Raphaël C. Assier
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View article: Scattering of transient waves by an interface with time-modulated jump conditions
Scattering of transient waves by an interface with time-modulated jump conditions Open
Time modulation of the physical parameters offers interesting new possibilities for wave control. Examples include amplification of waves, harmonic generation and non-reciprocity, without resorting to non-linear mechanisms. Most of the rec…
View article: Effective mass density for wave propagation in layered media: a study of the elastic/acoustic transition
Effective mass density for wave propagation in layered media: a study of the elastic/acoustic transition Open
It is well-known that the effective mass density of a layered elastic medium is isotropic, whereas its acoustic analogue is anisotropic. Given that the acoustics regime is recoverable from elasticity by taking the limit as the shear modulu…
View article: Acoustic wave diffraction by a quadrant of sound-soft scatterers
Acoustic wave diffraction by a quadrant of sound-soft scatterers Open
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 formation, which we have dubbed the quarter lattice. This l…
View article: Scattering of transient waves by an interface with time-modulated jump conditions
Scattering of transient waves by an interface with time-modulated jump conditions Open
Time modulation of the physical parameters offers interesting new possibilities for wave control. Examples include amplification of waves, harmonic generation and non-reciprocity, without resorting to non-linear mechanisms. Most of the rec…
View article: Matrix representation of Picard--Lefschetz--Pham theory near the real plane in $\mathbb{C}^2$
Matrix representation of Picard--Lefschetz--Pham theory near the real plane in $\mathbb{C}^2$ Open
A matrix formalism is proposed for computations based on Picard--Lefschetz theory in a 2D case. The formalism is essentially equivalent to the computation of the intersection indices necessary for the Picard--Lefschetz formula and enables …
View article: Propagation and non-reciprocity in time-modulated diffusion through the lens of high-order homogenization
Propagation and non-reciprocity in time-modulated diffusion through the lens of high-order homogenization Open
The homogenization procedure developed here is conducted on a laminate with periodic space–time modulation on the fine scale: at the leading order, this modulation creates convection in the low-wavelength regime if both parameters are modu…
View article: Acoustic wave diffraction by a quadrant of sound-soft scatterers
Acoustic wave diffraction by a quadrant of sound-soft scatterers Open
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 formation, which we have dubbed the quarter lattice. This l…
View article: High-Frequency Homogenization for Periodic Dispersive Media
High-Frequency Homogenization for Periodic Dispersive Media Open
High-frequency homogenization is used to study dispersive media, containing inclusions placed periodically, for which the properties of the material depend on the frequency (Lorentz or Drude model with damping, for example). Effective prop…
View article: Double Floquet-Bloch transforms and the far-field asymptotics of Green's functions tailored to periodic structures
Double Floquet-Bloch transforms and the far-field asymptotics of Green's functions tailored to periodic structures Open
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 integration surface to bypass the integrands' singularities, is p…
View article: Diffraction by a right-angled no-contrast penetrable wedge: recovery of far-field asymptotics
Diffraction by a right-angled no-contrast penetrable wedge: recovery of far-field asymptotics Open
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 penetrable wedge. To achieve this, we employ a two-complex-variabl…
View article: High-order homogenization of the time-modulated wave equation: non-reciprocity for a single varying parameter
High-order homogenization of the time-modulated wave equation: non-reciprocity for a single varying parameter Open
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 of low-frequency homogenization, it was so far only possib…
View article: Stress relaxation and thermo-visco-elastic effects in fluid-filled slits and fluid-loaded plates
Stress relaxation and thermo-visco-elastic effects in fluid-filled slits and fluid-loaded plates Open
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. We show that these two configurations can be studied via …
View article: A note on double Floquet-Bloch transforms and the far-field asymptotics of Green's functions tailored to periodic structures
A note on double Floquet-Bloch transforms and the far-field asymptotics of Green's functions tailored to periodic structures Open
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 integration surface to bypass the integrands' singularities, is p…
View article: A contribution to the mathematical theory of diffraction. Part II: Recovering the far-field asymptotics of the quarter-plane problem
