Effect of dimensionality on the percolation threshold of overlapping nonspherical hyperparticles

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

Volumn 87, Issue 2, 2013, Pages

  Torquato, S ^a   Jiao, Y ^b  

^a PRINCETON UNIVERSITY   (United States)

^b Princeton University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AFFINE TRANSFORMATIONS; ARBITRARY SHAPE; CONTINUUM PERCOLATION; EUCLIDEAN SPACES; EXPLICIT FORMULA; GEOMETRICAL PROPERTY; HIGH-DIMENSIONAL; HYPER-SPHERES; HYPERSPHERE; LOWER BOUNDS; MEAN CURVATURE; NON-SPHERICAL; PERCOLATION THRESHOLDS; PLATONIC SOLIDS; RANDOM ORIENTATIONS; SCALING RELATIONS; SPACE DIMENSIONS; SPHEROCYLINDERS; SURFACE AREA; UPPER BOUND;

GEOMETRY; PERCOLATION (FLUIDS); SOLVENTS;

PERCOLATION (COMPUTER STORAGE);

NANOPARTICLE;

ARTICLE; CHEMICAL MODEL; CHEMISTRY; COMPUTER SIMULATION; QUANTUM THEORY; STATISTICAL MODEL;

COMPUTER SIMULATION; MODELS, CHEMICAL; MODELS, STATISTICAL; NANOPARTICLES; QUANTUM THEORY;

EID: 84874280553     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.87.022111     Document Type: Article

References (37)

1. R. Zallen, The Physics of Amorphous Solids (Wiley, New York, 1983).
2. C. J. Brinker and G. W. Scherer, Sol-Gel Science: The Physics and Chemistry of Sol-Gel Processing (Academic, New York, 1990).
3. D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor & Francis, London, 1992).
4. M. Sahimi, Applications of Percolation Theory (Taylor and Francis, London, 1994).
5. S. Torquato, Random Heterogeneous Materials: Microstructure and Macroscopic Properties (Springer-Verlag, New York, 2002).
6. V. Myroshnychenko and C. Brosseau, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.2907769 103, 084112 (2008); (Pubitemid 351623616)
7. S. El Bouazzaoui, A. Droussi, M. E. Achour, and C. Brosseau, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.3253744 106, 104107 (2009).
8. S. Torquato, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.3679861 136, 054106 (2012).
9. S. Torquato and Y. Jiao, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.4742750 137, 074106 (2012).
10. I. Balberg, C. H. Anderson, S. Alexander, and N. Wagner, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.30.3933 30, 3933 (1984).
11. S. Torquato, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01020577 45, 843 (1986).
12. C. E. Zachary and S. Torquato, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.84.056102 84, 056102 (2011).
13. D. Stoyan, W. S. Kendall, and J. Mecke, Stochastic Geometry and Its Applications, 2nd ed. (Wiley, New York, 1995).
14. T. Boublík, Mol. Phys. MOPHAM 0026-8976 10.1080/00268977500100361 29, 421 (1975).
15. T. Kihara, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.25.831 25, 831 (1953).
16. R. Schneider, Convex Bodies: The Brunn-Minkowski Theory (Cambridge University Press, Cambridge, 1993).
17. L. Onsager, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.65.117 65, 117 (1944).
18. H. S. M. Coxeter, Regular Polytopes (Dover, New York, 1973).
19. H. Hadwiger, Math. Annalen MAANA3 0025-5831 10.1007/BF01351491 239, 271 (1979).
20. U. Betke and M. Henk, Monatsh. Math. 0026-9255 10.1007/BF01311208 115, 27 (1993).
21. M. Henk, J. Richter-Gebert, and G. M. Ziegler, Handbook of Discrete and Computational Geometry (CRC Press, New York, 1997).
22. D. R. Baker, G. Paul, S. Sreenivasan, and H. E. Stanley, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.66.046136 66, 046136 (2002). (Pubitemid 40606260)
23. S. Mertens and C. Moore, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.86.061109 86, 061109 (2012).
24. W. Xia and M. F. Thorpe, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.38.2650 38, 2650 (1988).
25. Y. B. Yi and A. M. Sastry, Proc. R. Soc. London A 1364-5021 10.1098/rspa.2004.1279 460, 2353 (2004). (Pubitemid 40268442)
26. E. J. Garboczi, K. A. Snyder, J. F. Douglas, and M. F. Thorpe, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.52.819 52, 819 (1995).
27. J. A. Quintanilla, S. Torquato, and R. M. Ziff, J. Phys. A: Math. Gen. 1361-6447 10.1088/0305-4470/33/42/104 33, L399 (2000).
28. J. Quintanilla and R. M. Ziff, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.76.051115 76, 051115 (2007). (Pubitemid 350126062)
29. C. D. Lorenz and R. M. Ziff, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1338506 114, 3659 (2000).
30. Y. B. Yi and E. Tawerghi, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.79.041134 79, 041134 (2009).
31. S. Torquato and Y. Jiao, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.86.011102 86, 011102 (2012).
32. Y. Jiao, F. H. Stillinger, and S. Torquato, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.79.041309 79, 041309 (2009).
33. Y. Jiao and S. Torquato, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.3653938 135, 151101 (2011).
34. S. Torquato and F. H. Stillinger, Experimental Math. 1058-6458 10.1080/10586458.2006.10128964 15, 307 (2006).
35. C. E. Zachary and S. Torquato, J. Stat. Mech.: Theory Exp. 1742-5468 10.1088/1742-5468/2011/10/P10017 (2011) P10017.
36. S. Torquato and Y. Jiao, Nature (London) NATUAS 0028-0836 10.1038/nature08239 460, 876 (2009).
37. S. Torquato and Y. Jiao, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.041104 80, 041104 (2009).