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Comptes Rendus Mathématique
Volume 344, n° 8
pages 519-522 (avril 2007)
Doi : 10.1016/j.crma.2007.03.002
Received : 14 February 2007 ;  accepted : 27 February 2007
A dynamic optimization problem related to organic aerosols
Un problème dʼoptimization dynamique lié à la modélisation dʼaérosols organiques

Neal R. Amundson a , Alexandre Caboussat a, 1 , Jiwen He a, 1 , Chantal Landry b , John H. Seinfeld c
a Department of Mathematics, University of Houston, Houston, TX 77204, USA 
b Institute of Analysis and Scientific Computing, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland 
c Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA 


A model that rigorously computes the gas-particle partitioning and liquid-liquid equilibrium for organic atmospheric aerosol particles is presented. The dynamics of the mass transfers between the particle and the gas phase are modeled with differential equations and are coupled with a constrained optimization problem for the thermodynamic equilibrium inside the particle. The nonlinear system composed by the first order optimality conditions coupled with the discretized differential equations is solved with an interior-point method and a Newton method. The resulting linear system is decoupled with sequential quadratic programming techniques. Numerical results and comparisons of time scales show the accuracy and efficiency of our algorithm. To cite this article: N.R. Amundson et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).

The full text of this article is available in PDF format.

Nous proposons un modèle pour le calcul de lʼéquilibre thermodynamique et la séparation de phases entre une particule et la phase gazeuse. La dynamique des transferts de masse entre particule et phase gazeuse est caractérisée par un système dʼéquations différentielles couplées avec un problème dʼoptimisation décrivant lʼéquilibre interne de la particule. Les conditions de premier ordre et une discrétisation implicite des équations différentielles forment un système dʼéquations non linéaires qui est traité avec une méthode de point intérieur couplée à une itération de Newton. Des résultats numériques et une comparaison des temps caractéristiques montrent la précision et lʼefficacité de notre algorithme. Pour citer cet article : N.R. Amundson et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).

The full text of this article is available in PDF format.
1  Supported by the United States Environmental Protection Agency Grant X-83234201.

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