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Abstract Seismic and magnetotelluric studies suggest hydrous silicate melts atop the 410 km discontinuity form 30–100 km thick layers. Importantly, in some regions, two layers are observed. These stagnant layers are related to their comparable density to the surrounding mantle, but their formation mechanisms and detailed structures remain unclear. Here we report a large decrease of silicate melt viscosity at ~14 GPa, from 96(5) to 11.7(6) mPa⋅s, as water content increases from 15.5 to 31.8 mol% H₂O. Such low viscosities facilitate rapid segregation of melt, which would typically prevent thick layer accumulation. Our 1D finite element simulations show that continuous dehydration melting of upwelling mantle material produces a primary melt layer above 410 km and a secondary layer at the depth of equal mantle-melt densities. These layers can merge into a single thick layer under low density contrasts or high upwelling rates, explaining both melt doublets and thick single layers. 

The Sun is the most studied of all stars, and thus constitutes a benchmark for stellar models. However, our vision of the Sun is still incomplete, as illustrated by the current debate on its chemical composition. The problem reaches far beyond chemical abundances and is intimately linked to microscopic and macroscopic physical ingredients of solar models such as radiative opacity, for which experimental results have been recently measured that still await the- oretical explanations. We present opacity profiles derived from helioseismic inferences and compare them with detailed theoretical computations of individual element contributions using three different opacity computation codes, in a complementary way to experimental results. We find that our seismic opacity is about 10% higher than theoretical values used in current solar models around 2 million degrees, but lower by 35% than some recent available theoretical values. Using the Sun as a laboratory of fundamental physics, we show that quantitative comparisons between various opacity tables are required to understand the origin of the discrepancies between reported helioseismic, theoretical and experimental opacity values. 

In the maximum coverage problem we are given d subsets from a universe [n], and the goal is to output k subsets such that their union covers the largest possible number of distinct items. We present the first algorithm for maximum coverage in the turnstile streaming model, where updates which insert or delete an item from a subset come one-by-one. Notably our algorithm only uses polylogn update time. We also present turnstile streaming algorithms for targeted and general fingerprinting for risk management where the goal is to determine which features pose the greatest re-identification risk in a dataset. As part of our work, we give a result of independent interest: an algorithm to estimate the complement of the pth frequency moment of a vector for p ≥ 2. Empirical evaluation confirms the practicality of our fingerprinting algorithms demonstrating a speedup of up to 210x over prior work. 

We consider the problem of finding a minimum cut of a weighted graph presented as a single-pass stream. While graph sparsification in streams has been intensively studied, the specific application of finding minimum cuts in streams is less well-studied. To this end, we show upper and lower bounds on minimum cut problems in insertion-only streams for a variety of settings, including for both randomized and deterministic algorithms, for both arbitrary and random order streams, and for both approximate and exact algorithms. One of our main results is an Õ(n/ε) space algorithm with fast update time for approximating a spectral cut query with high probability on a stream given in an arbitrary order. Our result breaks the Ω(n/ε²) space lower bound required of a sparsifier that approximates all cuts simultaneously. Using this result, we provide streaming algorithms with near optimal space of Õ(n/ε) for minimum cut and approximate all-pairs effective resistances, with matching space lower-bounds. The amortized update time of our algorithms is Õ(1), provided that the number of edges in the input graph is at least (n/ε²)^{1+o(1)}. We also give a generic way of incorporating sketching into a recursive contraction algorithm to improve the post-processing time of our algorithms. In addition to these results, we give a random-order streaming algorithm that computes the exact minimum cut on a simple, unweighted graph using Õ(n) space. Finally, we give an Ω(n/ε²) space lower bound for deterministic minimum cut algorithms which matches the best-known upper bound up to polylogarithmic factors. 

Abstract The mixed layer of polynyas is vital for local climate as it determines the exchange of properties and energy between ocean, sea ice, and atmosphere. However, its evolution is poorly understood, as it is controlled by complex interactions among these components, yet highly undersampled, especially outside summer. Here, we present a 2-month, high vertical-resolution, full-depth hydrographic dataset from the southeastern Amundsen Sea polynya in austral autumn (from mid-February to mid-April 2014) collected by a recovered seal tag. This novel dataset quantifies the changes in upper-ocean temperature and salinity stratification in this previously unobserved season. Our seal-tag measurements reveal that the mixed layer experiences deepening, salinification, and intense heat loss through surface fluxes. Heat and salt budgets suggest a sea ice formation rate of ∼3 cm per day. We use a one-dimensional model to reproduce the mixed layer evolution and further identify key controls on its characteristics. Our experiments with a range of reduced or amplified air–sea fluxes show that heat loss to the atmosphere and related sea ice formation are the principal determinants of stratification evolution. Additionally, our modeling demonstrates that horizontal advection is required to fully explain the mixed layer evolution, underlining the importance of the ice-covered neighboring region for determining sea ice formation rates in the Amundsen Sea polynya. Our findings suggest that the potential overestimation of sea ice production by satellite-based methods, due to the absence of oceanic heat flux, could be offset by horizontal advection inhibiting mixed layer deepening and sustaining sea ice formation. 

CoFe₂O₄–BaTiO₃core–shell nanowires with tunable magnetic anisotropy and magnetoelectric coupling are generated using a template-assisted synthetic procedure providing composition control. 

Abstract The mesoscale spectrum describes the distribution of kinetic energy in the Earth's atmosphere between length scales of 10 and 400 km. Since the first observations, the origins of this spectrum have been controversial. At synoptic scales, the spectrum follows a −3 spectral slope, consistent with two‐dimensional turbulence theory, but a shallower −5/3 slope was observed at the shorter mesoscales. The cause of the shallower slope remains obscure, illustrating our lack of understanding. Through a novel coarse‐graining methodology, we are able to present a spatio‐temporal climatology of the spectral slope. We find convection and orography have a shallowing effect and can quantify this using “conditioned spectra.” These are typical spectra for a meteorological condition, obtained by aggregating spectra where the condition holds. This allows the investigation of new relationships, such as that between energy flux and spectral slope. Potential future applications of our methodology include predictability research and model validation.