STUDY ON PATTERN FORMATION AND MORHOLOGICAL TRANSITION

为了考察相分离系统对外界条件的响应，我们研究了在非均匀时空外界条件下相分离的机理。特别是在相分离的初始阶段中的外部条件的变化剧烈地影响后期阶段中的图案形成。与本理论研究相对应的一个例子是通过从熔融材料中拉出一块晶体来形成大的完整晶体的情况。我们还提出了相同的实验为聚合物和聚合物共混物与溶剂。这些实验具有重要的实用意义，为制备理想晶体提供了一种有效的方法，同时也为解决非平衡态下的形态转变问题提供了理论依据。在这个项目中，我们的目标不仅是固体的相分离，而且是液体的相分离。因此，我们研究了液体的调幅分解的长度尺度的增长规律。由于相位分离的缩放特性，长度尺度L（t）作为时间t的函数与t^a成比例地增长。这里a称为增长指数，对于固体，a = 1/3，对于流体，a = 1。另一方面，已知流体的指数a = 1与长时限（t * *）的水动力演化规律相矛盾，并且认为a在长时限内变为2/3。我们通过模拟证实了增长指数a = 2/3。重要的是，从a = 1 * 2/3的交叉引起了长度尺度增长的减缓。例如，对于水+蒸汽系统，用a = 1预测的流体速度（7000 cm/sec）比用a = 2/3预测的10 cm/sec（在L（t）= 1 cm处）大3度。在没有引力场的情况下（例如在空间实验室中），这种显著的减速对物质的组成有重要影响。

We examined the mechanism of the phase separation under the inhomogeneous spatio-temporal external conditions, in order to examine the response of the phase separating system to the external conditions. In particular the change in the external condition in the initial stage of the phase separation drastically affects the pattern formation in later stages. An example corresponding to the present theoretical investigation is the case of the formation of large perfect crystal by drawing up a piece of crystal from molten material. We also propose the same experiment for the polymer and the polymer blend with solvent. These experiments are significant from practical purpose offering an efficient method of producing perfect crystem, and from academic point of view offering morphological transition in nonequilibrium state which should be solved. In this project we aim the phase separation not only of solid but also of liquid. We therefore examined the growth law of the length scale for the spinodal decomposition of liquid. Due to the scaling properties of the phase separation the length scale L(t) grows in proportion to t^a as a function of time t. Here a is called the growth exponent and is given as a = 1/3 for solid and a = 1 for fluid. On the other hand, the exponent a = 1 for fluid is known to contradict with the hydrodynamic evolution law in the long time limit ( t * *), and a is considered to become 2/3 in the long time limit. We confirmed the growth exponent a = 2/3 by the simulation The importance is that the cross-over from a = 1 * 2/3 gives rise to the slowing down of the growth of the length scale. For instance, for water + vapor system, the fluid velocity (7000 cm/sec) predicted with a = 1 is large by three degree than 10 cm/sec predicted with a = 2/3 (at L(t) = 1 cm). Such a remarkable slowing down has an important effect to the composition of material in the absence of the gravitational field (such as in the space laboratory).