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Volumn 107, Issue 9, 1997, Pages 3505-3520

High-accuracy discrete path integral solutions for stochastic processes with noninvertible diffusion matrices. II. Numerical evaluation

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DIFFUSION; EIGENVALUES AND EIGENFUNCTIONS; FAST FOURIER TRANSFORMS; MATHEMATICAL MODELS; MOLECULAR DYNAMICS; PHASE EQUILIBRIA; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES;

EID: 0031232559     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.474690     Document Type: Article
Times cited : (17)

References (80)
  • 1
    • 34547361024 scopus 로고
    • R. P. Feynman, Rev. Mod. Phys. 20, 367 (1948); R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
    • (1948) Rev. Mod. Phys. , vol.20 , pp. 367
    • Feynman, R.P.1
  • 3
    • 0003575440 scopus 로고
    • Benjamin, Reading
    • R. P. Feynman, Statistical Mechanics (Benjamin, Reading, 1972); L. S. Schulman, Techniques and Applications of Path Integration (Wiley, New York, 1981); F. Langouche, D. Roekaerts, and Tirapegui, Functional Integration and Semiclassical Expansions, Mathematics and Its Applications (Reidel, Dordrecht, 1982); D. C. Khandekar, S. V. Lawande, and K. Bhagwat, Path Integral Methods and Their Applications (World Scientific, Singapore, 1993); H. Kleinert, Path Integrals in Quantum Mechanics, Statistics, and Polymer Physics, 2nd ed. (World Scientific, Singapore, 1995).
    • (1972) Statistical Mechanics
    • Feynman, R.P.1
  • 4
    • 0003644102 scopus 로고
    • Wiley, New York
    • R. P. Feynman, Statistical Mechanics (Benjamin, Reading, 1972); L. S. Schulman, Techniques and Applications of Path Integration (Wiley, New York, 1981); F. Langouche, D. Roekaerts, and Tirapegui, Functional Integration and Semiclassical Expansions, Mathematics and Its Applications (Reidel, Dordrecht, 1982); D. C. Khandekar, S. V. Lawande, and K. Bhagwat, Path Integral Methods and Their Applications (World Scientific, Singapore, 1993); H. Kleinert, Path Integrals in Quantum Mechanics, Statistics, and Polymer Physics, 2nd ed. (World Scientific, Singapore, 1995).
    • (1981) Techniques and Applications of Path Integration
    • Schulman, L.S.1
  • 5
    • 0004010801 scopus 로고
    • Reidel, Dordrecht
    • R. P. Feynman, Statistical Mechanics (Benjamin, Reading, 1972); L. S. Schulman, Techniques and Applications of Path Integration (Wiley, New York, 1981); F. Langouche, D. Roekaerts, and Tirapegui, Functional Integration and Semiclassical Expansions, Mathematics and Its Applications (Reidel, Dordrecht, 1982); D. C. Khandekar, S. V. Lawande, and K. Bhagwat, Path Integral Methods and Their Applications (World Scientific, Singapore, 1993); H. Kleinert, Path Integrals in Quantum Mechanics, Statistics, and Polymer Physics, 2nd ed. (World Scientific, Singapore, 1995).
    • (1982) Functional Integration and Semiclassical Expansions, Mathematics and Its Applications
    • Langouche, F.1    Roekaerts, D.2    Tirapegui3
  • 6
    • 0003760123 scopus 로고
    • World Scientific, Singapore
    • R. P. Feynman, Statistical Mechanics (Benjamin, Reading, 1972); L. S. Schulman, Techniques and Applications of Path Integration (Wiley, New York, 1981); F. Langouche, D. Roekaerts, and Tirapegui, Functional Integration and Semiclassical Expansions, Mathematics and Its Applications (Reidel, Dordrecht, 1982); D. C. Khandekar, S. V. Lawande, and K. Bhagwat, Path Integral Methods and Their Applications (World Scientific, Singapore, 1993); H. Kleinert, Path Integrals in Quantum Mechanics, Statistics, and Polymer Physics, 2nd ed. (World Scientific, Singapore, 1995).
