A diffusional bimolecular propensity function

Journal of Chemical Physics

Volumn 131, Issue 16, 2009, Pages

  Gillespie, Daniel T ^a  

^a Dan T Gillespie Consulting   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CELLULAR SYSTEM; CHEMICAL MASTER EQUATION; DIFFUSION EQUATIONS; DILUTE GAS; DILUTE SOLUTION; EXPLICIT FORMULA; LIMITING CASE; ORGANIC STRUCTURES; REACTANT MOLECULES; SOLUTE MOLECULES; SOLVENT MOLECULES; STOCHASTIC SIMULATION ALGORITHMS; TEMPORAL SCALE;

GRAFTING (CHEMICAL); REACTION RATES; STOCHASTIC SYSTEMS; SYNTHESIS (CHEMICAL);

MOLECULES;

ARTICLE; CHEMICAL MODEL; DIFFUSION; KINETICS;

DIFFUSION; KINETICS; MODELS, CHEMICAL;

EID: 72049096926     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3253798     Document Type: Article

References (21)

1. D. Gillespie, Physica A 0378-4371 188, 404 (1992). 10.1016/0378-4371(92) 90283-V
2. D. Gillespie, J. Phys. Chem. B 1089-5647 113, 1640 (2009). 10.1021/jp806431b
3. B T m 12 -1.
4. R. D. Present, Kinetic Theory of Gases (McGraw-Hill, New York, 1958).
5. F. C. Collins and G. E. Kimball, J. Colloid Sci. 0095-8522 4, 425 (1949). 10.1016/0095-8522(49)90023-9
6. A. Einstein, Ann. Phys. 0003-3804 17, 549 (1905) 10.1002/andp.19053220806
7. A nice discussion of this paper is given in C. W. Gardiner, Handbook for Stochastic Methods in Physics, Chemistry and the Natural Sciences (Springer-Verlag, New York, 1985), Sec. 1.2.1.
8. P. Langevin, Comptes Rendues 146, 530 (1908).
9. See for example D. Gillespie, Am. J. Phys. 0002-9505 64, 225 (1996) 10.1119/1.18210
10. D. Gillespie, Am. J. Phys. 0002-9505 64, 1246 (1996). 10.1119/1.18387
11. 2. This analysis of the relative motion of two diffusing molecules obviously assumes that they do not collide with other solute molecules; that condition should be reasonably well satisfied in the dilute case we are considering here.
12. M. v. Smoluchowski, Z. Phys. Chem. 0942-9352 92, 129 (1917).
13. B. Sveshnikoff, Acta Physicochim. U.R.S.S. 3, 257 (1935).
14. t, and hence negligibly small; therefore, the reaction events can be regarded as being "mutually exclusive."
15. S. S. Andrews and D. Bray, Phys. Biol. 1478-3975 1, 137 (2004). 10.1088/1478-3967/1/3/001 (Pubitemid 44362291)
16. H. -X. Zhou and A. Szabo, J. Chem. Phys. 0021-9606 95, 5948 (1991) 10.1063/1.461616
17. I. Gopich and A. Szabo, Chem. Phys. 0301-0104 284, 91 (2002) 10.1016/S0301-0104(02)00541-4
18. I. Gopich and A. Szabo, J. Chem. Phys. 0021-9606 117, 507 (2002). 10.1063/1.1482701 (Pubitemid 34935262)
19. t is "infinitesimally small," for only then we can ignore the possibility that some other molecule might spoil things by colliding with either member of the pair before they collide with each other.
20. t be negligibly small.
21. To the best of the author's knowledge, this result and its implications for trajectory simulation were first articulated by C. Gillespie (private communication), who discovered it numerically by carrying out a series of Monte Carlo simulation experiments using Eq..