List of Publications of Raphaël Assier
- A ★ marks papers co-authored with current/former PhD students.
- A ★ marks papers for which I am corresponding author.
Peer-Reviewed Journal Articles
P39. A.I. Korolkov, R.C. Assier, A.V. Kisil (2026)
On an analogy between the Wiener--Hopf formulations of discrete and continuous diffraction problems.
Accepted in the IMA Journal of Applied Mathematics
Preprint on arXiv:2507.04979
P38. T. White★, R.C. Assier, W.J. Parnell (2025)
Sound propagation in slowly varying ducts.
Journal of Sound and Vibration, Vol 625, 119572
P37. M. Darche, R.C. Assier, S. Guenneau, B. Lombard, M. Touboul (2025)
Scattering of transient waves by an interface with time-modulated jump conditions
Comptes Rendus. Mécanique Volume 353, pp. 923 - 951
P36. M. Nethercote★, A. Kisil and R.C. Assier (2025)
Acoustic wave diffraction by a quadrant of sound-soft scatterers
IMA J. Appl. Math. hxaf016
Finalist UKAN Mathematical Acoustics Prize 2024
P35. G. Nunez★, W.J. Parnell, R.C. Assier (2025)
Effective mass density for wave propagation in layered media: a study of the elastic/acoustic transition
Proc. Roy. Soc. A 481:20250162
P34. E. García Neefjes★, D. Nigro, R. C. Assier, W. J. Parnell (2024)
Stress relaxation and thermo-visco-elastic effects in fluid-filled slits and fluid-loaded plates
Journal of Fluids and Structures. 131:104219
P33. M. Touboul, B. Lombard, R.C. Assier, S. Guenneau, R.V. Craster (2024)
Propagation and non-reciprocity in time-modulated diffusion through the lens of high-order homogenisation
Proc. Roy. Soc. A. 480: 20240513
P32. V.D. Kunz★ and R.C. Assier (2024)
Diffraction by a right-angled no-contrast penetrable wedge: recovery of far-field asymptotics.
IMA J. Appl. Math. 89(3):463-497
P31. M. Touboul, B. Vial, R.C. Assier, S. Guenneau and R. V. Craster (2024)
High-frequency homogenization for periodic dispersive media
SIAM Multiscale Modeling and Simulation, 22(3), 1136-1168
Finalist UKAN Mathematical Acoustics Prize 2023
P30. A.V. Shanin, R.C. Assier★, A.I. Korolkov, O.I. Makarov (2024)
Double Floquet-Bloch transforms and the far-field asymptotics of Green's functions tailored to periodic structures.
Phys. Rev. B. 110, 024310
P29. E. Medvedeva★, R.C. Assier, A.V. Kisil (2024)
Diffraction by a set of collinear cracks on a square lattice: an iterative Wiener-Hopf method
Wave Motion 129 (103332)
Finalist UKAN Mathematical Acoustics Prize 2023
P28. R.C. Assier★, A.V. Shanin and A. I. Korolkov (2024)
A contribution to the mathematical theory of diffraction. Part II: Recovering the far-field asymptotics of the quarter-plane problem.
Q. J. Mech. Appl. Math., 77(1-2):hbae005
P27. M. Touboul, B. Lombard, R.C. Assier, S. Guenneau and R. V. Craster (2024)
High-order homogenisation of the time-modulated wave equation: non-reciprocity for a single varying parameter.
Proc. Roy. Soc. A 480:20230776
P26. M.A. Nethercote★, A.V. Kisil, R.C. Assier (2023)
Diffraction of acoustic waves by multiple semi-infinite arrays
J. Acoust. Soc. Am. 154(3):1493-1504
P25. V.D. Kunz★ and R.C. Assier (2023)
Diffraction by a Right-Angled No-Contrast Penetrable Wedge: Analytical Continuation of Spectral Functions
Q. J. Mech. Appl. Math., 76(2):211-241,
Finalist IMA Lighthill-Thwaites Prize 2023 & UKAN Mathematical Acoustics Prize 2023
P24. M.A. Nethercote★, A.V. Kisil, I. Thompson and R.C. Assier (2022)
Array scattering resonance in the context of Foldy's approximation
Proc. Roy. Soc. A 478:20220604
P23. R.C. Assier★, A.V. Shanin, A.I. Korolkov (2022)
A contribution to the mathematical theory of diffraction. Part I: A note on double Fourier integrals.
