Disturbance growth rate

Substitution of Equation A7 into A6 gives the dispersion equation relating the disturbance growth rate and wavelength ... 

Figure 6.6 Comparison of Elmendorp s [52] results on disturbance growth rate in molten thermoplastics with Tomotika s predictions.

Actually, the system capacitance and the pressure-decay rate measure the rate of capacitance discharge of the system. Because the combustion process is known to be controlled by pressure, the pressure-decay rate will disturb the combustion process. If the decay rate is greater than the intrinsic pressure-growth rate of the controlling reaction, the combustion process will not recover. This suggests that the pressure-decay rate dP/dt is the intrinsic term, rather than the capacitance term (L ). 

The nondimensional growth rate, ftm, is a unique function of the wave-number andp. Kuhn (1953) estimated the magnitude of the initial amplitude of the disturbances (ao) to be 10-9 m based on thermal fluctuations. Mikami et al. (1975) gave a higher estimate of 10 8 to 10"7 m. 

Flat Sheets. Generally, the interface between a liquid sheet and air can be perturbed by aerodynamic, turbulent, inertial, surface tension, viscous, acoustic, or electrical forces. The stability of the sheet and the growth rate of unstable disturbances are determined by the relative magnitude of these forces. Theoretical and experimental studies 255112561 on disintegration mechanisms of flat sheets showed that the instability and wave formation at the interface between the continuous and discontinuous phases are the maj or factors leading to... 

Short wavelengths of disturbance on thick sheets are stable unless wind velocities or Weber numbers are very high. The optimum wavelength for sheet disintegration corresponds to the maximum growth rate /3max. For We 1, these are formulated as 258 ... 

This behavior seems to be measurable by surface dynamic light scattering. Furthermore, in the unstable region 8 < 8Cf we predict a spinodal decomposition on the surface. The growth rate of the surface disturbances takes a maximum at an intermediate wave number km. The balance of the two terms in the last brackets of Eq. (7.22) yields [93]... 

An important factor to remember when comparing these forecasts is the business environment under which they were made. The reference forecast was prepared during 1971, when world paper demand had been expanding at five percent annually for more than a decade. By contrast, the forecasts published in 1977 were prepared in the wake of the strong cyclical disturbance caused by the 1975 recession. In the case of the composite forecast, most of the projections were made in 1978. All the forecasts have been extrapolated to 2000 using the prevailing growth rate for the last five-year period. 

In this way, photosynthates are constantly available. The importance of these remobilization mechanisms is highlighted when they are disturbed. For example, mutants of the crucifer Arabidopsis thaliana, which are unable to synthesize starch but can still synthesize sucrose, grow at the same rate as the wild type under continuous light, but the growth rate is drastically diminished if placed in a day-night regime (Caspar et al., 1986). 

One of the features of traditional eigenvalue analysis is that the disturbance held is assumed to grow either in space or in time. This distinction is only for ease of analysis and there are no general proofs or guidelines available that would tell an investigator which growth rate to investigate. Huerre Monkewitz (1985) have applied the so-called combined spatio-temporal... 

In Fig. 6.11, two sets of eigenfunctions are shown for the case with K = 5 X 10 and Re = 1000. In Fig. 6.11(a) the case corresponds to LVo = 0.1 for which the hydrodynamic mode attains its maximum growth and thus the eigenfunctions once again represent the disturbance velocity components. In Fig. 6.11(b) the case corresponds to loq = 0.7 and the eigenvalue for this case indicates the thermal mode to be at its maximum growth rate. Hence the plotted function corresponds to the disturbance temperature field. 

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