Programming

• I recently discovered Sage, an open source mathematics package written in Python. Sage aims to be a free replacement for the big commercial mathematical software package and, with 200+ developers around the world, is well on its way to do so. My own contributions so far are concerned with doing tensor calculus and symbolic differential geometry in Sage:
  • Trac #10132: Helping out with this patch for the extrinsic geometry of surfaces in Sage. Work in progress.
  • Trac #9650: patch for adding support for differential forms in Sage. Included in Sage 4.6.
  • Tensor calculus: more resources for doing tensor calculus with various software packages.
• I designed a number of Sage worksheets for a class on fluid dynamics. Currently, only one is polished enough to be published on the web:
  • Rigid bodies in potential flow with circulation.
  • Here's a worksheet on Hopf bifurcations with noise.

• During the summer of 2009, I mentored an FSRI student, Raymond Jimenez, who made some outstanding visualizations of Lagrangian Coherent Structures in 2D fluid flows. As LCS computations are eminently parallelizable, Raymond's code used the nVidia CUDA interface to speed up these computations by several orders of magnitude.

  Raymond's web page has the latest version of the software as well as images and movies, but here is a particularly nice example of a pair of vortices in a time-varying straining flow.