Key points are not available for this paper at this time.
We present a computationally efficient scheme of modeling the phase-ordering dynamics of thermodynamically unstable phases. The scheme utilizes space-time discrete dynamical systems, viz. , cell dynamical systems (CDS). Our proposal is tantamount to proposing new Ansaiuml---tze for the kinetic-level description of the dynamics. Our present exposition consists of two parts: part I (this paper) deals mainly with methodology and part II S. Puri and Y. Oono, Phys. Rev. A (to be published) gives detailed demonstrations. In this paper we provide a detailed exposition of model construction, structural stability of constructed models (i. e. , insensitivity to details), stability of the scheme, etc. We also consider the relationship between the CDS modeling and the conventional description in terms of partial differential equations. This leads to a new discretization scheme for semilinear parabolic equations and suggests the necessity of a branch of applied mathematics which could be called ``qualitative numerical analysis. ''
Oono et al. (Fri,) studied this question.