Derivation of magnetic Coulomb's law for thin, semi-infinite solenoids

The self-interaction force on an arbitrarily moving point-charge and its energy-momentum radiation rate: A mathematically rigorous derivation of the Lorentz-Dirac equation of motion

The classical theory of radiating point-charges is revisited: the retarded potentials, fields, and currents are defined as nonlinear generalized functions and all calculations are made in a Colombeau algebra. The total rate of energy-momentum radiated by an arbitrarily moving relativistic point-charge under the effect of its own field is shown to be rigorously equal to minus the self-interaction force due to that field. This solves, without changing anything in Maxwell's theory, numerous long-standing problems going back to more than a century. As an immediate application an unambiguous deriva…

摩擦耦合到弹性地基上的壳体及与两体库仑静摩擦定律的比较

A Shell Frictionally Coupled to an Elastic Foundation and a Comparison Against the Two-Body Coulomb's Law of Static Friction

本文推导了摩擦耦合到弹性地基上的壳体模型，基于库仑静摩擦定律提出位移型摩擦定律，并证明解的存在唯一性；数值分析显示高模量、高泊松比及高摩擦系数或曲率下两模型位移场更一致，为首次相关推导。

Derivation of the self-interaction force on an arbitrarily moving point-charge and of its related energy-momentum radiation rate: The Lorentz-Dirac equation of motion in a Colombeau algebra

The classical theory of radiating point-charges is revisited: the retarded potentials, fields, and currents are defined as nonlinear generalized functions. All calculations are made in a Colombeau algebra, and the spinor representations provided by the biquaternion formulation of classical electrodynamics are used to make all four-dimensional integrations exactly and in closed-form. The total rate of energy-momentum radiated by an arbitrarily moving relativistic point-charge under the effect of its own field is shown to be rigorously equal to minus the self-interaction force due to that field.…

两个匀速运动带电粒子间的电磁相互作用：使用Minkowski图的几何推导

Electromagnetic interaction between two uniformly moving charged particles: a geometrical derivation using Minkowski diagrams

本文基于2空间+1时间维度的Minkowski图，通过几何投影推导了速度的相对论加法及匀速运动带电粒子间的电磁相互作用，并从Coulomb力出发结合4-力与4-速度的正交性导出了Lorentz力。

Expressions for frictional and conservative force combinations within the dissipative Lagrange-Hamilton formalism

Dissipative Lagrangians and Hamiltonians having Coulomb, viscous and quadratic damping,together with gravitational and elastic terms are presented for a formalism that preserves the Hamiltonian as a constant of the motion. Their derivations are also shown. The resulting L's and H's may prove useful in exploring new types of damped quantum systems.

二维Vlasov-Poisson系统的平均场极限研究

On the mean-field limit for the Vlasov-Poisson system in two dimensions

本文通过概率方法证明了二维带库仑相互作用的N粒子系统在N相关截断下的平均场极限及混沌传播，基于Gronwall估计验证了牛顿轨迹向Vlasov-Poisson系统特征曲线的收敛性。