Coordinate system, used to describe

Figure 8.3. Spherical polar coordinate systems used to describe the fluorescence excitation problem.

Figure 8.8. Coordinate system used to describe the orientation of a dipole on the surface of a spherical particle.

Fig, 5. Coordinate system used to describe inert gas, hydrogen halide complexes. (Reproduced from Ref. 

Arbitrariness One hears comments that graph descriptors being arbitrary, do not have a deep physicochemical significance A misconception here is in confusing an input with an output of a mathematical treatment of a problem Surely die choice of descriptors selected to characterize grains is at the disposal of an investigator, hence arbitary But the same is true of a choice of coordinate systems used to describe a system of classical physics, or the choice of basis functions to compute a molecular structure in quantum chemistry I In each case we speak of input information, and the outcome of the analysis undertaken (when a complete basis is taken) does not depend on the choice of descriptors (coordinates) However, the amount of work, even its mere feasibility, will differ A poor selection of basis functions may... 

Figure 5.21. Imaging a spherical inclusion by phase contrast, (a) Coordinate system used to describe the inclusion, (b) Plot of Eq. (5.32). (c) Calculated intensity profile across the inclusion.

Figure 3.2 Coordinate system used to describe a single scattering event between a neutron of initial wave vector (ko) and a bound nucleus positioned at the origin.

To make practical use of fillers, a knowledge of filler orientation during the flow is needed The best description of orientation principles can be obtained from modelling Figure 9.10 gives the coordinate system used to describe orientation of fibers. 

Figure 7.1 Local coordinate system used to describe the direction of propagation and polarization state of a plane electromagnetic wave at the observation point O.

Figure 1. Overhead and side views of the coordinate system used to describe resist spin coating. The wafer revolves along the z-axis at an angular speed u>. The disk has a radius R. Film thickness, 6, is a function of time and radial position, r.

Figure 4.5. Coordinate system used to describe SRG inscription, with x running along the direction of light modulation. The two incident beams have their polarization state controlled. The s polarization is parallel to the surface, whereas the p state is parallel to the plane-of-incidence.

It is useful to describe the curvature tensor by its invariants, since these quantities do not change if one rotates the coordinate system used to describe the surface the invariants are intrinsic properties of the surface. For the implicit representation of the surface, F(jc, y, z) = 0, the curvature along a general direction is related to the tensor, Q, defined in Eq. (1.104). In three dimensions, Q is a 3 x 3 matrix with three eigenvalues. One can show by... 

Coordinated Reference coordinate system used to describe the properties in the direction of the principal axes (x and y). 

Figure 8.12 Polar and cartesian coordinate systems used to describe stress field around a crack.

Fig. 7.2. Polar and Cartesian coordinate systems used to describe the position of an electron in the hydrogen molecule ion. The stippled lines indicate a plane containing the z-axis and the electron.

Figure 3.9 The coordinate system used to describe the light propagation in the Berreman 4x4 method.

Fig. 1. The Arrangement of Two Molecules and a Diagram Showing the Coordinate System Used to Describe the Relative Position of Molecule II with Respect to I. The molecules are shown in the best arrangement, which is also described in Table II and Figure 5. The molecular model is displayed with single vectors connecting a carbon atoms, and the hemes are represented by filled black squares. The coordinate system shown is that used to describe the primary contact. The secondary contact is generated by a rotational transformation about the helix axis of the filament which arises from the repeated application of the primary pairwise relationship.

The coordinate systems used to describe propagation of light in hehcal medium. 

Like the stress tensor, the deformation gradient has up to nine components, each with a scalar magnitude dxildxj and two directions for each of them. One direction comes from the unit vectors of the coordinate system used to describe x and the other from the x unit vectors. And like the stress tensor, F is a machine, a mathematical operator. It transforms little material displacement vectors from their past to present state, faithfully following the material deformation. 

Figure 3.12. The xyz coordinate system used to describe the orientations in space of orbitals around the nucleus of an atom.

Fig. 2. The coordinate system used to describe the orientation of the optic axis a in volume-element j with respect to the optic axis a in volume-element i and the vector r j connecting both the elements.

Fig. 3.6 Rectangular coordinate system used to describe a freely-jointed polymer chain of displacement length r with one end fixed at the origin O.

The center-of-mass coordinate system used to describe the scat- tering of an atom from a linear rigid rotor is shown in Fig. 6. R,... 

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