Langevin equations for fluctuating surfaces

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

Volumn 72, Issue 5, 2005, Pages

  Chua, Alvin L S ^a   Haselwandter, Christoph A ^a   Baggio, Chiara ^a   Vvedensky, Dimitri D ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

FOKKER-PLANCK EQUATION; LIMIT THEOREM;

DEPOSITION; DIFFUSION; MATHEMATICAL MODELS; PARAMETER ESTIMATION; PROBABILITY;

SURFACES;

EID: 28844498753     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.72.051103     Document Type: Article

References (84)

1. A. Madhukar and S. V. Ghaisas, CRC Crit. Rev. Solid State Mater. Sci. CCRSDA 1040-8436 14, 1 (1988).
2. H. Metiu, Y.-T. Liu, and Z. Zhang, Science SCIEAS 0036-8075 255, 1088 (1992).
3. T. Shitara, D. D. Vvedensky, M. R. Wilby, J. Zhang, J. H. Neave, and B. A. Joyce, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.46.6815 46, 6815 (1992).
4. A.-L. Barabási and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, England, 1995).
5. T. Halpin-Healy and Y.-C. Chang, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(94)00087-J 254, 215 (1995)
6. J. Krug, Adv. Phys. ADPHAH 0001-8732 46, 139 (1997).
7. A. Pimpinelli and J. Villain, Physics of Crystal Growth (Cambridge University Press, Cambridge, England, 1999).
8. I. V. Markov, Crystal Growth for Beginners: Fundamentals of Nucleation, Crystal Growth and Epitaxy, 2nd ed. (World Scientific, Singapore, 2003).
9. J. Villain, J. Phys. I JPGCE8 1155-4304 10.1051/jp1:1991114 1, 19 (1991).
10. Z. W. Lai and S. Das Sarma, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.66.2348 66, 2348 (1991).
11. M. Kardar, G. Parisi, and Y.-C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.56.889 56, 889 (1986).
12. T. Hwa and M. Kardar, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.45.7002 45, 7002 (1992).
13. M. Marsili, A. Maritan, F. Toigo, and J. R. Banavar, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.68.963 68, 963 (1996).
14. S.-C. Park, D. Kim, and J.-M. Park, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.015102 65, 015102 (R) (2001).
15. C.-H. Lam and L. M. Sander, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.561 71, 561 (1993).
16. Z. Rácz, M. Siegert, D. Liu, and M. Plischke, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.43.5275 43, 5275 (1991)
17. D. D. Vvedensky, A. Zangwill, C. N. Luse, and M. R. Wilby, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.48.852 48, 852 (1993).
18. M. Předota and M. Kotrla, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.54.3933 54, 3933 (1996).
19. G. Costanza, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.55.6501 55, 6501 (1997).
20. F. Family, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/19/8/006 19, L441 (1986).
21. J. M. Kim and S. Das Sarma, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.2903 72, 2903 (1994).
22. M. R. Wilby, D. D. Vvedensky, and A. Zangwill, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.46.12896 46, R 12896 (1992);
23. M. R. Wilby, D. D. Vvedensky, and A. Zangwill, Phys. Rev. B PRBMDO 0163-1829 47, 16068 (1993).
24. J. Krug, M. Plischke, and M. Siegert, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.70.3271 70, 3271 (1993).
25. M. Kotrla and P. Amilauer, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.53.13777 53, 13777 (1996).
26. P. Punyindu and S. Das Sarma, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.57.R4863 57, R4863 (1998).
27. S. Das Sarma, P. P. Chatraphorn, and Z. Toroczkai, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.036144 65, 036144 (2002).
28. S. Pal and D. P. Landau, Physica A PHYADX 0378-4371 10.1016/S0378-4371(98)00641-4 267, 406 (1999).
29. S. Pal, D. P. Landau, and K. Binder, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.021601 68, 021601 (2003).
30. C. Baggio, R. Vardavas, and D. D. Vvedensky, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.045103 64, 045103 (R) (2001).
31. S. F. Edwards and D. R. Wilkinson, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 381, 17 (1982).
32. S. Clarke and D. D. Vvedensky, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.37.6559 37, R 6559 (1988).
33. D. E. Wolf and J. Villain, Europhys. Lett. EULEEJ 0295-5075 13, 389 (1990).
34. S. Das Sarma and P. Tamborenea, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.66.325 66, 325 (1991).
35. C. M. Horowitz and E. V. Albano, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/34/3/303 34, 357 (2001).
36. M. C. Bartelt and J. W. Evans, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.46.12675 46, 12675 (1992).
37. C. Ratsch, P. Amilauer, A. Zangwill, and D. D. Vvedensky, Surf. Sci. SUSCAS 0039-6028 10.1016/0039-6028(95)00353-3 329, L599 (1995).
38. J. G. Amar and F. Family, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.2066 74, 2066 (1995).
39. M. D. Johnson, C. Orme, A. W. Hunt, D. Graff, J. Sudijono, L. M. Sander, and B. G. Orr, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.116 72, 116 (1994).
40. P. Amilauer and D. D. Vvedensky, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.52.14263 52, 14263 (1995).
41. M. Itoh, G. R. Bell, A. R. Avery, T. S. Jones, B. A. Joyce, and D. D. Vvedensky, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.633 81, 633 (1998).
