A theory of magnetic-like fields for viscoelastic fluids

2019 ◽  
Vol 865 ◽  
pp. 460-491
Author(s):  
Thibault Vieu ◽  
Innocent Mutabazi
Keyword(s):  
Magnetic Field ◽  
Stress Tensor ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Viscoelastic Fluids ◽  
Point Of View ◽  
Viscoelastic Flows ◽  
Maxwell Stress Tensor ◽  
Viscoelastic Instability ◽  
Theoretical Issues

We formulate the Oldroyd-B model for viscoelastic fluids in terms of magnetic-like fields obeying a set of equations analogous to Maxwell’s equations. In the limit of infinite relaxation time for the polymer, the polymeric stress tensor can be identified with the Maxwell stress tensor of a magnetic field. Away from this asymptotic case, the stress tensor of the polymer cannot be decomposed in terms of a tensor product of a magnetic field any more and several theoretical issues arise. We show that the analogy between the Oldroyd-B model and Maxwell’s equations can still be rigorously extended provided that one defines three magnetic-like fields obeying Maxwell’s equations with magnetic currents and charges. This solves the theoretical caveats and leads to a better understanding of the viscoelastic instability. In particular, we evidence a gauge symmetry which unifies some previous works, and we investigate several gauge choices. As an illustration we apply our method to viscoelastic Taylor–Couette flow but this theory of ‘viscoelastic fields’ is general and may be useful in a large variety of viscoelastic flows. The present study may also be of interest from the electromagnetic point of view, as it provides real systems possessing magnetic-like charges (monopoles) and currents.

XXVI.—On a Polarised Light Quantum

1927 ◽  
Vol 46 ◽  
pp. 306-313
Author(s):  
J. M. Whittaker
Keyword(s):  
Electromagnetic Waves ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Point Of View ◽  
Light Quantum ◽  
Electric Force ◽  
Polarised Light

In the theory of radiation recently advanced by Sir J. J. Thomson it is supposed that electromagnetic waves and quanta are both present in a beam of light. The quanta, which are responsible for the photoelectric effects, are closed rings of electric force propagated in the direction normal to the plane of the ring. Professor Whittaker has discussed this conception from the point of view of Maxwell's equations, and has shown that it is consistent with them ; or rather with an extension of them in which a magnetic density μ analogous to the electric density ρ is introduced.

scholarly journals Two-dimensional hybrid model for magnetic field calculation in electrical machines: exact subdomain technique and magnetic equivalent circuit

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Brahim Ladghem Chikouche ◽  
Kamel Boughrara ◽  
Dubas Frédéric ◽  
Rachid Ibtiouen
Keyword(s):  
Magnetic Field ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Current Density Distribution ◽  
Electrical Machines ◽  
Field Calculation ◽  
Two Dimensional ◽  
Content Type ◽  
The Magnetic Field ◽  
Load Conditions

Purpose The purpose of this paper is to propose a two-dimensional (2-D) hybrid analytical model (HAM) in polar coordinates, combining a 2-D exact subdomain (SD) technique and magnetic equivalent circuit (MEC), for the magnetic field calculation in electrical machines at no-load and on-load conditions. Design/methodology/approach In this paper, the proposed technique is applied to dual-rotor permanent magnet (PM) synchronous machines. The magnetic field is computed by coupling an exact analytical model (AM), based on the formal resolution of Maxwell’s equations applied in subdomains, in regions at unitary relative permeability with a MEC, using a nodal-mesh formulation (i.e. Kirchhoff's current law), in ferromagnetic regions. The AM and MEC are connected in both directions (i.e. r- and theta-edges) of the (non-)periodicity direction (i.e. in the interface between teeth regions and all its adjacent regions as slots and/or air-gap). To provide accurate solutions, the current density distribution in slot regions is modeled by using Maxwell’s equations instead to MEC and characterized by an equivalent magnetomotive force (MMF) located in the slots, teeth and yoke. Findings It is found that whatever the iron core relative permeability, the developed HAM gives accurate results for both no-load and on-load conditions. Finite element analysis demonstrates the excellent results of the developed technique. Originality/value The main objective of this paper is to achieve a direct coupling between the AM and MEC in both directions (i.e. r- and theta-edges). The current density distribution is modeled by using Maxwell’s equations instead to MEC and characterized by an MMF.

scholarly journals Extension of the electrodynamics in the presence of the axion and dark photon

2019 ◽  
Vol 34 (03n04) ◽  
pp. 1950012 ◽  
Author(s):  
Fa Peng Huang ◽  
Hye-Sung Lee
Keyword(s):  
Magnetic Field ◽  
Maxwell’S Equations ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Dark Photon

We present the extended electrodynamics in the presence of the axion and dark photon. We derive the extended versions of Maxwell’s equations and dark Maxwell’s equations (for both massive and massless dark photons) as well as the wave equations. We discuss the implications of this extended electrodynamics including the enhanced effects in the particle conversions under the external magnetic or dark magnetic field. We also discuss the recently reported anomaly in the redshifted 21 cm spectrum using the extended electrodynamics.

