Sentence examples for as the length scale from inspiring English sources

As the length scale of materials decreases to the nanometer regime, grain boundaries occupy a relatively larger volume fraction.

Interestingly, for many surfaces the roughness varies in a well defined way as the length scale is varied (so-called self afine surfaces).

The volume fractions of these three microstructures, as well as the length scale of each microstructure, are shown to determine the properties of the material.

As the length scale and strain gradient affect only the constitutive relation, it is unnecessary to introduce either additional model variables or higher order stress components.

We use the shell thickness D=r cmb−r icb as the length scale, the viscous diffusion time D 2/ν as the time scale, and 1/2 as the magnetic scale.

However, experimental evidence points at turbulence being a typical multifractal process, which suggests that the statistics at different scales of atmospheric turbulence are not strictly self-similar but exhibit stronger non-Gaussianity as the length scale decreases.

Examined more closely, the dendrites produced by method (i) perform progressively better as the length scales become smaller.

As the length scales being examined in these studies have progressively shrunk, progress in interpreting the nanoworld has become increasingly dependent on techniques capable of nanoscale measurements within physiologically relevant environments.

Chemical gradient systems can also be applied to other fields such as drug design, chemical synthesis, chemotaxis, etc. Microfluidic systems are particularly amenable to gradient formation, as the length scales used in chips enable fluid processes that cannot be conducted in bulk scale.

Curvature effects become more significant as we decrease the length scale of the problem at hand and thus accurate computation of curvature is especially important when considering microscale multiphase flows.

As a consequence, the length scale ξ is determined self-consistently via (A2) ξ = m   log (K ξ s 0 ) s 0. Up to logarithmic corrections, we thus have test ≈ 1/ s0 and ξ ∼ m / s 0, which corresponds to the width of a Fisher wave (Fisher 1937).