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An analysis of lipid membrane morphology in the presence of coordinate-dependent non-uniformity. (English) Zbl 1486.74091

Summary: A model for the mechanics of lipid membranes with non-uniform (coordinate-dependent) properties is discussed. The coordinate-dependent responses of the membranes are incorporated via the augmented non-uniform energy function and material parameters, which are dependent explicitly on the surface coordinates. We formulate the associated normal and tangential Euler equilibrium equations through which the coordinate-dependent responses of membranes are characterized. The admissible boundary conditions are taken from the existing non-linear model but reformulated and adopted to the present framework. Within the prescription of superposed incremental deformations, a compatible linear model is also formulated, from which a complete analytical solution describing the non-uniform responses of the membrane subjected to substrate-membrane interactions is obtained.

MSC:

74K15 Membranes
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