solenoidal field
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2021 ◽  
Vol 76 (3) ◽  
Author(s):  
Alexey Vladimirovich Borisov ◽  
Andrey Vladimirovich Tsiganov

2018 ◽  
Vol 14 (1) ◽  
pp. 5193-5203
Author(s):  
Valerij Disan Petushchak

Classical electromagnetic theory uses axial pseudo-vectors to describe magnetic interactions. It is impossible to explain adequately magnetic interaction at the micro level (elements of conductors and the magnetic interactions of charges) by axial vectors. As a result, the correct form of interactions in classical electrodynamics is only an integral one. The differential formulas for magnetic interactions violate the third Newton’s law. In the paper, we use polar vectors (real physical vectors) to describe magnetic interactions. On this way, we show that the real physical magnetic field, in contrast to the solenoidal field of the axial vector magnetic induction B, has two components: a potential field with nonvanishing divergence and a solenoidal field with vanishing divergence. These two fields act separately and independently and have different models of interactions. Doing so, we can write differential form  for the Ampere’s law obtaining correct formula for the magnetic interactions and adequate interpretation of the Biot-Savart law.


2016 ◽  
Vol 0 (39) ◽  
pp. 14
Author(s):  
Yu. Batygin ◽  
E. Chaplygin ◽  
M. Barbashova ◽  
S. Shinderuk ◽  
T. Gavrilova

2016 ◽  
Vol 809 ◽  
pp. 585-600 ◽  
Author(s):  
Javier Jiménez

It is remarked that fluxes in conservation laws, such as the Reynolds stresses in the momentum equation of turbulent shear flows, or the spectral energy flux in anisotropic turbulence, are only defined up to an arbitrary solenoidal field. While this is not usually significant for long-time averages, it becomes important when fluxes are modelled locally in large-eddy simulations, or in the analysis of intermittency and cascades. As an example, a numerical procedure is introduced to compute fluxes in scalar conservation equations in such a way that their total integrated magnitude is minimised. The result is an irrotational vector field that derives from a potential, thus minimising sterile flux ‘circuits’. The algorithm is generalised to tensor fluxes and applied to the transfer of momentum in a turbulent channel. The resulting instantaneous Reynolds stresses are compared with their traditional expressions, and found to be substantially different. This suggests that some of the alleged shortcomings of simple subgrid models may be representational artefacts, and that the same may be true of the intermittency properties of the turbulent stresses.


2008 ◽  
Vol 23 (26) ◽  
pp. 2177-2188 ◽  
Author(s):  
PULAK RANJAN GIRI

We discuss Dirac equation and its solution in the presence of solenoid (infinitely long) field in (3+1) dimensions. Starting with a very restricted domain for the Hamiltonian, we show that a one-parameter family of self-adjoint extensions are necessary to make sure the correct evolution of the Dirac spinors. Within the extended domain bound state (BS) and scattering state (SS) solutions are obtained. We argue that the existence of bound state in such system is basically due to the breaking of classical scaling symmetry by the quantization procedure. A remarkable effect of the scaling anomaly is that it puts an open bound on both sides of the spectrum, i.e. E ∈ (-M, M) for ν2[0, 1)! We also study the issue of relationship between scattering state and bound state in the region ν2 ∈ [0, 1) and recovered the BS solution and eigenvalue from the SS solution.


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