Stiffening of fluid membranes due to thermal undulations: density-matrix renormalization-group study

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Abstract

It has been considered that the effective bending rigidity of fluid membranes should be reduced by thermal undulations. However, recent thorough investigation by Pinnow and Helfrich revealed the significance of measure factors for the partition sum. Accepting the local curvature as a statistical measure, they found that fluid membranes are stiffened macroscopically. In order to examine this remarkable idea, we performed extensive ab initio simulations for a fluid membrane. We set up a transfer matrix that is diagonalized by means of the density-matrix renormalization group. Our method has an advantage, in that it allows us to survey various statistical measures. As a consequence, we found that the effective bending rigidity flows toward strong coupling under the choice of local curvature as a statistical measure. On the contrary, for other measures such as normal displacement and tilt angle, we found a clear tendency toward softening.

Original languageEnglish
Pages (from-to)61907
Number of pages1
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume66
Issue number6
Publication statusPublished - Dec 1 2002

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stiffening
Matrix Groups
Density Matrix
Renormalization Group
Membrane
Hot Temperature
membranes
Fluid
Membranes
fluids
rigidity
Rigidity
Curvature
curvature
Softening
Transfer Matrix
Strong Coupling
Tilt
softening
partitions

ASJC Scopus subject areas

  • Medicine(all)

Cite this

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abstract = "It has been considered that the effective bending rigidity of fluid membranes should be reduced by thermal undulations. However, recent thorough investigation by Pinnow and Helfrich revealed the significance of measure factors for the partition sum. Accepting the local curvature as a statistical measure, they found that fluid membranes are stiffened macroscopically. In order to examine this remarkable idea, we performed extensive ab initio simulations for a fluid membrane. We set up a transfer matrix that is diagonalized by means of the density-matrix renormalization group. Our method has an advantage, in that it allows us to survey various statistical measures. As a consequence, we found that the effective bending rigidity flows toward strong coupling under the choice of local curvature as a statistical measure. On the contrary, for other measures such as normal displacement and tilt angle, we found a clear tendency toward softening.",
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