Structures dissipative

TNC.20. 1. Prigogine, Structure, dissipation and life, in Theoretical Physics and Biology, M. Marois, ed., North Holland, Amsterdam, 1969. 

TNC.33.1. Prigogine et P. Glansdorff, L ecart a I equilibre interprets comme une source d ordre. Structures dissipatives (The departure from equilibrium interpreted as a source of order), Bull. Cl. Set Acad. Roy. Belg. 59, 673-702 (1973). 

However at a critical distance from equilibrium, the system must choose between two possible pathways, represented by the bifurcation point Ac. The continuation of the initial pathway, indicated by a broken hne, indicates the region of instability. The concentration of the species A and the value of A assume quite different values, and the more so, the further from equilibrium. An important point is that the choice between the two branching directions is casual, with 50 50 probability of either. The critical point Ac has particular importance because beyond it, the system can assume an organized structure. Here the term self-organization is introduced as a consequence of the dissipative structures, dissipative in the sense that it results from an exchange of matter and energy between system and environment (we are considering open systems). 

This model will primarily account for the resolving of local activity "spots during the reaction. But in models of such kind, periodic spatial structures ("dissipative structures ) can also be formed and these have recently become of great interest. 

Viscosity is an important rheological characteristic of a foam. The values of the structural (dissipation) viscosity and the effective viscosity, derived by different authors, range in a wide interval, depending on foam expansion ratio and dispersity, as well as on shear rate. Wenzel et al. [9] have shown that the viscosity falls with the increase in the shear rate, according to the following relation... 

The electron bubble s structural dissipation lifetime in the image potential is td = 4 x 10 s for... 

IIIK) 1980 Koros, E., Orban, M., Habon, I. Chemical Oscillations during the Uncatalyzed Reaction of Aromatic Compounds with Bromate, 3. Effect of One-Electron Redox Couples on Uncatalyzed Bromate Oscillators, J. Phys. Chem., vol. 84, 559-560 (III I) 1968 Lefever, R. Stabilite de Structure dissipative, Acad. Royal des Science de Belgique, Class des Sciences, Bulletin, vol. 54, 712-719... 

When the spatially homogeneous stationary state (x, y) loses stability and crosses a sensitive state, then in case (5.125a) travelling waves of a finite amplitude may be generated while in case (5.125b) stationary periodical spatial structures (dissipative structures) may be generated. 

While Belousov was describing his e)q)eriments into oscillatory chemical reactions, Ilya Prigogine in Brussels was developing theoretical models of nonequilibrium thermodynamics and ended with the notion of "structure dissipative" for which he was awarded the 1977 Nobel Prize in Chemistry. The concept of "Dissipative Structure" is ejq)licitly mentioned in the Nobel quotation "The 1977 Nobel Prize in Chemistry has been awarded to Professor Ilya Prigogine, Brussels, for his contributions to non-equilibrium thermodynamics, particularly the theory of dissipative structures". In the first half of the 1950s, Glansdorff and Balescu defined with Prigogine the thermodynamic criteria necessary for oscillatory behavior in dissipative systems [7]. Nicohs and Lefever then applied these to models of autocatalytic reactions [8]. 

The tetrahedral arrangement that characterizes the local ordering of water molecules in the V structure dissipates after about 10 s (at 283 K) because the nearest neighbors of a given molecule are relatively free to change their positions in response to thermal perturbations. This relaxation time is about one order of magnitude smaller than the time scale for diffusive translational and rotational motion of the molecules in liquid water at 283 K, as can be inferred from Table 2.2. The physical meaning of... 

In introducing the sense of dissipative structures, Prigogine and Stengers state, In far-from-equilibrium conditions we may have transformation from disorder, from thermal chaos, into order. New dynamic states of matter may originate, states that reflect the interaction of a given system with its surroundings. We have called these new structures dissipative structures to emphasize the constructive role of dissipative processes in their formation. ... 

Equilibrium stmctures are maintained without any exchange of energy and/or matter. A crystal is the prototype of an equilibrium structure. Dissipative structures, on the other hand, are maintained through exchange of energy (and in some cases also exchange of matter) with the outside world. Since entropy is dissipated in open systems under specific circumstances, emerging structures in such systems are called dissipative structures. 

Squat Spherical Collapse of structure Dissipative bracings... 

Energy Dissipation Systems External devices fixed to the structure dissipate energy. Input earthquakes, wind, etc. They are installed in the structure with the aim of dissipating most seismic energy entering the same structure (Aiken et al., 1993, Tsai etal., 1993). 

Manneville, P., Structures Dissipatives et Turbulence Faible (Alea, Saclay, 1991). 

However, in real structures dissipation of energy does occur at each impact. For this reason, the block will attain a reduced maximum tilt after each impact, and the period of free vibrations will continuously decrease. Using Eq. 8,... 

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