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8
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84927852012
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contains additional references.
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9
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84927852011
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H. G. Döbereiner, Ph.D. thesis, Simon Fraser University, 1995 (unpublished).
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22
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84927852009
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This paper treats v=0.70, 0.85, and 0.95 (only) but for a range of α.
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30
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84927852007
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(now: W. Wintz), Diplomarbeit, RWTH Aachen, 1993 (unpublished).
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Schnitzler, W.1
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32
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84927852005
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An irrelevant topological term associated with the local Gaussian curvature has been omitted.
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33
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84927852004
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The origin Δ A0 is the different number of lipid molecules in the inner and outer leaves of the bilayer and the fact that this difference relaxes slowly on mechanical time scales. See Ref. citeADE.
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34
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84927852003
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For a pure spontaneous curvature (SC) model with a reduced spontaneous curvature barc0, for which only the first term of Eq. ( refADE) occurs, it is easy to show that the variational equation takes the form [ δ F = kappa (δ G[S] 2 barc_0}δ m[S])=0. ] It follows immediately that the shape S that solves Eq. (11) is also a stationary shape of a pure spontaneous curvature model with spontaneous curvature [ barc_0= fracα{2( barm_0 m[S]). ]
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35
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84927852002
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Note from Ref. [30] that partial G(n)/ partial m is just twice the reduced spontaneous curvature barc0 of the corresponding SC model.
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36
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84927852001
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Reference [22] focuses on computing the thermal fluctuations and implements the constraints as strict delta functions inside the appropriate partition function. Here, we focus principally on the spectrum and are led to implement the constraint projections.
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39
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84927852000
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We follow the sign conventions of Ref. [22]. In Ref. [22], the stability matrix is denoted Sij.
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40
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84927851999
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In principle, the constraint space might turn out to be of dimension less than two, which would require minor modifications of what follows. In practice, this does not happen.
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41
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84927851998
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Note that this condition forces a particular choice of axes on shape experiments that would make contact with the theory.
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42
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0001636465
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Measure factors, tension, and correlations of fluid membranes
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The thermal shifts as given here might be modified, if nontrivial measure factors become relevant, such as the Liouville factor discussed in
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(1994)
Journal de Physique II
, vol.4
, pp. 931
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Cai, W.1
Lubensky, T.2
Nelson, P.3
Powers, T.4
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43
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84927851997
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See the comments in Appendix A of Ref. [22].
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44
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84927851996
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U. Seifert, Habilitation thesis, Ludwig Maximilians Universität München, 1995 (unpublished).
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47
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84927851995
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In such a situation, an extended stability diagram, showing the overlapping regions of local stability of the various coexisting shapes would still be useful, as would predictions of postinstability destinations.
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48
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84927851994
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Certain inferences are possible, based on the lines we do control. For example, as long as Mpro(m=s,l even) remains below (in barm0) the continuation of Dpro/obl (shown in Fig. 6) it must be higher in energy than W(obl ), so the phase boundary nas pro certainly cannot be second order for reduced volumes between this point and the CEP.
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49
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84927851993
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Note, of course, that in any nas phase these labels no longer apply.
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50
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84927851992
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An example is thermally induced budding out of the prolate phase, which commonly leads to a vesiculated shape rather than to one in the adjacent pear phase. See Refs. citeADE,thesis,Doeb95.
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51
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84927851991
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Note how Dnas/pro emerges from the CEP parallel to Dpro/obl because of the bifurcation structure at Mobl(m=2, l even), where W(obl )( barm0) and W(nas )( barm0) are locally parallel.
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52
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84927851990
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It is probably also valid beyond this region, except possibly for very high values of α, where the nonaxisymmetric region penetrates close to v=1. See Ref. [13].
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53
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84927851989
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Of course, α is in principle measurable in experiments like those of Ref. [40], so in this sense the theory is zero parameter. In practice, the difficulty in comparing theory and experiment is usually the fact that barm0 is not directly accessible to experiment. A technique for handling this difficulty is discussed in Ref. [8].
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