Project Details
Projekt
Ropelength for periodic links (A12)
Subject Area
Mathematics
Term
from 2016 to 2020
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 195170736
The ropelength problem studies the shape of knots and links when tied tight in (idealized) rope. We consider ropelength for links in the three-torus, that is, for triply periodic networks of filaments in space. Such networks arise throughout materials science, for instance in polymers and proteins. We have extended the theory of ropelength criticality to this periodic case and will work to understand the behavior of minimizers as the lattice of periodicity is varied. We have enumerated singly periodic links, and will extend this enumeration to the doubly and triply periodic cases. We will search for further cases where tight shapes can be described exactly, and will investigate more complicated examples numerically.
DFG Programme
CRC/Transregios
Subproject of
TRR 109:
Discretisation in Geometry and Dynamics
Applicant Institution
Technische Universität Berlin
