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We apply binary classification theory to assess the (in)stability prediction accuracy of thermoacoustic models. It is shown that by applying such methods to compare a large set of stability predictions and experiments it is possible to gain valuable qualitative insight in different aspects of prediction quality. The approach is illustrated with a 2-port model and a large experimental data set. The presented framework provides an unified and practical tool to answer questions such as (i) What is the chance that a stable prediction will be correct? and (ii) How conservative is the model? It is shown that the most suitable quality indicator is strongly dependent on the actual purpose of the model. The method provides a solid starting point for model comparison and optimization.
We study mixing of isothermal fluids by controlling the global hydrodynamic entropy ͗s͘. In particular, based on the statistical coupling between the evolution of ͗s͘ and the global viscous dissipation ͗⑀͘, we analyze stirring protocols such that ͗s͘ϳt ␣ ⇔ ͗⑀͘ϳt ␣−1 , with 0 Ͻ ␣ Յ 1. For a model array of vortices ͓Fukuta and Murakami, Phys. Rev. E 57, 449 ͑1998͔͒, we show that: ͑i͒ feedback control can be achieved via input-output linearization, ͑ii͒ mixing is monotonically enhanced for increasing entropy production, and ͑iii͒ the mixing time t m scales as t m ϳ͗⑀͘ −1/2 .
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