Sentence examples for microscopic length scale from inspiring English sources

and then consider the limiting case ε → 0. This idea is motivated by physical diffusion which broadens sincere discontinuities to differentiable steep gradients at the (microscopic) length scale of the mean free path of the particles.

That real systems may be pictured as fractal set on the nanometer (and thus microscopic) length scale was first demonstrated by the analysis by Avnir, Farin and Pfeifer for the surfaces of several porous adsorbents [25 27].

Attention has been drawn to the fact that chirality present at the molecular level (at the microscopic length scale) is responsible for driving the chiral shape of the domains composed of such molecules which are of mesoscopic dimension.

Here, it is assumed that the size of holes in the porous plate is much larger than a characteristic microscopic length scale of the micropolar fluid to simplify formulation of the boundary conditions.

On the other hand, there are processes with a dominant microscopic length scale, such as small Nernst diffusion thickness in heat/mass transfer [13], small hydraulic radius in microfluidics [14 17], small pore diameter in filtration [5], etc., where the bulk rheology characteristics should be completed using another kind of information.

It is known that the assumption of normal or shear stresses at the free surface and no-slip at the plate gives solutions with a force singularity on a microscopic length scale, and predicts a constant free surface velocity somewhat less than the strip velocity.

The diffusional processes that govern such densification occur on microscopic length scales, and depend on the type of material and the nature of the porosity.

The influence of these microscopic length scales is elucidated via a series of numerical examples performed using the finite element method.

The multiscale problem, which involves both macroscopic and microscopic length scales, is analyzed using asymptotic expansion homogenization coupled with the finite element method.

Therefore, this investigation aims at articulating a rigorous theoretical and experimental framework in order to assess the fracture toughness at both the macroscopic and the microscopic length scales, using scratch tests.

Features of the diffusion-time dependence of the diffusion-weighted magnetic resonance imaging (MRI) signal provide a new contrast that could be altered by numerous biological processes and pathologies in tissue at microscopic length scales.