Doughnut-shaped

The intensity of the vertically polarized scattered light is proportional to sin 0 which, in polar coordinates, is described by a figure 8-shaped curve centered at the origin and having maximum values of 1 at 0 = 90°, Because 0 is symmetrical with respect to the z axis, this component of scattered light is described in three dimensions by a doughnut-shaped surface in which the hole has shrunk to a point - centered symmetrically in the xy plane. 

Dielectric Constant The dielectric constant of material represents its ability to reduce the electric force between two charges separated in space. This propei ty is useful in process control for polymers, ceramic materials, and semiconduc tors. Dielectric constants are measured with respect to vacuum (1.0) typical values range from 2 (benzene) to 33 (methanol) to 80 (water). TEe value for water is higher than for most plastics. A measuring cell is made of glass or some other insulating material and is usually doughnut-shaped, with the cylinders coated with metal, which constitute the plates of the capacitor. 

Refer to Fig. 15-39. The tower is formed into compartments by horizontal doughnut-shaped or annular baffles, and within each compartment agitation is provided by a rotating, centrally located, horizontal disk. Somewhat similar devices have been known for some time. The features here are that the rotating disk is smooth and flat and of a diameter less than that of the opening in the stationaiy baffles, which facihtates fabrication and apparently improves extraction rates. The typical proportions of the internals of the RDC are as follows ... 

Under the hghtest winds, the air rises over the warmest part of the urban core, drawing cooler air from all directions from the surroundings (Fig. 17-21). Subsidence replaces this air in rural areas, and a closed torus (doughnut)-shaped circulation occurs with an outflow above the urban... 

Thunissen, A.-M., et al. Doughnut-shaped stmcture of a bacterial muramidase revealed by x-ray crystallography. Nature 367 750-753, 1994. 

The plasma is initiated by a spark from a Tesla coil probe and is thereafter self-sustaining. The plasma itself has a characteristic torroidal doughnut shape... 

To obtain pictures of the orbital ip = R0< >, we would need to combine a plot of R with that of 0, which requires a fourth dimension. There are two common ways to overcome this problem. One is to plot contour values of ip for a plane through the three-dimensional distribution as shown in Figures 3.8a,c another is to plot the surface of one particular contour in three dimensions, as shown in Figures 3.8b,d. The shapes of these surfaces are referred to as the shape of the orbital. However, plots of the angular function 0 (Figure 3.7) are often used to describe the shape of the orbital ip = RQ because they are simple to draw. This is satisfactory for s orbitals, which have a spherical shape, but it is only a rough approximation to the true shape of p orbitals, which do not consist of two spheres but rather two squashed spheres or doughnut shapes. 

Concerning the nature and structure of such amyloid peptide or protein channels, oligomers with annular morphologies have in fact been observed by EM for a-synuclein (Lashuel et al., 2002) and equine lysozyme (Malisauskas et al., 2003) even in the absence of any lipids or membranes. Channel-like structures have also been reconstituted in liposomes and observed by SFM for A/ i 4o, A/ j 42, human amylin, a-synuclein, ABri, ADan, and serum amyloid A (Fig. 5A Lin et al., 2001 Quist et al., 2005). Doughnut-shaped structures with a diameter of 10-12 nm and a central hole size of 1-2 nm (Fig. 5B) were imaged on top of lipid membranes (Quist et al., 2005). However, the radius of curvature of the SFM tips meant that it is not possible to say whether the pores were really traversing the lipid bilayer. 

We will pick as our system a small, doughnut-shaped element, half of which is shown in Fig. 2.9. Since the fluid is incompressible there is no radial flow of fluid, or V, = 0. The system is symmetrical with respect to the angular coordinate (around the circumference of the pipe), and therefore we need consider only the two dimensions r and z. The forces in the z direction acting on the element are... 

Cyclodextrins are cyclic oligosaccharides made up of several o-glucose units. Depending on the number of units, these doughnut-shaped molecules are able to host different sized molecules or the same molecule with different association... 

Cyclodextrins are doughnut-shaped, macrocyclic oligosaccharides constructed of glucose units linked by a a(l - 4) bond. Hexamer, heptamer, and octamer are the most common, often called the a-, / -, and y-cyclodextrins, respectively (Fig. 1). Although cyclodextrin has been known as one of the oligoglucoses produced by Bacillus macerans since 1891 (2), its spectacular behavior as the possible enzyme model was first observed by Cramer and his co-worker (J). 

Cyclodextrins, also called cycloamylases, doughnut-shaped oligosaccharides, have attracted much attention as enzyme models. Although this area of research was surveyed in Volume 23, much subsequent progress in this field through multifunctionalization of cyclodextrin necessitates a new review. This contribution was written by I. Tabushi and Y. Kuroda, active researchers in this area. 

Betatron A doughnut-shaped accelerator in which electrons, traveling in an orbit of constant radius, are accelerated by a changing electromagnetic field. Energies up to 340 MeV have been attained in betatrons. 

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