Rayleigh s criterion

Extensive reviews of active instability suppression techniques are found in McManus et al. [18] and Candel [19]. Also, Zinn and Neumeier [20] provide an overview of research and developmental needs for practical applications. Most of the previous studies have used actuators impractical in liquid-fueled systems, such as loudspeakers that impose acoustic perturbations on gaseous flow. The major emphasis in the present study was to establish active instability suppression using liquid-fuel injection. According to Rayleigh s criterion [21, 22], combustion-acoustics interaction can be used to damp the undesirable oscillations provided that pressure fluctuations p and heat release fluctuations q satisfy the proper phase relation such that... 

On purely qualitative grounds Low and Brunt (L8), in 1925, proposed that the presence of a solid wall in place of a free surface should double Rayleigh s criterion for instability and that solid walls at both top and bottom should quadruple the critical Rayleigh number. 

Figure 1. Rayleigh s criterion for the effects of heat release on the amplitude and phase of a sound wave.

Fig. 4.7. Rayleigh s criterion for the resolution of two nearly overlapping lines...

The first condition will be recognized as Rayleigh s criterion, which is easy to satisfy, for example if the liner is initially in rigid rotation. If satisfied initially it will be satisfied throughout the cycle. The second condition is that the effective gravity at the inner surface should always be directed radially outwards this condition is most severe at turnaround. The third condition is necessary because the outer gas-liquid interface cannot be stabilized by rotation. 

The theoretical spatial resolution is determined by the numerical aperture (NA) of the objective and the wavelength of radiation used for the imaging measurement. The theoretical spatial resolution R according to Rayleigh s criterion for a microscopic measurement is given as [1, 2]... 

Projection printing involves no contact between the mask and the wafer. It employs a large gap between the wafer and the mask such that Fresnel diffraction is no longer valid. Instead, Fraunhofer diffraction is valid. It has well-designed objective lens between the mask and the wafer. The resolution of projection printing system governed by Rayleigh s criterion is... 

Figure 6.18 Image of two distant point objects formed by a converging lens (a) the angnlar separation of the objects is so small tbat tbe images are not resolved, (b) the objects are fartber apart and tbe images obey Rayleigh s criterion of resolntion, (c) the objects are stUl farther apart and the images are well resolved.

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