Vector diagrams

Figure B2.3.2. Velocity vector diagram for a crossed-beam experiment, with a beam intersection angle of 90°. The laboratory velocities of the two reagent beams are and while the corresponding velocities in the centre-of-mass coordinate system are and U2, respectively. The laboratory and CM velocities for one of the products (assumed here to be in the plane of the reagent velocities) are denoted if and u, respectively.

Fig. 1. Contact angles. The shapes of drops that are A, wetting and B, nonwetting with respect to the soHd (B), and C, penetration of a wetting Hquid into a pore to compress the gas (D) inside. The vector diagram shows the balance of forces at the perimeter of the Hquid drop on the soHd plate.

Figure 4 Schematic vector diagrams illustrating the use of coherent inelastic neutron scattering to determine phonon dispersion relationships, (a) Scattering m real space (h) a scattering triangle illustrating the momentum transfer, Q, of the neutrons in relation to the reciprocal lattice vector of the sample t and the phonon wave vector, q. Heavy dots represent Bragg reflections.

Veitstanz, m. St. Vitus s dance, chorea. Vektorengleichung,/. vector equation. Vektorgeriist, n. vector diagram, vektorieil, a. vectorial. 

Note 9 = vector diagram angle of current between apparent power and active power Reactive power = EISin9, or VAR, or kVAR Compute power factor ... 

Figure 4-225. Vector diagram of the inclination measurement with three accelerometers.

Figure 4-231. Vector diagram for the tool-face determination.

Figure 4-234. Vector diagram showing the mud motor axis as weil as the steering tooi axis.

Figure 3. Wave vector diagram for the reaction X + HD + - XI+ + J where I and J may he H or D according to the isotopic product considered...

Consider the wave vector diagram in Figure 3, where... 

A convenient way to understand the modern 2D NMR experiment is in terms of magnetization vectors. Figure 3.2 presents a pulse sequence and the corresponding vector diagram of a 2D NMR experiment of a single-line C spectrum (e.g., the deuterium decoupled C-NMR spectrum of CDCl,). 

J.C. Gower, Adding a point to vector diagrams in multivariate analysis. Biometrika, 55 (1968) 582-585. 

Fig. 2.1.12 Vector diagram of the velocity distribution of flowing water driven by a paddle with holes. The diagram was calculated by the AM IRA software (http //ami ra.zib.de).

If the structure of a molecule and the bond moments are known, an approximate dipole moment can be obtained by treating the polar bonds as vectors. Figure 6.1 provides the vector diagram from which we obtain the resultant for two bonds as... 

Figure 10.4 Vector diagram of the effect of convolution of many structure factors in reciprocal space. In (a) is shown the true structure factor (thick arrow) and the initial, unmodified structure factor (thin arrow). In (b) the convolution operator applied to the initial structure factor (thin arrow) results in a closer estimate (dashed arrow) of the true structure factor (thick arrow).

Fig. 146. Anomalous scattering in a non-centrosymmetrie crystal. Effect on -f and — reflections. Left representation of amplitudes and phases of waves. Right corresponding vector diagrams (scale of amplitudes doubled), a and b 002 and 002 reflections of structure of Fig. 145, when scattering is normal for both atoms, c and d the same reflections when scattering is anomalous for atom giving wave E.

The usefulness of the F2 synthesis is subject to the inherent limitation of a vector diagram vectors are all erected from a single point. The vector diagram, when obtained, must be interpreted in terms of actual atomic coordinates. (For the relations between peak positions on vector maps and the equivalent points in the 17 plane-groups, see Patterson, 1935 6.) For simple structures this presents little difficulty,... 

Fig. 223. Fourfold positions in space-group P4l21. a. View along 110. b. Corresponding vector diagram.

For a single valence electron S is equal to and there are only two possible values for J, namely, L + and L — J. Vector diagrams showing the composition of the spin angular momentum and the orbital angular momentum for the two states and 2Df are shown in Figure 2-10. 

Figure 10.2 Vector diagrams showing how a threefold rotation transforms v into vi, and how the latter is a linear combination of v and v36 specifically, vi = — h 3, +...

Fig. 2.50. Generation of /-resolved two-dimensional 13C NMR spectra (a) flux diagram (b) /-modulation of Cl l doublets, CH2 triplets and CH3 quartets during evolution, vector diagrams in the x y plane and cosine curves described by the signal maxima (c) series of 13C NMR spectra of CHn groups with t1 dependent /-modulation of the signal amplitudes (d) series of /-resolved two-dimensional 13C NMR spectra formethine, methylene and methyl carbon atoms, stacked plots and contour plots (e).

When the X-ray wavelength is near the heavy-atom absorption edge, a fraction of the radiation is absorbed by the heavy atom and re-emitted with altered phase. The effect of this anomalous scattering on a given structure factor fhp in the heavy-atom data is depicted in vector diagrams as consisting of two perpendicular contributions, one real (AFr) and the other imaginary (AFj). 

Fig. 10.21. Schematic illustration of the angular momentum vectors in the photodissociation of H2O2. The left-hand side depicts the situation before the dissociation. The right-hand side shows the appropriate vector diagrams before and after the dissociation.

Figure 2.8 is a vector diagram describing the principal axes of the refractive index tensor of this material. Using equation (2.47), the Jones matrix is given by (2.46) with parameters ... 

Figure 2.8 Vector diagram of the refractive index tensor for a material with noncoaxial...

Figure 5.4 Vector diagram describing the orientation of the absorption cross section tensor...

Fig. 9.28 Velocity vector diagram for calculating the velocity difference between barrel and solid plug. This is the velocity of the barrel surface observed by a viewer on the plug the direction of its...

Fig. 10.15. Vector diagram (left frame) of feature misalignment in a composite stamp designed for an active matrix circuit for a display. The histogram in the right frame shows the distribution of alignment errors observed in this system. These micron-level...

Fig. 10.29. Distortion measurements collected at 36 points equally spaced across a 12-inch x 12-inch stamp supported by a 250 pm thick Mylar backing. In this case a vacuum plate was used to hold down the Mylar backing on the glass master during the composite stamp curing step (67 °C on a hot plate for 18 h). (a) The top frame shows a vector diagram...

---