Peer-reviewed publications
- 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.
Accepted in Proc Roy Soc A, Preprint on Hal:hal-04247270
- 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 - 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 - 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 - 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
- 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 - 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 - 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
Preprint on ArXiv: 2112.03173 - 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
Preprint on ArXiv: 2108.12632 - E.R. Russell, R.C. Assier and W.J. Parnell (2022)
Manipulating thermal fields with inhomogeneous heat spreaders
Applied Mathematical Modelling, 106:225-240
Preprint on ArXiv: 2108.04881
- 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
- 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
- R.C. Assier and I.D. Abrahams (2021) (open access)
A surprising observation in the quarter-plane diffraction problem
SIAM J. Appl. Math. 81(1), 60-90 - R.C. Assier and A.V. Shanin (2021) (open access)
Analytical continuation of two-dimensional wave fields
Proc. Roy. Soc. A, 477:2020081 - R.C. Assier, M. Touboul, B. Lombard, C. Bellis (2020) (open access)
High-frequency homogenisation in periodic media with imperfect interfaces
Proc. Roy. Soc. A, 476:20200402 (Hal: 02615237) - R.C. Assier and I.D. Abrahams (2020)
On the asymptotic properties of an interesting diffraction integral
Proc. Roy. Soc. A, 476:20200150 (ArXiv: 2003.00237) - M. Nethercote, R.C. Assier and I.D. Abrahams (2020) (open access)
High-contrast approximation for penetrable wedge diffraction
IMA J. Appl. Math. 85(3):421-466 (Video) - M. Nethercote, R.C. Assier and I.D. Abrahams (2020)
Analytical methods for perfect wedge diffraction: a review
Wave Motion, 93(102479)
- G. Lynott, V. Andrew, I.D. Abrahams, M.J. Simon, W.J. Parnell, R.C. Assier (2019) (open access)
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 - 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 - 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 (Video) - D. Joyce, W.J. Parnell, R.C. Assier and I.D. Abrahams (2017) (open access)
An integral equation method for the homogenization of unidirectional fibre-reinforced media; antiplane elasticity and other potential problems
Proc. Roy. Soc. A 473:20170080
- R.C. Assier, C. Poon and N. Peake (2016) (open access)
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 - Parnell, W.J., Nguyen, V.-H, Assier, R.C., Naili, S. and Abrahams, I.D. (2016) (open access)
Transient thermal mixed boundary value problems in the half-space
SIAM J. Appl. Math. 76(3):845-866 - R.C. Assier and X. Wu, (2014) (open access)
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 (Video) - 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 - R.C. Assier and N. Peake. (2012)
On the diffraction of acoustic waves by a quarter-plane.
Wave Motion, 49(1):64-82
Submitted
- E. García Neefjes, D. Nigro, R. C. Assier, W. J. Parnell
Stress relaxation and thermo-visco-elastic effects in fluid-filled slits and fluid-loaded plates
Submitted to the Journal of Fluids and Structures. Preprint on ArXiv:2403.11089
- 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
Submitted to Wave Motion. Preprint on ArXiv:2402.15799
- A.V. Shanin, R.C. Assier, A.I. Korolkov, O.I. Makarov (2024)
A note on double Floquet-Bloch transforms and the far-field asymptotics of Green's functions tailored to periodic structures.
Submitted to Phys. Rev. B. Preprint on ArXiv:2402.08076. (Video)
- V.D. Kunz and R.C. Assier (2023)
Diffraction by a right-angled no-contrast penetrable wedge: recovery
of far-field asymptotics.
Submitted to IMA J. Appl. Math. Preprint on ArXiv:2310.19892
- R.C. Assier, A.V. Shanin and A. I. Korolkov (2023)
A contribution to the mathematical theory of diffraction.
Part II: Recovering the far-field asymptotics of the quarter-plane problem.
Submitted to Q. J. Mech. Appl. Math. Preprint on ArXiv:2310.18031 - M. Touboul, B. Vial, R.C. Assier, S. Guenneau and R. V. Craster (2023)
High-frequency homogenization for periodic dispersive media
Submitted to SIAM Multiscale Modeling and Simulation, Preprint on ArXiv:2308.08559
Conference Proceedings
- M. Touboul, R.C. Assier, B. Lombard, C. Bellis, P. Cotterill, D. Nigro, W.J. Parnell. High-frequency homogenisation in periodic media with imperfect interfaces and elastodynamic co-dipole metaclusters. Proceedings of Waves 2022, Paris, France, May 2022.
- C. Bellis, B. Lombard, M. Touboul, R.C. Assier. Effective dynamics for low-amplitude transient elastic waves in a 1D periodic array of non-linear interfaces. Proceedings of Waves 2022, Paris, France, May 2022.
- T. White, R.C. Assier, W.J. Parnell. Sound propagation in Slowly-Varying Lined Ducts. Proceedings of Waves 2022, Paris, France, May 2022.
- M. Moschou, R. C. Assier. A step towards the embedding formula for the 'varying' Robin half-plane diffraction. Proceedings of Waves 2019, Vienna, Austria, May 2019
- M. Nethercote, R.C. Assier and I.D. Abrahams. Electromagnetic wave diffraction of perfect electric conducting wedges with arbitrary linear polarization. Proceedings of Waves 2017, Minneapolis, USA, May 2017
- R. Davey, R.C. Assier, I.D. Abrahams and R. Hewitt. An efficient semi-analytical scheme for determining the reflection of Lamb waves in a semi-infinite waveguide. Proceedings of Waves 2017, Minneapolis, USA, May 2017
- R. C. Assier and Xuesong Wu. A combustion instability model accounting for dynamic flame-flow-acoustic interactions. In 7th AIAA Theoretical Fluid Dynamic Conference, AIAA 2014-3342:1-15, 2014.
- R. C. Assier and X. Wu. Flame instability under the influence of its spontaneous sound. 19th AIAA/CEAS Aeroacoustics Conference, 2013-2005:1-8, 2013.
- C. M. Luzzato, R. C. Assier, A. S. Morgans, and X. Wu. Modelling thermo-acoustic instabilities of an anchored laminar flame in a simple lean premixed combustor: including hydrodynamic effects. 19th AIAA/CEAS Aeroacoustics Conference, 2013-2003:1-15, 2013.
- R. C. Assier and X. Wu. Influence of vortical disturbances on flame-acoustics interactions. In Proceedings of AIA-DAGA2013, pages 1-4, 2013.
- R. C. Assier and X. Wu. Acoustic coupling in combustion instability. In Proceedings of the 19th International Congress on Sound and Vibration, pages 1-8, 2012.
Unpublished work
- My PhD thesis will be available as soon as possible.
- Here is my Part III essay on orthogonal polynomials and their links with fractal sets