chb@sas

Fall 2008:

Nematic Films and Radially Anisotropic Delaunay Surfaces (older arxiv version) Work with Prof. Randy Kamien. In this paper we discuss shapes of axisymmetric soap bubbles with nematic order -- specifically, we restrict the director field to lie on latitude lines. This leads us to a generalized / perturbed version of Delaunay (axisymmetric constant mean curvature) surfaces. In a sequel we'll talk about coarsening of double nematic bubbles of the sort. Eur. Phys. J. E 28 (2009) 315

Fall 2007:

On ``an apparent truth about matrices'' Upon reading a paper by Waterfall et al., (see also this page for sloppy models in context) I was inspired to try to prove a conjectured asymptotic result on the eigenvalues of matrices perturbed by multiplication by Vandermonde matrices, using the dominant balance techniques I'm familiar with. After I communicated my proof to Jim Sethna and Veit Elser, they informed me that Ari Turner had already shown them a similar result, and we got in communication. At some point, Ari and I will write our two proofs up together more formally. I found later this paper which likely contains more powerful techniques on perturbative matrix eigenvalue problems like this one.
The Wetting Agent Required for Swarming in Salmonella enterica Serovar Typhimurium is not a Surfactant Work with Prof. Howard Berg and Linda Turner at Harvard. As an undergraduate, I worked on finding the best way to make surface tension measurements of bacterial surfactant in the swarming phase. N.b. This paper was actually written in full by Prof. Berg, using my data. Journal of Bacteriology, December 2007, p. 8750-8753, Vol. 189, No. 23.

Spring 2007:

Does every polynomial root have a simple approximation? More to come on this topic when I have time... Interested readers should consult Gelfand, Kapronov and Zelevinsky for more of this story; I wish I had when I wrote this. You should also check out the rest of the HCMR. Harvard College Mathematics Review, volume 1, issue 1, pp 50-56.

Fall 2006:

Possible feeding habits of Cyclotosaurus cf. posthumus. My final paper for OEB 139: Vertebrate Evolution speculating on just what a curious late Triassic amphibian might have eaten, given its skull and some of its teeth.

Summer 2006:

The dotted circle method of drawing 4-manifold 1-handles. Assignment for a Harvard summer math tutorial. They paid me $700 for this and reimbursed my purchase of Milnor's Morse Theory as well as Gompf and Stipsicz!

Summer 2005:

Excitations in a 2D metal-insulator array. A venture into photonic band-gap structures. Thanks to Professor David Stroud and the Ohio State University REU program.