Symmetry-breaking instabilities

Prigogine I and Lefever R 1968 Symmetry breaking instabilities in dissipative systems J. Chem. Phys. 48 1695-700... 

The year 1967 appears as a crucial year In an important paper by Prigogine and Nicohs, On symmetry-breaking instabilities in dissipative systems (TNC.16), there appears for the first time the term dissipative stmctures. The filiation of this concept with the half-principle of Glansdorff and Prigogine can be clearly perceived in the works of that period (particularly in the paper TNG.17). However, the new approach required a radical change of the theoretical methods. 

Once the door was opened to these new perspectives, the works multiplied rapidly. In 1968 an important paper by Prigogine and Rene Lefever was published On symmetry-breaking instabilities in dissipative systems (TNC.19). Clearly, not any nolinear mechanism can produce the phenomena described above. In the case of chemical reactions, it can be shown that an autocatalytic step must be present in the reaction scheme in order to produce the necessary instability. Prigogine and Lefever invented a very simple model of reactions which contains all the necessary ingerdients for a detailed study of the bifurcations. This model, later called the Brusselator, provided the basis of many subsequent studies. 

In 1969 a paper by I. Prigogine, R. Lefever, A. Goldbveter, and M. Hershkowitz-Kaufman was published Symmetry-breaking instabilities in... 

Prigogine, I. Lefever, R. Goldbeter, A. Herschkowitz-Kaufman, M. Symmetry breaking instabilities in biological systems. Nature 1969, 223 913-916. Westerhoff, H. V. Van Dam, K. Thermodynamics and control of biologicalfree-energy transduction. Elsevier Science, Amsterdam, 1987. 

The performance of the RB-CCD method (which is analogous to the conventional unrestricted B-CCD method) has been tested on the nitrate radical, NO3, and the C A2 state of NO2, both of which have presented difficulties for a variety of theoretical methods due in part to symmetry-breaking instabilities in the Ffartree-Fock reference wavefunction. The RB-CCD method was found to provide results in excellent agreement with the B-CCD method, including the correct prediction of C symmetry for the equilibrium geometry of the C state of NO2 Ajyork is presently under way for extension of the RB-... 

Less general in some respect, it emphasizes the chemical-bonding nature of the JT effect. Most important, in every JT case, its chemical nature can be revealed in a similar way. In any JT molecule, its symmetry-breaking instability is due to an energy stabilization of the respective chemical bonds. 

Physicochemical systems with coupled processes having different length scales can exhibit stationary spatially periodic structures. These arise from symmetry-breaking instabilities. 

King, H., Schroll, R.D., Davidovitch, B., Menon, N. Elastic sheet on a liquid drop reveals wrinkling and crumpling as distinct symmetry-breaking instabilities. PNAS 109, 9716-9720... 

In a reaction-diffusion (R-D) system with two intermediates X and Y where X is an activator and Y is an inhibitor, criterion for Turing symmetry breaking instability is that... 

Prigogine, 1. Lefever, R. 1968. Symmetry Breaking Instabilities in Dissipative Systems. II, J. Chem. Phys. 48, 1695-1700,... 

I. Prigogine and R. Lefever, Symmetry Breaking Instabilities in Dissi-... 

In the second aspect, we again picture the catalytic material itself to have spatially invariant properties, but now we ask questions about the stability of a spatially uniform reaction state to spatial perturbations. This stability question is similar to that posed in studies of hydrodynamic stability and of the other reaction-diffusion problems considered by Turing [62], Prigogine [63,64], Nicolis [63], Othmer and Scriven [65,66] and their co-workers. Prigogine and his co-workers labeled this phenomena "symmetry-breaking" instabilities. The key idea is that since there is a finite rate of transport, the complex interactions between the rate of communication by diffusive transport and the rate of chemical change may make it dynamically impossible for a spatially uniform state to be sustained. 

There are two other levels of spatial variation of a catalyst. First, within an individual particle, not only is the surface very rough and porous, but the catalyst itself is dispersed on the support material in the form of small crystallites. As suggested in Figure 12, a detailed analysis would have to account for interactions between particles or crystallites. Second, though studies of symmetry-breaking instabilities in the case of exactly identical particles were discussed earlier, no two... 

At the suggestion of the author. Flicker and Ross [11] allowed a uniform Phl2 sol to age to see if a symmetry breaking instability would occur - see also [12,13] The system did indeed pattern, displaying phenomenon (vi). To explain this phenomenon a new mechanism of precipitate pattern formation, the "competitive particle growth" (CPG) model was introduced [4,5,12, 14] and found strong experimental support [4,5,12-15] ... 

As in the isotropic case [1] this model displays a symmetry breaking instability. Indeed the homogeneous solution aQ = A, = B/A becomes unstable for B > B = (l + ATi) < 1 + where... 

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). 

---