Maxwell's role in turning the concept of model into the methodology of modeling

This is a contribution towards a history and philosophy of modeling in its early stages in electromagnetism. In 1873, James Clerk Maxwell (1831–1879) hinted at the methodology of modeling at the end of his Treatise on Electricity and Magnetism. We focus on Maxwell's impact on physicists who immediately followed him, specifically Oliver Lodge (1851–1940) and George Francis FitzGerald (1851–1901). We begin with the role that the scientific concept of model played in the late nineteenth century, as assessed by Ludwig Boltzmann (1844–1906). We then discuss the role of hypothesis as a methodology, the appeal to (dynamical) illustration, and the way Maxwell applied model and working model in his studies of electromagnetism. We show that for Maxwell these key terms were kept distinct, but Lodge did not maintain these distinctions and, in this regard, FitzGerald followed Lodge. Notwithstanding Lodge's influence, Fitzgerald modified Maxwell's theory based on the mechanical model he designed, thereby implicitly taking the first step towards modeling. This methodology consists in drawing consequences from the (mechanical) model to the (electrodynamic) theory and modifying the latter in light of the functioning of the former. At the core of our argument is the thesis that it was a methodological novelty to move from the concept of model to the methodology of modeling. The introduction of modeling as a new methodology into physics in the late nineteenth century was a major event which deserves proper recognition.     

The Nature of Light and Twentieth Century Experimental Physics

In the popular literature of physics the electromagnetic field isoften treated as though it has an intrinsic particle nature. When thetheory is examined carefully, quantum theory only makes the weakerrequirement that the emission and absorption of light are restricted todiscrete amounts of energy. There are very few realizable experiments inoptics for which the classical Maxwell theory and the quantum theorymake a different prediction. I discuss some of these experiments with anemphasis on the distinction between what the experiments tell us aboutthe measurement process, and what they tell us about the nature of thelight field.     

由麦克斯韦方程组推导出毕奥-萨伐尔定律的几种方法

从稳定情况下的麦克斯韦方程组(文中简称为麦氏方程)出发，采用三种不同的方法，从理论上直接推导出毕奥-萨伐尔(Biot-Savart)定律，加深了对麦克斯韦方程组和毕奥-萨伐尔定律的认识．     

流体静力学的外微分形式

用几何的观点，把微分形式引进流体静力学，从而得到了热力学第一定律的一次形式．并利用外微分的性质，导出了流体静力学的一些基本关系．     

康威-麦斯威尔-泊松分布及其统计与概率性质

康威-麦斯威尔-泊松分布是一个有用的离散分布,它是扩展的两参数泊松分布,有关此分布的统计和概率性质被广泛研究和探索;文章以矩母函数为工具讨论了该分布的数字特征和矩,给出了参数点估计的隐式方程和费希尔信息矩阵;最后研究了参数的共轭分布、共轭分布的边际分布和条件分布.     

Maxwell's color statistics: From reduction of visible errors to reduction to invisible molecules

This paper presents a cross-disciplinary and multi-disciplinary account of Maxwell's introduction of statistical models of molecules for the composition of gases. The account focuses on Maxwell's deployment of statistical models of data in his contemporaneous color researches as established in Cambridge mathematical physics, especially by Maxwell's seniors and mentors. The paper also argues that the cross-disciplinary, or cross-domain, transfer of resources from the natural and social sciences took place in both directions and relied on the complex intra-disciplinary, or intra-domain, dynamics of Maxwell's researches in natural sciences, in color theory, physical astronomy, electromagnetism and dynamical theory of gases, as well as involving a variety of types of communicating and mediating media, from material objects to concepts, techniques and institutions.     

八元向量代数及其在电动力学中的应用

本文建立了八元向量代数,它既是一种方阵代数,又作为一个更加完备的运算系统而包含了复数、矢量和四元数.应用八元向量代数,可以十分方便地导出 Maxwell 方程组的对称变换,并将其拓展成为一个更加完整而对称的电磁场结构定律,从而构成进一步发展经典电动力学的理论基础.     

压电驱动器的非线性建模

在研究了各种非线性模型的基础上,采用Maxwell迟滞模型建立了压电驱动器的非线性模型,给出了该模型参数的求解准则和方法．实验结果表明,所建立的非线性模型与实际测量结果一致,提出的非线性参数的求解方法简单实用．该模型可用于对驱动器的前馈控制,以达到提高驱动器位移控制精度的目的．     

建立麦克斯韦方程组的两种方法

从最基本假定出发，利用洛仑兹变换和最小作用原理两种方法，建立麦克斯韦方程组     

气体分子的平均相对速率

根据麦克斯韦速度分布律,表示出系统内分子相对某一个分子的平均相对速率,进而求出两分子间的平均相对速率.