Density of states for a specified correlation function and the energy landscape

[en] The degeneracy of two-phase disordered microstructures consistent with a specified correlation function is analyzed by mapping it to a ground-state degeneracy. We determine for the first time the associated density of states via a Monte Carlo algorithm. Our results are described in terms of the roughness of the energy landscape, defined on a hypercubic configuration space. The use of a Hamming distance in this space enables us to define a roughness metric, which is calculated from the correlation function alone and related quantitatively to the structural degeneracy. This relation is validated for a wide variety of disordered systems.

Disciplines :

Physics
Mathematics

Author, co-author :

Gommes, Cédric ; Université de Liège - ULiège > Département de chimie appliquée > Génie chimique - Génie catalytique

Jiao, Yang; Princeton University > Chemistry

Torquato, Salvatore; Princeton University > Princeton Center for theoretical sciences

Language :

English

Title :

Density of states for a specified correlation function and the energy landscape

Publication date :

2012

Journal title :

Physical Review Letters

ISSN :

0031-9007

eISSN :

1079-7114

Publisher :

American Physical Society, Ridge, United States - New York

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 15 February 2012

Statistics

Number of views

444 (5 by ULiège)

Number of downloads

0 (0 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

Bibliography

R. Zallen, The Physics of Amorphous Solids (Wiley, New York, 1983).
J.-P. Chilès and P. Delfiner, Geostatistics: Modeling Spatial Uncertainty (Wiley, New York, 1999).
J. Serra, Image Analysis and Mathematical Morphology (Academic, London, 1982), Vol. 1.
D. Chandler, Introduction to Modern Statistical Mechanics (Oxford University Press, New York, 1987).
S. Torquato, Random Heterogeneous Materials (Springer, New York, 2000).
M. Sahimi, Heterogeneous Materials I: Linear Transport and Optical Properties (Springer, New York, 2003), Vol. 1.
L. Feigin and D. Svergun, Structure Analysis by Small-Angle X-Ray and Neutron Scattering (Springer, Berlin, 1987).
J.M. Drake, J. Klafter, and P. Levitz, Science 251, 1574 (1991). SCIEAS 0036-8075 10.1126/science.2011737
G.A. Barral, L. Frydman, and G.C. Chingas, Science 255, 714 (1992). SCIEAS 0036-8075 10.1126/science.255.5045.714
A. Filipponi, A. DiCicco, and C.R. Natoli, Phys. Rev. B PRBMDO 0163-1829 52, 15122 (1995). 10.1103/PhysRevB.52.15122
G. Matheron, Random Sets and Integral Geometry (Wiley, New York, 1975).
A.L. Patterson, Phys. Rev. 65, 195 (1944). PHRVAO 0031-899X 10.1103/PhysRev.65.195
R. Hosemann and S.N. Bagchi, Acta Crystallogr. ACCRA9 0365-110X 7, 237 (1954). 10.1107/S0365110X54000709
A. Aubert and D. Jeulin, Pattern Recogn. PTNRA8 0031-3203 33, 1083 (2000). 10.1016/S0031-3203(99)00166-1 (Pubitemid 30589466)
Y. Jiao, F.H. Stillinger, and S. Torquato, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 106, 17634 (2009). 10.1073/pnas.0905919106
Y. Jiao, F.H. Stillinger, and S. Torquato, Phys. Rev. E PLEEE8 1539-3755 81, 011105 (2010). 10.1103/PhysRevE.81.011105
