Derivation of Cahn-Hilliard equations from Ginzburg-Landau models

Journal of Statistical Physics

Volumn 88, Issue 1-2, 1997, Pages 365-381

  Bertini, L ^a   Landim, C ^b,c   Olla, S ^d,e  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b IMPA   (Brazil)

^c UNIVERSITÉ DE ROUEN   (France)

^d UNIVERSITÉ DE CERGY PONTOISE   (France)

^e CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

Author keywords

Cahn Hilliard equation; Ginzburg Landau models; Hydro dynamic limits; Large deviations; Surface diffusion

Indexed keywords

EID: 0031184916     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02508476     Document Type: Article

References (14)

1. O. Benois, C. Kipnis, and C. Landim, Large deviations from the hydrodynamical limit of mean zero asymmetric zero-range processes, Stoch. Proc. Applic. 55:65-89 (1995).
2. P. Collet, F. Dunlop, and T. Gobron, Conservative Langevin dynamics of solid-on-solid interface, J. Stat. Phys. 79:215-229 (1995).
3. A. De Masi, P. Ferrari, and J. L. Lebowitz, Reaction-diffusion equations for interacting particle systems, J. Stat. Phys. 44:589-644 (1986).
4. A. De Masi, E. Orlandi, E. Presutti, and L. Triolo, Glauber evolution with Kac potential I. Mesoscopic and macroscopic limits, interface dynamics, Nonlinearity 7:633-696 (1994).
5. M. D. Donsker and S. R. S. Varadhan, Large deviations from a hydrodynamic scaling limit, Comm. Pure Appl. Math. 42:243-270 (1989).
6. T. Funaki and H. Spohn, Motion by mean curvature from the Ginzburg-Landau ∇φ interface model, preprint (1994).
7. D. Gabrielli, G. Jona-Lasinio, C. Landim, and M. E. Vares, Microscopic reversibility and thermodynamic fluctuations, to appear in The proceedings of the conference "Boltzmann's Legacy" Roma, 1994.
8. G. Giacomin and J. L. Lebowitz, Exact macroscopic description of phase segregation in model alloys with long range interactions, Phys. Rev. Let. 76:1094-1097 (1996).
9. M. Z. Guo, G. C. Papanicolaou, and S. R. S. Varadhan, Nonlinear diffusion for a system with nearest neighbor interactions, Commun. Math. Phys. 118:31-59 (1988).
10. G. Jona-Lasinio, C. Landim, and M. E. Vares, Large deviations for a reaction-diffusion model, Prob. Th. Rel. Fields 97:339-361 (1993).
11. C. Kipnis, S. Olla, and S. R. S. Varadhan, Hydrodynamics and large deviations for simple exclusion processes, Comm. Pure Appl. Math. 42:115-137 (1989).
12. C. Landim and H. T. Yau, Large deviations of interacting particle systems in infinite volume, Comm. Pure Appl. Math. 48:339-379 (1995).
13. H. Spohn, Interface motion in models with stochastic dynamics, J. Stat. Phys. 71:1081-1132 (1993).
14. S. R. S. Varadhan, Large Deviations and Applications. CBMS-NSF Regional Conference Series in Applied Mathematics, vol.46, 1984.