# Registered Data

## [00280] Canonical Scattering Theory and Application

**Session Date & Time**:- 00280 (1/2) : 3D (Aug.23, 15:30-17:10)
- 00280 (2/2) : 3E (Aug.23, 17:40-19:20)

**Type**: Proposal of Minisymposium**Abstract**: A resurging interest in metamaterials, in particular acoustic metamaterials, comprising multi-scale rigid, porous, and/or elastic materials with subwavelength resonators renews the need for a mathematical theory capable of dealing with wave interactions with such objects. This session will comprise advances across a range of canonical scattering and diffraction problems applicable to acoustic metamaterials. This lays the foundation for understanding and exploiting these materials across a range of industrial applications such as sound absorbent linings, acoustic cloaking devices, and acoustic lensing**Organizer(s)**: Lorna Ayton**Classification**:__76Qxx__,__74Jxx__,__78Axx__,__35Jxx__,__35Qxx__**Speakers Info**:- Shiza Naqvi (University of Cambridge)
- Huansheng Chen (Lehigh University)
- Sonya Tiomkin (Lehigh University)
- Georg Maierhofer (Sorbonne University)
- Andrew Horning (MIT)
- Benshuai Lyu (king University)
- Matthew Nethercote (University of Manchester)

**Talks in Minisymposium**:**[01576] A Mathematical Method to Solve Diffraction Problems with Generalised Linear Boundary Conditions****Author(s)**:**Alistair Hales**(University of Cambridge)

**Abstract**: The Wiener—Hopf Technique is a popular method used in the analysis of diffraction problems and elsewhere. We present a novel methodology that can solve the gust diffraction problem for a surface with a general linear boundary condition, with the view of applying said solutions to leading or trailing edge noise problems for general (possibly non-rigid) materials. We discuss how solving such a problem is primarily difficult due to the factorization procedure required for the Wiener—Hopf technique to work. However, such boundary conditions may be simplified using a transformation of variables to a trigonometric polynomial, whose roots give the information required to split the scalar kernel into individual factors. This methodology provides insight into the underlying structure of the kernel while also allowing numerical methods to be easily applied thanks to the Maliuzhinets function that originates from wedge diffraction problems. As an initial demonstration of the theory, we compare different canonical choices for impedance boundaries and demonstrate not only how changing the impedance of the surface can affect the solution, but how choosing a correct boundary condition initially may prove cruci

**[02368] Analysis of oversampled collocation methods for wave scattering problems****Author(s)**:**Georg Maierhofer**(Sorbonne Université)

**Abstract**: In this talk, we will explore the extent to which the convergence properties of collocation methods for Fredholm integral equations can be improved by least-squares oversampling. We provide rigorous analysis to show that superlinear oversampling can enhance the convergence rates of the collocation method and reduce its sensitivity to the distribution of collocation points. We support our analysis with several numerical examples for the two-dimensional Helmholtz equation. This is joint work with Daan Huybrechs.

**[02735] Diffraction of acoustic waves by multiple independent semi-infinite arrays.****Author(s)**:**Matthew Allan Nethercote**(University of Manchester)- Raphael Assier (University of Manchester)
- Anastasia Kisil (University of Manchester)

**Abstract**: We consider multiple wave scattering problems with several semi-infinite periodic arrays of point scatterers. For each array, a coupled system of equations must be satisfied by the scattering coefficients. All of these systems are solved using the discrete Wiener--Hopf technique and the result leads to a invertible matrix equation. In particular, we look at two arrays forming a wedge interface and will make comparisons with numerical methods that do not rely on the array periodicity.

**[03067] Revisiting the frozen-gust assumption for edge scattering using spatially-varying wavepackets****Author(s)**:- Sonya Tiomkin (Lehigh University)
**Justin Jaworski**(Lehigh University)

**Abstract**: An analytic solution for the noise generated by a wavepacket traveling near the edge of a rigid semi-infinite flat plate is determined in closed form in the time domain. The spatially-varying wavepacket constitutes a surrogate model for turbulent flow distortions engendered by the edge geometry. This approach permits a relaxation of the common frozen gust assumption for trailing-edge noise prediction, whereby the local vorticity is assumed to be unaffected by the edge.

**[03068] Acoustic emission of a vortex ring near a porous edge****Author(s)**:- Huansheng Chen (Lehigh University)
- Zachary Yoas (General Dynamics Electric Boat)
- Mitchell Swann (Applied Research Laboratory, Pennsylvania State University)
**Justin Jaworski**(Lehigh University)- Michael Krane (Applied Research Laboratory, Pennsylvania State University)

**Abstract**: The sound of a vortex ring in a quiescent fluid passing near a semi-infinite porous edge is investigated analytically to determine its time-dependent pressure signal and directivity in the acoustic far field as a function of a single dimensionless parameter. Results for this configuration furnish an analogue to scaling results from standard trailing-edge noise analyses and permit a direct comparison to companion experiments that circumvent measurement contamination by background noise sources of a mean flow.

**[03187] Spectral computations for defect scattering in disordered topological insulators****Author(s)**:**Andrew Horning**(Massachusetts Institute of Technology)- Matthew Colbrook (University of Cambridge)
- Kyle Thicke (Texas A&M University)
- Alex Watson (University of Minnesota)

**Abstract**: Topological insulators (TIs) support remarkable electronic wave phenomena that persist even in the presence of material defects and disorder. However, these phenomena are governed by an infinite-dimensional Hamiltonian with exotic spectral properties, which has frustrated the development of rigorous computational methods for disordered TIs. We use recent advances in computational spectral theory to rigorously and efficiently calculate conductivities and the generalized eigenstates that mediate interfacial electronic transport in two-dimensional TIs.

**[03239] Green's function for wave scattering by a semi-inifinite flat plate with a serrated edge****Author(s)**:**Benshuai Lyu**(Peking University)

**Abstract**: An analytical Green’s function is developed to study the wave scattering by a semi-infinite flat plate with a serrated edge. The scattered pressure is solved using the Wiener-Hopf technique in conjunction with the adjoint technique. The kernel decomposition can be performed analytically in the high-frequency regime, which yields closed-form analytical Green's functions for any arbitrary piecewise linear serrations. The Green's function is shown to agree well with Finite Element Method (FEM) computations at high frequencies.

**[05383] Extending the Unified Transform Method for Periodic Scattering Problems****Author(s)**:**Shiza Batool Naqvi**(University of Cambridge)- Lorna Ayton (University of Cambridge)

**Abstract**: The Unified Transform method (also known as Fokas method) is employed in unbounded convex domains to model wave scattering governed by the Helmholtz equation. The method is extended to consider periodic boundary conditions allowing for computation of infinite scattering patterns which have been previously studied using periodic Green's functions and large-dimension Wiener--Hopf matrices. The method is amenable to impedance and elastic surfaces. Furthermore, complex arrangements of scatterers, such as non-parallel cascading plates, are considered.