toroidal surface

toroidal surface

[tə′rȯid·əl ‚sər·fəs]
(mathematics)
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At the same time, real superconducting toroidal storages are made as a system of individual coils, the axial lines of which are located on a toroidal surface. The parameters of such systems differ from the results of the calculation according to the idealized model [11, 12].
For a real magnetic system, which is a system of individual coils with axial lines located on the surface of the torus, the magnetic field extends beyond the toroidal surface. A qualitative picture of the magnetic flux density lines in the xOy plane of the storage with eight coils is shown in Fig.
Outside the toroidal surface, only a <<buckling>> of the field in the region between the coils is shown for lines with a common magnetic flux density direction, which coincides with the field direction in the central part of the torus.
For a current loop spread over a toroidal surface, the flux density within the central aperture, [B.sub.ap], whose radius is a can, due to the conservation of charge on the torus and the integrated flux threading the aperture, be approximated by [B.sub.ap] [approximately equal to] [(r/a).sup.2]B(0) [approximately equal to][[mu].sub.0]Ir/2[a.sup.2].
We focus on a few types of such toroidal surface current densities and their energies.
is used, which is the radius of the vertical section of the (unique) toroidal surface corresponding to the current value of [alpha].
It is worth noting that, alternatively, for D [greater than or equal to] 0.5 [R.sub.eq], the LV interface can accurately be approximated by a toroidal surface (that is, considering the vertical section of the interface to be an arc of a circle).
It is apparent that the vertical section of the LV interface is very close to a circle, and therefore the LV interface shape can overall be approximated by a toroidal surface. It should be stressed that the numerical integration of the interface shape is not a trivial problem, due to the difference in scale between the radius a of the upper sphere and the radius R1 of the vertical section of the LV interface.
Although readily produced by advanced amateurs, the toroidal surface was a bit intimidating for me.
At least some moorings were apparently lost to pirates--Richardson claimed to have seen one of his distinctive orange toroidal surface floats on the deck of a Russian trawler.
The latter encompasses both cylindrical and toroidal surfaces and these are collectively known as conic sections since they are curved forms which originate from sections of a cone (Figure 1).
Analytical surfaces commonly used to provide boundaries and trimming for B-Rep solid models have been defined, including direction and plane, right circular cylindrical and conical, spherical, and toroidal surfaces. A parameterization has been defined for each analytical surface entity, allowing a 3-D model space to be mapped into two dimensions.