Continuum theory of a moving membrane

Dan Hu, Pingwen Zhang, Weinan E

    Research output: Contribution to journalArticle

    Abstract

    We derive a set of equations for the dynamics of evolving fluid membranes, such as cell membranes, in the presence of bulk fluids. We model the membrane as a surface endowed with a director field, which describes the local average orientation of the molecules on the membrane. A model for the elastic energy of a surface endowed with a director field is derived using liquid crystal theory. This elastic energy reduces to the well-known Helfrich energy in the limit when the directors are constrained to be normal to the surface. We then derive the full dynamic equations for the membrane that incorporate both the elastic and viscous effects, with and without the presence of bulk fluids. We also consider the effect of local spontaneous curvature, arising from the presence of membrane proteins. Overall, the systems of equations allow us to carry out stable, accurate, and robust numerical modeling for the dynamics of the membranes.

    Original languageEnglish (US)
    Article number041605
    JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
    Volume75
    Issue number4
    DOIs
    StatePublished - Apr 26 2007

    Fingerprint

    Continuum
    Membrane
    membranes
    continuums
    Fluid
    fluids
    Energy
    Membrane Protein
    Numerical Modeling
    Dynamic Equation
    Liquid Crystal
    System of equations
    energy
    Curvature
    liquid crystals
    curvature
    Molecules
    proteins
    Cell
    Model

    ASJC Scopus subject areas

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

    Cite this

    Continuum theory of a moving membrane. / Hu, Dan; Zhang, Pingwen; E, Weinan.

    In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 75, No. 4, 041605, 26.04.2007.

    Research output: Contribution to journalArticle

    Hu, Dan ; Zhang, Pingwen ; E, Weinan. / Continuum theory of a moving membrane. In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2007 ; Vol. 75, No. 4.
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