scholarly journals Hamiltonian for a particle in a magnetic field on a curved surface in orthogonal curvilinear coordinates

2016 ◽  
Vol 380 (36) ◽  
pp. 2876-2880 ◽  
Author(s):  
M.S. Shikakhwa ◽  
N. Chair
Keyword(s):  
Magnetic Field ◽  
Curvilinear Coordinates ◽  
Curved Surface ◽  
Orthogonal Curvilinear Coordinates

scholarly journals Design of a New 1D Halbach Magnet Array with Good Sinusoidal Magnetic Field by Analyzing the Curved Surface

Sensors ◽  
2021 ◽  
Vol 21 (7) ◽  
pp. 2522
Author(s):  
Guangdou Liu ◽  
Shiqin Hou ◽  
Xingping Xu ◽  
Wensheng Xiao
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Permanent Magnet ◽  
Flux Density ◽  
Permanent Magnets ◽  
Air Gap ◽  
Curved Surface ◽  
Magnetic Flux Density ◽  
Sinusoidal Magnetic Field ◽  
The Magnetic Field

In the linear and planar motors, the 1D Halbach magnet array is extensively used. The sinusoidal property of the magnetic field deteriorates by analyzing the magnetic field at a small air gap. Therefore, a new 1D Halbach magnet array is proposed, in which the permanent magnet with a curved surface is applied. Based on the superposition of principle and Fourier series, the magnetic flux density distribution is derived. The optimized curved surface is obtained and fitted by a polynomial. The sinusoidal magnetic field is verified by comparing it with the magnetic flux density of the finite element model. Through the analysis of different dimensions of the permanent magnet array, the optimization result has good applicability. The force ripple can be significantly reduced by the new magnet array. The effect on the mass and air gap is investigated compared with a conventional magnet array with rectangular permanent magnets. In conclusion, the new magnet array design has the scalability to be extended to various sizes of motor and is especially suitable for small air gap applications.

XVI.—On Triple Systems of Surfaces and Non-Orthogonal Curvilinear Coordinates

1927 ◽  
Vol 46 ◽  
pp. 194-205 ◽  
Author(s):  
C. E. Weatherburn
Keyword(s):  
Curvilinear Coordinates ◽  
Triple Systems ◽  
Orthogonal Curvilinear Coordinates ◽  
Orthogonal Systems ◽  
Considerable Detail

The properties of “triply orthogonal” systems of surfaces have been examined by various writers and in considerable detail; but those of triple systems generally have not hitherto received the same attention. It is the purpose of this paper to discuss non-orthogonal systems, and to investigate formulæ in terms of the “oblique” curvilinear coordinates u, v, w which such a system determines.

Influence of magnetic field on the director profile in nematic layer with curved surface

2010 ◽  
Vol 55 (2) ◽  
pp. 300-304
Author(s):  
A. N. Vasil’ev ◽  
N. P. Podolyak
Keyword(s):  
Magnetic Field ◽  
Curved Surface

A 2D Numerical Model for Simulation of Two-Dimensional Circular Dam-Break

2011 ◽  
Vol 130-134 ◽  
pp. 2993-2996
Author(s):  
Ming Qin Liu ◽  
Y.L. Liu
Keyword(s):  
Solution Procedure ◽  
Dam Break ◽  
Curvilinear Coordinates ◽  
Two Dimensional ◽  
Proposed Model ◽  
Curvilinear Coordinate ◽  
Orthogonal Curvilinear Coordinate System ◽  
Orthogonal Curvilinear Coordinates ◽  
Averaged Model ◽  
The Mathematical Model

The purpose of this paper is to present a 2D depth-averaged model under orthogonal curvilinear coordinates for simulating two-dimensional circular dam-break flows. The proposed model uses an orthogonal curvilinear coordinate system efficiently and accurately to simulate the flow field with irregular boundaries. As for the numerical solution procedure, The SIMPLEC solution procedure has been used for the transformed governing equations in the transformed domain. Practical application of the model is illustrated by an example, which demonstrates that the mathematical model can capture hydraulic discontinuities accurately such as steep fronts, hydraulic jump and drop, etc.

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