2024
On the elastodynamics of rotating planets
This paper, written with my former PhD advisor David, presents new equations of motion to be used for studying the elastic motions of variably rotating planets. Once implemented in code (for that, keep an eye on Alex Myhill) these equations will allow seismologists to carry out new studies into the density structure of Earth’s mantle.
Cosserat elasticity as the weak-field limit of Einstein-Cartan relativity
As noted below, general relativity is very close to my heart. This project — which I worked on with my friend and one-time sparring partner Jeroen Tromp — united GR with another beloved subject: continuum mechanics. Cosserat elasticity is a richer theory of continuum mechanics that accounts for spin; Einstein-Cartan theory accounts for spin too, giving rise to a richer geometric structure than ‘original’ Einstein GR. We showed that Cosserat elasticity is the weak-field limit of Einstein-Cartan theory, analogously to how classical continuum mechanics is the weak-field limit of Einstein GR.
2023
Waves in the Earth’s core. III. A perturbative approach to quasi-free-decay modes
I wrote this paper with two new colleagues at ETH, Jiawen Luo and my PI Andy Jackson. We sought analytical insight into some recent numerical calculations of ‘quasi-free-decay modes’, these being normal modes of the fluid iron and its associated magnetic field in the Earth’s core. (Andy suggested that I work on this problem in order to learn magnetohydrodynamic techniques quickly… it was a good idea!)
2021
Some more problems of geodynamics
My PhD dissertation. It combines the results of my previous papers with a third chapter that details much of the theory required to analyse the elastodynamics of rotating planets. This new chapter was later rewritten (!) to become ‘On the elastodynamics of rotating planets‘ (above).
2020
On the stress dependence of the elastic tensor
My supervisor and I have derived a new expression for the elastic tensor as a function of equilibrium stress, with a view towards both forward- and inverse-modelling. This work revisits papers of Dahlen, Tromp and others, but approaches the problem from a slightly different perspective.
2019
Written with my supervisor David, this paper forms the basis of our approach to solving numerically the equations of motion of gravitationally-interacting elastic bodies. More to follow on this theme in the coming months; if you want a flavour, then have a look at my poster from EGU 2018. This was one of the two papers to win the 2019 Student Author Award from GJI.
2018
A quiet year as regards the writing of papers — but lots of code was written!
2017
This paper is the result of research I conducted with Professor Clifford Martin Will in the summer of 2016 after I had finished my third year of undergraduate study. General Relativity remains a subject very close to my heart!
Matthew Maitra 