A Study of the Sensitivity of Coupled Reaction Systems to Uncertainties in Rate Coefficients. I. Theory

Abstract

A method has been developed to investigate the sensitivity of the solutions of large sets of coupled, non-linear rate equations to uncertainties in the rate coefficients. This method is based on varying all the rate coefficients simultaneously through the introduction of a parameter in such a way that the output concentrations become periodic functions of this parameter at any given time t. The concentration of the chemical species are then Fourier analysed at time t. The authors show via an application of Weyl's ergodic theorem that a subset of the Fourier coefficients is related to the rate of change of the concentration of species i with respect to the l rate constant for reaction l averaged over the uncertainties of all the other rate coefficients. The Fourier method developed is not limited to chemical rate equation, but can be applied to the study of the sensitivity of any large system of coupled, non- linear differential equations with respect to the uncertainties in the modeling parameters.

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Document Details

Document Type
Technical Report
Publication Date
Jan 18, 1973
Accession Number
AD0762420

Entities

People

  • A. G. Petschek
  • C. M. Fortuin
  • J. H. Schaibly
  • K. E. Shuler
  • R. I. Cukier

Organizations

  • University of California, San Diego

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Chemical Kinetics
  • Chemical Reaction Properties
  • Chemical Reactions
  • Chemistry
  • Complex Systems
  • Computers
  • Contracts
  • Differential Equations
  • Equations
  • Errors
  • Fourier Analysis
  • Frequency
  • Integrals
  • Linear Differential Equations
  • Periodic Functions
  • Physics

Readers

  • Analytical Chemistry
  • Calculus or Mathematical Analysis
  • Control Systems Engineering.