Phase angle difference

When multiple circuit elements are involved, the resultant phase angle difference between the current and the potential will result from the contribution of each element. 

Note that 0 is not the phase angle difference between line potential and line current. 

For a number of 1907 acentric reflexions up to 0.463 A resolution, the mean and rms phase angle differences between the noise-free structure factors for the full multipolar model density and the structure factors for the spherical-atom structure (in parentheses we give the figures for 509 acentric reflexions up to 0.700A resolution only) were (Acp) = 1.012(2.152)°, rms(A( >) = 2.986(5.432)° while... 

Tangent of the phase angle difference (< between stress and strain during forced oscillations. 

Recent studies show that nonlinear stress response can be represented in terms of a time-dependent phase angle difference 8 between the nonlinear elastic stress and viscoelastic stress. This approach appears to have an advantage over the numerical treatments used by previous workers because it provides some information about the reversible structural changes which occur during the cycle. However, such analyses require instruments which can subject the specimen simultaneously to two cyclic deformations of different amplitude and frequency. 

When Ay is very small (Ay < 0.1%), the stress response caused by the sinusoidal straining given by Equation 1 is approximately sinusoidal, and the viscoelastic behavior falls in the region of linear viscoelasticity. In this case, the phase angle difference 8 between the stress wave and strain wave is constant throughout the cycle, and the stress response can be expressed by ... 

A part of this peculiar variation in the stress-strain phase angle difference comes from the variation of elastic modulus with the phase angle. Therefore, to determine the phase angle difference which is caused by the nonelastic contribution, it is necessary to determine and to subtract the contribution from the variation of elastic modulus as a function of the strain. 

In Figure 5, the elastic stress curve falls between the strain curve and the viscoelastic stress curves during the contracting phase, showing that a part of the phase angle difference between the strain and viscoelastic stress is contributed by the nonlinear elasticity of the specimen. 

Phase Angle Difference between the Nonlinear Viscoelastic Stress and Nonlinear Elastic Stress. The phase angle difference 8 between the nonlinear viscoelastic stress and nonlinear elastic stress is defined by the relation ... 

This phase angle difference represents the net effect of the nonelastic contribution, and its physical significance corresponds to that of constant 8 measured for the linear viscoelastic material. 

First, either by visual reading or by computerized data acquisition system, read off the coordinates of ad and y corresponding to each other. Since y is controlled to the sine form of Equation 1, it is easy to determine the phase angle difference 8 (0) between ad and y as defined by ... 

ANGLE OF LAG OR LEAD - The phase angle difference, between two sinusoidal wave forms having the same frequency. 

Plots of phase angle difference in the interferometer arms vs. time are related to heat-production vs. time, and this in turn is related to the concentration of the species responsible for heat production. Typical instrument output for the urea/urease system is shown in Figure 3. Calibration curves can be constructed as shown in Figure The system is quite stable, and reasonably sensitive. Minimum detectable levels of urea are 5 mM, compared to the 0.1-5 mM limits for traditional detectors. Over extended time periods (7 days) the relative standard deviation at 5 mM concentrations is better than 5 /.. The optimum FIA conditions were around 1.0 ml/min flow rate, with a sample loop of 0.1-0.25 ml. 

It proved impossible to derive consistent area or height information from repeat runs using either visual methods, or standard peak-picking algorithms. Reliable quantitative calibration curves could only be derived from evaluation of the slope of the phase angle difference curve as a function of time at a fixed arbitrary point near the beginning of the heat evolution. 

A further interesting aspect of the phase difference or die demodulation between F and R is the potential of measuring the levene reaction rate fa. This reverse rale can be obtmned fiom the phase-angle difference between the R and F states, or from the modulation of the R state reladve to the F state. For a reversible reaction, these expressions are... 

Am Differentia] polarized phase angle, difference in phase between the parallel and perpendicular components of the emission Phase angle at a light modulation frequency... 

In the Y-A connection, there is a 30° phase angle shift between the primary and secondary sides. The phase angle difference can be made either lagging or leading depending on the external connections of the transformer bank. The case with the primary side lagging is shown in Fig. 10.109, and the case with the primary side leading is shown in Fig. 10.110. The transformation ratio is %/3 times the ratio of turns in each of the phases. 

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