Hyperuniformity and its generalizations

Physical Review E

Volumn 94, Issue 2, 2016, Pages

  Torquato, Salvatore ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPIC MEDIA; ANISOTROPY; ELECTRIC FIELDS; GROUND STATE; HIGH ENERGY PHYSICS; MICROSTRUCTURE; PHYSICAL PROPERTIES; POROUS MATERIALS; SPECTROSCOPY; SPINODAL DECOMPOSITION; VECTOR SPACES;

ACOUSTIC CHARACTERISTIC; ANISOTROPIC STRUCTURE; FLUID SATURATED POROUS MEDIA; GROUND STATE CONFIGURATION; MAGNETIC AND ELECTRIC FIELDS; MANY-PARTICLE SYSTEMS; MINKOWSKI FUNCTIONALS; TWO-PHASE MICROSTRUCTURES;

DENSITY OF LIQUIDS;

EID: 84983539681     PISSN: 24700045     EISSN: 24700053     Source Type: Journal    
DOI: 10.1103/PhysRevE.94.022122     Document Type: Article

References (130)

1. B. Widom, Equation of state in the neighborhood of the critical point, J. Chem. Phys. 43, 3898 (1965). JCPSA6 0021-9606 10.1063/1.1696618
2. L. P. Kadanoff, Scaling laws for Ising models near (Equation presented), Physics 2, 263 (1966).
3. M. E. Fisher, The theory of equilibrium critical phenomena, Rep. Prog. Phys. 30, 615 (1967). RPPHAG 0034-4885 10.1088/0034-4885/30/2/306
4. K. G. Wilson and J. Kogut, The renormalization group and the (Equation presented) expansion, Phys. Rep. 12, 75 (1974). PRPLCM 0370-1573 10.1016/0370-1573(74)90023-4
5. P. J. E. Peebles, Principles of Physical Cosmology (Princeton University Press, Princeton, NJ, 1993).
6. S. Warr and J.-P. Hansen, Relaxation of local density fluctuations in a fluidized granular medium, Europhys. Lett. 36, 589 (1996). EULEEJ 0295-5075 10.1209/epl/i1996-00273-1
7. P. R. ten Wolde and D. Frenkel, Enhancement of protein crystal nucleation by critical density fluctuations, Science 277, 1975 (1997). SCIEAS 0036-8075 10.1126/science.277.5334.1975
8. E. R. Nowak, J. B. Knight, E. Ben-Naim, H. M. Jaeger, and S. R. Nagel, Density fluctuations in vibrated granular materials, Phys. Rev. E 57, 1971 (1998). 1063-651X 10.1103/PhysRevE.57.1971
9. A. M. Kulkarni, A. P. Chatterjee, K. S. Schweizer, and C. F. Zukoski, Depletion Interactions in the Protein Limit: Effects of Polymer Density Fluctuations, Phys. Rev. Lett. 83, 4554 (1999). PRLTAO 0031-9007 10.1103/PhysRevLett.83.4554
10. K. Lum, D. Chandler, and J. D. Weeks, Hydrophobicity at small and large length scales, J. Phys. Chem. B 103, 4570 (1999). JPCBFK 1520-6106 10.1021/jp984327m
11. A. Gabrielli, F. Sylos Labini, M. Joyce, and L. Pietronero, Statistical Physics for Cosmic Structures (Springer-Verlag, New York, 2005).
