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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 presents 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. Yet, 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. In contrast, for systems with small separation of time scales, NM-DPD can reproduce correct short-time properties thatmore » are related to how the system responds to high-frequency disturbances, which cannot be captured by the Markovian-based DPD model.« less

Authors:
ORCiD logo [1]; ORCiD logo [1];  [2];  [1]
  1. Brown Univ., Providence, RI (United States)
  2. Pennsylvania State Univ., University Park, PA (United States)
Publication Date:
Research Org.:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1565466
Alternate Identifier(s):
OSTI ID: 1225984
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 143; Journal Issue: 24; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Li, Zhen, Bian, Xin, Li, Xiantao, and Karniadakis, George Em. 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, Li, Xiantao, & Karniadakis, George Em. 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, Li, Xiantao, and Karniadakis, George Em. Fri . "Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism". United States. https://doi.org/10.1063/1.4935490. https://www.osti.gov/servlets/purl/1565466.
@article{osti_1565466,
title = {Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism},
author = {Li, Zhen and Bian, Xin and Li, Xiantao and Karniadakis, George Em},
abstractNote = {The Mori-Zwanzig formalism for coarse-graining a complex dynamical system typically presents 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. Yet, 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. In contrast, 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},
journal = {Journal of Chemical Physics},
number = 24,
volume = 143,
place = {United States},
year = {Fri Nov 13 00:00:00 EST 2015},
month = {Fri Nov 13 00:00:00 EST 2015}
}

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Works referenced in this record:

Microscopic theory of Brownian motion revisited: The Rayleigh model
journal, March 2013


Mori–Zwanzig formalism as a practical computational tool
journal, January 2010

  • Hijón, Carmen; Español, Pep; Vanden-Eijnden, Eric
  • Faraday Discuss., Vol. 144
  • DOI: 10.1039/B902479B

Energy-conserving dissipative particle dynamics with temperature-dependent properties
journal, May 2014


Frontiers in Molecular Dynamics Simulations of DNA
journal, August 2011

  • Pérez, Alberto; Luque, F. Javier; Orozco, Modesto
  • Accounts of Chemical Research, Vol. 45, Issue 2
  • DOI: 10.1021/ar2001217

Mesoscale modeling of phase transition dynamics of thermoresponsive polymers
journal, January 2015

  • Li, Zhen; Tang, Yu-Hang; Li, Xuejin
  • Chemical Communications, Vol. 51, Issue 55
  • DOI: 10.1039/C5CC01684C

Improving efficiency of large time-scale molecular dynamics simulations of hydrogen-rich systems
journal, June 1999


Statistical Mechanics of Dissipative Particle Dynamics
journal, May 1995


Rheology, Microstructure and Migration in Brownian Colloidal Suspensions
journal, January 2010

  • Pan, Wenxiao; Caswell, Bruce; Karniadakis, George Em
  • Langmuir, Vol. 26, Issue 1
  • DOI: 10.1021/la902205x

Dissipative particle dynamics with energy conservation
journal, December 1997


A coarse-grained molecular dynamics model for crystalline solids
journal, August 2010

  • Li, Xiantao
  • International Journal for Numerical Methods in Engineering, Vol. 83, Issue 8-9
  • DOI: 10.1002/nme.2892

Role of Repulsive Forces in Determining the Equilibrium Structure of Simple Liquids
journal, June 1971

  • Weeks, John D.; Chandler, David; Andersen, Hans C.
  • The Journal of Chemical Physics, Vol. 54, Issue 12
  • DOI: 10.1063/1.1674820

Globalized Nelder–Mead method for engineering optimization
journal, September 2004


Interatomic Potentials from First-Principles Calculations: The Force-Matching Method
journal, June 1994


Equation of motion for coarse-grained simulation based on microscopic description
journal, May 2007


Hydrodynamics from dissipative particle dynamics
journal, August 1995


A Multiscale Coarse-Graining Method for Biomolecular Systems
journal, February 2005

  • Izvekov, Sergei; Voth, Gregory A.
  • The Journal of Physical Chemistry B, Vol. 109, Issue 7
  • DOI: 10.1021/jp044629q

Discrete approach to stochastic parametrization and dimension reduction in nonlinear dynamics
journal, July 2015

  • Chorin, Alexandre J.; Lu, Fei
  • Proceedings of the National Academy of Sciences, Vol. 112, Issue 32
  • DOI: 10.1073/pnas.1512080112

