Effective Coupling Coefficient

In this situation the coupling coefficient of the piezoelectric material is especially important. Though there are many specific forms of the coupling coefficient, an effective coupling coefficient may be used for a transducer operating near a particular resonance ... 

A coupling coefficient describes the efficiency of energy transfer from one form to another in a material or physical mechanism. The effective coupling coefficient is determined based on measurement of a mechanism s characteristics rather than relying on a derivation of the coefficient Synonyms from underlying principles. The effective coupling coefficient often combines several disparate phenomena in these cases. 

Lekhnitskii defines the coefficients of mutual influence and the Poisson s ratios with subscripts that are reversed from the present notation. The coefficients of mutual influence are not named very effectively because the Poisson s ratios could also be called coefficients of mutual influence. Instead, the rijjj and ri y are more appropriately called by the functional name shear-exitension coupling coefficients. 

Note that the Chentsov coefficients are more effectively called the functional name of shear-shear coupling coefficients. 

The mixing coefficients a and b in (4.10) depend upon the efficiency of the spin-orbit coupling process, parameterized by the so-called spin-orbit coupling coefficient A (or for a single electron). As A O, so also do a or b. Spin-orbit coupling effects, especially for the first period transition elements, are rather small compared with either Coulomb or crystal-field effects, so the mixing coefficients a ox b are small. However, insofar that they are non-zero, we might write a transition moment as in Eq. (4.11). 

The expressions (4.22)-(4.23) found in chap. 4 for the isomer shift 5 in nonrelativ-istic form may be applied to lighter elements up to iron without causing too much of an error. In heavier elements, however, the wave function j/ is subject to considerable modification by relativistic effects, particularly near the nucleus (remember that the spin-orbit coupling coefficient increases with Z ). Therefore, the electron density at the nucleus l /(o)P will be modified as well and the aforementioned equations for the isomer shift require relativistic correction. This has been considered [1] in a somewhat restricted approach by using Dirac wave functions and first-order perturbation theory in this approximation the relativistic correction simply consists of a dimensionless factor S (Z), which is introduced in the above equations for S,... 

Exposure of bulk GaAs Si wafers to a capacitively coupled rf deuterium plasma at different temperatures generates deuterium diffusion profiles as shown in Fig. 1. These profiles are close to a complementary error function (erfc) profile. At 240°C, the effective diffusion coefficient is 3 x 10 12 cm2/s. The temperature dependence of the hydrogen diffusion coefficient is given by (Jalil et al., 1990) ... 

In this section, we will analyze the effects of a nano-sized HRI overlay on the distribution of the cladding modes (transversal fields, effective indices, coupling coefficients) to changes of its thickness and refractive index and to changes of the SRI. 

The coupling coefficients vs. the SRI are reported in Fig. 3.6 b-d for overlay thicknesses of 200, 250, 300 nm, respectively, always with the same coating index of 1.578. From these figures, it can be clearly inferred that increasing the overlay thickness the coupling coefficients curves shift toward lower SRIs as it happens for the effective refractive index curves. 

If x = 1, critical coupling is obtained and the dip depth attains its maximum value of 100% the microresonator is said to be undercoupled if x < 1 and overcoupled for x > 1. While the coupling loss remains constant, the effective intrinsic loss can be changed by interaction of the evanescent fraction (/) of the WGM with the surrounding medium. The effective loss coefficient can then be written as a = a +/aa f /as, where the three terms denote true intrinsic loss, absorption (and perhaps also scattering) by the analyte, and absorption in the solvent (or ambient). 

Here, P0 is the input transmission power, and the parameters yc and ya are the coupling and attenuation parameters, respectively. They are expressed through the attenuation constant, a, the circumference, S, the effective refractive index, n, and the coupling coefficient, k, as follows ... 

The broadly successful application of these formulas to the paramagnetism of lanthanide complexes was due to the wide multiplet widths in the/block metals (large spin—orbit coupling coefficients X) and to the small effect of the ligand field on the deep-lying / orbitals. No comparably useful formula for the magnetic moments of d block complexes exists, except perhaps for the spin-only formula ... 

In Eqs. 2.20 and 2.22, the diagonal terms, Laa, are called direct coefficients they couple each flux to its conjugate driving force. The off-diagonal terms are called coupling coefficients and are responsible for the coupling effects (also called cross effects) identified above. 

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