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Ill-posedness for the compressible Navier–Stokes equations has been proved by Chen et al. [On the ill-posedness of the compressible Navier–Stokes equations in the critical Besov spaces, Revista Mat. Iberoam.31 (2015), 1375–1402] in critical Besov space
framework. In this paper, we prove ill-posedness with the initial data satisfying
To accomplish this goal, we require a norm inflation coming from the coupling term
and construct a new decomposition of the density.
Bragg coherent X-ray diffraction imaging has been used to determine the structure of the initial clusters of α-Fe nano crystals which form upon annealing of an iron-based amorphous alloy or metallic glass. The method is able to identify the shapes and strain of these crystallites without any need for cutting the sample, so can visualize them in three dimensions in their intact state. In this way, the delicate dendritic structures on the exterior of the crystallites can be seen and its density versus radius relationship identifies a fractal dimension of the porous region that is consistent with diffusion-limited aggregation models. The crystal sizes were found to be around 60 nm after annealing at 700 °C growing to about 330 nm after annealing at 750 °C. This article introduces the BCDI method and describes its application to characterize previously recrystallized samples of iron-based amorphous alloys. It paves the way for a possible future in situ nucleation/growth investigation of the relationship between kinetics and nanostructure of metallic glass.
A combinatorial approach has been utilized for researching the luminescence of rare-earth ions complexes (RE(DBM)3·Phen, RE=Dy3+, La3+, Gd3+, Sm3+, Y3+) sensitized Eu3+ complex in PMMA matrix. The results show that the La3+ complex has the maximum sensitization efficiency among these sensitization ions. The luminescent intensities increase as the Eu content increase in PMMA matrix. The La3+ complex exhibits higher sensitization efficiency at lower Eu content in PMMA matrix. At a content of 5% Eu complex, the maximum sensitization efficiency of La3+ is more than 20 times.
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