메뉴 건너뛰기




Volumn 121, Issue 18, 2004, Pages 8716-8730

Reducing a chemical master equation by invariant manifold methods

Author keywords

[No Author keywords available]

Indexed keywords

FRASER'S METHOD; GEOMETRIC METHODS; MASTER EQUATIONS; TIME-SCALE ANALYSIS;

EID: 9744247592     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1802495     Document Type: Article
Times cited : (12)

References (54)
  • 3
    • 0000870544 scopus 로고
    • L. Michaelis and M. L. Menten, Biochem. Z. 49, 333 (1913); D. L. Chapman and L. K. Underbill, J. Chem. Soc. 103, 496 (1913); M. Bodenstein, Z. Phys. Chem. 85, 329 (1913); G. E. Briggs and J. B. S. Haldane, Biochem. J. 19, 338 (1925).
    • (1913) Biochem. Z. , vol.49 , pp. 333
    • Michaelis, L.1    Menten, M.L.2
  • 4
    • 0042699072 scopus 로고
    • L. Michaelis and M. L. Menten, Biochem. Z. 49, 333 (1913); D. L. Chapman and L. K. Underbill, J. Chem. Soc. 103, 496 (1913); M. Bodenstein, Z. Phys. Chem. 85, 329 (1913); G. E. Briggs and J. B. S. Haldane, Biochem. J. 19, 338 (1925).
    • (1913) J. Chem. Soc. , vol.103 , pp. 496
    • Chapman, D.L.1    Underbill, L.K.2
  • 5
    • 0000240761 scopus 로고
    • L. Michaelis and M. L. Menten, Biochem. Z. 49, 333 (1913); D. L. Chapman and L. K. Underbill, J. Chem. Soc. 103, 496 (1913); M. Bodenstein, Z. Phys. Chem. 85, 329 (1913); G. E. Briggs and J. B. S. Haldane, Biochem. J. 19, 338 (1925).
    • (1913) Z. Phys. Chem. , vol.85 , pp. 329
    • Bodenstein, M.1
  • 6
    • 0000292524 scopus 로고
    • L. Michaelis and M. L. Menten, Biochem. Z. 49, 333 (1913); D. L. Chapman and L. K. Underbill, J. Chem. Soc. 103, 496 (1913); M. Bodenstein, Z. Phys. Chem. 85, 329 (1913); G. E. Briggs and J. B. S. Haldane, Biochem. J. 19, 338 (1925).
    • (1925) Biochem. J. , vol.19 , pp. 338
    • Briggs, G.E.1    Haldane, J.B.S.2
  • 7
    • 0000416179 scopus 로고
    • J. R. Bowen, A. Acrivos, and A. K. Oppenheim, Chem. Eng. Sci. 18, 177 (1963); F. G. Heineken, H. M. Tsuchiya, and R. Aris, Math. Biosci. 1, 95 (1967); F. Battelli and C. Lazzari, ibid. 75, 229 (1985).
    • (1963) Chem. Eng. Sci. , vol.18 , pp. 177
    • Bowen, J.R.1    Acrivos, A.2    Oppenheim, A.K.3
  • 8
    • 0002595354 scopus 로고
    • J. R. Bowen, A. Acrivos, and A. K. Oppenheim, Chem. Eng. Sci. 18, 177 (1963); F. G. Heineken, H. M. Tsuchiya, and R. Aris, Math. Biosci. 1, 95 (1967); F. Battelli and C. Lazzari, ibid. 75, 229 (1985).
    • (1967) Math. Biosci. , vol.1 , pp. 95
    • Heineken, F.G.1    Tsuchiya, H.M.2    Aris, R.3
  • 9
    • 0022006330 scopus 로고
    • J. R. Bowen, A. Acrivos, and A. K. Oppenheim, Chem. Eng. Sci. 18, 177 (1963); F. G. Heineken, H. M. Tsuchiya, and R. Aris, Math. Biosci. 1, 95 (1967); F. Battelli and C. Lazzari, ibid. 75, 229 (1985).
    • (1985) Math. Biosci. , vol.75 , pp. 229
    • Battelli, F.1    Lazzari, C.2
  • 10
    • 0001034113 scopus 로고
    • S. J. Fraser, J. Chem. Phys. 88, 4732 (1988); A. H. Nguyen and S. J. Fraser, ibid. 91, 186 (1989).
    • (1988) J. Chem. Phys. , vol.88 , pp. 4732
    • Fraser, S.J.1
  • 14
    • 0006030995 scopus 로고
