Abstract
We present a reversible and symplectic algorithm called ROLL, for integrating the equations of motion in molecular dynamics simulations of simple fluids on a hypersphere $\mathcal{S}^d$ of arbitrary dimension $d$. It is derived in the framework of geometric algebra and shown to be mathematically equivalent to algorithm RATTLE. An application to molecular dynamics simulation of the one component plasma is briefly discussed.
Highlights
It is a great pleasure for me to contribute to this special issue of Condensed Matter Physics dedicated to my colleague and friend I
I hope that this paper, which deals with the theory of molecular dynamics (MD) simulations, will be of some interest to him
The main application of ROLL should be for MD simulations of simple fluids
Summary
It is a great pleasure for me to contribute to this special issue of Condensed Matter Physics dedicated to my colleague and friend I. The idea of using the two dimensional (2D) surface of an ordinary sphere, i.e., space S2, to perform Monte Carlo (MC) and/or MD simulations of a 2D fluid can be tracked back to a paper by J.-P. The generalization to MC simulations of 3D systems, implying the use of the 3D surface S3 of a 4D-hypersphere, is due to Caillol and Levesque [2] in their study of 3D ionic liquids. A symplectic integrator for MD simulations of 2D systems on 2-spheres was proposed in references [3, 4]. ROLL is shown to be equivalent to algorithm RATTLE [11] in appendix B from which it inherits all its properties (reversibility and symplecticity).
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