Overview

The book develops the dynamical theory of scattering from random media from first principles. Its key findings are to characterize the time evolution of the scattered field in terms of stochastic differential equations, and to illustrate this framework in simulation and experimental data analysis. The physical models contain all correlation information and higher order statistics, which enables radar and laser scattering experiments to be interpreted. An emphasis is placed on the statistical character of the instantaneous fluctuations, as opposed to ensemble average properties. This leads to various means for detection, which have important consequences in radar signal processing and statistical optics. The book is also significant also because it illustrates how ideas in mathematical finance can be applied to physics problems in which non-Gaussian noise processes play an essential role. This pioneering book represents a significant advance in this field, and should prove valuable to leading edge researchers and practitioners at the postgraduate level and above.

Full Product Details

Author:   Timothy R. Field (McMaster University, Hamilton, Ontario, Canada)
Publisher:   Oxford University Press
Imprint:   Oxford University Press
Volume:   144
Dimensions:   Width: 16.10cm , Height: 1.40cm , Length: 24.20cm
Weight:   0.462kg
ISBN:  

9780198570776

ISBN 10:   0198570775
Pages:   200
Publication Date:   18 December 2008
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   To order  
Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us.

Table of Contents

PART I: STOCHASTIC CALCULUS 1: Heat equation and Brownian motion 2: Ito calculus 3: Stochastic differential geometry 4: Examples of stochastic differential equations PART II: SCATTERING DYNAMICS 5: Diffusion models in electromagnetic scattering 6: Rayleigh scattering 7: Population dynamics 8: Dynamics of K-scattering 9: Models of weak scattering 10: Scattering from general populations PART III: SIMULATION AND EXPERIMENT 11: Simulation of K-scattering 12: Experimental tests 13: Non-linear dynamics of sea clutter 14: Observability of scattering cross-section APPENDICES A: Stability and infinite divisibility B: Ito versus Stratonovich stochastic integrals C: Filtrations, conditional probability and Markov property D: Girsanov's theorem E: Partition function solution to BDI model F: Summary of K-scattering G: Iterative solution for vector processes H: Open problems I: Suggested further reading References Index

Reviews

... a resource that will help readers focus on the key methods and results [...], a very valuable and timely publication. Waves in Random and Complex Media Timely and significant, well pitched, and with adequate introductory and tutorial material to give less specialist readers the necessary background and motivation. John McWhirter, Cardiff University

Author Information

Dr Timothy R. Field Associate Professor McMaster University Ontario, Canada Timothy Field studied undergraduate mathematics at King's College, Cambridge University, and went on to receive a doctorate in mathematics from New College and the Mathematical Institute, Oxford University in 1997, where he studied mathematical physics under Sir Roger Penrose. He formerly held a UK government sponsored research fellowship for research into stochastic techniques in electromagnetic scattering problems. Currently Timothy is an Associate Professor in the Department of Electrical and Computer Engineering, an Associate Member in the Department of Mathematics, and faculty member of the Brain Body Institute at McMaster University, Canada. He was recently awarded a five year NSERC Discovery grant for his pioneering research into 'Applications of stochastic differential equations to electromagnetic phenomena'. He has lectured worldwide on topics in mathematical physics.

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