Tangential plane

Beriihrung, /. contact touching tangency. Beruhnmgs-ebene, /. tangential plane. - lek-triziUlt, /. contact electricity, -fiache, /. sur-... 

A section in the full-bed models was isolated that was comparable to the WS model. The layout of these different sections was identical, except that the WS model had a two-layer periodicity and the full-bed models had a six-layer periodicity. To be able to make direct comparisons of velocity profiles, several sample-points needed to be defined. In the three different models seven tangential planes were defined and on each plane three axial positions were defined. This reduced the data to single radial velocity profiles at corresponding positions in all three models, as shown in Fig. 10, for the WS model. Identical planes were defined in the full-bed models. Some spheres and sample planes 4 and 5 are not displayed to improve the visibility of the sample planes and lines. In the right-hand part of the figure, plane 4 is shown with the axial positions at which data were taken and compared. 

Fig. 10. Comparison section with seven tangential planes and axial profile lines indicated.

Consider two frictionless spheres in contact as shown in Fig. 2.9. M is a point on the surface of sphere 1 with a distance r from the Z -axis. N is the opposite point on the surface of sphere 2 with the same distance r from the Z2-axis. O is the contact point and also serves as the origin of both Zi-axis and Z2-axis. N, M, and O are in the same plane. The distances from M or N to the tangential plane which is normal to the Z i -axis and Z2-axis are denoted by i and Z2, respectively. In Fig. 2.9, the triangle O2AO is similar to the triangle NBO. Hence, the theorem of similarity of triangles gives... 

From the three-dimensional projection of the response surface in Fig. 7 it is seen that there is a maximum point on the surface within the explored domain. At this maximum point, the tangential plane to the surface has a zero slope in all... 

Growth rings and the types and distribution of cells therein give rise to the situation whereby the general structure of wood tissue can be referenced by three major planes or surfaces. Each surface has a unique appearance that stems from the manner in which cells of specific orientations are cut by planes directed either parallel or perpendicular to the tree s longitudinal axis. These three planes are the cross-sectional or transverse plane, the radial plane, and the tangential plane. They are illustrated and defined in Figure 7. 

The POAVI analysis [16] of the bond-equalized structure leads to s - p hybridization for the n orbital and sp -2 8 hybridization for the three a orbitals. The angle between the a and it orbitals is found to be 101.6°, and hence the abends may be considered to be inclined at an angle of 11.6° below a tangential plane to the surface (this angle is 0° in... 

Quantitative studies on the distribution of respiratory tract DC populations, at least those present within the epithelium of the conducting airways, has been facilitated by the development in our laboratory of techniques for sectioning isolated airway segments in a tangential plane parallel to the long axis of the airway (Holt et ol., 1989,... 

If there is a true optimum within the explored domain there will be a turning point on the response surface which will either be a maximum or a minimum. A tangential plane to the surface at this point will have a zero slope in all directions. This is equivalent to saying that the partial derivatives of the response surface model with regard to all experimental variables will be zero at this point. 

It follows from the mapping of the points on a sphere to a tangential plane using central or gnomonic projection through the centre O of the sphere as... 

Aiming to analyze the direction of this vector in relation with the dispersion described by the Eq. (5.196), a tangential plane to DS is considered, so that the modified wave vector of transmitted direction... 

At all other dividing surfaces than the surface of tension, the mechanical tensions in the tangential plane at a certain point are given by a surface tension tensor different from This tensor as can be written as ... 

By inserting a A plate at an angle of 45° to the polarizer/analyser pair, quadrants 1 and 3 of the spherulites appear either blue or yellow, and quadrants 2 and 4 of the spherulites appear with the reverse colour. This colour combination shows the sign of the spherulites. Negative spherulites, the common case, have a higher refractive index in the tangential plane than... 

Figure 2 elucidates this formula. At E=E(Xi,X2) we define the tangential plane of the PES. Its slope is given by the partial derivatives (8E/8Xi)= gi and (dE/ax )==g, which we collect in the gradient vector g=(gi,g2). g(x) is independent of the terms of second order which form the harmonic part of the surface. This part may be characterized by the distances over the corners of the tangential plane sector. We denote the purely harmonic terms with... 

By constructing PV we obtain the derivative in the tangential plane of the hypersurface E const. In the direction of this tangential plane we have to satisfy the extremal condition... 

Figure 30. Dupin s cyclides and their deformations, (a) A toroidal Dupin cyclide and its circular lines of curvature y and /, the planes of which intersect along the axes A (joining O and Q) and A, respectively. Two tangential planes along two symmetrical circles T intersect along A. (b) A parabolic Dupin s cyclide, with its two focal parabolae P and P, its circular curvature lines y and /, and its axes A and A, (c) Three parallel, but separated, parabolic Dupin s cyclides. The lines represent sections by planes x=0,y = 0 and = 0 at the top of the figure, two conical points are present, as in (b), but the spindle-shaped sheet has been removed (Rosenblatt et al.

The projection of the relative velocity onto the tangential plane is denoted through t. If the tangential force component exceeds a critical value, which by Cundall and S track is the Coulombic friction iiF , the spring will be set to... 

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