Based on the "exact" acoustic pressure wave equation, it is also concluded that flow-meter errors become independent of ultrasound frequency and cylinder radius, a point that the LPW approximation fails to predict.
This conceptually clean approach is very general and can be applied to various settings where the Newtonian approximation fails or becomes inaccurate, ranging from simulations of models with dynamical dark energy3 or warm/hot dark matter4 to core collapse supernova explosions5.
In contrast for bound chaotic systems the orbits start coalescing in increasing numbers on the scale of \(t_{E}\), implying that the semi-classical approximation fails by \(t_{E}\).
Remark 4.2 For the Euler equation u ″ ( t ) + R A ( t ) u ( t ) = 0 with R A ( t ) = 1 4 t 2, we have r ( t ) ≡ − 1, and the Hartman-Wintner approximation fails.
Further, as we using scaling to bring our problem to the standard one, we see that in the zone ({x:,d(x asymp B^{-1/4}}), the effective semiclassical parameter is (h_{{mathsf {eff}}} = B^{1/5}Z^{-3/5} 1/5}Z^{-3/5}re unless (Bll Z^3), the semiclandical approximatherefores and the correct answer shounless expressed in completely different terms [18]; compare with [19].
They are just present in much smaller amount, and when this amount grows, then the QSS approximation fails.
We set values of µs' in accordance with Mie theory, which may cause large errors in reflectance at short SDSs where diffusion approximation fails.
However, this approximation fails to describe several bacterial species, for which large additional replicons are present as secondary chromosomes, megaplasmids, etc.
When the normality approximation fails due to extremely low MAF, the p-values were validated by the Fisher's exact test.
Smith's and Fatti's approximations failed to estimate reservoir porosity because of associated uncertainties.
