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Geometric mechanics of charged ribbons, or orientation-dependent nonlocal interactions along charged filaments

Vakhtang Putkaradze
Dept of Mathematics, Colorado State Univ


We derive equations of motion for the dynamical folding of biological molecules (such as DNA), that are modeled as continuous filamentary distributions of interacting rigid charge conformations. The equations of motion for the dynamics of such a system are nonlocal when the screened Coulomb interactions, or Lennard-Jones potentials between pairs of charges are included. These nonlocal dynamical equations are derived using Euler-Poincar'e variational formulations, extending earlier work for exact geometric rods. In the absence of nonlocal interactions, the equations reduce to the Kirchhoff theory of elastic rods. An elegant change of variables separates the dynamics geometrically into "horizontal" and "vertical" components. This is joint work with Francois Gay-Balmaz(EPFL), David Ellis (Imperial), Darryl D. Holm (Imperial), and Tudor Ratiu (EPFL).

Thursday, June 26, 2008
11:00AM AP&M 2402