Parametric crossover model

The first step in quantitative description of pure polyamorphic fluid is a selection of the model that can qualitatively describe a possible multiplicity of critical points in wide range of temperatures and pressures. A great many of explanations of multicriticality in monocomponent fluids (perturbation theory models semiempirical models lattice models, two-state models, field theoretic models, two-order-parameter models, and parametric crossover model has been disseminated after the pioneering work by Hemmer and Stell Here we test more extensively the modified van der Waals equation of state (MVDW) proposed in work and refine this model by introducing instead of the classical van der Waals repulsive term a very accurate hard sphere equation of state over the entire stable and metastable regions... 

Kiselev S., Ely J. (2002) Parametric crossover model and physical limit of stability in supercooled water, J. Chem. Phys. 116 (3), 5657. 

Kiselev, S.B. and Sengers, J.V. (1993) An improved parametric crossover model for the thermodynamic properties of fluids in the critical region, Int. J. Thermophys. 14, 1-32. 

Belyakov et al. (1997) developed a parametric crossover model for the phase behavior of H2O + NaCl solutions that corresponds to the Leimg-Criffiths model in the critical region and is transformed into the regular classical expansion far away from the critical point. The model was optimized, and leads to excellent agreement with vapor-liquid equilibrimn data for dilute aqueous solutions of NaCl near the critical points. This crossover model is capable of representing the thermodynamic surface of H2O + NaCl solutions in the critical and supercritical regions. 

In these equations k, a, ct, d ( = Pu in eq 10.29), and g are system-dependent coefficients with g being related to the inverse of the Ginzburg number AIq. Slightly different versions for the crossover function R q) have also been used. In the critical limit 0 one recovers the linear-model parametric equation in Section 10.2.2 with coefficients a and k. In the classical limit q-rcc. Ad becomes an analytic function of AT and Ap. For a comparison of this phenomenological parametric crossover equation with the crossover Landau models the reader is referred to some previous publications. " " ... 

Analysis of variance (ANOVA) is also a common parametric statistic for comparing data from more than two groups [2]. There are a number of variants of this model, depending upon the number and combination of groups, categories, and levels one desires to evaluate. Common ones include one-factor, two-factor, and three-factor designs, as well as crossover and nested designs. 

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