Happenings – 2012 May 5

According to the USGS, I slept through a magnitude 4.1 earthquake last night. Okay, strictly speaking, all they vouch for is that there was such an earthquake… I’m responsible for the assertion that I slept through it.

The frequency seems to be up recently: there have been 7 earthquakes in the Bay Area since last Saturday, of magnitude at least 2.5. For the record, however, let me show the count is 4 so far in May, through yesterday. I don’t want to count today yet, because it isn’t over.

So much for experimental seismology.

Theoretical seismology, on the other hand, has led me back to continuum mechanics – which includes solids as well as liquids and gases. I finally understand why the combination

\frac{\partial f}{\partial t}+ v\cdot \nabla f

is called “the material derivative” of f – that is, I understand why we say it is computed for a fixed particle. Certainly one can – and I did – do a lot of work treating it as a handy combination to look out for, but I finally understand its interpretation, instead of taking it on faith. I hope to write this up and publish it soon.

I guess I’ve decided that my alter ego Jimmie is the one doing continuum mechanics. He has continued making progress on the next regression post… and I’m beginning to think he’s going to take up control theory seriously.

This is a good thing. Before I can look at the control of aircraft, I need to show you the long–promised “magic omega formula”. Actually, of course, what I need to do is explain it and derive it. For a time-dependent rotation, it relates the instantaneous axis of rotation to an Euler angle decomposition and the rates of change of the Euler angles.

In the meantime, my alter ego the kid picked up a book on color last weekend, Kang’s “computational color technology”… and Jimmie is now working slowly through it. The good news is that my monitor profile has not changed since the last time I talked about it. (That means that my functions are still correct for converting from tristimulus XYZ to my monitor RGB. I revised them here.)

The kid also picked up Barnes’ “mathematical modelling with case studies”… which is just elementary differential equations and an introduction to dynamical systems. What shocked me is that I hadn’t picked up the associated Mathematica® notebook in 7 years! I knew it had been a while, but I really thought it had only been 2 years at most.

Oh, the nanny who cleans up after the kid finally did some work… on a long–planned post about computing the final tableau of a linear programming problem, given the initial tableau and the solution. The point is to be able to follow the textbook which works through tableaux, without having to do the row operations to get the final tableau.

My alter ego the graduate student continues to add material to a first post about rings.

In a nutshell, dividing my work up among several alter egos has made it easier for me to make a little progress on each of several topics.

And with that, I’m off to math.

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