Shear, first-order fluctuations

Since this is still a differential equation, albeit in the variable qy, a simple interpretation is not straightforward. Hence it is necessary to consider the time dependence of Eq. 38, which can be foimd using the method of characteristics. Through a transformation of variables, a first-order partial differential equation is converted into a first-order ordinary differential equation, which can then be solved using standard techniques. Due to the usefulness of this method for solving equations describing coupled shear flow and concentration fluctuation dynamics, it is worth briefly outlining the ideas. If we introduce a variable, t, such that. 

The assumption of membrane softness is supported by a theoretical argument of Nelson et al., who showed that a flexible membrane cannot have crystalline order in thermal equilibrium at nonzero temperature, because thermal fluctuations induce dislocations, which destroy this order on long length scales.188 189 The assumption is also supported by two types of experimental evidence for diacetylenic lipid tubules. First, Treanor and Pace found a distinct fluid character in NMR and electron spin resonance experiments on lipid tubules.190 Second, Brandow et al. found that tubule membranes can flow to seal up cuts from an atomic force microscope tip, suggesting that the membrane has no shear modulus on experimental time scales.191 However, conflicting evidence comes from X-ray and electron diffraction experiments on diacetylenic lipid tubules. These experiments found sharp diffraction peaks, which indicate crystalline order in tubule membranes, at least over the length scales probed by the diffraction techniques.123,192 193... 

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