Growth isotropic

Since there is an isotropic growth stress in the plane of the oxide it is necessary to consider the two principal stresses and given by... 

Fig. 2.3 The development of polarity and asymmetric division in Saccharomyces cerevisiae. The diagram is reproduced in a slightly simplified form from the work of Lew Reed (1995) with the permission of Current Opinion in Genetics and Development, (a) The F-actin cytoskeleton strands = actin cables ( ) cortical actin patches, (b) The polarity of growth is indicated by the direction of the arrows (arrows in many directions signifies isotropic growth), (c) 10-nm filaments which are assembled to form a ring at the neck between mother and bud. (d) Construction of the cap at the pre-bud site. Notice that the proteins of the cap become dispersed at the apical/isotropic switch, first over the whole surface of the bud, then more widely. Finally, secretion becomes refocussed at the neck in time for cytokinesis, (e) The status and distribution of the nucleus and microtubules of the spindle. Notice how the spindle pole body ( ) plays an important part in orientation of the mitotic spindle.

The structural and equilibrium forms of crystals are predicted assuming that the crystal is perfect and that the ambient phase is isotropic. Growth forms, however, describe real crystals containing lattice defects growing in a real ambient phase. We should therefore consider the following factors, which may affect the growth forms. 

Number of Nuclei Expected in the Time Cone, (N)c. For time-dependent nucleation rates J (t) and isotropic growth rates R (t) (such as in nonisothermal transformations under conditions in which thermal gradients can be neglected), the number of nuclei in Vc is given for the d = 3 case as... 

This model simplifies in the case of isotropic growth where the perpendicular and parallel rates are equal (a = b). This simplification was found to be suitable for describing the kinetics of CBD CdS in [30]. When coalescence is complete 6 — 1), the exponential term in (37) disappears and the predicted deposition rate is hence-forth constant with time (linear regime). 

For a time-independent constant growth rate u and assuming isotropic growth (i.e., spheres), the radius of the sphere after time t will be... 

Figure 6.4 (a) Determination of the crystal growth rates of COM crystals reference and reduced growth rates in the presence of citrate, (b) Isotropic growth of the control sample (top) and inhibited growth in the presence of citrate (bottom) (19). 

The transition from the solely anisotropic growth of the CdS shell at low temperatures (120 °C) to isotropic growth at 280 °C can be explained if we consider both thermodynamic and kinetic factors affecting the shell growth. The difference... 

The procedure for the determination of the whole course of conversion in the overall time t depends on the analytical expression of the instantaneous volume of the crystallized phase V(t) as a function of the rates of nucleation dN/dt and growth dG/dt. This volume of nuclei capable of further spontaneous growth at time x is, e.g., = (4/3)tik,t(t-T/ for the case of 3-D isotropic growth... 

The predictions based on this model have been well confirmed by experimental observations. Materials characterized by large entropies of fusion freeze with a faceted interface morphology, while materials with low entropies of fusion exhibit under similar conditions the nonfaceted interface morphologies characteristic of nearly isotropic growth. Examples of such morphological differences are shown by Jackson in Chapter 12 of this volume. 

Figure 9.5. Isotropic growth on a surface (a) outward development (b) inward development...

In the isotropic growth, the three motion velocity components of the interfaces are identical and thus the formed solid can have the shape of a portion of sphere (Figure 9.5). 

Ultimately, it is noted that in all the cases, except that of the isotropic growth on a sphere (also true for a cylinder) with inward development and the rate-determining step located at the internal interface, the space function of growth of a nucleus is a monotonous function of time, either constantly increasing or constantly decreasing, or constant in time if the active surface is of invariable area. 

Two-process model with surface nucleation and isotropic growth 10.5.1. Qualitative approach... 

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