Hamilton-Jacobi equation for the least-action/least-time dynamical path based on fast marching method

Journal of Chemical Physics

Volumn 121, Issue 14, 2004, Pages 6667-6679

  Dey, Bijoy K ^a   Janicki, Marek R ^a   Ayers, Paul W ^a  

^a MCMASTER UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; ERROR ANALYSIS; FREQUENCIES; FUNCTIONS; HYDROGEN; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; POTENTIAL ENERGY; RANDOM PROCESSES; REACTION KINETICS; STATISTICAL METHODS; WAVEFRONTS;

HAMILTON-JACOBI (HJ) EQUATION; LEAST-TIME DYNAMICAL PATH; REACTION DYNAMICS; STOCHASTIC MODEL;

MOLECULAR PHYSICS;

ALGORITHM; ARTICLE; COMPUTER SIMULATION; THEORETICAL MODEL;

ALGORITHMS; COMPUTER SIMULATION; MODELS, THEORETICAL;

EID: 7544228185     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1790851     Document Type: Article

References (46)

1. V. S. Pande, A. Y. Grosberg, T. Tanaka, and D. S. Rokhsar, Curr. Opin. Struct. Biol. 8, 68 (1998).
2. P. Eastman, N. Gronbech-Jensen, and S. Doniach, J. Chem. Phys. 114, 3823 (2001).
3. R. Elber, in Recent Developments in Theoretical Studies of Proteins, edited by R. Elber (World-Scientific, Singapore, 1996).
4. J. E. Straub, in Computational Biochemistry and Biophysics, edited by M. Becker, A. D. MacKorell, Jr., B. Roux, and M. Watanabe (Dokker, New York, 2001).
5. P. Hanggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990).
6. K. Muller and L. D. Brown, Theor. Chim. Acta 53, 75 (1979).
7. R. Czerminski and R. Eiber, J. Chem. Phys. 92, 5580 (199).
8. C. Choi and R. Elber, J. Chem. Phys. 94, 751 (1991).
9. S. Fischer and M. Karplus, Chem. Phys. Lett. 194, 252 (1992).
10. R. Olender and R. Elber, J. Mol. Struct.: THEOCHEM 398-399, 63 (1997).
11. J. Schlitter, M. Engels, P. Kruger, E. Jacoby, and A. Wollmer, Mol. Simul. 10, 291 (1993).
12. F. S. Csajka and D. Chandler, J. Chem. Phys. 109, 1125 (1998).
13. C. Dellago, P. G. Bolhuis, and D. Chandler, J. Chem. Phys. 108, 9236 (1998).
14. R. Abraham and J. E. Marsden, Foundation of Mechanics, 2nd ed. (Benjamin, New York, 1978).
15. K. Fukui, Acc. Chem. Res. 14, 363 (1981).
16. M. Berkowitz, J. D. Morgan, J. A. McCammon, and S. H. Northrup, J. Chem. Phys. 79, 5563 (1983).
17. S. Huo and J. E. Straub, J. Chem. Phys. 107, 5000 (1997).
18. R. Elber, A. Ghosh, and A. Cardenas, Acc. Chem. Res. 35, 396 (2002).
19. A. Ghosh, R. Elber, and H. A. Scheraga, Proc. Natl. Acad. Sci. U.S.A. 99, 10394 (2002).
20. A. Banerjee and N. P. Adams, J. Chem. Phys. 92, 7330 (1990).
21. J. A. Sethian, Proc. Natl. Acad. Sci. U.S.A. 93, 1591 (1996).
22. J. A. Sethian, SIAM Rev. 41, 199 (1999).
23. J. A. Sethian, Level Set Methods and Fast Marching Methods, 2nd ed. (Cambridge University Press, Cambridge, 1999).
24. L. D. Cohen and R. Kimmel, Int. J. Comput. Vis. 24, 57 (1997).
25. A. F. Voter, Phys. Rev. Lett. 78, 3908 (1997).
26. A. F. Voter, J. Chem. Phys. 106, 4665 (1997).
27. M. A. Balsera, W. Wriggers, Y. Oono, and K. Schulten, J. Phys. Chem. 100, 2567 (1996).
28. M. R. Sorensen and A. F. Voter, J. Chem. Phys. 112, 9599 (2000).
29. B. Space, H. Rabitz, and A. Askar, J. Chem. Phys. 99, 9070 (1993).
30. A. Askar, B. Space, and H. Rabitz, J. Phys. Chem. 99, 7730 (1995).
31. B. K. Dey, H. Rabitz, and A. Askar, J. Chem. Phys. 119, 5379 (2003).
32. A. Amadei, A. B. M. Linssen, and H. J. C. Berendsen, Proteins 17, 412 (1993).
33. R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley, New York, 1989), Vol. 2, Chap. 2.
34. M. Spivak, A Comprehensive Introduction to Differential Geometry, 2nd ed. (Perish Inc., Berkely, 1979), Vol. 5.
35. V. Cerveny, J. Geophys. 58, 2 (1985).
36. J. E. Vidale, Bull. Seismol. Soc. Am. 78, 2062 (1988).
37. J. V. Trier and W. W. Symes, Geophys. J. 56, 812 (1995).
38. J. E. Vidale, Geophys. J. 55, 521 (1990).
39. S. J. Osher and J. A. Sethian, J. Comput. Phys. 79, 12 (1988).
40. M. G. Crandall, H. Ishii, and P. L. Lions, Bull., New Ser., Am. Math. Soc. 27, 1 (1992).
41. B. K. Dey and P. W. Ayers (unpublished).
42. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Parallel Scientific Computing, 2nd ed. (Cambridge University Press, Cambridge, 1996).
43. M. J. D. Powel, in Algorithms for Approximation of Functions and Data, edited by J. C. Mason and M. G. Cox (Oxford University Press, 1987), pp. 143-167.
44. M. D. Buhmann, Acta Numerica 9, 1 (2000).
45. S. Huo and J. E. Straub, J. Chem. Phys. 107, 5000 (1997).
46. B. Liu, J. Chem. Phys. 58, 1925 (1973).