Typical bifurcation diagram of the isothermal two-variable lumped model [Eq. (2)] showing the temperature dependence of the steady state (a), (b), and of the rate (c) with various sets of pressure and the subsurface oxygen concentration : (300 Pa, 0.3), line 1: (400 Pa, 0.3), 2; (400 Pa, 0.4), 3; and (400 Pa, 0.5) 4. Plate (d) shows the steady-state rate as a function of CO concentration with fixed and .
Domain of multiple steady-state solutions of system (2). .
Effect of the gas temperature on the relation between the steady-state heat generation term (, dashed-dotted lines) and the heat removal term [, dashed lines] showing an extinguished front [(a) ], different stationary fronts [(b) 478 K (line 1) and 489 K (2)], and an ignited front [(c) 497 K]. Solid lines denote the reaction rate obtained in simulations with nonisothermal model [Eqs. (2), (3a), and (3b)]. Dotted line in (b) denotes the average rate for a SF solution. Shaded regions illustrate the Maxwell condition. , , and .
Effect of the gas temperature on the spatial temperature profile (a), maximal and minimal temperatures of the front (b) and the front velocity (c) simulated on a wire. In plate (a) , (1), 478 K (2), 489 K (3), and 497 K (4); arrows show the direction of the front propagation. In plates (b) and (c) (solid lines), 400 Pa (dashed lines); dash-dotted line in (c) denotes simulations with a finite diffusivity of species (, ). Other parameters as in Fig. 3.
The domain of SF solution with respect to during CO oxidation showing a bifurcation map (a) and a diagram of the reaction rate [(b) , , and ]. Solid and dashed lines in (b) denote the stable and unstable homogeneous steady states, respectively, while the thick solid line denotes the SF solutions in the form of the average reaction rate simulated on a wire of . (c) Multiplicity patterns observed during oxidation in oxygen on a Pt wire at an ambient room temperature , showing five branches, of which the three intermediate were interpreted to be inhomogeneous solutions, after Ref. 25.
Stationary patterns on a disk. Row (a) shows two different target patterns simulated with symmetric IC and different initial front positions : 0.2 (1) and 0.8 (2), and an asymmetric pattern (3) simulated with IC shown in plate (4). Plates (b) and (c) show the many target patterns obtained with symmetric IC and different : 0.2 (1) 0.4 (2), 0.6 (3), and 0.8 (4). , , , and .
Global control effects: Stationary fronts on a wire (a) and a ring (b) in the bistable kinetic model [Eqs. (2) and (3)] subject to global control that keeps the average temperature (). Plate (a) shows the many fronts obtained with and different initial front positions ( (1), 0.75 (2), 0.875 (3), and 0.94 (4)); plate (b) demonstrates the effect of the set point on a ring ( (1), 500 K (2), 510 K (3), 520 K (4), 530 K (5), and 540 K (6)). ; , and .
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