    • (1993) Path Integral Methods and Their Applications
    • Khandekar, D.C.1    Lawande, S.V.2    Bhagwat, K.3
  • 7
    • 0004048494 scopus 로고
    • World Scientific, Singapore
    • R. P. Feynman, Statistical Mechanics (Benjamin, Reading, 1972); L. S. Schulman, Techniques and Applications of Path Integration (Wiley, New York, 1981); F. Langouche, D. Roekaerts, and Tirapegui, Functional Integration and Semiclassical Expansions, Mathematics and Its Applications (Reidel, Dordrecht, 1982); D. C. Khandekar, S. V. Lawande, and K. Bhagwat, Path Integral Methods and Their Applications (World Scientific, Singapore, 1993); H. Kleinert, Path Integrals in Quantum Mechanics, Statistics, and Polymer Physics, 2nd ed. (World Scientific, Singapore, 1995).
    • (1995) Path Integrals in Quantum Mechanics, Statistics, and Polymer Physics, 2nd Ed.
    • Kleinert, H.1
  • 8
    • 5944250381 scopus 로고
    • For a recent review see the special thematic issue on functional integration, J. Math. Phys. 36 (5) (1995), edited by C. DeWitt-Morette.
    • (1995) J. Math. Phys. , vol.36 , Issue.5
    • DeWitt-Morette, C.1
  • 14
    • 0000692987 scopus 로고
    • R. Phythian, J. Phys. A 10, 777 (1977); P. Hänggi, Proceedings of the International Conference on Path integrals from meV to MeV, Tulzing 1992, edited by H. Grabert, A. Inomata, L. Schulman, and U. Weiss (World Scientific, Singapore, 1993), p. 289; S. J. B. Einchcomb and A. J. McKane, Phys. Rev. E 51, 2974 (1995); Physica A 216, 128 (1995).
    • (1977) J. Phys. A , vol.10 , pp. 777
    • Phythian, R.1
  • 15
    • 0000692987 scopus 로고
    • edited by H. Grabert, A. Inomata, L. Schulman, and U. Weiss World Scientific, Singapore
    • R. Phythian, J. Phys. A 10, 777 (1977); P. Hänggi, Proceedings of the International Conference on Path integrals from meV to MeV, Tulzing 1992, edited by H. Grabert, A. Inomata, L. Schulman, and U. Weiss (World Scientific, Singapore, 1993), p. 289; S. J. B. Einchcomb and A. J. McKane, Phys. Rev. E 51, 2974 (1995); Physica A 216, 128 (1995).
    • (1993) Proceedings of the International Conference on Path Integrals from meV to MeV, Tulzing 1992 , pp. 289
    • Hänggi, P.1
  • 16
    • 25344453588 scopus 로고
    • R. Phythian, J. Phys. A 10, 777 (1977); P. Hänggi, Proceedings of the International Conference on Path integrals from meV to MeV, Tulzing 1992, edited by H. Grabert, A. Inomata, L. Schulman, and U. Weiss (World Scientific, Singapore, 1993), p. 289; S. J. B. Einchcomb and A. J. McKane, Phys. Rev. E 51, 2974 (1995); Physica A 216, 128 (1995).
    • (1995) Phys. Rev. E , vol.51 , pp. 2974
    • Einchcomb, S.J.B.1    McKane, A.J.2
  • 17
    • 0000692987 scopus 로고
    • R. Phythian, J. Phys. A 10, 777 (1977); P. Hänggi, Proceedings of the International Conference on Path integrals from meV to MeV, Tulzing 1992, edited by H. Grabert, A. Inomata, L. Schulman, and U. Weiss (World Scientific, Singapore, 1993), p. 289; S. J. B. Einchcomb and A. J. McKane, Phys. Rev. E 51, 2974 (1995); Physica A 216, 128 (1995).
    • (1995) Physica A , vol.216 , pp. 128
  • 18
    • 1442289165 scopus 로고
    • Leipzig
    • A. Fokker, Ann. Phys. (Leipzig) 43, 810 (1914); M. Planck, Sitzungsber. K. Preuss. Akad. Wiss. 324 (1917).
