Sci. Form Vol. 3 (No. 2), pp. 79-86, 1988
To the memories of Edward Barankin and Akira Ono

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.