    • M. Okuda, Prog. Theor. Phys. 68, 1827 (1982); B. O. Palsson and E. N. Lightfoot, J. Theor. Biol. 111, 273 (1984); A. N. Yannacopoulos, A. S. Tomlin, J. Brindley, J. H. Merkin, and M. J. Pilling, Physica D 83, 421 (1995); M. Stiefenhofer, J. Math. Biol. 36, 593 (1998); B. Krauskopf and H. Osinga, Chaos 9, 768 (1999); R. T. Skodje and M. J. Davis, J. Phys. Chem. A 105, 10356 (2001); S. Singh, J. M. Powers, and S. Paolucci, J. Chem. Phys. 117, 1482 (2002).
    • (1982) Prog. Theor. Phys. , vol.68 , pp. 1827
    • Okuda, M.1
  • 15
    • 0021734908 scopus 로고
    • M. Okuda, Prog. Theor. Phys. 68, 1827 (1982); B. O. Palsson and E. N. Lightfoot, J. Theor. Biol. 111, 273 (1984); A. N. Yannacopoulos, A. S. Tomlin, J. Brindley, J. H. Merkin, and M. J. Pilling, Physica D 83, 421 (1995); M. Stiefenhofer, J. Math. Biol. 36, 593 (1998); B. Krauskopf and H. Osinga, Chaos 9, 768 (1999); R. T. Skodje and M. J. Davis, J. Phys. Chem. A 105, 10356 (2001); S. Singh, J. M. Powers, and S. Paolucci, J. Chem. Phys. 117, 1482 (2002).
    • (1984) J. Theor. Biol. , vol.111 , pp. 273
    • Palsson, B.O.1    Lightfoot, E.N.2
  • 16
    • 58149210464 scopus 로고
    • M. Okuda, Prog. Theor. Phys. 68, 1827 (1982); B. O. Palsson and E. N. Lightfoot, J. Theor. Biol. 111, 273 (1984); A. N. Yannacopoulos, A. S. Tomlin, J. Brindley, J. H. Merkin, and M. J. Pilling, Physica D 83, 421 (1995); M. Stiefenhofer, J. Math. Biol. 36, 593 (1998); B. Krauskopf and H. Osinga, Chaos 9, 768 (1999); R. T. Skodje and M. J. Davis, J. Phys. Chem. A 105, 10356 (2001); S. Singh, J. M. Powers, and S. Paolucci, J. Chem. Phys. 117, 1482 (2002).
    • (1995) Physica D , vol.83 , pp. 421
    • Yannacopoulos, A.N.1    Tomlin, A.S.2    Brindley, J.3    Merkin, J.H.4    Pilling, M.J.5
  • 17
    • 0000415561 scopus 로고    scopus 로고
    • M. Okuda, Prog. Theor. Phys. 68, 1827 (1982); B. O. Palsson and E. N. Lightfoot, J. Theor. Biol. 111, 273 (1984); A. N. Yannacopoulos, A. S. Tomlin, J. Brindley, J. H. Merkin, and M. J. Pilling, Physica D 83, 421 (1995); M. Stiefenhofer, J. Math. Biol. 36, 593 (1998); B. Krauskopf and H. Osinga, Chaos 9, 768 (1999); R. T. Skodje and M. J. Davis, J. Phys. Chem. A 105, 10356 (2001); S. Singh, J. M. Powers, and S. Paolucci, J. Chem. Phys. 117, 1482 (2002).
    • (1998) J. Math. Biol. , vol.36 , pp. 593
    • Stiefenhofer, M.1
  • 18
    • 0033196117 scopus 로고    scopus 로고
    • M. Okuda, Prog. Theor. Phys. 68, 1827 (1982); B. O. Palsson and E. N. Lightfoot, J. Theor. Biol. 111, 273 (1984); A. N. Yannacopoulos, A. S. Tomlin, J. Brindley, J. H. Merkin, and M. J. Pilling, Physica D 83, 421 (1995); M. Stiefenhofer, J. Math. Biol. 36, 593 (1998); B. Krauskopf and H. Osinga, Chaos 9, 768 (1999); R. T. Skodje and M. J. Davis, J. Phys. Chem. A 105, 10356 (2001); S. Singh, J. M. Powers, and S. Paolucci, J. Chem. Phys. 117, 1482 (2002).
    • (1999) Chaos , vol.9 , pp. 768
    • Krauskopf, B.1    Osinga, H.2
  • 19
    • 0035892189 scopus 로고    scopus 로고
    • M. Okuda, Prog. Theor. Phys. 68, 1827 (1982); B. O. Palsson and E. N. Lightfoot, J. Theor. Biol. 111, 273 (1984); A. N. Yannacopoulos, A. S. Tomlin, J. Brindley, J. H. Merkin, and M. J. Pilling, Physica D 83, 421 (1995); M. Stiefenhofer, J. Math. Biol. 36, 593 (1998); B. Krauskopf and H. Osinga, Chaos 9, 768 (1999); R. T. Skodje and M. J. Davis, J. Phys. Chem. A 105, 10356 (2001); S. Singh, J. M. Powers, and S. Paolucci, J. Chem. Phys. 117, 1482 (2002).
    • (2001) J. Phys. Chem. A , vol.105 , pp. 10356
