Exact geometric theory of dendronized polymer dynamics

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• 作者：Franç ; ois Gay-Balmaz^a ; ^{francois.gay-balmaz@lmd.ens.fr} ; Darryl D. Holm^b ; ^{d.holm@imperial.ac.uk} ; Vakhtang Putkaradze^c ; ^{putkarad@math.colostate.edu} ; Tudor S. Ratiu^d ; ^{tudor.ratiu@epfl.ch}
• 关键词：51 ; 70 ; 74
• 刊名：Advances in Applied Mathematics
• 出版年：2012
• 期刊代码：61_01968858
• 类别：mt
• 出版时间：April, 2012
• 卷：48
• 期：4
• 页码：535-574
• 文件大小：514 K

摘要

Dendronized polymers consist of an elastic backbone with a set of iterated branch structures (dendrimers) attached at every base point of the backbone. The conformations of such molecules depend on the elastic deformation of the backbone and the branches, as well as on nonlocal (e.g., electrostatic, or Lennard-Jones) interactions between the elementary molecular units comprising the dendrimers and/or backbone. We develop a geometrically exact theory for the dynamics of such polymers, taking into account both local (elastic) and nonlocal interactions. The theory is based on applying symmetry reduction of Hamilton始s principle for a Lagrangian defined on the tangent bundle of iterated semidirect products of the rotation groups that represent the relative orientations of the dendritic branches of the polymer. The resulting symmetry-reduced equations of motion are written in conservative form.