When hot water freezes before cold

I suggest that the origin of the Mpemba effect (the freezing of hot water before cold) is freezing-point depression by solutes, either gaseous or solid, whose solubility decreases with increasing temperature so that they are removed when water is heated. They are concentrated ahead of the freezing front by zone refining in water that has not been heated, reduce the temperature of the freezing front, and thereby reduce the temperature gradient and heat flux, slowing the progress of the front. I present a simple calculation of this effect, and suggest experiments to test this hypothesis.Comment: 7 pages, 1 figur

Proton Spin-Lattice Relaxation in Organic Molecular Solids: Polymorphism and the Dependence on Sample Preparation

We report solid‐state nuclear magnetic resonance 1H spin‐lattice relaxation, single‐crystal X‐ray diffraction, powder X‐ray diffraction, field emission scanning electron microscopy, and differential scanning calorimetry in solid samples of 2‐ethylanthracene (EA) and 2‐ethylanthraquinone (EAQ) that have been physically purified in different ways from the same commercial starting compounds. The solid‐state 1H spin‐lattice relaxation is always non‐exponential at high temperatures as expected when CH3 rotation is responsible for the relaxation. The 1H spin‐lattice relaxation experiments are very sensitive to the “several‐molecule” (clusters) structure of these van der Waals molecular solids. In the three differently prepared samples of EAQ, the relaxation also becomes very non‐exponential at low temperatures. This is very unusual and the decay of the nuclear magnetization can be fitted with both a stretched exponential and a double exponential. This unusual result correlates with the powder X‐ray diffractometry results and suggests that the anomalous relaxation is due to crystallites of two (or more) different polymorphs (concomitant polymorphism)

Asymptotic Least-Squares Estimation Efficiency Considerations and Applications.

This paper is concerned with the large sample efficiency of the asymptotic least-squares (ALS) estimators introduced by Gourieroux, Monfort, and Trognon (1982, 1985) and Chamberlain (1982, 1984). We show how the efficiency of these estimators is affected when additional information is incorporated into the estimation procedure. The relationship between ALS and maximum likelihood is discussed. It is shown that ALS can be used to obtain asymptotically efficient estimates for a large range of econometric models. Many results from the literature on estimation are special cases of the framework adopted in this paper. An application of ALS to a dynamic rational expectation factor demand model in the manufacturing sector in the Netherlands demonstrates the potential of the method in the estimation of the parameters in models which are subject to nonlinear cross-equation restrictions. Copyright 1990 by John Wiley & Sons, Ltd.