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Gravitational lenses typically consist of either two or four images (doubles and quads) of the background source. However, it has been shown that gravitational lensing by transparent extended matter distributions should produce an odd number of images. An upper limit for the flux of the missing ‘odd image’ can be obtained using high sensitivity radio observations, such as 5GHz MERLIN (Multi-Element Radio Linked Interferometer Network) data. Limits on the ‘odd image’ flux can then be converted into an upper limit on the core radius of the lensing galaxy.
In the combined stage sintering model previously introduced[l], a single equation was derived that quantifies sintering as a continuous phenomenon from beginning to end. The microstructure is characterized by two separate parameters representing the geometry (Γ) and the scale (G). Calculations of Γ from experimental data show the effect of surface diffusion and microstructural geometry on Γ. The model is reviewed and discussed with respect to the sintering of alumina and spherical nickel powder.
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