The interaction between heat and elasticity

The problem When subject to an increase in temperature, a solid object will usually expand, and this expansion will act to increase internal stresses. In this way, variations in temperature affect solids’ mechanical properties. On the other hand, inside a solid body, heat transfer occurs mostly by diffusion from hot to colder zones. This depen... Read more 16 Aug 2024 - 12 minute read

Reinventing the wheel: simulating collisions

Our task I am not a game designer; I have never used any engines such as Unity, nor have I done any 3D modeling before. Buuuuut…. I really like simulating physical systems. In my opinion, most Physics undergraduate curricula lack one thing in common: more emphasis on numerical simulations, be it solving the relevant differential equations (e.g... Read more 16 May 2024 - 15 minute read

Attention: a tale of three spaces

Motivation I admit I always had some trouble understanding Attention in the context of Transformers. There are several good references for this - Jay Alammar’s The Illustrated Transformer is a common example. Still, I always had some difficulties building a mental model of what the attention mechanism does. Some references explain very thoroug... Read more 18 Dec 2023 - 16 minute read

13.8 billion years on a 10.1'' screen

Context Some moments in one’s life can be awe-inspiring. You know, those moments when you feel deeply connected to something; when things make sense. Some people would label this feeling as spiritual; not being a very spiritual person myself (at least according to the common definition), I don’t really know how appropriate this attribution is,... Read more 04 Aug 2023 - 9 minute read

Lie derivatives and cluttered notation

The situation I’ve always had a love-hate relationship with notation in mathematics. On the one hand, I am an intuitive person who needs to understand the big picture of something before jumping into the details. In this sense, I prefer my math to be uncluttered and focusing on the key steps of a derivation. On the other hand, I also need my... Read more 25 Jun 2023 - 11 minute read