Approximate affine linear relationship between L1 norm objective functional values and L2 norm constraint bounds

For an optimization problem with an norm objective function subject to an norm inequality constraint, this paper shows that there is an approximately linear relationship between the norm objective functional values and the norm specifications. This relationship is verified through the use of random and real world industrial data. The obtained results can be employed for 1) estimating the norm output objective functional value without solving the optimization problem numerically; 2) providing an insight for defining the norm specification in which a simple method is proposed in this paper; and 3) testing whether the obtained solutions are the globally optimal solutions or not. These advantages are demonstrated via the use of random data

Developing an inverted Barrovian sequence; insights from monazite petrochronology

In the Himalayan region of Sikkim, the well-developed inverted metamorphic sequence of the Main Central Thrust (MCT) zone is folded, thus exposing several transects through the structure that reached similar metamorphic grades at different times. In-situ LA-ICP-MS U–Th–Pb monazite ages, linked to pressure–temperature conditions via trace-element reaction fingerprints, allow key aspects of the evolution of the thrust zone to be understood for the first time. The ages show that peak metamorphic conditions were reached earliest in the structurally highest part of the inverted metamorphic sequence, in the Greater Himalayan Sequence (GHS) in the hanging wall of the MCT. Monazite in this unit grew over a prolonged period between ~37 and 16 Ma in the southerly leading-edge of the thrust zone and between ~37 and 14.5 Ma in the northern rear-edge of the thrust zone, at peak metamorphic conditions of ~790 ◦C and 10 kbar. Monazite ages in Lesser Himalayan Sequence (LHS) footwall rocks show that identical metamorphic conditions were reached ~4–6 Ma apart along the ~60 km separating samples along the MCT transport direction. Upper LHS footwall rocks reached peak metamorphic conditions of ~655 ◦C and 9 kbar between ~21 and 16 Ma in the more southerly-exposed transect and ~14.5–12 Ma in the northern transect. Similarly, lower LHS footwall rocks reached peak metamorphic conditions of ~580 ◦C and 8.5 kbar at ~16 Ma in the south, and 9–10 Ma in the north. In the southern transect, the timing of partial melting in the GHS hanging wall (~23–19.5 Ma) overlaps with the timing of prograde metamorphism (~21 Ma) in the LHS footwall, confirming that the hanging wall may have provided the heat necessary for the metamorphism of the footwall. Overall, the data provide robust evidence for progressively downwards-penetrating deformation and accretion of original LHS footwall material to the GHS hanging wall over a period of ~5 Ma. These processes appear to have occurred several times during the prolonged ductile evolution of the thrust. The preserved inverted metamorphic sequence therefore documents the formation of sequential ‘paleothrusts’ through time, cutting down from the original locus of MCT movement at the LHS–GHS protolith boundary and forming at successively lower pressure and temperature conditions. The petrochronologic methods applied here constrain a complex temporal and thermal deformation history, and demonstrate that inverted metamorphic sequences can preserve a rich record of the duration of progressive ductile thrusting

The ELFIN mission

The Electron Loss and Fields Investigation with a Spatio-Temporal Ambiguity-Resolving option (ELFIN-STAR, or heretoforth simply: ELFIN) mission comprises two identical 3-Unit (3U) CubeSats on a polar (∼93∘ inclination), nearly circular, low-Earth (∼450 km altitude) orbit. Launched on September 15, 2018, ELFIN is expected to have a >2.5 year lifetime. Its primary science objective is to resolve the mechanism of storm-time relativistic electron precipitation, for which electromagnetic ion cyclotron (EMIC) waves are a prime candidate. From its ionospheric vantage point, ELFIN uses its unique pitch-angle-resolving capability to determine whether measured relativistic electron pitch-angle and energy spectra within the loss cone bear the characteristic signatures of scattering by EMIC waves or whether such scattering may be due to other processes. Pairing identical ELFIN satellites with slowly-variable along-track separation allows disambiguation of spatial and temporal evolution of the precipitation over minutes-to-tens-of-minutes timescales, faster than the orbit period of a single low-altitude satellite (Torbit ∼ 90 min). Each satellite carries an energetic particle detector for electrons (EPDE) that measures 50 keV to 5 MeV electrons with Δ E/E 1 MeV. This broad energy range of precipitation indicates that multiple waves are providing scattering concurrently. Many observed events show significant backscattered fluxes, which in the past were hard to resolve by equatorial spacecraft or non-pitch-angle-resolving ionospheric missions. These observations suggest that the ionosphere plays a significant role in modifying magnetospheric electron fluxes and wave-particle interactions. Routine data captures starting in February 2020 and lasting for at least another year, approximately the remainder of the mission lifetime, are expected to provide a very rich dataset to address questions even beyond the primary mission science objective.Published versio