PACE REPORT

For the standard parameter settings the systems enters a stationary situation where spots are maintained by the flow of free energy through the system, as shown in Fig. 1d (--> simulation 1d).

A reduction of the flow rate by a factor of 10 to f=0.5 results in a smaller inflow of free energy, and after an initial period when free energy is abundant the system settles into a situation that can only support a smaller number of concentration peaks closer to the inlet, see Fig. 2a (--> simulation 2a).

The characteristics of the spatio-temporal behaviour critical dependend on the decay rate k₃. A change of the value, either up to 0.71 or down to 0.69 (from 0.70) leads to no angular pattern formation, but appears again if, e.g., u*_in is increased to 210, see Fig. 2b.

(a)               (b)                (c)                 (d)                (e)

Figure 2.  Simulation exmaples illustrating various patterns depending on parameter choices.

A reduction of the decay constant to k₃=0.65 (with other parameters at standard settings) results again in sustained spots patterns, see Fig. 2c (--> simulation 2c). There is a long initial perdiod when there is no angular symmetry break but there is a radial spatio-temporal chaos-like behaviour.

An even lower decay constant, k₃=0.60, in combination with a lower flow, f = 3, results in a more stable pattern of spots, see Fig. 2d (--> simulation 2d).

With an increased free energy inflow by higher concentration of the fuel precursor, u*_in = 230, complex patterns can be supported also with a higher decay constant, k₃=0.73. In this case more unstable dynamics is seen including more complex waves with some spiral-like structures, see Fig. 2e.