Cummings collapse

As can be seen from Fig. 13, the first peak of the goH(r) correlation function broadens and shifts to longer distances, while the first minimum rises on approaching the critical conditions. In the supercritical state, represented in plot 3, a sharp decrease in the intensity of the first peak can be observed. Although it does not correspond exactly to a complete collapse of the peak, such behaviour is undoubtedly in much closer qualitative accordance with the experimental findings and with the recent simulations performed by Chialvo and Cummings [60] by means of a properly modified model potential. 

Nevertheless, immiscibility and Al-Si ordering are minimized when specimens anneal at high temperatures for long periods and then are rapidly quenched. In natural and synthetic specimens that have experienced such cooling histories, the effects of cationic substitutions can be analyzed independent of other factors. For instance, a number of authors have examined transition temperatures from CUm to CT symmetry in completely disordered alkali feldspars (Nai- cK cAlSisOg), and the results (Fig. 26) indicate that the critical temperature decreases linearly with K content, since the larger K cation inhibits structural collapse (Kroll et al. 1980, 1986 Salje 1985, Harrison and Salje 1994... 

It can be shown that cavitation probably does not occur at the equilibrium bubble size at atmospheric pressure. However, the bubble can be driven to cavitation by reducing the pressure. Conversely, higher pressures require greater ultrasonic energy to induce cavitation. This leads to a larger intensity of cavita-tional collapse and therefore to a considerably enhanced ultrasonic effect, as demonstrated in the oxidation of indane to indane-l-one using potassium permanganate (Cum et al., 1988). 

As first shown by Cummings [16], p.(t) first exhibits a collapse, i.e., there is a range of interaction times for which p (t) becomes essentially independent of time, and this, in the absence of decay mechanisms in the model. This collapse is described 2in the case of resonant excitation by the approximate envelope exp(g t /2), independent of the photon number . (This independence does not hold for nonresonant excitation.) For longer times, p (t) exhibits then recorrelations (revivals) and starts oscillating again in a very complex way. The recorrelations occur at times of the order [18]... 

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