Ray Fu

🌙

Hello, I'm Rueih-Sheng Fu (傅瑞生), though I mainly go by Ray Fu nowadays. I am a third-year Ph.D. candidate in physical chemistry at Northwestern, working with Prof. Todd Gingrich on non-equilibrium statistical mechanics. As an undergraduate, I majored in chemical engineering at UC Berkeley and worked on the computational simulation and screening of macromolecular frameworks. I like strategic board games and staying at home. I'm looking forward to Tristan Needham's Visual Differential Geometry and Forms (in June!), after his excellent Visual Complex Analysis.

Here is a review of various textbooks I've read.

Here is a translation of Jorge Luis Borges' El libro de arena.

I've also written notes on various topics,

in mathematics,

sketching out why martingales are useful, and providing some examples thereof.
introducing the generalized mean and proving its monotonicity.
summarizing the integration techniques of multivariable calculus.
introducing the Laplace transformation, along with identities and transforms of common functions.
giving an overview of complex analysis and its applications, and a brief guide on obtaining residues.
providing a small grab bag of useful mathematical tricks.
demonstrating how constructing fair games can be used to solve problems involving stochastic processes.

and in chemistry and physics,

describing error analysis and propagation for experimental measurements.
introducing and elaborating on thermodynamic potentials.
generalizing the various thermodynamic processes with the polytropic process.
on converting between Cartesian and fractional coordinates in unit cells.
explaining why magnetically equivalent protons don't couple in NMR.
providing a short geometric proof regarding the maximal efficiency of the Carnot cycle.
introducing the concepts of activity and fugacity.
discussing diffusion into a falling film.
giving a brief exposition on statistical mechanics and thermodynamics. (The former attempt here is discarded.)
providing a guided tutorial through the statistical mechanics of hydrogen.

Some time ago I made an animation [21 MB, may take a while to load] illustrating Larmor precession with a time-dependent magnetic-field perturbation. This trajectory is a loxodrome, a curve which has the same angle with each meridian on the surface of the sphere. The color of the loxodrome at a point represents the speed at that point: darker colors represent slower speeds, and lighter colors faster speeds.

Here is an interesting question:

Let two independent \(\zeta\)-systems, with energies \(\epsilon_n = \ln n\), \(n \geq 1\), exist in contact with a heat bath with inverse temperature \(\beta > 1\). Let a third system have system state \(\text{gcf}(n_1,n_2)\), where \(n_i\) is the energy state of the \(i^\text{th}\) system, and \(\text{gcf}\) stands for greatest common factor. Find the energy distribution \(\{\epsilon_n'\}\) of an independent fourth system that will reproduce the statistics of the third system when the fourth system is in contact with a heat bath at the same inverse temperature \(\beta\). Can you explain the name "\(\zeta\)-system"?

Previous interesting questions.