Renormalization group approach to multiscale simulation of polycrystalline materials using the phase field crystal model

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

Volumn 72, Issue 2, 2005, Pages

  Goldenfeld, Nigel ^a   Athreya, Badrinarayan P ^a   Dantzig, Jonathan A ^a  

^a United States of America   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COVARIANT EQUATIONS; PHASE FIELD CRYSTAL MODEL; RENORMALIZATION GROUP;

CRYSTALS; NUCLEATION;

POLYCRYSTALLINE MATERIALS;

EID: 27344443572     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.72.020601     Document Type: Article

References (34)

1. R. Phillips, Crystals, Defects and Microstructures: Modeling Across Scales (Cambridge University Press, Cambridge 2001).
2. D. D. Vvedensky, J. Phys.: Condens. Matter JCOMEL 0953-8984 16, R1537 (2004).
3. E. B. Tadmor, M. Ortiz, and R. Phillips, Philos. Mag. A PMAADG 0141-8610 73, 1529 (1996).
4. V. B. Shenoy, R. Miller, E. B. Tadmor, R. Phillips, and M. Ortiz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.742 80, 742 (1998).
5. J. Knap and M. Ortiz, J. Mech. Phys. Solids JMPSA8 0022-5096 10.1016/S0022-5096(01)00034-5 49, 1899 (2001).
6. R. E. Miller and E. B. Tadmor, J. Comput.-Aided Mater. Des. JCODES 0928-1045 10.1023/A:1026098010127 9, 203 (2002).
7. W. E, B. Enquist, and Z. Huang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.092101 67, 092101 (2003).
8. W. E and Z. Huang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 87.135501 87, 135501 (2001).
9. R. E. Rudd and J. Q. Broughton, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.58.R5893 58, R5893 (1998).
10. J. Q. Broughton, F. F. Abraham, N. Bernstein, and E. Kaxiras, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.60.2391 60, 2391 (1998).
11. C. Denniston and M. O. Robbins, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.021505 69, 021505 (2004).
12. S. Curtarolo and G. Ceder, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.255504 88, 255504 (2002).
13. J. Fish and W. Chen, Comput. Methods Appl. Mech. Eng. CMMECC 0045-7825 193, 1693 (2004).
14. J. A. Warren, R. Kobayashi, A. E. Lobkovsky, and W. C. Carter, Acta Mater. ACMAFD 1359-6454 10.1016/S1359-6454(03)00388-4 51, 6035 (2003).
15. W. E and X. Li (unpublished), http://www.math.princeton.edu/multiscale/ el.ps
16. K. R. Elder, M. Katakowski, M. Haataja, and M. Grant, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.245701 88, 245701 (2002).
17. K. R. Elder and M. Grant, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.051605 70, 051605 (2004).
18. N. Goldenfeld, O. Martin, Y. Oono, and F. Liu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64.1361 64, 1361 (1990).
19. N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group (Addison-Wesley, Reading, MA, 1992).
20. C. Bowman and A. C. Newell, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.70.289 70, 289 (1998).
21. L. Y. Chen, N. Goldenfeld, and Y. Oono, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.54.376 54, 376 (1996).
22. R. Graham, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.2185 76, 2185 (1996).
23. K. Nozaki, Y. Oono, and Y. Shiwa, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.62.R4501 62, R4501 (2000).
24. S. Sasa, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(97)00027-4 108, 45 (1997).
25. Y. Shiwa, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.016119 63, 016119 (2000).
26. M. C. Cross and A. C. Newell, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(96)00181-9 10, 299 (1984).
27. T. Passot and A. C. Newell, Physica D PDNPDT 0167-2789 10.1016/0167-2789(94)90199-6 74, 301 (1994).
28. A. C. Newell, T. Passot, and J. Lega, Annu. Rev. Fluid Mech. ARVFA3 0066-4189 10.1146/annurev.fluid.25.1.399 25, 399 (1993).
29. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.65.851 65, 851 (1993).
30. S. A. Brazovskii, Zh. Eksp. Teor. Fiz. ZETFA7 0044-4510 68, 175 (1975).
31. J. Swift and P. C. Hohenberg, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.15.319 15, 319 (1977).
32. G. H. Gunaratne, Q. Ouyang, and H. Swinney, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.50.2802 50, 2802 (1994).
33. W. T. Read and W. Shockley, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.78.275 78, 275 (1950).
34. N. Provatas, N. Goldenfeld, and J. Dantzig, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.3308 80, 3308 (1998).