All Outputs (7)

A caustic terminating at an inflection point (2023)
Journal Article

We present an asymptotic and numerical study of the evolution of an incoming wavefield which has a caustic close to a curve with an inflection point. Our results reveal the emergence of a wavefield which resembles that of a shadow boundary but has a... Read More about A caustic terminating at an inflection point.

Friedlander-Keller ray expansions in electromagnetism: Monochromatic radiation from arbitrary surfaces in three dimensions (2022)
Journal Article

The standard approach to applying ray theory to solving Maxwell’s equations in the large wave-number limit involves seeking solutions that have (i) an oscillatory exponential with a phase term that is linear in the wave-number and (ii) has an amplitu... Read More about Friedlander-Keller ray expansions in electromagnetism: Monochromatic radiation from arbitrary surfaces in three dimensions.

Thin-layer solutions of the Helmholtz equation (2020)
Journal Article

This paper gives a brief overview of some configurations in which highfrequency wave propagation modelled by Helmholtz equation gives rise to solutions that vary rapidly across thin layers. The configurations are grouped according to their mathematic... Read More about Thin-layer solutions of the Helmholtz equation.

Asymptotics of near-cloaking (2020)
Journal Article

This paper describes how asymptotic analysis can be used to gain new insights into the theory of cloaking of spherical and cylindrical targets within the context of acoustic waves in a class of linear elastic materials. In certain cases these configu... Read More about Asymptotics of near-cloaking.

Reflection and transmission of high-frequency acoustic, electromagnetic and elastic waves at a distinguished class of irregular, curved boundaries (2019)
Journal Article

Reflection and transmission phenomena associated with high-frequency linear wave incidence on irregular boundaries between adjacent acoustic or electromagnetic media, or upon the irregular free surface of a semi-infinite elastic solid, are studied in... Read More about Reflection and transmission of high-frequency acoustic, electromagnetic and elastic waves at a distinguished class of irregular, curved boundaries.

Asymptotic solutions of the Helmholtz equation: Generalised Friedlander–Keller ray expansions of fractional order (2018)
Journal Article

Applications of a WKBJ-type `ray ansatz' to obtain asymptotic solutions of the Helmholtz equation in the high{frequency limit are now standard, and underpin the construction of `geometrical optics' ray diagrams in many electromagnetic, acoustic and e... Read More about Asymptotic solutions of the Helmholtz equation: Generalised Friedlander–Keller ray expansions of fractional order.

Friedlander-Keller ray expansions and scalar wave reflection at canonically-perturbed boundaries (2018)
Journal Article

This paper concerns the reflection of high-frequency, monochromatic linear waves of wavenumber k (>>1) from smooth boundaries which are O (k-1/2) perturbations away from either a specified near-planar boundary or else from a given smooth, two-dimensi... Read More about Friedlander-Keller ray expansions and scalar wave reflection at canonically-perturbed boundaries.