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The distance between the two boundaries corresponds to a film, and its thickness is given by an analytical expression in terms of the Lambert W function.
For Péclet numbers Pe < 10−6 (small particles) the specific interactions play a less important role and the Sherwood number can be accurately approximated by an analytical expression derived for neglible particle dimensions (ions).
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The present paper explains and demonstrates the SAFE diagram by introducing an analytical expression to identify bladed wheel resonance conditions.
The fracture energy and fracture process zone length of a shear crack in foam near the interface are deduced by fitting an analytical expression for size effect to the test data.
In this paper we address the issue of various constellations and power loading in the MC signal as well as the effect of an arbitrary magnitude clipping response by giving an analytical expression in the form of a power series for computing the EVM of the generalized case.
The relationship between neck profile and the true stress-true strain curve was established by combining an analytical expression for the macroscale mechanics of the flow process with a constitutive equation describing the true stress, true strain and true strain rate dependence of the material.
The acidity in the pit is explained by the hydrolysis of Al3+; an analytical expression for the pH values at the pit bottom for a given dissolution current density is presented.
By applying statistical considerations to an analytical expression of the net power transmission it is possible numerically to calculate an average value of the ratio of reflected to incident wave amplitude at the junction.
Shading of only one of the probes causes specific changes in the electric field, and using the potential difference ΔV between the two probes created by the shading we obtain an analytical expression for the photocurrent density.
In recent studies by Kissick et al., an analytical expression was derived for the uncertainty in the Poisson mean obtained by binomial counting and used to interpret second harmonic generation (SHG) measurements generated from a pulsed laser.
The yield surfaces tabulated in Lee and Parks [7] are consistently fitted by a concise analytical expression whose form is suggested by the present approach.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com