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Matrix realization of dual quaternionic electromagnetism

100%
Demir S.
Open Physics
|
2007
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vol. 5
|
issue 4
487-506
EN
In this paper, a new representational model based on dual quaternionic matrices is proposed for classical electromagnetism. After demonstrating the isomorphic matrix representations of dual quaternions, Maxwell’s equations and the constitutive relations for electromagnetism are expressed in terms of dual quaternionic matrices. For this purpose, new 8 × 8 matrices connected with quaternion basis elements have been introduced.
2
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On Generalized Landau Levels

76%
Krasoń P., Milewski J.
Acta Physica Polonica A
|
2017
|
vol. 132
|
issue 1
94-96
EN
We consider the dispersion of energy levels for both standard and inverted quantum harmonic oscillators in the presence of a uniform electromagnetic field. For this analysis we use a solution of the corresponding eigenproblem in terms of the Kummer functions. We find a complete description of the energy levels for a particle of mass m and electric charge q subject to the action of a harmonic oscillator and simultaneous uniform magnetic and electric fields. We also analyze the effect of spin on energy levels for an electron.
3
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Mechanical model of the Lorentz force and Coulomb interaction

64%
Dmitriyev V.
Open Physics
|
2008
|
vol. 6
|
issue 3
711-716
EN
The centripetal and Coriolis accelerations experienced by a cart traveling over a rotating turntable are usually calculated proceeding from the known kinematics of the problem. Respective forces can be regarded as due to the entrainment of the cart in the moving solid environs. We extend the approach to the general case of a particle entrained in the flow of the surrounding medium. The expression for the driving force on the particle obtained from the kinematics of the entrainment prescribed appears to be isomorphic to the Lorentz and Coulomb force on a positive electric charge. The inverse direction of the electromagnetic force on a negative charge implies that a growing applied flow induces the upstream motion of the particle. A possible microscopic mechanism for it may be the Magnus force dynamics of a kink in a vortex tangle. The loop on a straight vortex filament can be taken as a model of the electron, the loop with a cavitation models the positron. The Lorentz force is concerned with the Coriolis acceleration. The Coulomb interaction is due to the centripetal or centrifugal force that arises in the turbophoresis of the kink in the perturbation field generated in the medium by the center of pressure.
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