Deterministic chaos, fundamentals

The description of small scale turbulent fields in confined spaces by fundamental approaches, based on statistical methods or on the concept of deterministic chaos, is a very promising and interesting research task nevertheless, at the authors knowledge, no fundamental approach is at the moment available for the modeling of large-scale confined systems, so that it is necessary to introduce semi-empirical models to express the tensor of turbulent stresses as a function of measurable quantities, such as geometry and velocity. Therefore, even in this case, a few parameters must be adjusted on the basis of independent measures of the fluid dynamic behavior. In any case, it must be underlined that these models are very complex and, therefore, well suited for simulation of complex systems but neither for identification of chemical parameters nor for online control and diagnosis [5, 6],... 

The main contribution of non-linear chemistry is the pitchfork bifurcation diagram. A stable state becomes uixstable and bifurcates into two new stable branches. We are unable to foresee which one of these states will be chosen by the nature of the physico-chemical reaction. The multiplicity of choices gives its full importance to Ae evolution of the systems. This paper has aimed to show the extent to which the concepts of non-equilibrium and of deterministic chaos sublimate the fundamental physical laws by leading us to the creation of new structures and to auto-organization. Chemistry is no exception to this rule. The final conclusion is given by Jean-Marie Lehn [21], Nobel Prize Winner in... 

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