By Marshall Slemrod (auth.), Alexander N. Gorban, Dirk Roose (eds.)
This quantity includes the prolonged model of chosen talks given on the foreign examine workshop "Coping with Complexity: version aid and information Analysis", Ambleside, united kingdom, August 31 – September four, 2009. The booklet is intentionally wide in scope and goals at selling new principles and methodological views. the themes of the chapters variety from theoretical research of advanced and multiscale mathematical types to functions in e.g., fluid dynamics and chemical kinetics.
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Extra resources for Coping with Complexity: Model Reduction and Data Analysis
In general however, we would be interested in peak NO2 levels rather than lower concentrations so the model may still be suitable for such 0 purposes. For both NNO2 and NO , the main parameter driving the variance was the 2 0 fraction of NO in the emission source (64% for NNO2 , 50% for NO ). The structure 2 function coefficient had a fairly low influence on the output variance (9% for NNO2 , 0 ) and ˛ had a low influence on NNO2 (10%) but quite a strong influ1:5% for NO 2 0 ence on NO2 (30%). The only chemical parameter with any significance was again the activation energy for the reaction NO C O3 .
In this paper standard linear matrix inequalities (LMI) are used to set up the problem and model reduction is achieved using standard LMI solvers. Moreover, H1 model reduction has been studied for a number of systems in the context of controller design, where the resulting reduced model has an a priori prescribed error bound (see  and references within). In  switched stochastic systems are reduced using average dwell time and Liapunov functions to ensure the stability of the error and an optimisation problem is solved to perform the actual projection in order to obtain the reduced system.
In order to address these questions the model case presented combines a Reynolds Averaged representation of atmospheric turbulence with a Lagrangian stochastic particle dispersion model with micro-mixing and chemical sub-models . The complex modelling system was used to investigate a reactive plume of nitrogen oxides (NOx ) released into an approximately homogeneous turbulent grid flow doped with ozone (O3 ) for comparison against the wind tunnel experiments of . The case was also extended to include possible photolysis reactions which were not present in the original wind tunnel experiments.