that successfully has been designed and manufactured, is introduced and de- scribed. The main body is a dual-sided flat plate with an elliptic leading edge and a blunt trailing edge. Permeable surfaces enable boundary layer suction and/or blowing that introduce the unique feature of adjusting the inlet condition of the wake created behind the plate. This, in combination with a trailing edge that is easily modified, makes it an ideal experiment for studies of different control methods for the wake flow instability as well as extensive parameter studies. Experimental validation of the setup has been performed by means of measurements of the wake symmetry and boundary layer velocity profiles at the trailing edge. Some preliminary results on the Strouhal number versus different inlet conditions are reported. Additionally, an in-house vortex detection (VD) program has been developed in order to detect, analyse and compare small-scale vortical structures in instantaneous velocity fields from flow measurements. This will be a powerful tool for comparison of wake characteristics for varying inlet conditions and control methods in the new experimental setup. Measurements from three completely separate experimental setups with different geometries and flow cases, have been analysed by the VD-program.          i.     In order to obtain improved ventilation we have studied the effect of pulsating inflow into a closed volume compared to having the inflow at a constant flow rate. We show that the number of small-scale eddies is significantly increased and that the stagnation zones are reduced in size, which enhances the mixing.         ii.     Instantaneous velocity fields in the wake behind a porous cylinder subjected to suction or blowing through the entire cylinder surface have also been analysed using the VD-program. The results show that the major change for different levels of blowing or suction is the location of vortices while the most common vortex size and strength are essentially unchanged.        iii.     Another study on how the geometry of a V-shaped mixer in a pipe flow affects the mixing have also been examined, where no general differences were found between different thicknesses, why a thickness that is favourable from an acoustic point of view can be chosen.   We also propose a new method, using global mode analysis on experimental data, showing that randomly ordered snapshots of the velocity field behind the porous cylinder can be re-ordered and phase-averaged. / QC 20111108 / Active control of vortex shedding behind bluff bodies

We consider the motion of a Brownian particle trapped in an arbitrary bounded two or three-dimensional domain, whose boundary is reflecting except for a small absorbing window through which the particle can escape. We use the method of matched asymptotic expansions to calculate the mean first passage time, defined as the time taken for the Brownian particle to escape from the domain through the absorbing window. This is known as the narrow escape problem. Since the mean escape time diverges as the window shrinks, the calculation is a singular perturbation problem. We extend our results to include N absorbing windows of varying length in two dimensions and varying radius in three dimensions. We present findings in two dimensions for the unit disk, unit square and ellipse and in three dimensions for the unit sphere. The narrow escape problem has various applications in many fields including finance, biology, and statistical mechanics.

Bibliography: leaves 95-97 / iv, 97 leaves : ill ; 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 Applied Mathematics, 1986

We present limit theory for tests of homogeneity for finite mixture models. More specifically, we derive the asymptotic distribution of certain random quantities used for testing that a mixture of two distributions is in fact just a single distribution. Our methods apply to cases where the mixture component distributions come from one of a wide class of one-parameter exponential families, both continous and discrete. We consider two random quantities, one related to testing simple hypotheses, the other composite hypotheses. For simple hypotheses we consider the maximum of the standardised score process, which is itself a test statistic. For composite hypotheses we consider the maximum of the efficient score process, which is itself not a statistic (it depends on the unknown true distribution) but is asymptotically equivalent to certain common test statistics in a certain sense. We show that we can approximate both quantities with the maximum of a certain Gaussian process depending on the sample size and the true distribution of the observations, which when suitably normalised has a limiting distribution of the Gumbel extreme value type. Although the limit theory is not practically useful for computing approximate p-values, we use Monte-Carlo simulations to show that another method suggested by the theory, involving using a Studentised version of the maximum-score statistic and simulating a Gaussian process to compute approximate p-values, is remarkably accurate and uses a fraction of the computing resources that a straight Monte-Carlo approximation would.

Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references (leaves 114-117). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references (leaves 114-117). Also available on the Internet.

Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (p. 213-219).