Nous établir les équations de la dynamique hamiltonienne d'une courbe (chaine moléculaire) dans l'espace physique sujette á des interactions élastiques ainsi que non-locales (électrostatiques par exemple). Les équations dynamiques des variables réduites par symétrie sont écrites sur l'espace dual de l'algèbre de Lie (produit semidirect) avec trois 2-cocycles. Nous démontrons aussi que l'interaction non-locale produit un nouvel terme intéressant, qui dérive de l'action coadjointe du group de Lie sur son algébre . Les nouvelles équations du filament sont écrites sous une forme conservative grâce aux actions coadjointes correspondantes.
Time-dependent Hamiltonian dynamics is derived for a strand of charged units in held together by both nonlocal (for example, electrostatic) and elastic interactions. The dynamical equations in the symmetry-reduced variables are written on the dual of the semidirect-product Lie algebra with three 2-cocycles. We also demonstrate that the nonlocal interaction produces an interesting new term deriving from the coadjoint action of the Lie group on its Lie algebra . The new strand equations are written in conservative form by using the corresponding coadjoint actions.
Accepté le :
Publié le :
Darryl D. Holm 1 ; Vakhtang Putkaradze 2, 3
@article{CRMATH_2009__347_17-18_1093_0, author = {Darryl D. Holm and Vakhtang Putkaradze}, title = {Nonlocal orientation-dependent dynamics of charged strands and ribbons}, journal = {Comptes Rendus. Math\'ematique}, pages = {1093--1098}, publisher = {Elsevier}, volume = {347}, number = {17-18}, year = {2009}, doi = {10.1016/j.crma.2009.06.009}, language = {en}, }
TY - JOUR AU - Darryl D. Holm AU - Vakhtang Putkaradze TI - Nonlocal orientation-dependent dynamics of charged strands and ribbons JO - Comptes Rendus. Mathématique PY - 2009 SP - 1093 EP - 1098 VL - 347 IS - 17-18 PB - Elsevier DO - 10.1016/j.crma.2009.06.009 LA - en ID - CRMATH_2009__347_17-18_1093_0 ER -
Darryl D. Holm; Vakhtang Putkaradze. Nonlocal orientation-dependent dynamics of charged strands and ribbons. Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1093-1098. doi : 10.1016/j.crma.2009.06.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.06.009/
[1] Elastic rod model of a DNA loop in the lac operon, Phys. Rev. Lett., Volume 83 (1999), pp. 4900-4903
[2] Structural motifs of macromolecules, Proc. Natl. Acad. Sci., Volume 104 (2007), pp. 17283-17286
[3] Investigation of bend and shear waves in a geometrically exact elastic rod model, J. Comp. Phys., Volume 193 (2004), pp. 642-665
[4] Geometric mechanics and the dynamics of asteroid pairs, Dynamical Systems, Volume 20 (2005), pp. 3-21
[5] H. Cendra, J.E. Marsden, T.S. Ratiu, Lagrangian Reduction by Stages, Memoirs American Mathematical Society, vol. 152, 2001
[6] Helices, Proc. Natl. Acad. Sci., Volume 103 (2006), pp. 9398-9403
[7] Hamiltonian formulations and symmetries in rod mechanics, Minneapolis, MN, 1994 (IMA Vol. Math. Appl.), Volume vol. 82, Springer, New York (1996), pp. 71-113
[8] The geometric structure of complex fluids, Adv. Appl. Math., Volume 42 (2009) no. 2, pp. 176-275
[9] Gauge-invariant Poisson brackets for chromohydrodynamics, Phys. Lett. A, Volume 90 (1982), pp. 281-283
[10] Bistable helixes, Phys. Rev. Lett., Volume 84 (2000), pp. 1631-1634
[11] Viscous nonlinear dynamics of twist and writhe, Phys. Rev. Lett., Volume 80 (1998), pp. 5232-5235
[12] Repeat protein architectures predicted by a continuum representation of fold space, Protein Sci., Volume 15 (2006), pp. 1-8
[13] Euler–Poincaré dynamics of perfect complex fluids, Geometry, Mechanics and Dynamics, Special Volume in Honor of J.E. Marsden (2001), pp. 113-167
[14] The analogy between spin glasses and Yang–Mills fluids, J. Math. Phys., Volume 29 (1988), pp. 21-30
[15] On the dynamics of molecular conformation, Proc. Natl. Acad. Sci., Volume 103 (2006), pp. 7542-7547
[16] The Hamiltonian structure of nonlinear elasticity: The material and convective representations of solids, rods, and plates, Arch. Rational Mech. Anal., Volume 104 (1988), pp. 125-183
Cité par Sources :
Commentaires - Politique