论文标题
核心外壳和双重泡泡在加权非本地等等问题中
Core shells and double bubbles in a weighted nonlocal isoperimetric problem
论文作者
论文摘要
我们考虑了$ abc $ triblock共聚物的尖锐接口模型，在该接口上，从阶段$ i $与阶段$ j $分隔$ i $的表面张力$σ_{ij} $可能取决于组件。我们研究了$ \ mathbb {r}^2 $中相关三元本地等级问题的全球最小化器，并展示最小化器的几何形状随表面张力$σ_{ij {ij {ij} $变化，从对称的表面紧张汇总，$ sells $ sells $ sells，$ sells $ sells $ selly $ yj $ seles core y $ ij y $ ij ij不同的。然后，我们考虑了在液滴缩放方案中非局部相互作用的影响，其中消失了两个相的小颗粒，分布在第三阶段的海洋中。我们对$σ_{ij} $的退化情况特别感兴趣，其中最小化器表现出核心外壳的几何形状，因为这种相位构型预计是在非局部三元系统中的物理基础上。
We consider a sharp-interface model of $ABC$ triblock copolymers, for which the surface tension $σ_{ij}$ across the interface separating phase $i$ from phase $j$ may depend on the components. We study global minimizers of the associated ternary local isoperimetric problem in $\mathbb{R}^2$, and show how the geometry of minimizers changes with the surface tensions $σ_{ij}$, varying from symmetric double-bubbles for equal surface tensions, through asymmetric double bubbles, to core shells as the values of $σ_{ij}$ become more disparate. Then we consider the effect of nonlocal interactions in a droplet scaling regime, in which vanishingly small particles of two phases are distributed in a sea of the third phase. We are particularly interested in a degenerate case of $σ_{ij}$ in which minimizers exhibit core shell geometry, as this phase configuration is expected on physical grounds in nonlocal ternary systems.
