Piecewise analytical integration of chemical rate equations. II. Error analysis, implementation, and applications

1982 ◽  
Vol 77 (6) ◽  
pp. 2912-2927 ◽  
Author(s):  
Sergio Bienstock ◽  
Roy G. Gordon
Keyword(s):  
Error Analysis ◽  
Rate Equations ◽  
Analytical Integration ◽  
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.

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

SIMULATION ◽  
1968 ◽  
Vol 10 (2) ◽  
pp. 70-72
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 hybrid system due to the fast solution of the differential equations on the analog and the automated search pro cedure on the digital.

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