42. P. Kratzer and M. Scheffler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.036102 88, 036102 (2002).
43. N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981).
44. A. K. Myers-Beaghton and D. D. Vvedensky, Surf. Sci. SUSCAS 0039-6028 10.1016/0039-6028(90)90596-Z 232, 161 (1990).
45. J. W. Evans and M. C. Bartelt, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.49.1061 49, 1061 (1994).
46. T. G. Kurtz, Math. Program. MHPGA4 0025-5610 5, 67 (1976).
47. T. G. Kurtz, Stochastic Proc. Appl. STOPB7 0304-4149 10.1016/0304-4149(96)00056-7 6, 223 (1978).
48. R. F. Fox and J. Keizer, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.43.1709 43, 1709 (1991).
49. J. Krug, P. Meakin, and T. Halpin-Healy, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.45.638 45, 638 (1992).
50. E. Marinari, A. Pagnani, G. Parisi, and Z. Rácz, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.026136 65, 026136 (2002).
51. D. D. Vvedensky, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67. 025102 67, 025102 (R) (2003).
52. D. D. Vvedensky, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68. 010601 68, 010601 (R) (2003).
53. P. Amilauer, M. R. Wilby, and D. D. Vvedensky, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.47.4119 47, R 4119 (1993).
54. M. Siegert and M. Plischke, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.50.917 50, 917 (1994).
55. A. Zangwill, Physics at Surfaces (Cambridge University Press, Cambridge, UK, 1988).
56. J. L. Doob, Ann. Math. ANMAAH 0003-486X 43, 351 (1942);
57. J. L. Doob, reprinted in Noise and Stochastic Processes, edited by, N. Wax, (Dover, New York, 1954), pp. 319-337.
58. J. F. Kenney and E. S. Keeping, Mathematics of Statistics, Part 2, 2nd ed. (Van Nostrand, Princeton, NJ, 1951), pp. 298-300.
59. A. L.-S. Chua, Ph.D. thesis, University of London, 2004.
60. M. Schroeder, M. Siegert, D. E. Wolf, J. D. Shore, and M. Plischke, Europhys. Lett. EULEEJ 0295-5075 24, 563 (1993).
61. K. Park, B. Kahng, and S. S. Kim, Physica A PHYADX 0378-4371 10.1016/0378-4371(94)00094-8 210, 146 (1994).
62. P. Amilauer and M. Kotrla, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.49.5769 49, R5769 (1994).
63. C. S. Ryu and I. M. Kim, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.51.3069 51, 3069 (1995);
64. C. S. Ryu and I. M. Kim, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.52.2424 52, 2424 (1995).
65. Z.-F. Huang and B.-L. Gu, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.54.5935 54, 5935 (1996).
66. G. Costanza, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/31/35/003 31, 7211 (1998).
67. C. Herring, in The Physics of Powder Metallurgy, edited by, W. E. Kingston, (McGraw-Hill, New York, 1951), pp. 143-179.
68. W. W. Mullins, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.1722742 28, 333 (1957).
69. P. I. Tamborenea and S. Das Sarma, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.48.2575 48, 2575 (1993).
70. C. Ratsch, M. F. Gyure, S. Chen, M. Kang, and D. D. Vvedensky, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.61.R10598 61, R10598 (2000).
71. B. J. Spencer, P. W. Voorhees, and S. H. Davis, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.353815 73, 4955 (1993).
72. B. J. Spencer, S. H. Davis, and P. W. Voorhees, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.47.9760 47, 9760 (1993).
73. A. A. Golovin, S. H. Davis, and P. W. Voorhees Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.056203 68, 056203 (2003).
74. Y. Saito, H. Uemura, and M. Uwaha, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.63.045422 63, 045422 (2001).
75. A. C. Schindler, M. F. Gyure, G. D. Simms, D. D. Vvedensky, R. E. Caflisch, C. Connell, and E. Luo, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.075316 67, 075316 (2003).
76. W. A. Curtin and R. E. Miller, Modell. Simul. Mater. Sci. Eng. MSMEEU 0965-0393 10.1088/0965-0393/11/3/201 11, R33 (2003).
77. C. Haselwandter and D. D. Vvedensky, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/35/41/104 35, L579 (2002).
78. C. A. Haselwandter and D. D. Vvedensky, in Modeling of Morphological Evolution at Surfaces and Interfaces, edited by, J. Evans, C. Orme, M. Asta, and, Z. Zhang, Mater. Res. Soc. Symp. Proc. MRSPDH 0272-9172 No. 859E (Materials Research Society, Pittsburgh, PA, 2005), pp. JJ8.8.1-JJ8.8.6.
79. J. P. Aparicio and H. G. Solari, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.4183 86, 4183 (2001).
80. W.-Y. Chen and S. Bokka, J. Theor. Biol. JTBIAP 0022-5193 234, 455 (2005).
81. T. S. Chang, D. D. Vvedensky, and J. F. Nicoll, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(92)90041-W 217, 279 (1992).
82. G. R. Jafari, S. M. Fazeli, F. Ghasemi, S. M. Vaez Allaei, M. R. Tabar, A. Iraji Zad, and G. Kavei, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.226101 91, 226101 (2003).
83. A. Ballestad, B. J. Ruck, M. Adamcyk, T. Pinnington, and T. Tiedje, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.2377 86, 2377 (2001).
84. H.-C. Kan, S. Shah, T. T. Tadyyon-Eslami, and R. J. Phaneuf, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.146101 92, 146101 (2004).