Numerical Integration of the Chemical Rate Equations via a Discretized Adomian Decomposition

2011 ◽  
Vol 50 (6) ◽  
pp. 3100-3109 ◽  
Author(s):  
Jarod M. Younker
Keyword(s):  
Numerical Integration ◽  
Rate Equations ◽  
Adomian Decomposition ◽  
Chemical Rate

An example program for the determination of chemical rate coefficients from experimental data

SIMULATION ◽  
1967 ◽  
Vol 8 (3) ◽  
pp. 133-137 ◽  
Author(s):  
Richard A. Nesbit ◽  
Robert D. Engel
Keyword(s):  
Experimental Data ◽  
Rate Coefficients ◽  
Rate Equations ◽  
Search Procedure ◽  
Squared Error ◽  
Fast Solution ◽  
Data Points ◽  
Chemical Rate ◽  
Param Eters

A program for matching experimental data to the com puted concentrations of various components of a dynamic chemical process is implemented. The digital subsection of the computer is programmed to execute a steepest descent search procedure. The analog section is programmed to solve the chemical rate equations which simulate the re action dynamics. These equations form a two-point bound ary value problem. The search procedure changes param eters in the rate equations, and it compares the computed concentrations to the experimental ones. The squared error is summed over all data points, and this sum is minimized by the search. Significant speedup of the solution to this type of problem is possible with the hy brid system due to the fast solution of the differential equations on the analog and the automated search pro cedure on the digital.

Investigation of Midgap Defects in GaAs Induced By Heat-Treatment (EL2), Electron-Irradiation, and Plastic Deformation

1987 ◽  
Vol 104 ◽  
Author(s):  
Toru Haga ◽  
Masashi Suezawa ◽  
Koji Sumino
Keyword(s):  
Heat Treatment ◽  
Plastic Deformation ◽  
Low Temperature ◽  
Electron Irradiation ◽  
Grown Crystal ◽  
Isothermal Annealing ◽  
Rate Equations ◽  
Kinetics Of ◽  
Absorption Measurements ◽  
Chemical Rate

ABSTRACTThermal behavior of midgap defects generated in GaAs by different procedures has been followed by means of optical absorption measurements at low temperature. EL2 centers existing in as-grown crystals or generated by thermal annealing at temperatures lower than about 1000°C, which are characterized by a perfectly quenchable absorption at a wavelength of 1.0 μm, are found to diminish at temperature higher than 1000°C. The generation kinetics of EL2 centers has been traced during isothermal annealing of a crystal in which grown-in EL2 centers have previously been eliminated by annealing at 1200°C. The result of an analysis with the use of simplified chemical rate equations favors the model that an EL2 center is composed of an As antisite and two Ga vacancies. Both quenchable and unquenchable absorptions are associated with the midgap defects induced by plastic deformation or electron -irradiation. Isochronal annealing reveals that such defects are not identical with EL2 centers that are found in an as-grown crystal even if they accompany the quenchable absorption.

scholarly journals Combining simulation to nonlinear fitting for the determination of rate constants of elementary reactions by using Excel spreadsheets

2012 ◽  
Vol 8 (4) ◽  
Author(s):  
Ammar M. Tighezza ◽  
Daifallah M. Aldhayan ◽  
Nouir A. Aldawsari
Keyword(s):  
Experimental Data ◽  
Numerical Integration ◽  
Chemical Kinetics ◽  
Chemical Reactions ◽  
Rate Constants ◽  
Model Equation ◽  
Rate Equations ◽  
Unknown Parameters ◽  
Elementary Reactions ◽  
Nonlinear Fitting

A common problem in chemistry is to determine parameters (constants) in an equation used to represent experimental data. Examples are fitting a set of data to a model equation (straight line or curve) to obtain unknown parameters. In chemical kinetics, a set of data is usually a number of concentrations versus time, but the model equation is not well defined! Instead of a well defined model equation we have a set of coupled ODE’s (ordinary differential equations) which represent rate equations for reactants and products. The analytical integration of these ODE’s is rarely possible. The numerical integration is the alternative. In this work are combined the simulation of chemical reactions, by using numerical integration, and nonlinear regression (curve fitting) by using “Solver add-in” of Microsoft Excel to find rate constants of elementary reactions from experimental data. This method is illustrated on three complex mechanisms. The simulation of chemical reactions in Excel spreadsheets is illustrated with/without VBA programming. The automation (automatic obtaining of rate equations from mechanism: no need of chemical kinetics knowledge from the end user!) of mechanism simulation is demonstrated on many example.

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