Q. J. Mech. Appl. Math., 76(1):1-47
P22. E. Garcia Neefjes★, D. Nigro, A. L. Gower, R.C. Assier, V.J. Pinfield, W.J. Parnell (2022)
A unified framework for linear thermo-visco-elastic wave propagation including the effects of stress-relaxation
Proc. R. Soc. A 478:20220193
P21. R.C. Davey★, R.C. Assier, I.D. Abrahams (2022)
An efficient semi-analytical scheme for determining the reflection of Lamb waves in a semi-infinite elastic waveguide
Applied Sciences, 12(13), 6468
P20. V.D. Kunz★ and R.C. Assier (2022)
Diffraction by a right-angled no-contrast penetrable wedge revisited: a double Wiener-Hopf approach
SIAM journal on Applied Mathematics 82(4), 1495-1519
P19. M.A. Nethercote★, A.V. Kisil and R.C. Assier (2022)
Diffraction of acoustic waves by a wedge of point scatterers
SIAM journal on Applied Mathematics 82(3), 872-898
P18. E.R. Russell★, R.C. Assier and W.J. Parnell (2022)
Manipulating thermal fields with inhomogeneous heat spreaders
Applied Mathematical Modelling, 106:225-240
P17. R.C. Assier★ and A.V. Shanin (2021)
Vertex Green’s functions of a quarter-plane. Links between the functional equation, additive crossing and Lamé functions.
Q.J. Mech. Appl. Math., 74(3):251-295
P16. C. Bellis, B. Lombard, M. Touboul, R.C. Assier (2021)
Effective dynamics for low-amplitude transient elastic waves in a 1D periodic array of non-linear interfaces
Journal of the Mechanics and Physics of Solids 149:104321
P15. R.C. Assier★ and I.D. Abrahams (2021)
A surprising observation in the quarter-plane diffraction problem
SIAM J. Appl. Math. 81(1), 60-90
P14. R.C. Assier★ and A.V. Shanin (2021)
Analytical continuation of two-dimensional wave fields
Proc. Roy. Soc. A, 477:2020081
P13. R.C. Assier★, M. Touboul, B. Lombard, C. Bellis (2020)
High-frequency homogenisation in periodic media with imperfect interfaces
Proc. Roy. Soc. A, 476:20200402
P12. R.C. Assier★ and I.D. Abrahams (2020)
On the asymptotic properties of an interesting diffraction integral
Proc. Roy. Soc. A, 476:20200150
P11. M. Nethercote★, R.C. Assier and I.D. Abrahams (2020)
High-contrast approximation for penetrable wedge diffraction
IMA J. Appl. Math. 85(3):421-466
Finalist IMA Lighthill-Thwaites Prize 2019
P10. M. Nethercote★, R.C. Assier and I.D. Abrahams (2020)
Analytical methods for perfect wedge diffraction: a review
Wave Motion, 93(102479)
P9. G. Lynott, V. Andrew, I.D. Abrahams, M.J. Simon, W.J. Parnell, R.C. Assier (2019)
Acoustic scattering from a one-dimensional array; tail-end asymptotics for efficient evaluation of the quasi-periodic Green's function
Wave Motion, 89:232-244
P8. N. Gorbushin, V-H. Nguyen, W.J. Parnell, R.C. Assier, S. Naili (2019)
Transient thermal boundary value problems in the half-space with mixed convective boundary conditions
J. Eng. Math. 114 (1): 141-158
P7. R.C. Assier★ and A.V. Shanin (2018)
Diffraction by a quarter-plane. Analytical continuation of spectral functions
Q. Jl. Mech. Appl. Math. 72 (1):51-86
P6. D. Joyce, W.J. Parnell, R.C. Assier and I.D. Abrahams (2017)
An integral equation method for the homogenization of unidirectional fibre-reinforced media;
antiplane elasticity and other potential problems
Proc. Roy. Soc. A 473:20170080
Finalist IMA Lighthill-Thwaites Prize 2017
P5. R.C. Assier★, C. Poon and N. Peake (2016)
Spectral study of the Laplace-Beltrami operator arising in the problem of acoustic wave scattering by a quarter-plane
Q. J. Mech. Appl. Math. 69 (3):281-317
P4. W.J. Parnell, V.-H Nguyen, R.C. Assier, S. Naili and I.D. Abrahams (2016)
Transient thermal mixed boundary value problems in the half-space
SIAM J. Appl. Math. 76(3):845-866
P3. R.C. Assier★ and X. Wu (2014)
Linear and weakly nonlinear instability of a curved premixed flame under the influence of its spontaneous acoustic field
J. Fluid Mech. 758, pp 180-220
P2. R.C. Assier★ and N. Peake (2012)
Precise description of the different far fields encountered in the problem of diffraction of acoustic waves by a quarter-plane.
