Hydraulic fracturing is the most widely used primary method for stimulation of unconventional oil and gas resources. While knowledge hydraulic fracture parameters critical to reservoir productivity, predicting initiation important determining complexity network. Subcritical crack growth in rock plays an role forming networks, but understanding influence conditions on subcritical still lacking. ...

This paper introduces a methodology for the reliability-based design optimization of systems with nonlinear aeroelastic constraints. The approach is based on the construction of explicit flutter and subcritical limit cycle oscillation boundaries in terms of deterministic and random design variables. The boundaries are constructed using a support vector machine that provides a way to efficiently...

Confirming previous heuristic analyses à la Belinskii-Khalatnikov-Lifshitz, it is rigorously proven that certain “subcritical” Einstein-matter systems exhibit a monotone, generalized Kasner behaviour in the vicinity of a spacelike singularity. The D−dimensional coupled Einstein-dilaton-p-form system is subcritical if the dilaton couplings of the p-forms belong to some dimension dependent open n...