2018/05/20 by S. Ciccariello, Salvino Ciccariello, Piero Riell +4
Materials Science · Physics and Astronomy · #Classical Physics (physics.class-ph) #FOS: Physical sciences #Glass properties and applications #Material Dynamics and Properties #Theoretical and Computational Physics #physics.class-ph
paper · pdf · doi:10.48550/arxiv.1805.07727
35 pages, 5 figure (2 figures consist of four panels)
arxiv created 2018/05/20 · openalex publication_date 2018/05/20 · arxiv updated 2018/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using some rigorous results by Wiener [(1930). \em Acta Math. \bf 30, 118-242] on the Fourier integral of a bounded function and the condition that small-angle scattering intensities of amorphous samples are almost everywhere continuous, we obtain the conditions that must be obeyed by a function η(\br) for this may be considered a physical scattering density fluctuation. It turns out that these conditions can be recast in the form that the V→∞ limit of the modulus of the Fourier transform of η(\br), evaluated over a cubic box of volume V and divided by √(V), exists and that its square obeys the Porod invariant relation. Some examples of one-dimensional scattering density functions, obeying the aforesaid condition, are also numerically illustrated.