    • Skodje, R.T.1    Davis, M.J.2
  • 20
    • 0037158091 scopus 로고    scopus 로고
    • M. Okuda, Prog. Theor. Phys. 68, 1827 (1982); B. O. Palsson and E. N. Lightfoot, J. Theor. Biol. 111, 273 (1984); A. N. Yannacopoulos, A. S. Tomlin, J. Brindley, J. H. Merkin, and M. J. Pilling, Physica D 83, 421 (1995); M. Stiefenhofer, J. Math. Biol. 36, 593 (1998); B. Krauskopf and H. Osinga, Chaos 9, 768 (1999); R. T. Skodje and M. J. Davis, J. Phys. Chem. A 105, 10356 (2001); S. Singh, J. M. Powers, and S. Paolucci, J. Chem. Phys. 117, 1482 (2002).
    • (2002) J. Chem. Phys. , vol.117 , pp. 1482
    • Singh, S.1    Powers, J.M.2    Paolucci, S.3
  • 25
    • 0017030517 scopus 로고
    • D. T. Gillespie, J. Comput. Phys. 22, 403 (1976); D. T. Gillespie, J. Phys. Chem. 81, 2340 (1977).
    • (1976) J. Comput. Phys. , vol.22 , pp. 403
    • Gillespie, D.T.1
  • 26
    • 33645429016 scopus 로고
    • D. T. Gillespie, J. Comput. Phys. 22, 403 (1976); D. T. Gillespie, J. Phys. Chem. 81, 2340 (1977).
    • (1977) J. Phys. Chem. , vol.81 , pp. 2340
    • Gillespie, D.T.1
  • 29
    • 0001144902 scopus 로고    scopus 로고
    • M. A. Gibson and J. Bruck, J. Phys. Chem. A 104, 1876 (2000); D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001); D. T. Gillespie and L. R. Petzold, ibid. 119, 8229 (2003).
    • (2000) J. Phys. Chem. A , vol.104 , pp. 1876
    • Gibson, M.A.1    Bruck, J.2
  • 30
    • 0035933994 scopus 로고    scopus 로고
    • M. A. Gibson and J. Bruck, J. Phys. Chem. A 104, 1876 (2000); D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001); D. T. Gillespie and L. R. Petzold, ibid. 119, 8229 (2003).
    • (2001) J. Chem. Phys. , vol.115 , pp. 1716
    • Gillespie, D.T.1
  • 31
    • 0242425970 scopus 로고    scopus 로고
    • M. A. Gibson and J. Bruck, J. Phys. Chem. A 104, 1876 (2000); D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001); D. T. Gillespie and L. R. Petzold, ibid. 119, 8229 (2003).
    • (2003) J. Chem. Phys. , vol.119 , pp. 8229
    • Gillespie, D.T.1    Petzold, L.R.2
  • 35
    • 0142116225 scopus 로고    scopus 로고
    • T. Shibata, J. Chem. Phys. 119, 6629 (2003). Shibata's method is closely related to the Mori-Zwanzig formalism. The former defines the projection operator as a mapping of functions of (x,y,t) into functions of x, the fast variables, times functions of (y,t), while the latter defines a mapping of functions of (x,y,t) into functions of (y,t) only. For the original derivation of the Mori-Zwanzig formalism, see H. Mori, Prog. Theor. Phys. 33, 423 (1965); R. Zwanzig, J. Stat. Phys. 9, 215 (1973).
    • (2003) J. Chem. Phys. , vol.119 , pp. 6629
    • Shibata, T.1
  • 36
    • 0000514837 scopus 로고
    • T. Shibata, J. Chem. Phys. 119, 6629 (2003). Shibata's method is closely related to the Mori-Zwanzig formalism. The former defines the projection operator as a mapping of functions of (x,y,t) into functions of x, the fast variables, times functions of (y,t), while the latter defines a mapping of functions of (x,y,t) into functions of (y,t) only. For the original derivation of the Mori-Zwanzig formalism, see H. Mori, Prog. Theor. Phys. 33, 423 (1965); R. Zwanzig, J. Stat. Phys. 9, 215 (1973).
    • (1965) Prog. Theor. Phys. , vol.33 , pp. 423
    • Mori, H.1
  • 37
    • 18844402460 scopus 로고
