Frequency limits

In linear, spherical and synnnetric tops the components of a along and perpendicular to the principal axis of synnnetry are often denoted by a and respectively. In such cases, the anisotropy is simply Aa = tty -If the applied field is oscillating at a frequency w, then the dipole polarizability is frequency dependent as well a(co). The zero frequency limit of the dynamic polarizability a(oi) is the static polarizability described above. 

The triac may, however, have some limitations in handling frequencies higher than normal. In such cases, they can be simulated by using two SCRs in inverse parallel combinations as illustrated in Figure 6.22(b). Now it is known as a reverse conducting thyristor. An SCR has no frequency limitations at least up to ten times the normal. The required voltage and current ratings are obtained by series-parallel connections of more than one thyristor unit. 

Frequency limiting is also provided on all the resonant controllers on the market today. The resonant frequency of the tank circuit is given by... 

Once again, high and low frequency limiting must be introduced on the control IC in order to minimize output ripple voltage and zero switching loss conditions. 

This compensation method now exhibits a -180 degree phase lag at low frequencies, then beginning at one-tenth the error amplifier s Alter pole (/ep) the phase lag increases to its high frequency limit of -270 degrees. 

Hochfrequenzgrenze, /. high-frequency limit, hochfrequenzmassig, a. relating to high frequency. 

Constant speed frequency analysis Constant-speed machinery generates a relatively fixed set of frequency components within its signature. Therefore, specific APSs can be established to monitor using frequency analysis. Since speed is relatively constant, the location of specific frequency components (e.g., running speed) will not change greatly. Therefore, the broadband and each narrowband window can be established with a constant minimum and maximum frequency limit, which are referred to as fixed filters. 

Boundary conditions and resolution The frequency boundary conditions and resolution for the full FFT signature depends on the specific system being used. Typically, the full-signature capability of various predictive-maintenance systems has a lower frequency limit of 10 Hz and an upper limit of 10 to 30 kHz. A few special low-frequency analyzers have a lower limit of 0.1 Hz, but retain the upper limit of 30 kHz. Typical resolutions are 100 to 12,800 lines. 

Channels with frequency limited input and output. A function of time, (t), is said to be frequency limited to W cps (cycles per second) if it has a Fourier transform,... 

We now apply Eqs. (4-194) to (4-201) to the frequency limited, power limited, additive white gaussian noise channel. If N is the block length of a code in samples, then T = N/2W is the block length in time. Furthermore if is the available signal power and if N0 is the noise power per unit bandwidth, then the signal to noise ratio, A, is 8/N0W. Finally we let JRT> the rate in nats per second, be 2 WB. Substituting these relations into Eqs. (4-194) and (4-197), we get... 

Whichever physical interpretation is chosen, the difference between the high-frequency real axis intercept [Z (high) and the low-frequency limiting real impedance [Z (low)] is one-third of the film s ionic resistance (i.e., R[ = 3[Z (low) - Z (high)]). Ideally, the real component of the... 

It has been suggested [115, 116] to solve the inverse problem using the simplified relation which is actually a high-frequency limit of Eq. (2.73). This relation can be found, if we take into account that... 

In the low-frequency limit, they show that the normalized response of the flame is given by... 

If not otherwise stated the four-component Dirac method was used. The Hartree-Fock (HF) calculations are numerical and contain Breit and QED corrections (self-energy and vacuum polarization). For Au and Rg, the Fock-space coupled cluster (CC) results are taken from Kaldor and co-workers [4, 90], which contains the Breit term in the low-frequency limit. For Cu and Ag, Douglas-Kroll scalar relativistic CCSD(T) results are used from Sadlej and co-workers [6]. Experimental values are from Refs. [91, 92]. 

Stated in other words, the zero-frequency limit of Axc is used for treating the finite frequency perturbations. For details see in particular Casida, 1995. 

On the magnitude plot, the low frequency (also called zero frequency) asymptote is a horizontal line at Kp. On the phase angle plot, the low frequency asymptote is the 0° line. On the polar plot, the zero frequency limit is represented by the point Kp on the real axis. In the limit of high frequencies,... 

