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Exact Green's function of the reversible diffusion-influenced reaction for an isolated pair in two dimensions
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10.1063/1.4737662
/content/aip/journal/jcp/137/5/10.1063/1.4737662
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/5/10.1063/1.4737662
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Integration contour used in Eq. (19).

Image of FIG. 2.
FIG. 2.

The reversible Green's function and survival probability for an initially unbound isolated pair in 2D. The parameters are: a = 1, D = 2, r 0 = 1.1, κ a = 2πD. The left panel shows the r dependence of the reversible GF 2πrg(r, t|r 0) at time t = 10η for various values of the dissociation constant κ d = 1 η−1, 0.5 η−1, 0.1 η−1, 0.01 η−1, where η = a 2 D −1 denotes the natural time scale of the system. The solid lines correspond to the analytical expression Eq. (26). The various markers refer to numerical solutions that were obtained using the SSDP software, ver. 2.66. The right panel shows the time dependence of the survival probability S(t|r 0). The dissociation constant is κ d = 0.5 η−1. The solid line refers to the analytical expression in Eq. (29). The markers indicate the SSDP results.

Image of FIG. 3.
FIG. 3.

The reversible Green's function and survival probability for an initially bound isolated pair in 2D. The parameters are: a = 1, D = 2, κ a = 2πD. The left panel shows the r dependence of the reversible GF 2πrg(r, t|*) at time t = 10 η for various values of the dissociation constant κ d = 1 η−1, 0.5 η−1, 0.1 η−1, 0.025 η−1, where η = a 2 D −1 denotes the natural time scale of the system. The solid lines are obtained from the analytical expression Eq. (31). The various markers indicate the corresponding numerical solutions generated by the SSDP software. The right panel shows the time dependence of the survival probability S(t|*). The dissociation constant is κ d = 0.5 η−1. The solid line refers to the analytical expression Eq. (32). The markers indicate the SSDP results.

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/content/aip/journal/jcp/137/5/10.1063/1.4737662
2012-08-01
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Exact Green's function of the reversible diffusion-influenced reaction for an isolated pair in two dimensions
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/5/10.1063/1.4737662
10.1063/1.4737662
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