IMA J. Appl. Math., 77(5):605-625
P1. R.C. Assier★ and N. Peake (2012)
On the diffraction of acoustic waves by a quarter-plane.
Wave Motion, 49(1):64-82
Winner IMA Lighthill-Thwaites Prize 2011 & UKAN Mathematical Acoustics Prize 2023
On an analogy between the Wiener--Hopf formulations of discrete and continuous diffraction problems.
Accepted in the IMA Journal of Applied Mathematics
Preprint on arXiv:2507.04979
P38. T. White★, R.C. Assier, W.J. Parnell (2025)
Sound propagation in slowly varying ducts.
Journal of Sound and Vibration, Vol 625, 119572
P37. M. Darche, R.C. Assier, S. Guenneau, B. Lombard, M. Touboul (2025)
Scattering of transient waves by an interface with time-modulated jump conditions
Comptes Rendus. Mécanique Volume 353, pp. 923 - 951
P36. M. Nethercote★, A. Kisil and R.C. Assier (2025)
Acoustic wave diffraction by a quadrant of sound-soft scatterers
IMA J. Appl. Math. hxaf016
Finalist UKAN Mathematical Acoustics Prize 2024
P35. G. Nunez★, W.J. Parnell, R.C. Assier (2025)
Effective mass density for wave propagation in layered media: a study of the elastic/acoustic transition
Proc. Roy. Soc. A 481:20250162
P34. E. García Neefjes★, D. Nigro, R. C. Assier, W. J. Parnell (2024)
Stress relaxation and thermo-visco-elastic effects in fluid-filled slits and fluid-loaded plates
Journal of Fluids and Structures. 131:104219
P33. M. Touboul, B. Lombard, R.C. Assier, S. Guenneau, R.V. Craster (2024)
Propagation and non-reciprocity in time-modulated diffusion through the lens of high-order homogenisation
Proc. Roy. Soc. A. 480: 20240513
P32. V.D. Kunz★ and R.C. Assier (2024)
Diffraction by a right-angled no-contrast penetrable wedge: recovery of far-field asymptotics.
IMA J. Appl. Math. 89(3):463-497
P31. M. Touboul, B. Vial, R.C. Assier, S. Guenneau and R. V. Craster (2024)
High-frequency homogenization for periodic dispersive media
SIAM Multiscale Modeling and Simulation, 22(3), 1136-1168
Finalist UKAN Mathematical Acoustics Prize 2023
P30. A.V. Shanin, R.C. Assier★, A.I. Korolkov, O.I. Makarov (2024)
Double Floquet-Bloch transforms and the far-field asymptotics of Green's functions tailored to periodic structures.
Phys. Rev. B. 110, 024310
P29. E. Medvedeva★, R.C. Assier, A.V. Kisil (2024)
Diffraction by a set of collinear cracks on a square lattice: an iterative Wiener-Hopf method
Wave Motion 129 (103332)
Finalist UKAN Mathematical Acoustics Prize 2023
P28. R.C. Assier★, A.V. Shanin and A. I. Korolkov (2024)
A contribution to the mathematical theory of diffraction. Part II: Recovering the far-field asymptotics of the quarter-plane problem.
