### 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 language | English |
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Pages (from-to) | 61907 |

Number of pages | 1 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 66 |

Issue number | 6 |

Publication status | Published - Dec 1 2002 |

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### ASJC Scopus subject areas

- Medicine(all)

### Cite this

**Stiffening of fluid membranes due to thermal undulations : density-matrix renormalization-group study.** / Nishiyama, Yoshihiro.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Stiffening of fluid membranes due to thermal undulations

T2 - density-matrix renormalization-group study

AU - Nishiyama, Yoshihiro

PY - 2002/12/1

Y1 - 2002/12/1

N2 - 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.

AB - 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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M3 - Article

C2 - 12513318

AN - SCOPUS:84930067962

VL - 66

SP - 61907

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 6

ER -