Curvature main direction

Every minimization departs from an initial estimation for the vector field. The minimizations were carried out with a starting configuration obtained by randomizing the coefficients aj and a the resulting vector field has no preferential orientation and the distribution of curvature in the simulation box exhibits a long tail mainly due to abrupt changes in the direction of the stream lines (see Fig. 3.2A). 

In the persistent chain there are no points of easy bending the persistent macromole-cule prefers the conformations exhibiting a constant small curvature. Thus, as soon as the chain elements in the liquid-crystalline globule are oriented mainly in the tangential direction (see Sect. 4), the small globule formed by the persistent chain must display the tendency to form the cavity in the middle of the globule. In this case, the globule assumes the shape of either a torus or a spherical layer. 

Such an inductor generates a temperature field of almost square symmetry. The main slit in the inductor, which forms the current loop, however, is not completely equivalent to the other three slits as seen in Fig. 3.9b. Furthermore, the surface tension surrounds the corners by minimizing the melt surface, which is not desired because the goal are quadratic wafers directly cut from the crystals. Additionally, on the straight sides, where the horizontal curvature is almost zero, growth instabilities can occur. Regarding the application for the solar industry, which would save material loss and the costs of cutting the round crystal into a square one, it is essential to get a stable... 

Clavin [5] performed quasi-steady analysis of the direct initiation process. They developed the critical curvature model, which states that the failure mechanism of the detonation is mainly caused by the nonlinear curvature effect of the wave front. Eckett et al. [6] proposed the critical decay-rate model and pointed out that the critical mechanism of a failed detonation initiation process is due to the unsteadiness of the reacting flow. Their theory for spherical detonation initiation has been supported by numerical simulation and experimental data. 

From the above examples, it may be concluded that simple thermodynamic information, as boiling points of pure components and azeotropes, is sufficient to sketch the main features of a RCM, as the direction of trajectories and distillation boundaries. However, drawing correctly the curvature of boundaries needs accurate knowledge of phase equilibrium. 

---