We establish the criterion for chaos in three-planet systems, for systems similar to those discovered by the Kepler spacecraft. Our main results are as follows: (i) The simplest criterion, which is based on overlapping mean motion resonances (MMRs), only agrees with numerical simulations at a very crude level. (ii) Much...
We establish the criterion for chaos in three-planet systems, for systems similar to those discovered by the Kepler spacecraft. Our main results are as follows: (i) The simplest criterion, which is based on overlapping mean motion resonances (MMRs), only agrees with numerical simulations at a very crude level. (ii) Much...
Missing data are often described as an annoyance in research and generally presented as a source of error or bias during analysis. To this end, methods that center on planned missingness are an underappreciated and powerful tool that can actually be used to improve data collection and the validity of...
Modeling the mechanical performance of metal produced with additive manufacturing (AM) has proven to be a challenging task. In the as-built state, these materials have been shown to exhibit strong heterogeneity and anisotropy. Even after post-processing, such as heat treatment or hot isostatic pressing and depending on the alloy, some...
In the last two decades the number of innovative applications for advanced materials has been rapidly increasing. Shape memory alloys (SMAs) are an exciting class of these materials which exhibit large reversible stresses and strains due to a thermoelastic phase transformation. SMAs have been employed in the biomedical field for...