About the Author
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.
Table of ContentsTranslator’s Introduction.- 1 Introduction.- 2 The Ray Method.- 2.1 The Starting Point: Formulas for the Scalar Case.- 2.2 The Eikonal Equation; Rays; Wave Fronts.- 2.3 Ray Coordinates.- 2.4 Fundamental Recurrence Formulas.- 2.5 Reflection of a Wave Given by a Ray Expansion.- 3 The Caustic Problem.- 3.1 Ray Expansion in the Neighborhood of a Caustic.- 3.2 The Analytic Nature of the Eikonal for Incoming and Outgoing Waves Near a Caustic.- 3.3 Ray Series in (s,n) and (s,?) Coordinates.- 3.4 The Field in a Boundary Layer Surrounding the Caustic.- 3.5 Fundamental Formulas.- 4 Whispering Gallery and Creeping Waves.- 4.1 Whispering Gallery Waves.- 4.2 Whispering Gallery Quasimodes.- 4.3 Creeping Waves.- 4.4 The Friedlander-Keller Solution (Diffraction Rays).- 4.5 Matching of Creeping Waves and Diffraction Rays.- 5 Oscillations Concentrated in the Neighborhood of a Ray (Gaussian Beams).- 5.1 Rays in the First Approximation.- 5.2 Derivation of the Boundary-Layer Equation.- 5.3 Solution of the System of Recurrence Equations for Vj.- 5.4 Stability of an Extremal Diameter of a Region.- 5.5 Quasimodes of the “Bouncing-Ball” Type in the First Approximation.- 5.6 Construction of Higher Approximations.- 6 Shortwave Diffraction from a Smooth Convex Body.- 6.1 The Parabolic Equation Method.- 6.2 The Analytic Nature of the Functions $$
and Vj..- 6.3 The Boundary Layer in the Deep Shadow Zone.- 6.4 Continuation of the Solution from the Vicinity of the Point C into the Transition Region.- 6.5 Analytic Representation of the Incident Wave in the Neighborhood of the Limiting Ray.- 6.6 System of Recurrence Equations for the Neighborhood of the Limiting Ray.- 6.7 Extension of the Transition Region Formulas into the Neighborhood of the Limiting Ray.- 6.8 Formulas for the Field in the Shadow and in the Penumbra.- 7 The Problem of an Oscillating Point Source.- 7.1 The Ray Method for a Central Field of Rays.- 7.2 Expansion in the Transition Region.- 7.3 Expansions in the Neighborhood of the Origin.- 8 Survey of Literature.- References.