Local pulses

Fig. 5.2.7 Identification of location and size of local pulses within the trickle bed. A high spatial resolution image (in-plane spatial resolution 1 75 [tm x 175 im slice thickness 1 mm) is overlayed with a standard deviation map calculated from images acquired at a spatial resolution of in-plane spatial resolution 1.4 mm x 2.8 mm slice thickness 2 mm.

As an example of applying the Fourier transform method to a non-periodic function, consider the localized pulse... 

Now integrate over the whole xyt domain. Note that all terms except the first and the dz (implicit in V.) are derivatives that give rise to surface terms after integration over x,y,t. Since we consider spatially and temporally localized pulse-like solutions, these terms vanish. The only surviving derivative will be dz from V. ... 

Karu TI. Local pulsed heating of absorbing chromophores as a possible primary mechanism of low-power laser effects. In Galetti G, Bolognani L, Ussia G (eds), Laser Applications in Medicine and Surgery. Bologna Monduzzi Editore, 1992. 

Fig. 35. Identification of location and size of local pulses within the trickle bed. A high spatial resolution image (in-plane spatial resolution 175 pm x 175 pm slice thickness 1mm) is overlayed with a standard deviation map calculated from images acquired at a spatial resolution of in-plane spatial resolution 1.4 mm x 2.8 mm, and slice thickness 2 mm. The standard deviation maps have been linearly interpolated to the same in-plane spatial resolution as the high resolution data. Images are shown for a constant gas velocity of 112mm/s (a) increasing liquid velocity, and (b) decreasing liquid velocity. The liquid velocities increase left to right 2.8, 3.7, 6.1 and 7.6 mm/s. Reprinted from Lim et al. (2004), with permission from Elsevier. Copyright (2004).

Fig. 36. (a) The binary-gated map derived from the SD map shown in Fig. 34b. The pixels identified as being associated with local pulsing are identified as white pixels associated with constant gas-liquid distribution are identified as black, (b) The temporal autocorrelation function...

Besides PDMS and PET, the other polymer materials also attract increasing interests and have been synthesized hy various methods. For instance, localized pulsed laser irradiation was used to rapidly convert the pristine PI surface into an electrically... 

Cavitation near the liquid-solid interface differs from cavitation in the pure liquid. Near the solid surface, the bubble collapse becomes nonspherical and causes a shock-wave action on the surface. Velocity of microjets reaches hundreds of meters per second. The shock wave created by jets transfer strong local pulse, which is able to damage the surface of solids and crush brittle materials [248]. 

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