Analysis of a generalized Becker-Döring model of self-reproducing micelles

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 452, Issue 1952, 1996, Pages 2079-2102

  Coveney, Peter V ^a   Wattis, Jonathan A D ^b  

^a SCHLUMBERGER CAMBRIDGE RESEARCH   (United Kingdom)

^b UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746737619     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1996.0110     Document Type: Article

References (25)

1. Abramowitz, M. & Stegun, I. A. 1972 Handbook of mathematical functions. New York: Dover.
2. Aniansson, G. E. A. 1978 Theory of micelle formation kinetics. Ber. BunsenGes. Phys. Chem. 82, 981-988.
3. Aniansson, G. E. A. & Wall, S. N. 1974 On the step-wise micelle association. J. Phys. Chem. 78, 1024.
4. Aniansson, G. E. A. & Wall, S. N. 1975 Correction to On the step-wise micelle association. J. Phys. Chem. 79, 857-858.
5. Bachmann, P., Luisi, P. L. & Lang, J. 1992 Autocatalytic self-replicating micelles as models for prebiotic structures. Nature 357, 57-59.
6. Ball, J. M., Carr, J. & Penrose, O. 1986 The Becker-Döring cluster equations: basic properties and asymptotic behaviour of solutions. Communs Math. Phys. 104, 657-692.
7. Becker, R. & Döring, W. 1935 Ann. Phys. 24, 719-752.
8. Billingham, J. & Coveney, P. V. 1994 Kinetics of self-replicating micelles. J. Chem. Soc. Faraday Trans. 90, 1953-1959.
9. Boghosian, B. M., Coveney, P. V. & Emerton, A. N. 1996 A lattice-gas model of microemulsions. Proc. R. Soc. Land. A 452, 1221-1250.
10. Carr, J. 1981 Applications of centre manifold theory. New York: Springer.
11. Gates, M. E. 1993 Isotropie phases of self-assembled amphiphilic aggregates. Phil. Trans. R. Soc. Land. A 344 339-356.
12. Colonna, S., Fleischaker, G. & Luisi, P. L. (eds) 1994 Self-production of supramolecular structures: from synthetic structures to models of minimal living systems. NATO ASI Series. Dordrecht: Kluwer.
13. Chizmadzhew, Y. A., Maestro, M. & Mavelli, F. 1994 A simplified kinetic model for an autopoietic synthesis of micelles. Chem. Phys. Lett. 226, 56-62.
14. Coveney, P. V., Emerton, A. N. & Boghosian, B. M. 1996 Simulations of self-reproducing micelles using a lattice-gas automaton. Preprint.
15. Guckenheimer, J. &: Holmes, P. 1983 Nonlinear oscillations, dynamical systems and bifurcations of vector fields. New York: Springer.
16. Penrose, O. 1989 Metastable states for the Becker-Döring cluster equations. Communs Math. Phys. 124, 515-541.
17. Penrose, O. & Lebowitz, J. L. 1976 Towards a rigorous theory of metastability. In Studies in statistical mechanics, vol. VII. Fluctuation phenomena (ed. E. Montroll & J. L. Lebowitz), pp. 322-375 (particularly pp. 352-358). Amsterdam: North Holland.
18. Szathmâry, E. & Maynard Smith, J. 1995 The major evolutionary transitions. Nature 374, 227-232.
19. Toschev, S. 1973 Homogeneous nucleation. In Crystal growth: an introduction (éd. P. Hartman). Amsterdam: North-Holland
20. Varela, F. 1979 Principles of biological autonomy. Amsterdam: North-Holland.
21. Varela, F. 1981 Autopoiesis: a theory of living organisation. "New York: North-Holland.
22. Varela, F., Maturana, H. & Uribe, R. 1974 Autopoiesis: the organisation of living systems, its characterisation and a model. Biosystems 5, 187-196.
23. Wall, S. N. & Elvingson, C. 1985 Equilibrium and kinetic properties of mixed micelles. J. Phys. Chem. 89, 2695-2705.
24. Wattis, J. A. D. 1995 Continuum analogue of the Becker-Doring equations. Preprint.
25. Wattis, J. A. D. 1996 Metastability in the kinetics of spherical micelle formation. Proc. LMS Durham Symposium on Mathematical Models of Liquid Crystals and Related Polymeric Systems (ed. I. W. Stewart). Cambridge University Press.