    • (1914) Ann. Phys. , vol.43 , pp. 810
    • Fokker, A.1
  • 25
    • 5544275148 scopus 로고
    • H. S. Wio, J. Chem. Phys. 88, 5251 (1988); C. D. Batista, G. Drazer, D. Reidel, and H. S. Wio, Phys. Rev. E 54, 86 (1996); A. Pelster and H. Kleinert, Phys. Rev. Lett. 78, 565 (1997).
    • (1988) J. Chem. Phys. , vol.88 , pp. 5251
    • Wio, H.S.1
  • 26
    • 0011720536 scopus 로고    scopus 로고
    • H. S. Wio, J. Chem. Phys. 88, 5251 (1988); C. D. Batista, G. Drazer, D. Reidel, and H. S. Wio, Phys. Rev. E 54, 86 (1996); A. Pelster and H. Kleinert, Phys. Rev. Lett. 78, 565 (1997).
    • (1996) Phys. Rev. E , vol.54 , pp. 86
    • Batista, C.D.1    Drazer, G.2    Reidel, D.3    Wio, H.S.4
  • 27
    • 4243501939 scopus 로고    scopus 로고
    • H. S. Wio, J. Chem. Phys. 88, 5251 (1988); C. D. Batista, G. Drazer, D. Reidel, and H. S. Wio, Phys. Rev. E 54, 86 (1996); A. Pelster and H. Kleinert, Phys. Rev. Lett. 78, 565 (1997).
    • (1997) Phys. Rev. Lett. , vol.78 , pp. 565
    • Pelster, A.1    Kleinert, H.2
  • 28
    • 0004058796 scopus 로고
    • U. Weiss, Phys. Rev. A 25, 2444 (1982); T. Morita and H. Hara, Physica A 127, 113 (1984); V. F. Baibuz, V.Yu. Zitserman, and A. N. Drozdov, ibid. 127, 173 (1984).
    • (1982) Phys. Rev. A , vol.25 , pp. 2444
    • Weiss, U.1
  • 29
    • 0007327760 scopus 로고
    • U. Weiss, Phys. Rev. A 25, 2444 (1982); T. Morita and H. Hara, Physica A 127, 113 (1984); V. F. Baibuz, V.Yu. Zitserman, and A. N. Drozdov, ibid. 127, 173 (1984).
    • (1984) Physica A , vol.127 , pp. 113
    • Morita, T.1    Hara, H.2
  • 30
  • 32
    • 5544246005 scopus 로고
    • I. Hosokawa, J. Phys. Soc. Jpn. 25, 271 (1967); G. Rosen, J. Math. Phys. 12, 812 (1970).
    • (1967) J. Phys. Soc. Jpn. , vol.25 , pp. 271
    • Hosokawa, I.1
  • 33
    • 36849110240 scopus 로고
    • I. Hosokawa, J. Phys. Soc. Jpn. 25, 271 (1967); G. Rosen, J. Math. Phys. 12, 812 (1970).
    • (1970) J. Math. Phys. , vol.12 , pp. 812
    • Rosen, G.1
  • 39
    • 5544255045 scopus 로고
    • A. N. Drozdov and V. Yu. Zitserman, Phys. Lett. A 94, 17 (1983); A. N. Drozdov, V. Yu. Zitserman, and V. F. Baibuz, Chem. Phys. 88, 81 (1984).
    • (1983) Phys. Lett. A , vol.94 , pp. 17
    • Drozdov, A.N.1    Zitserman, V.Yu.2
  • 43
    • 5544294159 scopus 로고
    • M. F. Wehner and W. G. Wolfer, Phys. Rev. A 27, 2663 (1983); 28, 3003 (1983).
    • (1983) Phys. Rev. A , vol.28 , pp. 3003
  • 44
    • 0000907605 scopus 로고
    • L. Ingber, Phys. Rev. E 49, 4652 (1994); L. Ingber and P. L. Nunez, ibid. 51, 5074 (1995).
