Did someone say there's some rotini in the state of Denmark? What are we waiting for, let's eat!
The first day lecture of the semester went well. It looks like the first two weeks of the fluid mechanics course will be an introduction to the engineering flavor of tensor calculus. Ask a mathematician what a tensor is, and he'll start telling you about forms and multilinear algebra. Ask an engineer what a tensor is, and he'll hand you a symbol decorated with a pile of eyesight-ruining subscripts and superscripts. You need the superscripts and subscripts in order to actually perform computations, and sometimes they are even handy for doing some symbolic calculations. But I much prefer coordinate-free notation, if only for the way it preserves my eyesight for another day. Naetheless, this is something I can do.
I spent part of the evening looking closely at the thermoelasticity equations I copied from Sanjay on Friday. I'm not sure whether he made a minor error, or I copied something incorrectly, or I just am suffering a misunderstanding. Anyhow, right now I have two formulas for the stress power term in the thermal energy balance equations, and those two formulas cannot be consistent with each other. One or the other is wrong; now I just need to figure out if the error is in my calculation or if it's in the formula from the notes. Ah, the joy of continuum mechanics.
I've learned a few things in graduate school, but I think one of the deeper lessons was how important physics is. I so easily miscopy terms in equations and flip signs in my codes; without a picture of the physics of the problem, those errors are difficult (sometimes nigh unto impossible) to find and fix. Of course, I also know people who have an excellent intuition for the physics of their area, but who will bend over backward to avoid the mathematical descriptions that make those physics precise. If physical problems are stories, then the physics is the plot line and the mathematics is the language. It's possible to skimp one or the other -- people still make silent films, and there exist rambling stories full of fine language and no particular plot. I suppose it's possible to skimp both plot and language, actually, as evinced by some summer blockbusters driven by explosions and sex appeal and precious little else. But it's very satisfying to read a story with both plot and well thought-out sentences, and I find it very satisfying to attack mathematical problems that come from physics I understand.
Currently drinking: Peppermint tea