Generalizing Ellipsoidal Growth

This paper generalizes previous work of Rios and Villa on spherical growth. The generalized equation applies to nucleation of ellipsoids according to an inhomogeneous Poisson point process. Microstructural evolution in three dimensions of nucleation and growth transformations of ellipsoids is simulated using the causal cone method. In the simulation, nuclei are located in space according to an inhomogeneous Poisson point process. The transformed regions grow with prolate and oblate ellipsoidal shapes. The ellipsoids have their corresponding axes parallel. The simulation and the exact analytica...