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For a comprehensive review of physics of biomembranes refer to Structure and Dynamics of Membranes: From Cells to Vesicles; Generic and Specific Interactions, Vol. 1A-B of Handbook of Biological Physics, edited by R. Lipowsky and E. Sackmann (North-Holland, Amsterdam, 1995).
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The numerical prefactor [Formula Presented] in Eq. (3) is chosen merely for the convenience of normalization regarding Eq. (6)
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The numerical prefactor 1/2 in Eq. (3) is chosen merely for the convenience of normalization regarding Eq. (6).
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D. Andelman, in Structure and Dynamics of Membranes: From Cells to Vesicles; Generic and Specific Interactions (Ref. 1), Chap. 12
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85036165934
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fact, [Formula Presented], where [Formula Presented] is a unity operator, form an Abelian group
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In fact, I,O1,O2,O3, where I is a unity operator, form an Abelian group.
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43
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85036222045
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this paper, the phase diagrams are given when the two control parameters are chosen to be either [Formula Presented] or [Formula Presented]. However, the phase diagrams have also been calculated in the parameter space spanned by [Formula Presented], for [Formula Presented] and different (fixed) values of [Formula Presented] those phase diagrams have been presented in Ref. c35
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In this paper, the phase diagrams are given when the two control parameters are chosen to be either (tΔ,γ12) or (tΔ,μ). However, the phase diagrams have also been calculated in the parameter space spanned by (tΔ,σ¯0), for μ=0 and different (fixed) values of γ12; those phase diagrams have been presented in Ref. 35.
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L. Miao, P. L. Hansen, and J. H. Ipsen, in Dynamical Networks in Physics and Biology, edited by. D. Beysens and G. Forgać (Springer, New York, in press)
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85036175984
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It follows from Eqs. (121314) that the two effective parameters resulted from [Formula Presented] [Formula Presented] [Formula Presented] are [Formula Presented] [Formula Presented]
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It follows from Eqs. (121314) that the two effective parameters resulted from σ¯0, κ, and C0 are ξc-2 and λsc-2.
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46
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85036295196
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It is likely that more types of modulated structures would appear as equilibrium states, if the ansatz is made more sophisticated to include modes of higher multiples of the wave number [Formula Presented]
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It is likely that more types of modulated structures would appear as equilibrium states, if the ansatz is made more sophisticated to include modes of higher multiples of the wave number q0.
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49
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85036299804
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The small-[Formula Presented] expansion implies that [Formula Presented]
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The small-q expansion implies that q≪λsc-1.
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