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So, it is necessary to use finer elements until the deformed solution converges to an accepted value.
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It was found that the regular laminar flow patterns for low-Reynolds-number Newtonian fluid flow in different microchannels were strongly deformed in solution flows: either asymmetrical flow structures or time-dependent vortical fluid motions appeared.
However, post-processing, the severely deformed solid solution was found to be unstable at room temperature and copious precipitation of θ occurred at grain boundaries within the deformed state, leading to recovery of the deformation structure and a loss of strength.
A theoretical framework, which considers the effect of strong inter-polymer associations on phase separation of a deforming polyacrylamide solution is presented.
Both interface geometry based deformed meshes and solution gradient based deformed meshes are constructed to reduce the L∞ and L2 errors in solving elliptic interface problems.
Kondo et al. (2005) conducted microstructural observations on samples from the outcrop and documented that the shale-dominated zones were deformed by pressure solution whereas plastic flow associated with dynamic recrystallization of quartz aggregates occurred in the sandstones and mineral veins.
In this way, one obtains a family of approximate solutions of the minimal surface equation, and Kapouleas and Yang showed that these surfaces can be deformed to exact solutions of the minimal surface equation by means of the implicit function theorem.
Here is our main result which expresses that there does persist a large Cantor sub-family of rotational (mathbb{Z} -tori which are only slightly deformed, thus the solutions starting from the persisted tori are almost-periodic breathers of (1.1).
Kawabata et al. (2007) determined the variation in whole-rock geochemistry of scaly shales in the Mugi mélange, and used a Ti-normalized isocon approach (Grant 1986) to estimate a total volume loss of 17 to 54 vol.% from the deformed mélanges during pressure solution deformation, the majority of which was fluid-mobile SiO2.
The shear stress inferred from the metachert is consistent with dislocation creep (Fig. 6), as is also suggested by the microstructure, but it appears to be inconsistent with the fact that the metagreywackes deformed predominantly by pressure solution, which in pure quartz would require lower stress or smaller grain size, or both (Fig. 6).
An Al 0.2 wt% Sc alloy was solution treated, deformed by equal channel angular pressing (ECAP) to an effective true strain of 9.2 then aged for 3 h at 350 °C to produce a fine-grained (0.8 μm diameter) microstructure containing a large fraction (∼0.7) of high angle grain boundaries (HAGBs).
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