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A finite permeation rate could make the response of the system be sensitive to the increment of increase, and to the rate of increase, of the shear rate. However, even in such situations we expect our assumption of zero permeation rate to be correct under certain conditions, for instance, when the shear rate increment (increase) is large. In this case the buckling texture develops fast and relaxes very slowly (via permeation), which makes our analysis useful.
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38
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note
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This constraint breaks the rotational invariance even in the absence of shear. This is because even a simple (virtual) rotation away from the initial orientation (parallel to the walls) implies streching of the membranes if the area of projection on the walls (the geometrical projected area) and the total membrane area in each layer are not allowed to change. Note however that simple rotation of the whole phase is in fact not allowed because of the boundary conditions U(0) = U(D) = 0.
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