Root mean square amplitude value

The power dissipated in an AC circuit with current of maximum amplitude flowing through a resistance is less than the power produced by a constant DC current of magnitude flow ing through the same resistance. For a sinusoidal AC current, the root mean square (rms) value of current I is the magnitude of the DC current producing the same power as the AC current with maximum amplitude I. The rms value I is given by... 

Fig. 12.1 (continued) (c) Isotope effects on mean square amplitudes (upper curve) and root mean square amplitudes (lower curve) as a function of temperature for hypothetical nondissociating molecules. At low temperatures the molecules are in the ground state and the amplitude is nearly independent of temperature. At higher temperature the vibrational amplitudes increase due to excitation into upper levels (Fig. 12.1) but the ratios drop smoothly to the classical value of unity at very high temperature (Fig. 12.1)... 

Normalized structure factor The ratio of the value of the structure amplitude I F I to its root-mean-square expectation value. This ratio is denoted E(hkl). 

Essentially the characteristic temperature is a measure of the temperature at which the atomic heat capacity is changing from zero to 6 cal deg for silver (0 = 215 K) this occurs around 100 K, but for diamond (0 = 1860 K) with a much more rigid structure, the atomic heat capacity does not reach 5 cal deg i until 900 K. Those elements that resist compression and that have high melting points have high characteristic temperatures. Equations have been derived relating y/ u ) to the characteristic temperature 0. At room temperature diamond, with a characteristic temperature of 1860 K, has a root-mean-square amplitude of vibration, / u ) of 0.02 A, while copper and lead, with characteristic temperatures of 320 and 88 K, respectively, have values of 0.14 and 0.28 A for (u ). - Similar types of values are obtained for crystals with mixed atom (or ion) types. For example, average values of / u ) for Na+ and Cl in sodium chloride (0 = 281 K) are 0.14 A at 86 K and 0.23 A at 290 K. ° ... 

Results on a large number of linear-chain complexes of platinum are summarised in Table 11. Harmonic wavenumbers and anharmonicity constants have been determined in all cases. The normal coordinate seems to be related to the halogen movements involved in the proposed hopping process for the conductivity of these linear-chain mixed-valence complexes (95). The chain halogen atoms would need to move, on average, 0.54,0.38 and 0.22 A for chlorides, bromides and iodides, respectively, in order to reach the point midway between the two platinum atoms, i.e. to the situation of a platinum (III) chain. These values only differ by a factor of about two from the root-mean-square amplitudes of vibration of Vi in the Vj = 16 states these are calculated (91) to be 0.22 A for X = Cl (wi = 319.5 cm-i) and 0.20 A for X = Br (cji = 179.6 cm ). These distance changes are related to the shift in the equilibrium... 

The lower detection limit is influenced by the noise frequency and amplitude distribution compared with the signal band width and height. The noise level is usually measured over a given time period which is a multiple of the signal width. The noise can be expressed as peak-to-peak (p-t-p) or root-mean-square (rms) values. The latter gives about 70-80% lower noise levels. Figure 15-7 summarizes the detection limits of some selected chromatographic detectors. 

The crest factor C is a measure for the ratio between peak amplitude and Root Mean Square (RMS) value of a signal ... 

The averaged values of the root-mean-square amplitude of the elastic vibrations of structural complexes of the crystal lattices of refractory compounds were calculated from the Debye—Waller relationship [372], by means of the characteristic temperatures and the masses of the vibrating complexes 3 2j r x ]... 

The standard Hilbert transform attributes [41] are given by the complex trace analysis, and produce the well-known reflection strength (amplitude of the envelope), instantaneous phase, instantaneous frequency, or apparent polarity. In this approach, the information obtained is time, amplitude, frequency or attenuation, and is used as an input into industry s standard grid-based classification. Additional information can be derived directly from the reflection amplitude or from summation of amplitude value within intervals. This is the case for composite amplitude, average absolute amplitude, root-mean-square amplitude, number of zero crossings, and of minima or maxima. 

Root-mean-square (RMS) is the statistical average value of the amplitude generated by a machine, one of its components, or a group of components. Referring to Figure 43.11, RMS is equal to 0.707 of the zero-to-peak value, A. Normally, RMS data are used in conjunction with relative vibration data acquired using an accelerometer or expressed in terms of acceleration. 

We require only three parameters not available through the model, the root mean square thermal displacement amplitude and estimates of and cop, in order to recreate the entire fiber diffractogram. For our universal isotropic thermal displacement factor we employed the B value used successfully by Noitholt (1) for the experimental analysis of scattering from PPTA ... 

However, in a magnitude of root-mean-square noise amplitude, i.e. DC noise, the SUL without the generation of spike noise takes poor level. Figure 7.3 shows a variation in DC noise voltage of the Co-Ni-Fe-B SUL with in-plane coercivity. DC noise was increased with increasing the value of coercivity [18]. Since the coercivity... 

We now estimate the minimum value, cmin, of the rotary force constant c. For c < cmin the above-used approximation of small oscillation amplitudes becomes inapplicable The point is in the following. The root-mean-square angular deflection 0, pertaining to the covalent bond of the lefthand molecule20 (see Fig. 39a), according to (102) and (137), increases with decreasing of c. As follows from the indicated formulas, the limiting deflection is... 

The stability of proteins refers to the maintenance of a defined three-dimensional structure with specific thermodynamic and functional properties. High-resolution structures in the crystalline state and in solution have reached a stage at which the atomic coordinates of proteins can be compared with an accuracy down to root mean square deviation (r.m.s.d.) values less than 1 A. However, even this precision does not allow the fi ee energy of stabilization to be calculated from the coordinates, nor does it allow predictions with respect to the dynamics of functionally relevant local interactions in active or regulatory sites of homologous proteins. The fluctuations between preferred conformations of native proteins involved in such functionally important motions may very well show amplitudes and angles of up to 50 A and 20°, respectively. ... 

The peak value is called the amplitude Vp, cp is the phase angle. To define (p, we must define a reference sine wave for instance, the known excitation signal. Although the mean value of a full period is 0, it is usual to quote the mean of half a period 2Vp/TC. The rms (root mean square) value is Vp/ /2. 

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