## Peer-reviewed publications

- 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**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

- G. Lynott, V. Andrew, I.D. Abrahams, M.J. Simon, W.J. Parnell,
**R.C. Assier**(2018)*Acoustic scattering from a one-dimensional array; tail-end asymptotics for efficient evaluation of the quasi-periodic Green's function*

**Submitted to Wave Motion** - N. Gorbushin, V-H. Nguyen, W.J. Parnell,
**R.C. Assier**, S. Naili (2018)*Transient thermal boundary value-problems in the half-space with mixed convective boundary conditions***Submitted to SIAM J. Appl. Math.** **R.C. Assier**and A.V. Shanin (2018)*Diffraction by a quarter-plane. Analytical continuation of spectral functions***Submitted to Q. Jl. Mech. Appl. Math.**- M. Nethercote,
**R.C. Assier**and I.D. Abrahams (2018)*Analytical methods for perfect wedge diffraction: a review***Submitted to Wave Motion**

## Conference Proceedings

- 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