The Langevin equation is a stochastic differential equation frequently used in molecular dynamics for simulating systems with a constant temperature. Recent developments have given rise to wide uses of Langevin dynamics at different levels of spatial resolution, which necessitate time step and friction parameter choices outside of the range for which many existing temporal discretization methods were originally developed. We first study the GJ--F, BAOAB and BBK numerical algorithms, originally developed for atomistic simulations, on a coarse-grained polymer melt, paying close attention to the large time step regime. The results of this study then inspire our search for new algorithms and lead to a general class of velocity Verlet-based time-stepping schemes designed to perform well for all parameter regions, by ensuring that they faithfully reproduce statistical quantities for the case of a free particle and harmonic oscillator. This family of methods depends on the choice of a single free parameter function and we explore some of the methods defined for certain choices of this parameter on realistic coarse-grained and atomistic molecular systems relevant in material and bio-molecular science. In addition, we provide an equivalent splitting formulation of this one-parameter family which allows for enhanced insight into the hidden time scaling induced by the choice of the free parameter in the Hamiltonian and stochastic time scales. / Mathematics
| Identifer | oai:union.ndltd.org:TEMPLE/oai:scholarshare.temple.edu:20.500.12613/293 |
| Date | January 2020 |
| Creators | Finkelstein, Joshua |
| Contributors | Seibold, Benjamin, Fiorin, Giacomo, Queisser, Gillian, Yilmaz, Atilla |
| Publisher | Temple University. Libraries |
| Source Sets | Temple University |
| Language | English |
| Detected Language | English |
| Type | Thesis/Dissertation, Text |
| Format | 128 pages |
| Rights | IN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available., http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | http://dx.doi.org/10.34944/dspace/277, Theses and Dissertations |
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