Koehler equation

Pande and Suenaga [ ] have recently claimed that grain boundary flux pinning is caused by the elastic interaction between the dislocations constituting the grain boundaries and the fluxoids. The interactions between dislocations and fluxoids have long been the subject of studies. The two modes of interaction are (1) the first-order, or volume difference, effect, and (2) the second-order, or shear modulus difference, effect. The former usually dominates The Peach-Koehler equation [ ] can be used to calculate the interaction force between the stress field of the fluxoid lattice (a calculation of which has recently become available [ " ]) and the strain field of the dislocations. In the experiments of this study, the calculation of fpL... 

Here we used the fact that the force is perpendicular on the dislocation line. If the orientation between the stress tensor a, the dislocation line /i and the Burgers vector b is arbitrary, the Peach-Koehler equation... 

As the energies must agree for arbitrary I2, the Peach-Koehler equation results ... 

Some of the data are shown in Fig. 8, where it can be seen that at a given input level of PPi, activity increases with addition of Mg up to a point after that activity diminishes with additional Mg. A computer program to analyze these data was designed by Dr. R. A. Damm-koehler of Washington University, St. Louis, Missouri (59). Because so many of the tested kinetic equations were nonlinear and contained interdependent parameters, the computer procedure required extensive trial-and-error strategy to determine optimal global fit for each possible... 

The interest in the mechanisms of SchifF base hydrolysis stems largely from the fact that the formation and decomposition of SchifF base linkages play an important role in a variety of enzymatic reactions, for example, carbonyl transfers involving pyridoxal phosphate, aldol condensations, /3-decarboxylations and transaminations. The mechanisms for the formation and hydrolysis of biologically important SchifF bases, and imine intermediates, have been discussed by Bruice and Benkovic (1966) and by Jencks (1969). As the consequence of a number of studies (Jencks, 1959 Cordes and Jencks, 1962, 1963 Reeves, 1962 Koehler et al., 1964), the mechanisms for the hydrolysis of comparatively simple SchifF bases are reasonably well understood. From the results of a comprehensive kinetic investigation, the mechanisms for the hydrolysis of m- and p-substituted benzylidine-l,l-dimethylethylamines in the entire pH range (see, for example, the open circles in Fig. 13) have been discussed in terms of equations (23-26) (Cordes and Jencks, 1963) ... 

A model for predicting logP values in different solvent systems [Dunn III et al., 1987 Koehler et al., 1988], defined by the equation ... 

The term "designer correlation" is modified from A. J. Hopfinger, M. G. Koehler, R. A. Pearlstein and S. K. Tripathy, J. Polym. Sci, Polym. Phys. Ed., 26, 2007-2028 (1988), who referred to "designer equations" for calculating the glass transition temperatures of structurally related polymers. 

The following equation, which is misprinted in Koehler (1968), Is very useful in evaluating kinetic energy matrix elements ... 

This is the generalization of (3,14) and (3,17), and it is a self-consistent equation for the effective force constants, as the wavefunction T depends on G (or O), This equation has been used to obtain the force constants by iterations (Koehler, 1966), and once the force constants are known,... 

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