Moving boundary and boundary value problems occur in many physical and engineering processes involving heat transfer and phase changes, they range from icing problems, for example the Stefan problem, to the melting of metals and plastics using lasers. This book reviews and compares some well known and some recently developed methods to solve these problems. Recent advances in the finite difference solution of linear and non-linear partial differential equations are presented and algorithmic manipulations that enhance the computational efficiency are incorporated into the overall schemes. In this new approach, the the finite difference substitutions are made into the solutions of the partial differential equation rather than classically into the partial differential equation itself. This approach can be exploited for many types of partial differential equation and they may therefore be of interest to researchers studying a wide range of applications in physical problems such as diffusion and heat transfer equations, optoelectronic paraxial wave equations, the quantum mechanical wave equations, time dependent pulse propagation, and similar WKB-derived problemsM

This paper considers the filter-encoding constraints applied to construction of the synthetic discriminant function (SDF), with a view of synthesizing the SDF such that it is contains mostly higher frequency components of the individual training-set image, by using a linear combination of a set of preprocessed training images i.e filter modulated. This filter-encoding constraint id applied to the SDF and termed modified filter SDF or MfSDF. Comparison of the performance of the MfSDF filter with that of the fSDF filter using modulators set to be binary phase-only filter (BPOF) and a phase-only filter (POF) shows the BPOF/MfSDF is not subject to distortions for in-plane object rotation upto 65°, whereas the BPOF/fSDF achieves only 45°. The MfSDF also provides better discrimination and signal-to-noise ratio. Applications to real-time optical correlation using commercially available modulators is discussed.

In the past decade the understanding of stability and chaotic behaviour of nonlinear systems has made significant progress. Such systems include: structure of turbulence, oscillations in mechanical structures, multistable biological systems, etc. Laser machining is now an established industrial production method for: prototyping, small batch manufacture, cutting refractory materials and specialist applications such as micromachining. Within narrowly bounded limits, many models exist that can be used to predict the necessary machining control parameters such as cutting rate, power, pulse repetition frequency, etc. However, in an unconstrained machining process, chaotic phenomena can be observed to occur. The objective of this paper is to prove the existence of chaos, for the laser-material interaction, which can be described by Poincaré-Birkhoff-Smale horseshoes. Furthermore, to exploit the phase portrait of the process to predict the optimal laser machining control parameters. © 1994.

A hierarchically structured environment that integrates a knowledge- based expert system, adaptive process control and pattern recognition techniques for controlling a laser cutting process is described. Knowledge of the laser cutting process for different materials is organised and encoded into a rule-based system. An adaptive control algorithm based on on-line recursive parameter estimation and on-line control law synthesis was adopted for the highly non-linear cutting process control. Cutting speed was selected as the major control variable. Irradiance emitted from the cut front is used for the feedback signal to this adaptive controller. The irradiance signal feeds the recursive parameter estimator for system identification. Techniques of pattern recognition, which have been well developed in coherent optics, were applied to assess cut quality by characterising the exit spark cone images of the gas assisted laser cutting process. Images from the cutting processes were grabbed, edge enhanced and correlated with a synthetic discriminant function filter which was synthesised from reference images to give good cut quality. Results from digital simulations based on these pattern recognition algorithms are also presented. © 1994.