A contribution to the mathematical theory of diffraction. Part II: Recovering the far-field asymptotics of the quarter-plane problem Open
Summary We apply the stationary phase method developed in Assier, Shanin and Korolkov, QJMAM, 76 (2022) to the problem of wave diffraction by a quarter-plane subjected to Dirichlet boundary conditions. The wave field is written as a double…
View article: Diffraction by a right-angled no-contrast penetrable wedge: recovery of far-field asymptotics
Diffraction by a right-angled no-contrast penetrable wedge: recovery of far-field asymptotics Open
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 penetrable wedge. To achieve this, we employ a two-complex-variabl…
View article: A contribution to the mathematical theory of diffraction. Part II: Recovering the far-field asymptotics of the quarter-plane problem
A contribution to the mathematical theory of diffraction. Part II: Recovering the far-field asymptotics of the quarter-plane problem Open
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 as a double Fourier transform of an unknown spectral functi…
View article: High-order homogenisation of the time-modulated wave equation:\n non-reciprocity for a single varying parameter
High-order homogenisation of the time-modulated wave equation:\n non-reciprocity for a single varying parameter Open
Laminated media with material properties modulated in space and time in the\nform of travelling waves have long been known to exhibit non-reciprocity.\nHowever, when using the method of low frequency homogenisation, it was so far\nonly pos…
View article: High-order homogenisation of the time-modulated wave equation: non-reciprocity for a single varying parameter
High-order homogenisation of the time-modulated wave equation: non-reciprocity for a single varying parameter Open
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 of low frequency homogenisation, it was so far only possib…
View article: Diffraction of acoustic waves by multiple semi-infinite arrays
Diffraction of acoustic waves by multiple semi-infinite arrays Open
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 sharp transitions in boundary conditions on a plane/plate. How…
View article: High-frequency homogenization for periodic dispersive media
High-frequency homogenization for periodic dispersive media Open
High-frequency homogenization is used to study dispersive media, containing inclusions placed periodically, for which the properties of the material depend on the frequency (Lorentz or Drude model with damping, for example). Effective prop…
View article: Diffraction of acoustic waves by multiple semi-infinite arrays
Diffraction of acoustic waves by multiple semi-infinite arrays Open
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 sharp transitions in boundary conditions on a plane/plate. How…
View article: Diffraction by a Right-Angled No-Contrast Penetrable Wedge: Analytical Continuation of Spectral Functions
Diffraction by a Right-Angled No-Contrast Penetrable Wedge: Analytical Continuation of Spectral Functions Open
Summary 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 of the unknown (spectral) functions of the two-com…
View article: A contribution to the mathematical theory of diffraction: a note on double Fourier integrals
A contribution to the mathematical theory of diffraction: a note on double Fourier integrals Open
Summary We consider a large class of physical fields $u$ written as double inverse Fourier transforms of some functions $F$ of two complex variables. Such integrals occur very often in practice, especially in diffraction theory. Our aim is…
View article: Array scattering resonance in the context of Foldy’s approximation
Array scattering resonance in the context of Foldy’s approximation Open
This article provides an overview of resonance phenomena in wave scattering by infinite and semi-infinite periodic arrays of small cylindrical scatterers, in the context of Foldy’s approximation. It briefly summarizes well-known results fr…
View article: Diffraction by a Right-Angled No-Contrast Penetrable Wedge: Analytical Continuation of Spectral Functions
Diffraction by a Right-Angled No-Contrast Penetrable Wedge: Analytical Continuation of Spectral Functions Open
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 of the unknown (spectral) functions of the two-complex-var…
View article: A unified framework for linear thermo-visco-elastic wave propagation including the effects of stress-relaxation
A unified framework for linear thermo-visco-elastic wave propagation including the effects of stress-relaxation Open
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 media admit two thermo-compressional modes and a shear mode. We…
View article: A unified framework for linear thermo-visco-elastic wave propagation including the effects of stress-relaxation
A unified framework for linear thermo-visco-elastic wave propagation including the effects of stress-relaxation Open
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 media admit two thermo-compressional modes and a shear mode. We…