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Combinatoric analysis of heterogeneous stochastic self-assembly
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10.1063/1.4817202
/content/aip/journal/jcp/139/12/10.1063/1.4817202
http://aip.metastore.ingenta.com/content/aip/journal/jcp/139/12/10.1063/1.4817202
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

A schematic of the heterogeneous self-assembly process in a closed system. The open hexagons represent seed particles on which the monomers (filled circles) aggregate. In this example, the total mass, the number of seed particles, and the maximum cluster size are = 30, = 6, and = 6, respectively.

Image of FIG. 2.
FIG. 2.

State space for a self-assembling system consisting of = 5 total monomers, = 2 seeds, and a maximum cluster size of = 3. In this example, σ = /( ) = 5/6.

Image of FIG. 3.
FIG. 3.

Mean cluster sizes ⟨ ()⟩ obtained from averaging 10 KMC simulations of the stochastic process in Eq. (9) with = 5, = 10, and ɛ = 10. The dashed curves represent solutions from BD equations for comparison. (a) = 5 corresponding to σ = 0.1, (b) = 15 corresponding to σ = 0.3, and (c) = 25 (σ = 1/2).

Image of FIG. 4.
FIG. 4.

The difference δ() ≡ ⟨ ()⟩ − () for = 0, 1, 2, 3, 4, 5. In this example, = 25, = 5, and = 10.

Image of FIG. 5.
FIG. 5.

Expected metastable and equilibrium cluster numbers calculated as a function of using numerical methods and combinatoric algorithms. Here, as in Fig. 3 , = 10, = 5. For metastable concentrations, (a) and (b), the differences between the mean-field and exact results are small except for the largest cluster sizes = 4, 5. For comparison, is shown by the dashed grey curve in (b). (c) and (d) show and , respectively. The differences between and are more subtle but are generally most noticeable for σ ∼ 0.1, 0.9. All densities are symmetric in about = /2, with , to order ɛ, forming an isosbestic point at = /2.

Image of FIG. 6.
FIG. 6.

Plot of Δ() ( = 5, = 10) for = 5, 25, 45. These curves were generated from KMC simulation of the stochastic process and numerical evaluation of Eqs. (1) for (). Note that the error in the metastable regime (1 ≪ ≪ ɛ) is largest for = 45, while at equilibrium ( ≫ ɛ) the errors are largest for ≈ 5, 45.

Image of FIG. 7.
FIG. 7.

The overall error of mass-action kinetics. (a) The averaged error in the metastable regime Δ*. (b) The averaged error Δ in the equilibrium limit ≫ ɛ.

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/content/aip/journal/jcp/139/12/10.1063/1.4817202
2013-08-01
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Combinatoric analysis of heterogeneous stochastic self-assembly
http://aip.metastore.ingenta.com/content/aip/journal/jcp/139/12/10.1063/1.4817202
10.1063/1.4817202
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