The transfer-matrix and max-plus algebra method for global combinatorial optimization: Application to cyclic and polyhedral water clusters

Physica A: Statistical Mechanics and its Applications

Volumn 388, Issue 8, 2009, Pages 1431-1445

  Kirov, M V ^a  

^a EARTH CRYOSPHERE INSTITUTE   (Russian Federation)

Author keywords

Frustration; Global optimization; Max plus algebra; Transfer matrix method; Water clusters

Indexed keywords

COMBINATORIAL MATHEMATICS; COMBINATORIAL OPTIMIZATION; GLOBAL OPTIMIZATION; HYDROGEN BONDS;

ARITHMETIC OPERATIONS; FRUSTRATION; INTERMOLECULAR INTERACTIONS; LARGE COMPLEX SYSTEMS; LOWEST ENERGY LEVEL; MAX-PLUS ALGEBRA; QUASI-ONE-DIMENSIONAL SYSTEMS; WATER CLUSTER;

TRANSFER MATRIX METHOD;

EID: 59449104318     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2008.12.050     Document Type: Article

References (42)

1. Zimm B.H., and Bragg J.K. J. Chem. Phys. 31 (1959) 526-531
2. Lifson S., and Roig A. J. Chem. Phys. 34 (1961) 1963-1974
3. Onsager L. Phys. Rev. 65 (1944) 117-149
4. Baxter R.J. Exactly Solved Models in Statistical Mechanics (1982), Academic Press, London
5. Cuninghame-Green R.A. Minimax Algebra. Lecture Notes in Econ. and. Math. Systems vol. 166 (1979), Springer, Berlin
6. Baccelli F.L., Cohen G., Olsder G.J., and Quadrat J.P. Synchronization and Linearity, An Algebra for Discrete Event Systems (1992), John Wiley & Sons, New York
7. Maslov V.P., and Kolokoltsov V.N. Idempotent Analysis and its Applications to Optimal Control Theory (1994), Nauka, Moscow (in Russian)
8. Gaubert S., and Plus M. Lecture Notes in Computer Science vol. 1200 (1997), Springer-Verlag, London 261-282
9. Litvinov G.L., and Maslov V.P. The correspondence principle for idempotent calculus and some computer applications. In: Gunawardena J. (Ed). Idempotency (1998), Cambridge Univ. Press, Cambridge, UK 420-443
10. Litvinov G.L. J. Math. Sci. 140 (2007) 426-444
11. Bernal J.D., and Fowler R.H. J. Chem. Phys. 1 (1933) 515-548
12. Radhakrishnan T.P., and Herndon W.C. J. Phys. Chem. 95 (1991) 10609-10617
13. Miyake T., and Aida M. Chem. Phys. Lett. 363 (2002) 106-110
14. McDonald S., Ojamäe L., and Singer S.J. J. Phys. Chem. A 102 (1998) 2824-2832
15. Kuo J.-L., Ciobanu C.V., Ojamäe L., Shavitt I., and Singer S.J. J. Chem. Phys. 118 (2003) 3583-3588
16. Anick D.J. J. Chem. Phys. 119 (2003) 12442-12456
17. Belair S.D., and Francisco J.S. Phys. Rev. A 67 (2003) 063206 1-6
18. Chihaia V., Adams S., and Kuhs W.F. Chem. Phys. 297 (2004) 271-287
19. Kirov M.V. J. Struct. Chem. 37 (1996) 84-91
20. Kirov M.V. J. Struct. Chem. 46 (2005) S188-S194
21. Kirov M.V. Classification of low-energy configurations of polyhedral water clusters from cube up to backminsterfullerene. In: Kuhs W.F. (Ed). Physics and Chemistry of Ice (2007), Royal Society of Chemistry, Cambridge 305-312
22. Kirov M.V., Fanourgakis G.S., and Xantheas S.S. Chem. Phys. Lett. 461 (2008) 180-188
23. Stanley H.E., Kumar P., Xu L., Yan Z., Mazza M.G., Buldyrev S.V., Chen S.-H., and Mallamace F. Physica A 386 (2007) 729-743
24. Wales D.J., and Hodges M.P. Chem. Phys. Lett. 286 (1998) 65-72
25. Hartke B. Phys. Chem. Chem. Phys. 5 (2003) 275-284
26. Fanourgakis G.S., Aprà E., and Xantheas S.S. J. Chem. Phys. 121 (2004) 2655-2663
27. Kirov M.V. J. Struct. Chem. 37 (1996) 92-98
28. Keutsch F.N., and Saykally R.J. Proc. Natl. Acad. Sci. USA 98 (2001) 10533-10540
29. Xantheas S.S. Chem. Phys. 258 (2000) 225-231
30. Kirov M.V. J. Struct. Chem. 35 (1994) 126-128
31. Stanley R.S. Enumerative Combinatorics, Vol. 1 (1997), Cambridge University Press, Cambridge, UK
32. Pauling L. J. Am. Chem. Soc. 57 (1935) 2680-2684
33. Stillinger F.H., and Rahman A. J. Chem. Phys. 60 (1974) 1545-1557
34. Mahoney M.W., and Jorgensen W.L. J. Chem. Phys. 112 (2000) 8910-8922
35. Kirov M.V. J. Struct. Chem. 48 (2007) 81-87
36. Ilyin V.A., and Pozdnyak E.G. Linear Algebra (1974), Nauka, Moscow (in Russian)
37. Kirov M.V. J. Struct. Chem. 34 (1993) 557-561
38. Kirov M.V. J. Struct. Chem. 47 (2006) 691-698
39. Sloan D. Clathrate Hydrates of Natural Gases (1997), Marcel Dekker Inc. Pub., New York
40. James T., Wales D.J., and Hernández-Rojas J. Chem. Phys. Lett. 415 (2005) 302-307. http://www-wales.ch.cam.ac.uk/~wales/CCD/TIP5P_ccd_page/TIP5P.html
41. Kirov M.V. J. Struct. Chem. 43 (2002) 266-273
42. http://www-rocq.inria.fr/MaxplusOrg/