Nonlinear least squares methods: A direct grid search approach

Becsey, J. C.; Berke, L.; Callan, James R.

doi:10.1021/ed045p728

Cited by 38 publications

(13 citation statements)

References 2 publications

(2 reference statements)

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“…(13) to yield an expression [X-] = f(r, z) is meaningless. Therefore, it is further assumed that (19) io e., that the difference between the electron number density at r= 0 and z = L with [X 2 ] = 0 (that is, [e-]o) and the electron number density at r= 0 and z = L with [X 2 ] '" 0 (that is, [eO]) is due to the formation of negative ions which undergo negligible radial diffusion in their transit through the reaction tube. Substitution of Eq.…”

Section: Vo(1-r2/ a 2 ) A[x -]!Az = (Djr)a(ra[x -]!Ar)/ar+ K[e-][x 2 ]mentioning

confidence: 99%

“…Substitution of Eq. (19) and z = L into Eqo (18) then yields (20) which is applicable to the flowing afterglow apparatus in the filament source configuration. The validity of this equation was tested by measuring known reaction rates.…”

Section: Vo(1-r2/ a 2 ) A[x -]!Az = (Djr)a(ra[x -]!Ar)/ar+ K[e-][x 2 ]mentioning

confidence: 99%

“…However, if the initial guesses for these parameters are not reasonable, the successive iterations may diverge and no solution will be found. In order to overcome this limitation and to curve fit data to more complex equations, where the Taylor series approximation requires the initial guesses to be quite near the true values (for example, in the case of several nonlinear parameters), the technique of Becsey et al 19 was used o This technique uses a grid search method to locate the values of the unknown parameters which yield the minimum sum of the squares of the deviation.…”

Section: Data Reductionmentioning

confidence: 99%

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Measurement of thermal electron dissociative attachment rate constants for halogen gases using a flowing afterglow technique

Sides

Tiernan

Hanrahan

1976

The Journal of Chemical Physics

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Articles you may be interested inDissociative electron attachment near threshold, thermal attachment rates, and vertical attachment energies of chloroalkanes Thermal electron attachment to NO. I. The mechanism and the threebody rate constants Electron dissociative attachment rate constants for F2 and NF3 at 300 and 500°K Appl. Phys. Lett. 35, 920 (1979); 10.1063/1.91005 Thermal energy electron attachment rate constants for some polyatomic molecules A flowing afterglow apparatus was constructed and used to measure thermal electron attachment rate constants in the halogen gases fluorine, chlorine, and bromine. The operation of the afterglow system and the mathematical models applied in treating the data were tested by measuring the thermal attachment rate constant for electrons in sulfur hexafluoride. The average value obtained for this rate constant is 4.2± 1.1 X 10-8 cm' molecule-1 sec-1 when a microwave discharge was used as the electron source and 3.6± 1.8x 10-8 cm' molecule-1 sec-1 when a filament was used as the electron source. The average electron temperature was estimated to be approximately 6OO'K for the microwave discharge source and approximately 350'K for the filament source. A charge transfer reaction between sulfur hexafluoride and the ion O 2 was also investigated in the present study to further assess the operation of the flowing afterglow apparatus in the microwave discharge source configuration, The average rate constant obtained for this reaction is 3.7 ±O.4X 10-11 cm' molecule-1 sec-1 for an estimated ion temperature of 300-325'K, The average rate constants obtained for the dissociative attachment of electrons in fluorine are 4.6±1.2XIO-9 cm' molecule-1 sec-1 for an electron temperature of approximately 600'K and 3.1 ± 1.2X 10-9 cm' molecule" 1 sec-1 for an electron temperature of approximately 350'K. The average rate constants obtained for dissociative electron attachment in chlorine and bromine are 3.7± 1.7X 10,·9 and I.O±O.9X 10-11 cm' molecule-1sec-1 , respectively, for an electron temperature of approximately 350'K, The rate constant for the three-body attachment reaction Br-+Br,+Ar to form Bri' was also measured and found to be 1.9±O.5XIO-28 cm 6 molecule--'sec· 1 .

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Section: Vo(1-r2/ a 2 ) A[x -]!Az = (Djr)a(ra[x -]!Ar)/ar+ K[e-][x 2 ]mentioning

confidence: 99%

Section: Vo(1-r2/ a 2 ) A[x -]!Az = (Djr)a(ra[x -]!Ar)/ar+ K[e-][x 2 ]mentioning

confidence: 99%

Section: Data Reductionmentioning

confidence: 99%

See 1 more Smart Citation

Measurement of thermal electron dissociative attachment rate constants for halogen gases using a flowing afterglow technique

Sides

Tiernan

Hanrahan

1976

The Journal of Chemical Physics

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“…The fittest rate constant values for various reactions were obtained using a grid search method 13) . The Hamming method and a fourth-order Runge-Kutta method were used for the numerical calculation 14) .…”

Section: Calculation Methods Of Rate Constantsmentioning

confidence: 99%

Hydrolytic Behavior of Vinylsulfonyl Reactive Dyes - Easiness of Dimerization -

Kim¹

2015

Textile Coloration and Finishing

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Abstract:The aim of the current study is to identify the dimerization and decomposition kinetics of the F-DM type.The regeneration of F-VS from FiFj-DM or the reversibility of the dimerizations were investigated. The order of real rate constants of the dimerization(′ D ij ) would seem to be similar to that of rate constants of a dimerization( D ij ) for VS dyes at a given pH because of the constancy of the equilibrium constants( a j -value). The reverse reactions of the DM types are appeared to occur in two steps, the deprotonation of α-carbon of the DM types and disproportionation. The ratio of the decomposition of the DM type to F-Hy and F-VS appears to be related with the ratio of i/ j. Similarities were also found among various other reactions, including homo-and mixed dimerization. VS dyes undergoing fast hydrolysis have difficulty in forming a dimer. The higher the reactivity with cellulose or hydroxide ion, the smaller the dimerization. The easiness of the dimerization was thus found to be inversely proportional to the rate of hydrolysis.

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“…The initial conditions were the experimental concentrations for each type in the first sampling aliquot of the reaction solution. The boundary condition is: (5) When the hydrolysis of VS dyes is carried out below pH 8, only the hydrolysis of the SES type occurs.…”

Section: Reactive Dyesmentioning

confidence: 99%