Critical cutting radius

An initial distribution function within geminate pairs directly defines their stability. In terms of the black sphere model, dissimilar defects (v, i) disappear instantly when approaching to within, or when just created by irradiation at the critical relative distance tq (called also clear-cut radius) - see... 

A pulling/cutting device two opposed rolls that rotate and trap between them one or more roving, pulling them from their storage. A blade - held in one of the two rolls -forces the fibres to bend beyond their critic radius until they break ... 

The complex phase speed must lie inside a closed region of the complex phase speed plane with abscissa Cr and ordinate C as in Fig. 6. Because the upper half plane represents unstable perturbations, the complex phase speed c for an instability must be located within the semicircle with radius Ur and center at 0). Part of the semicircle is cut off because it may be shown that Cr < Umax- It may be demonstrated that as wavenumber k approaches zero, the growth rate must also approach zero. Furthermore, with the exception of the small region within the semicircle to the left of i/min barotropic instabilities always have a critical level yc, where Cr — u(yc) = 0. 

Fig. 6.29. The critical mismatch strain Cm, plotted as a function of normalized quantum wire height h/b, for core cut off radius Tq = 6/2, as determined by the computational procedure based on Figure 6.28 adapted from Freund and Gosling (1995). The shaded area represents the range of values of mismatch strain and wire size within which degradation of the optical characteristics was observed to occur. Adapted from Arakawa et al. (1993).

The physical system studied is depicted in Figure 7.1. A thin film of thickness h is epitaxially bonded to relatively thick substrate, and the lateral extent of the interface is assumed to be very large compared to h. The lattice mismatch between the film and substrate materials is represented by the mismatch shear strain 7m. Prior to formation of any dislocations in the film, the elastic strain in the film is uniform and is given by xz = lyz = 0. Dislocation formation occurs at the expense of the energy stored in this strain field. The critical thickness condition for dislocation formation is given in (6.46) for general cut off radius ro, and it is restated here for the particular value Vo= as... 

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