12. R. Chang and A. Yethiraj, Strongly charged flexible polyelectrolytes in poor solvents: Molecular dynamics simulations with explicit solvent, J. Chem. Phys. 118, 6634 (2003). JCPSA6 0021-9606 10.1063/1.1558312
13. Z. Ou and M. Muthukumar, Entropy and enthalpy of polyelectrolyte complexation: Langevin dynamics simulations, J. Chem. Phys. 124, 154902 (2006). 10.1063/1.2178803
14. L. Berthier, G. Biroli, J.-P. Bouchaud, W. Kob, K. Miyazaki, and D. R. Reichman, Spontaneous and induced dynamic fluctuations in glass formers. I. General results and dependence on ensemble and dynamics, J. Chem. Phys. 126, 184503 (2007). 10.1063/1.2721554
15. Y. Jiao, H. Berman, T.-R. Kiehl, and S. Torquato, Spatial organization and correlations of cell nuclei in brain tumors, PLoS ONE 6, e27323 (2011). 1932-6203 10.1371/journal.pone.0027323
16. S. Torquato and F. H. Stillinger, Local density fluctuations, hyperuniform systems, and order metrics, Phys. Rev. E 68, 041113 (2003). 1063-651X 10.1103/PhysRevE.68.041113
17. J. P. Hansen and I. R. McDonald, Theory of Simple Liquids (Academic Press, New York, 1986).
18. C. E. Zachary and S. Torquato, Hyperuniformity in point patterns and two-phase heterogeneous media, J. Stat. Mech.: Theory Exp. (2009) P12015. 10.1088/1742-5468/2009/12/P12015
19. C. E. Zachary and S. Torquato, Anomalous local coordination, density fluctuations, and void statistics in disordered hyperuniform many-particle ground states, Phys. Rev. E 83, 051133 (2011). PLEEE8 1539-3755 10.1103/PhysRevE.83.051133
20. S. Torquato, G. Zhang, and F. H. Stillinger, Ensemble Theory for Stealthy Hyperuniform Disordered Ground States, Phys. Rev. X 5, 021020 (2015). 2160-3308 10.1103/PhysRevX.5.021020
21. O. U. Uche, F. H. Stillinger, and S. Torquato, Constraints on collective density variables: Two dimensions, Phys. Rev. E 70, 046122 (2004). PLEEE8 1539-3755 10.1103/PhysRevE.70.046122
22. R. D. Batten, F. H. Stillinger, and S. Torquato, Classical disordered ground states: Super-ideal gases, and stealth and equi-luminous materials, J. Appl. Phys. 104, 033504 (2008); JAPIAU 0021-8979 10.1063/1.2961314
23. Novel Low-Temperature Behavior in Classical Many-Particle Systems, Phys. Rev. Lett. 103, 050602 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.103.050602
24. J. L. Lebowitz, Charge fluctuations in Coulomb systems, Phys. Rev. A 27, 1491 (1983). 0556-2791 10.1103/PhysRevA.27.1491
25. A. Gabrielli, M. Joyce, and F. Sylos Labini, Glass-like universe: Real-space correlation properties of standard cosmological models, Phys. Rev. D 65, 083523 (2002). 0556-2821 10.1103/PhysRevD.65.083523
26. G. Zhang, F. Stillinger, and S. Torquato, Ground states of stealthy hyperuniform potentials. I. Entropically favored configurations, Phys. Rev. E 92, 022119 (2015). PLEEE8 1539-3755 10.1103/PhysRevE.92.022119
27. G. Zhang, F. Stillinger, and S. Torquato, Ground states of stealthy hyperuniform potentials: II. Stacked-slider phases, Phys. Rev. E 92, 022120 (2015). PLEEE8 1539-3755 10.1103/PhysRevE.92.022120
