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, and for which I wrote most of the article.
Peer-Reviewed Journal Articles
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
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
S2. A.V. Shanin, A.I. Korolkov, R.C. Assier (2024)
Matrix representation of the results of Picard–Lefschetz–Pham theory near the real plane in ℂ².
Preprint on arXiv: 2412.02481
S1. M. Nethercote★, A. Kisil and R.C. Assier (2024)
Acoustic wave diffraction by a quadrant of sound-soft scatterers
Preprint on arXiv: 2410.23647
Finalist UKAN Mathematical Acoustics Prize 2024
Matrix representation of the results of Picard–Lefschetz–Pham theory near the real plane in ℂ².
Preprint on arXiv: 2412.02481
S1. M. Nethercote★, A. Kisil and R.C. Assier (2024)
Acoustic wave diffraction by a quadrant of sound-soft scatterers
Preprint on arXiv: 2410.23647
Finalist UKAN Mathematical Acoustics Prize 2024