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Distinguishing similar patterns with different underlying instabilities: Effect of advection on systems with Hopf, Turing-Hopf, and wave instabilities
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10.1063/1.4766591
/content/aip/journal/chaos/22/4/10.1063/1.4766591
http://aip.metastore.ingenta.com/content/aip/journal/chaos/22/4/10.1063/1.4766591
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Space-time plots with size 80 space units (horizontal) × 200 time units (downwards). All systems are started from random initial conditions, and no-flux boundary conditions are used. The diffusion coefficients are Dx  = Dy  = Dz  = 0.1 (a); Dx  = 0.1 and Dy  = Dz  = 2 (b); and Dx  = Dz  = 0.1 and Dy  = 2 (c). For other parameters see text. Light (dark) color represents high (low) concentration of the activator x.

Image of FIG. 2.
FIG. 2.

Effect of advective flow for a system with Dx  = Dy  = Dz  = 0.1. Space-time plots with size 80 space units (horizontal) and 400 time units (downwards). For the initial 100 time units, the velocity v is 0 and then is turned to 0.2 (a), 0.5 (b), and 1.5 (c). The square in (a), with 80 space units × 20 time units is expanded at the right. Light (dark) color represents high (low) concentration of the activator x. (d) Phase diagram for patterns at different velocities of the advective flow.

Image of FIG. 3.
FIG. 3.

Effect of advective flow for a system with Dx  = 0.1 and Dy  = Dz  = 2. Space-time plots with size 80 space units (horizontal) and 400 time units (downwards). For the initial 100 time units, the velocity v is 0 and then is turned to 1.5 (a) and 3.0 (b). The square in (b), with 80 space units × 20 time units is expanded at the right. Light (dark) color represents high (low) concentration of the activator x. (c) Phase diagram for patterns at different velocities of the advective flow.

Image of FIG. 4.
FIG. 4.

Effect of advective flow for a system with Dx  = Dz  = 0.1 and Dy  = 2. Space-time plots with size 80 space units (horizontal) and 400 time units (downwards). For the initial 100 time units, the velocity v is 0 and then is turned to 0.3 (a), 0.7 (b), 1.5 (c), and 2.5 (d). Light (dark) color represents high (low) concentration of the activator x. (e) Phase diagram for patterns at different velocities of the advective flow.

Image of FIG. 5.
FIG. 5.

Effect of advective flow for a system with Dx  = 0.1 and Dy  = Dz  = 2 and f y = f z = 1. Space-time plots with size 80 space units (horizontal) and 300 time units (downwards). For the initial 100 time units, the velocity v is 0 and then is turned to 0.1 (a) and 2.5 (b). The square in (b), with 30 space units × 20 time units is expanded at the right. Light (dark) color represents high (low) concentration of the activator x. (c) Phase diagram for patterns at different velocities of the advective flow.

Image of FIG. 6.
FIG. 6.

Effect of advective flow on a system with Dx  = Dy  = 0.1 and Dz  = 2. Space-time plots with size 80 space units (horizontal) and 300 time units (downwards). For the initial 100 time units, the velocity v is 0 and then is turned to 0.2 (a), 0.4 (b), and 1.0 (c). Light (dark) color represents high (low) concentration of the activator x. (d) Phase diagram for patterns at different velocities of the advective flow.

Image of FIG. 7.
FIG. 7.

Detail of space-time plots with size 100 space units (horizontal) and 40 time units (downwards) when changing v from 0 to 1.0 ((a) and (c)) or to 3.0 ((b) and (d)) on systems with Du  = 0.1, Dw  = 2, and ξ = 0 ((a) and (b)) and for Du  = Dw  = 0.1 and ξ = −10 ((c) and (d)). Phase diagram for the effect of advective flow on systems with Du  = 0.1, Dw  = 2, and ξ = 0 (e) and for Du  = Dw  = 0.1 and ξ = −10 (f).

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/content/aip/journal/chaos/22/4/10.1063/1.4766591
2012-11-13
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Distinguishing similar patterns with different underlying instabilities: Effect of advection on systems with Hopf, Turing-Hopf, and wave instabilities
http://aip.metastore.ingenta.com/content/aip/journal/chaos/22/4/10.1063/1.4766591
10.1063/1.4766591
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