Numerical treatment of the dynamics of a conserved order parameter in the presence of walls

Jun Ichi Fukuda, Makoto Yoneya, Hiroshi Yokoyama

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

We discuss how the diffusive dynamics of a conserved order parameter should be numerically treated when impenetrable wall surfaces are present and interact with the degrees of freedom characterized by the order parameter. We derive the discretization scheme for the dynamics, paying particular attention to the conservation of the order parameter in the strict numerical sense. The discretized chemical potential, or the functional derivative of the free energy, contains a surface contribution inversely proportional to the grid spacing Δz, which was proposed heuristically in a recent paper of Henderson and Clarke [Macromol. Theory Simul. 14, 435 (2005)]. Although apparently that surface contribution diverges in the continuum limit Δz→0, we can show, by an analytic argument and numerical calculations, that this divergence does not yield any anomalies, and that our discretization scheme is well defined in this limit. We also discuss the correspondence of our treatment to the model proposed by Puri and Binder [Phys. Rev. A 46, R4487 (1992)] extensively used for the present problem.

Original languageEnglish
Article number066706
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume73
Issue number6
DOIs
Publication statusPublished - Jun 30 2006
Externally publishedYes

Fingerprint

Order Parameter
Discretization Scheme
Continuum Limit
Chemical Potential
Diverge
Numerical Calculation
Spacing
Anomaly
Well-defined
Conservation
conservation
Free Energy
Divergence
divergence
Correspondence
degrees of freedom
Degree of freedom
Directly proportional
free energy
grids

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Numerical treatment of the dynamics of a conserved order parameter in the presence of walls. / Fukuda, Jun Ichi; Yoneya, Makoto; Yokoyama, Hiroshi.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 73, No. 6, 066706, 30.06.2006.

Research output: Contribution to journalArticle

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