Chemical turbulence

Ouyang Q and Swinney FI L 1991 Transition to chemical turbulence Chaos 1 411-20... 

In the second type of transport process, a chemical moves from one location in the air or water where its concentration is relatively high to another location where its concentration is lower, due to random motion of the chemical molecules (molecular diffusion), random motion of the air or water that carries the chemical (turbulent diffusion), or a combination of the two. Transport by such random motions, also called diffusive transport, is often... 

IIIJ) 1976-3 Rossler, O. E. Chemical Turbulence Chaos in a Simple Reaction-Diffusion System, Z. Naturforschung, vol. 31 a, 1168-1172... 

M. Kim, M. Bertram, M. Pollmann, A. v. Oertzen, A. S. Mikhailov, H. H. Rotermund, and G. Ertl. Controlling chemical turbulence by global delayed feedback pattern formation in catalytic co oxidation reaction on pt(llO). Science, 292 1357-1360, 2001. 

FIGURE 8.11. Slight variation of the control parameters leads to breakup of the spirals and emergence of chemical turbulence [25]. 

FIGURE 8.12. PEEM image showing the appearance of chemical turbulence in the CO oxidation on Pt(l 10) [18]. 

Roux, J. C. Rossi, A. Bachelart, S. Vidal, C. 1980. Representation of a Strange Attractor from an Experimental Study of Chemical Turbulence, Phys. Lett. A77, 391-393. 

Equation (2.4.18) is not like the usual reaction-diffusion equations since the diffusion matrix has an antisymmetric part. This seemingly peculiar property is actually a general consequence of contracting the usual reaction-diffusion equations, for which the diffusion matrix may be a diagonal matrix of positive diffusion constants. On account of its sound physical basis, we shall use the Ginzburg-Landau equation in later chapters in preference to the A-co model. In particular, the existence of the Cj terms will turn out to be crucial to the destabilization of uniform oscillations (see Appendix A) and hence to the occurrence of a certain type of chemical turbulence. 

People often speak of chemical turbulence whereby either of two distinct chaotic phenomena may be meant. One is the spatially uniform but temporally chaotic dynamics exhibited by the concentrations of chemical species, while the other involves spatial chaos too. For chemical turbulence in the latter sense, our attention is usually focused upon systems in which the local dynamics itself is non-chaotic, while such non-chaotic elements are coupled through diffussion to produce spatio-temporal chaos. In fact, if the local elements were already chaotic, the fields composed of them would trivially exhibit spatio-temporal chaos. Hence non-trivial chemical turbulence involving spatio-temporal chaos may be called diffusion-induced chemical turbulence. 

There may be an additional value in studying spatio-temporal chemical turbulence, in connection with its possible relevance to some biological problems. This is expected from the fact that the fields of coupled limit cycle oscillators (or nonoscillating elements with latent oscillatory nature) are often met in living systems. In some cases, such systems show orderly wavelike activities much the same as those observed in the Belousov-Zhabotinsky reaction. There seems to be no reason why we should not expect such organized motion to become unstable and hence show turbulent behavior. The recent work by Ermentrout (1982) who derived a Ginzburg-Landau type equation for neural field seems to be of particular interest in this connection. 

By taking the complex conjugate of this equation, and changing the sign before C2 at the same time, the equation remains invariant. This says that the only relevant parameter is the absolute value of C2. As we see below, sufficiently large c21 causes turbulence. Since C2 = Im /Re, where g is the nonlinear parameter in the original form of the Ginzburg-Landau equation (2.4.10), c2 oo as Re 0 (i.e., as the system approaches the borderline between supercritical and subcritical bifurcations). A number of kinetic models can have parameter values for which Re = 0, so that such systems should in principle exhibit chemical turbulence of the type discussed below. 

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