Weighted Jacobi method

Figure 6. Computed vibration-rotation contributions to the Gibbs free energy and 4th-order polynomial curve fits for H20, HDO, and D20 as a function of temperature. AH computations were carried out using the AOSS-U Monte Carlo method in mass-weighted Jacobi coordinates. Three hundred Fourier coefficients were used per degree of freedom and 106 Monte Carlo samples were used for each calculation. Error bars at the 95% confidence level, as weU as all free energy fluctuations, are smaller than the width of the lines showing the curve fits. An increment of 10 was used over the temperature interval (1000-4000 K).

The confuBion which has arisen in iniblical.ions concerning these compounds is due to the fact that they form mixtures which are hard to separate and addition products with salts, water, alcohol and other solvents, and like all substances of the kind give rise to false values of molecular weight by the ordinary methods (translated from Freudenberg and Jacobi "). 

Fahey RC and Newton GL (1987) Determination of low molecular weight thiols using monobromobi-mane fluorescent labeling and hi -performance liquid chromatography. In Jacoby WB, ed. Methods in Enzymology, Vol 143, pp. 85-96. Academic Press Inc., London. 

Bacterial strains bearing plasmids of known sizes, to serve as molecular weight markers during electrophoresis, were obtained from Drs. P. Walsh and G. Jacoby. Lysates of these were prepared by the method described above. 

Based on the above assumptions, the model equations are shown in Table 4. The mass balance equations at the pellet and crystal level are based in the double linear driving model equations or bidisperse model[30]. The solution of the set of parabolic partial differential equations showed in Table 4 was performed using the method of lines. The spatial coordinate was discretized using the method of orthogonal collocation in finite elements. For each element 2 internal collocation points were used and the basis polynomial were calculated using the shifted Jacobi polynomials with weighting function W x) = (a = Q,p=G) hat has equidistant roots inside each element [31]. The set of discretized ordinary differential equations are then solved with DASPK solver [32] which is based on backward differentiation formulas. 

There are two common values for the weighting w x ). These are u = 1 and w = —x. Roots for these Jacobi polynomials are presented in Table 8.8 for all three geometries, both values of w and various orders of N. The roots presented in Table 8.8 specify specific collocation points to be used in the method of weighted residuals. The collocation method satisfies the describing differential equation at the collocation points. In order to implement this, we need to evaluate the function and its derivatives at the collocation points. The trial function of equation (8.12.21) can also be written as... 

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