Effective Interaction between Star Polymers
journal, June 1999

  • Jusufi, A.; Watzlawek, M.; Löwen, H.
  • Macromolecules, Vol. 32, Issue 13
  • DOI: 10.1021/ma981844u

Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation
journal, September 1997

  • Groot, Robert D.; Warren, Patrick B.
  • The Journal of Chemical Physics, Vol. 107, Issue 11
  • DOI: 10.1063/1.474784

Mesoscale modeling: solving complex flows in biology and biotechnology
journal, July 2013


Coarse-Graining Methods for Computational Biology
journal, May 2013


Fluid particle model
journal, March 1998


Canonical dynamics: Equilibrium phase-space distributions
journal, March 1985


Transport, Collective Motion, and Brownian Motion
journal, March 1965


Perspective: Coarse-grained models for biomolecular systems
journal, September 2013

  • Noid, W. G.
  • The Journal of Chemical Physics, Vol. 139, Issue 9
  • DOI: 10.1063/1.4818908

Direct construction of mesoscopic models from microscopic simulations
journal, February 2010


Construction of dissipative particle dynamics models for complex fluids via the Mori–Zwanzig formulation
journal, January 2014

  • Li, Zhen; Bian, Xin; Caswell, Bruce
  • Soft Matter, Vol. 10, Issue 43
  • DOI: 10.1039/C4SM01387E

Dissipative particle dynamics for a harmonic chain: A first-principles derivation
journal, February 1996


Direct Molecular Dynamics Simulation of Branch Point Motion in Asymmetric Star Polymer Melts
journal, May 2007

  • Zhou, Qiang; Larson, Ronald G.
  • Macromolecules, Vol. 40, Issue 9
  • DOI: 10.1021/ma070072b

Bottom-up construction of interaction models of non-Markovian dissipative particle dynamics
journal, October 2013


Optimal prediction with memory
journal, June 2002


A unified formulation of the constant temperature molecular dynamics methods
journal, July 1984

  • Nosé, Shuichi
  • The Journal of Chemical Physics, Vol. 81, Issue 1
  • DOI: 10.1063/1.447334

Deriving effective mesoscale potentials from atomistic simulations: Mesoscale Potentials from Atomistic Simulations
journal, August 2003

  • Reith, Dirk; Pütz, Mathias; Müller-Plathe, Florian
  • Journal of Computational Chemistry, Vol. 24, Issue 13
  • DOI: 10.1002/jcc.10307

Computing generalized Langevin equations and generalized Fokker-Planck equations
journal, June 2009

  • Darve, E.; Solomon, J.; Kia, A.
  • Proceedings of the National Academy of Sciences, Vol. 106, Issue 27
  • DOI: 10.1073/pnas.0902633106

The fluctuation-dissipation theorem
journal, January 1966


Dynamics of entangled linear polymer melts:  A molecular‐dynamics simulation
journal, April 1990

  • Kremer, Kurt; Grest, Gary S.
  • The Journal of Chemical Physics, Vol. 92, Issue 8
  • DOI: 10.1063/1.458541

Transport dissipative particle dynamics model for mesoscopic advection-diffusion-reaction problems
journal, July 2015

  • Li, Zhen; Yazdani, Alireza; Tartakovsky, Alexandre
  • The Journal of Chemical Physics, Vol. 143, Issue 1
  • DOI: 10.1063/1.4923254

Probing red blood cell mechanics, rheology and dynamics with a two-component multi-scale model
journal, August 2014

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

Fluid Particle Model
book, January 2008


Amorphization-induced surface electronic states modulation of cobaltous oxide nanosheets for lithium-sulfur batteries
journal, May 2021


Globalized Nelder-Mead Method for Engineering Optimization
conference, September 2002

  • Luersen, M. A.; Le Riche, R.
  • The Third International Conference on Engineering Computational Technology, Civil-Comp Proceedings
  • DOI: 10.4203/ccp.76.65

Works referencing / citing this record:

Functional Macromolecular Systems: Kinetic Pathways to Obtain Tailored Structures
journal, November 2018

  • Abetz, Volker; Kremer, Kurt; Müller, Marcus
  • Macromolecular Chemistry and Physics, Vol. 220, Issue 2
  • DOI: 10.1002/macp.201800334

A note on hydrodynamics from dissipative particle dynamics
journal, December 2017


