An optimization problem related to the modeling of atmospheric inorganic aerosols

Neal R. Amundson; Alexandre Caboussat; Jiwen He; John H. Seinfeld; Kee-Youn Yoo

doi:10.1016/j.crma.2005.01.025

Numerical Analysis

An optimization problem related to the modeling of atmospheric inorganic aerosols

Presented by: Roland Glowinski

Neal R. Amundson ¹; Alexandre Caboussat ¹; Jiwen He ¹; John H. Seinfeld ²; Kee-Youn Yoo ³

¹ Department of Mathematics, University of Houston, Houston, TX 77204, USA
² Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
³ Department of Chemical Engineering, Seoul National University of Technology, Seoul 139-743, South Korea

Comptes Rendus. Mathématique, Volume 340 (2005) no. 9, pp. 683-686.

Abstract
Résumé

A mathematical model for the computation of chemical equilibrium of atmospheric inorganic aerosols is proposed. The equilibrium is given by the minimum of the Gibbs free energy for a system involving an aqueous phase, a gas phase and solid salts. A primal-dual method solving the Karush–Kuhn–Tucker conditions is detailed. An active set/Newton method permits the computation of the minimum and track solid salts at the equilibrium.

Nous proposons un modèle pour l'étude de l'équilibre chimique d'un aérosol inorganique dilué dans l'air. L'état d'équilibre est caracterisé par le minimum d'énergie de Gibbs pour un système chimique faisant intervenir une phase liquide, une phase gazeuse et plusieurs phases solides. Nous présentons une méthode pour la résolution des conditions de Karush–Kuhn–Tucker. Nous utilisons un algorithme de type active set, couplé avec une méthode de Newton pour déterminer le minimum d'énergie ainsi que les phases solides apparaissant à l'équilibre.

Received: 2004-12-31
Accepted: 2005-01-25
Published online: 2005-05-01

DOI: 10.1016/j.crma.2005.01.025

Author's affiliations:

Neal R. Amundson ¹; Alexandre Caboussat ¹; Jiwen He ¹; John H. Seinfeld ²; Kee-Youn Yoo ³

¹ Department of Mathematics, University of Houston, Houston, TX 77204, USA
² Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
³ Department of Chemical Engineering, Seoul National University of Technology, Seoul 139-743, South Korea

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     author = {Neal R. Amundson and Alexandre Caboussat and Jiwen He and John H. Seinfeld and Kee-Youn Yoo},
     title = {An optimization problem related to the modeling of atmospheric inorganic aerosols},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {683--686},
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Neal R. Amundson; Alexandre Caboussat; Jiwen He; John H. Seinfeld; Kee-Youn Yoo. An optimization problem related to the modeling of atmospheric inorganic aerosols. Comptes Rendus. Mathématique, Volume 340 (2005) no. 9, pp. 683-686. doi : 10.1016/j.crma.2005.01.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.01.025/

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