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A model for jumping and bubble waves in the Belousov–Zhabotinsky-aerosol OT system
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10.1063/1.3231488
/content/aip/journal/jcp/131/10/10.1063/1.3231488
http://aip.metastore.ingenta.com/content/aip/journal/jcp/131/10/10.1063/1.3231488
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Comparison of the Oregonator model (curve 1) and model (29′)–(32′) (curves 2–4). Parameters: , , , and , , (4) 0.879, , (3) 0.0857, , (3) 0.0404.

Image of FIG. 2.
FIG. 2.

Phase diagram in the plane for models (29)–(32). All curves correspond to the onset of Hopf instability. Parameters: , (2, 6) 0.2, (4 and 5) 0.4, , (2, 3) 0.2, (4) 0.06, (5, 6) 0.1. “Osc” denotes the oscillatory region. Curves 1–3 are well fitted by lines , where , (2) 3, (3) 1.92, while curves 4 and 5 are well fitted by lines , where and , (5) 0.064, and (6) 0.0207. For curves 1–3, the SS (reduced) is above and to the left of the curves, while for curves 4–6, the SS (oxidized) is below and to the right.

Image of FIG. 3.
FIG. 3.

Dispersion curves for model (B). (a) Turing instability. (b) Wave instability. Curves 1 and 2 are, respectively, and , where is the eigenvalue of the linearized model (B) with the largest real part. Parameters: (a) , , , , , , , , , , , is calculated from Eq. (28) at and , , . (b) , , , , , , , , , , , , , .

Image of FIG. 4.
FIG. 4.

(a) Space-time plot for JWs found in model (B) in 1D with zero-flux boundary conditions and a small perturbation of the SS at the left end. Total length is 280 a.u. for dimensionless diffusion coefficients , or 5.6 mm for dimensional coefficients and . Total time . White short segments correspond to high concentration of the oxidized catalyst . Dotted line is drawn through the first wave. (b) Four concentration profiles of the catalyst and inhibitor . Space is in a.u.; concentrations are in milimolar. Parameters of model (B) are the same as in Fig. 3(a).

Image of FIG. 5.
FIG. 5.

Space-time plot for JWs in model (B) for 1D with zero-flux boundary conditions, small perturbation of the SS at the left end, and bulk oscillations (Hopf bifurcation). Parameters as in Fig. 4 except . .

Image of FIG. 6.
FIG. 6.

(a) Turing pattern found in model (B) in 1D with zero-flux boundary conditions and small local perturbation of the SS at the center. Total Concentrations of and are in M. Parameters are the same as in Fig. 3(a) except . (b) Space-time plot of a simple (continuous) traveling pulse in model (B) in 1D with zero-flux boundary conditions and small local perturbation of the SS at the left end of the segment. Parameters: , , , , , , , , other parameters as in Fig. 3(a).

Image of FIG. 7.
FIG. 7.

Snapshots of JWs found in model (B) in 2D with a small perturbation at the center of a circle of radius 80; zero-flux boundary conditions, -variable. Darker color indicates higher concentration of . All parameters are the same as in Fig. 3(a).

Image of FIG. 8.
FIG. 8.

Snapshots of bubble waves in model (B) in 2D with a small perturbation in the center of a circle of radius 30; zero-flux boundary condition, -variable. Darker color indicates higher concentration of . Parameters: , , , , , , , , all other parameters as in Fig. 3(a).

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/content/aip/journal/jcp/131/10/10.1063/1.3231488
2009-09-14
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A model for jumping and bubble waves in the Belousov–Zhabotinsky-aerosol OT system
http://aip.metastore.ingenta.com/content/aip/journal/jcp/131/10/10.1063/1.3231488
10.1063/1.3231488
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