What is the microscopic formula for temperature?
These notes present a simple derivation of a very general microscopic expression for the temperature of a system of particles. Particular attention is given to the oft-neglected configurational temperature, which allows one to calculate the temperature with zero knowledge of particle velocity. These notes end with some opinionated commentary on microscopic definitions of temperature.

Notes on Small-Gradient Membrane Dynamics at Low Reynolds Number
These notes derive the equations of motion for a nearly-flat membrane by first calculating the hydrodynamic interaction between point particles. This is then used to derive an algorithm for simulating a thermally fluctuating membrane by propagating the stochastic dynamics in Fourier space, as presented by Lin and Brown (2004). Emphasis is placed on showing the intermediate steps leading to each result and trying not to leave unspoken assumptions. Please contact me if you notice any mistakes!