    • T. Shibata, J. Chem. Phys. 119, 6629 (2003). Shibata's method is closely related to the Mori-Zwanzig formalism. The former defines the projection operator as a mapping of functions of (x,y,t) into functions of x, the fast variables, times functions of (y,t), while the latter defines a mapping of functions of (x,y,t) into functions of (y,t) only. For the original derivation of the Mori-Zwanzig formalism, see H. Mori, Prog. Theor. Phys. 33, 423 (1965); R. Zwanzig, J. Stat. Phys. 9, 215 (1973).
    • (1973) J. Stat. Phys. , vol.9 , pp. 215
    • Zwanzig, R.1
  • 39
    • 0001564972 scopus 로고
    • A. F. Bartholomay, Ann. N.Y. Acad. Sci. 96, 897 (1962); Biochemistry 1, 223 (1962).
    • (1962) Biochemistry , vol.1 , pp. 223
  • 40
    • 0001574243 scopus 로고
    • C. J. Jachimowski, D. A. McQuarrie, and M. E. Russell, Biochemistry 3, 1732 (1964); I. G. Darvey and P. J. Staff, J. Theor. Biol. 14, 157 (1967); C. C. Heyde and E. Heyde, ibid. 25, 159 (1969); P. J. Staff, ibid. 27, 221 (1970).
    • (1964) Biochemistry , vol.3 , pp. 1732
    • Jachimowski, C.J.1    McQuarrie, D.A.2    Russell, M.E.3
  • 41
    • 0014051980 scopus 로고
    • C. J. Jachimowski, D. A. McQuarrie, and M. E. Russell, Biochemistry 3, 1732 (1964); I. G. Darvey and P. J. Staff, J. Theor. Biol. 14, 157 (1967); C. C. Heyde and E. Heyde, ibid. 25, 159 (1969); P. J. Staff, ibid. 27, 221 (1970).
    • (1967) J. Theor. Biol. , vol.14 , pp. 157
    • Darvey, I.G.1    Staff, P.J.2
  • 42
    • 0014590294 scopus 로고
    • C. J. Jachimowski, D. A. McQuarrie, and M. E. Russell, Biochemistry 3, 1732 (1964); I. G. Darvey and P. J. Staff, J. Theor. Biol. 14, 157 (1967); C. C. Heyde and E. Heyde, ibid. 25, 159 (1969); P. J. Staff, ibid. 27, 221 (1970).
    • (1969) J. Theor. Biol. , vol.25 , pp. 159
    • Heyde, C.C.1    Heyde, E.2
  • 43
    • 0014789591 scopus 로고
    • C. J. Jachimowski, D. A. McQuarrie, and M. E. Russell, Biochemistry 3, 1732 (1964); I. G. Darvey and P. J. Staff, J. Theor. Biol. 14, 157 (1967); C. C. Heyde and E. Heyde, ibid. 25, 159 (1969); P. J. Staff, ibid. 27, 221 (1970).
    • (1970) J. Theor. Biol. , vol.27 , pp. 221
    • Staff, P.J.1
  • 45
    • 9744285255 scopus 로고    scopus 로고
    • note
    • i, and its derivative implicitly.
  • 46
    • 9744271981 scopus 로고    scopus 로고
    • note
    • 26 On the other hand, simultaneous iteration should have more efficient implementations in parallel computers. Since we have in mind the application of these methods to very large systems for which parallel computing may become necessary, we have preferred simultaneous iteration in this work. We have not however tested our method on a parallel computer, nor have we made any comparative study of the convergence rates of simultaneous and cyclic iteration in the linear problem treated here.
  • 50
    • 1842516202 scopus 로고    scopus 로고
    • The MathWorks
    • MATLAB 6.5 (The MathWorks, 2003).
    • (2003) MATLAB 6.5
  • 52
    • 0035043342 scopus 로고    scopus 로고
    • R. Thomas, J. Richelle, and R. d'Ari, Bull. Cl. Sci., Acad. R. Belg. 73, 62 (1987); R. Thomas and R. d'Ari, C. R. Acad. Sci., Ser. III 324, 285 (2001).
    • (2001) C. R. Acad. Sci., Ser. III , vol.324 , pp. 285
    • Thomas, R.1    D'Ari, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.