Geometric AlgebraWhen: Wednesday, March 20, 2013 at 12:00 pm
Where: EG 306
Speaker: Patrick Wong
Organization: President SPS, Northeastern University
Geometric algebra is presented as a streamlined formalism of mathematical physics. One of the most significant qualities of geometric algebra is that it is independent of coordinate frames. Geometric algebra contains a range of usually distinct mathematical formalisms, such as vector algebra, complex variables, and differential geometry. Fluid mechanics is presented as a case study highlighting the power of geometric algebra. The mathematics of fluid flow are reanalyzed using the new formalism of geometric algebra. An overview of geometric algebra is presented followed by presentations of Navier-Stokes equations and fluid vorticity equations in this new formalism. Differences between traditional vector algebra formulations and geometric algebra are discussed. In particular, defining vorticity as a bivector in geometric algebra produces a different version of the vorticity equation. Additionally, the Lie derivative from differential geometry is implemented to propose a single compactified equation containing all the equations of fluid mechanics.