On bifurcations in framed curves and chains.
(English)Manuscript (preprint) (Other academic)
A closed framed curve can be characterized by the value of its self-linking number. However, in general the self-linking number is not uniquely determined. In particular, it depends on the way how the curve has been framed. Moreover, the self-linking number can also change, when a bifurcation called perestroika takes place. Here we devise a simple Hamiltonian energy function to study perestroikas during the time evolution of a closed, piecewise linear polygonal chain. We analyze several examples to follow the progress of the discrete Frenet framing during the time evolution of the chain, and we observe how self-linking number changing perestroikas occur whenever there is an inflection point along the chain.
Research subject Physics
IdentifiersURN: urn:nbn:se:uu:diva-199983OAI: oai:DiVA.org:uu-199983DiVA: diva2:621890