Phase-field-crystal and Swift-Hohenberg equations with fast dynamics

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 79, Issue 5, 2009, Pages

  Galenko, Peter ^a,b   Danilov, Denis ^c   Lebedev, Vladimir ^d  

^a GERMAN AEROSPACE CENTER DLR   (Germany)

^b RUHR UNIVERSITY BOCHUM   (Germany)

^c KARLSRUHE UNIVERSITY OF APPLIED SCIENCES   (Germany)

^d UDMURT STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

DEGREES OF FREEDOM; DRIVING FORCES; EXPONENTIAL FORM; FAST DYNAMICS; INERTIA EFFECTS; MEMORY FUNCTIONS; MESOSCOPIC SCALE; PERIODIC MODELS; PHASE FIELDS; PHENOMENOLOGICAL DESCRIPTION; STABLE PHASE; SWIFT-HOHENBERG EQUATIONS;

MECHANICS;

EQUATIONS OF MOTION;

EID: 66749097815     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.051110     Document Type: Article

References (58)

1. L. D. Landau, Zh. Eksp. Teor. Fiz. 7, 19 (1937)
2. see also Collected Papers of L. D. Landau, edited by, D. ter Haar, (Pergamon, Oxford, 1965), p. 193
3. L. D. Landau and I. M. Khalatnikov, Dokl. Akad. Nauk SSSR 96, 469 (1954)
4. see also Collected Papers of L. D. Landau, edited by, D. ter Haar, (Pergamon, Oxford, 1965), p. 626.
5. V. L. Ginzburg and L. D. Landau, Zh. Eksp. Teor. Fiz. 20, 1064 (1950)
6. see also Collected Papers of L. D. Landau, edited by, D. ter Haar, (Pergamon, Oxford, 1965), p. 546.
7. L. Q. Chen, Annu. Rev. Mater. Res. 32, 113 (2002) 10.1146/annurev.matsci. 32.112001.132041
8. W. J. Boettinger, J. A. Warren, C. Beckermann, and A. Karma, Annu. Rev. Mater. Res. 32, 163 (2002) 10.1146/annurev.matsci.32.101901.155803
9. H. Emmerich, Adv. Phys. 57, 1 (2008) 10.1080/00018730701822522
10. I. Singer-Loginova and H. M. Singer, Rep. Prog. Phys. 71, 106501 (2008). 10.1088/0034-4885/71/10/106501
11. K. R. Elder, M. Katakowski, M. Haataja, and M. Grant, Phys. Rev. Lett. 88, 245701 (2002) 10.1103/PhysRevLett.88.245701
12. N. Goldenfeld, B. P. Athreya, and J. A. Dantzig, Phys. Rev. E 72, 020601 (R) (2005) 10.1103/PhysRevE.72.020601
13. J. Mellenthin, A. Karma, and M. Plapp, Phys. Rev. B 78, 184110 (2008). 10.1103/PhysRevB.78.184110
14. S. A. Brazovskii, Zh. Eksp. Teor. Fiz. 68, 175 (1975)
15. S. A. Brazovskii, [Sov. Phys. JETP 41, 85 (1975)].
16. J. Swift and P. C. Hohenberg, Phys. Rev. A 15, 319 (1977) 10.1103/PhysRevA.15.319
17. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993). 10.1103/RevModPhys.65.851
18. K. R. Elder and M. Grant, Phys. Rev. E 70, 051605 (2004). 10.1103/PhysRevE.70.051605
19. J. Berry, M. Grant, and K. R. Elder, Phys. Rev. E 73, 031609 (2006). 10.1103/PhysRevE.73.031609
20. J. Berry, K. R. Elder, and M. Grant, Phys. Rev. E 77, 061506 (2008). 10.1103/PhysRevE.77.061506
21. P. F. Tupper and M. Grant, EPL 81, 40007 (2008). 10.1209/0295-5075/81/ 40007
22. L. I. Mandel'shtam and M. A. Leontovich, Zh. Eksp. Teor. Fiz. 7, 438 (1937).
23. L. Kramer, E. Ben-Jacob, H. Brand, and M. C. Cross, Phys. Rev. Lett. 49, 1891 (1982) 10.1103/PhysRevLett.49.1891
24. U. Ebert and W. van Saarlos, Phys. Rep. 337, 139 (2000). 10.1016/S0370-1573(00)00059-4
25. P. Galenko and D. Jou, Phys. Rev. E 71, 046125 (2005). 10.1103/PhysRevE.71.046125
26. E. M. Lifshitz and L. P. Pitaevskii, Physical Kinetics: Course Theoretical Physics (Pergamon, Oxford, 1981), Vol. 10.
