Baker’s transformation

In the MPC theory, the problem is not even posed. One starts defining the purely mathematical concept of dynamical system without any reference to a representation of reality. (The baker s transformation or the Bernoulli shift are obvious examples.) From here on, one proves mathematically the existence of a class of abstract dynamical systems (K-flows) that are intrinsically stochastic —that is, that possess precise mathematical properties (including a temporal symmetry breaking that can be revealed by a change of representation). 

At the time of publication of La Nouvelle Alliance the Prigoginian theory was still at the MPC stage. It is thus significant that aU general statements be illustrated only by the baker s transformation. It is only in Les Lois du Chaos (1994) and in La Fin des Certitudes (1996) that the Large Poincare Systems (LPS) show up. As stated in Section I.D 4, this concept results from the quest of real physical systems satisfying the criteria of intrinsic stochasticity. In this case, however, Prigogine and Petrosky were led to introduce a true modification... 

E., and Baba, Y. (2011) Microfluidic baker s transformation device for three-dimensional rapid mixing. Lab Chip, 11 (19), 3356-3360. 

MIcrofluldic Mixing, Figure 2 (a) Baker s transformation consists of stretching, cutting, and rejoining the domain. After each transformation, the... 

Fig. 1. Induced chaotic motion in a continuous chaotic advection blender (CCB) causes melt domains to become stretched and folded to give rise to baker s transformations. Novel, encapsulated multi-layers form that can also lead to solid additive orientation and promote molecular organization [4]. 

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