论文标题
连接的库仑柱：分析和数字
Connected Coulomb Columns: Analysis and Numerics
论文作者
论文摘要
我们考虑了Gamow液滴模型的一个版本，其较短的吸引人的外围含量潜力以及$ \ r^3 $的均匀充电质量的远程库仑相互作用。在这里，我们将自己限制为最大程度地减少柱状形状类别，即沿一个空间方向恒定。在能量中使用标准周长将导致由于无限质量在恒定空间方向上的无限质量而导致任何规定的横截面区域不存在。为了治愈此缺陷，我们使用连接的周长。我们证明存在与长期相互作用的相互连接的等值问题的最小化器，并研究了大小不一的大小横截面方案中的最小化器的形状。对于中间状态，我们使用具有连接性约束的Ohta-Kawasaki相位场模型来数值研究最小化器的形状。
We consider a version of Gamow's liquid drop model with a short range attractive perimeter-penalizing potential and a long-range Coulomb interaction of a uniformly charged mass in $\R^3$. Here we constrain ourselves to minimizing among the class of shapes that are columnar, i.e., constant in one spatial direction. Using the standard perimeter in the energy would lead to non-existence for any prescribed cross-sectional area due to the infinite mass in the constant spatial direction. In order to heal this defect we use a connected perimeter instead. We prove existence of minimizers for this connected isoperimetric problem with long-range interaction and study the shapes of minimizers in the small and large cross section regimes. For an intermediate regime we use an Ohta-Kawasaki phase field model with connectedness constraint to study the shapes of minimizers numerically.
