Numerical Analysis Seminars: Applications of contact geometry and topology
1 March 2013 14:00 in CM105
Ensuring that tubular structures do not overlap is a vital consideration for realistic modelling in both biophysics and astrophysics. I will discuss two aspects of my research in which these considerations feature strongly. The first is a model for helically wound elastic rope structures, a model for coiled-coil molecules. The key aspect of this model is the non-linear behaviour induced by the diverging mutual pressure exerted when the structure tightens (a result of its helical geometry), which can explain the higher than expected values of the ratio of torsional to bending rigidity of DNA molecules.
I will also discuss a topological framework for quantifying the entanglement of flows which do not close upon themselves, i.e. they are braided rather than knotted. Again I have a particular interest in rope structures and I will introduce an open extension of the Calugareanu theorem a tool commonly used as a topological constraint in polymer physics for closed DNA rings. Finally, I will briefly discuss potential applications for this framework in biophysics and solar physics.
Contact David.Bourne@durham.ac.uk for more information