The Pattern of Multiple Rings from Morphogenesis in Development
The Pattern of Multiple Rings from Morphogenesis in Development
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DOI：
10.1007/s00332-010-9072-z
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发表时间：
2010-06
影响因子：
3
通讯作者：
Xiaosong Kang;Xiaofeng Ren
中科院分区：
文献类型：
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作者：
Xiaosong Kang;Xiaofeng Ren
在一定条件下，显影中的形态发生问题和嵌段共聚物中的形态问题可以归结为一个几何问题。在二维空间中，我们发现了两种新的解：第一种解是由许多分支组成的不连通集，每个分支都接近于一个环。环的大小和位置由问题的参数和域形状精确确定。第二种类型的解决方案具有共存模式。溶液的每个组分要么接近环，要么接近圆盘。第一类解对某些参数值是稳定的，但对其他参数值是不稳定的;第二类解总是不稳定的。在这两种情况下，都建立了等面积条件：溶液中的所有组分都具有渐近相同的面积。
Under certain conditions the problem of morphogenesis in development and the problem of morphology in block copolymers may be reduced to one geometric problem. In two dimensions two new types of solutions are found. The first type of solution is a disconnected set of many components, each of which is close to a ring. The sizes and locations of the rings are precisely determined from the parameters and the domain shape of the problem. The solution of the second type has a coexistence pattern. Each component of the solution is either close to a ring or to a round disc. The first-type solutions are stable for certain parameter values but unstable for other values; the second-type solutions are always unstable. In both cases one establishes the equal area condition: the components in a solution all have asymptotically the same area.