-
1
-
-
0000754354
-
-
(Comprehensive Chemical Kinetics), edited by M. J. Pilling (Elsevier, Amsterdam), Chap. 4
-
A. S. Tomlin, T. Turányi, and M. J. Pilling, in Low-Temperature Combustion and Autoignition (Comprehensive Chemical Kinetics, Vol. 35), edited by M. J. Pilling (Elsevier, Amsterdam, 1997) Chap. 4.
-
(1997)
Low-temperature Combustion and Autoignition
, vol.35
-
-
Tomlin, A.S.1
Turányi, T.2
Pilling, M.J.3
-
3
-
-
0000870544
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
24
-
-
0033153581
-
-
A. Massias, D. Diamantis, E. Mastorakos, and D. A. Goussis, Combust. Flame 117, 685 (1999).
-
(1999)
Combust. Flame
, vol.117
, pp. 685
-
-
Massias, A.1
Diamantis, D.2
Mastorakos, E.3
Goussis, D.A.4
-
25
-
-
0017030517
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
32
-
-
0039235344
-
-
M. Frankowicz, M. Moreau, P. P. Szczȩsny, J. Tóth, and L. Vicente, J. Phys. Chem. 97, 1891 (1993).
-
(1993)
J. Phys. Chem.
, vol.97
, pp. 1891
-
-
Frankowicz, M.1
Moreau, M.2
Szczȩsny, P.P.3
Tóth, J.4
Vicente, L.5
-
35
-
-
0142116225
-
-
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
-
-
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
-
-
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
-
-
A. F. Bartholomay, Ann. N.Y. Acad. Sci. 96, 897 (1962); Biochemistry 1, 223 (1962).
-
(1962)
Biochemistry
, vol.1
, pp. 223
-
-
-
40
-
-
0001574243
-
-
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
-
-
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
-
-
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
-
-
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
-
-
note
-
i, and its derivative implicitly.
-
-
-
-
46
-
-
9744271981
-
-
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
-
-
The MathWorks
-
MATLAB 6.5 (The MathWorks, 2003).
-
(2003)
MATLAB 6.5
-
-
-
51
-
-
0005151565
-
-
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).
-
(1987)
Bull. Cl. Sci., Acad. R. Belg.
, vol.73
, pp. 62
-
-
Thomas, R.1
Richelle, J.2
D'Ari, R.3
-
52
-
-
0035043342
-
-
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
|