Study of Polymers Nonlinear Dynamics: Exploring the Nonlinear Dynamics of Inextensible Stiff Polymers (Journal of Advances and Scholarly Researches in Allied Education, 2011)
A formalismis presented for the nonlinear dynamics of inextensible stiff polymers withinthe model of local viscous dissipation. By casting the internal elastic forcesin an intrinsic representation, enforcing the constraint of localinextensibility through a Lagrange multiplier function, and utilizingtechniques from the differential geometry of curve motion, the dynamics ofconfigurations of arbitrary complexity is reduced to a scalar partialdifferential equation amenable to analytical and efficient numerical study. Asan example, the formalism is applied to the "folding" dynamics ofstiff polymers with pairwise self-interactions and intrinsic curvature. Imaging and manipulation techniquescapable of probing the conformation and dynamics of biological macromoleculeshave revealed a variety of phenomena involving complex molecularconfigurations. Among these are long DNA molecules undergoing electrophoreticmotion in structured environments [1] and collapse from near full extension[2], and actin filaments moved by molecular motors on surfaces [3]. In contrastto studies focusing on the statisticalproperties of ensembles of molecules, these studies are dynamical investigations of single molecules..