Q. J. Mech. Appl. Math., 77(1-2):hbae005
P27. M. Touboul, B. Lombard, R.C. Assier, S. Guenneau and R. V. Craster (2024)
High-order homogenisation of the time-modulated wave equation: non-reciprocity for a single varying parameter.
Proc. Roy. Soc. A 480:20230776
P26. M.A. Nethercote★, A.V. Kisil, R.C. Assier (2023)
Diffraction of acoustic waves by multiple semi-infinite arrays
J. Acoust. Soc. Am. 154(3):1493-1504
P25. V.D. Kunz★ and R.C. Assier (2023)
Diffraction by a Right-Angled No-Contrast Penetrable Wedge: Analytical Continuation of Spectral Functions
Q. J. Mech. Appl. Math., 76(2):211-241,
Finalist IMA Lighthill-Thwaites Prize 2023 & UKAN Mathematical Acoustics Prize 2023
P24. M.A. Nethercote★, A.V. Kisil, I. Thompson and R.C. Assier (2022)
Array scattering resonance in the context of Foldy's approximation
Proc. Roy. Soc. A 478:20220604
P23. R.C. Assier★, A.V. Shanin, A.I. Korolkov (2022)
A contribution to the mathematical theory of diffraction. Part I: A note on double Fourier integrals.
Q. J. Mech. Appl. Math., 76(1):1-47
P22. E. Garcia Neefjes★, D. Nigro, A. L. Gower, R.C. Assier, V.J. Pinfield, W.J. Parnell (2022)
A unified framework for linear thermo-visco-elastic wave propagation including the effects of stress-relaxation
Proc. R. Soc. A 478:20220193
P21. R.C. Davey★, R.C. Assier, I.D. Abrahams (2022)
An efficient semi-analytical scheme for determining the reflection of Lamb waves in a semi-infinite elastic waveguide
Applied Sciences, 12(13), 6468
P20. V.D. Kunz★ and R.C. Assier (2022)
Diffraction by a right-angled no-contrast penetrable wedge revisited: a double Wiener-Hopf approach
SIAM journal on Applied Mathematics 82(4), 1495-1519
P19. M.A. Nethercote★, A.V. Kisil and R.C. Assier (2022)
Diffraction of acoustic waves by a wedge of point scatterers
SIAM journal on Applied Mathematics 82(3), 872-898
P18. E.R. Russell★, R.C. Assier and W.J. Parnell (2022)
Manipulating thermal fields with inhomogeneous heat spreaders
Applied Mathematical Modelling, 106:225-240
P17. R.C. Assier★ and A.V. Shanin (2021)
Vertex Green’s functions of a quarter-plane. Links between the functional equation, additive crossing and Lamé functions.
Q.J. Mech. Appl. Math., 74(3):251-295
P16. C. Bellis, B. Lombard, M. Touboul, R.C. Assier (2021)
Effective dynamics for low-amplitude transient elastic waves in a 1D periodic array of non-linear interfaces
Journal of the Mechanics and Physics of Solids 149:104321
P15. R.C. Assier★ and I.D. Abrahams (2021)
A surprising observation in the quarter-plane diffraction problem
SIAM J. Appl. Math. 81(1), 60-90
P14. R.C. Assier★ and A.V. Shanin (2021)
Analytical continuation of two-dimensional wave fields
Proc. Roy. Soc. A, 477:2020081
P13. R.C. Assier★, M. Touboul, B. Lombard, C. Bellis (2020)
High-frequency homogenisation in periodic media with imperfect interfaces
Proc. Roy. Soc. A, 476:20200402
P12. R.C. Assier★ and I.D. Abrahams (2020)
On the asymptotic properties of an interesting diffraction integral
Proc. Roy. Soc. A, 476:20200150
P11. M. Nethercote★, R.C. Assier and I.D. Abrahams (2020)
High-contrast approximation for penetrable wedge diffraction
IMA J. Appl. Math. 85(3):421-466
Finalist IMA Lighthill-Thwaites Prize 2019
P10. M. Nethercote★, R.C. Assier and I.D. Abrahams (2020)