By choosing xD < (i.e., comer frequencies l/xD > 1/Xj), the magnitude plot has a notch shape. How sharp it is will depend on the relative values of the comer frequencies. The low frequency asymptote below 1/Xj has a slope of-1. The high frequency asymptote above l/xD has a slope of +1. The phase angle plot starts at -90°, rises to 0° after the frequency l/xIs and finally reaches 90° at the high frequency limit. 

Tests were run with N80 steel in 15% and 28% HC1 at 25 C with and without octynol for periods extending up to 2 hours. Immediately after injection of octynol into the acid, two phenomena were observed. First, near the low-frequency limit of the tests, a prominent inductive loop (below the Z axis) appeared which then vanished within a few minutes. Secondly, fits of the data above 1 Hz to the Rfl+P/Rfc circuit, i.e. ignoring the inductive loop, gave rise to a higher CPE n-value, which then remained relatively constant for the duration of each experiment. This result is shown in Figure 5. 

Limitations of the experiment at low frequencies come from the long experimental times, during which the sample structure may change so much that the entire experiment becomes meaningless. At high frequencies, limitations... 

Similar analysis of the MDT may be performed for arbitrary initial phase / 7 0. We note that, depending on the initial phase, x( ) may vary significantly (especially in the low-frequency limit). This is due to the fact that the height of the potential barrier at initial instant of time has a large variation (from zero to some maximal value). Because in real experiments the initial phase is usually... 

The charts are arranged in order of increasing element content. Correlations given in one chart (e.g. those for Cl I2 and CH3) are not repeated in subsequent charts. The frequency limits within which the band of a particular grouping is usually found are indicated by the black strips and extensions of the range to include unusual examples are shown as thin lines, e g. relative intensities are given in a very approximate fashion (see below). Both the position and the intensity of some absorptions are dependent on state, solvent, etc., and the actual frequency quoted is that most commonly observed. 

Kieffer has estimated the heat capacity of a large number of minerals from readily available data [8], The model, which may be used for many kinds of materials, consists of three parts. There are three acoustic branches whose maximum cut-off frequencies are determined from speed of sound data or from elastic constants. The corresponding heat capacity contributions are calculated using a modified Debye model where dispersion is taken into account. High-frequency optic modes are determined from specific localized internal vibrations (Si-O, C-0 and O-H stretches in different groups of atoms) as observed by IR and Raman spectroscopy. The heat capacity contributions are here calculated using the Einstein model. The remaining modes are ascribed to an optic continuum, where the density of states is constant in an interval from vl to vp and where the frequency limits Vy and Vp are estimated from Raman and IR spectra. 

This result, that the low frequency limit of the in phase component of the viscosity equates to the viscosity of the dashpot, means that for a single Maxwell model it is possible to replace rj by rj(0). Thus far we have concentrated on the description of experimental responses to the application of a strain. Similar constructions can be developed for the application of a stress. For example the application of an oscillating stress to a sample gives rise to an oscillating strain. We can define a complex compliance J which is the ratio of the strain to the stress. We will explore the relationship between different experiments and the resulting models in Section 4.6. 

In order to obtain a general model of the creep and recovery functions we need to use a Kelvin model or a Kelvin kernel and retardation spectrum L. However, there are some additional subtleties that need to be accounted for. One of the features of a Maxwell model is that it possesses a high frequency limit to the shear modulus. This means there is an instantaneous response at all strains. The response of a simple Kelvin model is shown in Equation 4.80 ... 

This result is very interesting because whilst we have shown that G(0) has been excluded from the relaxation spectrum H at all finite times (Section 4.4.5), it is intrinsically related to the retardation spectrum L through Jc. Thus the retardation spectrum is a convenient description of the temporal processes of a viscoelastic solid. Conversely it has little to say about the viscous processes in a viscoelastic liquid. In the high frequency limit where co->oo the relationship becomes... 

The fluctuation in elasticity is given by the difference between the elasticity in the high frequency limit and the elasticity of the new configuration ... 

The expression for the real component of the complex viscosity allows us to express the relaxation times as experimentally realisable parameters. In the low frequency limit we can rewrite Equation (5.88) in terms of the concentration c in gem-3 ... 

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