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Coarse-grained kinetic Monte Carlo models: Complex lattices, multicomponent systems, and homogenization at the stochastic level
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10.1063/1.3005225
/content/aip/journal/jcp/129/18/10.1063/1.3005225
http://aip.metastore.ingenta.com/content/aip/journal/jcp/129/18/10.1063/1.3005225

Figures

Image of FIG. 1.
FIG. 1.

Flowchart of null-event CGMC algorithm. The cell coverage and cell CG transition rate will only be used if CG cell homogenization is applied.

Image of FIG. 2.
FIG. 2.

(a) Schematic of top (T) and bridge (B) sites of a (100) surface and (b) layout of CG cells over the microscopic lattice in example A. CG cells are uniform squares with a side length of four lattice constants. Periodic boundary conditions are used. (c) Coverage evolution against simulated time.

Image of FIG. 3.
FIG. 3.

(a) Schematic of the CG mesh. Each CG cell encompasses microscopic sites. Periodic boundary conditions are used. (b) Coverage of vacancies at increasing times (, , and ). CGMC is compared against traditional KMC. The slight difference is attributed to the well-mixed assumption along the -axis.

Image of FIG. 4.
FIG. 4.

Schematic of 1D diffusion through window and intercage sites. Traditional KMC will store and simulate all potential events shown in (a). The CGMC method with assumes neighboring and sites are in equilibrium with each other (b). The two diffusion rates between neighbors are lumped into one coarse process via homogenization (c).

Image of FIG. 5.
FIG. 5.

(a) Steady state loading profiles in a 1D zeolite membrane with Dirichlet boundary conditions. CGMC using a stochastic LMF closure with varying levels coarse graining compares well with traditional KMC. Steady state solution based on the deterministic LMF closure ( only is shown for clarity; not shown for clarity). (b) Zeolite loading vs time. (c) CPU relative to traditional KMC of simulating the same amount of time at steady state with varying levels of spatial coarse graining on two lattice sizes.

Image of FIG. 6.
FIG. 6.

Examples of MF coverages within CG cells using the deterministic and stochastic LMF approximation. The error in the deterministic LMF solution relative to the accurate stochastic LMF solution increases as the CG cell size, , decreases: (a) , (b) .

Tables

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Table I.

Major nomenclature.

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Table II.

Summary of transition probability rates for CGMC (without homogenization).

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Table III.

Summary of processes and transition probability rates for example A.

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Table IV.

Summary of processes and transition probability rates for example B.

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Table V.

Summary of transition probability rates for CGMC (with homogenization).

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Table VI.

Summary of processes and transition probability rates for Example C.

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Table VII.

Transition probability rate constants for example C.

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/content/aip/journal/jcp/129/18/10.1063/1.3005225
2008-11-10
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Coarse-grained kinetic Monte Carlo models: Complex lattices, multicomponent systems, and homogenization at the stochastic level
http://aip.metastore.ingenta.com/content/aip/journal/jcp/129/18/10.1063/1.3005225
10.1063/1.3005225
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