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Register a new userElementary structural building blocks encountered in silicon surface reconstructions
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Driven by the reduction of dangling bonds and the minimization of surface stress, reconstruction of silicon surfaces leads to a striking diversity of outcomes. Despite this variety even very elaborate structures are generally comprised of a small number of structural building blocks. We here identify important elementary building blocks and discuss their integration into the structural models as well as their impact on the electronic structure of the surface.
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The link between chemical orbitals described by local degrees of freedom and band theory, which is defined in momentum space, was proposed by Zak several decades ago for spinless systems with and without time-reversal in his theory of elementary band representations. In Nature 547, 298-305 (2017), we introduced the generalization of this theory to the experimentally relevant situation of spin-orbit coupled systems with time-reversal symmetry and proved that all bands that do not transform as band representations are topological. Here, we give the full details of this construction. We prove that elementary band representations are either connected as bands in the Brillouin zone and are described by localized Wannier orbitals respecting the symmetries of the lattice (including time-reversal when applicable), or, if disconnected, describe topological insulators. We then show how to generate a band representation from a particular Wyckoff position and determine which Wyckoff positions generate elementary band representations for all space groups. This theory applies to spinful and spinless systems, in all dimensions, with and without time reversal. We introduce a homotopic notion of equivalence and show that it results in a finer classification of topological phases than approaches based only on the symmetry of wavefunctions at special points in the Brillouin zone. Utilizing a mapping of the band connectivity into a graph theory problem, which we introduced in Nature 547, 298-305 (2017), we show in companion papers which Wyckoff positions can generate disconnected elementary band representations, furnishing a natural avenue for a systematic materials search.
There are two dominant and contrasting classes of origin of life scenarios: those predicting that life emerged in submarine hydrothermal systems, where chemical disequilibrium can provide an energy source for nascent life; and those predicting that life emerged within subaerial environments, where UV catalysis of reactions may occur to form the building blocks of life. Here, we describe a prebiotically plausible environment that draws on the strengths of both scenarios: surface hydrothermal vents. We show how key feedstock molecules for prebiotic chemistry can be produced in abundance in shallow and surficial hydrothermal systems. We calculate the chemistry of volcanic gases feeding these vents over a range of pressures and basalt C/N/O contents. If ultra-reducing carbon-rich nitrogen-rich gases interact with subsurface water at a volcanic vent they result in 1 mM to 1 M concentrations of diacetylene, acetylene, cyanoacetylene, hydrogen cyanide, bisulfite, hydrogen sulfide and soluble iron in vent water. One key feedstock molecule, cyanamide, is not formed in significant quantities within this scenario, suggesting that it may need to be delivered exogenously, or formed from hydrogen cyanide either via organometallic compounds, or by some as yet-unknown chemical synthesis. Given the likely ubiquity of surface hydrothermal vents on young, hot, terrestrial planets, these results identify a prebiotically plausible local geochemical environment, which is also amenable to future lab-based simulation.
Four rigid panels connected by hinges that meet at a point form a 4-vertex, the fundamental building block of origami metamaterials. Here we show how the geometry of 4-vertices, given by the sector angles of each plate, affects their folding behavior. For generic vertices, we distinguish three vertex types and two subtypes. We establish relationships based on the relative sizes of the sector angles to determine which folds can fully close and the possible mountain-valley assignments. Next, we consider what occurs when sector angles or sums thereof are set equal, which results in 16 special vertex types. One of these, flat-foldable vertices, has been studied extensively, but we show that a wide variety of qualitatively different folding motions exist for the other 15 special and 3 generic types. Our work establishes a straightforward set of rules for understanding the folding motion of both generic and special 4-vertices and serves as a roadmap for designing origami metamaterials.
The stellar halos of galaxies encode their accretion histories. In particular, the median metallicity of a halo is determined primarily by the mass of the most massive accreted object. We use hydrodynamical cosmological simulations from the APOSTLE project to study the connection between the stellar mass, the metallicity distribution, and the stellar age distribution of a halo and the identity of its most massive progenitor. We find that the stellar populations in an accreted halo typically resemble the old stellar populations in a present-day dwarf galaxy with a stellar mass $sim 0.2-0.5$ dex greater than that of the stellar halo. This suggest that had they not been accreted, the primary progenitors of stellar halos would have evolved to resemble typical nearby dwarf irregulars.
The future of main memory appears to lie in the direction of new non-volatile memory technologies that provide strong capacity-to-performance ratios, but have write operations that are much more expensive than reads in terms of energy, bandwidth, and latency. This asymmetry can have a significant effect on algorithm design, and in many cases it is possible to reduce writes at the cost of reads. In this paper, we study which algorithmic techniques are useful in designing practical write-efficient algorithms. We focus on several fundamental algorithmic building blocks including unordered set/map implemented using hash tables, ordered set/map implemented using various binary search trees, comparison sort, and graph traversal algorithms including breadth-first search and Dijkstras algorithm. We introduce new algorithms and implementations that can reduce writes, and analyze the performance experimentally using a software simulator. Finally we summarize interesting lessons and directions in designing write-efficient algorithms.
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