Notes & Expository Writing
Here are some expository notes on certain pieces of fluid dynamics/applied mathematics, that I wrote up when self-teaching myself certain concepts.
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Viscoelastic Instabilities
These are the slides from a talk I gave at the Part III seminar series in Michaelmas term 2025. The talk explores various elastic instabilities in Non-Newtonian fluids, that occur at low Reynolds numbers. We focus on providing heuristic explanations for the physics behind the mechanisms underpinning these instabilities.
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Derivation of Darcy's Law using Homogenisation
A systematic derivation of Darcy's law for porous media flow using the method of multiple scales and asymptotic homogenisation.
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A Proof of the Partial Converse to the Cauchy -
Riemann Equations
A set of notes, I wrote up as a second-year undergraduate, because I was never satisfied with the level of detail in any of proofs of this theorem in the recommended reading.