27. A. Z. Patashinskii and V. L. Pokrovskii, Fluctuation Theory of Phase Transitions (Pergamon, Oxford, 1979).
28. P. Stefanovic, M. Haataja, and N. Provatas, Phys. Rev. Lett. 96, 225504 (2006). 10.1103/PhysRevLett.96.225504
29. A. Archer, J. Chem. Phys. 130, 014509 (2009). 10.1063/1.3054633
30. S. Majaniemi and M. Grant, Phys. Rev. B 75, 054301 (2007). 10.1103/PhysRevB.75.054301
31. D. Joseph and L. Preziosi, Rev. Mod. Phys. 61, 41 (1989) 10.1103/RevModPhys.61.41
32. D. Joseph and L. Preziosi, Rev. Mod. Phys. 62, 375 (1990). 10.1103/RevModPhys.62.375
33. W. E. Olmstead, S. H. Davis, S. Rosenblat, and W. L. Kath, SIAM J. Appl. Math. 46, 171 (1986) 10.1137/0146013
34. B. R. Duffy, P. Freitas, and M. Grienfeld, SIAM J. Math. Anal. 33, 1090 (2002). 10.1137/S0036141001388592
35. T. Garel and S. Doniach, Phys. Rev. B 26, 325 (1982). 10.1103/PhysRevB.26.325
36. C. Sagui and R. C. Desai, Phys. Rev. E 52, 2807 (1995) 10.1103/PhysRevE.52.2807
37. I. I. Potemkin and S. V. Panyukov, Phys. Rev. E 57, 6902 (1998). 10.1103/PhysRevE.57.6902
38. P. K. Galenko and D. A. Danilov, Phys. Lett. A 235, 271 (1997) 10.1016/S0375-9601(97)00562-8
39. P. K. Galenko and D. A. Danilov, J. Cryst. Growth 197, 992 (1999). 10.1016/S0022-0248(98)00977-4
40. D. Jou, J. Casas-Vazquez, and G. Lebon, Rep. Prog. Phys. 51, 1105 (1988) 10.1088/0034-4885/51/8/002
41. B. C. Eu, Kinetic Theory and Irreversible Thermodynamics (Wiley, New York, 1992)
42. S. Sieniutycz and P. Salamon, Extended Thermodynamic Systems (Taylor and Francis, New York, 1992)
43. I. Müller and T. Ruggery, Extended Thermodynamics (Springer, New York, 1993)
44. D. Y. Tzou, Macroscale to Microscale Heat Transport: The Lagging Behavior (Taylor and Francis, New York, 1997)
45. D. Jou, J. Casas-Vazquez, and G. Lebon, Rep. Prog. Phys. 62, 1035 (1999). 10.1088/0034-4885/62/7/201
46. D. Jou, J. Casas-Vazquez, and G. Lebon, Extended Irreversible Thermodynamics, 3rd ed. (Springer, Berlin, 2001).
47. P. Galenko and D. Jou, Physica A (to be published).
48. G. J. B. van den Berg, L. A. Peltier, and W. C. Troy, Arch. Ration. Mech. Anal. 158, 91 (2001). 10.1007/PL00004243
49. G. Schneider, Commun. Math. Phys. 178, 679 (1996) 10.1007/BF02108820
50. I. S. Aranson, B. A. Malomed, L. M. Pismen, and L. S. Tsimring, Phys. Rev. E 62, R5 (2000). 10.1103/PhysRevE.62.R5
51. K. Elder, Phase Field Modeling, Preprint of DFG-German Research Foundation Summer School on Priority Programme SPP-1296 (DFG, Aachen, 2008).
52. W. Eckhaus, Studies in Nonlinear Stability Theory (Springer, Berlin, 1965)
53. L. S. Tuckerman and D. Barkley, Physica D 46, 57 (1990). 10.1016/0167-2789(90)90113-4
54. E. Brener and D. Temkin, Phys. Rev. E 51, 351 (1995). 10.1103/PhysRevE.51.351
55. D. Herlach, P. Galenko, and D. Holland-Moritz, Metastable Solids from Undercooled Melts (Elsevier, Amsterdam, 2007).
56. D. M. Herlach and P. K. Galenko, Mater. Sci. Eng., A 449-451, 34 (2007) 10.1016/j.msea.2006.02.303
57. H. Hartmann, P. K. Galenko, D. Holland-Moritz, M. Kolbe, D. M. Herlach, and O. Shulishova, J. Appl. Phys. 103, 073509 (2008). 10.1063/1.2903920
58. P. Galenko, Phys. Rev. E 76, 031606 (2007). 10.1103/PhysRevE.76.031606