Distortion coefficient

Figure 2.63 illustrates the effect of the distortion coefficient (Dc) on the characteristics of a linear and an equal-percentage valve. As the ratio of the minimum to maximum pressure drop increases, the Dc drops and the equal-percentage characteristics of the valve shift toward linear and the linear characteristics shift toward QO. In addition, as the Dc drops, the controllable minimum flow increases, and therefore, the rangeability (the flow range within which the valve characteristic remains as specified) of the valve also drops. 

These figures illustrate the effects of the distortion coefficient (DJ on inherently linear (left) and inherently equal-percentage valves (right), according to Boger. 

The cosine coefficient of this series, A , is a product of the two cpiantities N /N3 and cos27tlZ ). N /N3 only depends on the length of the colnnms and therefore corresponds to a size. The other term depends on Z , which means that it is related to the distortions of the lattice. It represents the contributions from the microstrains. This means that the cosine term is the product of the size and distortion coefficients. If we denote these two terms by A and A , respectively, we get ... 

After this modification, the camera model is established and the system of equations defined by equation 7 is solved, having previously performed the change of variable proposed. After the first calculation stage and based on the solution p and using a linear iterative resolution process we will solve the entire camera system, including the determination of distortion coefficients. We will minimize the normalized distance between the center of grid distortion target dots... 

After solving the least squares problem defined by equation 14 and after undoing the normalization performed to the coordinates the calibration matrix P and the geometric distortion coefficients will be obtained. 

Another example of Coriolis interaction is presented in Section 4.13. J. Watson recently published an excellent paper on the determination of the centrifugal distortion coefficient of asymmetric top molecules. [ 1-... 

Microstructural imperfections (lattice distortions, stacking faults) and the small size of crystallites (i.e. domains over which diffraction is coherent) are usually extracted from the integral breadth or a Fourier analysis of individual diffraction line profiles. Lattice distortion (microstrain) represents departure of atom position from an ideal structure. Crystallite sizes covered in line-broadening analysis are in the approximate range 20-1000 A. Stacking faults may occur in close-packed or layer structures, e.g. hexagonal Co and ZnO. The effect on line breadths is similar to that due to crystallite size, but there is usually a marked / fe/-dependence. Fourier coefficients for a reflection of order /, C( ,/), corrected from the instrumental contribution, are expressed as the product of real, order-independent, size coefficients A n) and complex, order-dependent, distortion coefficients C (n,l) [=A n,l)+iB n,l)]. Considering only the cosine coefficients A(n,l) [=A ( ).AD( ,/)] and a series expansion oiAP(n,l), A (n) and the microstrain e (n)) can be readily separated, if at least two orders of a reflection are available, e.g. from the equation... 

The LUMO, which is the frontier orbital in reactions with nucleophiles, has a larger coefficient on the /3-carbon atom, whereas the two occupied orbitals are distorted in such a way as to have larger coefficients on oxygen. The overall effect is that the LUMO is relatively low-lying and has a high coefficient on the /3-carbon atom. The frontier orbital theory therefore predicts that nucleophiles will react preferentially at the /3-carbon atom. 

It follows that as the peak velocity is inversely proportional to the distribution coefficient, then the higher concentrations in the peak will migrate faster than the lower concentrations. As a consequence, the peak is distorted with sharp front and a sloping back. This distortion is shown in Figure 9. 

In both Equations (4.100) and (4.101), the six Oj are the coefficients of thermal deformation (expansion or contraction and distortion, I.e., shear), and AT is the temperature difference. In Equation (4.101), the terms CjjCXjAT are the thermal stresses if the total strain is zero. 

For out-of-plane distortion the coefficient /2 = A2/ 2 is expected to be proportional to alL, since becomes nonzero for the finite eurvature. Thus, the coupling constant is proportional to (afL)2 and the gap decreases very rapidly with the diameter as exp[-(L/a) ]. It is eoncluded that metallic CNTs arc quite... 

The above technique has the practical inconvenience of requiring as many different sets of Tchebyschev coefficients as the unit cell non equivalent sublattices. Furthermore, for non cubic systems, these coefficients depend on the lattice distortion ratios. Namely, for tetragonal lattices different sets of coefficients are required for each value of c/a. This situation has made difficult the implementation of KKR and KKR-CPA calculations for complex lattice structures as, for example, curates. 

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