28. A. Donev, F. H. Stillinger, and S. Torquato, Unexpected Density Fluctuations in Disordered Jammed Hard-Sphere Packings, Phys. Rev. Lett. 95, 090604 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.95.090604
29. C. E. Zachary, Y. Jiao, and S. Torquato, Hyperuniform Long-Range Correlations are a Signature of Disordered Jammed Hard-Particle Packings, Phys. Rev. Lett. 106, 178001 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.106.178001
30. Y. Jiao and S. Torquato, Maximally random jammed packings of Platonic solids: Hyperuniform long-range correlations and isostaticity, Phys. Rev. E 84, 041309 (2011). PLEEE8 1539-3755 10.1103/PhysRevE.84.041309
31. D. Chen, Y. Jiao, and S. Torquato, Equilibrium phase behavior and maximally random jammed state of truncated tetrahedra, J. Phys. Chem. B 118, 7981 (2014). JPCBFK 1520-6106 10.1021/jp5010133
32. L. Berthier, P. Chaudhuri, C. Coulais, O. Dauchot, and P. Sollich, Suppressed Compressibility at Large Scale in Jammed Packings of Size-Disperse Spheres, Phys. Rev. Lett. 106, 120601 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.106.120601
33. R. Kurita and E. R. Weeks, Incompressibility of polydisperse random-close-packed colloidal particles, Phys. Rev. E 84, 030401 (2011). PLEEE8 1539-3755 10.1103/PhysRevE.84.030401
34. G. L. Hunter and E. R. Weeks, The physics of the colloidal glass transition, Rep. Prog. Phys. 75, 066501 (2012). RPPHAG 0034-4885 10.1088/0034-4885/75/6/066501
35. R. Dreyfus, Y. Xu, T. Still, L. A. Hough, A. G. Yodh, and S. Torquato, Diagnosing hyperuniformity in two-dimensional, disordered, jammed packings of soft spheres, Phys. Rev. E 91, 012302 (2015). PLEEE8 1539-3755 10.1103/PhysRevE.91.012302
36. I. Lesanovsky and J. P. Garrahan, Out-of-equilibrium structures in strongly interacting Rydberg gases with dissipation, Phys. Rev. A 90, 011603 (2014). PLRAAN 1050-2947 10.1103/PhysRevA.90.011603
37. M. Florescu, S. Torquato, and P. J. Steinhardt, Designer disordered materials with large complete photonic band gaps, Proc. Natl. Acad. Sci. USA 106, 20658 (2009). PNASA6 0027-8424 10.1073/pnas.0907744106
38. D. Hexner and D. Levine, Hyperuniformity of Critical Absorbing States, Phys. Rev. Lett. 114, 110602 (2015). PRLTAO 0031-9007 10.1103/PhysRevLett.114.110602
39. R. L. Jack, I. R. Thompson, and P. Sollich, Hyperuniformity and Phase Separation in Biased Ensembles of Trajectories for Diffusive Systems, Phys. Rev. Lett. 114, 060601 (2015). PRLTAO 0031-9007 10.1103/PhysRevLett.114.060601
40. J. H. Weijs, R. Jeanneret, R. Dreyfus, and D. Bartolo, Emergent Hyperuniformity in Periodically Driven Emulsions, Phys. Rev. Lett. 115, 108301 (2015). PRLTAO 0031-9007 10.1103/PhysRevLett.115.108301
41. E. Tjhung and L. Berthier, Hyperuniform Density Fluctuations and Diverging Dynamic Correlations in Periodically Driven Colloidal Suspensions, Phys. Rev. Lett. 114, 148301 (2015). PRLTAO 0031-9007 10.1103/PhysRevLett.114.148301
