Elliptical ridges

Fig. 9. Top H-2D exchange spectrum of dimethylsulfone. The inset shows the corresponding theoretical spectrum for a two-site jump with a jump angle of 106°. The angular information is encoded in the shape of the elliptical ridges perpendicular to the main-diagonal spectrum. Bottom Theoretical ridge pattern (contour plots) for different jump angles. (Adapted with permission from Refs. 138,140.)...

Fig. 9.25 A static exchange experiment recorded for a sample of methyl-deuterated isotactic polypropylene (iPP) at T = 387 K. The observed elliptical ridges are characteristic of...

According to his deduction the common finding of ellipsoidal deformation of the reflections is indicative for affine deformation. Moreover, he arrives at an equation that permits to determine with high accuracy the microscopical draw ratio, Xd, of the structural entities from the ellipticity of the deformed Debye sphere. This value can be compared to the macroscopical draw ratio. Even the intensity distribution along the ellipsoidal ridge is predicted for a bcc-lattice of spheres, and deviations of experimental data are discussed. 

In Figure 14b we show the potential energy surface for a model elliptic conical intersection46 plotted in the branching plane (xt, x2). Because, as stated earlier, the cone is elliptic in the linear approximation (i.e., the base of the cone is an ellipse rather than a circle), there are two steep sides of the ground state cone surface and two ridges . There are two preferred directions for downhill motion located on the steep sides of the ground state cone surface. A simple... 

Both males and females carry horns, which are long, slightly curved and elliptical. The inside of the curve, close to the base, is ridged. They are usually an almost even, dark brown to black in colour, though the horns of a young animal can be paler and show more colour variation (Fig. 7.2). The horns are mostly hollow with a solid tip, but are thicker than ox horn. 

The response surfaces in Figs. 2 and 3b are a part of distorted parabolic cylinder, which show a minimum ridge in the experimental domain. The response surface in Figure 3a is an inverted paraboloid (dome), and the corresponding contour plot is elliptical. The stationary point, which is the point at which the slope of the response surface is zero when taken in all directions, on this surface is within the design domain however, it is a minimum point. The response surfaces in Figs. 4a and 4b have a saddle behavior or minimax nature. The stationary point is not a maximum or a minimum point, but a saddle point. 

In Figure 2.20b these transition structures locate the energy ridges that separate the IRD valleys located by Mi and Mg. Thus, although there is no analogue of the transition vector for a conical intersection, the simple case of an elliptic cone shows that the IRDs are still uniquely defined in terms of Ml and Mg. 

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