    • (1994) Phys. Rev. E , vol.49 , pp. 4652
    • Ingber, L.1
  • 46
    • 0042973847 scopus 로고
    • M. D. Feit, J. A. Fleck, and A. Steiger, J. Comput. Phys. 47, 412 (1982); D. Koslof and R. Kosloff, ibid. 52, 35 (1983); R. Kosloff, J. Phys. Chem. 92, 2087 (1988); B. Carmeli, V. Mujica, and A. Nitzau, Ber. Bunsenges. Phys. 95, 319 (1991); J. Gómez-Ordóñez and M. Morillo, Physica A 183, 490 (1992).
    • (1982) J. Comput. Phys. , vol.47 , pp. 412
    • Feit, M.D.1    Fleck, J.A.2    Steiger, A.3
  • 47
    • 0342702498 scopus 로고
    • M. D. Feit, J. A. Fleck, and A. Steiger, J. Comput. Phys. 47, 412 (1982); D. Koslof and R. Kosloff, ibid. 52, 35 (1983); R. Kosloff, J. Phys. Chem. 92, 2087 (1988); B. Carmeli, V. Mujica, and A. Nitzau, Ber. Bunsenges. Phys. 95, 319 (1991); J. Gómez-Ordóñez and M. Morillo, Physica A 183, 490 (1992).
    • (1983) J. Comput. Phys. , vol.52 , pp. 35
    • Koslof, D.1    Kosloff, R.2
  • 48
    • 1142279256 scopus 로고
    • M. D. Feit, J. A. Fleck, and A. Steiger, J. Comput. Phys. 47, 412 (1982); D. Koslof and R. Kosloff, ibid. 52, 35 (1983); R. Kosloff, J. Phys. Chem. 92, 2087 (1988); B. Carmeli, V. Mujica, and A. Nitzau, Ber. Bunsenges. Phys. 95, 319 (1991); J. Gómez-Ordóñez and M. Morillo, Physica A 183, 490 (1992).
    • (1988) J. Phys. Chem. , vol.92 , pp. 2087
    • Kosloff, R.1
  • 49
    • 0042973847 scopus 로고
    • M. D. Feit, J. A. Fleck, and A. Steiger, J. Comput. Phys. 47, 412 (1982); D. Koslof and R. Kosloff, ibid. 52, 35 (1983); R. Kosloff, J. Phys. Chem. 92, 2087 (1988); B. Carmeli, V. Mujica, and A. Nitzau, Ber. Bunsenges. Phys. 95, 319 (1991); J. Gómez-Ordóñez and M. Morillo, Physica A 183, 490 (1992).
    • (1991) Ber. Bunsenges. Phys. , vol.95 , pp. 319
    • Carmeli, B.1    Mujica, V.2    Nitzau, A.3
  • 50
    • 0009956256 scopus 로고
    • M. D. Feit, J. A. Fleck, and A. Steiger, J. Comput. Phys. 47, 412 (1982); D. Koslof and R. Kosloff, ibid. 52, 35 (1983); R. Kosloff, J. Phys. Chem. 92, 2087 (1988); B. Carmeli, V. Mujica, and A. Nitzau, Ber. Bunsenges. Phys. 95, 319 (1991); J. Gómez-Ordóñez and M. Morillo, Physica A 183, 490 (1992).
    • (1992) Physica A , vol.183 , pp. 490
    • Gómez-Ordóñez, J.1    Morillo, M.2
  • 59
    • 0000431067 scopus 로고
    • E. Nelson, J. Math. Phys. 5, 332 (1964); R. M. Wilcox, ibid. 8, 962 (1967).
    • (1964) J. Math. Phys. , vol.5 , pp. 332
    • Nelson, E.1
  • 60
    • 0042638530 scopus 로고
    • E. Nelson, J. Math. Phys. 5, 332 (1964); R. M. Wilcox, ibid. 8, 962 (1967).
    • (1967) J. Math. Phys. , vol.8 , pp. 962
    • Wilcox, R.M.1
  • 68
    • 0001744604 scopus 로고
    • R. P. Feynman and H. Kleinert, Phys. Rev. A 34, 5080 (1986); P. Zhang, R. M. Levi, and R. A. Friesner, Chem. Phys. Lett. 144, 236 (1988); G. A. Voth, D. Chandler, and W. H. Miller, J. Chem. Phys. 91, 7749 (1989); C. H. Mak and H. C. Andersen, ibid. 92, 2953 (1990); J Cao and B. J. Berne, ibid. 92, 7531 (1990); M. Messina, B. C. Garrett, and K. Schenter, ibid. 100, 6570 (1994).
