Iterative localization Reliability

We anticipate two advantages of using the more realistic electron densities obtained by the AFDF methods. More reliable theoretical electronic charge densities calculated for each assumed nuclear geometry in the course of the iterative structure refinement process will improve the reliability of comparisons with the experimental di action pattern. In particular, AFDF electron densities are expected to serve as more sensitive and more reliable criteria for accepting or rejecting an assumed structure than the locally spherical or possibly elliptical electron density models used in the conventional approach. We also expect that the more accurate density representations within the QCR-AFDF framework will facilitate a more complete utilization and interpretation of the structural information contained in the observed X-ray diffraction pattern. 

Results of the Numerical Iterative Methods.—The application of more sophisticated local isotherms than the Langmuir or Jovanovic dictates the use of numerical iterative methods. The advantages of these methods are they do not require curve fitting of the experimental data to establish a total isotherm equation, nor assumptions regarding the general form of the adsorption energy distribution. However they generally necessitate extensive and reliable experimental data, the measurement of which has been made possible by the more... 

The iteration between film pressure and elastic deflection fields. Involved in direct elastohydrodynamic solutions, was avoided and the non-linearity of the integrated Reynolds equation was handled within the library routine (IMSL-DGEAR), Reliability checks,were performed by varying the allowable local truncation error within DGEAR and the number of discrete pressure values used in the integration for the load. 

To make Eq. (26) and Eq. (27) true (solving for the equlity in Eq. 27) requires iteratively finding the value of the service time te that satisfies the equality, however, this is computationally intensive. Fortunately, in order to perform the attenuated reliability analysis for the component only the sign of the inequality in Eq. (18) needs to be established locally at This means that iteration is not necessary. Instead Eq. (26) is used to establish tmin,i,eff( ), which is used on the left-hand side of the inequality in Eq. (18). The right-hand side of the inequality in Eq. (18) is determined by computing tq i eff( ) from Eq. (25) and tp i eff( ) from Eq. (23). 

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