Contacts
Dept. Mathematics & Applications
University of Milano - Bicocca
Via Cozzi, 55
20125 Milano, ITALY

Building U5, III floor, Room 3065

Email: renzo.ricca@unimib.it
Direct line: (+39) 02 6448 5762
Department: (+39) 02 6448 5755
Fax: (+39) 02 6448 5705

Articles in Primary Journals and Refereed Volumes

  1. Ricca, R.L. (1991) Intrinsic equations for the kinematics of a classical vortex string in higher dimensions. Physical Review A 43, 4281-4288.
  2. Ricca, R.L. (1991) Rediscovery of Da Rios equations. Nature 352, 561-562.
  3. Moffatt, H.K. & Ricca, R.L. (1991) Interpretation of invariants of the Betchov-Da Rios equations and of the Euler equations. In The Global Geometry of Turbulence (ed. J. Jimènez), NATO ASI B 268, pp. 257-264. Plenum Press.
  4. Moffatt, H.K. & Ricca, R.L. (1992) The helicity of a knotted vortex filament. In Topological Aspects of the Dynamics of Fluids and Plasmas (ed. H.K. Moffatt et al.), pp. 225-236. Kluwer.
  5. Ricca, R.L. (1992) Physical interpretation of certain invariants for vortex filament motion under LIA. Physics of Fluids A 4, 938-944.
  6. Moffatt, H.K. & Ricca, R.L. (1992) Helicity and the Calugareanu invariant. Proc. R. Soc. London A 439, 411-429. [Also in: (1995) Knots and Applications (ed. L.H. Kauffman), pp. 251-269. World Scientific.]
  7. Ricca, R.L. (1993) Torus knots and polynomial invariants for a class of soliton equations. Chaos 3, 83-91. [(1995) Erratum. Chaos 5, 346.]
  8. Ricca, R.L. (1994) The effect of torsion on the motion of a helical vortex filament. J. Fluid Mech. 273, 241-259.
  9. Ricca, R.L. (1994) Writhe and twist helicity contributions to an isolated magnetic flux tube and hammock configuration. In Poster Papers Presented at the VII European Meeting on Solar Physics (ed. G. Belvedere et al.), pp. 151-154. Catania Astrophys. Observatory, Catania.
  10. Ricca, R.L. (1995) The energy spectrum of a twisted flexible string under elastic relaxation. J. Phys. A: Math. & Gen. 28, 2335-2352.
  11. Ricca, R.L. (1995) Geometric and topological aspects of vortex filament dynamics under LIA. In Small Scale Structures in Three-Dimensional Hydro- and Magnetohydro-dynamics Turbulence (ed. M. Meneguzzi et al.), pp. 99-104. Lecture Notes in Physics 462. Springer-Verlag.
  12. Ricca, R.L. (1996) The contributions of Da Rios and Levi-Civita to asymptotic potential theory and vortex filament dynamics. Fluid Dyn. Res. 18, 245-268.
  13. Ricca, R.L. & Berger, M.A. (1996) Topological ideas and fluid mechanics. Phys. Today 49 (12), 24-30. [Also in: (1997) Parity 10, 20-28]
  14. Ricca, R.L. (1996) Minimum energy configurations of a twisted flexible string under elastic relaxation.. In ZAMM ICIAM/GAMM 95 (ed. E. Kreuzer & O. Mahrenholtz), pp. 421-422. Applied Sciences (Contributed Papers) 5. Akademie Verlag, Berlin.
  15. Ricca, R.L. (1997) Evolution and inflexional instability of twisted magnetic flux tubes. Solar Physics172, 241-248.
  16. Barenghi, C.F., Ricca, R.L. & Samuels, D.C. (1998) Quantized vortex knots. J. Low Temp. Physics 110, 509-514.
  17. Ricca, R.L. (1998) Applications of knot theory in fluid mechanics. In Knot Theory (ed. V.F.R. Jones et al.), pp. 321-346. Banach Center Publs. 42, Polish Academy of Sciences, Warsaw.
