43 citations · 115 across the 26 of their papers we have counts for
30 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…
Direct Numerical Simulation of Thermoacoustically Unstable Flames Via Non-Drifting Acoustic Delay Characteristic Boundary Conditions
Benjamin L. Cookman, Jack R. C. King, Raphaël C. Assier +1
Thermoacoustic instability in premixed flames results from the coupling between the flame's heat release, as determined by combustion parameters, and surrounding acoustics, as dete…
Effective mass density for wave propagation in periodic layered media in the elasto-acoustic transition
Gabriel Núñez, William J. Parnell, Raphaël C. Assier
This article investigates the effective mass density for acoustic and elastic wave propagation in layered media, with emphasis on its transition between these regimes. Conventional…
Waves within a network of slowly time-modulated interfaces: time-dependent effective properties, reciprocity and high-order dispersion
Michaël Darche, Raphaël Assier, Sébastien Guenneau +2
We consider wave propagation through a 1D periodic network of slowly time-modulated interfaces. Each interface is modelled by time-dependent spring-mass jump conditions, where mass…
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…
Wave scattering by a transversal defect in a discrete waveguide
Elena Medvedeva, Raphael Assier, Anastasia Kisil
We study wave scattering by a finite transversal strip in a discrete square-lattice waveguide with Dirichlet boundary conditions imposed on the strip and the waveguide walls. The s…
On an analogy between the Wiener--Hopf formulations of discrete and continuous diffraction problems
A. I. Korolkov, R. C. Assier, A. V. Kisil
This article is dedicated to unifying the framework used to derive the Wiener--Hopf equations arising from some discrete and continuous wave diffraction problems.The main tools are…
Acoustic wave diffraction by a quadrant of sound-soft scatterers
Matthew Nethercote, Anastasia Kisil, Raphael Assier
Motivated by research in metamaterials, we consider the challenging problem of acoustic wave scattering by a doubly periodic quadrant of sound-soft scatterers arranged in a square…
Propagation and non-reciprocity in time-modulated diffusion through the lens of high-order homogenization
Marie Touboul, Bruno Lombard, Raphaël Assier +2
The homogenization procedure developed here is conducted on a laminate with periodic space-time modulation on the fine scale: at leading order, this modulation creates convection i…
Stress relaxation and thermo-visco-elastic effects in fluid-filled slits and fluid-loaded plates
Erik García Neefjes, David Nigro, Raphaël C. Assier +1
In this paper, we theoretically analyse wave propagation in two canonical problems of interest: fluid-filled thermo-visco-elastic slits and fluid-loaded thermo-visco-elastic plates…
Diffraction by a set of collinear cracks on a square lattice: an iterative Wiener-Hopf method
Elena Medvedeva, Raphael Assier, Anastasia Kisil
The diffraction of a time-harmonic plane wave on collinear finite defects in a square lattice is studied. This problem is reduced to a matrix Wiener-Hopf equation. This work adapts…
A note on double Floquet-Bloch transforms and the far-field asymptotics of Green's functions tailored to periodic structures
Andrey V. Shanin, Raphael C. Assier, Andrey I. Korolkov +1
We propose a general procedure to study double integrals arising when considering wave propagation in periodic structures. This method, based on a complex deformation of the integr…
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…
A contribution to the mathematical theory of diffraction. Part II: Recovering the far-field asymptotics of the quarter-plane problem
Raphael C. Assier, Andrey V. Shanin, Andrey I. Korolkov
We apply the stationary phase method developed in (Assier, Shanin \& Korolkov, QJMAM, 76(1), 2022) to the problem of wave diffraction by a quarter-plane. The wave field is written…
High-order homogenisation of the time-modulated wave equation: non-reciprocity for a single varying parameter
Marie Touboul, Bruno Lombard, Raphaël Assier +2
Laminated media with material properties modulated in space and time in the form of travelling waves have long been known to exhibit non-reciprocity. However, when using the method…
High-frequency homogenization for periodic dispersive media
Marie Touboul, Benjamin Vial, Raphaël Assier +2
High-frequency homogenization is used to study dispersive media, containing inclusions placed periodically, for which the properties of the material depend on the frequency (Lorent…
Diffraction of acoustic waves by multiple semi-infinite arrays
Matthew Nethercote, Anastasia Kisil, Raphael Assier
Analytical methods are fundamental in studying acoustics problems. One of the important tools is the Wiener-Hopf method, which can be used to solve many canonical problems with sha…
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…
A unified framework for linear thermo-visco-elastic wave propagation including the effects of stress-relaxation
Erik García Neefjes, David Nigro, Artur L. Gower +3
We present a unified framework for the study of wave propagation in homogeneous linear thermo-visco-elastic (TVE) continua, starting from conservation laws. In free-space such medi…
A contribution to the mathematical theory of diffraction. Part I: A note on double Fourier integrals
Raphaël C. Assier, Andrey V. Shanin, Andrey I. Korolkov
We consider a large class of physical fields written as double inverse Fourier transforms of some functions of two complex variables. Such integrals occur very often in pra…
Diffraction by a Right-Angled No-Contrast Penetrable Wedge Revisited: A Double Wiener-Hopf Approach
Valentin D. Kunz, Raphael C. Assier
In this paper, we revisit Radlow's innovative approach to diffraction by a penetra ble wedge by means of a double Wiener-Hopf technique. We provide a constructive way of obtaining…
Diffraction of acoustic waves by a wedge of point scatterers
M. A. Nethercote, A. V. Kisil, R. C. Assier
This article considers the problem of diffraction by a wedge consisting of two semi-infinite periodic arrays of point scatterers. The solution is obtained in terms of two coupled s…
Manipulating thermal fields with inhomogeneous heat spreaders
Eleanor R. Russell, Raphaël C. Assier, William J. Parnell
We design a class of spatially inhomogeneous heat spreaders in the context of steady-state thermal conduction leading to spatially uniform thermal fields across a large convective…
Analytical continuation of two-dimensional wave fields
Raphael C. Assier, Andrey V. Shanin
Wave fields obeying the 2D Helmholtz equation on branched surfaces (Sommerfeld surfaces) are studied. Such surfaces appear naturally as a result of applying the reflection method t…