Amplitude equations for systems with long-range interactions

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 66, Issue 2, 2002, Pages

  Kassner, Klaus ^a   Misbah, Chaouqi ^b  

^a OTTO VON GUERICKE UNIVERSITY   (Germany)

^b UNIV GRENOBLE ALPES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; DESORPTION; DIFFUSION; DISPERSIONS; ELASTIC MODULI; EPITAXIAL GROWTH; MASS TRANSFER; POISSON RATIO;

AMPLITUDE EQUATIONS; ELASTIC EQUATIONS; NONLOCAL EFFECTS; PATTERN FORMING SYSTEMS;

NONLINEAR EQUATIONS;

EID: 41349087051     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.026102     Document Type: Article

References (27)

1. K. Kassner, J.-M. Debierre, B. Billia, N. Noël, and H. Jamgotchian, Phys. Rev. E 57, 2849 (1998).
2. C. Misbah, H. Müller-Krumbhaar, and D. Temkin, J. Phys. I 1, 585 (1991).
3. K. Kassner, C. Misbah, H. Müller-Krumbhaar, and A. Valance, Phys. Rev. E 49, 5477 (1994);
4. Phys. Rev. EK. KassnerC. MisbahH. Müller-KrumbhaarA. Valance49, 5495 (1994).
5. G. I. Sivashinsky, Acta Astron. 4, 1177 (1977).
6. A. K. Hobbs and P. Metzener, J. Cryst. Growth 118, 319 (1992).
7. Y. Marietti, J.-M. Debierre, T. M. Bock, and K. Kassner, Phys. Rev. E 63, 066301 (2001);
8. Phys. Rev. EY. MariettiJ.-M. DebierreT. M. BockK. Kassner63, 066302 (2001).
9. F. J. Elmer, Physica D 30, 321 (1988).
10. T. Christen and F. J. Elmer, Phys. Lett. A 150, 16 (1990).
11. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
12. M. A. Grinfeld, Dokl. Akad. Nauk. SSSR 290, 1358 (1986) [Sov. Phys. Dokl. 31, 831 (1986)].
13. R. H. Torii and S. Balibar, J. Low Temp. Phys. 89, 391 (1992).
14. P. Nozières, J. Phys. I 3, 681 (1993).
15. J. Müller and M. Grant, Phys. Rev. Lett. 82, 1736 (1999).
16. K. Kassner and C. Misbah, Europhys. Lett. 46, 217 (1999).
17. K. Kassner and C. Misbah (unpublished).
18. I. Cantat, K. Kassner, C. Misbah, and H. Müller-Krumbhaar, Phys. Rev. E 58, 6027 (1998).
19. I. Durand, K. Kassner, C. Misbah, and H. Müller-Krumbhaar, Phys. Rev. Lett. 76, 3013 (1996).
20. K. Kassner, C. Misbah, J. Müller, J. Kappey, and P. Kohlert, Phys. Rev. E 63, 036117 (2001).
21. A. Griffith, Philos. Trans. R. Soc. London, Ser. A 221, 163 (1920).
22. Actually (Formula presented) and (Formula presented) are complex while the other quantities are real, but they have to satisfy (Formula presented) and (Formula presented), where the star denotes complex conjugation, to make the Fourier transforms in Eqs. (27), (28), (31), and (32) real.
23. K. Kassner and C. Misbah (unpublished).
24. C. Misbah and A. Valance, Phys. Rev. E 49, 166 (1994).
25. This is true generically under the condition that no constraint, such as conservation laws for h, is imposed and that the system is nonvariational. Still, the equation has a partial differential form.
26. O. Pierre-Louis, C. Misbah, Y. Saito, J. Krug, and O. Politi, Phys. Rev. Lett. 80, 4221 (1998).
27. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978).