scholarly journals On differential equations of the natural electromagnetic field, ascending to differential equations Maxwell-Parker-Moffat and their properties

2018 ◽  
Author(s):  
V. V. Aksenov
Keyword(s):  
Electromagnetic Field ◽  
Differential Equations ◽  
Natural Electromagnetic Field

scholarly journals Normal modes of a waveguide as eigenvectors of a self-adjoint operator pencil

2021 ◽  
Vol 29 (1) ◽  
pp. 14-21
Author(s):  
Mikhail D. Malykh
Keyword(s):  
Electromagnetic Field ◽  
Differential Equations ◽  
Wave Equations ◽  
Adjoint Operator ◽  
Normal Modes ◽  
Operator Pencil ◽  
Homogeneous Case ◽  
Permittivity And Permeability ◽  
Simply Connected ◽  
Magnetic Potentials

A waveguide with a constant, simply connected section S is considered under the condition that the substance filling the waveguide is characterized by permittivity and permeability that vary smoothly over the section S, but are constant along the waveguide axis. Ideal conductivity conditions are assumed on the walls of the waveguide. On the basis of the previously found representation of the electromagnetic field in such a waveguide using 4 scalar functions, namely, two electric and two magnetic potentials, Maxwells equations are rewritten with respect to the potentials and longitudinal components of the field. It appears possible to exclude potentials from this system and arrive at a pair of integro-differential equations for longitudinal components alone that split into two uncoupled wave equations in the optically homogeneous case. In an optically inhomogeneous case, this approach reduces the problem of finding the normal modes of a waveguide to studying the spectrum of a quadratic self-adjoint operator pencil.

An Synergistic Dynamic 2D FEM Model of an Active Magnetic Bearing with Three Electromagnets

2014 ◽  
Vol 214 ◽  
pp. 106-112 ◽  
Author(s):  
Adam Krzysztof Pilat
Keyword(s):  
Electromagnetic Field ◽  
Differential Equations ◽  
Electromagnetic Force ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Comsol Multiphysics ◽  
Mesh Deformation ◽  
Arbitrary Lagrangian Eulerian ◽  
Fem Model ◽  
Mathematical Formulas

This elaboration presents a dynamic model of an Active Magnetic Bearing (AMB) developed in COMSOL Multiphysics. The electromagnetic field is calculated on the basis of Partial Differential Equations (PDEs). The calculated electromagnetic force is applied to the rotor, which is free to move. The Arbitrary Lagrangian-Eulerian (ALE) method for mesh deformation is applied to achieve rotor motion on the bearing plane. The planar rotor motion is described by a set of Ordinary Differential Equations (ODEs) solved in parallel to the electromagnetic field calculations. To enable rotor levitation, three local PD controllers are applied. The mathematical formulas of the control action are coded in the form of COMSOL equations and embedded into the rotor motion ODEs.

scholarly journals Some applications of the Riesz potential to the theory of the electromagnetic field and the meson field

1946 ◽  
Vol 188 (1012) ◽  
pp. 18-31 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Differential Equations ◽  
Riesz Potential ◽  
Analytical Continuation ◽  
Neutral Meson ◽  
Meson Field ◽  
Hyperbolic Differential Equations ◽  
Proper Energy

This paper contains some applications of the method of Marcel Riesz in the solution of normal hyperbolic differential equations, in particular the wave equation, where the known difficulties, due to the occurrence of divergent integrals, are avoided by a process of analytical continuation. In the theory of the electromagnetic field the method yields simple deductions of classical results, but also the results recently obtained by Dirac regarding the proper energy and proper momentum of an electron are obtained without any addition of new assumptions. The corresponding problem in Bhabha’s analogous theory for the neutral meson field are also studied.

scholarly journals Charged radiating stars with Lie symmetries

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
G. Z. Abebe ◽  
S. D. Maharaj
Keyword(s):  
Electromagnetic Field ◽  
Differential Equations ◽  
Equations Of State ◽  
Lie Symmetries ◽  
Boundary Equation ◽  
Symmetries Of Differential Equations ◽  
Radiating Stars ◽  
Barotropic Equation ◽  
Radiating Star ◽  
General Relativistic

Abstract We consider the general model of an accelerating, expanding and shearing radiating star in the presence of charge. Using a new set of variables arising from the Lie symmetries of differential equations we transform the boundary equation into ordinary differential equations. We present several new exact models for a charged gravitating sphere. A particular family of solution may be interpreted as a generalised Euclidean star in the presence of the electromagnetic field. This family admits a linear barotropic equation of state. In the uncharged limit, we regain general relativistic stellar models where proper and areal radii are equal, and its generalisations. Our group theoretical approach selects the physically important cases of Euclidean stars and equations of state.

