Stochastic Kinetics on Networks - American Chemical Society

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Stochastic Kinetics on Networks: When Slow is Fast Xin Li, Anatoly B. Kolomeisky, and Angelo Valleriani J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp506668a • Publication Date (Web): 20 Aug 2014 Downloaded from http://pubs.acs.org on August 26, 2014

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

µ i

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a2

am

λ

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λ µ

µ

bn

b2 àEZ~'*qOm

Page 24 of 30

ûu

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j

1 0.95

A

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Probability U

Page 25 of 30

0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0

0.2

0.4

0.6

x = µ/λ

0.8

1

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X

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Average time [1/µ]


15

[1/µ] [1/µ] λ=2

10

5

0 0

1

2

λ [µ]

3

4

5

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Page 26 of 30

0.1 0.09

s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Threshold time t

Page 27 of 30

0.08

Exact solution Approximation

0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0.5

0.6

0.7

0.8

0.9

Value of the probability θ

1

àEZ~'*qOm Õ u

|



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

a2 a1 i

am

λ

λ

λ µ b1

j µ

µ

Page 28 of 30

bn

b2

àEZ~'*qOm ÿ u


Page 29 of 30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


!#"%$

&('



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

µ i

a1 λ µ µ b1

µ

a2

am

λ

µ

λ µ

µ

µ µ

bn

b2

W

àEZ~'*qOm

Å

u[ª ¶

Page 30 of 30

Î

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Stochastic Kinetics on Networks - American Chemical Society

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