Curvature model

Figure 8.18 Effect of cure temperature on dimensionless curvature [model and experimental results]...

It is impossible to determine the electron density distribution within the unit cell wid a resolution at the atomic scale. Hence there is no straightforward way of determining the exact structure. In summary the evidence for the zero average curvature model structure of cubic lipid-water phases then rests on ... 

It is hoped that lattice models - and membrane curvature models - will lead... 

Acosta, E., Szekeres, E., Sabatini, D.A. and Harwell, J.H. (2003) Net-average curvature model for solubilization and supersolubilization in surfactant microemulsion. Langmuir, 19, 186-195. 

Clavin [5] performed quasi-steady analysis of the direct initiation process. They developed the critical curvature model, which states that the failure mechanism of the detonation is mainly caused by the nonlinear curvature effect of the wave front. Eckett et al. [6] proposed the critical decay-rate model and pointed out that the critical mechanism of a failed detonation initiation process is due to the unsteadiness of the reacting flow. Their theory for spherical detonation initiation has been supported by numerical simulation and experimental data. 

According to the local curvature model used in predicting bond reactivities, the minor Cy-symmetrical diastereoisomeric pair (67/68) most probably results from malonate addition across the apical a-type bond C( 1) - C(6) intersected by... 

An alternative approach is the so-called spontaneous curvature model. 1 2,183 Here, the asymmetry between the two layers is taken into account as a modification on the mean curvature. In this case, the new bending energy is derived from Eq. [27] by changing H into hi + where the new... 

Papageorgiou and Orellana [53], attempt a regularization of the ill-posed leading order system of Ting and Keller by retention of higher order terms. Mathematically, this introduce a dispersive regularization to the equations and these are studies asymptotically and numerically. The details of the derivation as well as inclusion of a second annular phase in a tube, are given in [53]. We just state the systems of PDEs to be addressed and in particular two models to be compared (i) The asymptotic model, (ii) The full curvature model. These are... 

A subtle refutation of the simple spontaneous curvature model without the bilayer aspect follows from the observation of vesicles of non-spherical topology, i.e. vesicles with holes (like anchor rings) or with handles. For vesicles with at least two holes or handles, the shape of lowest total energy is not unique but rather one fold continuously degenerate due to conformal invariance. This theoretical finding led to the prediction that such vesicles should permanently change their shape, a phenomenon termed conformal diffusion [21], This was indeed verified experimentally somewhat later [22]. Apart from the esthetic pleasure when visualizing conformal transformations under the microscope, this observation also shows the spontaneous curvature model to be incomplete with out the additional term. 

Solvent-free models, triangulated surfaces and other discretized curvature models have the disadvantage that they do not contain a solvent, and therefore do not describe the hydrodynamic behavior correctly. However, this apparent disadvantage can be turned into an advantage by combining these models with a mesoscopic hydrodynamics technique. This approach has been employed for dynamically triangulated surfaces [37,180] and for meshless membrane models in combination with MPC [188], as well as for fixed membrane triangulations in combination with both MPC [187] and the LB method [189]. 

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