Singularity free hypothesis

Reviews on water structure models include Mishima and Stanley (1998), Wallqvist and Mountain (1999), and Ludwig (2001). Mishima and Stanley (1998) concentrated their review on three relatively recent water structure hypotheses (1) the stability limit hypothesis (Speedy, 1982), (2) the singularity-free hypothesis (Sastry et al., 1996), and (3) the liquid-liquid phase transition hypothesis (Poole et al., 1992). 

The Singularity Free Hypothesis Sastry et al. [60] proposed that a minimal scenario that was consistent with the salient anomalies did not require recourse to any thermodynamic singularities, such as a critical point or a retracing spinodal. They analyzed the interrelationship between the locus of density and the compressibility extrema and showed that the change of slope of the locus of density maxima (TMD) was associated with an intersection with the locus of compressibility extrema (TEC) (Fig. 3c). The relationship between the temperature dependence of isothermal compressibility at the TMD and the slope of the TMD is given by... 

Several explanations have been proposed to account for the anomalies of water (i) the stability limit conjecture [18], (ii) the metastable liquid-liquid critical point (LLCP) hypothesis [19], and (iii) the singularity free (SF) scenario [20]. An excellent review of the properties of supercooled water and the explanations proposed can be found in Ref. [16]. We just give here a brief overview. 

In its simplest application, PG analysis effectively identifies genotype(s) related to a singular phenotype. Here, in a hypothesis-free context made more complex by inclusion of multiple phenotypes, we describe the expansion of PG analysis to incorporate multiple phenotypes and then generate PG contours which depict the most significant relationships among genetic markers and phenotypes. 

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