no. 9
Numerical Analysis
An optimization problem related to the modeling of atmospheric inorganic aerosols
[Un problème d'optimisation lié à la modélisation d'aérosols inorganiques]

Présenté par : Roland Glowinski

Amundson, Neal R.1 ; Caboussat, Alexandre1 ; He, Jiwen1 ; Seinfeld, John H.2 ; Yoo, Kee-Youn3
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, Tome 340 (2005) no. 9, pp. 683-686.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.01.025
Amundson, Neal R. 1 ; Caboussat, Alexandre 1 ; He, Jiwen 1 ; Seinfeld, John H. 2 ; Yoo, Kee-Youn 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 
@article{CRMATH_2005__340_9_683_0,
     author = {Amundson, Neal R. and Caboussat, Alexandre and He, Jiwen and Seinfeld, John H. and Yoo, Kee-Youn},
     title = {An optimization problem related to the modeling of atmospheric inorganic aerosols},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {683--686},
     publisher = {Elsevier},
     volume = {340},
     number = {9},
     year = {2005},
     doi = {10.1016/j.crma.2005.01.025},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.01.025/}
}
TY  - JOUR
AU  - Amundson, Neal R.
AU  - Caboussat, Alexandre
AU  - He, Jiwen
AU  - Seinfeld, John H.
AU  - Yoo, Kee-Youn
TI  - An optimization problem related to the modeling of atmospheric inorganic aerosols
JO  - Comptes Rendus. Mathématique
PY  - 2005
SP  - 683
EP  - 686
VL  - 340
IS  - 9
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.crma.2005.01.025/
DO  - 10.1016/j.crma.2005.01.025
LA  - en
ID  - CRMATH_2005__340_9_683_0
ER  - 
%0 Journal Article
%A Amundson, Neal R.
%A Caboussat, Alexandre
%A He, Jiwen
%A Seinfeld, John H.
%A Yoo, Kee-Youn
%T An optimization problem related to the modeling of atmospheric inorganic aerosols
%J Comptes Rendus. Mathématique
%D 2005
%P 683-686
%V 340
%N 9
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.crma.2005.01.025/
%R 10.1016/j.crma.2005.01.025
%G en
%F CRMATH_2005__340_9_683_0
Amundson, Neal R.; Caboussat, Alexandre; He, Jiwen; Seinfeld, John H.; Yoo, Kee-Youn. An optimization problem related to the modeling of atmospheric inorganic aerosols. Comptes Rendus. Mathématique, Tome 340 (2005) no. 9, pp. 683-686. doi : 10.1016/j.crma.2005.01.025. http://archive.numdam.org/articles/10.1016/j.crma.2005.01.025/

[1] Ansari, A.S.; Pandis, S.N. Prediction of multicomponent inorganic atmospheric aerosol behavior, Atmospheric Environment, Volume 33 (1999) no. 5, pp. 745-757

[2] Gill, P.E.; Murray, W.; Saunders, M.A.; Wright, M.H. Inertia-controlling methods for general quadratic programming, SIAM Rev., Volume 33 (1991) no. 1, pp. 1-36

[3] Gould, N.I.M. On practical conditions for the existence and uniqueness of solutions to the general equality quadratic programming problem, Math. Programming, Volume 32 (1985), pp. 90-99

[4] Kunisch, K.; Rendl, F. An infeasible active set method for quadratic problems with simple bounds, SIAM J. Optim., Volume 14 (2003) no. 1, pp. 35-52

[5] Nenes, A.; Pandis, S.N.; Pilinis, C. Continued development and testing of a new thermodynamic aerosol module for urban and regional air quality models, Atmospheric Environment, Volume 33 (1999) no. 10, pp. 1553-1560

[6] Yoo, K.-Y.; He, J.-W.; Amundson, N.R. Canonical form and mathematical interpretation of electrolyte solution systems, Korean J. Chem. Eng., Volume 21 (2004) no. 2, pp. 303-307

Cité par Sources :