Quick Search:
Prog. Theor. Phys. Vol. 48 No. 5 (1972) pp. 1451-1467
Development of Coherent Macroscopic Motion from Systems of Brownian Particles
Hiroshi Shimizu
Department of Biology, Faculty of Science, Kyushu University, Fukuoka 812
(Received March 13, 1972)
Abstract:
A stochastic theory of self-organization process of coherent macroscopic motion from system of Brownian particles is presented, starting with a set of coupled Langevin equations for the particles in potential that is not able to yield the macroscopic motion alone without interactions among the particles. A non-linear Fokker-Planck equation describing the self-organization processes is derived by utilizing the averaged field approximation. The Fokker-Planck equation is then discussed by using linear approximation. Instead of solving the Fokker-Planck equation except in a simple example, mechanochemical conversion is conveniently discussed by means of phenomenological equation in the velocity space by deriving the equation of motion from the Langevin equation. Hill's empirical equation that describes the dynamics of muscle contraction is easily obtained.
URL :
http://ptp.ipap.jp/link?PTP/48/1451/
DOI : 10.1143/PTP.48.1451
References:
-
P. Glansdorff and I. Prigogine, Physica 30 (1964), 351[CrossRef].
- P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations (John Wiley & Sons Ltd., New York, 1971), Chap. IX.
-
H. Shimizu, J. Phys. Soc. Jpn. 32 (1972), 1323[JPSJ]; Protein, Nucleic Acid and Enzyme 15 (1970), 1288 (in Japanese).
- H. Haken, Z. Phys. 219 (1969), 411.
-
B. Robertson and W. C. Mitchell, J. Math. Phys. 12 (1971), 563[CrossRef].
-
F. Haake, Phys. Rev. A 3 (1971), 1723[APS].
- H. Mori, Prog. Theor. Phys. 33 (1965), 423[PTP].
- S. Glasstone, K. J. Laider and H. Eyring, The Theory of Rate Processes (McGraw-Hill Book Company, Inc., New York, 1941).
-
H. Shimizu, J. Phys. Soc. Jpn. 29 (1970), 808[JPSJ]; unpublished data first reported at the research meeting on dynamical properties of biopolymers (Nov. 1969, Kyoto).
- L. D. Landau and E. M. Lifshitz, Statistical Physics (Pergamon Press, London, 1959), Chaps. I and XII.
-
M. C. Wang and G. E. Uhlenbeck, Rev. Mod. Phys. 17 (1945), 323[APS].
- H. Shimizu and T. Yamada, Prog. Theor. Phys. 47 (1972), 350[PTP].
- K. Tawada and F. Oosawa, J. Mechanochemistry and Cell Motility, in press.
- A. V. Hill, Proc. R. Soc. B 126 (1938), 136.
- H. Haken, Z. Phys. 181 (1964), 96.
- K. Tomita, private communication.
- K. Kometani, private communication.
- J. Meixner, Z. Phys. 219 (1969), 79.
- I. Prigogine, Theoretical Physics and Biology, edited by M. Marois (North-Holland Publishing Company, Amsterdam, 1969), p. 23.
