Charged Knots

  "Ideal Knots," and "Knot Energies:" Can the knot type be determined from the `ideal' shape of the curve that minimizes a particular (two-body) potential? (ram video)

Jonathan Simon in Ideal Knots (1998):

  Consider a Charged Trefoil



  Prime charged knots ... are tight

  Composite charged knots ... are factored

  Model & Simulations:

Screened interactions

  In most physically relevant situations, Coulomb interactions are highly screened;

   The (dimensionless) screened Coulomb interaction depends on two lengths:

   Do tight knots disappear for finite screening lengths?


   Electrostatic (Odijk-Skolnick-Fixman) persistence length: