Real part

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. 

The isotropic part has not changed. The quasi pressure (qP) curve splits up into a real and an imaginary branch . During this real part the transversal share of the polarization increases until the wave becomes a quasi shear vertical wave. Furthermore, the wave is not anymore a propagating but an evanescent wave in this part. The branch is again only real, it is part of the quasi shear vertical (qSV) curve of the homogeneous case (dotted line), its polarization is dominated by the transversal share and the wave is a propagating one. For the branches (real) and... 

The real part increases slightly with the frequency (Joule effect). 

Fia 5 Real Part of Calculated Field Distribution around Exciter Coil... 

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

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

Figure Al.3.20. Real part of the dielectric function for silicon. The experimental work is from [31]. The theoretical work is from an empirical pseudopotential calculation [25].

It is possible to use the quantum states to predict the electronic properties of the melt. A typical procedure is to implement molecular dynamics simulations for the liquid, which pemiit the wavefiinctions to be detemiined at each time step of the simulation. As an example, one can use the eigenpairs for a given atomic configuration to calculate the optical conductivity. The real part of tire conductivity can be expressed as... 

The real part of n , the dispersive (reactive) part of and the definition of Xy implies a relation between tr yand -/which is known as the Kramers-Kronig relation. 

Here -E is the amplitude of theyth field and the real part of oi. is its (circular) frequency or colour . The real... 

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.

Figure 12.2. Real part of the dominant eigenvalue versus Lewis number for steady state E of Figure 12,1, (From Hite and Jackson CSl].)...

A eomplex number has a real part and an imaginary part and is usually denoted ... 

A very useful way to simplify Eq. (10.65) involves the complex number e in which i = / 1 equals cos y + i sin y. Therefore cos y is given by the real part of e y. Since exponential numbers are easy to manipulate, we can gain useful insight into the nature of the cosine term in Eq. (10.65) by working with this identity. Remembering that only the real part of the expression concerns us, we can write Eq. (10.65) as... 

Fig. 5. Complex magnetic permeabihty vs frequency for a series of ferrites used for power transformers and inductors at 25°C, S <0.1 mT (—) represents real parts ]l (-----------------------) show the imaginary parts ]l". The arrows indicate the frequencies where tan6 = fi/fi = 1 (57).

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