Hertz factor

In Fig. 1 results are presented concerning the evolution of profiles of the Hertz factor. This parameter is a useful measure of cohesiveness of the material since it is proportional to the compressive strength of a granular medium. The profiles shown were obtained for Ad = 0.042 W m K The modeling concerns the period from the discovery of the comet until the present time. 

Fig. 1. Evolution of profiles of Hertz factor versus depth, calculated for the evolving orbit see text. The curves are drawn for consecutive perihehon passages.

The time-temperature superpositioning principle was applied f to the maximum in dielectric loss factors measured on poly(vinyl acetate). Data collected at different temperatures were shifted to match at Tg = 28 C. The shift factors for the frequency (in hertz) at the maximum were found to obey the WLF equation in the following form log co + 6.9 = [ 19.6(T -28)]/[42 (T - 28)]. Estimate the fractional free volume at Tg and a. for the free volume from these data. Recalling from Chap. 3 that the loss factor for the mechanical properties occurs at cor = 1, estimate the relaxation time for poly(vinyl acetate) at 40 and 28.5 C. 

The first derivative is the hyperfine coupling constant g (as measured by ESR), the second derivative with respect to two different nuclear spins is the NMR coupling constant, J (Planck s constant appears owing to the convention of reporting coupling constants in Hertz, and the factor of 1/2 disappears since we implicitly only consider distinct pairs of nuclei). 

The mechanical properties of a material play an important role in powder flow and compaction by influencing particle-particle interaction and cohesion, that is to say, by influencing the true area of contact between particles. For example, Hertz [26] demonstrated that both the size and shape of the zone of contact followed simply from the elastic properties of a material. Clearly then, the true area of contact is affected by elastic properties. From the laws of elasticity, one can predict the area of contact between two elastic bodies. More recent work has demonstrated, however, that additional factors must be taken... 

To add to the confusion, some workers take 6, as the negative of the definition (8.35). Some workers use factors of 105 or 107 instead of 106. Some workers use 8, to mean the shift in hertz their 8, is equal to (8.35) multiplied by spectromcter- Pri°r t0 introduction (by Tiers in 1958) of TMS as the reference for proton shifts, a variety of reference compounds (such as benzene, cyclohexane, and water) were used. When examining reported shifts, the definitions used should be noted. 

Since the s orbitals do not have orbital magnetic moment, g — ge — 2.0023. A is an eneigy, which in SI units is expressed in joule. Sometimes it is convenient to have it expressed in frequency units, i.e. in hertz or in radians per second, and then we have to divide A by h or by h (ft = h/2n). In magnetic resonance there often is a factor 2jt which complicates life. The frequency which we refer to is the angular frequency or the Larmor precession frequency. Such frequency co is... 

For their Hertz potential, Rodrigues and Vaz chose the factor < )(f,x) = 4>(x) exp (j fl t). Now, since II satisfies the wave equation, we conclude that the factor (<))x) in turn satisfies the Helmholtz equation ... 

The precession frequency, also called the Larmor frequency, is represented as v0 ( new-zero, in hertz or cycles per second). The division by In is sometimes omitted because the units of y can be expressed in hertz per tesla rather than radians per seconds per tesla. When the Larmor frequency is represented in units of radians per second it is called the angular velocity or co0. These are related by a factor of In ... 

To use this form to describe the oscillations of a wave, we can say that 6 increases with time t as 9 = cot in terms of "radial frequency" o> that has the units of radians per second. This a> differs by a factor of 2it from usual frequency v, whose units are cycles per second, or hertz. With... 

Perform the real and imaginary transforms on diis data (note you may have to write a small program to do this, but it can be laid out in a spreadsheet without a program). Notice diat n and m should start at 0 rather than 1, and if angles are calculated in radians it is necessary to include a factor of In. Plot the real and imaginary transforms using a scale of hertz for the horizontal axis. 

The impedance response of a resistor in parallel to a capacitor is shown in Figure 4.7 as a function of frequency / in units of Hz. When plotted as a function of frequency co in units of s ( e upper axis), the minimum in the imaginary part of the impedance appears clearly at a characteristic frequency of a c = 1/Tc- The dashed line corresponds to the characteristic frequency of 1 s. When plotted against frequency in units of Hertz, the characteristic frequency is shifted by a factor of 27T, i.e., fc = l2nXc. 

It is conventional to express frequency in terms of wavenumbers (in reciprocal centimeters) rather than hertz, using the symbol v (v = vjc = K with c the speed of light and X the wavelength). Accordingly, Eq. (2.7) becomes (2.8), with the factor of c contained in the constant /x ... 

Hertz, M.I., Henke, C.A., Nakhleh, RE. et al. (1992). Obliterative bronchiolitis after lung transplantation A fibroproliferative disorder associated with platelet derived growth factor. Proc. Natl. Acad. Sci. USA 89, 10385-10389. 

The electrical properties of a number of semiconductor polyoximes was studied.209,210 These structures offer whole-chain resonance, where the polymer backbone consists entirely of alternating double bonds with the exception of the metal atom. Values for D (dissipation factor) ranged from 3 to 10 (at 103 hertz), bulk resistivity from 0.05 to 0.6 (at 103 hertz), and bulk capacitance from 0.2 K to 0.9 K. 

Table 9.4. Measurement frequency v in Hertz, dielectric dissipation factor tan 8 and dielectric constant e observed at room temperature at the specified frequency of measurement, and the fitted value of tan 8 calculated as described in the text, for 206 data points covering a wide variety of polymers. Most measurements were made on commercial samples containing various plasticizers, fillers and other additives, so that the (exp) values listed for many polar polymers differ significantly from (i.e., exceed) the more "intrinsic" e(exp) values listed in Table 9.1. 

Hertz, R., Magenheim, J., Berman, I., and Bar-Tana, J. (1998) Fatty acyl-CoA thioesters are ligands of hepatic nuclear factor-4alpha. Nature 392, 512-516. 

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