Imaginary parts

The comparison between measured data and simulated data are good for both real and imaginary parts. The measured signal has a low resolution due to the low interaction between the eddy current and the slot. 

The comparison between measured data and simulated data are good for the imaginary part, but differences appear for the real part. The ratio between simulated data and measured data is about 0.75 for TRIFOU calculation, and 1.33 for the specialised code. Those differences for the real part of the impedance signal can be explained because of the low magnitude of real part compared to imaginary part signal. 

Interpretation of the impedance signal for set 2 (imaginary part function of the probe position along the slot)... 

The variation response of the real and imaginary parts of the impedance in function of the frequency, with or without the sample presence. 

When we equalize the real part and the imaginary part, we obtain ... 

Measurement of real- and imaginary part of a coil complex impedance... 

A common known method to get eddy-current informations about material flaws is the measurement of real- and imaginary part of the complex impedance of a coil in absolute circuit. The measurement, shown in this paper, are done with an impedance analyzer (HP4192A). The device measures the serial inductance L, and the serial resistance Rs of the complex impedance with an auto-balance bridge measurement circuit [5]. 

In contrast to metals, most studies have concentrated on insulators and semiconductors where the optical structure readily lends itself to a straightforward interpretation. Within certain approximations, the imaginary part of the dielectric fiinction for semiconducting or insulating crystals is given by... 

Once the imaginary part of the dielectric function is known, the real part can be obtained from the Kramers-Kronig relation ... 

It is possible to understand the fine structure in the reflectivity spectrum by examining the contributions to the imaginary part of the dielectric fiinction. If one considers transitions from two bands (v c), equation A1.3.87 can be written as... 

In figure A1.3.20 and figure Al.3.21 the real and imaginary parts of the dielectric fimction are illustrated for... 

Figure Al.3.21. Imaginary part of the dielectric function for silicon. The experimental work is from [31], The theoretical work is from an empirical pseudopotential calculation [25],...

The transverse magnetization may be described in this frame by a complex variable, m, the real and imaginary parts of which represent the real and imagmary components of observable magnetization respectively ... 

Figure Bl.26.13. Plot of versus K, the imaginary part of the refractive index.

The observable NMR signal is the imaginary part of the sum of the two steady-state magnetizations, and Mg. The steady state implies that the time derivatives are zero and a little fiirther calculation (and neglect of T2 tenns) gives the NMR spectrum of an exchanging system as equation (B2.4.6)). 

As was mentioned above, the observed signal is the imaginary part of the sum of and Mg, so equation (B2.4.17)) predicts that the observed signal will be tire sum of two exponentials, evolving at the complex frequencies and X2- This is the free induction decay (FID). In the limit of no exchange, the two frequencies are simply io3 and ici3g, as expected. When Ids non-zero, the situation is more complex. 

In this equation, the index j runs over all the transitions and the exponents have both real and imaginary parts, which... 

In this equation, the primes on the imaginary parts indicate that the Lamior frequencies and coupling constants will be different. Also, if the equilibrium constant for the exchange is not 1, then the forward and reverse rates will not be equal. Note that the 1,2 block, in the top right, represents the rate from site 2 into site 1. 

Figure B3.2.5. The imaginary part of the dieleetrie fiinetion of GaAs, aeeording to tire AFC ELAPW-/c p method (solid eiirve) [195] and the experiment (dashed enrve) [196], To eorreet for the band gap underestimated by the loeal density approximation, the eonduetion bands have been shifted so that tlie 2 peaks agree in theory and experiment.

Figure C2.1.14. (a) Real part and (b) imaginary part of tire dynamic shear compliance of a system whose mechanical response results from tire transition between two different states characterized by a single relaxation time X.

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