Phase segregation dynamics for the Blume-Capel model with Kac interaction

Stochastic Processes and their Applications

Volumn 88, Issue 1, 2000, Pages 79-124

  Marra, R ^a   Mourragui, M ^b  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b UNIVERSITÉ DE ROUEN   (France)

Author keywords

Hydrodynamic limits; Interacting particle and spin systems; Kac potential; Phase segregation

Indexed keywords

EID: 0002315933     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(99)00120-9     Document Type: Article

References (29)

1. 2 Phys. Rev. 141:1966;517.
2. 4 mixtures Phys. Rev. A. 4:1971;1071-1077.
3. Bricmont J., Slawny J. Phase transition in systems with a finite number of dominant ground states. J. Statist. Phys. 54:1989;89.
4. Capel H.W. Physica. 32:1966;966.
5. Carlen, E.A., Carvalho, M.C., Orlandi, E., 1999a. Algebraic rate of decay for the excess free energy and stability of fronts for a non-local phase kinetics equation with a conservation law, I. J. Stat. Phys. 95, 1069-1117.
6. Carlen, E.A., Carvalho, M.C., Orlandi, E., 1999b. Algebraic rate of decay for the excess free energy and stability of fronts for a non-local phase kinetics equation with a conservation law, II. Comm. Partial Differential Equations, to appear.
7. De Masi A., Orlandi E., Triolo L., Presutti E. Glauber evolution with Kac potentials I. Mesoscopic and macroscopic limits, interface dynamics. Nonlinearity. 7:1996;287-301.
8. De Masi A., Orlandi E., Triolo L., Presutti E. Glauber evolution with Kac potentials II. Fluctuation. Nonlinearity. 9:1996;27-51.
9. De Masi A., Orlandi E., Triolo L., Presutti E. Glauber evolution with Kac potentials III. Spinodal decomposition. Nonlinearity. 9:1996;53-114.
10. De Masi A., Presutti E. Mathematical Methods for Hydrodynamic Limits. Lecture Notes in Mathematics. Vol. 1501. 1991;Springer, Berlin.
11. Fritz J. On the diffusive nature of the entropy flow in infinite systems: remarks to a paper by Guo-Papanicolau-Varadhan. Commun. Math. Phys. 133:1990;331-352.
12. Giacomin G., Lebowitz J.L. Phase segregation dynamics in particle systems with long range interaction I. Macroscopic limits. J. Statist. Phys. 87:1997;37-61.
13. Giacomin G., Lebowitz J.L. Phase segregation dynamics in particle systems with long range interaction II. Interface motion. SIAM J. Appl. Math. 58:1998;1707-1729.
14. Giacomin, G., Lebowitz, J.L., Marra, R., 2000. Macroscopic Evolution of Particle Systems with Short and Long Range Interactions, Preprint.
15. Giacomin, G., Lebowitz, J.L., Presutti, E., 1998. Deterministic and stochastic hydrodynamic equations arising from simple microscopic model systems. Preprint.
16. Guo M.Z., Papanicolaou G.C., Varadhan S.R.S. Nonlinear diffusion limit for a system with nearest neighbor interactions. Commun. Math. Phys. 118:1988;31-59.
17. Kac M., Uhlenbeck G.E., Hemmer P.C. On the van der Waals theory of the vapor-liquid equilibrium, I. Discussion of a one-dimensional model. J. Math. Phys. 4:1963;216-228.
18. Kipnis C., Landim C. Scaling Limits of Interacting Particle Systems. 1999;Springer, Berlin.
19. Kipnis C., Landim C., Olla S. Hydrodynamical limit for a nongradient model: the generalized exclusion processes. Commun. Pure Appl. Math. 47:1994;1475-1545.
20. Kipnis C., Olla S., Varadhan S.R.S. Hydrodynamics and large deviations for simple exclusion processes. Commun. Pure Appl. Math. 42:1989;115-137.
21. Liggett T.M. Interacting Particle Systems. Grundlehren der Mathematischen Wissenschaften. Vol. 276. 1985;Springer, Berlin.
22. Landim C., Mourragui M. Hydrodynamic limit of mean zero asymmetric zero range processes in infinite volume. Ann. Inst. Henri. Poincaré 33(1):1997;361-385.
23. Landim, C., Mourragui, M., Sellami, S., 1998. Hydrodynamical limit for a nongradient interacting particle system with stochastic reservoirs. Preprint.
24. Lebowitz J., Penrose O. Rigorous treatment of the Van der Waals Maxwell theory of the liquid vapour transition. J. Math. Phys. 7:1963;98-113.
25. Quastel J. Diffusion of a color in the simple exclusion process. Commun. Pure Appl. Math. XLV:1992;623-679.
26. Spohn H. Large Scale Dynamics of Interacting Particles. 1991;Springer, Berlin.
27. Varadhan S.R.S. Nonlinear diffusion limit for a system with nearest neighbor interactions II. Elworthy K., Ikeda N. Asymptotic Problems in Probability Theory: Stochastic Models and Diffusion on Fractals. Pitman Research Notes in Mathematics. Vol. 283. 1994;Wiley, New York.
28. Varadhan S.R.S., Yau H.T. Diffusive limit of lattice gas with mixing conditions. Asian J. Math. 1:1997;623-678.
29. Yau H.T. Metastability of Ginzburg-Landau model with a conservation law. J. Statist. Phys. 74:1994;705-742.