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Particle dynamics simulations of Turing patterns
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10.1063/1.4743983
/content/aip/journal/jcp/137/7/10.1063/1.4743983
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/7/10.1063/1.4743983
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Snapshot of the concentrations A (solid lines) and B (dashed lines) obtained from DSMC (orange) and the numerical integration of Eqs. (4) and (5) (black). System length is 2L 0 and there are 50 cells per L 0. The horizontal axis gives the scaled space coordinate x/L 0 and vertical axis, species concentrations.

Image of FIG. 2.
FIG. 2.

Time evolution of a stable 1.5-wavelength structure. System length is 2L 0. There are 50 cells per L 0. The horizontal axis gives scaled space coordinate x/L 0, vertical axis, scaled time t/τ and color gradation, the concentration of A species.

Image of FIG. 3.
FIG. 3.

As in Figure 2, but with the emergence of a 2-wavelength structure.

Image of FIG. 4.
FIG. 4.

As in Figure 2, but with a temporal transition from a 2-wavelength structure to a 1.5-wavelength structure.

Image of FIG. 5.
FIG. 5.

Concentration of species A versus time in two example cells located at x = 0.7L 0 (solid lines) and x = 1.2L 0 (dashed lines) in the case of the history presented in Figure 2. The orange lines are results of DSMC, the black lines represent the function A + + c 1(exp (λ(q 0)t) − 1), where c 1 is used as a fitting parameter.

Image of FIG. 6.
FIG. 6.

As in Figure 2, but for a large system of 40L 0 length. There are 20 cells per L 0.

Image of FIG. 7.
FIG. 7.

As in Figure 2, but for step function initial conditions with a Turing pattern emerging behind a moving wave front. System of 20L 0 length and with 20 cells per L 0.

Image of FIG. 8.
FIG. 8.

As in Figure 7, but for a system of 20L 0 length, with 30 cells per L 0 and for the following set of parameters close to the bifurcation: k 1/k 2 = 2.92 × 104, k 3/k 2 = 0.73 × 104, k −3/k 2 = 7.3 × 106, k 2 = 7.17 × 10−7, σ R = 0.0238, σ A = 2.2σ R , R = 30A +.

Image of FIG. 9.
FIG. 9.

Instantaneous concentration A versus scaled space x/L 0 for an inhomogeneous initial condition and for the same set of parameters as in Figure 8, close to the bifurcation. The black line gives the result of the numerical integration of Eqs. (4) and (5) and the orange line, the result of DSMC.

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/content/aip/journal/jcp/137/7/10.1063/1.4743983
2012-08-16
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Particle dynamics simulations of Turing patterns
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/7/10.1063/1.4743983
10.1063/1.4743983
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