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Asymptote angles

Fig. 31 (a) Transient behavior of the NMR splitting for an SDS/Dec nematic calamitic solution at concentration c = 29.5 wt. % and molar ratio [Dec]/[SDS] = 0.33 and sheared at 7= 0.32 s [284]. (b) Evolution of the orientation angle of the nematic director with respect to the magnetic field as function of the strain. The symbols correspond to the spectra in (a), and the continuous line is determined from Eq. 7, yielding an asymptotic angle of = 78 2°. Inset Orientation of the nematic director in presence of the flow and of the magnetic field... [Pg.57]

This description is traditional, and some further comment is in order. The flat region of the type I isotherm has never been observed up to pressures approaching this type typically is observed in chemisorption, at pressures far below P. Types II and III approach the line asymptotically experimentally, such behavior is observed for adsorption on powdered samples, and the approach toward infinite film thickness is actually due to interparticle condensation [36] (see Section X-6B), although such behavior is expected even for adsorption on a flat surface if bulk liquid adsorbate wets the adsorbent. Types FV and V specifically refer to porous solids. There is a need to recognize at least the two additional isotherm types shown in Fig. XVII-8. These are two simple types possible for adsorption on a flat surface for the case where bulk liquid adsorbate rests on the adsorbent with a finite contact angle [37, 38]. [Pg.618]

A convenience of electronic basis functions (53) is that they reduce at infinitesimal-amplitude bending to (28) with the same meaning of the angle 9 we may employ these asymptotic forms in the computation of the matrix elements of the kinetic energy operator and in this way avoid the necessity of carrying out calculations of the derivatives of the electronic wave functions with respect to the nuclear coordinates. The electronic part of the Hamiltonian is represented in the basis (53) by... [Pg.522]

Root locus asymptotes. For large values of k the root loei are asymptotie to straight lines, with angles given by... [Pg.125]

Find the asymptotes and angles of departure and hence sketch the root locus diagram. Locate a point on the complex locus that corresponds to a damping ratio of 0.25 and hence find... [Pg.130]

Note that the structures depicted in Fig. 5 are not self-similar because the angle of rotation of the faces differs for each layer. The layers should, therefore, not be called shells as they are called in the case of pure alkaline earth-metal clusters. With increasing size, the shape of the cluster will converge asymptotically to that of a perfect icosahedron. [Pg.174]

Symmetry 50. Intercepts 50. Asymptotes 50. Equations of Slope 51. Tangents 51. Equations of a Straight Line 52. Equations of a Circle 53. Equations of a Parabola 53. Equations of an Ellipse of Eccentricity e 54. Equations of a Hyperbola 55. Equations of Three-Dimensional Coordinate Systems 56. Equations of a Plane 56. Equations of a Line 57. Equations of Angles 57. Equation of a Sphere 57. Equation of an Ellipsoid 57. Equations of Hyperboloids and Paraboloids 58. Equation of an Elliptic Cone 59. Equation of an Elliptic Cylinder 59. [Pg.1]

To determine the shape of a root locus plot, we need other rules to determine the locations of the so-called breakaway and break-in points, the corresponding angles of departure and arrival, and the angle of the asymptotes if the loci approach infinity. They all arise from the analysis of the characteristic equation. These features, including item 4 above, are explained in our Web Support pages. With MATLAB, our need for them is minimal. [Pg.138]

To make the phase angle plot, we simply use the definition of ZGp(joo). As for the polar (Nyquist) plot, we do a frequency parametric calculation of Gp(jco) and ZGp(joo), or we can simply plot the real part versus the imaginary part of Gptjco).1 To check that a computer program is working properly, we only need to use the high and low frequency asymptotes—the same if we had to do the sketch by hand as in the old days. In the limit of low frequencies,... [Pg.148]

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,... [Pg.148]

The magnitude and phase angle plots are sort of "upside down" versions of first order lag, with the phase angle increasing from 0° to 90° in the high frequency asymptote. The polar plot, on the other hand, is entirely different. The real part of G(jco) is always 1 and not dependent on frequency. [Pg.151]

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]

The shape of the magnitude plot resembles that of a PI controller, but with an upper limit on the low frequency asymptote. We can infer that the phase-lag compensator could be more stabilizing than a PI controller with very slow systems.1 The notch-shaped phase angle plot of the phase-lag compensator is quite different from that of a PI controller. The phase lag starts at 0° versus -90°... [Pg.160]

In Example 8.12, we used the interacting form of a PID controller. Derive the magnitude and phase angle equations for the ideal non-interacting PID controller. (It is called non-interacting because the three controller modes are simply added together.) See that this function will have the same frequency asymptotes. [Pg.169]

Fig. 53. Small-angle neutron scattering data from the 12-arm polystyrene star PS120A (Mw = 1.49 x 105) where the 11 deuterated arms were matched by the solvent THF. In order to demonstrate the asymptotic Q behavior, the data are plotted in a generalized Kratky representation (Iq01 vs. Q with a = 1.5 and 5/3). The solid line marks the high Q-plateau. (Reprinted with permission from [149]. Copyright 1989 American Chemical Society, Washington)... Fig. 53. Small-angle neutron scattering data from the 12-arm polystyrene star PS120A (Mw = 1.49 x 105) where the 11 deuterated arms were matched by the solvent THF. In order to demonstrate the asymptotic Q behavior, the data are plotted in a generalized Kratky representation (Iq01 vs. Q with a = 1.5 and 5/3). The solid line marks the high Q-plateau. (Reprinted with permission from [149]. Copyright 1989 American Chemical Society, Washington)...
This simple fracture model has a major shortcoming. The exclusion of chain stretching in the model leads for small initial orientation angles to strength values that become infinite. It follows from Eq. 27 that the shear stress is a continuous function of the fibre stress and it increases asymptotically to the value of 2gtan . So for initial orientation angles... [Pg.28]

Notice that the construction rules are satisfied. The root loci start (K = 0) at the poles of the system openloop transfer function, s = — 1. There are three loci. The angle of the asymptotes is 180/3 = 60°. [Pg.363]


See other pages where Asymptote angles is mentioned: [Pg.127]    [Pg.131]    [Pg.137]    [Pg.187]    [Pg.200]    [Pg.188]    [Pg.127]    [Pg.131]    [Pg.137]    [Pg.187]    [Pg.200]    [Pg.188]    [Pg.374]    [Pg.2293]    [Pg.2297]    [Pg.74]    [Pg.56]    [Pg.628]    [Pg.222]    [Pg.120]    [Pg.202]    [Pg.153]    [Pg.158]    [Pg.64]    [Pg.58]    [Pg.66]    [Pg.119]    [Pg.287]    [Pg.48]    [Pg.305]    [Pg.196]    [Pg.155]    [Pg.106]    [Pg.358]    [Pg.364]   
See also in sourсe #XX -- [ Pg.127 , Pg.131 , Pg.137 ]




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