Vortex Dynamics in Any Dimension
| dc.contributor.author | Staley, Phillip Lee | |
| dc.date.accessioned | 2018-04-26T13:14:32Z | |
| dc.date.available | 2018-04-26T13:14:32Z | |
| dc.date.updated | 2018-04-26T13:14:32Z | |
| dc.description.abstract | We adapt the general method of moving frames and time-dependent submanifold geometry to investigate the <i>skew-mean curvature flow</i> of a 2-dimensional surface in R4; this is a natural generalization of the <i>vortex filament equation</i> (VFE) for the motion a vortex membrane in 4-dimensional space. (Haller and Vizman, Khesin, Shashinkanth.) We propose a geometric framework (the <i>Hasimoto bundle</i>) in which the connection between the VFE and the nonlinear Schrödinger equation (through the well-known <i>Hasimoto transformation</i>) becomes transparent, and that easily generalizes to the general codimension-2 case. Such framework reveals that the main obstruction to the existence of a parallel frame and to defining a natural Hasimoto transformation is the non-zero curvature of the normal bundle. | |
| dc.identifier.uri | http://hdl.handle.net/123456789/3554 | |
| dc.language.rfc3066 | en | |
| dc.title | Vortex Dynamics in Any Dimension |