Douglas Jones was an extremely creative and influential mathematician. His contributions to the theory of electromagnetic and acoustic waves and his development of original and exceptionally powerful mathematical techniques with which to study them has led to the solution of problems of both practical and social importance. His work is fundamental to the design and performance of radar antennae wherein it is necessary to optimize their transmitting and receiving characteristics. Jones also investigated the manner in which electromagnetic waves interact with objects having sharp edges. These studies are basic to the construction of ‘stealth’ aircraft, in which the geometrical shape is designed to minimize the aircraft’s signature. When supersonic airliner capability was realized in the development of Concorde there was considerable public concern regarding the excessive noise created during take-off and landing and the impact of ‘sonic boom’ on built-up areas. This prompted investigations into the noise levels experienced on the ground due to a moving acoustic source. This inspired Douglas to develop a mathematical theory of noise shielding. To address these difficult problems he developed powerful techniques of analysis: these included the asymptotic expansion of multidimensional integrals and the generalization of the method of stationary phase; the solution of integral equations arising in diffraction and obstacle scattering theory; the development of multidimensional generalized functions; uniform asymptotics and Stokes’ phenomenon; the Wiener–Hopf technique; and powerful numerical techniques to solve integral equations arising in electromagnetic wave theory.
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Published by the Royal Society