Amplitude-dependent frequency

Vibration Amplitude and Frequency Speed and amplitude of vibration should be designed to convey the material properly and to prevent blinding of the cloth. They are somewhat dependent upon the size and weight of the material being handled and are related to the angle of installation and the type of screen surface. The object, of course, is to see that the feed is properly stratified for the most efficient separation. 

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]. 

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. 

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...

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. 

Peak Amplitude Spectral Analysis Amplitude Based Pattern Recognition Spatial Averaging Directional Dependence Frequency Dependence Conventional Shear Wave ... 

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. 

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. 

In this situation, a periodic variation of coolant flow rate into the reactor jacket, depending on the values of the amplitude and frequency, may drive to reactor to chaotic dynamics. With PI control, and taking into account that the reaction is carried out without excess of inert (see [1]), it will be shown that it the existence of a homoclinic Shilnikov orbit is possible. This orbit appears as a result of saturation of the control valve, and is responsible for the chaotic dynamics. The chaotic d3mamics is investigated by means of the eigenvalues of the linearized system, bifurcation diagram, divergence of nearby trajectories, Fourier power spectra, and Lyapunov s exponents. 

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

An alternate approach, developed in a speech coding context [McAulay and Quatieri, 1986a, McAulay and Quatieri, 1992], uses a harmonically-dependent set of sine waves with a random phase modulation. Yet another related technique [Marques and Almeida, 1988], represents the signal by a sum of adjacent narrowband sines of uniformly-spaced center frequency, with random amplitude and frequency modulation. 

There are many other variables in addition to r that may be used to control the reaction products by manipulating the motion of wave packets. These include the time-dependent frequency, amplitude, and phase functions of the laser pulse. The use of tailored laser fields to alter the shape of a wave packet is a very general method for controlling the outcome of a chemical reaction. 

In the mechanism-based approach, a model is validated by its ability to reproduce observed temporal behaviors, i.e. wave forms, phase relationships, parameter dependences, and stability properties under many different conditions. For oscillatory phenomena, prediction of amplitudes and frequencies (using independently determined parameters) play a significant role. Further validation of the model is based on its ability to predict the outcome of new experiments, performed under conditions not previously examined. Among the advantages of this approach are that the model can be gradually expanded without changing already consolidated parts and that the model, in principle at least, allows translation by replacement of, e.g. parameters from animal studies by parameters relevant to man. 

For linear systems, the principle of superposition applies, and different oscillatory modes can evolve independently of one another. However, biological systems in general are not linear, and separation of different regulatory mechanisms may not be justified, even when they involve different time scales. One type of phenomenon that can arise from the interaction between two oscillatory modes is modulation of the amplitude and frequency of the faster mode in dependence of the phase of the slower mode. This type of phenomenon was demonstrated in Fig. 12.2c where the frequency of the myogenic mode fjast changes in step with the amplitude of the TGF-mediated mode. Similar modulation phenomena can be expected to occur in many other biological systems such as, for instance, the interaction between the circadian and the ultradian rhythms of hormone secretion [25]. 

Analysis shows that the system of equations, which governs the time evolution of the given 3-level system under the action of the laser field with a time-dependent amplitude and frequency, resembles its nonrelativistic counterpart [19] and has the form ... 

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