A Rotary Magnetic Damper Consisting of Several Sector Magnets and an Arbitrarily Shaped Conductor With a Circular Cavity

1986 ◽  
Vol 108 (4) ◽  
pp. 314-321
Author(s):  
Yasuo Karube ◽  
Kosuke Nagaya
Keyword(s):  
Boundary Condition ◽  
Electromagnetic Field ◽  
Magnetic Flux ◽  
Differential Equations ◽  
Fourier Expansion ◽  
Step Function ◽  
Circular Cavity ◽  
Damping Force ◽  
Damping Coefficients ◽  
Unit Step

In this paper, the damping force and the damping coefficient of a rotary magnetic damper consisting of several sector magnets and an arbitrarily shaped plate conductor with a circular cavity have been obtained theoretically. The unit step function is applied to solve the differential equations of the electromagnetic field, and the boundary condition of the outer arbitrarily shaped boundary of the plate conductor is satisfied directly by making use of the Fourier expansion collocation method. Numerical calculations have been carried out for the dimensionless damping coefficients with the variations of various factors such as the magnetic flux range, the outer shape and the radius of the inner circular cavity of the conductor, the position and the number of the magnets.

THE EFFECT OF A FAULT ON THE EARTH’S NATURAL ELECTROMAGNETIC FIELD

Geophysics ◽  
1962 ◽  
Vol 27 (5) ◽  
pp. 651-665 ◽  
Author(s):  
I. d’ Erceville ◽  
G. Kunetz
Keyword(s):  
Electromagnetic Field ◽  
Physical Properties ◽  
Vertical Plane ◽  
Lateral Variation ◽  
Infinite Depth ◽  
Mathematical Solution ◽  
Natural Electromagnetic Field

The main purpose of this paper is to study the effect on a natural electromagnetic field of a lateral variation in the physical properties of the ground. An exact mathematical solution is given for two media of different resistivities in contact along a vertical plane (fault) overlying a horizontal basement that is taken as being either infinitely resistive or infinitely conductive, or at infinite depth. Results are given in the form of curves along profiles perpendicular to the fault. Some practical inferences are drawn from the shape of the curves and from their comparison.

The wave equation for spin 1 in Hamiltonian form

1955 ◽  
Vol 229 (1176) ◽  
pp. 39-43 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Differential Equations ◽  
Matrix Equation ◽  
Hamiltonian Form ◽  
Initial Value ◽  
Potential Vector ◽  
Spin Number ◽  
Proca Equations ◽  
Derivatives Of

If from the differential equations that hold in a Proca field you select the ten that express the time derivatives of the ten components involved, i. e. of the ‘electromagnetic’ field and its potential vector, you obtain right away for the ten-componental entity an equation that may be said to be at the same time of the Schrödinger, the Dirac and the Kemmer type. The four 10 x 10-matrices that occur as coefficients are Hermitian and satisfy Kemmer’s commutation rules. The fifth is easily constructed. Those of the Proca equations that were not included are merely injunctions on the initial value. They are expressed by one matrix equation, that makes it evident that, once posited, they are preserved. The three spin matrices are indicated. The spin number is 1 or 0, but the aforesaid injunctions exclude 0.

scholarly journals Diffraction of Electromagnetic Waves on a Waveguide Joint

2018 ◽  
Vol 173 ◽  
pp. 02014 ◽  
Author(s):  
Mikhail Malykh ◽  
Leonid Sevastianov ◽  
Anastasiya Tyutyunnik ◽  
Nikolai Nikolaev
Keyword(s):  
Hilbert Space ◽  
Electromagnetic Field ◽  
Differential Equations ◽  
Helmholtz Equation ◽  
Computer Algebra ◽  
Electromagnetic Waves ◽  
Computer Algebra System ◽  
Infinite System ◽  
Hamiltonian Form ◽  
Helmholtz Equations

In general, the investigation of the electromagnetic field in an inhomogeneous waveguide doesn’t reduce to the study of two independent boundary value problems for the Helmholtz equation. We show how to rewrite the Helmholtz equations in the “Hamiltonian form” to express the connection between these two problems explicitly. The problem of finding monochromatic waves in an arbitrary waveguide is reduced to an infinite system of ordinary differential equations in a properly constructed Hilbert space. The calculations are performed in the computer algebra system Sage.

scholarly journals Invariant Inhomogeneous Bianchi Type-I Cosmological Models with Electromagnetic Fields Using Lie Group Analysis in Lyra Geometry

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Ahmad T. Ali
Keyword(s):  
Electromagnetic Field ◽  
Differential Equations ◽  
Lie Group ◽  
Magnetic Permeability ◽  
Bianchi Type ◽  
Group Analysis ◽  
Type I ◽  
Lie Group Analysis ◽  
Bianchi Type I ◽  
New Class

We find a new class of invariant inhomogeneous Bianchi type-I cosmological models in electromagnetic field with variable magnetic permeability. For this, Lie group analysis method is used to identify the generators that leave the given system of nonlinear partial differential equations (NLPDEs) (Einstein field equations) invariant. With the help of canonical variables associated with these generators, the assigned system of PDEs is reduced to ordinary differential equations (ODEs) whose simple solutions provide nontrivial solutions of the original system. A new class of exact (invariant-similarity) solutions have been obtained by considering the potentials of metric and displacement field as functions of coordinatesxandt. We have assumed thatF12is only nonvanishing component of electromagnetic field tensorFij. The Maxwell equations show thatF12is the function ofxalone whereas the magnetic permeabilityμ¯is the function ofxandtboth. The physical behavior of the obtained model is discussed.

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