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- W2099122372 abstract "Thin elastic surfaces containing molecules influencing the mechanical properties of the surface itself are wide spreaded structures of dierent scales in biological systems. Prominent examples are bilayer membranes and cell tissues. In this paper we present a continuous dynamical model of deforming lateral inhomogeneous surfaces, using the example of biological membranes. In agreement with experimental observations the membrane consists of different molecule species undergoing lateral phase separation and influencing the mechanical properties of the membrane. The presented model is based on the minimization of a free energy leading to a coupled nonlinear PDE system of fourth order, related to the Willmore flow and the Cahn-Hilliard equation. First simulations show the development of budding structures from stochastic initial conditions as a result of the gradient flow, which is comparable to experimentally observed structures. In our model mechanical properties are described via macroscopic mechanical moduli. However, the qualitative and quantitative relationships of mechanical moduli and the local composition of the membrane are unkown. Since the exact relationship significantly influences the emerging structures, this study motivates the development of techniques allowing for upscaling from the molecular scale." @default.
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- W2099122372 date "2011-01-01" @default.
- W2099122372 modified "2023-09-27" @default.
- W2099122372 title "A continuous mechanobiological model of lateral inhomogeneous biological surfaces" @default.
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