Generalized Langevin dynamics: construction and numerical integration of non-Markovian particle-based models
journal, January 2018

  • Jung, Gerhard; Hanke, Martin; Schmid, Friederike
  • Soft Matter, Vol. 14, Issue 46
  • DOI: 10.1039/c8sm01817k

Generalised dissipative particle dynamics with energy conservation: density- and temperature-dependent potentials
journal, January 2019

  • Avalos, Josep Bonet; Lísal, Martin; Larentzos, James P.
  • Physical Chemistry Chemical Physics, Vol. 21, Issue 45
  • DOI: 10.1039/c9cp04404c

Numerical approximation and fast evaluation of the overdamped generalized Langevin equation with fractional noise
journal, February 2020

  • Fang, Di; Li, Lei
  • ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 54, Issue 2
  • DOI: 10.1051/m2an/2019067

The relative entropy is fundamental to adaptive resolution simulations
journal, July 2016

  • Kreis, Karsten; Potestio, Raffaello
  • The Journal of Chemical Physics, Vol. 145, Issue 4
  • DOI: 10.1063/1.4959169

Computing the non-Markovian coarse-grained interactions derived from the Mori–Zwanzig formalism in molecular systems: Application to polymer melts
journal, January 2017

  • Li, Zhen; Lee, Hee Sun; Darve, Eric
  • The Journal of Chemical Physics, Vol. 146, Issue 1
  • DOI: 10.1063/1.4973347

Adaptive resolution simulations coupling atomistic water to dissipative particle dynamics
journal, September 2017

  • Zavadlav, Julija; Praprotnik, Matej
  • The Journal of Chemical Physics, Vol. 147, Issue 11
  • DOI: 10.1063/1.4986916

Memory-induced acceleration and slowdown of barrier crossing
journal, January 2018

  • Kappler, Julian; Daldrop, Jan O.; Brünig, Florian N.
  • The Journal of Chemical Physics, Vol. 148, Issue 1
  • DOI: 10.1063/1.4998239

Mesoscopic coarse-grained representations of fluids rigorously derived from atomistic models
journal, July 2018

  • Han, Yining; Dama, James F.; Voth, Gregory A.
  • The Journal of Chemical Physics, Vol. 149, Issue 4
  • DOI: 10.1063/1.5039738

The multi-dimensional generalized Langevin equation for conformational motion of proteins
journal, May 2019

  • Lee, Hee Sun; Ahn, Surl-Hee; Darve, Eric F.
  • The Journal of Chemical Physics, Vol. 150, Issue 17
  • DOI: 10.1063/1.5055573

Bottom-up approach to represent dynamic properties in coarse-grained molecular simulations
journal, December 2018

  • Deichmann, Gregor; van der Vegt, Nico F. A.
  • The Journal of Chemical Physics, Vol. 149, Issue 24
  • DOI: 10.1063/1.5064369

Data-driven parameterization of the generalized Langevin equation
journal, November 2016

  • Lei, Huan; Baker, Nathan A.; Li, Xiantao
  • Proceedings of the National Academy of Sciences, Vol. 113, Issue 50
  • DOI: 10.1073/pnas.1609587113

Atomic theory of viscoelastic response and memory effects in metallic glasses
journal, September 2017


Long-time persistence of hydrodynamic memory boosts microparticle transport
journal, October 2019


Parametrizing coarse grained models for molecular systems at equilibrium
journal, October 2016

  • Kalligiannaki, E.; Chazirakis, A.; Tsourtis, A.
  • The European Physical Journal Special Topics, Vol. 225, Issue 8-9
  • DOI: 10.1140/epjst/e2016-60145-x

Molecular Dynamics Simulation of High Density DNA Arrays
journal, January 2018


Parameterization of Coarse-Grained Molecular Interactions through Potential of Mean Force Calculations and Cluster Expansion Techniques
journal, August 2017

  • Tsourtis, Anastasios; Harmandaris, Vagelis; Tsagkarogiannis, Dimitrios
  • Entropy, Vol. 19, Issue 8
  • DOI: 10.3390/e19080395

Atomic theory of viscoelastic response and memory effects in metallic glasses
text, January 2017

  • Cui, Bingyu; Yang, J.; Qiao, J.
  • Apollo - University of Cambridge Repository
  • DOI: 10.17863/cam.17006

Data-driven parameterization of the generalized Langevin equation
preprint, January 2016