Random response of nonlinear continuous systems

This thesis presents a technique for obtaining the stochastic response of a nonlinear continuous system. First, the general method of nonstationary continuous equivalent linearization is developed. This technique allows replacement of the original nonlinear system with a time-varying linear continuous system. Next, a numerical implementation is described which allows solution of complex problems on a digital computer. In this procedure, the linear replacement system is discretized by the finite element method. Application of this method to systems satisfying the one-dimensional wave equation with two different types of constitutive nonlinearities is described. Results are discussed for nonlinear stress-strain laws of both hardening and softening types.

Nonlinear oscillations in discrete and continuous systems

The first thesis topic is a perturbation method for resonantly coupled nonlinear oscillators. By successive near-identity transformations of the original equations, one obtains new equations with simple structure that describe the long time evolution of the motion. This technique is related to two-timing in that secular terms are suppressed in the transformation equations. The method has some important advantages. Appropriate time scalings are generated naturally by the method, and don't need to be guessed as in two-timing. Furthermore, by continuing the procedure to higher order, one extends (formally) the time scale of valid approximation. Examples illustrate these claims. Using this method, we investigate resonance in conservative, non-conservative and time dependent problems. Each example is chosen to highlight a certain aspect of the method.

The second thesis topic concerns the coupling of nonlinear chemical oscillators. The first problem is the propagation of chemical waves of an oscillating reaction in a diffusive medium. Using two-timing, we derive a nonlinear equation that determines how spatial variations in the phase of the oscillations evolves in time. This result is the key to understanding the propagation of chemical waves. In particular, we use it to account for certain experimental observations on the Belusov-Zhabotinskii reaction.

Next, we analyse the interaction between a pair of coupled chemical oscillators. This time, we derive an equation for the phase shift, which measures how much the oscillators are out of phase. This result is the key to understanding M. Marek's and I. Stuchl's results on coupled reactor systems. In particular, our model accounts for synchronization and its bifurcation into rhythm splitting.

Finally, we analyse large systems of coupled chemical oscillators. Using a continuum approximation, we demonstrate mechanisms that cause auto-synchronization in such systems.

Aluminium in Fisch und Fischereierzeugnissen

Recent reports associating aluminium with several skeletal (osteomalacia) and neurological disorders (encephalopathy and Alzheimer’s disease) in humans suggest that exposure to aluminium may pose a hazard to health. This requires the examination of aluminiumcontent in different foodstuffs. Therefore, an analytical method for the determination of aluminium in fish and fishery products, especially in fishery products packaged in aluminium cans, was developed using graphite furnace atomic absorption spectrometry. Fillets of lean and fatty fish showed aluminium levels lower than 1mg/kg wet weight, muscle of crustacean, molluscan and shellfish had apparently higher aluminium levels (up to 20 mg/kg wet weight). The aluminium content in some aluminum-canned herring was much higher than the content found in herring caught in the North Sea. These results indicate that aluminium is taken up by the herring fillets in aluminium cans, presumably through the slight and slow dissolution of aluminium from the can wall, due to some defects in the protective lacquer layer. A comparison of the aluminium levels measured in canned herring with the average aluminium-intake (normally between 3 and 5 mg/day) or with the provisional tolerable daily intake of 1mg/kg body weight per day (WHO 1989) indicated, that the aluminium content of the edible part of aquatic food does not play a significant role. High consumption of fish fillets does not pose any health risk.

Continuous radial superresolution filters with large focal depth

A new set of continuous superresolution filters is proposed which exhibits a radial superresolution performance with an extended depth of focus in an optical system by properly choosing the design parameters. Numerical simulation results of the performance parameters of the superresolution gain, the radial central core size, the Strehl ratio, the side-lobe factor and the depth of focus with different design parameters for the optimized patterns are displayed. We also give a design example for this kind of filter characterized by a birefringent element inserted between two parallel polarizers. This kind of filter would be useful in fields such as optical data storage systems.