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Models for twistable elastic polymers in Brownian dynamics, and their implementation for LAMMPS
6. C. R. Calladine and H. Drew, Understanding DNA (Academic Press, San Diego, 1992).
19. D. J. Clark and G. Felsenfeld, EMBO J. 10, 387 (1991).
39.In the case of a linear rod there are N position vectors describing the vertices of N − 1 segments, with tangents with i = 1, …, N − 1. For a circular rod there are N segments and .
42. C. A. Brackley, J. Allan, D. Keszenman-Pereyra, and D. Marenduzzo, “How to make chromatin: Topological enzymes aid chromatin self-assembly in silico” (unpublished).
43.The two potentials are however equivalent in the limit where all of αi, βi, and γi are small, a regime which is forced by the Hamiltonian considering either of the dihedrals.
44.The angles ζi are minimised by choosing a large alignment energy κa; in practice, this can be set as large as possible subject to numerical stability.
45.Source code for the LAMMPS orientation angle style discussed in Sec. V B is available on request from the authors.
50. G. H. Fredrickson, The Equilibrium Theory of Inhomogeneous Polymers (Oxford University Press, New York, 2006).
51.If R is a rotation matrix for rotating a vector by an angle δϕ about some axis , then . In the limit δϕ → 0, .
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An elastic rod model for semi-flexible polymers is presented. Theory for a continuum rod is reviewed, and it is shown that a popular discretised model used in numerical simulations gives the correct continuum limit. Correlation functions relating to both bending and twisting of the rod are derived for both continuous and discrete cases, and results are compared with numerical simulations. Finally, two possible implementations of the discretised model in the multi-purpose molecular dynamics software package LAMMPS are described.
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