Dissipative structures symmetry breaking

Physical processes Order-disorder structures, ordered-phase transitions, symmetry breaking, spontaneous magnetization, non-equilibrium crystallization phenomena, percolation, electrodeposition, formation of dissipative structures, turbulence and instabilities in fluid dynamics, and diffusion-limited aggregation process. Biological processes Excitation in muscles, pulsation of heart, calcium waves, natural fold-up of protein molecules, deposition of lipid bilayers, auto-regulation of homeostasis morphogenesis, hyper-cycles and autocatalytic networks, etc. 

Our next example of a dissipative structure illustrates how the breaking of time-translation symmetry leads to oscillatory behavior. Some early reports of concentration oscillations were discounted because it was widely believed that such behavior was not consistent with thermodynamics. That is why the report on oscillating reactions by Bray in 1921 and Belousov in 1959 were met with skepticism [20]. Although it is true that oscillations of the extent of reaction about its equilibrium value will violate the Second Law, oscillations of... 

Domain I represents the domain wherein the thermodynamic solution is stable. In domain II, with the parameters noted in Fig. 1, the thermodynamic branch has become unstable owing to fluctuations in the chemical composition of the system. Beyond the thermodynamic threshold (transition point), fluctuations increase uniformly in this domain (II), eventually resulting in a new steady state which corresponds to regular spatial distributions of X and Y (Fig. 2). This state represents a low entropy, dissipative structure localized in space and whose "natural" boundaries are determined by the system itself. The spatial localization of the resultant dissipative structure demonstrates the symmetry-breaking nature of the instability. It appears that the form which the dissipative structure takes depends on the type of initial perturbation thus, the system possesses a primitive "memory effect" since the initial perturbation determines the form of the dissipative structure established. 

Symmetry-Breaking Instabilities The Trimolecular Reaction. The "Brusselator" or trimolecular reaction is the simplest model which exhibits instabilities that may be symmetry-breaking in space and/or time. Although it does not represent an actual chemical reaction, it is nevertheless the best-studied and most widely known theoretical model for chemical instability phenomena. Historically it is the model on which the study of dissipative structures was begun by members of the Brussels. School of Thermodynamics (hence its popular name) a decade ago (44, 45, 46, 47). 

---