8 papers
Plane wave representations for wave scattering on a sphere
Valentin D. Kunz, Andrey V. Shanin, Raphael C. Assier
Motivated by three-dimensional wave diffraction by conical shapes, we consider the two-dimensional problem of wave scattering on the real sphere resulting from a po…
Extension of a mathematical analogy between vortical flows without surface tension and irrotational capillary flows
Valentin D. Kunz, Saleh Tanveer, Darren G. Crowdy
In a recent paper, a mathematical analogy was found between two physically distinct classes of two-dimensional free boundary problems in inviscid fluid mechanics. One class involve…
A mathematical analogy between certain hollow vortex and bubble flows - existence, uniqueness, and identical boundary shapes
Valentin D. Kunz, Saleh Tanveer, Darren G. Crowdy
We study two physically distinct steady free-boundary problems in a two-dimensional inviscid fluid: a hollow vortex in a constant-vorticity flow subject to simple shear, third orde…
Degree-Three Rational Sphere Maps: Sharp Denominator Region and Gram Normal Forms
Eden Danielsen-Jensen, Dusty Grundmeier, Abdullah Al Helal +4
We study degree-three rational sphere maps in two complex variables. After a standard normalization, the denominator of such a map takes the form \[ g_σ(z)=1+σ_1 z_1^2+σ_2 z_2^2, \…
Plane-wave representation for the Laplace--Beltrami equation on a sphere. Application to the Green's function
Andrey V. Shanin, Valentin D. Kunz, Raphael C. Assier
We propose an extension of the plane-wave representation for wave fields defined on the real sphere . This representation is well-known in the planar setting but has…
Diffraction by a right-angled no-contrast penetrable wedge: recovery of far-field asymptotics
Valentin D. Kunz, Raphael C. Assier
We provide a description of the far-field encountered in the diffraction problem resulting from the interaction of a monochromatic plane-wave and a right-angled no-contrast penetra…
Diffraction by a Right-Angled No-Contrast Penetrable Wedge: Analytical Continuation of Spectral Functions
Valentin D. Kunz, Raphael C. Assier
We study the problem of diffraction by a right-angled no-contrast penetrable wedge by means of a two-complex-variable Wiener-Hopf approach. Specifically, the analyticity properties…
Constructing Group-Invariant CR Mappings
Jennifer Brooks, Sean Curry, Dusty Grundmeier +4
We construct CR mappings between spheres that are invariant under actions of finite unitary groups. In particular, we combine a tensoring procedure with D'Angelo's construction of…