Advertisement

The European Physical Journal Special Topics

, Volume 225, Issue 8–9, pp 1411–1421 | Cite as

A principle in dynamic coarse graining–Onsager principle and its applications

Regular Article Methodological Aspects of Coarse Graining
Part of the following topical collections:
  1. Modern Simulation Approaches in Soft Matter Science: From Fundamental Understanding to Industrial Applications

Abstract

Dynamic coarse graining is a procedure to map a dynamical system with large degrees of freedom to a system with smaller degrees of freedom by properly choosing coarse grained variables. This procedure has been conducted mainly by empiricisms. In this paper, I will discuss a theoretical principle which may be useful for this procedure. I will discuss how to choose coarse grained variables (or slow variables), and how to set up their evolution equations. To this end, I will review the classical example of dynamic coarse graining, i.e., the Brownian motion theory, and show a variational principle for the evolution of the slow variables. The principle, called the Onsager principle, is useful not only to derive the evolution equations, but also to solve the problems.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. Fritz, K. Koschke, V.A. Harmandaris, V. van der, F.A. Nico, K. Kremer, Phys. Chem. Phys. 13, 10412 (2011)CrossRefGoogle Scholar
  2. 2.
    R. Potestio, C. Peter, K. Kremer, Entropy 16, 4199 (2014)ADSCrossRefGoogle Scholar
  3. 3.
    M. Jochum, D. Andrienko, K. Kremer, J. Chem. Phys. 137  10.1063/1.4742067 2012
  4. 4.
    S. Fritsch, S. Poblete, C. Junghans, G. Ciccotti, L. Delle Site, K. Kremer, Phys. Rev. Lett. 108 (2012)Google Scholar
  5. 5.
    R. Potestio, S. Fritsch, P. Espanol, R. Delgado-Buscalioni, K. Kremer, R. Everaers, D. Donadio, Phys. Rev. Lett. 110, 110.108301 (2013)Google Scholar
  6. 6.
    J.A. de la Torre, P. Espanol, A. Donev, J. Chem. Phys. 142, 094115 (2015)ADSCrossRefGoogle Scholar
  7. 7.
    L. Onsager, Phys. Rev. 37, 405 (1931)ADSCrossRefGoogle Scholar
  8. 8.
    L. Onsager, Phys. Rev. 38, 2265 (1931)ADSCrossRefGoogle Scholar
  9. 9.
    M. Doi, Soft Matter Physics (Oxford University Press, 2013)Google Scholar
  10. 10.
    M. Doi, M. Masato, Phys. Fluid 17, 043601 (2005)ADSCrossRefGoogle Scholar
  11. 11.
    M. Brian, T.A. Witten, Phys. Rev. Lett. 110, 028301 (2012), doi:  10.1103/PhysRevLett.110.028301 Google Scholar
  12. 12.
    M. Doi, Onsager's Variational Principle in Soft Matter Dynamics, in Non-Equilibrium Soft Matter Physics, edited by S. Komura, T. Ohta (World Scientific, 2012), p. 1Google Scholar
  13. 13.
    A.N. Beris, Rheol. Rev., 37 (2003)Google Scholar
  14. 14.
    H.C. Ottinger, Beyond Equilibrium Thermodynamics (Wiley, 2005)Google Scholar
  15. 15.
    J. Happel, H. Brenner, Low Reynolds Number Hydrodynamics (Kluwer, 1963)Google Scholar
  16. 16.
    L.D. Landau, E.M. Lifshitz, Mechanics (Butterworth-Heinemann, 1982)Google Scholar
  17. 17.
    M. Doi, Chin. Phys. B. 24, 020505 1–6 (2015)CrossRefGoogle Scholar
  18. 18.
    X. Man, M. Doi, Phys. Rev. Lett. 116, 066101 (2016)ADSCrossRefGoogle Scholar
  19. 19.
    Y. Di, X. Xu, M. Doi, EPL 113, 36001 (2016)ADSCrossRefGoogle Scholar
  20. 20.
    X. Xu, Y. Di, M. Doi, “Variational method for contact line problems in sliding liquids”, Phys. Fluids (submitted)Google Scholar
  21. 21.
    F. Meng, L. Luo, M. Doi, Z. Ouyang, Eur. Phys. J. E 39, 22 (2016)CrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2016

Authors and Affiliations

  • M. Doi
    • 1
  1. 1.Center of Soft Matter Physics and its Applications, Beihang UniversityBeijingChina

Personalised recommendations