42. K. J. Schrenk and D. Frenkel, Communication: Evidence for non-ergodicity in quiescent states of periodically sheared suspensions, J. Chem. Phys. 143, 241103 (2015). 10.1063/1.4938999
43. R. Dickman and S. D. da Cunha, Particle-density fluctuations and universality in the conserved stochastic sandpile, Phys. Rev. E 92, 020104 (2015). PLEEE8 1539-3755 10.1103/PhysRevE.92.020104
44. Y. Jiao, T. Lau, H. Hatzikirou, M. Meyer-Hermann, J. C. Corbo, and S. Torquato, Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem, Phys. Rev. E 89, 022721 (2014). PLEEE8 1539-3755 10.1103/PhysRevE.89.022721
45. L. M. Burcaw, E. Fieremans, and D. S. Novikov, Mesoscopic structure of neuronal tracts from time-dependent diffusion, NeuroImage 114, 18 (2015). NEIMEF 1053-8119 10.1016/j.neuroimage.2015.03.061
46. A. Mayer, V. Balasubramanian, T. Mora, and A. M. Walcza, How a well-adapted immune system is organized, Proc. Natl. Acad. Sci. USA 112, 5950 (2015). PNASA6 0027-8424 10.1073/pnas.1421827112
47. S. Torquato, A. Scardicchio, and C. E. Zachary, Point processes in arbitrary dimension from Fermionic gases, random matrix theory, and number theory, J. Stat. Mech.: Theory Exp. (2008) P11019. 10.1088/1742-5468/2008/11/P11019
48. R. P. Feynman and M. Cohen, Energy spectrum of the excitations in liquid helium, Phys. Rev. 102, 1189 (1956). PHRVAO 0031-899X 10.1103/PhysRev.102.1189
49. O. Leseur, R. Pierrat, and R. Carminati, High-density hyperuniform materials can be transparent, Optica 3, 763 (2016). 10.1364/OPTICA.3.000763
50. S. Yu, X. Piao, J. Hong, and N. Park, Bloch-like wave dynamics in disordered potentials based on supersymmetry, Nat. Commun. 6, 8269 (2015). 10.1038/ncomms9269
51. É. Marcotte, F. H. Stillinger, and S. Torquato, Nonequilibrium static growing length scales in supercooled liquids on approaching the glass transition, J. Chem. Phys. 138, 12A508 (2013). 10.1063/1.4769422
52. A. Coniglio and T. Aste, Cell theory for glass-forming materials and jamming matter, combining free volume and cooperative rearranging regions, arXiv:1505.05540.
53. V. Lubchenko and P. G. Wolynes, Theory of structural glasses and supercooled liquids, Annu. Rev. Phys. Chem. 58, 235 (2007). ARPLAP 0066-426X 10.1146/annurev.physchem.58.032806.104653
54. K. S. Schweizer, Dynamical fluctuation effects in glassy colloidal suspensions, Curr. Opin. Colloid Interface Sci. 12, 297 (2007). COCSFL 1359-0294 10.1016/j.cocis.2007.07.013
55. S. Karmakar, C. Dasgupta, and S. Sastry, Growing length and time scales in glass-forming liquids, Proc. Natl. Acad. Sci. USA 106, 3675 (2009). PNASA6 0027-8424 10.1073/pnas.0811082106
56. D. Chandler and J. P. Garrahan, Dynamics on the way to forming glass: Bubbles in space-time, Annu. Rev. Phys. Chem. 61, 191 (2010). ARPLAP 0066-426X 10.1146/annurev.physchem.040808.090405
57. G. M. Hocky, T. E. Markland, and D. R. Reichman, Growing Point-To-Set Length Scale Correlates with Growing Relaxation Times in Model Supercooled Liquids, Phys. Rev. Lett. 108, 225506 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.225506