  18. Ricca, R.L. (1998) New developments in topological fluid mechanics: from Kelvin's vortex knots to magnetic knots. In Ideal Knots (ed. A. Stasiak et al.), pp. 255-273. Series on Knots and Everything 19, World Scientific.
  19. Barenghi, C.F., Ricca, R.L. & Samuels, D.C. (1998) Vortex knots. In Advances in Turbulence VII (ed. U. Frisch), pp. 369-372. Kluwer.
  20. Barenghi, C.F., Ricca, R.L. & Samuels, D.C. (1999) Evolution of vortex knots. J. Fluid Mech.391, 29-44.
  21. Ricca, R.L. (2000) Towards a complexity measure theory for vortex tangles. In Knots in Hellas `98 (ed. C. McA. Gordon et al.), pp. 361-379. Series on Knots and Everything 24, World Scientific.
  22. Ricca, R.L. (2000) Knots and braids on the Sun. In Science and Art Symposium 2000 (ed. A. Gyr et al.), pp. 263-268. Kluwer.
  23. Barenghi, C.F., Ricca, R.L. & Samuels, D.C. (2001) How tangled is a tangle? Physica D 157, 197-206.
  24. Ricca, R.L. (2001) Geometric and topological aspects of vortex motion. In An Introduction to the Geometry and Topology of Fluid Flows (ed. R. L. Ricca), pp. 203-228. NATO ASI Series II 47, Kluwer.
  25. Ricca, R.L. (2001) Tropicity and complexity measures for vortex tangles. In Quantized Vortex Dynamics and Superfluid Turbulence (ed. C.F. Barenghi et al.), pp. 366-372. Springer Lecture Notes in Physics 571, Springer-Verlag.
  26. Ricca, R.L. (2002) Energy, helicity and crossing number relations for complex flows. In Tubes, Sheets and Singularities in Fluid Dynamics (ed. K. Bajer & H.K. Moffatt), pp. 139-144. NATO ASI Series, Kluwer.
  27. Barenghi, C.F., Ricca, R.L. & Samuels, D.C. (2002) Complexity measures of tangled vortex filaments. In Tubes, Sheets and Singularities in Fluid Dynamics (ed. K. Bajer & H.K. Moffatt), pp. 69-74. NATO ASI Series, Kluwer.
  28. Ricca, R.L. (2005) Knot theory. In Encyclopedia of Nonlinear Science (ed. A. Scott), pp. 499-501. Routledge, New York and London.
  29. Ricca, R.L. (2005) Structural complexity. In Encyclopedia of Nonlinear Science (ed. A. Scott), pp. 885-887. Routledge, New York and London.
  30. Ricca, R.L. (2005) Inflexional disequilibrium of magnetic flux tubes. Fluid Dyn. Res.36, 319-332.
  31. Maggioni, F. & Ricca, R.L. (2006) Twist and fold modeling of supercoiled filaments. In Aplimat '06 (ed. M. Covàcovà), pp. 123-130, Slovak U. of Tech., Bratislava.
  32. Maggioni, F. & Ricca, R.L. (2006) Writhing and coiling of closed filaments. Proc. R. Soc. London A 462, 3151-3166.
  33. Ricca, R.L. & Maggioni, F. (2007) A new stretch-twist-fold model for fast dynamo. Proc. Appl. Math. Mech. 7, 2100051-2100052.
  34. Maggioni, F. & Ricca, R.L. (2007) DNA supercoiling modeling of nucleosome and viral spooling. Proc. Appl. Math. Mech. 7, 2120011-2120012.
  35. Ricca, R.L. (2008) Topology bounds energy of knots and links. Proc. R. Soc. A 464, 293-300.
  36. Ricca, R.L. & Maggioni, F. (2008) Multiple folding and packing in DNA modeling. Comp. & Math. with Appl. 55, 1044-1053.
