Equal angle spacing

Kinks due to equal angle spacing are eliminated (Figure 28). That is, bends would occur in the backbone where chain atoms were quaternary. (Because acyclic secondary atoms are normally arranged as if they were tertiary, kinking would not generally be a problem for these atoms.)... 

Fixed Angle Spacing Equal Angle Spacing... 

Figure 28 Fixed versus equal angle spacing. The backbone is indicated by dashed lines.

Equal angle spacing (EqAS, Figure 28) is the equal division of an atom s available circular area among its unplaced substituents. In general, this is 360°/N, where N is the number of substituents. 

Usually, two conformations are regarded as geometrically different if their minimized RMS deviation is equal to or larger than 0.3 A in Cartesian space RMSx z)> or 30 " in torsion angle space (RMSja). respectively. 

Sometimes it is claimed that the double-centered biplot of latent variables 1 and 2 is identical to the column-centered biplot of latent variables 2 and 3. This is only the case when the first latent variable coincides with the main diagonal of the data space (i.e. the line that makes equal angles with all coordinate axes). In the present application of chromatographic data this is certainly not the case and the results are different. Note that projection of the compounds upon the main diagonal produces the size component. 

An easy way of visualizing the structure of fullerenes is to make a physical model, for example, to assemble equal angle planar trivalent connectors and equal length plastic tubes. Mechanically, the polyhedron-like structure so obtained can be considered as a space frame with equal rigid nodes and equal elastic bars such that three bars meet and form angles of 120° at each node. The closed net shape arises by deformation of the bars in a state of self-stress. The edges of the polyhedron obtained... 

Minerals of the tetragonal system are referrable to three crystallographic axes that make right angles with each other. The two horizontal axes aj and a2 have equal atomic spacing but the vertical axis c has an atomic spacing that is not equal to aj or... 

Minerals of the hexagonal system, such as quartz, are referrable to four crystallographic axes. Three axes, a, a2 and lie in a horizontal plane and have equal atomic spacing with angles of 120° between the positive ends. The fourth axis, c, is vertical and at right angles to the plane of ai, a2, and 83 with a different atomic spacing. 

We consider here a few particular space groups. The fee BL is generated by three primitive translation vectors making equal angles with one another. 

Figure 3.26 shows the origin of the cone by a construction in direct space. The incident and reflected beams make equal angles with a straight line contained in the reflecting plane. From this we can deduce that the reflections of a beam of light, produced by a mirror that rotates about an in-plane axis, form a cone. 

This generalized yield condition, which is usually referred to as the von Mises yield condition, has a simple geometrical visualization in principal stress space of o i,o 2,o 3 shown in Fig. 3.2. There the line making equal angles with the three principal stress axes represents the locus of pure mean normal stress a, along which all deviatoric stresses vanish and no plastic flow can occur. Thus, plastic flow requires a critical deviation from this line in the radial direction away from it... 

Figure B2.3.6. CM angle-velocity contour plot for the F + D2 reaction at an incident relative translational energy of 1.82 kcal mol [26], Contours are given at equally spaced intensity intervals. This CM differential cross section was used to generate the calculated laboratory angular distributions given in figure B2.3.4. (By pennission from AIP.)...

For a two-dimensional array of equally spaced holes the difftaction pattern is a two-dimensional array of spots. The intensity between the spots is very small. The crystal is a three-dimensional lattice of unit cells. The third dimension of the x-ray diffraction pattern is obtained by rotating the crystal about some direction different from the incident beam. For each small angle of rotation, a two-dimensional difftaction pattern is obtained. 

Maximum shell-side heat-transfer rates in forced convection are apparently obtained by cross-flow of the flmd at right angles to the tubes. In order to maximize this type of flow some heat exchangers are built with segmental-cut baffles and with no tubes in the window (or the baffle cutout). Maximum baffle spacing may thus equal maximum unsupported-tube span, while conventional baffle spacing is hmited to one-h f of this span. 

Until Jenike developed the rationale for storage-vessel design, a common criterion was to measure the angle of repose, use this value as the hopper angle, and then fit the bin to whatever space was available. Too often, bins were designed from an architectural or structural-engineering viewpoint rather than from the role they were to play in a process. Economy of space is certainly one vahd criterion in bin design, but others must be considered equally as well. Table 21-14 compares the principal characteristics of mass-flow and funnel-flow bins. 

Dislocations are characterized by the Burgers vector, which is the exua distance covered in traversing a closed loop around die core of the dislocation, compared with the conesponding distance traversed in a normal lattice, and is equal to about one lattice spacing. This circuit is made at right angles to the dislocation core of an edge dislocation, but parallel to the core of a screw dislocation. 

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