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JNS
2010

The Pattern of Multiple Rings from Morphogenesis in Development

13 years 7 months ago
The Pattern of Multiple Rings from Morphogenesis in Development
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. Key words. ring, disc, nonlocal geometric problem, mean curvature, approximate solution, Lyapunov-Schmidt reduction. 2010 Mathematics Subject Classification. ...
Xiaosong Kang, Xiaofeng Ren
Added 19 May 2011
Updated 19 May 2011
Type Journal
Year 2010
Where JNS
Authors Xiaosong Kang, Xiaofeng Ren
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