Y. Jiao, F.H. Stillinger, and S. Torquato, Phys. Rev. E PLEEE8 1539-3755 82, 011106 (2010). 10.1103/PhysRevE.82.011106
H. Hauptman, Science 233, 178 (1986). SCIEAS 0036-8075 10.1126/science.233.4760.178
M.G. Rozman and M. Utz, Phys. Rev. Lett. PRLTAO 0031-9007 89, 135501 (2002). 10.1103/PhysRevLett.89.135501
B.L. Hansen, B.L. Adams, M.E. Lyon, and A. Henrie, J. Comput.-Aided Mater. Des. JCODES 0928-1045 10, 163 (2005). 10.1007/s10820-005-0884-3 (Pubitemid 43273915)
D.T. Fullwood, S.R. Niezgoda, and S.R. Kalidindi, Acta Mater. 56, 942 (2008). ACMAFD 1359-6454 10.1016/j.actamat.2007.10.044
P.-G. DeGennes, Rev. Mod. Phys. 64, 645 (1992). RMPHAT 0034-6861 10.1103/RevModPhys.64.645
T.J. Barton, L.M. Bull, W.G. Klemperer, D.A. Loy, B. McEnaney, M. Misono, P.A. Monson, G. Pez, G.W. Scherer, J.C. Vartuli, and O.M. Yaghi, Chem. Mater. 11, 2633 (1999). CMATEX 0897-4756 10.1021/cm9805929
C.L.Y. Yeong and S. Torquato, Phys. Rev. E PLEEE8 1063-651X 57, 495 (1998); 10.1103/PhysRevE.57.495
C.L.Y. Yeong S. Torquato Phys. Rev. E PLEEE8 1063-651X 58, 224 (1998). 10.1103/PhysRevE.58.224
Y. Jiao, F.H. Stillinger, and S. Torquato, Phys. Rev. E PLEEE8 1539-3755 77, 031135 (2008). 10.1103/PhysRevE.77.031135 (Pubitemid 351466180)
F.G. Wang and D.P. Landau, Phys. Rev. Lett. 86, 2050 (2001). PRLTAO 0031-9007 10.1103/PhysRevLett.86.2050 (Pubitemid 32254758)
F.G. Wang and D.P. Landau, Phys. Rev. E PLEEE8 1063-651X 64, 056101 (2001). 10.1103/PhysRevE.64.056101
C. Yamaguchi and Y. Okabe, J. Phys. A JPHAC5 0305-4470 34, 8781 (2001). 10.1088/0305-4470/34/42/305
N. Rathore and J.J. de Pablo, J. Chem. Phys. 116, 7225 (2002). JCPSA6 0021-9606 10.1063/1.1463059 (Pubitemid 34537101)
S. Ermon, C. Gomes, and B. Selman, in Principles and Practice of Constraint Programming CP 2010, Lecture Notes in Computer Science Vol. 6308, edited by, D. Cohen, (Springer, Berlin, 2010), pp. 38-52.
D.J. Wales, M.A. Miller, and T.R. Walsh, Nature (London) NATUAS 0028-0836 394, 758 (1998). 10.1038/29487 (Pubitemid 28391634)
See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevLett.108.080601 for mathematical details and a list of microstructures used for Fig. .
C.J. Gommes, Y. Jiao, and S. Torquato (to be published).
B.L. Lu and S. Torquato, J. Chem. Phys. 93, 3452 (1990). JCPSA6 0021-9606 10.1063/1.458827
P. Dayal, S. Trebst, S. Wessel, D. Wurtz, M. Troyer, S. Sabhapandit, and S.N. Coppersmith, Phys. Rev. Lett. 92, 097201 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.92.097201
S. Torquato and G. Stell, J. Chem. Phys. 78, 3262 (1983). JCPSA6 0021-9606 10.1063/1.445245
C. Zachary and S. Torquato, Phys. Rev. E PLEEE8 1539-3755 84, 056102 (2011). 10.1103/PhysRevE.84.056102
L.L. Chavez, J.N. Onuchic, and C. Clementi, J. Am. Chem. Soc. 126, 8426 (2004). JACSAT 0002-7863 10.1021/ja049510+ (Pubitemid 38917965)
J. Puibasset, J. Chem. Phys. 133, 104701 (2010). JCPSA6 0021-9606 10.1063/1.3483790
P.G. Debenedetti and F.H. Stillinger, Nature (London) NATUAS 0028-0836 410, 259 (2001). 10.1038/35065704 (Pubitemid 32218700)
G. Parisi, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 103, 7948 (2006). 10.1073/pnas.0601120103 (Pubitemid 43801034)