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These theoretical results compare favorably with the experiments, when a semi-empirical correction is used to obtain the correct limit for pure bias flow.
Therefore, our results can also ease the procedure of 'guessing the correct limit'.
Hence, it might be objected that the presented method can only be used a posteriori in order to justify a macroscopic model from a constructed microscopic model and that somehow one has to 'guess' the correct limit in advance.
As opposed to the classical drift-diffusion limit where the stiff collisions are all in one scale, new difficulties arise in the two-scale stiff collision terms because the simple BGK penalization [15] fails to drive the solution to the correct limit.
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In addition to their simplicity, they exhibit the correct limiting behavior.
By knowing the natural laws of the market, political economy offered a way to tell the truth about the correct limits of governmental practice.
The method uses packing specific liquid holdup and pressure drop data to find model coefficients that both minimize relative error in the two-phase momentum equations and ensure correct limiting single phase behavior of the model.
By considering exact near-surface limiting profiles of turbulence quantities such as the eddy viscosity and the turbulent scalar flux, the prescribed turbulent diffusivity profile, which is a core assumption of the AWF, is modelled to have the correct limiting behaviour.
Accuracy-wise, the approach is free from the numerical pollution introduced by the discrete parallel transport term when the perpendicular to parallel transport coefficient ratio χ⊥/χ∥ becomes arbitrarily small, and is shown to capture the correct limiting solution when ϵ="χ⊥L∥2χ∥L⊥2→0 (with L∥, L⊥ the parallel and perpendicular diffusion length scales, respectively).
The "PT Landau Zener" parameter is 11.23where ω S is a characteristic solvent frequency, and the rate constant is 11.24awhere 11.24bThe first factor in eq 11.24b may be compared with eq 5.28, and the second interpolating factor is required to obtain the correct limiting forms of eqs 11.20 and 11.22.
This definition ensures that L eff has the correct limiting behavior as required by Eq. 9, i.e. L eff = L M = L for ε = 1 and L eff → L S = 1 as ε → 0. Note that the true allosteric constant L M increases as 1/ ε n when ε → 0. In Figure 4 we relate the occurrence of inward propagating waves to the properties of the effective Hill coefficient n H as described by Eq. 11.
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CEO of Professional Science Editing for Scientists @ prosciediting.com