Correlations, critical long-range spatial

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). 

The intensity of light scattered from a fluid system increases enormously, and the fluid takes on a cloudy or opalescent appearance as the gas-liquid critical point is approached. In binary solutions the same phenomenon is observed as the critical consolute point is approached. This phenomenon is called critical opalescence.31 It is due to the long-range spatial correlations that exist between molecules in the vicinity of critical points. In this section we explore the underlying physical mechanism for this phenomenon in one-component fluids. The extension to binary or ternary solutions is not presented but some references are given. 

In the disordered phase, the thermodynamic average of the order parameter vanishes, but its fluctuations are nonzero. When the critical point is approached, the spatial correlations of the order parameter fluctuations, as characterized by the correlation function G(x — y) = ((j)(x)())(y)), become long-ranged. Close to the critical point, their typical length scale, the correlation length diverges as... 

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