Geodesic
Existence of energy minimums for thin elastic rods in static helical configurations
Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 3, pp. 336-352 Cet article a éte moissonné depuis la source Math-Net.Ru

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We characterize families of solutions of the static Kirchhoff model of a thin elastic rod physically. These families, which are proved to exist, depend on the behavior of the so-called register and also on the radius and pitch. We describe the energy densities for each of the solutions in terms of the elastic properties and geometric shape of the unstrained rod, which allows determining the selection mechanism for thepreferred helical configurations. This analysis promises to be a fundamental tool for understanding the close connection between the study of elastic deformations in thin rods and coarse-grained models with widespread applications in the natural sciences.
Keywords: thin elastic rod, Kirchhoff equation, inverse problem, integrability
Mots-clés : helix. 
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     title = {Existence of energy minimums for thin elastic rods in static helical configurations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {159},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_159_3_a1/}
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M. Argeri; V. Barone; S. De Lillo; G. Lupo; M. Sommacal. Existence of energy minimums for thin elastic rods in static helical configurations. Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 3, pp. 336-352. http://geodesic.mathdoc.fr/item/TMF_2009_159_3_a1/

[1] R. Improta, V. Barone, K. N. Kudin, G. E. Scuseria, J. Chem. Phys., 114:6 (2001), 2541–2549 | DOI

[2] J. S̆poner, F. Lankas̆ (eds.), Computational Studies of RNA and DNA, Challenges and Advances in Computational Chemistry and Physics, 2, Springer, New York, 2006

[3] R. Improta, V. Barone, K. N. Kudin, G. E. Scuseria, J. Am. Chem. Soc., 123:14 (2001), 3311–3322 | DOI

[4] R. Improta, F. Mele, O. Crescenzi, C. Benzi, V. Barone, J. Am. Chem. Soc., 124:26 (2002), 7857–7865 | DOI

[5] H. Gohlke, M. F. Thorpe, Biophysical J., 91:6 (2006), 2115–2120 | DOI

[6] M. Argeri, V. Barone, S. De Lillo, G. Lupo, M. Sommacal, Physica D, 238 (2009), 1031–1049 | DOI | MR | Zbl

[7] E. Langella, R. Improta, V. Barone, Biophysical J., 87:6 (2004), 3623–3632 | DOI

[8] A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, Dover, New York, 1944 | MR | Zbl

[9] S. S. Antman, Nonlinear Problems of Elasticity, Appl. Math. Sci., 107, Springer, New York, 1995 | DOI | MR | Zbl

[10] G. Kirkhgof, Mekhanika, Lektsii po matematicheskoi fizike, AN SSSR, M., 1962 | Zbl

[11] S. R. Sanghani, K. Zakrzewska, S. C. Harvey, R. Lavery, Nucleic Acids Res., 24:9 (1996), 1632–1637 | DOI

[12] A. Goriely, M. Nizette, M. Tabor, J. Nonlinear Sci., 11:1 (2001), 3–45 | DOI | MR | Zbl

[13] N. Chouaieb, A. Goriely, J. H. Maddocks, Proc. Natl. Acad. Sci. USA, 103:25 (2006), 9398–9403 | DOI | MR | Zbl

[14] A. F. Bower, Applied mechanics of solids, , 2008 http://solidmechanics.org

[15] S. Zhang, X. Zuo, M. Xia, S. Zhao, E. Zhang, Phys. Rev. E, 70:5 (2004), 051902 | DOI