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We present a procedure that calculates the layout corresponding to a given slicing tree on the basis of bounding curves.
In addition to the incorporation of facilities with unequal areas we also integrate the possibility to specify various requirements regarding (rectangular) shape and dimensions of each individual facility by using bounding curves.
Numerical modeling of mixed-wet systems with a thick transition zone typically requires the full hysteresis option to be invoked in the reservoir simulator, and this requires preparing all the bounding curves for each rock type.
Capillary drainage and imbibition bounding curves (complete bounding cycle) and a number of scanning curves have been measured for a water-wet Berea core and an oil-wet reservoir core by the micropore membrane technique.
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For this problem, we first show how to lower bound the bending energy of an optimal curve with bounded curvature, and then use this lower bound to design a (1+ϵ -approximation algorithm for this restricted version of the MinBEP problem.
Through Figs. 3, 4, 5, 6, 7 and 8, capillary pressure hysteresis can be clearly observed from the secondary drainage and bounding imbibition curves.
This observation enables the establishment of two design approximations which are lower bound curves to finite element results.
We derive lower-bound curves for several problems, and prove that existing or new one-round algorithms solving these problems are optimal, i.e., incur the minimum possible communication cost for different parallelism levels.
Some of the knock-down factors applied in design of rocket launcher structures are based on design recommendations which rely on lower-bound curves from experimental data.
A comprehensive scenario of the stabilization regions is given in which lower-bound as well as upper-bound curves are evaluated, thus integrating results that recently appeared in the literature.
The separation performance of the polyimides for various gas pairs were also plotted for comparison to the upper bound curves, and it was found that this family of materials shows attractive performance.
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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