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Accurate Analytical Approximation Formulae for Large Deviation Analysis of Rain Formation by Salas, Christian P. H. is a scholarly article available to read on EtoBox.

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A 2016 paper by M Wilkinson in Physical Review Letters suggests that large-deviation theory is a suitable framework for studying unexpectedly rapid rain formation in collector-drop collision processes. Wilkinson derives asymptotic approximation formulae for a set of exact large-deviation functions, such as the cumulant generating function and the entropy function. The asymptotic approach assumes a large number of water droplet collisions and is motivated by the fact that the exact large-deviation functions are prohibitively difficult to deal with directly. Wilkinson uses his asymptotic formulae to obtain further results and also provides numerical work which suggests that a certain log-density function for the collector-drop model (which is a function of his asymptotic approximation formulae) is itself approximated satisfactorily. However, the numerical work does not test the accuracy of the individual asymptotic approximation formulae directly against their exact large-deviation theory counterparts. When these direct checks are carried out, they reveal that the asymptotic formulae are, in fact, rather inaccurate, even for very large numbers of collisions. Their individual inaccura

Author

Salas, Christian P. H.

Published

2022

Language

EN