Levine对液滴冻结温度分布预测的推广：冰成核的一般奇异模型
Generalisation of Levine's prediction for the distribution of freezing temperatures of droplets: A general singular model for ice nucleation
摘要：
没有明确的时间依赖性的模型，称为奇异模型，被广泛用于拟合水滴冻结时的温度分布。1950年，莱文提出了最初的奇异模型。他的关键假设是每个液滴包含许多成核位点，并且由于具有最高冻结温度的成核位点而发生冻结。由于大量成核温度中的最大值而发生冻结的事实意味着我们可以应用所谓的极值统计的结果。这是极端的统计数据，即，最大值或最小值，大量随机变量的值。在这里，我们使用极值统计的结果表明，我们可以概括莱文的模型，以产生最一般的奇异模型可能的。我们表明，当一个奇异的模型是一个很好的近似，冻结温度的分布应该总是由所谓的广义极值分布。此外，我们还表明，冻结温度的液滴的onesize的分布，可以用来预测的缩放的中值成核温度与液滴尺寸，反之亦然。
英文摘要：
Models without an explicit time dependence, called singular models, are widely used for fitting the distribution of temperatures at which water droplets freeze. In 1950 Levine developed the original singular model. His key assumption was that each droplet contained many nucleation sites, and that freezing occurred due to the nucleation site with the highest freezing temperature. The fact that freezing occurs due to the maximum value out of large number of nucleation temperatures, means that we can apply the results of what is called extreme-value statistics. This is the statistics of the extreme, i.e., maximum or minimum, value of a large number of random variables. Here we use the results of extreme-value statistics to show that we can generalise Levine's model to produce the most general singular model possible. We show that when a singular model is a good approximation, the distribution of freezing temperatures should always be given by what is called the generalised extreme-value distribution. In addition, we also show that the distribution of freezing temperatures for droplets of onesize, can be used to make predictions for the scaling of the median nucleation temperature with droplet size, and vice versa.
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