Structure spatial dissipative

A dissipative structure is formed in the nonequilibrium system when the mechanism of random fluxes does not allow the sufficient dissipation of coming negentropy, that results in the absence of a solution for Eq. (29). Then, one finds two possibilities (1) the formation of spatial dissipative structures where a large part of the negentropy is dissipated due to regular fluxes, or (2) the formation of temporary dissipative structures which can be described by means of Eq. (28) with a periodic solution W(t). What possibility in the concrete situation realizes depends on the specific properties of the system. 

We note that one can obtain two kinds of bifurcation sets resulting from little changes of the boundary conditions for spatial dissipative structures in continuous systems (1) the change of the parameter A that leads to the change of the form of the solution without change of the number of roots of Eq. (44), and (2) the change of the number of roots (or the number of positive roots) of Eq. (44). 

In transferring from the precritical to the supracritical modes, the system symmetry changes spontaneously by analogy with thermodynamic phase transitions. This is why the transitions to form spatial dissipative structures in nonequihbrium systems are sometimes referred to as kinetic phase transitions. 

When the CO disproportionation is catalyzed by cobalt, some ordered metastable structures are detected inside the active metal nanoparticles after the reaction. These structures are regular thin (approximately 5 atoms in thickness) alternating cobalt layers of different crystallographic modifications (Figure 4.17). Note that the appearance of such structures at thermodynamically equilibrium states of the catalyst substance is contrary to the Gibbs phase rule for the phase equilibria in solids. Thus, the metastable layered structures may be considered an analogue of spatial dissipative structures. 

The concept of coupled oscillators is important from the viewpoint of understanding oscillatory phenomena in biochemical systems where the basic question relates to the type of dynamic behaviour when two are more such systems are coupled together. The concept of coupling is quite relevant in the context of spatial dissipative structures in cases where chemical oscillators are coupled through diffusion. 

Further stochastic simulation studies now in progress are concerned with fluctuation and nucleation in evolving chemical systems (e.g., limit cycle oscillations, combustion and explosions) and at the transition to spatial dissipative structure (cf.. Figure 10). In the latter case, for example, stochastic simulations verify the existence of critical long-range spatial correlations predicted in a stochastic theoretical study of the model (cf.. Ref. 17). 

New Photochemical Reactions Leading to Spatial Dissipative Structures. Gimenez, M. Micheau, J.C. (Lab Chim.-Phys. II, Univ. Libre Bruxelles, B-1050 Brussels, Belg.). Naturwissenschaften 1983, 70 (2), 90-2 (Eng.). Spatial dissipative structures were formed during visible or UV light irradn. of shallow layer solns. of photochromic (reversible) or chromogenic (irreversible) compds. The origin of the structures was independent of the mechanisms involved in the chem. reaction. 

There is another type of bifurcation called Turing bifurcation, which results in a spatial pattern rather than oscillation. A typical example where a new spatial structure emerges from a spatially unique situation is Benard s convection cells. These have been well examined and are formed with increasing heat conduction.53 Prigogine called this type of structure a dissipative structure.54-56... 

The bulk properties of these temporal dissipative structures also differ from those of the thermodynamic solution. The time average of the concentrations at a given point in space is only a second-order correction (but spatially dependent). The spatial average, as in the stationary dissipative structures, varies even to the dominant order. 

Self-organization could be considered as a set intersecting self-assembly, ordered self-assembly, that would (1) contain the systems presenting a spontaneous emergence of order in either space or time or both (2) cover spatial (structural) and temporal (dynamic) order of both equilibrium structures and of non-equilibrium, dissipative structures, incorporating non-linear chemical processes, energy flow and the arrow of time (3) concern only the non-covalent, supramolecular level (4) be... 

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. 

A fundamental corollary of the Glansdorf Prigogine criterion (3.2) is a potentiality of the formation of ordered structures at the occurrence of irreversible processes in the region of nonlinear thermodynamics in open systems that are far from their equilibrium. Prigogine created the term dissipative structures to describe the structures that arise when some controlling parameters exceed certain critical values and are classified as spatial, temporal, or spatial temporal. Some typical dissipative structures are discussed in Sections 3.5 and 4.6. 

In real systems, especially in heterogeneous catalytic and biological sys terns, the reactants are often arranged irregularly in space. Therefore, an arising instability may cause simultaneous diffusion of substances from one point to another inside the system to make the reactant concentration oscillations arranged in a certain manner in space during the occurrence of nonlinear chemical transformations. As a result, a new dissipative structure arises with a spatially nonuniform distribution of certain reac tants. This is a consequence of the interaction between the process of diffusion, which tends to create uniformity of the system composition, and local processes of the concentration variations in the course of nonlinear... 

ON THE THEORY OF THE ORIGIN OF SPATIALLY NONUNIFORM STATIONARY STATES (DISSIPATIVE STRUCTURES) IN HETEROGENEOUS CATALYTIC SYSTEMS... 

The question of the existence of spatially inhomogeneous stationary states (in terms of dissipative structures, DSs) in heterogeneous catalysis was first... 

On The Theory Of The Origin Of Spatially Nonuniform Stationary States (Dissipative Structures) In Heterogeneous Catalytic Systems 551... 

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. 

The Belousov-Zhabotinskii (BZ) reaction has been selected as an example illustrating diverse dynamical states observable in chemical systems. The BZ reagent is very convenient both for experimental and theoretical investigations, since the BZ reaction has many dynamical states of interest, which will be described below. In the BZ reaction one may observe the steady state, the time periodic state (concentration oscillations), the spatially periodic state, the stationary state (dissipative structures), the time and spatially periodic state (propagating chemical waves) and turbulent states (chaotic oscillations, stochastic spatial structures, stochastic chemical waves). 

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