It has become almost a cliche to preface one's remarks about asymptotic tech niques with the statement that only a very few special problems in diffrac tion theory (be it electromagnetic, acoustic, elastic or other phenomena) are possessed of closed form solutions, but as with many cliches, this is because it is true. One only has to scan the literature to see the large amount of effort (both human and computer) expended to solve diffraction problems involving complicated geometries which do not permit such simplifications as separation of variables, It was a desire for techniques more straightforward than frontal numerical assaults, as well as for a theory hich ould explain the basic physical phenomena involved, which stimulated research into asymptot ic methods. Geometrical optics (GO) and, now, even Keller's geometrical theory of dif fraction (GTD) have been with us for some time, and have become standard tools in the analysis of high-frequency wave phenomena, Of course, it was always recognized that these approaches broke down in certain regions: GO in the shadow region; GTD along shadow boundaries and caustics. One remedy for these defects is to construct an expansion, based upon a more general ansatz than GO or GTD, which is made to be valid in one or more of the areas where GO or GTD break down."
MIGUEL MAROTO is a MRC Career Development Fellow and Lecturer at the University of Dundee, UK. He received his PhD in Biochemistry and Molecular Biology from the Department of Biochemistry of the Universidad Autonoma of Madrid, Spain. His research interests include investigating the biochemical basis of different signalling mechanisms implicated in the acquisition of specific cell fates during vertebrate development. In recent years he has been involved in the analysis of the mechanism of the molecular clock in the control of the process of somitogenesis.
NEIL V. WHITTOCK gained his PhD in Human Molecular Genetics whilst working at Guys’ and St Thomas’ Hospitals in London, UK. His research focussed on developing diagnostic genetic tests for Duchenne muscular dystrophy before moving on to identifying genes involved in bullous skin disorders. He then continued his research as a postdoctoral fellow at the University of Dundee before arriving at the University of Exeter where he spent three years working alongside Dr Peter Turnpenny. The work at Exeter focussed on the identification of genes involved in human genetic disorders that affected the development of the spine and ribs, specifically the spondylocostal dysostoses. He now works as an Ambulance Technician in Devon, UK. and runs his own antique clock restoration business.
