Chaos, 3, 323, Plate

The knight has stripes of different colors on his breast-plate black, white, yellow, and red. This is the first statement of the stages of the alchemical process, represented by colors. Black represents the nigredo or blackness—the initial chaos or undifferentiated state—which turns into white, or albedo, representing a rebirth or sense of renewal yellow announces a transitional stage from the white, and the red, the rubedo, represents the final result of transformation. Throughout the paintings of the Splendor Solis, we shall encounter this color symbolism. 

A direct simulation of the coupled system of the partial differential equations, Eq. 29, with appropriate boundary conditions (v = 0, n prescribed at the confining plates, etc.) is at the limits of the supercomputers of today. It will turn out that in the liquid crystal systems a rich scenario of patterns, including spatio temporal chaos, develops already near threshold so that perturbational calculations are useful. 

Swider, K. E. and Rolison, D. R. (2000) Reduced poisoning of platinum fuel-cell electrocatalysts supported on desulfurized carbon. Electrochem. Solid-State Lett. 3,4-6 Tandon, R. and Pintauro, P. N. (1997) Divalent/monovalent cation uptake selectivity in a Nafion cation-exchange membrane experimental and modeling studies. J. Membr. Sci. 136, 207-219 Tan, J., Chao, Y. J., Van Zee, J. W. and Lee, W.-K. (2007) Degradation of elastomeric gasket materials in PEM fuel cells. Mater. Sci. Eng. A, 445-446, 669-675 Tawfik, H., Hung, Y. and Mahajan, D. (2(X)7) Meted bipolar plates for PEM fuel cell - A review. J. Power Sources 163, 755-767... 

The simplest flow that can exhibit chaos is two-dimensional flow. Ottino and co-workers (Chien et al., 1986 Khakhar et al., 1986 Leong and Ottino, 1989) produced chaotic mixing in simple prototypical devices, such as cavity flow, partitioned-pipe mixer (e.g., a Kenics static mixer as discussed in Section 8.5), and eccentric helical annular mixer with Newtonian fluids. Of prime interest in the area of polymer processing, of course, is the work in cavity flows. A typical cavity was constructed with the ability of movement of both top and bottom plates. Typical cavity flow, which is described in Chapter 8, corresponds to the steady movement of the top plate only. However, corotational (in the opposite direction) movement of both plates in a periodic fashion induces chaos in the cavity. Leong and Ottino (1989) used two types of movement discontinuous and continuous in a sinusoidal manner (Fig. 6.28). In the discontinuous corotational flow, the top plate first moves for a half period, then it stops for 5 s, and the cycle ends with the bottom plate moving for a half period in the opposite direction. In the continuous type of movement, both plates move sinusoidally at the same time, but with a phase difference of %/2. 

Fig. 4. [Reproduced in colour in Plate 5 on page 423.] An example of a seismic cube with a chaotic pattern representing a gas chimney is shown in (a), its dip and Eizimuth attributes in (b) and (c) and a chaos texture attribute highlighting the gas migration path in (d).

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