Character Building

I suppose, now that I've created this silly blog, I ought to post in it once in a while. So far it's been rather like when I joined a gym--go once, have a light workout, and never darken their door again.

One thing I never fully appreciated about Caltech, which is probably true of any major university or research institution, is its library. At work we have a decent library, but it's pretty small, and its collection is rather limited. We have access to other materials through inter-library loan, which is nice, but that's sort of slow, and it would be better to be able to look things up faster when I'm trying to track something down.

For instance, a couple days ago I began trying to understand the differential equation governing the growth of aerosols as they undergo evaporation and condensation. The equation is stated in numerous places, but I wanted to see it derived. I followed a paper trail, as one publication cited another, which in turn cited another, and so on. Each time I thought this paper would offer a solution, but they kept citing an earlier paper until I felt like Charlie Brown trying to kick the football. Finally I got to one paper written by a single author who continually refers to himself as "we." He goes through most of the steps involved, until declaring "The last equation can be solved by the method of characteristics," as shown in (a paper not available at my work library).

Ah, the dreaded method of characteristics. Professor Flagan referred to the method of characteristics during aerosols class my first quarter at Caltech. I had no idea what he meant, and didn't look it up at the time. I had heard of discontinuities in initial conditions being propogated along characteristics, in the context of the wave equation, but this seemed entirely different. The next quarter, during a course on partial differential equations (PDEs), we spent some time learning about "the method of characteristics," but I don't see how the way it is being used in this paper bears any relation to what we studied in class. I have three books on differential equations and boundary value problems, and none of them speak of this method. There is a Wikipedia article on it, but alas, it is little more than a stub.

So, I have ordered this paper, from the Journal of Colloid Interface Sciences, and I have resolved to learn what is this method of characteristics. And if instead of presenting the solution the authors cite another journal article not available at work I may break down with a primal scream in the library.