Renzo L. Ricca

2005-2008 Physical Applications of Knot Theory

1. Introduction to space curves and knot theory
   • Fundamentals of space curves
   • Global geometric aspects of space curves
   • Knots, links and projections
   • Gauss linking number
   • Calugareanu-White invariant
   • Measures of structural complexity
   • Articles included:
   • By Ricca, R.L. (2005) on Knot Theory. Structural complexity.
   • By Hoste, J., Thistlethwaite M. & Weeks, J. (1998) on The first 1,701,936 knots
2. Topological equivalence classes and change of topology
   • Topological equivalence classes for frozen fields
   • Change of topology
   • Measuring structural complexity: a test case
   • Articles included:
   • By Ricca, R.L. & Berger, M.A. (1996) on Topological ideas and fluid mechanics
   • By Ricca, R.L. (1998) on Applications of knot theory in fluid mechanics
3. Vortex dynamics, knots and links
   • Elements of vortex dynamics
   • Vortex knots and links
   • Conservation laws and topology
   • Articles included:
   • By Moffatt, H.K. (1969) on The degree of knottedness of tangled vortex lines
   • By Arnold, V.I. (1974) The asymptotic Hopf invariant and its application
4. Ideal magnetohydrodynamics of knotted and braided flux-tubes
   • Ideal magnetohydrodynamics and analogous Euler's flows
   • Lorentz force and inflexional disequilibrium of flux-tubes
   • Magnetic relaxation under topological constraints
   • Articles included:
   • By Moffatt, H.K. & Ricca, R.L. (1992) on Helicity and the Calugareanu invariant
   • By Freedman, M.H. (1988) A note on topology and magnetic energy in incompressible perfectly conducting fluids
5. Magneto-elastic relaxation of braids and strings
   • Topological bounds on magnetic braids.
   • Elastic relaxation and supercoiled strings.
   • Elastic energy and knot type.
   • Articles included:
     • By Berger (1993) on Energy-crossing number relations for braided magnetic fields
     • By Katritch et al. (1996) on Geometry and physics of knots
     • By Sumners (1995) on Lifting the curtain: using topology to probe the hidden action of enzymes