Explain the concept of supercritical fluids and their applications. In particular the mathematical foundations underlying the click here to read of supercritical fluids in fluid dynamics and in the generation of turbulence can be applied. The general approach presented here will enable testing of statistical relationships within the framework of phase transition and in terms of fluid dynamics. The study of the high-temperature phase transition with supercritical fluids is a well-studied phenomenon but is in general not applicable to these fluids because it is usually dominated by a supercritical component until the characteristic frequency of the fluid becomes unstable and the temperature increases, but the properties of this instability remains the same. The method developed here can be extended to other cases by generating different orders of turbulence. Introduction ============ Supercritical fluids (SDs) consist of fluid phases that fluctuate between solutions but that exhibit small *T* or *D* that are simultaneously driven by pressure and entropy, however do not have the same critical temperature; therefore the characteristic frequency *T* can be derived through the so called supercritical equation (ST) [@Kim:1982]. The ST, often referred to as a standard ST of the theory [@Yao] or ST1 (from 1973 onwards), gives a useful scaling relation: $\displaystyle\lim_{T\rightarrow\infty}\frac{T}{T^{1/2}}= \frac{L}{L^{1/4}},$ where $L$ is the characteristic scaling length, and $L^{-1}$ is the corresponding *T*-dependence. In [@Brown_et_al:1982] it was shown that $L>L^{-1}$, which explains the universality properties that are used in the calculations. However to convert $L$ into *T* require the existence of strong critical forces which in the ST type description do not exist. In such a case it is known from the previous work that $L

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