Related papers: On sector magnets or transverse electromagnetic fi…
Any homogeneous polynomial $P(x, y, z)$ of degree $d$, being restricted to a unit sphere $S^2$, admits essentially a unique representation of the form $\lambda_0 + \sum_{k = 1}^d \lambda_k [\prod_{j = 1}^k L_{kj}]$, where $L_{kj}$'s are…
The Dirac equation with a scalar and an electromagnetic potentials is considered. In the time-harmonic case and when all the involved functions depend only on two spatial variables it reduces to a pair of decoupled bicomplex Vekua-type…
We present a theory and numerical evidence for the existence of a previously unexplored in-plane electric field in collisionless asymmetric magnetic reconnection. This electric field, dubbed the "Larmor electric field," is associated with…
We discuss the theory of electromagnetic fields, with an emphasis on aspects relevant to radiofrequency systems in particle accelerators. We begin by reviewing Maxwell's equations and their physical significance. We show that in free space,…
The paper aims to adopt the complex quaternion and octonion to formulate the field equations for electromagnetic and gravitational fields. Applying the octonionic representation enables one single definition to combine some physics contents…
Further thermodynamic investigations into the behaviour of a polar dielectric working fluid under non-equilibrium and negative pressure conditions are reported. The establishment of a long-range van der Waals interaction between clathrate…
The dynamics of a charged relativistic particle in electromagnetic field of a rotating magnetized celestial body with the magnetic axis inclined to the axis of rotation is studied. The covariant Lagrangian function in the rotating reference…
Precise knowledge of magnetic fields is crucial in many medical imaging applications like magnetic resonance imaging or magnetic particle imaging (MPI) as they are the foundation of these imaging systems. For the investigation of the…
Recently S. Gerhold and R. Garra-F. Polito independently introduced a new function related to the special functions of Mittag-Leffler family. This function is a generalization of the function studied by E. Le Roy in the period 1895-1905 in…
The magnetic scalar potential can be used to design electromagnets accurately and efficiently. I will describe a practical construction algorithm: the prescribed field in a "Target" region (constrained only by Maxwell's equations) specifies…
Using the technique of tridiagonal representation approach; for the first time, we extend this method to study quantum systems with literally perturbed Hamiltonians. Specifically, we consider a quantum system in a 3D spherical oscillator…
The direct current (DC) electric field near the reconnection region has been proposed as an effective mechanism to accelerate protons and electrons in solar flares. A power-law energy spectrum was generally claimed in the simulations of…
Using geometric algebra and calculus to express the laws of electromagnetism we are able to present magnitudes and relations in a gradual way, escalating the number of dimensions. In the one-dimensional case, charge and current densities,…
Solutions to Laplace's equation are called harmonic functions. Harmonic functions arise in many applications, such as physics and the theory of stochastic processes. Of interest classically are harmonic polynomials, which have a simple…
In this paper we examine the existence of bicomplexied inverse Laplacetransform as an extension of its complexied inverse version within theregion of convergence of bicomplex Laplace transform. In this course weuse the idempotent…
Various procedures for expressing the multipolar expansion of the electromagnetic field are considered with application to the calculation of the radiated power. Some results from literature are discussed and perspective of developing the…
We study the effect of regular and singular domain perturbations on layer potential operators for the Laplace equation. First, we consider layer potentials supported on a diffeomorphic image $\phi(\partial\Omega)$ of a reference set…
Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2x2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of…
Three thought experiments demonstrate that under certain circumstances electromagnetic fields have to be attenuated or amplified multiplicatively in order not to violate the conservation of energy. Modulation of radiation by means other…
Currently, some approaches to the associated Legendre functions based on different factorization methods are known. However, they have not allowed identifying new properties that permit to improve our knowledge of any physical system. In…