58. H. L. Montgomery, The pair correlation of zeros of the zeta function, in Proc. Symp. Pure Math. 181 (1973).
59. F. J. Dyson, Statistical theory of the energy levels of complex systems. I, J. Math. Phys. 3, 140 (1962). JMAPAQ 0022-2488 10.1063/1.1703773
60. W. Man, M. Florescu, K. Matsuyama, P. Yadak, G. Nahal, S. Hashemizad, E. Williamson, P. Steinhardt, S. Torquato, and P. Chaikin, Photonic band gap in isotropic hyperuniform disordered solids with low dielectric contrast, Opt. Express 21, 19972 (2013). OPEXFF 1094-4087 10.1364/OE.21.019972
61. W. Man, M. Florescu, E. P. Williamson, Y. He, S. R. Hashemizad, B. Y. C. Leung, D. R. Liner, S. Torquato, P. M. Chaikin, and P. J. Steinhardt, Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids, Proc. Natl. Acad. Sci. USA 110, 15886 (2013). PNASA6 0027-8424 10.1073/pnas.1307879110
62. J. Haberko, N. Muller, and F. Scheffold, Direct laser writing of three dimensional network structures as templates for disordered photonic materials, Phys. Rev. A 88, 043822 (2013). PLRAAN 1050-2947 10.1103/PhysRevA.88.043822
63. C. De Rosa, F. Auriemma, C. Diletto, R. Di Girolamo, A. Malafronte, P. Morvillo, G. Zito, G. Rusciano, G. Pesce, and A. Sasso, Toward hyperuniform disordered plasmonic nanostructures for reproducible surface-enhanced Raman spectroscopy, Phys. Chem. Chem. Phys. 17, 8061 (2015). PPCPFQ 1463-9076 10.1039/C4CP06024E
64. R. Degl'Innocenti, Y. D. Shah, L. Masini, A. Ronzani, A. Pitanti, Y. Ren, D. S. Jessop, A. Tredicucci, H. E. Beere, and D. A. Ritchie, THz quantum cascade lasers based on a hyperuniform design, Proc. SPIE 9370, 93700A (2015). PSISDG 0277-786X 10.1117/12.2083678
65. G. Zito, G. Rusciano, G. Pesce, A. Malafronte, R. Di Girolamo, G. Ausanio, A. Vecchione, and A. Sasso, Nanoscale engineering of two-dimensional disordered hyperuniform block-copolymer assemblies, Phys. Rev. E 92, 050601 (2015). PLEEE8 1539-3755 10.1103/PhysRevE.92.050601
66. M. Hejna, P. J. Steinhardt, and S. Torquato, Nearly hyperuniform network models of amorphous silicon, Phys. Rev. B 87, 245204 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.87.245204
67. R. Xie, G. G. Long, S. J. Weigand, S. C. Moss, T. Carvalho, S. Roorda, M. Hejna, S. Torquato, and P. J. Steinhardt, Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor, Proc. Natl. Acad. Sci. USA 110, 13250 (2013). PNASA6 0027-8424 10.1073/pnas.1220106110
68. S. Torquato, Random Heterogeneous Materials: Microstructure and Macroscopic Properties (Springer-Verlag, New York, 2002).
69. B. L. Lu and S. Torquato, Local volume fraction fluctuations in heterogeneous media, J. Chem. Phys. 93, 3452 (1990). JCPSA6 0021-9606 10.1063/1.458827
70. J. Quintanilla and S. Torquato, Local volume fraction fluctuations in random media, J. Chem. Phys. 106, 2741 (1997). JCPSA6 0021-9606 10.1063/1.473414
71. C. E. Zachary, Y. Jiao, and S. Torquato, Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres, Phys. Rev. E 83, 051308 (2011). PLEEE8 1539-3755 10.1103/PhysRevE.83.051308
72. C. E. Zachary, Y. Jiao, and S. Torquato, Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. II. Anisotropy in particle shape, Phys. Rev. E 83, 051309 (2011). PLEEE8 1539-3755 10.1103/PhysRevE.83.051309
73. D. Chen and S. Torquato, Confined disordered strictly jammed binary sphere packings, Phys. Rev. E 92, 062207 (2015). PLEEE8 1539-3755 10.1103/PhysRevE.92.062207
74. R. A. DiStasio, G. Zhang, F. H. Stillinger, and S. Torquato, Rational design of stealthy hyperuniform patterns with tunable order (unpublished).
