Hierarchical structures of amorphous solids characterized by persistent homology

Proceedings of the National Academy of Sciences of the United States of America

Volumn 113, Issue 26, 2016, Pages 7035-7040

  Hiraoka, Yasuaki ^a   Nakamura, Takenobu ^a   Hirata, Akihiko ^a   Escolar, Emerson G ^a   Matsue, Kaname ^b   Nishiura, Yasumasa ^a  

^a TOHOKU UNIVERSITY   (Japan)

^b INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

Author keywords

Amorphous solid; Hierarchical structure; Persistence diagram; Persistent homology; Topological data analysis

Indexed keywords

COPPER; GLASS; ZIRCONIUM;

ARTICLE; CHEMICAL STRUCTURE; DECOMPOSITION; DIFFRACTION; GEOMETRY; MOLECULAR DYNAMICS; PHYSICAL PARAMETERS; PRIORITY JOURNAL; SOLID; STRUCTURAL HOMOLOGY;

EID: 84976542864     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.1520877113     Document Type: Article

References (35)

1. Bernal JD (1964) The Bakerian Lecture, 1962 The structure of liquids. Proc R Soc Lond A Math Phys Sci 280(1382):299-322.
2. Polk DE (1971) Structural model for amorphous silicon and germanium. J Non-Cryst Solids 5:365-376.
3. Finney JL (1970) Random packings and the structure of simple liquids. I. The geometry of random close packing. Proc R Soc Lond A Math Phys Sci 319:479-493.
4. Elliott SR (1991) Origin of the first sharp diffraction peak in the structure factor of covalent glasses. Phys Rev Lett 67(6):711-714.
5. Elliott SR (1990) Physics of Amorphous Materials (Longman, New York), 2nd Ed.
6. Susman S, et al. (1991) Intermediate-range order in permanently densified vitreous SiO2: A neutron-diffraction and molecular-dynamics study. Phys Rev B Condens Matter 43(1):1194-1197.
7. Greaves GN, Sen S (2007) Inorganic glasses, glass-forming liquids and amorphizing solids. Adv Phys 56:1-166.
8. Roux SL, Petkov V (2010) ISAACS - Interactive structure analysis of amorphous and crystalline systems. J Appl Cryst 43:181-185.
9. Zachariasen WH (1932) The atomic arrangement in glass. J Am Chem Soc 54: 3841-3851.
10. Edelsbrunner H, Harer J (2010) Computational Topology: An Introduction (Am Mathematical Soc, Providence, RI).
11. Carlsson G (2009) Topology and data. Bull Am Math Soc 46:255-308.
12. Nicolau M, Levine AJ, Carlsson G (2011) Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival. Proc Natl Acad Sci USA 108(17):7265-7270.
13. Hirata A, et al. (2013) Geometric frustration of icosahedron in metallic glasses. Science 341(6144):376-379.
14. Kurtuldu H, Mischaikow K, Schatz MF (2011) Extensive scaling from computational homology and Karhunen-Loève decomposition analysis of Rayleigh-Bénard convection experiments. Phys Rev Lett 107(3):034503.
15. Nakamura T, Hiraoka Y, Hirata A, Escolar EG, Nishiura Y (2015) Persistent homology and many-body atomic structure for medium-range order in the glass. Nanotechnology 26(30):304001.
16. Kondic L, et al. (2012) Topology of force networks in compressed granular media. Europhys Lett 97:54001.
17. Hatcher A (2001) Algebraic Topology (Cambridge Univ Press, Cambridge, UK).
18. Dey T, et al. (2011) Optimal homologous cycles, total unimodularity, and linear programming. SIAM J Comput 40:1026-1044.
19. Escolar EG, Hiraoka Y (2015) Optimal cycles for persistent homology via linear programming. Optimization in the Real World -Towards Solving Real-World Optimization Problems. Mathematics for Industry, eds Fujisawa K, Shinano Y, Waki H (Springer, Tokyo), pp 79-96.
20. CGAL (2016) The Computational Geometry Algorithms Library. Available at www. cgal.org/.
21. PHAT (2014) Persistent Homology Algorithm Toolbox. Available at https://bitbucket. org/phat-code/phat.
22. Kramer GJ, van Beest BW, van Santen RA (1990) Force fields for silicas and aluminophosphates based on ab initio calculations. Phys Rev Lett 64(16):1955-1958.
23. Hansen JP, McDonald IR (2006) Theory of Simple Liquids (Academic, New York),3rd Ed.
24. Anikeenko AV, et al. (2005) A novel Delaunay simplex technique for detection of crystalline neuclei in dense packings of spheres. Computational Science and Its Applications - ICCSA 2005. Lecture Notes in Computer Science, eds Gervasi O, Gavrilova ML, Kumar V, Laganà A, Lee HP, Mun Y, Taniar D, Tan CJK (Springer, New York), Vol 3480, pp 816-826.
25. Yamamoto R, Doyama M (1979) The polyhedron and cavity analyses of a structural model of amorphous iron. J Phys F Metal Phys 9:617-627.
26. Pan SP, et al. (2011) Origin of splitting of the second peak in the pair-distribution function for metallic glasses. Phys Rev B 84:092201.
27. Barker JA, et al. (1975) Relaxation of the Bernal model. Nature 257:120-122.
28. Ma E (2015) Tuning order in disorder. Nat Mater 14(6):547-552.
29. Cheng YQ, Ma E (2011) Atomic-level structure and structure-property relationship in metallic glasses. Prog Mater Sci 56:379-473.
30. Guissani Y, Guillot B (1996) A numerical investigation of the liquid-vapor coexistence curve of silica. J Chem Phys 104:7633.
31. Vollmayr K, Kob W, Binder K (1996) Cooling-rate effects in amorphous silica: A computer-simulation study. Phys Rev B Condens Matter 54(22):15808-15827.
32. Soules TF, et al. (2011) Silica molecular dynamic force fields - a practical assessment. J Non-Cryst Solids 357(6):1564-1573.
33. Monaco G, Mossa S (2009) Anomalous properties of the acoustic excitations in glasses on the mesoscopic length scale. Proc Natl Acad Sci USA 106(40):16907-16912.
34. Mendelev MI, et al. (2007) Using atomistic computer simulations to analyze x-ray diffraction data from metallic glasses. J Appl Phys 102:043501.
35. Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 117:1-19.