Happenings – 2011 Jun 11

I feel like I’ve been stirring pots, instead of actually cooking. I’m messing around with a lot of things, but finishing none.

Mostly, I’ve continued playing with color. Mathematica®’s PieChart command is extremely convenient for displaying a palette of colors. Even better, it’s extremely convenient for displaying the two color wheels (the artist’s color wheel with green opposite red, and the other color wheel with cyan opposite red). At least it took a little mathematics to get a translation from one to the other.

Best of all, I can feed it a palette of colors and have it display them on a color wheel. (Yes, I had to write that myself.) I expect to discuss all this in more detail, but let me at least show it to you.

Here’s a palette out of Cabarga’s “Global Color Combinations”, p.25 (bibliography):

Here are those colors mapped to the artist’s color wheel (hue angle only, taking no account of tint-tone-shade):

The point of the second screenshot is that I clearly see that I have two sets of what are called analogous colors, and one complementary color.

I’ve made a little progress in the mechanics of solids… I’m finishing up looking at the maximum values of shear stress and normal stress. The maximum and minimum values of normal stress are eigenvalues and occur in the directions specified by eigenvectors. This is a very common result. What I’ve seen no analog of, elsewhere, is that the maximum values of shear stress occur halfway between the maximum values of normal stress. (A derivation of that is what I have to finish.) And maybe I’ll come across a similar result now that I’m sensitized to it.

As for the approximate stresses in thin shells, my grown up has taken that over from my alter ego the grad student. It’s time for the student to move on in the textbook. My grown up is waiting for a book to arrive. As I said before, I cannot reconcile the solutions in Landau and Lifshitz’ “Theory of Elasticity” with the customary engineering solutions. I did discover a useful book sitting on my shelves already: “Roark’s Formulas for Stress and Strain”. I remember thinking, when a friend gave it to me, that here was one book I would never need. Hah! Anyway, this book provides me with lots of answers – no derivations, just answers… but that’s a start. What I’m waiting for should have some derivations.

I’ve made good progress in dimensional analysis. I still want to work some more problems… but I have worked out the key example: Sir G. I. Taylor’s use of dimensional analysis to estimate the energy of the first atomic bomb blast. (I think he’s the guy who explained the Great Red Spot on Jupiter.)

I’ve made almost no progress in reaction rates. I’ve got four books, and they seem to have three different methods of solution. I’m sure I can reconcile them, but I need to work out more problems.

I’ve made a little progress understanding multicollinearity in the standardized and in the centered Hald data – if two columns of the matrix product X.v go to zero simultaneously, you’re looking at a two-dimensional subspace. Duh – I can’t believe that wasn’t blindingly obvious when I saw it happen.

Finally, my earthquake prediction is still on track: there has been at least one earthquake of at least magnitude 5 somewhere on earth every day in June, including today.

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