Amplitude dependence

CCF dependences on the -factor of loaded probe vibrators are shown in Fig.4. For s(l) pulses growth of 2 factor increase CCF maximum amplitude and selectivity. In this case the higher the Q, the longer the pulse duration and the more its periods contribute to the processing. F or q(t) pulses rising of g-factor decrease CCF maximum amplitudes and reduce the selectivity. As q(l) pulse consists of a few first periods only its maximum amplitude depends on Q. the higher the Q, the lower the final pulse amplitude, and therefore, CCF amplitude and selectivity. 

If we accept the assumption that the elastic wave can be treated to good aproximation as a mathematical discontinuity, then the stress decay at the elastic wave front is given by (A. 15) and (A. 16) in terms of the material-dependent and amplitude-dependent wave speeds c, (the isentropic longitudinal elastic sound speed), U (the finite-amplitude elastic shock velocity), and Cfi [(A.9)]. In general, all three wave velocities are different. We know, for example, that... 

The peculiarities of dynamic properties of filled polymers were described above in connection with the discussion of the method of determining a yield stress according to frequency dependence of elastic modulus (Fig. 5). Measurements of dynamic properties of highly filled polymer melts hardly have a great independent importance at present, first of all due to a strong amplitude dependence of the modulus, which was observed by everybody who carried out such measurements [3, 5]. 

A typical behavior of amplitude dependence of the components of dynamic modulus is shown in Fig. 14. Obviously, even for very small amplitudes A it is difficult to speak firmly about a limiting (for A -> 0) value of G, the more so that the behavior of the G (A) dependence and, respectively, extrapolation method to A = 0 are unknown. Moreover, in a nonlinear region (i.e. when a dynamic modulus depends on deformation amplitude) the concept itself on a dynamic modulus becomes in general not very clear and definite. 

The existence of the G (A) dependence even in the region of very small amplitudes is explained by a brittle pattern of fracture of a filler s structure, so that measuring virtually frequency (and amplitude) dependences of a dynamic modulus, a researcher always deals with a material in which the structure is partially fractured. 

Of course, measurements of amplitude dependence of the elastic modulus of a filled composition may, by itself, give an interesting material on thixotropic properties of such materials. Indeed, very strong effects are observed here. Thus, in a melt containing... 

Though due to the fact that it is difficult to interprete amplitude dependence of the elastic modulus and to unreliable extrapolation to zero amplitude, the treatment of the data of dynamic measurements requires a special caution, nevertheless simplicity of dynamic measurements calls attention. Therefore it is important to find an adequate interpretation of the obtained results. Even if we think that we have managed to measure correctly the dependences G ( ) and G"( ), as we have spoken above, the treatment of a peculiar behavior of the G (to) dependence in the region of low frequencies (Fig. 5) as a yield stress is debatable. But since such an unusual behavior of dynamic functions is observed, a molecular mechanism corresponding to it must be established. 

Fig. 14. Amplitude dependences (y0 is the amplitude of cyclic deformations) of the elastic modulus for frequency a) = 63 s 1 13% dispersion of acetylene carbon black in low- (/) and high-molecular (2) poly(isobutylene)s...

If sound vibrations are applied to an electrode being in contact with a solution, a variable electrode potential component AE is generated. Its amplitude depends on the electrode potential E. It shows a maximum at the Epzc Further details have been provided elsewhere [66Kuk2]. (Data obtained with this method are labelled AE). 

Leadbetter AJ, Norris EK (1979) Molec Phys 38 669. There are different contributions which give rise to a broadening a of the molecular centre of mass distribution function f(z). The most important are the long-wave layer displacement thermal fluctuations and the individual motions of molecules having a random diffusive nature. The layer displacement amplitude depends on the magnitude of the elastic constants of smectics ... 

Konecny et al. [9] suggested that there exists a linear correlation between dynamic mechanical characteristics from DMA and RPA for carbon black-hlled mbber compounds. The amplitude dependencies of the analogous dynamic mechanical characteristics obtained from DMA and RPA... 

