Ellis, David C. P. and Gay-Balmaz, François and Holm, Darryl D. and Putkaradze, Vakhtang and Ratiu, Tudor S. (2010) Symmetry Reduced Dynamics of Charged Molecular Strands. Archive for Rational Mechanics and Analysis, 197 (3). pp. 811-902. ISSN 0003-9527 http://resolver.caltech.edu/CaltechAUTHORS:20100809-122415232
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The equations of motion are derived for the dynamical folding of charged molecular strands (such as DNA) modeled as flexible continuous filamentary distributions of interacting rigid charge conformations. The new feature is that these equations are nonlocal when the screened Coulomb interactions, or Lennard–Jones potentials between pairs of charges, are included. The nonlocal dynamics is derived in the convective representation of continuum motion by using modified Euler–Poincaré and Hamilton–Pontryagin variational formulations that illuminate the various approaches within the framework of symmetry reduction of Hamilton’s principle for exact geometric rods. In the absence of nonlocal interactions, the equations recover the classical Kirchhoff theory of elastic rods. The motion equations in the convective representation are shown to arise by a classical Lagrangian reduction associated to the symmetry group of the system. This approach uses the process of affine Euler–Poincaré reduction initially developed for complex fluids. On the Hamiltonian side, the Poisson bracket of the molecular strand is obtained by reduction of the canonical symplectic structure on phase space. A change of variables allows a direct passage from this classical point of view to the covariant formulation in terms of Lagrange–Poincaré equations of field theory. In another revealing perspective, the convective representation of the nonlocal equations of molecular strand motion is transformed into quaternionic form.
|Additional Information:||© 2010 Springer-Verlag. Received February 17, 2009. Accepted October 25, 2009. Published online April 28, 2010. Communicated by M. Ortiz. DDH and VP were partially supported by NSF grants NSF-DMS- 05377891 and NSF-DMS-0908755. The work of DDH was also partially supported by the Royal Society of London Wolfson Research Merit Award. VP acknowledges the support of the European Science Foundation for partial support through the MISGAM program. FGB acknowledges the partial support of Swiss National Science Foundation grants 200020- 117511 and of a Swiss National Science Foundation Fellowship. TSR acknowledges the partial support of Swiss National Science Foundation grants 200020-117511 and 200020- 126630. We thank the referees for their helpful, thoughtful remarks and suggestions.|
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|Deposited By:||Tony Diaz|
|Deposited On:||09 Aug 2010 21:00|
|Last Modified:||26 Dec 2012 12:18|
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