A phase-field approach for minimizing the area of triply periodic surfaces with volume constraint

Computer Physics Communications

Volumn 181, Issue 6, 2010, Pages 1037-1046

  Yang, Seong Deog ^a   Lee, Hyun Geun ^a   Kim, Junseok ^a  

^a Korea University   (South Korea)

Author keywords

Constant mean curvature; Phase field model; Unconditionally gradient stable scheme

Indexed keywords

BIOMORPHIC; EFFICIENT ALGORITHM; MEAN CURVATURE; MINIMAL SURFACES; NODAL SURFACE; PERIODIC SURFACES; PHASE-FIELD APPROACHES; PHASE-FIELD MODELS; SCHWARZ; VOLUME CONSTRAINT;

MECHANICAL PROPERTIES; TITRATION;

ALGORITHMS;

EID: 77950518766     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cpc.2010.02.010     Document Type: Article

References (37)

1. Alexandrov O., and Santosa F. J. Comput. Phys. 204 (2005) 121
2. Brakke K. Experiment. Math. 1 (1992) 141
3. Burden R.L., and Faires J.D. Numerical Analysis (2004), Thomson
4. do Carmo M. Differential Geometry of Curves and Surfaces (1976), Prentice Hall
5. Choksi R., and Sternberg P. Interfaces Free Bound. 8 (2006) 371
6. Du Q., Liu C., Ryham R., and Wang X. Nonlinearity 18 (2005) 1249
7. Eyre D. An unconditionally stable one-step scheme for gradient systems. http://www.math.utah.edu/~eyre/research/methods/stable.ps
8. D. Eyre, in: Computational and Mathematical Models of Microstructural Evolution, 1998, p. 39
9. Gabbrielli R., Turner I.G., and Bowen C.R. Key Eng. Mater. Bioceramics 20 (2008) 903
10. Gandy P.J.F., Bardhan S., Mackay A.L., and Klinowski J. Chem. Phys. Lett. 336 (2001) 187
11. Góźgź W.T., and Holyst R. Phys. Rev. Lett. 76 (1996) 2726
12. Greer J.B., Bertozzi A.L., and Sapiro G. J. Comput. Phys. 216 (2006) 216
13. Grosse-Brauckmann K. J. Colloid Interface Sci. 187 (1997) 418
14. Hauswirth L., Perez J., Romon P., and Ros A. Trans. Amer. Math. Soc. 356 (2004) 2025
15. Hildebrandt S., and Tromba A. Mathematics and Optimal Form (1985), Scientific American Library
16. Hyde S.T. Curr. Opin. Solid State Mater. Sci. 1 (1996) 653
17. Jung Y., Chu K.T., and Torquato S. J. Comput. Phys. 223 (2007) 711
18. Jung Y., and Torquato S. Phys. Rev. E 72 (2005) 056319-1
19. Kim J., and Bae H. J. Korean Phys. Soc. 53 (2008) 672
20. Klinowski J., Mackay A.L., and Terrones H. Phil. Trans. R. Soc. Lond. A 354 (1996) 1975
21. Lord E.A., and Mackay A.L. Current Sci. 85 (2003) 346
22. Mackay A.L. Proc. R. Soc. Lond. A 442 (1993) 47
23. Mackay A.L. Chem. Phys. Lett. 221 (1994) 317
24. National Research Council. Biomolecular Self-Assembling Materials: Scientific and Technological Frontiers (1996), National Academies Press
25. Nitsche J.C.C. Introduction, Fundamentals, Geometry and Basic Boundary Value Problems. Lectures on Minimal Surfaces vol. 1 (1989), Cambridge University Press
26. Osher S.J., and Fedkiw R.P. Level Set Methods and Dynamic Implicit Surfaces (2002), Springer-Verlag
27. Osher S.J., and Santosa F. J. Comput. Phys. 171 (2001) 272
28. Rajagopalan S., and Robb R.A. Lecture Notes in Comput. Sci. 3749 (2005) 794
29. Ros A. The isoperimetric problem. Proceedings of the Clay Mathematics Institute Summer School on the Global Theory of Minimal Surfaces (2001). http://www.ugr.es/~aros/isoper.htm
30. von Schnering H.G., and Nesper R. Z. Phys. B: Condens. Matter 83 (1991) 407
31. Schwarz U.S., and Gompper G. Phys. Rev. E 59 (1999) 5528
32. Sethian J.A. Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (1999), Cambridge University Press
33. Siem E.J., and Carter W.C. Interface Sci. 10 (2002) 287
34. Trottenberg U., Oosterlee C., and Schüller A. MULTIGRID (2001), Academic Press
35. Vollmayr-Lee B.P., and Rutenberg A.D. Phys. Rev. E 68 (2003) 066703-1
36. Wang Y. Computer-Aided Design 39 (2007) 179
37. Xu G., and Zhang Q. Computer-Aided Design 39 (2007) 342