Articles in Primary Journals and Refereed Volumes

Scientific papers – click on hyperlink to download published version (PDF)


81 – Ricca, R.L. & Liu, X. (2023) A new framework for the Jones polynomial of fluid knots. J. Knot Theory & Its Ram., 2340024. Online version: https://www.worldscientific.com/doi/10.1142/S0218216523400242.

80 – Belloni, A. & Ricca, R.L. (2023) On the zero helicity condition for quantum vortex defects. J. Fluid Mech. 963, R2.

79 – Foresti, M. & Ricca, R.L. (2022) Instability of a quantum vortex by twist perturbation. J. Fluid Mech. 949, A19.

78 – Zuccher, S. & Ricca, R.L. (2022) Creation of quantum knots and links driven by minimal surfaces. J. Fluid Mech.942, A8.

77 – Roitberg, A. & Ricca, R.L. (2021) Hydrodynamic derivation of the Gross-Pitaevskii equation in general Riemannian metric. J. Phys. A: Math. Theor.54, 315201.

76 – Sumners, De W.L., Cruz-White, I.I. & Ricca, R.L. (2021) Zero helicity of Seifert framed defects. J. Phys. A: Math. Theor.54, 295203.

75 – Liu, X., Ricca, R.L. & Li, X-F. (2020) Minimal unlinking pathways as geodesics in knot polynomial space. Communications Physics 3, 136.

74 – Guan, H., Zuccher, S., Ricca, R.L. & Liu, X. (2020) Topological fluid mechanics and its new developments. (In Chinese)Scientia Sinica Phys. Mech. Astron. 50, 054701.

73 – Foresti, M. & Ricca, R.L. (2020) Hydrodynamics of a quantum vortex in the presence of twistJ. Fluid. Mech. 904, A25.

72 – Zuccher, S. & Ricca, R.L. (2019) Momentum of vortex tangles by weighted area informationPhys. Rev. E 100, 011101(R).

71 – Oberti, C. & Ricca, R.L. (2019) Influence of winding number on vortex knots dynamics. Sci. Rep. 9, 17284.

70 – Foresti, M. & Ricca, R.L. (2019) Defect production by pure phase twist injection as Aharonov-Bohm effectPhys. Rev. E 100, 023107.

69 – Ricca, R.L. & Maggioni, F. (2018) Groundstate energy spectra of knots and links: magnetic versus bending energy. In New Directions in Geometric and Applied Knot Theory (ed. S. Blatt, P. Reiter & A. Schikorra), pp. 276-288. OA Measure Theory, De Gruyter, Basel.

68 – Zuccher, S. & Ricca, R.L. (2018) Twist effects in quantum vortices and phase defectsFluid Dyn. Res. 50, 011414.

67 – Oberti, C. & Ricca, R.L. (2018) Energy and helicity of magnetic torus knots and braidsFluid Dyn. Res. 50, 011413.

66 – Ricca, R.L. & Liu, X. (2018) HOMFLYPT polynomial is the best quantifier for topological cascades of vortex knotsFluid Dyn. Res. 50, 011404.

65 – Zuccher, S. & Ricca, R.L. (2017) Relaxation of twist helicity in the cascade process of linked quantum vorticesPhys. Rev. E 95, 053109.

64 – Oberti, C. & Ricca, R.L. (2017) Induction effects of torus knots and unknotsJ. Phys A: Math Theor. 50, 365501.

63 – Oberti, C. & Ricca, R.L. (2016) On torus knots and unknotsJ. Knot Theory & Its Ramif. 25, 1650036.

62 – Liu, X. & Ricca, R.L. (2016) Knots cascade detected by a monotonically decreasing sequence of valuesSci. Rep. 6, 24118.

61 – Ricca, R.L. (2015) Vortex Knot Cascade in Polynomial Skein Relations. In Numerical Analysis and Applied Mathematics ICNAAM 2015 (ed. T. Simos & C. Tsitouras), pp. 150002-1-4. AIP Conf. Proc. 1738, AIP Publishing.

60 – Zuccher, S. & Ricca, R.L. (2015) Helicity conservation under quantum reconnection of vortex ringsPhys. Rev. E 92, 061001.

59 – Liu, X. & Ricca, R.L. (2015) Helicity conservation under quantum reconnection of vortex ringsJ. Fluid Mech. 773, 4-48.

58 – Laing, C.E., Ricca, R.L. & Sumners, De W.L. (2015) Conservation of writhe helicity under anti-parallel reconnectionSci. Rep. 5, 9224.

57 – Ricca, R.L. & Maggioni, F. (2014) On the groundstate energy spectrum of magnetic knots and linksJ. Phys. A: Math. & Theor. 47, 205501.

56 – Ricca, R.L. & Liu, X. (2014) The Jones polynomial as a new invariant of topological fluid dynamicsFluid Dyn. Res. 46, 061412.

55 – 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 – 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.

53 – 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.

52 – 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.

51 – Ricca, R.L. (2013) New energy lower bounds for knotted and braided magnetic fieldsGeophys. Astrophys. Fluid Dyn. 107, 385-402.

50 – Liu, X. & Ricca, R.L. (2012) The Jones’ polynomial for fluid knots from helicityJ. Phys. A: Math. & Theor. 45, 205501.

