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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >Equilibrium and uniform charge distribution of a classical two-dimensional system of point charges with hard-wall confinement
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Equilibrium and uniform charge distribution of a classical two-dimensional system of point charges with hard-wall confinement

机译：硬墙限制的古典二维系统的平衡和均匀电荷分布

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摘要

We study the minimum energy equilibrium configurations of a classical two-dimensional system of point charges confined by a triangular, square and disk region with a hard-wall boundary. It is assumed that the point charges interact via a repulsive Coulomb interaction potential. Monte Carlo simulations with the annealing algorithm suggest that the equilibrium configurations of a given system are strongly influenced by the external (isotropic/ anisotropic) geometry of the hard-wall boundary. The numerically obtained energies extrapolated in the bulk limit converge to the expected continuum equilibrium values (when known). It is found that the equilibrium charge distribution is non- uniform in the continuum limit for all the hard- wall confining regions considered in this work. Since the continuum equilibrium charge distribution is not known for the case of an equilateral triangle or a square domain we choose to compare the numerically obtained bulk energy results to corresponding values for a uniformly charged system. We calculated exactly the electrostatic energy of various uniformly charged planar objects and used the results to assess the discrepancy between such results and the numerically obtained equilibrium bulk energy values for the cases of equilateral triangle and square hard- wall boundaries. These estimates help us understand how an anisotropic boundary with the shape of an equilateral triangle or square influences the energy of an equilibrium charge distribution. The results indicate that the energy discrepancy between equilibrium and uniform charge distributions in the continuum limit is not very large. It is found that the order of magnitude of the relative deviation of the energy for all three different planar domains considered here is approximately the same.
机译：我们研究了具有硬壁边界的三角形，方形和圆盘区域限制的点电荷的古典二维系统的最小能量平衡配置。假设点电荷通过排斥库仑相互作用电位相互作用。与退火算法的蒙特卡罗模拟表明，给定系统的平衡配置受到硬墙边界的外部（各向同性/各向异性）几何形状的强烈影响。在批量限额中推断的数值所获得的能量会聚到预期的连续um平衡值（已知时）。结果发现，在这项工作中考虑的所有硬壁限制区域的连续内限制中，平衡电荷分布是非均匀的。由于对于等边三角形或平方域的情况，因此不知道连续平衡电荷分布，因此我们选择将数值所获得的本体能量结果与均匀电荷系统的相应值进行比较。我们计算出各种均匀电荷的平面物体的静电能量，并使用结果来评估这种结果与等边三角形和方形硬壁边界的情况下的数值所获得的平衡体能值之间的差异。这些估计有助于我们了解如何与等边三角形或平方形状的各向异性边界影响平衡电荷分布的能量。结果表明，连续统计极限平衡和均匀电荷分布之间的能量差异不是很大。发现这里考虑的所有三个不同平面域的能量相对偏差的级别的大致相同。

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