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Green's function for reversible geminate reaction with volume reactivity
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10.1063/1.4764357
/content/aip/journal/jcp/137/18/10.1063/1.4764357
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/18/10.1063/1.4764357
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The spatial arrangement of elements pertaining to the GF solution, which depends on the two distances and . The initial location of the particle, = , can be either inside or outside the reactive sphere, = σ. This divides space, in two different ways, into three regions (indicated by 1, 2, and 3). The particle can react only within the colored sphere, where ⩽ σ.

Image of FIG. 2.
FIG. 2.

The distance dependence of the Laplace transformed GF for an initially unbound particle at three values of : inside ( = 0.5), on the surface ( = 1), or outside ( = 2) the reaction sphere. Lines demonstrate Eqs. (3.5) and (3.6) , or (3.9) and (3.10) , for = 1 (full line), 5 (dashed line), and 10 (dashed–dot line). All the figures in this publication use the same parameters set: σ = 1, = 1, = 0.5, and = 3.

Image of FIG. 3.
FIG. 3.

The distance dependence of the GF in the time-domain, for an initially unbound particle starting outside the reaction sphere, at = 2 > σ. Black lines demonstrate the Laplace inverse of Eqs. (3.5) and (3.6) for (, | ), as well as that of Eq. (2.10) for the probability density of the bound state, (, | ).

Image of FIG. 4.
FIG. 4.

Same as Fig. 3 for = 1 = σ.

Image of FIG. 5.
FIG. 5.

Same as Fig. 3 for = 0.5 < σ, except that the times here are: = 0.02019, = 0.0307, and = 0.05361. Black lines were calculated by Laplace inverting Eqs. (3.9) and (3.10) .

Image of FIG. 6.
FIG. 6.

The time dependence of the GF for a particle that is initially bound at = 0.5. The LT of the GF for the unbound state is given by Eq. (3.9) multiplied by /( + ) and its Laplace inverse is depicted by the blue lines. The LT of the GF for the bound state, , is calculated from using Eq. (2.13) and its Laplace inverse is depicted by the red lines. The numerical solution of the PDE (2.1) for these initial conditions is shown by the dotted green lines.

Image of FIG. 7.
FIG. 7.

The time dependence of the survival probability, (| ), obtained by Laplace inverting Eqs. (A5) , as compared to numerically integrating the numerical solution of Eq. (2.1) using the software. Parameters are the same as in Fig. 2 .

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/content/aip/journal/jcp/137/18/10.1063/1.4764357
2012-11-12
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Green's function for reversible geminate reaction with volume reactivity
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/18/10.1063/1.4764357
10.1063/1.4764357
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