Abstract
Some statistical models are described that have been used to study growth of fluctuations in thermodynamically unstable systems. On the bases of these models we discuss the growth of fluctuations for the cases where the order parameter is not conserved and where it is conserved (spinodal decompositions). Some relevent experiments and computer simulation works are also briefly discussed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Nucleation Phenomena, ed. Zettlemoyer, Elsevier, Amsterdam (1977).
J. W. Cahn in Critical Phenomena in Alloys, Magnets and Superconductors, eds. Mills, Ascher and Jaffee, McGraw-Hill, New York (1971).
J. E. Hilliard, in Phase Transitions, ed. H. I. Aronson, American Society of Metals, Metals Park, Ohio (1970).
J. S. Langer, in Physics of Non-Equilibrium Systems, ed. T. Riste, Plenum Press, New York (1975).
R. Kubo, K. Matsuo and K. Kitahara, J. Stat. Phys. 9, 51 (1973)
[5.a]a Y. Saito and R. Kubo, J. Stat. Phys. 15, 233 (1976).
M. Suzuki, Prog. Theor. Phys. 56, 77 (1976), Lecture given at the XVII th Solvay Conference on Physics (1978, to be published) and the intervening publications
F.T. Arecchi and V. Degiorgio, Phys.Rev. A3, 1108 (1971).
F. Haake, Phys. Rev. Lett. 41, 1685 (1978) and the papers quoted therein.
R. Glauber, J. Math. Phys. 4, 294 (1963).
K. Kawasaki, in Phase Transitions and Critical Phenomena Vol. 2, eds. C. Domb and M. S. Green, Academic Press, New York (1972).
K. Kawasaki, Phys. Rev. 145, 224 (1966)
K. Kawasaki, Phys. Rev.148, 375 (1966).
K. Binder and M. H. Kalos, preprint.
K. Kawasaki, in Synergetics, ed. H. Haken, B. G. Teubner, Stuttgart (1973).
K. Kawasaki, Prog. Theor. Phys. 57, 826 (1977).
e.g. K. F. Freed, in Progress in Liquid Physics, ed. C. Croxton, Wiley, New York (1978).
e.g. P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys. 49, 435 (1977).
Order-Disorder Transformations in Alloys, ed. H. Warlimont, Springer Verlag, Berlin (1974).
Section 4D of Ref. 13.
T. Suzuki and M. Wuttig, Acta Met. 23, 1069 (1975).
K. Kawasaki, M. C. Yalabik and J. D. Gunton, Phys. Rev. A 17, 455 (1978).
T. Hashimoto, K. Nishimura and Y. Takeuchi, Phys. Lett. 65 A, 250 (1978).
C. Kawabata and K. Kawasaki, Phys. Lett. 65 A, 137 (1978)
J. VI. Cahn and S. M. Allen, J. de Physique Colloque C7–51 (1977).
J. S. Huang, W. I. Goldburg and A. W. Bjerkaas, Phys. Rev. Lett. 32, 921 (1974)
A. J. Schwartz, J. S. Huang and W. I. Goldburg. J. Chem. Phys. 62, 1847 (1975)
ibid.63, 599 (1975).
W. I. Goldburg, C.-H. Shaw, J. S. Huang and M. S. Pilant, J. Chem. Phys. 68, 484 (1978)
M.-C. Wong and C. M. Knobler, J. Chem. Phys. 66, 4707 (1977) and preprint.
M. W. Kim, A. J. Schwartz and W. I. Goldburg, Phys. Rev. Lett. 41, 657 (1978): W. I. Goldburg, A. J. Schwartz and M. W. Kim, to be published in Suppl. Prog. Phys.
K. Binder, Z. Physik 267, 213 (1974): J. Marro, J. Lebowitz and M. Kalos, preprint, and the earlier references quoted therein.
The author is indebted to conversations with J. W. Cahn and J. S. Langer on this point.
J. S. Langer and M. Bar-on, Ann. Phys. (N.Y.) 78, 421 (1973) and the earlier references quoted therein
J. S. Langer, M. Bar-on and H. D. Miller, Phys. Rev. A 11, 1417 (1975).
K. Kawasaki and T. Ohta, Prog. Theor. Phys. 59, 362 (1978).
E. Siggia, Cornell University preprint (1979).
J. S. Langer, Ann. Phys. (N.Y.) 65, 53 (1971).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1979 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kawasaki, K. (1979). Growth of Fluctuations in Thermodynamically Unstable Systems. In: Haken, H. (eds) Pattern Formation by Dynamic Systems and Pattern Recognition. Springer Series in Synergetics, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-67480-8_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-67480-8_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-67482-2
Online ISBN: 978-3-642-67480-8
eBook Packages: Springer Book Archive