Analytical methods for perfect wedge diffraction: a review
Wave Motion, 93(102479)
P9. G. Lynott, V. Andrew, I.D. Abrahams, M.J. Simon, W.J. Parnell, R.C. Assier (2019)
Acoustic scattering from a one-dimensional array; tail-end asymptotics for efficient evaluation of the quasi-periodic Green's function
Wave Motion, 89:232-244
P8. N. Gorbushin, V-H. Nguyen, W.J. Parnell, R.C. Assier, S. Naili (2019)
Transient thermal boundary value problems in the half-space with mixed convective boundary conditions
J. Eng. Math. 114 (1): 141-158
P7. R.C. Assier★ and A.V. Shanin (2018)
Diffraction by a quarter-plane. Analytical continuation of spectral functions
Q. Jl. Mech. Appl. Math. 72 (1):51-86
P6. D. Joyce, W.J. Parnell, R.C. Assier and I.D. Abrahams (2017)
An integral equation method for the homogenization of unidirectional fibre-reinforced media;
antiplane elasticity and other potential problems
Proc. Roy. Soc. A 473:20170080
Finalist IMA Lighthill-Thwaites Prize 2017
P5. R.C. Assier★, C. Poon and N. Peake (2016)
Spectral study of the Laplace-Beltrami operator arising in the problem of acoustic wave scattering by a quarter-plane
Q. J. Mech. Appl. Math. 69 (3):281-317
P4. W.J. Parnell, V.-H Nguyen, R.C. Assier, S. Naili and I.D. Abrahams (2016)
Transient thermal mixed boundary value problems in the half-space
SIAM J. Appl. Math. 76(3):845-866
P3. R.C. Assier★ and X. Wu (2014)
Linear and weakly nonlinear instability of a curved premixed flame under the influence of its spontaneous acoustic field
J. Fluid Mech. 758, pp 180-220
P2. R.C. Assier★ and N. Peake (2012)
Precise description of the different far fields encountered in the problem of diffraction of acoustic waves by a quarter-plane.
IMA J. Appl. Math., 77(5):605-625
P1. R.C. Assier★ and N. Peake (2012)
On the diffraction of acoustic waves by a quarter-plane.
Wave Motion, 49(1):64-82
Winner IMA Lighthill-Thwaites Prize 2011 & UKAN Mathematical Acoustics Prize 2023
General Audience Publications
Submitted Research Articles / Preprints
G1. R.C. Assier★ and I.D. Abrahams (2024).
Sir James Lighthill Centenary Meeting
Mathematics Today, Volume 60 Number 6
Sir James Lighthill Centenary Meeting
Mathematics Today, Volume 60 Number 6
Submitted Research Articles / Preprints
S3. E. Medvedeva★, R.C. Assier, A.V. Kisil (2026)
Wave scattering by a transversal defect in a discrete waveguide
Submitted to the IMA Journal of Applied Mathematics
Preprint on arXiv:2602.10227
S2. C. Charlton, R.C. Assier, P.A. Cotterill, W.J. Parnell (2026)
The elastodynamic giant monopole resonance of spherical void metaclusters
Submitted to Proc Roy Soc A
S1. A.V. Shanin, A.I. Korolkov, R.C. Assier (2025)
Matrix representation of Picard–Lefschetz–Pham theory near the real plane in ℂ².
Submitted to Memoirs of the AMS
Preprint on arXiv: 2412.02481
Wave scattering by a transversal defect in a discrete waveguide
Submitted to the IMA Journal of Applied Mathematics
Preprint on arXiv:2602.10227
S2. C. Charlton, R.C. Assier, P.A. Cotterill, W.J. Parnell (2026)
The elastodynamic giant monopole resonance of spherical void metaclusters
Submitted to Proc Roy Soc A
S1. A.V. Shanin, A.I. Korolkov, R.C. Assier (2025)
Matrix representation of Picard–Lefschetz–Pham theory near the real plane in ℂ².
Submitted to Memoirs of the AMS
Preprint on arXiv: 2412.02481