On a New Mathematical Approach to the Theory of Snow Crystal Growth

Yoshihiro Shikata¹, Kanenori Suwa² and Etienne Labeyrie³

¹Department of Mathematics, Nagoya University, Chikusaku, Nagoya 464, Japan
²Department of Earth Science, Nagoya University, Chikusaku, Nagoya 464, Japan
³Faculté de Médecine, Hôpital St. Pitié Paris 7, France

(Received August 10, 1988; Accepted December 25, 1988)

Keywords: Model with Necessity, Dendritic Growth, Snow Crystal, Differential Operator for Growth, Diffusion Efficiency

Abstract. Abstract: We determine a class of differential operators which will give the dendritic growth of snow crystals, on the basis of observations by Nakaya et al. We then introduce an effect function and a status function for the crystals to describe their interaction in terms of growth and the growing status itself. We conclude that, in order to have dendritic growth, a nonlinear term is necessary in addition to the Laplacian of the status function, which may correspond to the diffusion efficiency.