Journal of Chemical Physics
Feedback | Help | Exit
The Journal of Chemical Physics
Search:
   
 
 
 
Previous Article
Implementation of quantum gate operations in molecules with weak laser fields
We numerically propose a way to perform quantum computations by combining an ensemble of molecular states and weak laser pulses. A logical input state is expressed as a superposition state (a wave pac...
Next Article
Electrostatic field-adapted molecular fractionation with conjugated caps for energy calculations of charged biomolecules
An electrostatic field-adapted molecular fractionation with conjugated caps (EFA-MFCC) approach is implemented for treating macromolecules with several charge centers. The molecular fragmentation is p...

The invariant constrained equilibrium edge preimage curve method for the dimension reduction of chemical kinetics

J. Chem. Phys. 124, 114111 (2006); doi:10.1063/1.2177243

Published 20 March 2006

You are not logged in to this journal. Log in

Zhuyin Ren and Stephen B. Pope
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853

Alexander Vladimirsky and John M. Guckenheimer
Department of Mathematics, Cornell University, Ithaca, New York 14853
This work addresses the construction and use of low-dimensional invariant manifolds to simplify complex chemical kinetics. Typically, chemical kinetic systems have a wide range of time scales. As a consequence, reaction trajectories rapidly approach a hierarchy of attracting manifolds of decreasing dimension in the full composition space. In previous research, several different methods have been proposed to identify these low-dimensional attracting manifolds. Here we propose a new method based on an invariant constrained equilibrium edge (ICE) manifold. This manifold (of dimension nr) is generated by the reaction trajectories emanating from its (nr–1)-dimensional edge, on which the composition is in a constrained equilibrium state. A reasonable choice of the nr represented variables (e.g., nr "major" species) ensures that there exists a unique point on the ICE manifold corresponding to each realizable value of the represented variables. The process of identifying this point is referred to as species reconstruction. A second contribution of this work is a local method of species reconstruction, called ICE-PIC, which is based on the ICE manifold and uses preimage curves (PICs). The ICE-PIC method is local in the sense that species reconstruction can be performed without generating the whole of the manifold (or a significant portion thereof). The ICE-PIC method is the first approach that locally determines points on a low-dimensional invariant manifold, and its application to high-dimensional chemical systems is straightforward. The "inputs" to the method are the detailed kinetic mechanism and the chosen reduced representation (e.g., some major species). The ICE-PIC method is illustrated and demonstrated using an idealized H2/O system with six chemical species. It is then tested and compared to three other dimension-reduction methods for the test case of a one-dimensional premixed laminar flame of stoichiometric hydrogen/air, which is described by a detailed mechanism containing nine species and 21 reactions. It is shown that the error incurred by the ICE-PIC method with four represented species is small across the whole flame, even in the low temperature region. ©2006 American Institute of Physics
History: Received 14 October 2005; accepted 24 January 2006; published 20 March 2006
Permalink: http://link.aip.org/link/?JCPSA6/124/114111/1
BUY THIS ARTICLE   (US$24)
Download HTML Download Sectioned HTML Download PDF (470 kB) View Cart

KEYWORDS and PACS

Keywords
PACS
  • 82.20.Fd
    Collision theories and trajectory models of chemical kinetics
  • 82.40.-g
    Chemical kinetics and reactions: special regimes and techniques
  • 82.30.Cf
    Atom and radical chemical reactions; chain reactions, molecule-molecule reactions
  • YEAR: 2006

RELATED DATABASES


To view database links for this article,
you need to log in.
To view database links for this article,
you need to log in.

PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (42)
View in Separate Window/Tab
For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. R. Cao and S. B. Pope, Combust. Flame 143, 450 (2005).
  2. H. J. Curran, P. Gaffuri, W. J. Pitz, and C. K. Westbrook, Combust. Flame 129, 253 (2002).
  3. T. Lu and C. K. Law, Proc. Combust. Inst. 30, 1333 (2005).
  4. P. Pepiot and H. Pitsch, Fourth Joint Meeting of the U.S. Sections of the Combustion Institute, Philadelphia, PA, 21–23 March 2005 (unpublished).
  5. J. F. Griffiths, Prog. Energy Combust. Sci. 21, 25 (1995).
  6. A. S. Tomlin, T. Turányi, and M. J. Pilling, in Low-Temperature Combustion and Autoignition, Comprehensive Chemical Kinetics, Vol. 35 (Elsevier, Amsterdam, 1997).
  7. M. S. Okino and M. L. Mavrovouniotis, Chem. Rev. (Washington, D.C.) 98, 391 (1998).
  8. S. B. Pope, Combust. Theory Modell. 1, 41 (1997).
  9. M. Bodenstein and S. C. Lind, Z. Phys. Chem., Stoechiom. Verwandtschaftsl. 57, 168 (1906).
  10. Reduced Kinetic Mechanisms and Asymptotic Approximations for Methane-Air Flames, Lecture Notes in Physics, Vol. 384, edited by M. D. Smooke (Springer, Berlin, 1991).
  11. A. Zagaris, H. G. Kaper, and T. J. Kaper, J. Nonlinear Sci. 14, 59 (2004).
  12. A. Zagaris, H. G. Kaper, and T. J. Kaper, Multiscale Model. Simul. 2, 613 (2004).
  13. S. H. Lam and D. A. Goussis, Int. J. Chem. Kinet. 26, 461 (1994).
  14. Z. Ren and S. B. Pope, Combust. Theory Modell. (to be published).
  15. J. Y. Chen, Combust. Sci. Technol. 57, 89 (1988).
  16. Z. Ren and S. B. Pope, Combust. Flame 137, 251 (2004).
  17. J. C. Keck and D. Gillespie, Combust. Flame 17, 237 (1971).
  18. J. C. Keck, Prog. Energy Combust. Sci. 16, 125 (1990).
  19. Q. Tang and S. B. Pope, Proc. Combust. Inst. 29, 1411 (2002).
  20. U. A. Maas and S. B. Pope, Combust. Flame 88, 239 (1992).
  21. S. B. Pope and U. Maas, Cornell University, Report No. FDA 93-11, 1993 (unpublished).
  22. J. A. van Oijen and L. P. H. de Goey, Combust. Sci. Technol. 161, 113 (2000).
  23. M. R. Roussel and S. J. Fraser, J. Phys. Chem. 97, 8316 (1993).
  24. A. N. Gorban and I. V. Karlin, Chem. Eng. Sci. 58, 4751 (2003).
  25. Z. Ren and S. B. Pope, Proc. Combust. Inst. 30, 1293 (2005).
  26. M. J. Davis and R. T. Skodje, J. Chem. Phys. 111, 859 (1999).
  27. R. T. Skodje and M. J. Davis, J. Phys. Chem. A 105, 10356 (2001).
  28. S. Singh, J. M. Powers, and S. Paolucci, J. Chem. Phys. 117, 1482 (2002).
  29. J. Li, Z. Zhao, A. Kazakov, and F. L. Dryer, Fall Technical Meeting of the Eastern States Section of the Combustion Institute, Pennsylvania State University, University Park, PA, 26–29 October 2003 (unpublished).
  30. S. B. Pope, Cornell University Report No. FDA 03-02, 2003 (unpublished).
  31. S. B. Pope, Combust. Flame 139, 222 (2004).
  32. M. Caracotsios and W. E. Stewart, Comput. Chem. Eng. 9, 359 (1985).
  33. ADIFOR 2.0, Automatic Differentiation of Fortran, http://www-unix.mcs.anl.gov/autodiff/ADIFOR/
  34. W. C. Reynolds, "The Element Potential Method for Chemical Equilibrium Analysis: Implementation in the Interactive Program STANJAN," Technical Report, Mechanical Engineering Department, Stanford University, 1986 (unpublished).
  35. S. Gordon and B. J. McBride, NASA Reference Publication Report No. 1311, 1994 (unpublished).
  36. P. S. Bishnu, D. Hamiroune, M. Metghalchi, and J. C. Keck, Combust. Theory Modell. 1, 295 (1997).
  37. C. J. Sung, C. K. Law, and J. Y. Chen, Combust. Flame 125, 906 (2001).
  38. S. B. Pope, Flow, Turbul. Combust. 72, 219 (2004).
  39. T. Lu, Y. Ju, and C. K. Law, Combust. Flame 126, 1445 (2001).
  40. S. H. Lam, Combust. Sci. Technol. 89, 375 (1993).
  41. A. S. Tomlin, L. Whitehouse, R. Lowe, and M. J. Pilling, Faraday Discuss. 120, 125 (2002).
  42. J. Zobeley, D. Lebiedz, J. Kammerer, A. Ishmurzin, and U. Kummer, in "Transactions on Computational Systems Biology 1", Lecture Notes in Computer Science 3380 (Springer 2005).

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.


Copyright © American Institute of Physics