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Title: Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism

Abstract

The Mori-Zwanzig formalism for coarse-graining a complex dynamical system typically introduces memory effects. The Markovian assumption of delta-correlated fluctuating forces is often employed to simplify the formulation of coarse-grained (CG) models and numerical implementations. However, when the time scales of a system are not clearly separated, the memory effects become strong and the Markovian assumption becomes inaccurate. To this end, we incorporate memory effects into CG modeling by preserving non-Markovian interactions between CG variables, and the memory kernel is evaluated directly from microscopic dynamics. For a specific example, molecular dynamics (MD) simulations of star polymer melts are performed while the corresponding CG system is defined by grouping many bonded atoms into single clusters. Then, the effective interactions between CG clusters as well as the memory kernel are obtained from the MD simulations. The constructed CG force field with a memory kernel leads to a non-Markovian dissipative particle dynamics (NM-DPD). Quantitative comparisons between the CG models with Markovian and non-Markovian approximations indicate that including the memory effects using NM-DPD yields similar results as the Markovian-based DPD if the system has clear time scale separation. However, for systems with small separation of time scales, NM-DPD can reproduce correct short-time properties that aremore » related to how the system responds to high-frequency disturbances, which cannot be captured by the Markovian-based DPD model.« less

Authors:
; ;  [1]
  1. Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802 (United States)
Publication Date:
OSTI Identifier:
22493375
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 143; Journal Issue: 24; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ATOMS; COMPARATIVE EVALUATIONS; COMPLEXES; GRAIN SIZE; IMPLEMENTATION; KERNELS; MARKOV PROCESS; MOLECULAR DYNAMICS METHOD; PARTICLES; POLYMERS; YIELDS

Citation Formats

Li, Zhen, Bian, Xin, Karniadakis, George Em, E-mail: george-karniadakis@brown.edu, and Li, Xiantao. Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism. United States: N. p., 2015. Web. doi:10.1063/1.4935490.
Li, Zhen, Bian, Xin, Karniadakis, George Em, E-mail: george-karniadakis@brown.edu, & Li, Xiantao. Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism. United States. https://doi.org/10.1063/1.4935490
Li, Zhen, Bian, Xin, Karniadakis, George Em, E-mail: george-karniadakis@brown.edu, and Li, Xiantao. Mon . "Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism". United States. https://doi.org/10.1063/1.4935490.
@article{osti_22493375,
title = {Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism},
author = {Li, Zhen and Bian, Xin and Karniadakis, George Em, E-mail: george-karniadakis@brown.edu and Li, Xiantao},
abstractNote = {The Mori-Zwanzig formalism for coarse-graining a complex dynamical system typically introduces memory effects. The Markovian assumption of delta-correlated fluctuating forces is often employed to simplify the formulation of coarse-grained (CG) models and numerical implementations. However, when the time scales of a system are not clearly separated, the memory effects become strong and the Markovian assumption becomes inaccurate. To this end, we incorporate memory effects into CG modeling by preserving non-Markovian interactions between CG variables, and the memory kernel is evaluated directly from microscopic dynamics. For a specific example, molecular dynamics (MD) simulations of star polymer melts are performed while the corresponding CG system is defined by grouping many bonded atoms into single clusters. Then, the effective interactions between CG clusters as well as the memory kernel are obtained from the MD simulations. The constructed CG force field with a memory kernel leads to a non-Markovian dissipative particle dynamics (NM-DPD). Quantitative comparisons between the CG models with Markovian and non-Markovian approximations indicate that including the memory effects using NM-DPD yields similar results as the Markovian-based DPD if the system has clear time scale separation. However, for systems with small separation of time scales, NM-DPD can reproduce correct short-time properties that are related to how the system responds to high-frequency disturbances, which cannot be captured by the Markovian-based DPD model.},
doi = {10.1063/1.4935490},
url = {https://www.osti.gov/biblio/22493375}, journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 24,
volume = 143,
place = {United States},
year = {2015},
month = {12}
}

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  • Li, Xuejin; Peng, Zhangli; Lei, Huan
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 372, Issue 2021
  • https://doi.org/10.1098/rsta.2013.0389

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