Oscillatory mode

Haake has introduced other viscometers, including the RheoStress RSlOO, which offers controlled stress as well as controlled shear rate and oscillatory modes over a temperature range of —50 to 350°C (ambient to 500°C is also possible). This versatile viscometer covers a shear rate range of 10 ... 

The other possible mode is called the damped oscillatory mode and has a current versus time plot similar to Figure 3.9. This results in an irregular intensity versus time plot and the consequent loss of a considerable amount of light energy. A profile similar to Figure 3.8 results if R is high in comparison to L. Since R itself is only about 5 1 or less, the inductance must therefore be kept to a minimum. 

M. Markus and B. Hess, Transitions between oscillatory modes in a glycolytic model system. Proc. Natl. Acad. Sci. USA 81, 4394 4398 (1984). 

Fig. 13.10. Cooperation of two different oscillatory modes leading to a phase space trajectory...

Let us mention several papers by Ya.B. on various problems of molecular physics and quantum mechanics which have not been included in this volume. Among the problems considered are the peculiar distribution of molecules according to their oscillatory modes when the overall number of oscillatory quanta does not correspond to the temperature of translation [9], the influence of the nuclear magnetic moment on the diffusion coefficient [10] and on absorption of light by prohibited spectral lines [11],... 

In order to understand such complex oscillatory modes in terms of the underlying nonequilibrium chemistry, it is convenient to begin with a simplified version of the full BZ mechanism15 which describes the main features of earlier experimental observations of the closed BZ reaction. 

In addition to the steady-state mode, the double-cell device of Fig.7 can be operated in the so-called transient and oscillatory modes of operation(18.). In the transient mode, one measures the slope dVg/dt when the pumping current is changed in a stepwise fashion from zero to a constant value. A simple analysis(18) gives the following differential equations for Vg and Pv,... 

As demonstrated by the power spectra in Figs. 12.2a and 12.3b, regulation of the blood flow to the individual nephron involves several oscillatory modes. The two dominating time scales are associated with the period Tsiow 30—40 s of the slow TGF-mediated oscillations and the somewhat shorter time scale Tjast 5—10 s defined by the myogenic oscillations of the afferent arteriolar diameter. The two modes interact because they both involve activation of smooth muscle cells in the arteriolar wall. Our model describes these mechanisms and the coupling between the two modes, and it also reproduces the observed multi-mode dynamics. We can, therefore, use the model to examine some of the phenomena that can be expected to arise from the interaction between the two modes. 

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]. 

This measure can be used to characterize the various forms of frequency locking between the two modes. With varying feedback delay T and varying slope a of the open loop feedback curve, Fig. 12.11 shows how the two oscillatory modes can adjust their dynamics and attain states with different rational relations (p q) between... 

As discussed in Section 12.5, the two oscillatory modes associated with the pressure and flow regulation in the individual nephron may operate in synchrony or... 

Let us consider the case of a = 30 corresponding to a weakly developed chaotic attractor in the individual nephron. The coupling strength y = 0.06 and the delay time T2 in the second nephron is considered as a parameter. Three different chaotic states can be identified in Fig. 12.16. For the asynchronous behavior both of the rotation numbers ns and n f differ from 1 and change continuously with T2. In the synchronization region, the rotation numbers are precisely equal to 1. Here, two cases can be distinguished. To the left, the rotation numbers ns and n/ are both equal to unity and both the slow and the fast oscillations are synchronized. To the right (T2 > 14.2 s), while the slow mode of the chaotic oscillations remain locked, the fast mode drifts randomly. In this case the synchronization condition is fulfilled only for one of oscillatory modes, and we speak of partial synchronization. A detailed analysis of the experimental data series reveals precisely the same phenomena [31]. 

There exists a substantial history of interest in flow and deformation properties of monolayers. Perhaps, the first is the theoretical formulation of hydrodynamic coupling between the monolayer and subphase by Harkins and Kirkwook in 1938 [129], in determination of steady shear viscosity of mono-layers, which has since been augmented by Hansen [130] and Goodrich [131]. A variation of the method based on the Maxwell model was proposed by Mannheimher and Schechter [132] in an oscillatory mode in a canal. Experimentally, the method was implemented by joint efforts in our laboratories for determinations of steady shear viscosity of monolayers through the canal... 

Formally, the sum of random electromagnetic-field fluctuations in any set of bodies can be Fourier (frequency) decomposed into a sum of oscillatory modes extending through space. The "shaky step" in this derivation, already mentioned, is that we treat the modes extending over dissipative media as though they were pure sinusoidal oscillations. Implicitly this treatment filters all the fluctuations and dissipations to imagine pure oscillations only then does the derivation transform these oscillations into the smoothed, exponentially decaying disturbances of random fluctuation. 

The FIR spectrum is proportional to the Fourier transform of the dipole correlation function, (M(t) -M(0). As discussed above, at short times the correlation function is dominated by pseudo-oscillatory modes. Insofar as the dipole moment of the liquid is relatively weakly dependent on these pseudo-oscillatory coordinates, it is generally safe to truncate Eq. (1) after the second term in describing this short-time behavior. Thus, an IR-active intermolecular mode is considered to be one for which M-1 0. 

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