Spiral curves

In region II, y /4 < A, and therefore < 0, but k 0. This region relates to stable focuses where the system evolution toward the initial point is described by a spiral curve. Unstable focuses and nodes are arranged in regions III and IV > 0)> respectively, and also are separated by curve y /4 = A. On axis y = 0, there are center type points for which k = 0, 7 0, and ki 2 = i ir Region V relates to unstable exceptional points of the saddle type. Here, = 0 and k have different signs > 0, 2 0)-... 

The equations of the spiral curves are considerably simplified by the use of polar coordinates. For instance, the curve for the logarithmic spiral (Fig. 35), though somewhat complex in Cartesian coordinates, is represented in polar coordinates by the simple equation r = o, . (1)... 

This consists of gram-negative rods or spirally-curved rods with a half... 

Figure 8.42 Monochromator schematic with a logarithmic spiral curved crystal. www.bruker.com. Used with permission.)...

This equation is for Eigure 9 cyclone dimension ratios. The term the effective number of spirals the gas makes in the cyclone, was found to be approximately 5 for Lapple s system (134). The soHd line grade-efficiency curve of Eigure 7 is also used with Lapple s cyclone, which is a somewhat taller, less compact cyclone than many commercial designs. 

Spiral-roller units are usually equipped with tapered rollers to compensate for the difference in distance traveled by the inner and outer edges of the container. Tapered rollers are also used on curved sections of ordinary roller-conveyor lines. 

Campylobacter spp. are gram-negative bacilli that have a curved or spiral shape. Campylobacter are sensitive to stomach acidity as a result, diseases or medications that buffer gastric acidity may increase the risk of infection. Data suggest that the infectious dose for C. jejuni is similar to that for Salmonella spp. After an incubation period, infection is established in the jejunum, ileum, colon, and rectum. 

Figure 4.3 Sketch of convoluted track of a wandering coony, showing two series of clockwise spirals followed by a final counterclockwise spiral. The colony had increased considerably in size after coming to rest and showed curved radial markings indicating rotation. The total length of the track was about 2 cm.

Fig. 8.12. Relation between oxygen abundance of H II regions in irregular (open squares) and spiral galaxies (filled circles, taking abundances at 0.4 of the de Vaucouleurs isophotal radius R25) plotted against the gas fraction, after Pilyugin, Vilchez and Contini (2004). The heavy curve shows expectation from the Simple model with an oxygen yield of 0.0027 (or about 0.5 Z ) and the broken curves show the same with the yield 1.5 x higher or lower, whereas the dotted curve shows a yield 4 x lower. The effective yield, defined as Zo/(— ln/z), increases systematically with luminosity, and the gas fraction decreases.

Figure 3.15. Areas where rough and smooth interfaces are expected. The growth rate versus the driving force relations expected for the three models of growth are indicated on the growth rate, R (vertical), axis versus the driving force (A/x/kT) diagram. Curve A shows the spiral growth mechanism B represents the two-dimensional nucleation growth mechanism C denotes the adhesive-type mechanism.

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