A. PULSATILE FLOW IN A CIRCULAR TUBE REVISITED - ASYMPTOTIC SOLUTIONS FOR HIGH AND LOW FREQUENCIES [Pg.205]

To help understand MATLAB results, a sketch of the low and high frequency asymptotes is provided in Fig. E8.9. A key step is to identify the comer frequencies. In this case, the comer frequency of the first order lead is at 1/5 or 0.2 rad/s, while the two first order lag terms have their comer frequencies at 1/10, and 1/2 rad/s. The final curve is a superimposition of the contributions from each term in the overall transfer function. [Pg.154]

On the magnitude plot, the low frequency asymptote is a line with slope -1. The high frequency asymptote is a horizontal line at Kc. The phase angle plot starts at -90° at very low frequencies and approaches 0° in the high frequency limit. On the polar plot, the Gc(jco) locus is a vertical line that approaches from negative infinity at co = 0. At infinity frequency, it is at the Kc point on the real axis. [Pg.157]

The asymptotic limits of the real part of the impedance for the reactive circuit of Table 16.1(b) are Re at high frequencies and Re + R at low frequencies. These limits are indicated in the complex-impedance-plane plot, and the characteristic [Pg.312]

Caprani et al. [104], defining the cut-off frequency as the intersection of the low and high-frequency asymptotes, as indicated on Fig. 10.18, have given an approximate method to deduce the size of active sites on a partially blocked electrode from the ratio of the two cut-off frequencies [Pg.426]

The magnitude tends toward Re as frequency tends toward oo and toward + R as frequency tends toward zero. The transition between low frequency and high frequency asymptotes has a slope of —1 on a log-log scale. [Pg.315]

The real part of the impedance, shown in Figure 17.4(a), provides the same information as is available from the modulus plots presented in Figure 17.2(b). The high frequency asymptote reveals the Ohmic electrolyte resistance, and the low frequency as)miptote reveals the sum of the polarization impedance and the [Pg.338]

The Bode plots are shown in Fig. 12.15. One of the most convenient features of Bode plots is that the L curves can be easily sketched by considering the low-and high-frequency asymptotes. As a> goes to zero, L goes to zero. As to becomes very large, Eq. (12.39) reduces to [Pg.429]

Shamov (1966) has pointed out the importance of the time dependence of the Poisson ratio of polymers. Measurements on polymers at very low frequency will yield values near Z2, whereas data obtained at very high frequencies will yield values asymptotically approaching Ms. The value of v is thus a function of the rate of measurement. This fact is illustrated by data of Warfield and Barnet (1972) and Schuyer (1959) [Pg.390]

If a transfer-function model is desired, approximate transfer functions can be fitted to the experimental curves. First the log modulus Bode plot is used. The low-frequency asymptote gives the steadystate gain. The time constants can be found from the breakpoint frequency and the slope of the high-frequency asymptote. The damping coefficient can be found from the resonant peak. [Pg.505]

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. [Pg.159]

Usually, the exponents a and (3 are referred to as measures of symmetrical and unsymmetrical relaxation peak broadening. This terminology is a consequence of the fact that the imaginary part of the complex susceptibility for the HN dielectric permittivity exhibits power-law asymptotic forms Im e (( ) coa and Im s (co) co aP in the low- and high-frequency limits, respectively. [Pg.106]

Figure 16. xj (co) and xj ( ) versus cox evaluated from the exact matrix continued fraction solution (solid lines) for a = 0.5, t v = 10 and various values of and compared with those calculated from the approximate Eq. (215) (filled circles) and with the low-(dotted lines) and high-frequency (dashed lines) asymptotes Eqs. (184) and (185), respectively. [Pg.360]

Comparison of the Fp functions corresponding to nonisothermal and isothermal cases shows distinctive differences in the shapes of the amplimdes of the second-order functions. The differences in the first-order functions also exist, but they become more obvious if they are shown in the form of real and imaginary parts the imaginary part of Fi p(w) for isothermal case has one minimum, while for the nonisothermal case a curve with two minima is obtained [54,59]. Also, for the case of variable micropore diffusivity, the low- and high-frequency asymptotic values of F2,pp(

© 2019 chempedia.info