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On the geometry of stiff knots

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Abstract

We analyse the geometry of a thin knotted string with bending rigidity. Two types of geometric properties are investigated. First, following the approach of von der Mosel [H. von der Mosel, Asymptotic Anal. 18, 49 (1998)], we derive upper bounds for the multiplicity of crossings and braids. Then, using a general inequality for the length of 3D curves derived by Chakerian [G.D. Chakerian, Proc. of the American Math. Soc. 15, 886 (1964)], we analyze the size and confinement of a knot

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References

  1. L. Euler, Bousquet, Lausannae et Genevae 24, E65A (1744)

    Google Scholar 

  2. J. Langer, D.A. Singer, J. London Math. Soc. 30, 512 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  3. R. Gallotti, O. Pierre-Louis, Phys. Rev. E 75, 031801 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  4. B. Audoly, N. Clauvelin, S. Neukirch, Phys. Rev. Lett. 99, 164301 (2007)

    Article  ADS  Google Scholar 

  5. E. Guitter, E. Orlandini, J. Phys. A 32 1359 (1999); R. Metzler, A. Hanke, P.G. Dommersnes, Y. Kantor, M. Kardar, Phys. Rev. Lett. 88, 188101 (2002)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  6. P.G. Dommersnes, Y. Kantor, M. Kardar, Phys. Rev. E 66, 031802 (2002)

    Article  ADS  Google Scholar 

  7. X.R. Bao, H.J. Lee, S.R. Quake, Phys. Rev. Lett. 91 265506 (2003)

    Article  ADS  Google Scholar 

  8. A.Y. Grosberg, Y. Rabin, Phys. Rev. Lett. 99, 217801 (2007)

    Article  ADS  Google Scholar 

  9. J.W. Milnor, Ann. Math. 52, 248 (1949)

    Article  MathSciNet  Google Scholar 

  10. H. von der Mosel, Asymptotic Anal. 18, 49 (1998)

    MATH  ADS  Google Scholar 

  11. G.D. Chakerian, Proc. of the American Math. Soc. 15, 886 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  12. SA. Wasserman, NR. Cozzarelli, Science 232 951 (1986); D. Buck, E. Flapan, Knot Theory for Scientific Objects, OCAMI Studies (2007), p. 75

    Article  ADS  Google Scholar 

  13. J. O’Hara, Energy of knots and conformal geometry (World Scientific, Singapore, 2003); J. O’Hara, Ideal Knots (World Scientific, River Edge, NJ, 1998)

    MATH  Google Scholar 

  14. G. Buck, E.J. Rawdon Phys. Rev. E 70, 011803 (2004)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Laboratoire de Spectrométrie Physique, CNRS Univ. J. Fourier, BP87, Grenoble 1, 38402, Saint Martin d’Hères, France

    O. Pierre-Louis

  2. Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, UK

    O. Pierre-Louis

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  1. O. Pierre-Louis
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Correspondence to O. Pierre-Louis.

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Pierre-Louis, O. On the geometry of stiff knots. Eur. Phys. J. B 71, 281–288 (2009). https://doi.org/10.1140/epjb/e2009-00301-6

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  • DOI: https://doi.org/10.1140/epjb/e2009-00301-6

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