Homogeneous dynamos and terrestrial magnetism

1954 ◽  
Vol 247 (928) ◽  
pp. 213-278 ◽  
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Point Of View ◽  
Hydrodynamic Equations ◽  
Dynamo Theory ◽  
Homogeneous Fluid ◽  
Terrestrial Magnetism ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Linear Differential

The main object of the paper is to discuss the possibility of a body of homogeneous fluid acting as a self-exciting dynamo. The discussion is for the most part confined to the solution of Maxwell’s equations for a sphere of electrically conducting fluid in which there are specified velocities. Solutions are obtained by expanding the velocity and the fields in spherical harmonics to give a set of simultaneous linear differential equations which are solved by numerical methods. Solutions exist when harmonics up to degree four are included. The convergence of the solutions when more harmonics are included is discussed, but convergence has not been proved. The simultaneous solution of Maxwell’s equations and the hydrodynamic equations has not been attempted, but a velocity system has been chosen that seems reasonable from a dynamical point of view. A parameter in the velocity system has been adjusted to satisfy the conservation of angular momentum in a rough way. Orders of magnitude are derived for a number of quantities connected with the dynamo theory of terrestrial magnetism. It is concluded that the dynamo theory does provide a self-consistent account of the origin of the earth’s magnetic field and raises no insuperable difficulties in other directions.

scholarly journals Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 987
Author(s):  
Tomasz P. Stefański ◽  
Jacek Gulgowski
Keyword(s):  
Wave Propagation ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Momentum Conservation ◽  
Point Of View ◽  
Classical Electrodynamics ◽  
Classical Solutions ◽  
Systems With Memory ◽  
Energy And Momentum ◽  
With Memory

In this paper, the formulation of time-fractional (TF) electrodynamics is derived based on the Riemann-Silberstein (RS) vector. With the use of this vector and fractional-order derivatives, one can write TF Maxwell’s equations in a compact form, which allows for modelling of energy dissipation and dynamics of electromagnetic systems with memory. Therefore, we formulate TF Maxwell’s equations using the RS vector and analyse their properties from the point of view of classical electrodynamics, i.e., energy and momentum conservation, reciprocity, causality. Afterwards, we derive classical solutions for wave-propagation problems, assuming helical, spherical, and cylindrical symmetries of solutions. The results are supported by numerical simulations and their analysis. Discussion of relations between the TF Schrödinger equation and TF electrodynamics is included as well.

scholarly journals Analytical magnetic field calculation for flat permanent-magnet linear machines with dual-rotor by using improved two-dimensional hybrid analytical method

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Brahim Ladghem Chikouche ◽  
Kamel Boughrara ◽  
Dubas Frédéric ◽  
Rachid Ibtiouen
Keyword(s):  
Magnetic Field ◽  
Density Distribution ◽  
Relative Permeability ◽  
Current Density ◽  
Analytical Method ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Current Density Distribution ◽  
Two Dimensional ◽  
Content Type

Purpose This paper aims to propose an improved two-dimensional hybrid analytical method (HAM) in Cartesian coordinates, based on the exact subdomain technique and the magnetic equivalent circuit (MEC). Design/methodology/approach The magnetic field solution is obtained by coupling an exact analytical model (AM), calculated in all regions having relative permeability equal to unity, with a MEC, using a nodal-mesh formulation (i.e. Kirchhoff’s current law) in ferromagnetic regions. The AM and MEC are connected in both axes (x, y) of the (non-)periodicity direction (i.e. in the interface between the tooth regions and all its adjacent regions as slots and/or air-gap). To provide accuracy solutions, the current density distribution in slot regions is modeled by using Maxwell’s equations instead of the MEC characterized by an equivalent magnetomotive force (MMF) located in slots, teeth and yokes. Findings It is found that whatever the iron core relative permeability, the developed HAM gives accurate results for no- and on-load conditions. The finite-element analysis demonstrates excellent results of the developed technique. Originality/value The main objective of this paper is to make a direct coupling between the AM and MEC in both directions (i.e. x- and y-edges). The current density distribution is modeled by using Maxwell’s equations instead of the MEC and characterized by an MMF.

VIII.—Reciprocity. Part VI: The Wave Function of the Meson

1941 ◽  
Vol 61 (1) ◽  
pp. 77-92
Author(s):  
Kathleen Sarginson
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Dirac Equation ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Electro Magnetic Field ◽  
Electro Magnetic ◽  
Special Case

In this paper the equations of the meson are treated in the same manner as the Dirac equation in a previous paper (K. Fuchs, 1940, Part IV). We use the formulae developed by Kemmer (1939), with a small modification, introduced so that the set of Maxwell's equations for the electro-magnetic field is obtained as a special case.

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