Predicting Fatigue Crack Growth via Path Slicing and Re-Weighting

Predicting potential risks associated with the fatigue of key structural components is crucial in engineering design. However, fatigue often involves entangled complexities of material microstructures and service conditions, making diagnosis and prognosis of fatigue damage challenging. We report a statistical learning framework to predict the growth of fatigue cracks and the life-to-failure of the components under loading conditions with uncertainties. Digital libraries of fatigue crack patterns and the remaining life are constructed by high-fidelity physical simulations. Dimensionality reduction and neural network architectures are then used to learn the history dependence and nonlinearity of fatigue crack growth. Path-slicing and re-weighting techniques are introduced to handle the statistical noises and rare events. The predicted fatigue crack patterns are self-updated and self-corrected by the evolving crack patterns. The end-to-end approach is validated by representative examples with fatigue cracks in plates, which showcase the digital-twin scenario in real-time structural health monitoring and fatigue life prediction for maintenance management decision-making

Finite groups with some H-subgroups

AbstractA subgroup H is said to be an H-subgroup of a finite group G if Hg∩NG(H)≤H for all g∈G. For every prime p dividing the order of G, let P be a Sylow p-subgroup of G and D a subgroup of P with 1<|D|<|P|. We investigate the structure of G under the assumption that each subgroup H of P with |H|=|D| is an H-subgroup of G. Some earlier results are generalized. Some results about formation are obtained

Perturbative Unitarity and NEC Violation in Genesis Cosmology

Explorations of the violation of null energy condition (NEC) in cosmology could enrich our understanding of the very early universe and the related gravity theories. Although a fully stable NEC violation can be realized in the “beyond Horndeski” theory, it remains an open question whether a violation of the NEC is allowed by some fundamental properties of UV-complete theories or the consistency requirements of effective field theory (EFT). We investigate the tree-level perturbative unitarity for stable NEC violations in the contexts of both Galileon and “beyond Horndeski” genesis cosmology, in which the universe is asymptotically Minkowskian in the past. We find that the constraints of perturbative unitarity imply that we may need some unknown new physics below the cut-off scale of the EFT other than that represented by the “beyond Horndeski” operators