75. S. Torquato and F. H. Stillinger, New conjectural lower bounds on the optimal density of sphere packings, Exp. Math. 15, 307 (2006). 1058-6458 10.1080/10586458.2006.10128964
76. P. Debye and A. M. Bueche, Scattering by an inhomogeneous solid, J. Appl. Phys. 20, 518 (1949). JAPIAU 0021-8979 10.1063/1.1698419
77. P. Debye, H. R. Anderson, and H. Brumberger, Scattering by an inhomogeneous solid. II. The correlation function and its applications, J. Appl. Phys. 28, 679 (1957). JAPIAU 0021-8979 10.1063/1.1722830
78. S. Torquato and G. Stell, Microstructure of two-phase random media: I. The (Equation presented)-point probability functions, J. Chem. Phys. 77, 2071 (1982). JCPSA6 0021-9606 10.1063/1.444011
79. S. Torquato and G. Stell, Microstructure of two-phase random media. II. The Mayer-Montroll and Kirkwood-Salsburg hierarchies, J. Chem. Phys. 78, 3262 (1983). JCPSA6 0021-9606 10.1063/1.445245
80. S. Torquato, Effective electrical conductivity of two-phase disordered composite media, J. Appl. Phys. 58, 3790 (1985). JAPIAU 0021-8979 10.1063/1.335593
81. J. G. Berryman and G. W. Milton, Normalization constraint for variational bounds on fluid permeability, J. Chem. Phys. 83, 754 (1985). JCPSA6 0021-9606 10.1063/1.449489
82. J. G. Berryman and G. W. Milton, Microgeometry of random composites and porous media, J. Phys. D: Appl. Phys. 21, 87 (1988). JPAPBE 0022-3727 10.1088/0022-3727/21/1/013
83. A. K. Sen and S. Torquato, Effective conductivity of anisotropic two-phase composite media, Phys. Rev. B 39, 4504 (1989). PRBMDO 0163-1829 10.1103/PhysRevB.39.4504
84. L. V. Gibiansky and S. Torquato, Geometrical-parameter bounds on effective moduli of composites, J. Mech. Phys. Solids 43, 1587 (1995). JMPSA8 0022-5096 10.1016/0022-5096(95)00049-O
85. G. W. Milton, The Theory of Composites (Cambridge University Press, Cambridge, UK, 2002).
86. D. C. Pham and S. Torquato, Strong-contrast expansions and approximations for the effective conductivity of isotropic multiphase composites, J. Appl. Phys. 94, 6591 (2003). JAPIAU 0021-8979 10.1063/1.1619573
87. S. Torquato and D. C. Pham, Optimal Bounds on the Trapping Constant and Permeability of Porous Media, Phys. Rev. Lett. 92, 255505 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.92.255505
88. S. Torquato, Exact Expression for the Effective Elastic Tensor of Disordered Composites, Phys. Rev. Lett. 79, 681 (1997). PRLTAO 0031-9007 10.1103/PhysRevLett.79.681
89. M. C. Rechtsman and S. Torquato, Effective dielectric tensor for electromagnetic wave propagation in random media, J. Appl. Phys. 103, 084901 (2008). JAPIAU 0021-8979 10.1063/1.2906135
90. S. Torquato, Disordered hyperuniform heterogeneous materials, J. Phys.: Condens. Matter 28, 414012 (2016).
91. M. Doi, A new variational approach to the diffusion and the flow problem in porous media, J. Phys. Soc. Jpn. 40, 567 (1976). JUPSAU 0031-9015 10.1143/JPSJ.40.567
92. J. Rubinstein and S. Torquato, Diffusion-controlled reactions: Mathematical formulation, variational principles, and rigorous bounds, J. Chem. Phys. 88, 6372 (1988). JCPSA6 0021-9606 10.1063/1.454474
93. J. Rubinstein and S. Torquato, Flow in random porous media: Mathematical formulation, variational principles, and rigorous bounds, J. Fluid Mech. 206, 25 (1989). JFLSA7 0022-1120 10.1017/S0022112089002211
94. S. Torquato and G. Stell, Microstructure of two-phase random media. V. The (Equation presented)-point matrix probability functions for impenetrable spheres, J. Chem. Phys. 82, 980 (1985). JCPSA6 0021-9606 10.1063/1.448475
95. B. L. Lu and S. Torquato, General formalism to characterize the microstructure of polydispersed random media, Phys. Rev. A 43, 2078 (1991). PLRAAN 1050-2947 10.1103/PhysRevA.43.2078
96. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevE.94.022122 for explicit formulas of the autocovariance function (Equation presented) and spectral density (Equation presented) of polydisperse sphere packings.
