Role of topology in study of cascade evolutions of physical knot/link complex systems
Xin Liu (Institute of Theoretical Physics, Faculty of Science, Beijing University of Technology - China)
Abstract: Recent laboratory and numerical experiments in classical and quantum fluids and in recombinant DNA plasmids show that physical knots/links are highly unstable, decaying from a high-topological complexity state to a low-complexity state through a series of reconnection events. A possible theoretical picture for this phenomenon is that hierarchy of topological complexity is closely related to spectrum of energy or other dynamical properties. For this study the following progress would be reviewed: (i) ropelengths/crossing numbers of prime knots and links versus the groundstate energy spectrum; (ii) adapted HOMFLYPT polynomial values used to quantify complexity of torus knots and links; (iii) complexity degree of a knot defined in a Legendre polynomial basis in a suitably defined knot polynomial space. Some relevant undergoing numerical simulation work is introduced as well. Our emphasis will be placed on the role that topologically non-conservative transitions play in the evolution of a knot complex system, in the hope of finding a scalar topological invariant to manage energy or other spectrums.
geometric topology
Audience: researchers in the topic
Series comments: Web-seminar series on Applications of Geometry and Topology
| Organizers: | Alicia Dickenstein, José-Carlos Gómez-Larrañaga, Kathryn Hess, Neza Mramor-Kosta, Renzo Ricca*, De Witt L. Sumners |
| *contact for this listing |