DOI: 10.1063/1.456169. Diffusion theory of multidimensional activated rate processes: The role of anisotropy

Diffusion theory of multidimensional activated rate processes: The role of anisotropy

10.1063/1.456169

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

We consider an anisotropic multidimensional barrier crossing problem, in the Smoluchowski (diffusion) limit. The anisotropy arises from either or both the shape of the potential energy surface and anisotropic diffusion. In such situations, the separatrix, which separates reactant and product regions of attraction, does not coincide with the ridge of the potential surface, which separates reactant and product wells, thus giving rise to a complicated time evolution. In the asymptotically long time limit, the time evolution is governed by crossing the separatrix and is exponential with a rate which may be obtained as a generalization of Kramers’ theory to the anisotropic situation. In contrast, in long, though not asymptotically long times, the time evolution is dominated by repeated crossings of the ridge, and is nonexponential. Such nonexponential time evolution has been observed in many biochemical reactions, where many degrees of freedom and anisotropic diffusion processes lead to complicated dynamical behavior. Our model provides a simple prototype of such situations.

Bibliography

Kl/osek-Dygas, M. M., Hoffman, B. M., Matkowsky, B. J., Nitzan, A., Ratner, M. A., & Schuss, Z. (1989). Diffusion theory of multidimensional activated rate processes: The role of anisotropy. The Journal of Chemical Physics, 90(2), 1141â1148.

Authors 6

M. M. Kl/osek-Dygas (first)
B. M. Hoffman (additional)
B. J. Matkowsky (additional)
A. Nitzan (additional)
M. A. Ratner (additional)
Z. Schuss (additional)

References 32 Referenced 56

10.1016/S0031-8914(40)90098-2 / Physica (Utrecht) (1940)
{'key': '2024021007183158200_r2', 'first-page': '149', 'volume': '22', 'year': '1956', 'journal-title': 'Physics'} / Physics (1956)
10.1016/0022-3697(57)90059-8 / J. Phys. Chem. Solids (1957)
10.1103/PhysRev.121.1668 / Phys. Rev. (1961)
10.1103/RevModPhys.39.373 / Rev. Mod. Phys. (1967)
10.1103/PhysRevLett.21.973 / Phys. Rev. Lett. (1968)
10.1016/0003-4916(69)90153-5 / Ann. Phys. (N.Y.) (1969)
{'key': '2024021007183158200_r2f', 'first-page': '604', 'volume': '35', 'year': '1979', 'journal-title': 'SIAM J. Appl. Math.'} / SIAM J. Appl. Math. (1979)
{'key': '2024021007183158200_r2g'}
10.1063/1.441634 / J. Chem. Phys. (1981)
10.1063/1.442331 / J. Chem. Phys. (1981)
10.1063/1.443951 / J. Chem. Phys. (1982)
10.1063/1.443727 / J. Chem. Phys. (1982)
10.1016/0378-4371(86)90077-4 / Physica A (1986)
10.1063/1.454689 / J. Chem. Phys. (1988)
{'key': '2024021007183158200_r5', 'first-page': '347', 'volume': '3', 'year': '1986', 'journal-title': 'Comments Mol. Cell. Biophys.'} / Comments Mol. Cell. Biophys. (1986)
10.1063/1.444643 / J. Chem. Phys. (1983)
10.1063/1.445988 / J. Chem. Phys. (1983)
10.1063/1.451952 / J. Chem. Phys. (1987)
10.1063/1.450804 / J. Chem. Phys. (1986)
10.1063/1.451951 / J. Chem. Phys. (1987)
{'key': '2024021007183158200_r8'}
{'key': '2024021007183158200_r9', 'first-page': '356', 'volume': '33', 'year': '1977', 'journal-title': 'SIAM J. Appl. Math.'} / SIAM J. Appl. Math. (1977)
{'key': '2024021007183158200_r9a', 'first-page': '604', 'volume': '35', 'year': '1979', 'journal-title': 'SIAM J. Appl. Math.'} / SIAM J. Appl. Math. (1979)
10.1137/0142057 / SIAM J. Appl. Math. (1982)
10.1137/0143046 / SIAM J. Appl. Math. (1983)
10.1016/0375-9601(83)90606-0 / Phys. Lett. A (1983)
10.1137/0146019 / SIAM J. Appl. Math. (1986)
{'key': '2024021007183158200_r11'}
{'key': '2024021007183158200_r12'}
10.1137/0140020 / SIAM J. Appl. Math. (1981)
10.1021/bi00409a057 / Biochemistry (1988)

Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 9:20 a.m.)
Deposited	1 year, 6 months ago (Feb. 10, 2024, 4:12 a.m.)
Indexed	1 year, 6 months ago (Feb. 11, 2024, 1:39 a.m.)
Issued	36 years, 7 months ago (Jan. 15, 1989)
Published	36 years, 7 months ago (Jan. 15, 1989)
Published Print	36 years, 7 months ago (Jan. 15, 1989)

Funders 0

None

BibTeX

@article{Kl_osek_Dygas_1989, title={Diffusion theory of multidimensional activated rate processes: The role of anisotropy}, volume={90}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.456169}, DOI={10.1063/1.456169}, number={2}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Kl/osek-Dygas, M. M. and Hoffman, B. M. and Matkowsky, B. J. and Nitzan, A. and Ratner, M. A. and Schuss, Z.}, year={1989}, month=jan, pages={1141–1148} }

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