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Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

7.4K
A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half...
7.4K
Gauss's Law: Problem-Solving01:10

Gauss's Law: Problem-Solving

1.7K
Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area...
1.7K
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

7.5K
A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
7.5K
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

7.9K
A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
7.9K
Gauss's Law01:07

Gauss's Law

7.2K
If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
7.2K
Gauss's Law in Dielectrics01:17

Gauss's Law in Dielectrics

4.3K
Consider a polar dielectric placed in an external field. In such a dielectric, opposite charges on adjacent dipoles neutralize each other, such that the net charge within the dielectric is zero. When a polar dielectric is inserted in between the capacitor plates, an electric field is generated due to the presence of net charges near the edge of the dielectric and the metal plates interface. Since the external electrical field merely aligns the dipoles, the dielectric as a whole is neutral. An...
4.3K

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Updated: Jun 14, 2025

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

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对于静电相互作用,Gauss-Legendre-spherical-t方法的一个平行CUDA实现.

James E Gonzales1,2, Wonmuk Hwang1,3,4,5, Bernard R Brooks2

  • 1Department of Biomedical Engineering, Texas A&M University, College Station, Texas 77843, USA.

The Journal of chemical physics
|June 9, 2025
PubMed
概括
此摘要是机器生成的。

我们开发了高斯-莱根德-球形-t (GLST) 算法,以加速分子动力学 (MD) 模拟中的静电相互作用. 在平行架构上,GLST提供了O(N) 缩放,以实现高效的远程计算.

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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

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相关实验视频

Last Updated: Jun 14, 2025

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Three-Dimensional Particle Shape Analysis Using X-ray Computed Tomography: Experimental Procedure and Analysis Algorithms for Metal Powders
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Three-Dimensional Particle Shape Analysis Using X-ray Computed Tomography: Experimental Procedure and Analysis Algorithms for Metal Powders

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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

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科学领域:

  • 计算物理学的计算物理.
  • 分子动力学模拟的模拟.
  • 算法开发的发展算法.

背景情况:

  • 计算静电相互作用是分子动力学 (MD) 模拟中的一个主要瓶.
  • 现有的加速静电计算的方法在缩放和并行通信方面存在局限性.

研究的目的:

  • 介绍高斯-莱金德-球形-t (GLST) 算法的计算细节和性能分析.
  • 评估GLST在MD模拟中加速远程静电相互作用的适用性.

主要方法:

  • 开发了基于球形网格和树代码的高斯-莱根德-球形-t (GLST) 算法.
  • 分析了GLST的计算复杂性和并行通信需求.
  • 将GLST性能与粒子网格Ewald和快速多极方法进行比较.

主要成果:

  • GLST算法实现了O(N) 缩放,这表明系统大小随着增加而提高计算效率.
  • 与粒子网格Ewald相比,GLST显示了降低并行通信需求.
  • 在通信成本方面,GLST的性能与快速多极方法相美.
  • 该算法为静电计算提供了高度可调的精度.

结论:

  • 在MD模拟中,GLST非常适合快速计算远程静电相互作用.
  • 该算法在大规模并行计算架构上表现出极好的可扩展性.
  • 为了更广泛的可访问性,GLST软件作为GitHub上的独立库可用.