京都大学大学院理学研究科

物理学専攻

大学院講義

村瀬

雅俊

京都大学基礎物理学研究所

２００８年６月２３日

The model equation

The moment-balance equation for a flagellum is written by:

MS

+ ME

+ MV

= 0

where MS , ME

and MV

are the viscous, shear and elastic moments, respectively.

where S is the shear force, σ

is the shear, EB

is the bending resistance, CN

is theexternal viscous drag coefficient and γ

is the internal viscous drag coefficient.

See Appendix

Masatoshi Murase “The Dynamics of Cellular Motility” Wiley, 1992,p237

γ

>> CN

Masatoshi Murase “The Dynamics of Cellular Motility” Wiley, 1992,p237

γ

<< CN

Masatoshi Murase “The Dynamics of Cellular Motility” Wiley, 1992,p243

γ

<< CN

Masatoshi Murase “The Dynamics of Cellular Motility” Wiley, 1992, p248, 250

γ

>> CN γ

<< CN

Masatoshi Murase “The Dynamics of Cellular Motility” Wiley, 1992, p251

γ

>> CN γ

<< CN

Masatoshi Murase “The Dynamics of Cellular Motility” Wiley, 1992, p238

Masatoshi Murase “The Dynamics of Cellular Motility” Wiley, 1992, p239

Robert L. Solso “Dognition and the Visual Arts”MIT Press 1994

+

－－

Light

+

－－

Light

Light

From: J. M. T. Thompson and H. B. Stewart “Nonlinear Dynamics and Chaos” Wiley, 1986

Chemical Engineering ScienceVol. 41, No.11, p2747-2760 (1986)

Chemical Engineering ScienceVol. 41, No.11, p2747-2760 (1986)

Chemical Engineering ScienceVol. 41, No.11, p2747-2760 (1986)

Chemical Engineering ScienceVol. 41, No.11, p2747-2760 (1986)

Leon Glass and Michael C. MackeyFrom Clocks to Chaos: The Rhythms of LifePrinceton University Press (1988)

Leon Glass and Michael C. MackeyFrom Clocks to Chaos: The Rhythms of LifePrinceton University Press (1988)

Leon Glass and Michael C. MackeyFrom Clocks to Chaos: The Rhythms of LifePrinceton University Press (1988)

P. Berge, Y. Pomeauand C. Vidal“Order within Chaos”Wiley, 1984, p287

The loss of memory of initial conditions

Zero volume of attractor

P. Berge, Y. Pomeauand C. Vidal“Order within Chaos”Wiley, 1984, p112-113

Lie derivative:the relative rate of changeof a volume v

Loss of information: concerning the relative positions initially contained

P. Berge, Y. Pomeauand C. Vidal“Order within Chaos”Wiley, 1984, p115

P. Berge, Y. Pomeauand C. Vidal“Order within Chaos”Wiley, 1984, p116-117

P. Berge, Y. Pomeauand C. Vidal“Order within Chaos”Wiley, 1984, p119

The loss of memory of initial conditions

Creation of information:A set of imperceptibly different initial stateson the attractor lead to many final states.

P. Berge, Y. Pomeauand C. Vidal“Order within Chaos”Wiley, 1984, p120

P. Berge, Y. Pomeauand C. Vidal“Order within Chaos”Wiley, 1984, p122

P. Berge, Y. Pomeauand C. Vidal“Order within Chaos”Wiley, 1984, p121

P. Berge, Y. Pomeauand C. Vidal“Order within Chaos”Wiley, 1984, p124

The Lorenz attractor

P. Berge, Y. Pomeauand C. Vidal“Order within Chaos”Wiley, 1984, p125-126

Z = r － 1Lie derivative:the relative rate of changeof a volume v

P. Berge, Y. Pomeauand C. Vidal“Order within Chaos”Wiley, 1984, p127

dZ/dt = 0

XY － bZ = 0

P. Berge, Y. Pomeauand C. Vidal“Order within Chaos”Wiley, 1984, p128r = 28

r < 24.06

Leon Glass and Michael C. MackeyFrom Clocks to Chaos: The Rhythms of LifePrinceton University Press (1988)

dx/dt = 0y + z = 0