具有库仑排斥的二维非局域Ginzburg-Landau模型中的液滴相
Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions
摘要：
我们建立了在两个空间维度上，在多液滴模式的开始附近，具有库仑排斥的非局部Ginzburg-Landau能量极小值的能量行为。在背景电荷密度与消失的表面张力的适当缩放下，非局部的Ginzburg-Landau能变得渐近等价于具有屏蔽库仑相互作用的尖锐界面能。在发病附近的尖锐的界面能的极小值由几乎相同的小尺寸的圆形液滴分离的大距离。在极限下，液滴变得均匀地分布在整个域中。得到了分叉阈值、最小能量、液滴半径和液滴密度的精确渐近极限。
英文摘要：
We establish the behavior of the energy of minimizers of non-local Ginzburg-Landau energies with Coulomb repulsion in two space dimensions near the onset of multi-droplet patterns. Under suitable scaling of the background charge density with vanishing surface tension the non-local Ginzburg-Landau energy becomes asymptotically equivalent to a sharp interface energy with screened Coulomb interaction. Near the onset the minimizers of the sharp interface energy consist of nearly identical circular droplets of small size separated by large distances. In the limit the droplets become uniformly distributed throughout the domain. The precise asymptotic limits of the bifurcation threshold, the minimal energy, the droplet radii, and the droplet density are obtained.
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