标题： 二维非局部Ginzburg-Landau模型中带库仑排斥的液滴相 显示英文标题

标题： Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions

摘要： 我们确定了在二维空间中具有库仑排斥的非局部Ginzburg-Landau能量的极小值的能量行为，在多滴模式开始时附近。在背景电荷密度适当缩放且表面张力趋于零的情况下，非局部Ginzburg-Landau能量渐近等价于具有屏蔽库仑相互作用的尖界面能量。在接近开始时，尖界面能量的极小值由大小较小且几乎相同的圆形滴组成，这些滴之间相距较远。在极限情况下，这些滴在整个区域内均匀分布。得到了分岔阈值、最小能量、滴半径和滴密度的精确渐近极限。 显示英文摘要

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.