    • (1986) Phys. Rev. A , vol.34 , pp. 5080
    • Feynman, R.P.1    Kleinert, H.2
  • 69
    • 0001139970 scopus 로고
    • R. P. Feynman and H. Kleinert, Phys. Rev. A 34, 5080 (1986); P. Zhang, R. M. Levi, and R. A. Friesner, Chem. Phys. Lett. 144, 236 (1988); G. A. Voth, D. Chandler, and W. H. Miller, J. Chem. Phys. 91, 7749 (1989); C. H. Mak and H. C. Andersen, ibid. 92, 2953 (1990); J Cao and B. J. Berne, ibid. 92, 7531 (1990); M. Messina, B. C. Garrett, and K. Schenter, ibid. 100, 6570 (1994).
    • (1988) Chem. Phys. Lett. , vol.144 , pp. 236
    • Zhang, P.1    Levi, R.M.2    Friesner, R.A.3
  • 70
    • 0041290286 scopus 로고
    • R. P. Feynman and H. Kleinert, Phys. Rev. A 34, 5080 (1986); P. Zhang, R. M. Levi, and R. A. Friesner, Chem. Phys. Lett. 144, 236 (1988); G. A. Voth, D. Chandler, and W. H. Miller, J. Chem. Phys. 91, 7749 (1989); C. H. Mak and H. C. Andersen, ibid. 92, 2953 (1990); J Cao and B. J. Berne, ibid. 92, 7531 (1990); M. Messina, B. C. Garrett, and K. Schenter, ibid. 100, 6570 (1994).
    • (1989) J. Chem. Phys. , vol.91 , pp. 7749
    • Voth, G.A.1    Chandler, D.2    Miller, W.H.3
  • 71
    • 0001156357 scopus 로고
    • R. P. Feynman and H. Kleinert, Phys. Rev. A 34, 5080 (1986); P. Zhang, R. M. Levi, and R. A. Friesner, Chem. Phys. Lett. 144, 236 (1988); G. A. Voth, D. Chandler, and W. H. Miller, J. Chem. Phys. 91, 7749 (1989); C. H. Mak and H. C. Andersen, ibid. 92, 2953 (1990); J Cao and B. J. Berne, ibid. 92, 7531 (1990); M. Messina, B. C. Garrett, and K. Schenter, ibid. 100, 6570 (1994).
    • (1990) J. Chem. Phys. , vol.92 , pp. 2953
    • Mak, C.H.1    Andersen, H.C.2
  • 72
    • 36549097752 scopus 로고
    • R. P. Feynman and H. Kleinert, Phys. Rev. A 34, 5080 (1986); P. Zhang, R. M. Levi, and R. A. Friesner, Chem. Phys. Lett. 144, 236 (1988); G. A. Voth, D. Chandler, and W. H. Miller, J. Chem. Phys. 91, 7749 (1989); C. H. Mak and H. C. Andersen, ibid. 92, 2953 (1990); J Cao and B. J. Berne, ibid. 92, 7531 (1990); M. Messina, B. C. Garrett, and K. Schenter, ibid. 100, 6570 (1994).
    • (1990) J. Chem. Phys. , vol.92 , pp. 7531
    • Cao, J.1    Berne, B.J.2
  • 73
    • 0001279093 scopus 로고
    • R. P. Feynman and H. Kleinert, Phys. Rev. A 34, 5080 (1986); P. Zhang, R. M. Levi, and R. A. Friesner, Chem. Phys. Lett. 144, 236 (1988); G. A. Voth, D. Chandler, and W. H. Miller, J. Chem. Phys. 91, 7749 (1989); C. H. Mak and H. C. Andersen, ibid. 92, 2953 (1990); J Cao and B. J. Berne, ibid. 92, 7531 (1990); M. Messina, B. C. Garrett, and K. Schenter, ibid. 100, 6570 (1994).
