A characterization of optimal two-phase multifunctional composite designs

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 463, Issue 2086, 2007, Pages 2543-2556

  Silvestre, Luis ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

Composites; Free boundary problems; Upper bounds

Indexed keywords

EID: 36348985082     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2007.1884     Document Type: Article

References (13)

1. Aguilera, N., Alt, H. W. & Caffarelli, L. A. 1986 An optimization problem with volume constraint. SIAM J. Control Optim. 24, 191-198. (doi:10.1137/0324011)
2. Andersson, J. & Weiss, G. S. 2006 Cross-shaped and degenerate singularities in an unstable elliptic free boundary problem. J. Differ. Equations 228, 633-640. (doi:10.1016/j.jde.2005.11.008)
3. Bergman, D. J. 1978 The dielectric constant of a composite material - a problem in classical physics. Phys. Rep. 43, 377-407. (doi:10.1016/0370-1573(78)90009-1)
4. Caffarelli, L. A. 1998 The obstacle problem revisited. J. Fourier Anal. Appl. 4, 383-402. (doi:10.1007/BF02498216)
5. Caffarelli, L. & Salsa, S. 2005 A geometric approach to free boundary problems, vol. 68. Graduate Studies in Mathematics. Providence, RI: American Mathematical Society.
6. Gandy, P. J. F., Bardhan, S., Mackay, A. L. & Klinowski, J. 2001 Nodal surface approximations to the p, g, d and i-wp triply periodic minimal surfaces. Chem. Phys. Lett. 336, 187-195. (doi:10.1016/S0009- 2614(00)01418-4)
7. Henrik Shahgholian, N. U. & Weiss G. S. In press. The two-phase membrane problem-regularity in higher dimensions. Int. Math. Res. Not.
8. Liu, L., James, D. & Leo, H. Submitted. Inclusions for which constant magnetization implies constant field, and their applications.
9. Milton, G. W. 2002 The theory of composites. Cambridge Monographs on Applied and Computational Mathematics, no. 6, pp. 719. Cambridge, UK: Cambridge University Press.
10. Schwarz, U. S. & Gompper, G. 1999 Systematic approach to bicontinuous cubic phases in ternary amphiphilic systems. Phys. Rev. E 59, 5528-5541. (doi:10.1103/PhysRevE.59.5528)
11. Torquato, S. & Donev, A. 2004 Minimal surfaces and multifunctionality. Proc. R. Soc. A 460, 1849-1856. (doi:10.1098/rspa.2003.1269)
12. Torquato, S., Hyun, S. & Donev, A. 2002 Multifunctional composites: optimizing microstructures for simultaneous transport of heat and electricity. Phys. Rev. Lett. 89, 266 601. (doi:10.1103/PhysRevLett.89.266601)
13. Torquato, S., Hyun, S. & Donev, A. 2003 Optimal design of manufacturable three-dimensional composites with multifunctional characteristics. J. Appl. Phys. 94, 5748-5755. (doi:10.1063/1.1611631)