Spherical angle model

Note that the polar angle is again defined as 0 = n at the front stagnation point and 0 = 0 at the back. We thus see that either the interface velocity is zero or that T = 0 and the tangential-stress must be continuous across the interface [see, e g., (7-264)]. This physical picture has been called the spherical-cap model. It is sketched in Fig. 7 20. The problem then is to determine the velocity fields in the two fluids and determine the critical angle 0C. 

When the Gaussian curvature of the surface is not constant (for example, for a prolate spheroid) the wave s tip experiences varying curvature F as it moves over the surface. This results in the systematic drift of spiral waves on the nonuniformly curved surfaces [51 ]. To check this prediction, the numerical simulation of the spiral wave on the surface of a prolate spheroid has been performed in [28] using full reaction-diffusion equations of the model (60)-(62). Figure 13 shows the computed trajectory of motion of the tip of a spiral wave on the coordinate plane (0, ) where 6 and are the spherical angles. We see that the spiral wave drifts approximately along the equator of the spheroid. 

Fig. 9. A, Model for the apex of a carbon nanocone with a cone angle of 19.2 [94] B, polyhedral and spherical forms of a multiwall carbon particle formed from and...

Muller et al. focused on polybead molecules in the united atom approximation as a test system these are chains formed by spherical methylene beads connected by rigid bonds of length 1.53 A. The angle between successive bonds of a chain is also fixed at 112°. The torsion angles around the chain backbone are restricted to three rotational isomeric states, the trans (t) and gauche states (g+ and g ). The three-fold torsional potential energy function introduced [142] in a study of butane was used to calculate the RIS correlation matrix. Second order interactions , reflected in the so-called pentane effect, which almost excludes the consecutive combination of g+g- states (and vice-versa) are taken into account. In analogy to the polyethylene molecule, a standard RIS-model [143] was used to account for the pentane effect. 

For a number of 1907 acentric reflexions up to 0.463 A resolution, the mean and rms phase angle differences between the noise-free structure factors for the full multipolar model density and the structure factors for the spherical-atom structure (in parentheses we give the figures for 509 acentric reflexions up to 0.700A resolution only) were (Acp) = 1.012(2.152)°, rms(A( >) = 2.986(5.432)° while... 

Modeling the initial structure by spherical domains in a bcc-lattice1, the theoretical intensity along the ellipsoidal ridge as a function of the angle y1 between fiber axis and the direction of the radial beam is... 

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