49 – Ricca, R.L. (2012) Tackling fluid tangles complexity by knot polynomials. In Numerical Analysis and Applied Mathematics, pp. 646-649. ICNAAM 2012 Conf. Proc. 1479. AIP.

48 – Ricca, R.L. (2012) On simple energy–complexity relations for filament tangles and networksComplex Systems 20, 195-204.

47 – Ricca, R.L. (2011) Energy-complexity relations by structural complexity methods. In Numerical Analysis and Applied Mathematics ICNAAM 2011 AIP Conf. Proc. 1389, 962-964.

46 – 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.

45 – Ricca, R.L. & Nipoti, B. (2011) Gauss’ linking number revisitedJ. Knot Theory & Its Ram. 20, 1325-1343.

44 – Maggioni, F., Alamri, S.Z., Barenghi, C.F. & Ricca, R.L. (2010) Velocity, energy and helicity of vortex knots and unknotsPhys. Rev. E 82, 26309-26317.

43 – Goldstein, R.E., Moffatt, H.K., Pesci, A.I. & Ricca, R.L. (2010) Soap film Möbius strip changes topology with a twist singularityProc. Natnl. Acad. Sci. 107, 21979-21984.

42 – Maggioni, F. & Ricca, R.L. (2009) On the groundstate energy of tight knotsProc. R. Soc. A 465, 2761-2783.

41 – Maggioni, F., Alamri, S.Z., Barenghi, C.F. & Ricca, R.L. (2009) Kinetic energy of vortex knots and unknotsNuovo Cimento C 32, 133-142.

40 – Ricca, R.L. (2009) New developments in topological fluid mechanicsNuovo Cimento C 32, 185-192.

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.

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.

37 – Ricca, R.L. (2008) Momenta of a vortex tangle by structural complexity analysisPhysica D 237, 2223-2227.

36 – Ricca, R.L. & Maggioni, F. (2008) Multiple folding and packing in DNA modelingComp. & Math. with Appl. 55, 1044-1053.

35 – Ricca, R.L. (2008) Topology bounds energy of knots and linksProc. R. Soc. A 464, 293-300.

34 – Maggioni, F. & Ricca, R.L. (2007) DNA supercoiling modeling of nucleosome and viral spoolingProc. Appl. Math. Mech. 7, 2120011-2120012.

33 – Ricca, R.L. & Maggioni, F. (2007) A new stretch-twist-fold model for fast dynamoProc. Appl. Math. Mech. 7, 2100051-2100052.

32 – Maggioni, F. & Ricca, R.L. (2006) Writhing and coiling of closed filamentsProc. R. Soc. London A 462, 3151-3166.

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.

30 – Ricca, R.L. (2005) Inflexional disequilibrium of magnetic flux tubesFluid Dyn. Res. 36, 319-332.

29 – Ricca, R.L. (2005) Structural complexity. In Encyclopedia of Nonlinear Science (ed. A. Scott), pp. 885-887. Routledge, New York and London.

28 – Ricca, R.L. (2005) Knot theory. In Encyclopedia of Nonlinear Science (ed. A. Scott), pp. 499-501. Routledge, New York and London.

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.

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.

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.

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.

23 – Barenghi, C.F., Ricca, R.L. & Samuels, D.C. (2001) How tangled is a tangle? Physica D 157, 197-206.

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.

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.

20 – Barenghi, C.F., Ricca, R.L. & Samuels, D.C. (1999) Evolution of vortex knotsJ. Fluid Mech. 391, 29-44.

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.

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.

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.

16 – Barenghi, C.F., Ricca, R.L. & Samuels, D.C. (1998) Quantized vortex knotsJ. Low Temp. Physics 110, 509-514.

15 – Ricca, R.L. (1997) Evolution and inflexional instability of twisted magnetic flux tubesSolar Physics 172, 241-248.

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.

13 – Ricca, R.L. & Berger, M.A. (1996) Topological ideas and fluid mechanicsPhys. Today 49 (12), 24-30. [Also in: (1997) Parity 10, 20-28]

12 – Ricca, R.L. (1996) The contributions of Da Rios and Levi-Civita to asymptotic potential theory and vortex filament dynamicsFluid Dyn. Res. 18, 245-268.

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.

10 – Ricca, R.L. (1995) The energy spectrum of a twisted flexible string under elastic relaxationJ. Phys. A: Math. & Gen. 28, 2335-2352.

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.

8 – Ricca, R.L. (1994) The effect of torsion on the motion of a helical vortex filamentJ. Fluid Mech. 273, 241-259.

7 – Ricca, R.L. (1993) Torus knots and polynomial invariants for a class of soliton equationsChaos 3, 83-91. [(1995) Erratum. Chaos 5, 346.]

6 – Moffatt, H.K. & Ricca, R.L. (1992) Helicity and the Calugareanu invariantProc. R. Soc. London A 439, 411-429. [Also in: (1995) Knots and Applications (ed. L.H. Kauffman), pp. 251-269. World Scientific.]

5 – Ricca, R.L. (1992) Physical interpretation of certain invariants for vortex filament motion under LIAPhysics of Fluids A 4, 938-944.

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.

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.

2 – Ricca, R.L. (1991) Rediscovery of Da Rios equationsNature 352, 561-562.

1 – Ricca, R.L. (1991) Intrinsic equations for the kinematics of a classical vortex string in higher dimensionsPhys. Rev. A 43, 4281-4288.