Bowl, parabolic

Figure 12.18 Response surface representing a parabolic bowl opening upward.

Figure 12.20 Response surface representing a flattened parabolic bowl opening downward.

Visual presentation of data treatment results can sometimes be misleading if scaling factors are not taken into account. For example, the parabolic bowl shown in Figure 12.19 could be made to look like the ridge in Figure 12.21 if the scaling for... 

Parabolas show up in a variety of places. The path of a bomb dropped from an airplane is a section of a parabola. The cables of a well-designed suspension bridge follow a parabolic curve. The surface of the water in a bowl that is rotating on a turntable will assume the shape of a parabola rotated around its axis. The area of a circle is a parabolic function of its radius, hi fact, the graphs of all polynomial functions y = ax +bx + c, of degree two are parabolic in shape. 

It s easy to understand why saddle-node bifurcations typically have this algebraic form. We just ask ourselves how can two fixed points of x = /(x) collide and disappear as a parameter r is varied Graphically, fixed points occur where the graph of /(x) intersects the x-axis. For a saddle-node bifurcation to be possible, we need two nearby roots of /(x) this means /(x) must look locally bowl-shaped or parabolic (Figure 3.1.7). 

The electrodes in Figure 2 are truncated for practical purposes but, in theory, they extend to infinity and meet the asymptotes shown. The electrode geometries are defined so that, when an RF potential is applied to the ring electrode with the end-cap electrodes grounded, a near-ideal quadrupole field is produced, which creates a parabolic potential well for ion confinement. Figure 3. As shown in Figure 3, the potential well in the axial directioims of depth D, while that in the radial direction D ] since 2Dr, the potential well resembles more a flower vase than a bowl. 

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