Our renormalization procedure is internally consistent in that the physical value of the tunneling amplitude depends on the scaling variable—the bare coupling Aq—only logarithmically. This bare coupling must scale with the only quantum scale in the problem—the Debye frequency, as pointed out in the first section. 

Notice that in the limit of small By [where eqns (5.14) and (5.15) are valid] the derivative amplitude increases linearly with B, that the width is independent of Bi and that neither width nor amplitude depends on 7). At higher power,, ylB2T T2 cannot be neglected in eqn (5.13b), the amplitude is no longer linear... 

The oscillations in the reflectivity curves arise from interference between the X-rays reflected from the various interfaces. The frequency of the oscillations is proportional to layer thickness and the amplitude depends on the interface roughness. 

We know from Chapter 2 that the harmonic amplitudes depend on the rise and fall times. That is one reason why engineers often try to slow down the Mosfet (increase its transition time), usually at the expense of some efficiency, though sometimes it can even help improve the efficiency, as we will see. 

The settling of certain particular amplitude depends on the initial conditions. When the motion becomes stationary the amplitude s value practically does not depend on the wave s intensity when the latter changes over a significant range above a certain threshold value. This is reminiscent of Einstein s explanation of the photoelectric effect using Planck s quantization hypothesis. In this case the absorption is also independent of the incoming wave s intensity. Besides, the absorbed... 

The excitation of oscillations with a quasi-natural system frequency and numerous discrete stationary amplitudes, depending only on the initial conditions (i.e. discretization of the processes of absorption by the system of energy, coming from the high-frequency source). A new in principle property is the possibility for excitation of oscillations with the system s natural frequency under the influence of an external high-frequency force on unperturbed linear and conservative linear and non-linear oscillating systems. 

There is actually a considerable literature on the approximate amplitude dependence of the simple pendulum [9-11], although this is the only one we know of which is based on approximating the physics rather than the mathematics. The formula is remarkably accurate even for initial angular displacements of 90° from the downward vertical. The corresponding equations for the spherical pendulum in generalised coordinates are altogether more complicated, very... 

P. E. Rapp, Frequency encoded biochemical regulation is more accurate than amplitude dependent control, J. Theor. Biol, 90, 531-544 (1981). 

The relative lifetimes of the two terraee types at any one saddle point location has been measured[31] to differ by a factor of 6 at 1060C. The change in terrace type occurs by the bridging of the short dimension by step fluctuations. Since the probability of a fluctuation of a particular amplitude depends linearly on the step stiffness[8] the observed lifetime ratio is consistent with measured step stiffnesses[37] and the geometrical picture given above[38]. 

The enhancement factor E, that is, the quantity in the parenthesis in this equation, is displayed in Fig. 5.10. Because the corrugation amplitude depends only on the relative intensities of different components, we normalize it through... 

The threshold amplitude depends on the applied normal force. 

For 7 > 7C the system did not approach any steady state at all but rather oscillated with p and E amplitudes dependent on the increment of the current above the critical value. With the current increasing above 7C, the stabilized shape of the oscillations soon received a relaxation character, schematically depicted in Fig. 6.1.2. 

The exjsessions used are valid for crystals of all types, from cubic to tridinic the structure amplitude depends on atomic coordinates (as fractions of the unit cell edges), irrespective of the shape of the cell. 

Thus, the linear polarizability a (responsible for the value of the refractive index n) can be treated as an electric field amplitude-dependent quantity, i.e., aeff = a + (3-yEo)/4. Remembering that the light intensity is proportional to the square of the field amplitude, this means that the third-order nonlinearity leads to the linear dependence of the refractive index on the light intensity and that, for example, the phase of the propagating beam is modified at high light intensities due to this dependence. 

The amplitude of vibration is proportional to a", and therefore the squared amplitude depends on... 

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