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 »
- Authors:
-
- Brown Univ., Providence, RI (United States)
- 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}
}
Web of Science
Works referenced in this record:
Microscopic theory of Brownian motion revisited: The Rayleigh model
journal, March 2013
- Kim, Changho; Karniadakis, George Em
- Physical Review E, Vol. 87, Issue 3
Mori–Zwanzig formalism as a practical computational tool
journal, January 2010
- Hijón, Carmen; Español, Pep; Vanden-Eijnden, Eric
- Faraday Discuss., Vol. 144
Energy-conserving dissipative particle dynamics with temperature-dependent properties
journal, May 2014
- Li, Zhen; Tang, Yu-Hang; Lei, Huan
- Journal of Computational Physics, Vol. 265
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
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
Improving efficiency of large time-scale molecular dynamics simulations of hydrogen-rich systems
journal, June 1999
- Feenstra, K. Anton; Hess, Berk; Berendsen, Herman J. C.
- Journal of Computational Chemistry, Vol. 20, Issue 8
Statistical Mechanics of Dissipative Particle Dynamics
journal, May 1995
- Español, P.; Warren, P.
- Europhysics Letters (EPL), Vol. 30, Issue 4
Rheology, Microstructure and Migration in Brownian Colloidal Suspensions
journal, January 2010
- Pan, Wenxiao; Caswell, Bruce; Karniadakis, George Em
- Langmuir, Vol. 26, Issue 1
Dissipative particle dynamics with energy conservation
journal, December 1997
- Español, P.
- Europhysics Letters (EPL), Vol. 40, Issue 6
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
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
Globalized Nelder–Mead method for engineering optimization
journal, September 2004
- Luersen, Marco A.; Le Riche, Rodolphe
- Computers & Structures, Vol. 82, Issue 23-26
Interatomic Potentials from First-Principles Calculations: The Force-Matching Method
journal, June 1994
- Ercolessi, F.; Adams, J. B.
- Europhysics Letters (EPL), Vol. 26, Issue 8
Equation of motion for coarse-grained simulation based on microscopic description
journal, May 2007
- Kinjo, Tomoyuki; Hyodo, Shi-aki
- Physical Review E, Vol. 75, Issue 5
Hydrodynamics from dissipative particle dynamics
journal, August 1995
- Español, Pep
- Physical Review E, Vol. 52, Issue 2
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
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
Effective Interaction between Star Polymers
journal, June 1999
- Jusufi, A.; Watzlawek, M.; Löwen, H.
- Macromolecules, Vol. 32, Issue 13
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
Mesoscale modeling: solving complex flows in biology and biotechnology
journal, July 2013
- Mills, Zachary Grant; Mao, Wenbin; Alexeev, Alexander
- Trends in Biotechnology, Vol. 31, Issue 7
Coarse-Graining Methods for Computational Biology
journal, May 2013
- Saunders, Marissa G.; Voth, Gregory A.
- Annual Review of Biophysics, Vol. 42, Issue 1
Canonical dynamics: Equilibrium phase-space distributions
journal, March 1985
- Hoover, William G.
- Physical Review A, Vol. 31, Issue 3
Transport, Collective Motion, and Brownian Motion
journal, March 1965
- Mori, Hazime
- Progress of Theoretical Physics, Vol. 33, Issue 3
Perspective: Coarse-grained models for biomolecular systems
journal, September 2013
- Noid, W. G.
- The Journal of Chemical Physics, Vol. 139, Issue 9
Direct construction of mesoscopic models from microscopic simulations
journal, February 2010
- Lei, Huan; Caswell, Bruce; Karniadakis, George Em
- Physical Review E, Vol. 81, Issue 2
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
Dissipative particle dynamics for a harmonic chain: A first-principles derivation
journal, February 1996
- Español, Pep
- Physical Review E, Vol. 53, Issue 2
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
Bottom-up construction of interaction models of non-Markovian dissipative particle dynamics
journal, October 2013
- Yoshimoto, Yuta; Kinefuchi, Ikuya; Mima, Toshiki
- Physical Review E, Vol. 88, Issue 4
Optimal prediction with memory
journal, June 2002
- Chorin, Alexandre J.; Hald, Ole H.; Kupferman, Raz
- Physica D: Nonlinear Phenomena, Vol. 166, Issue 3-4
A unified formulation of the constant temperature molecular dynamics methods
journal, July 1984
- Nosé, Shuichi
- The Journal of Chemical Physics, Vol. 81, Issue 1
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
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
The fluctuation-dissipation theorem
journal, January 1966
- Kubo, R.
- Reports on Progress in Physics, Vol. 29, Issue 1
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
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
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
Amorphization-induced surface electronic states modulation of cobaltous oxide nanosheets for lithium-sulfur batteries
journal, May 2021
- Li, Ruilong; Rao, Dewei; Zhou, Jianbin
- Nature Communications, Vol. 12, Issue 1
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
Interatomic potentials from first-principles calculations: the force-matching method
text, January 1993
- Ercolessi, Furio; Adams, James B.
- arXiv
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
A note on hydrodynamics from dissipative particle dynamics
journal, December 2017
- Bian, X.; Li, Z.; Adams, N. A.
- Applied Mathematics and Mechanics, Vol. 39, Issue 1
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
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
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
A comparative study of coarse-graining methods for polymeric fluids: Mori-Zwanzig vs. iterative Boltzmann inversion vs. stochastic parametric optimization
journal, July 2016
- Li, Zhen; Bian, Xin; Yang, Xiu
- The Journal of Chemical Physics, Vol. 145, Issue 4
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
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
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
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
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
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
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
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
Atomic theory of viscoelastic response and memory effects in metallic glasses
journal, September 2017
- Cui, Bingyu; Yang, Jie; Qiao, Jichao
- Physical Review B, Vol. 96, Issue 9
Long-time persistence of hydrodynamic memory boosts microparticle transport
journal, October 2019
- Seyler, Sean L.; Pressé, Steve
- Physical Review Research, Vol. 1, Issue 3
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
Molecular Dynamics Simulation of High Density DNA Arrays
journal, January 2018
- Podgornik, Rudolf; Zavadlav, Julija; Praprotnik, Matej
- Computation, Vol. 6, Issue 1
Recent Progress towards Chemically-Specific Coarse-Grained Simulation Models with Consistent Dynamical Properties
journal, August 2019
- Rudzinski, Joseph F.
- Computation, Vol. 7, Issue 3
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
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
Long-time persistence of hydrodynamic memory boosts microparticle transport
preprint, June 2019
- Seyler, Sean L.; Pressé, Steve
Data-driven parameterization of the generalized Langevin equation
preprint, January 2016
- Lei, Huan; Baker, Nathan; Li, Xiantao
- arXiv
Non-Markovian Closure Models for Large Eddy Simulations using the Mori-Zwanzig Formalism
text, January 2016
- Parish, Eric J.; Duraisamy, Karthik
- arXiv
Parameterization of Coarse-grained Molecular Interactions through Potential of Mean Force Calculations and Cluster Expansions Techniques
text, January 2016
- Tsourtis, Anastasios; Harmandaris, Vagelis; Tsagkarogiannis, Dimitrios
- arXiv
Recent progress towards chemically-specific coarse-grained simulation models with consistent dynamical properties
preprint, January 2019
- Rudzinski, Joseph F.
- arXiv