We consider the so-called Thomson problem which refers to finding the equilibrium distribution of a finite number of mutually repelling point charges on the surface of a sphere, but for the case where the sphere is re...We consider the so-called Thomson problem which refers to finding the equilibrium distribution of a finite number of mutually repelling point charges on the surface of a sphere, but for the case where the sphere is replaced by a spheroid or ellipsoid. To get started, we first consider the problem in two dimensions, with point charges on circles (for which the equilibrium distribution is intuitively obvious) and ellipses. We then generalize the approach to the three-dimensional case of an ellipsoid. The method we use is to begin with a random distribution of charges on the surface and allow each point charge to move tangentially to the surface due to the sum of all Coulomb forces it feels from the other charges. Deriving the proper equations of motion requires using a projection operator to project the total force on each point charge onto the tangent plane of the surface. The position vectors then evolve and find their final equilibrium distribution naturally. For the case of ellipses and ellipsoids or spheroids, we find that multiple distinct equilibria are possible for certain numbers of charges, depending on the starting conditions. We characterize these based on their total potential energies. Some of the equilibria found turn out to represent local minima in the potential energy landscape, while others represent the global minimum. We devise a method based on comparing the moment-of-inertia tensors of the final configurations to distinguish them from one another.展开更多
The heat transfer processis simulated in a nano-sized cone-shaped cathode. A model of heat transfer is constructed using the phase field system and theNottingham effect. We considerinfluence of the free boundary curva...The heat transfer processis simulated in a nano-sized cone-shaped cathode. A model of heat transfer is constructed using the phase field system and theNottingham effect. We considerinfluence of the free boundary curvature and the Nottingham effect on the heat balance in the cathode.展开更多
提出一种能精确而有效的计算方法,用于计算分子各种表面积如容剂可及性表面积、范德华表面积和体积,对计算蛋白质溶剂化能、表征分子形状、计算药物分子在蛋白质分子表面的对接及预测有机小分子生物活性均有重要意义。本文针对n个单位...提出一种能精确而有效的计算方法,用于计算分子各种表面积如容剂可及性表面积、范德华表面积和体积,对计算蛋白质溶剂化能、表征分子形状、计算药物分子在蛋白质分子表面的对接及预测有机小分子生物活性均有重要意义。本文针对n个单位点电荷在单位球面上均匀分布问题-Thomson问题,采用Metropolis Monte Carlo模拟退火方法数值求解,得到了与其它方法一致的结果,并用于小分子和大分子的容剂可及性表面积及范德华表面积和体积的快速计算,提出采用高时斯定理计算分子体积的新方法,结果很好。展开更多
文摘We consider the so-called Thomson problem which refers to finding the equilibrium distribution of a finite number of mutually repelling point charges on the surface of a sphere, but for the case where the sphere is replaced by a spheroid or ellipsoid. To get started, we first consider the problem in two dimensions, with point charges on circles (for which the equilibrium distribution is intuitively obvious) and ellipses. We then generalize the approach to the three-dimensional case of an ellipsoid. The method we use is to begin with a random distribution of charges on the surface and allow each point charge to move tangentially to the surface due to the sum of all Coulomb forces it feels from the other charges. Deriving the proper equations of motion requires using a projection operator to project the total force on each point charge onto the tangent plane of the surface. The position vectors then evolve and find their final equilibrium distribution naturally. For the case of ellipses and ellipsoids or spheroids, we find that multiple distinct equilibria are possible for certain numbers of charges, depending on the starting conditions. We characterize these based on their total potential energies. Some of the equilibria found turn out to represent local minima in the potential energy landscape, while others represent the global minimum. We devise a method based on comparing the moment-of-inertia tensors of the final configurations to distinguish them from one another.
文摘The heat transfer processis simulated in a nano-sized cone-shaped cathode. A model of heat transfer is constructed using the phase field system and theNottingham effect. We considerinfluence of the free boundary curvature and the Nottingham effect on the heat balance in the cathode.
文摘提出一种能精确而有效的计算方法,用于计算分子各种表面积如容剂可及性表面积、范德华表面积和体积,对计算蛋白质溶剂化能、表征分子形状、计算药物分子在蛋白质分子表面的对接及预测有机小分子生物活性均有重要意义。本文针对n个单位点电荷在单位球面上均匀分布问题-Thomson问题,采用Metropolis Monte Carlo模拟退火方法数值求解,得到了与其它方法一致的结果,并用于小分子和大分子的容剂可及性表面积及范德华表面积和体积的快速计算,提出采用高时斯定理计算分子体积的新方法,结果很好。
