THE LAGUERRE MODEL OF GRAIN-GROWTH IN 2 DIMENSIONS .1. CELLULAR STRUCTURES VIEWED AS DYNAMICAL LAGUERRE TESSELLATIONS

The basic concepts of a deterministic model for simulating grain growt h or foam coarsening in two dimensions are presented, and the fundamen tal tools necessary for its implementation into computer codes are pro vided. It is assumed that the actual cell structure can be satisfactor ily represented by a Laguerre (or weighted Voronoi) diagram, entirely determined by a collection of weighted sites or circles. The cellular motion (including the induced elementary topological transformations) is subjected to the motion of this collection, allowing for the design of robust and efficient algorithms. An example of a simple motion equ ation, previously used in vertex models of grain growth, is reformulat ed to be operational for the collection of the circles generating Lagu erre diagrams. The model as a whole can be extended in three dimension s without principle difficulty. Part II of the paper will report and d iscuss simulation results obtained in two dimensions.