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It is noteworthy to mention that researchers using NSM and PM oftentimes assume that the fractality of the aggregates is conserved between two- and three-dimensions within the aggregate length scale.
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In contrast, the simple filler PA1 forms large irregular aggregates on the length scale of hundreds of nanometers.
Large fractions of both ionomers do not exhibit visible aggregates on the STEM length scale.
To characterize the surface morphology and to evaluate the light trapping efficiency of the thin film, aggregate surface roughness and slope corresponding to length scale of visible light are introduced as the root-mean squares of the aggregate surface height profile and aggregate surface slope profile.
LDPM-F is a three-dimensional model that simulates concrete at the length scale of coarse aggregate pieces (meso-scale) through the adoption of a discrete modeling framework for both fiber reinforcement and embedding matrix heterogeneity.
With mesoscale constitutive laws governing cohesive fracture, strain hardening in compression and compaction due to pore collapse, LDPM naturally captures the failure mechanisms at the length scale of coarse aggregate of concrete.
The DEM simulations, which consider the length scale of porous aggregates, are used as numerical triaxial experiments to obtain the behavior of a small volume element of powder under a given load.
There is clearly a defined length scale to the process, as only aggregates of a certain size undergo the unique event.
In an attempt to trace the origins of these rheological properties in shrikhand we characterized its microstructure and showed that there exist two different microstructures: one composed of crystallites of milk fats having a length scale of ∼50 100 μm, and the other composed of aggregates of colloidal casein micelles of ∼0.5 10 μm size.
As this length scale is larger than the wavelength of visible light, these aggregates serve as significant light scattering centers.
Quantitative phase field simulations are then employed to investigate the effect of microstructural length scale on microstructure and texture evolution by stressed grain growth in an elastically deformed polycrystalline aggregate.
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