Contact
Teaching Summary
No current teaching responsibilities. Taught small groups at the University of Warwick. (First year supervisions) Mathematical Analysis at UCL (Faculty of Engineering, Flipped Hybrid learning, in… read more
Research Summary
I am currently working on experimental Dynamical Energy Analysis (xDEA) with Gregor Tanner and Martin Richter as part of a collaboration with the University of Salford, connecting present Dynamical… read more
Selected Publications
KING, MATTHEW J, TREEBY, BE and COX, BT, 2025. Non-uniform time-stepping in k-space pseudospectral time domain models of acoustic propagation Journal of Theoretical and Computational Acoustics.
KING, MATTHEW J, GUTLEB, TIMON S, TREEBY, BE and COX, BT, 2025. Modelling power-law ultrasound absorption using a time-fractional, static memory, Fourier pseudo-spectral method The Journal of the Acoustical Society of America. 157(3), 1761-1771
KING, MATTHEW J, BRAMBLEY, EDWARD J, LIUPEKEVICIUS, RENAN, RADIA, MIREN, LAFOURCADE, PAUL and SHAH, TAUQEER H, 2022. The critical layer in quadratic flow boundary layers over acoustic linings Journal of Fluid Mechanics. 950, A8
KING, MATTHEW J and BRAMBLEY, EDWARD J, 2023. Stabilisation of Hydrodynamic Instabilities by Critical Layers in Acoustic Lining Boundary Layers AIAA Journal. 61(11), 4897-4912
I am a qualified Mental Health First Aider and can be approached at any time to discuss topics on mental health. If I can not be found in person I am happy to arrange a meeting by email. I have access and can direct anyone towards resources, as well as just discuss general concerns and topics. With only case of extreme risk these meetings are confidential and prioritize your well-being and, like all MHFAs, I am trained across a variety of topics. As a member of the LGBTQIA+ community myself (gay cis male) I am particularly familiar with matters involving these communities and difficulties. As a mathematician I have found myself transferring between multiple institutions at a Postdoctoral stage and additionally have first hand experience on the difficulties this can bring.
No current teaching responsibilities. Taught small groups at the University of Warwick. (First year supervisions) Mathematical Analysis at UCL (Faculty of Engineering, Flipped Hybrid learning, in person sessions, first years.)
Current Research
I am currently working on experimental Dynamical Energy Analysis (xDEA) with Gregor Tanner and Martin Richter as part of a collaboration with the University of Salford, connecting present Dynamical Energy Analysis (DEA) to experimental set-ups. In the process we are studying a variety of wave sources and connections between plates. DEA is a numerical technique for high frequency waves under a continuous source, treating the source as a ray density and computing the reflection/transmission of the rays across the domain of interest. My current focus of this research is in the transition between the wave solutions and the ray-densities, which has typically been treated by a quasi-homogeneity assumption within the Wigner transform. It has been found however that this assumption does not hold for a typical source, however can be reproduced under suitable smoothing, similar to that of the Huisimi transform.
Past Research
My previous work, at UCL was in Biomedical Ultrasound. Implementing pseudo-spectral time domain methods in the k-wave-ii software. This included building an understanding of Fractional Calculus, and the k-space correction, expanding upon the previous software by allowing for vary time increments across a simulation but also spatially varying power-law attenuation. My PhD was completed at the University of Warwick with a focus on AeroAcoustics. Modeling acoustic linings in ducts, such as air intakes of jet engines, through Impedance boundary conditions. The governing Pridmore-Brown equation is not Sturm-Liouville type and so can not be described in terms of the typical wave modes, requiring insights into non-modal wave solutions, and construction the appropriate Green's function. Making use of this Wiener-Hopf Scattering was explored as part of the extensions toward interpreting how the found dominant non-modal waves could impact the far-field within a realistic setting.
Future Research
Progressing this we hope to implement the phase-space ray-denisty numerically allowing the comparison between numerical results computed through DEA and experiments with our Collaborators at the University of Salford, with a focus on the ray paths and their comparison to structural intensity.