At present, there is a consensus that various Stress Driven Rearrangement Instabilities (SDRI) are the implications of the mathematically rigorous theoretical Gibbs thermodynamics. Many applied researchers and practitioners believe that SDRI are also universal physical phenomena occurring over a large range of length scales and applied topics. There is a multitude of publications claiming experimental observation of the SDRI based phenomena. This opinion is challenged by other highly respected scholars claiming theoretical inconsistencies and multiple experimental counterexamples. Such an uncertainty is too costly for further progress on the SDRI topic. The ultimate goal of our project is to resolve this controversy. The project includes experimental, theoretical, and numerical studies. Among various plausible manifestations of SDRI, the authors focused only on two most promising for which the validity of the SDRI has already been claimed by other researchers: a) stress driven corrugations of the solid-melt phase interface in macroscopic quantum ~4He and b) the dislocation-free Stranski-Krastanov pattern of growth of semiconductor quantum dots. We devised a program and experimental set-ups for testing applicability of the SDRI mechanisms using the same physical systems as before but using implications of the SDRI theory for 2D patterning which have never been tested in the past.
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