97. J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys. 28, 258 (1958). JCPSA6 0021-9606 10.1063/1.1744102
98. J. Swift and P. C. Hohenberg, Hydrodynamic fluctuations at the convective instability, Phys. Rev. A 15, 319 (1977). 0556-2791 10.1103/PhysRevA.15.319
99. S. Torquato, Microstructure characterization and bulk properties of disordered two-phase media, J. Stat. Phys. 45, 843 (1986). JSTPBS 0022-4715 10.1007/BF01020577
100. S. Torquato, Interfacial surface statistics arising in diffusion and flow problems in porous media, J. Chem. Phys. 85, 4622 (1986). JCPSA6 0021-9606 10.1063/1.451783
101. S. Torquato, Statistical description of microstructures, Annu. Rev. Mater. Res. 32, 77 (2002). ARMRCU 1531-7331 10.1146/annurev.matsci.32.110101.155324
102. J. R. Crawford, S. Torquato, and F. H. Stillinger, Aspects of correlation function realizability, J. Chem. Phys. 119, 7065 (2003). JCPSA6 0021-9606 10.1063/1.1606678
103. O. U. Uche, F. H. Stillinger, and S. Torquato, On the realizability of pair correlation functions, Phys. A (Amsterdam, Neth.) 360, 21 (2006). PHYADX 0378-4371 10.1016/j.physa.2005.03.058
104. S. Torquato and F. H. Stillinger, Exactly solvable disordered sphere-packing model in arbitrary-dimensional Euclidean spaces, Phys. Rev. E 73, 031106 (2006). PLEEE8 1539-3755 10.1103/PhysRevE.73.031106
105. M. Sahimi, Heterogeneous Materials. I. Linear Transport and Optical Properties (Springer-Verlag, New York, 2003).
106. G. K. Batchelor, The Theory of Homogeneous Turbulence (Cambridge University Press, Cambridge, UK, 1959).
107. A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence (MIT Press, Cambridge, MA, 1975), Vol. 2.
108. D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, Diffusing Wave Spectroscopy, Phys. Rev. Lett. 60, 1134 (1988). PRLTAO 0031-9007 10.1103/PhysRevLett.60.1134
109. D. S. Wiersma, The physics and applications of random lasers, Nat. Phys. 4, 359 (2008). 1745-2473 10.1038/nphys971
110. A. Dogariu and R. Carminati, Electromagnetic field correlations in three-dimensional speckles, Phys. Rep. 559, 1 (2015). PRPLCM 0370-1573 10.1016/j.physrep.2014.11.003
111. D. Di Battista, D. Ancora, M. Leonetti, and G. Zacharakis, From amorphous speckle pattern to reconfigurable Bessel beam via wavefront shaping, arXiv:1511.04964v1.
