Symmetry axis, artificial

The nonzero solutions of these held components either diverge at the origin or become divergent at large distances from the axis of symmetry. Such solutions are therefore not physically relevant to conhgurations that are extended over the entire vacuum space. The introduction of artificial internal boundaries within the vacuum region would also become irrelevant from the physical point of view, nor would it remove the difficulties with the boundary conditions. 

The individual crystals in wire are so oriented that the same crystallographic direction [m w] in most of the grains is parallel or nearly parallel to the wire axis. Because a similar texture occurs in natural and artificial fibers, it is called 3i fiber texture and the axis of the wire is called the fiber axis. Materials having a fiber texture have rotational symmetry about an axis in the sense that all crystal orientations about this axis are equally probable, like those of beads on a string. A fiber texture is therefore to be expected in any material formed by forces that have... 

Symmetry.—The Ising model, like the phenomenon of ferromagnetism which it was designed to simulate, has as an essential feature an exact symmetry. All the thermodynamic functions are symmetric or antisymmetric with respect to an axis of zero magnetic field. Transcription of this model to that of a one-component fluid leads to the highly artificial lattice-gas in which the critical density is exactly half the density po of the close-packed lattice. 

The symmetry point group of the molecule in the quadrupolar field is thus C2v, which bears the same relation to Coov as D2/1 does to Doo/i- The reduction of symmetry from Doo/i to Coov or from D2/1 to C2V - is a result of a dipolar field along the z axis. The greater electronegativity of oxygen than carbon is the natural equivalent of the artificial dipolar field introduced in Section 2.2.6, the effect of which on an isolated atom was illustrated in Fig. 2.9. 

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