Systematic derivation of hybrid coarse-grained models

Di Pasquale, Nicodemo; Hudson, Thomas; Icardi, Matteo

Abstract

Molecular dynamics represents a key enabling technology for applications ranging from biology to the development of new materials. However, many real-world applications remain inaccessible to fully-resolved simulations due their unsustainable computational costs and must therefore rely on semi-empirical coarse-grained models. Significant efforts have been devoted in the last decade towards improving the predictivity of these coarse-grained models and providing a rigorous justification of their use, through a combination of theoretical studies and data-driven approaches. One of the most promising research effort is the (re)discovery of the Mori-Zwanzig projection as a generic, yet systematic, theoretical tool for deriving coarse-grained models. Despite its clean mathematical formulation and generality, there are still many open questions about its applicability and assumptions. In this work, we propose a detailed derivation of a hybrid multi-scale system, generalising and further investigating the approach developed in [Español, P., EPL, 88, 40008 (2009)]. Issues such as the general coexistence of atoms (fully-resolved degrees of freedom) and beads (larger coarse-grained units), the role of the fine-to-coarse mapping chosen, and the approximation of effective potentials are discussed. The theoretical discussion is supported by numerical simulations of a monodimen-sional nonlinear periodic benchmark system with an open-source parallel Julia code, easily extensible to arbitrary potential models and fine-to-coarse mapping functions. The results presented highlight the importance of introducing, in the macroscopic model, non-constant fluctuating and dissipative terms, given by the Mori-Zwanzig approach, to correctly reproduce the reference fine-grained results, without requiring ad-hoc calibration of interaction potentials and thermostats.

Citation

Di Pasquale, N., Hudson, T., & Icardi, M. (2019). Systematic derivation of hybrid coarse-grained models. Physical Review E, 99(1), https://doi.org/10.1103/PhysRevE.99.013303

• Journal Article Type: Article
• Acceptance Date: Dec 13, 2018
• Online Publication Date: Jan 7, 2019
• Publication Date: Jan 7, 2019
• Deposit Date: Jan 7, 2019
• Publicly Available Date: Jan 8, 2019
• Journal: Physical Review E
• Print ISSN: 2470-0045
• Electronic ISSN: 1550-2376
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 99
• Issue: 1
• Article Number: 013303
• DOI: https://doi.org/10.1103/PhysRevE.99.013303
• Keywords: Chemical Physics
• Public URL: https://nottingham-repository.worktribe.com/output/1449043
• Publisher URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.99.013303
• Additional Information: ©2019 American Physical Society