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Model Reduction, Structure-property Relations and Optimization Techniques for the Production of Nanoscale Particles

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Constrained Optimization and Optimal Control for Partial Differential Equations

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 160))

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Abstract

The production of nanoscaled particulate products with exactly pre-defined characteristics is of enormous economic relevance. Although there are different particle formation routes they may all be described by one class of equations. Therefore, simulating such processes comprises the solution of nonlinear, hyperbolic integro-partial differential equations. In our project we aim to study this class of equations in order to develop efficient tools for the identification of optimal process conditions to achieve desired product properties. This objective is approached by a joint effort of the mathematics and the engineering faculty. Two model-processes are chosen for this study, namely a precipitation process and an innovative aerosol process allowing for a precise control of residence time and temperature. Since the overall problem is far too complex to be solved directly a hierarchical sequence of simplified problems has been derived which are solved consecutively. In particular, the simulation results are finally subject to comparison with experiments.

Mathematics Subject Classification (2000). Primary 35R09; Secondary 35Q70.

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Authors and Affiliations

  1. Lehrstuhl für Angewandte Mathematik II, Friedrich-Alexander-Universität Erlangen-Nürnberg, Martensstrasse 3, D-91058, Erlangen, Germany

    Michael Gröschel & Günter Leugering

  2. Lehrstuhl für Feststoff- und Grenzflächenverfahrenstechnik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstraße 4, D-91058, Erlangen, Germany

    Wolfgang Peukert

Authors
  1. Michael Gröschel
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  2. Günter Leugering
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  3. Wolfgang Peukert
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Corresponding author

Correspondence to Michael Gröschel .

Editor information

Editors and Affiliations

  1. , Department Mathematik, Universität Erlangen-Nürnberg, Martensstr. 3, Erlangen, 91058, Germany

    Günter Leugering

  2. , Fakultät Bio- und Chemieingenieurwesen, Technische Universität Dortmund, Geschossbau 2, Dortmund, 44221, Germany

    Sebastian Engell

  3. , Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25, Berlin, 12489, Germany

    Andreas Griewank

  4. , Fachbereich Mathematik, Universität Hamburg, Bundesstr. 55, Hamburg, 20146, Germany

    Michael Hinze

  5. , Institut für Angewandte Mathematik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 293, Heidelberg, 69120, Germany

    Rolf Rannacher

  6. , FB 4 - Department Mathematik, Universität Trier, Trier, 54286, Germany

    Volker Schulz

  7. Fakultät für Mathematik, M1, Lehrstuhl für Mathematische Optimierung, Technische Universität München, Boltzmannstr. 3, Garching bei München, 85748, Germany

    Michael Ulbrich

  8. , Fachbereich Mathematik, Technische Universität Darmstadt, Dolivostrasse 15, Darmstadt, 64293, Germany

    Stefan Ulbrich

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Gröschel, M., Leugering, G., Peukert, W. (2012). Model Reduction, Structure-property Relations and Optimization Techniques for the Production of Nanoscale Particles. In: Leugering, G., et al. Constrained Optimization and Optimal Control for Partial Differential Equations. International Series of Numerical Mathematics, vol 160. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0133-1_28

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