Sentence examples for be valid in limiting from inspiring English sources

A fully coupled three-dimensional finite-element model for hydraulic fractures in permeable rocks is presented, and used to investigate the ranges of applicability of the classical analytical solutions that are known to be valid in limiting cases.

A very simple approximate explicit expression is also given for the mass transfer coefficient, that is shown to be valid in the low oxygen flux limit or when the primary combustion product is CO2.

While the results reported here are limited to the yeast S. cerevisiae, we expect our approach to be valid in other organisms as well, including human.

The model is limited to a constant respiratory resistance throughout inspiration which may not be valid in some cases.

That may be valid in the abstract.

Whatever is valid in the rest of Europe must also be valid in Greece.

Equation 9.5 provides the expected relation that is valid in the limit where the background count rate b is small compared with the source count rate sl, that the signal-to-noise ratio scales with the square root of the exposure time.

Thus, our result is valid in the limit | λ | ≪ 1.

Note that this has been constructed using a matched asymptotic expansion, using (17), and is valid in the limit τ → 0. For weak forcing, where ε ≪ 1, P 1, 2 vary slowly through the kick and can be approximated by their values at ( θ n, ρ n ) so that to O ( ε 2 ) θ n + 1 = [ θ n + T + ε P 1 ( θ n, ρ n ) + σ λ ( ρ n + ε P 2 ( θ n ) ) ( 1 − e − λ T ) ] mod 1, (24).

This assumption is valid in the limit of weak selection (Bulmer 1980; Turelli and Barton 1994), but in real climate change events selection is likely to be strong and to vary in time.

These mode energy values would be accurate only for heptamers made of very small nanoparticles, as the boundary integral method is valid in the static limit only.