2 problems

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Upper-bound conjecture for unequal-volume-fraction microstructures
Consider a composite material whose two phases have unequal volume fractions and are separated by a surface minimizing the total surface area. The upper bound of effective transpor…
Conjecturerefutedcomposite-materials effective-transport surface-minimizationarXiv posted 2 days ago
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Local-minimality conjecture for unreproduced curve portions in triply periodic surface optimization
The computed curves describe triply periodic surfaces parametrized by volume fraction, with points $B$ and $C$ marking portions that the numerical method was unable to reproduce. A…
Conjecturerefutednumerical-methods surface-minimization triply-periodic-surfacesarXiv posted 2 days ago

Upper-bound conjecture for unequal-volume-fraction microstructures