  37. Ricca, R.L. (2008) Momenta of a vortex tangle by structural complexity analysis. Physica D 237, 2223-2227.
  38. Ricca, R.L. (2009) Structural complexity and dynamical systems. In Lectures on Topological Fluid Mechanics (ed. R.L. Ricca), pp. 169-188. Springer-CIME Lecture Notes in Mathematics 1973. Springer-Verlag.
  39. Ricca, R.L. (2009) Detecting structural complexity: from visiometrics to genomics and brain research. In Mathknow (ed. M. Emmer & A. Quarteroni), pp. 167-181. Springer-Verlag.
  40. Ricca, R.L. (2009) New developments in topological fluid mechanics. Nuovo Cimento C 32, 185-192.
  41. Maggioni, F., Alamri, S.Z., Barenghi, C.F. & Ricca, R.L. (2009) Kinetic energy of vortex knots and unknots. Nuovo Cimento C 32, 133-142.
  42. Maggioni, F. & Ricca, R.L. (2009) On the groundstate energy of tight knots. Proc. R. Soc. A 465, 2761-2783.
  43. Maggioni, F., Alamri, S.Z., Barenghi, C.F. & Ricca, R.L. (2010) Velocity, energy and helicity of vortex knots and unknots. Phys. Rev. E 82, 26309-26317.
  44. Goldstein, R.E., Moffatt, H.K., Pesci, A.I. & Ricca, R.L. (2010) Soap film Möbius strip changes topology with a twist singularity. Proc. Natnl. Acad. Sci. 107, 21979-21984.
  45. Ricca, R.L. & Nipoti, B. (2011) Derivation and interpretation of the Gauss linking number. In Introductory Lectures on Knot Theory. (ed. L.H. Kauffman, S. Lambropoulou, S. Jablan, J.H. Przytycki), pp. 482-501. Series on Knots and Everything 46. World Scientific.
  46. Ricca, R.L. & Nipoti, B. (2011) Gauss' linking number revisited. J. Knot Theory & Its Ram., 20, 1325-1343.
  47. Ricca, R.L. (2012) On simple energy–complexity relations for filament tangles and networks. Complex Systems, 20, 195-204.
  48. Liu, X. & Ricca, R.L. (2012) The Jones’ polynomial for fluid knots from helicity. J. Phys. A: Math. & Theor., 45, 205501.
  49. Ricca, R.L. (2013) Impulse of vortex knots from diagram projections. In Topological Fluid Dynamics: Theory and Applications (ed. H.K. Moffatt et al.), pp. 21-28. Procedia IUTAM 7. Elsevier.
  50. Liu, X. & Ricca, R.L. (2013) Tackling fluid structures complexity by the Jones polynomial. In Topological Fluid Dynamics: Theory and Applications (ed. H.K. Moffatt et al.), pp. 175-182. Procedia IUTAM 7. Elsevier.
  51. Maggioni F., Alamri S.Z., Barenghi C.F. & Ricca R.L. (2013) Vortex knots dynamics in Euler fluids. In Topological Fluid Dynamics: Theory and Applications (ed. H.K. Moffatt et al.), pp. 29-38. Procedia IUTAM 7. Elsevier.
  52. Ricca, R.L. (2013) New energy lower bounds for knotted and braided magnetic fields. Geophys. Astrophys. Fluid Dyn., 107, 385-402.
  53. Ricca, R.L. (2014) Structural complexity of vortex flows by diagram analysis and knot polynomials. In How Nature Works , (ed. I. Zelinka et al.), pp. 81-100. Emergence, Complexity and Computation 5. Springer-Verlag.
  54. Ricca, R.L. & Liu, X. (2014) The Jones polynomial as a new invariant of topological fluid dynamics. Fluid Dyn. Res., in press.
  55. Ricca, R.L. & Maggioni, F. (2014) On the groundstate energy spectrum of magnetic knots and links. J. Phys. A: Math. & Theor., in press.