Topology Seminar: Eleni Panagiotou (UCSB), 'The linking number in systems of curves with Periodic Boundary Conditions'

Event Date: 

Tuesday, October 8, 2013 -
3:30pm to 4:30pm

Event Location: 

  • 4607B South Hall

Event Contact: 

Daryl Cooper

Email: cooper@math.ucsb.edu

Periodic Boundary Conditions (PBC) are often used for the simulation of complex physical systems of open and closed curve models of polymers or vortex lines in a fluid flow. Using the Gauss linking number, we define the periodic linking number as a measure of entanglement for two oriented curves in a system employing PBC. In the case of closed curves in PBC, the periodic linking number is a topological invariant that depends on a finite number of components in the periodic system. For open curves, the periodic linking number depends upon the entire infinite system and we prove that it converges to a real number that varies continuously with the configuration. Finally, we define two cut-offs of the periodic linking number and we compare these measures when applied to a PBC model of polyethylene melts.