112. E. Komatsu, A. Kogut, M. R. Nolta, C. L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, M. Limon, S. S. Meyer, L. Page, D. N. Spergel, G. S. Tucker, L. Verde, E. Wollack, and E. L. Wright, First-year Wilkinson microwave anisotropy probe (WMAP) observations: Tests of Gaussianity, Astrophys. J. Suppl. Ser. 148, 119 (2003). APJSA2 0067-0049 10.1086/377220
113. R. Blumenfeld and S. Torquato, Coarse-graining procedure to generate and analyze heterogeneous materials-Theory, Phys. Rev. E 48, 4492 (1993). 1063-651X 10.1103/PhysRevE.48.4492
114. N. F. Berk, Scattering Properties of a Model Bicontinuous Structure with a Well Defined Length Scale, Phys. Rev. Lett. 58, 2718 (1987). PRLTAO 0031-9007 10.1103/PhysRevLett.58.2718
115. N. F. Berk, Scattering properties of the leveled-wave model of random morphologies, Phys. Rev. A 44, 5069 (1991). PLRAAN 1050-2947 10.1103/PhysRevA.44.5069
116. M. Teubner, Level surfaces of Gaussian random fields and microemulsions, Europhys. Lett. 14, 403 (1991). EULEEJ 0295-5075 10.1209/0295-5075/14/5/003
117. P. A. Crossley, L. M. Schwartz, and J. R. Banavar, Image-based models of porous media-Application to Vycor glass and carbonate rocks, Appl. Phys. Lett. 59, 3553 (1991). APPLAB 0003-6951 10.1063/1.105630
118. A. P. Roberts and M. Teubner, Transport properties of heterogeneous materials derived from Gaussian random fields: Bounds and simulation, Phys. Rev. E 51, 4141 (1995). 1063-651X 10.1103/PhysRevE.51.4141
119. A. P. Roberts, Morphology and thermal conductivity of model organic aerogels, Phys. Rev. E 55, R1286 (1997). 1063-651X 10.1103/PhysRevE.55.R1286
120. P. G. Saffman, The large-scale structure of homogeneous turbulence, J. Fluid Mech. 27, 581 (1967). JFLSA7 0022-1120 10.1017/S0022112067000552
121. S. Martis, É. Marcotte, F. H. Stillinger, and S. Torquato, Exotic ground states of directional pair potentials via collective-density variables, J. Stat. Phys. 150, 414 (2013). JSTPBS 0022-4715 10.1007/s10955-012-0619-2
122. P. G. De Gennes and J. Prost, The Physics of Liquid Crystals (Oxford University Press, Oxford, UK, 1995).
123. J. P. Huang, Z. W. Wang, and C. Holm, Computer simulations of the structure of colloidal ferrofluids, Phys. Rev. E 71, 061203 (2005). PLEEE8 1539-3755 10.1103/PhysRevE.71.061203
124. J. L. Lebowitz and J. W. Perram, Correlation functions for nematic liquid crystals, Mol. Phys. 50, 1207 (1983). MOPHAM 0026-8976 10.1080/00268978300102981
125. F. Lado and S. Torquato, Two-point probability function for distributions of oriented hard ellipsoids, J. Chem. Phys. 93, 5912 (1990). JCPSA6 0021-9606 10.1063/1.459501
126. G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, M. A. Klatt, F. M. Schaller, M. J. F. Hoffmann, N. Kleppmann, P. Armstrong, A. Inayat, D. Hug, M. Reichelsdorfer, W. Peukert, W. Schwieger, and K. Mecke, Minkowski tensor shape analysis of cellular, granular and porous structures, Adv. Mater. 23, 2535 (2011). ADVMEW 0935-9648 10.1002/adma.201100562
127. B. Jancovici, Exact Results for the Two-Dimensional One-Component Plasma, Phys. Rev. Lett. 46, 386 (1981). PRLTAO 0031-9007 10.1103/PhysRevLett.46.386
128. F. H. Stillinger, Molecular distribution and elasticity in crystals, Phys. Rev. 142, 237 (1966). PHRVAO 0031-899X 10.1103/PhysRev.142.237
129. E. Chertkov, R. A. DiStasio, Jr., G. Zhang, R. Car, and S. Torquato, Inverse design of disordered stealthy hyperuniform spin chains, Phys. Rev. B 93, 064201 (2016). 2469-9950 10.1103/PhysRevB.93.064201
130. S. Torquato and B. Lu, Rigorous bounds on the fluid permeability: Effect of polydispersivity in grain size, Phys. Fluids A 2, 487 (1990). PFADEB 0899-8213 10.1063/1.857748