相关论文: Synge's dynamic problem for two isolated point cha…
Due to the finite speed of light, direct electrodynamic interaction between point charges can naturally be described by a system of ordinary differential equations involving delays. As electrodynamics is time-symmetric, these delays appear…
We re-visit the problem of two (oppositely) charged particles interacting electromagnetically in one dimension with retarded potentials and no radiation reaction. The specific quantitative result of interest is the time it takes for the…
The present work proposes a discussion on the self-energy of charged particles in the framework of nonlinear electrodynamics. We seek magnet- ically stable solutions generated by purely electric charges whose electric and magnetic fields…
We develop a systematic approach to calculating the electrostatic force between point charges in an arbitrary geometry with arbitrary boundary conditions. When the boundary is present, the simple expression for the force acting on a charge…
Dislocation dynamic is a typically gradient flow problem, and most of work solves it just as ODE, which means that the interacting energy of dislocations is ignored. We take the interaction energy into account and use it to introduce new…
We study the equations of Wheeler-Feynman electrodynamics which is an action-at-a-distance theory about world-lines of charges that interact through their corresponding advanced and retarded Li\'enard-Wiechert field terms. The equations are…
The electromagnetic self-force equation of motion is known to be afflicted by the so-called runaway problem. A similar problem arises in the semiclassical Einstein's field equation and plagues the self-consistent semiclassical evolution of…
We propose a methodology to address two analysis problems concerning complex systems, namely bounding state functionals of stochastic differential equations (SDEs) and verifying set avoidance of systems described by partial differential…
Born-Infeld nonlinear electrodynamics with point singularities having both electric and magnetic charges are considered. Problem of interaction between the associated soliton dyon solutions is investigated. For the case of long-range…
In this paper, we investigate some electrically charged magnetic solutions of the SU(2) Yang-Mills-Higgs field theory in the net zero topological charge sector. We only examine the case when the Higgs field vanishes at two points along the…
Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such system results in solving path constrained SDEs. Broadly, these problems fall under the…
When studying gauge theories in the presence of boundaries, local symmetry transformations are typically classified as gauge or physical depending on whether the associated charges vanish or not. Here, we propose that physical charges…
We consider two point charges in electrostatic interaction between them within the framework of a nonlinear model, associated with QED, that provides finiteness of their field energy. We argue that if the two charges are equal to each other…
How will the electrostatic interaction between two point charges change if they are shielded from the other by a dielectrical slab? While the physical setting of this electromagnetic problem is relatively simple, it is easy to be wronged…
The interaction between two chemically identical charge-regulated surfaces is studied using the classical density functional theory. In contrast to common expectations and assumptions, under certain realistic conditions we find a…
The coupled system of the spherically symmetric Einstein--Maxwell differential equations is solved under two different source conditions: non-zero electric charge and pressure anisotropy. Expressions for the metric functions, and pressures…
Equations of motion for an electrically charged string with a current in an external electromagnetic field with regard to the first correction due to the self-action are derived. It is shown that the reparametrization invariance of the free…
We consider an infinite system of coupled stochastic differential equations (SDE) describing dynamics of the following infinite particle system. Each partricle is characterised by its position $x\in \mathbb{R}^{d}$ and internal parameter…
Here we present a new approach to deal with first order ordinary differential equations (1ODEs), presenting functions. This method is an alternative to the one we have presented in [1]. In [2], we have establish the theoretical background…
The following inverse problem is discussed. A static electromagnetic field generated by a limited system of charges and currents is supposed to be known with its first derivatives at a point somewhere far from the system. This allows to…