Turing pattern, structure

The rich consequences of adding a diffusive mechanism of transport to chemical or biological activity are described in Chapter 4. Fisher waves and other types of fronts, excitable waves, Turing patterns, and other spatiotemporal phenomena produce striking structures which are observed in chemical and biological media. Understanding them is needed before addressing the additional impact that advection has on these systems. 

Genuine Turing patterns are nonequilibrium structures and can occur only in open systems. This requirement represents the first obstacle on the way to an experimental realization of Turing patterns. Needed is an open reactor, an unstirred flow reactor, which can play the same role for spatial patterns that the CSTR plays for temporal patterns. This instrumentation problem was solved in the second half of the 1980s by the Austin group. They developed two types of open spatial reactors, the Couette reactor [433,335,456,336] and the continuously fed unstirred reactor (CFUR) [322, 432,431, 323]. The latter proved to be instrumental in the experimental realization of Turing patterns. 

Some of spatio-temporal patterns and time-evolving patterns in dissipative structures can be frozen to obtain stationary structure. Addition of Ag ions in the BZ reaction records the spiral pattern (8), and quenching the photoinduced phase separation in a polymer mixture results in a Turing-type structure (9). 

When a reaction is carried out under the condition where the thickness of the solution mixture is less, the colored spatial patterns arise due to the variations in chemical concentrations and this pattern depends on the lime. The other important pattern which is stationary in time and periodic in space, or periodic in both time and space is known as Turing structures. Turing pattern looks like very beautiful and has close resemblance with biological and chemical systems. 

If a system of the form of eq. (14.1) satisfies conditions (14.5), (14.6), (14.17), (14.19), and (14.21), then it can give rise to Turing pattern formation when the homogeneously stable steady state (x, y,) is subject to inhomogeneous perturbations whose spatial scale, is such that q satisfies eq. (14.15). In such a system, the initial, infinitesimal perturbation will grow, and the system will ultimately evolve to a stable, spatially inhomogeneous structure, the Turing pattern. 

The two inequalities (14.45) are satisfied only within the dashed lines of Figure 14.8. Thus, Turing pattern formation can occur in at most about 20% of the thickness of the gel. If the gel were much thicker, perhaps 20-50 times the wavelength of the structures, we would almost surely find multiple layers of patterns. Mechanical problems with thick slabs of gel put a practical upper limit of a few millimeters on the usable thickness of cylindrical slabs of polyacrylamide or agar gel. 

Figure 14.11 Transient Turing patterns in the CDIMA reaction in a Petri dish, (a) Hexagonal pattern of (mostly) spots and (a few) stripes, (b) networklike structure. [ClOjlo = 5 X 10" M, fblo = 8 X 10 M, [MA]o = 1 x 10 M in (a) and 3 x 10 M in (b), [starch] - 1 g per 100 mL, [acetic acid] = 10%, 7" = 4 C. (Reprinted with permission from Lengyel, 1. Kadar, S. Epstein, 1. R. 1993. Transient Turing Structures in a Gradient-Free Closed System." Science 359. 493-495. v 1993 American Association for the Advancement of Science.)...

Perraud, J, J. Agladze, K. Dulos, E, De Kepper, P. 1992, Stationary Turing Patterns versus Time-Dependent Structures in the Chlorite-Iodide Malonic Acid Reaction, Physica A 188, 1-16. 

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