    • (1994) J. Chem. Phys. , vol.100 , pp. 6570
    • Messina, M.1    Garrett, B.C.2    Schenter, K.3
  • 74
    • 0001546517 scopus 로고
    • P. Talkner, Z. Phys. B 68, 201 (1987); A. N. Drozdov, Physica A 187, 329 (1992).
    • (1987) Z. Phys. B , vol.68 , pp. 201
    • Talkner, P.1
  • 75
    • 0039558225 scopus 로고
    • P. Talkner, Z. Phys. B 68, 201 (1987); A. N. Drozdov, Physica A 187, 329 (1992).
    • (1992) Physica A , vol.187 , pp. 329
    • Drozdov, A.N.1
  • 76
    • 0842265496 scopus 로고
    • For recent reviews, see B. J. Berne, M. Borkovec, and J. E. Straub, J. Phys. Chem. 92, 3711 (1988); P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990); V. I. Mel'nikov, Phys. Rep. 209, I (1991); Activated Barrier Crossing, edited by P. Hänggi and G. Fleming (World Scientific, Singapore, 1992); New Trends in Kramers' Reaction Rate Theory, edited by P. Talkner and P. Hänggi (Kluwer Academic, Dordrecht, 1995).
    • (1988) J. Phys. Chem. , vol.92 , pp. 3711
    • Berne, B.J.1    Borkovec, M.2    Straub, J.E.3
  • 77
    • 0347193736 scopus 로고
    • For recent reviews, see B. J. Berne, M. Borkovec, and J. E. Straub, J. Phys. Chem. 92, 3711 (1988); P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990); V. I. Mel'nikov, Phys. Rep. 209, I (1991); Activated Barrier Crossing, edited by P. Hänggi and G. Fleming (World Scientific, Singapore, 1992); New Trends in Kramers' Reaction Rate Theory, edited by P. Talkner and P. Hänggi (Kluwer Academic, Dordrecht, 1995).
    • (1990) Rev. Mod. Phys. , vol.62 , pp. 251
    • Hänggi, P.1    Talkner, P.2    Borkovec, M.3
  • 78
    • 0002652153 scopus 로고
    • For recent reviews, see B. J. Berne, M. Borkovec, and J. E. Straub, J. Phys. Chem. 92, 3711 (1988); P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990); V. I. Mel'nikov, Phys. Rep. 209, I (1991); Activated Barrier Crossing, edited by P. Hänggi and G. Fleming (World Scientific, Singapore, 1992); New Trends in Kramers' Reaction Rate Theory, edited by P. Talkner and P. Hänggi (Kluwer Academic, Dordrecht, 1995).
    • (1991) Phys. Rep. , vol.209
    • Mel'nikov, V.I.1
  • 79
    • 0842265496 scopus 로고
    • World Scientific, Singapore
    • For recent reviews, see B. J. Berne, M. Borkovec, and J. E. Straub, J. Phys. Chem. 92, 3711 (1988); P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990); V. I. Mel'nikov, Phys. Rep. 209, I (1991); Activated Barrier Crossing, edited by P. Hänggi and G. Fleming (World Scientific, Singapore, 1992); New Trends in Kramers' Reaction Rate Theory, edited by P. Talkner and P. Hänggi (Kluwer Academic, Dordrecht, 1995).
    • (1992) Activated Barrier Crossing
    • Hänggi, P.1    Fleming, G.2
  • 80
    • 0842265496 scopus 로고
    • Kluwer Academic, Dordrecht
    • For recent reviews, see B. J. Berne, M. Borkovec, and J. E. Straub, J. Phys. Chem. 92, 3711 (1988); P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990); V. I. Mel'nikov, Phys. Rep. 209, I (1991); Activated Barrier Crossing, edited by P. Hänggi and G. Fleming (World Scientific, Singapore, 1992); New Trends in Kramers' Reaction Rate Theory, edited by P. Talkner and P. Hänggi (Kluwer Academic, Dordrecht, 1995).
    • (1995) New Trends in Kramers' Reaction Rate Theory
    • Talkner, P.1    Hänggi, P.2


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