Study on side-branching structure of dynamical pattern formation in diffusion field.

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1. We have performed simulation of two-dimensional diffusion-limited aggregation (DLA) and found a new formulation between the fractal dimension and Eucledian dimension. The formulation is obtained by making continuous DLA discrete and referring similarity dimension. Some formulations are proposed, however, our formulation is more precise than those. We are performing the simulation in higher Eucledian dimensions and are going to generalize the formulation.2. We have performed simulation of dendrite, dense-branching morphology and DLA with a coupled map lattice model. We have found the relation between those patterns and the anisotropy of surface tension, the anisotropy of surface kinetics and the influence of surface noise. We have also made the physical mechanism of transition of the patterns clear and found doublon pattern in dense-branching morphology region which grow with a pair of asymmetric dendrite and can grow faster than dendrite.3. We have performed the experiment of viscous fingering with Hele-Shaw cell and studied the global envelope of dendrite. We have found that there exist three regions in the envelope ; premature side-branches, competing side-branches and independent side-branches. We have found an interesting result that the competing side-branches which cease other side-branches can grow faster than the tip of the stem. We conjecture that the competing side-branches grow as doublons.