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

1.对二维扩散限制凝聚(DLA)进行了数值模拟，发现了分形维与欧几里德维之间的关系式。通过对连续DLA进行离散化，引用相似维度，得到了该公式。有人提出了一些公式，然而，我们的公式比那些公式更精确。我们在更高的欧几里德维度上进行模拟，并将公式2推广。我们用耦合映象格子模型模拟了枝晶、密集分枝形貌和DLA。发现了表面张力的各向异性、表面动力学的各向异性和表面噪声的影响之间的关系。我们还明确了花纹转变的物理机制，发现密集分枝区域的双子花纹与一对不对称的枝晶一起生长，并且比树枝晶生长得更快。我们用Hele-Shaw池进行了粘性指进实验，研究了树枝晶的整体包络。我们发现包络中存在三个区域：未成熟的侧枝、竞争的侧枝和独立的侧枝。我们发现了一个有趣的结果，停止其他侧枝的竞争侧枝可以比茎尖生长得更快。我们推测，相互竞争的侧枝以双峰的形式生长。

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.