Cross section undulations

Undulator radiation also has specific polarization properties, e.g., the fundamental radiation of a plane undulator as shown in Fig. 1.9 is completely linearly polarized, an undulator with helical magnetic structure produces circularly polarized light, and two crossed plane undulators with a dispersive section between them are capable of producing optional polarization which depends on the phase shift introduced by the dispersive element. 

The general shape of the cross sections as functions of E, n, and j resembles the initial distribution function in the electronic ground state. If the parent molecule is initially in its lowest vibrational state, the partial cross section behaves qualitatively like a three-dimensional bell-shape function of E,n, and j. If the photodissociation starts from an excited vibrational state, a(E, n,j) will exhibit undulations which reflect the nodal structures of the corresponding bound-state wavefunction [more of this in Chapter 13 see also Shapiro (1981) and Child and Shapiro (1983)]. 

Fig. 2.18 A cross-section of a much-quoted model (following Freeze and Cherry, 1979, who cited Hubbert, 1940). The surface is described as undulating in a mode that can be expressed by a simple mathematical equation, and the water table is assumed to follow topography in a fixed mode. The stippled section describes a water system from a low-order divide to a nearby low-order valley the thick lines mark there impermeable planes that are an intrinsic part of the U-shape flow paths model, enlarged in Fig. 2.19. The cross-section emphasizes topographic undulations and disregards the location of the terminal base of drainage and the location of the main water divide.

Fig. 5. Differential cross section (weighted with sin 9) as a function of the deflection angle 9 and the reduced parameter A = krm which is proportional to the velocity. The calculation was performed for a LJ 12-6 potential with B = 5000. In the upper part the total cross section multiplied by v° is plotted versus A. The close connection between the number of supernumerary rainbows and the number of the glory undulations is clearly demonstrated. Note that another rainbow oscillation is buried under the forward diffraction peak and not shown in the figure.

There are indications that the measured cross sections show undulations, as predicted by Olson (see equation 40). Unfortunately the resolution is too bad and the energy range too small to allow any conclusion to be drawn with respect to the potential energy curves. 

The fact that the LZ-theory describes the total cross sections so well, apart from the undulations, indicates that the information which can be extracted from these experiments is rather limited and only concerns the crossing point. More information on the dynamics of the collisions can be expected from the differential cross section, as we have discussed in Section I.A.2. 

A camera with a bent mirror/bent monochromator optics (Fig. 10a) has the advantage of a high flexibility in its focusing conditions and allows to minimize the beam cross section at the sample for a given SAXS-resolution, which is especially of interest for small samples like single muscle fibres. This implies that a high- i undulator will be used (Table 2). Note that beam compression via an asymmetric cut monochromator [32] is not necessary in view of the highly symmetric source. 

Center of mass differential cross sections (presented here only for 0( D) + H2) present a quasi forward-backward symmetry and small undulations. The degree of polarisation (ratio of DCS for forward/sideways or backward/sideways) is high ( 3) for initial rotational state j = 0 and decreases with j. The for-... 

The fabrics are made by crossing thick tows of glass or graphite fibres these tows are undulating, as can be seen in any cross-section. Any attempt to include an optical fibre inside the tow will cause a continuous bending of the OF, with large optical losses the optical signal will be lost in less than 50 cm. Even when the OF is located at the surface of the fabric, if squeezed... 

Fig. 10.2 Two bars a perfect bar with initial cross-sectional area Aq and an imperfect bar with periodic undulations of wave length X having an average area (dA/dz)dz = Aq.

In contrast, the AFM pictures as well as cryo-TEM of sample CB-PLL55 prepared from 5 mM NaBr aqueous solution (Fig. 20) show extended cylinders. The cylinders exhibit undulations of the cross-section that are reminiscent of the pinned clusters [74, 91] postulated by scaling arguments. The occurrence of pearl-necklace-type structures, where pinned clusters of side chains alternate with regimes that are almost free of side chains, has also been seen in simulations of bottlebrushes, provided one has poor solvent conditions. These clusters are formed by collective collapse of several neighboring side chains [92]. We return to this problem in Sect. 3.5. 

Tear Fracture. Normal stresses, such as flexure, that are distributed unevenly across the cross section may cause the material to tear from an external or an internal surface, eg, from a material defect. In such cases, the peaks stand at an angle in the fracture surfaces. If elongation is imiform, rims form at the crack front that remain visible in both fracture surfaces as beads with undulating crests after separation (Fig. 4). Further characteristics of tear fracture are V- and U-shaped ramps, whose tips point against the direction of fracture propagation. 

---