Topological Ideas and Fluid Mechanics
Topological Ideas and Fluid Mechanics
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DOI：
10.1063/1.881574
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发表时间：
1996-12
期刊：
影响因子：
3.5
通讯作者：
Renzo L. Ricca;M. Berger
中科院分区：
文献类型：
--
作者：
Renzo L. Ricca;M. Berger
拓扑思想在物理学和流体力学中的应用可以追溯到拓扑学作为一门独立科学的起源。在 1833 年的一篇简短笔记中，卡尔·高斯在哀叹“位置几何”（或几何位置，拓扑学当时被称为 I）方面缺乏进展的同时，给出了拓扑学与可测量物理量（例如电流）之间关系的一个显着例子。他考虑了两个不可分割的连接电路，每个电路都是两端相连的铜线，并流动着电流。他没有评论地提出了一个公式，给出了电流感应的磁作用与纯磁力之间的关系。这个数是一个拓扑不变量，现在被称为链接数。该公式以及约翰·本尼迪克特·李林在 1847 年所做的第一个拓扑研究，为英国的开尔文（当时的威廉·汤姆森）、詹姆斯·克拉克·麦克斯韦和彼得·格思里·泰特所熟知。
The use of topological ideas in physics and fluid mechanics dates back to the very origin of topology as an independent science. In a brief note in 1833 Karl Gauss, while lamenting the lack of progress in the “geometry of position” (or Geometria Situs, as topology was then known I, gives a remarkable example of the relationship between topology and measurable physical quantities such as electric currents. He considers two inseparably linked circuits, each of them a copper wire with ends joined, and flowing electric current. Without comment he puts forward a formula that gives the relationship between the magnetic action induced by the currents and a pure number that depends only on the type of link, and not on the geometry. This number is a topological invariant now known as the linking number. The formula, as well as the very first studies in topology done by Johann Benedict Listing in 1847, became known to Kelvin (then William Thomson), James Clerk Maxwell and Peter Guthrie Tait in Britain.