Orthogonal intersection

The lowest order contributions to the energy are described by the conical parameters g, h, and s, k = x,y,z, or by d, A = 1,2 and s, k = x,y,z-Here and below the superscript ij is suppressed when no confusion will result. We also will use the nonrelativistic convention g - x,fi" y and h J z, where is real is parallel to. These parameters [9] are reported in Figure 4a and b. Their continuity is attributable to the use of orthogonal intersection adapted coordinates. For comparison, Figure 4a and b reports the nonrelativistic quantities g , and s, respectively. While noting that there is no unique correspondence... 

Titanium disulfide can also be made by pyrolysis of titanium trisulfide at 550°C. A continuous process based on the reaction between titanium tetrachloride vapor and dry, oxygen-free hydrogen sulfide has been developed at pilot scale (173). The preheated reactants ate fed iato a tubular reactor at approximately 500°C. The product particles comprise orthogonally intersecting hexagonal plates or plate segments and have a relatively high surface area (>4 /g), quite different from the flat platelets produced from the reaction between titanium metal and sulfur vapor. The powder, reported to be stable to... 

Intersecting spheres, radii a and 2, with orthogonal intersection... 

These results can be simplified by introducing scaled orthogonal intersection adapted coordinates x =, y = and z = In these coordinates,... 

So-called orthogonal intersection occurs for an infinite value of this tangent, that is, for p= (v -l)/2 = l/, the inverse of the golden ratio, whieh Yablonsky et al. (2010) call the... 

Examples of orthogonal intersection adapted coordinates are provided in Sec. 4. 

Figures 6(a) and 6(b) report the conical parameters Sy and g, h, respectively, obtained from orthogonal intersection adapted coordinates. If orthogonal g and h had not been used g and h would vary erratically along the path, making interpolation and extrapolation impossible. Significantly, from Figs. 6(a) and 6(b), it can be seen that although these conical parameters are by no means constant, the inequalities > g > h, discussed above for Tl trans,p, 2.95), are, in a qualitative sense, typical.

Similarly the M = 2 case is also the 3D extension of the squares v — l jkm) = 0). It consists of two orthogonally intersecting sets of lamellae corresponding to prisms with a square section when this section is made perpendicularly to ki x k2. They are also unstable when go < gND-... 

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