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Dynamics of semi-flexible tethered sheets

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Abstract

The dynamics of a semi-flexible sheet or tethered membrane in a solvent is studied using the method of stochastic rotation dynamics. Hydrodynamic interactions between different parts of the sheet are naturally included in this method. We confirm the scaling law for the radius of gyration versus sheet size predicted for a self-avoiding tethered membrane. The mean-square displacement shows both sub-diffusive and diffusive behavior similar to linear polymers. In the intermediate scattering function the sub-diffusive behavior appears as stretched exponential which we reproduce in our simulations. Thereby, we confirm an early prediction between the roughness and the sub-diffusion exponent derived from Zimm dynamics (E. Frey, D.R. Nelson, J. Phys. I 1, 1715 (1991)). Finally, we show that the diffusion coefficient of the square sheet is inversely proportional to the edge length of the sheet again in good agreement with theoretical predictions.