Deconstructing the energy landscape: new algorithms for folding heteropolymers

We apply the computational methodology of phase retrieval to the problem of folding heteropolymers. The ground state fold of the polymer is defined by the intersection of two sets in the configuration space of its constituent monomers: a geometrical chain constraint and a threshold constraint on the contact energy. A dynamical system is then defined in terms of the projections to these constraint sets, such that its fixed points solve the set intersection problem. We present results for two off-lattice HP models: one with only rotameric degrees of freedom, and one proposed by Stillinger et al. with flexible bond angles. Our phase retrieval inspired algorithm is competitive with more established algorithms and even finds lower energy folds for one of the longer polymer chains.Comment: 7 pages, 8 figure

The Influence of Shape on Ordering of Granular Systems in Two Dimensions

We investigate ordering properties of two-dimensional granular materials using several shapes created by welding ball bearings together. Ordered domains form much more easily in two than in three dimensions, even when configurations lack long-range order. The onset of ordered domains occurs near a packing density of 0.8, a phenomenon observed previously for disks. One of our shapes, the trapezoid, has packings that remain disordered and near the transition density even after annealing by shaking. Since random packings are unstable for disks and many other shapes in two dimensions, trapezoid packings provide a new approach to studying two-dimensional randomness. We also find that the rotational symmetry of a shape is an excellent predictor of how easily it orders, and a potential guide to identifying two-dimensional shapes that remain random after annealing.Comment: 10 pages, 10 figures, conclusions rewritten and minor changes elsewher

Osmium Isotope Systematics of Ureilites

The Os-187/Os-188 for twenty-two ureilite whole rock samples, including monomict, augite-bearing, and polymict lithologies, were examined in order to constrain the provenance and subsequent magmatic processing of the ureilite parent body (or bodies). The Re/Os ratios of most ureilites show evidence for a recent disturbance, probably related to Re mobility during weathering, and no meaningful chronological information can be extracted from the present data set. The ureilite Os-187/Os-188 ratios span a range from 0.11739 to 0.13018, with an average of 0.1258+/-0.0023 (1(sigma)), similar to typical carbonaceous chondrites, and distinct from ordinary or enstatite chondrites. The similar mean of Os-187/Os-188 measured for the ureilites and carbonaceous chondrites suggests that the ureilite parent body probably formed within the same region of the solar nebula as carbonaceous chondrites. From the narrow range of the 187Os/188Os distribution in ureilite meteorites it is further concluded that Re was not significantly fractionated from Os during planetary differentiation and was not lost along with the missing ureilitic melt component. The lack of large Re/Os fractionations requires that Re/Os partitioning was controlled by a metal phase, and thus metal had to be stable throughout the interval of magmatic processing on the ureilite parent body

Two-dimensional Packing in Prolate Granular Materials

We investigate the two-dimensional packing of extremely prolate (aspect ratio $\alpha=L/D>10$) granular materials, comparing experiments with Monte-Carlo simulations. The average packing fraction of particles with aspect ratio $\alpha=12$ is $0.68\pm0.03$. We quantify the orientational correlation of particles and find a correlation length of two particle lengths. The functional form of the decay of orientational correlation is the same in both experiments and simulations spanning three orders of magnitude in aspect ratio. This function decays over a distance of two particle lengths. It is possible to identify voids in the pile with sizes ranging over two orders of magnitude. The experimental void distribution function is a power law with exponent $-\beta=-2.43\pm0.08$. Void distributions in simulated piles do not decay as a power law, but do show a broad tail. We extend the simulation to investigate the scaling at very large aspect ratios. A geometric argument predicts the pile number density to scale as $\alpha^{-2}$. Simulations do indeed scale this way, but particle alignment complicates the picture, and the actual number densities are quite a bit larger than predicted.Comment: 6 pages + 10 ps/eps figure

A petrological, mineralogical and chemical analysis of the lunar mare basalt meteorites LaPaz Icefield 02205, 02224 and 02226

LaPaz Icefield (LAP) 02205, 02226, and 02224 are paired stones of a crystalline basaltic lunar meteorite with a low-Ti (3.21–3.43% TiO2) low-Al (9.93–10.45% Al2O3), and low-K (0.11–0.12% K2O) composition. They consist mainly of zoned pyroxene and plagioclase grains, with minor ilmenite, spinel, and mesostasis regions. Large, possibly xenocrystic, forsteritic olivine grains (<3% by mode) contain small trapped multiphase melt inclusions. Accessory mineral and mesostasis composition shows that the samples have experienced residual melt crystallization with silica oversaturation and late-stage liquid immiscibility. Our section of LAP 02224 has a vesicular fusion crust, implying that it was at one time located sufficiently close to the lunar surface environment to have accumulated solar-wind-implanted gases. The stones have a comparable major element composition and petrography to low-Ti, low-Al basalts collected at the Apollos 12 and 15 landing sites. However, the LAP stones also have an enriched REE bulk composition and are more ferroan (Mg numbers in the range of 31 to 35) than similar Apollo samples, suggesting that they represent members of a previously unsampled fractionated mare basalt suite that crystallized from a relatively evolved lunar melt

Testing the ureilite projectile hypothesis for the El'gygytgyn impact: determination of siderophile element abundances and Os isotope ratios in ICDP drill core samples and melt rocks

The geochemical nature of the impactites from International Continental Scientific Drilling Project-El'gygytgyn lake drill core 1C is compared with that of impact melt rock fragments collected near the western rim of the structure and literature data. Concentrations of major and trace elements, with special focus on siderophile metals Cr, Co, Ni, and the platinum group elements, and isotope ratios of osmium (Os), were determined to test the hypothesis of an ureilite impactor at El'gygytgyn. Least squares mixing calculations suggest that the upper volcanic succession of rhyolites, dacites, and andesites were the main contributors to the polymict impact breccias. Additions of 2-13.5 vol% of basaltic inclusions recovered from drill core intervals between 391.6 and 423.0 mblf can almost entirely account for the compositional differences observed for the bottom of a reworked fallout deposit at 318.9 mblf, a polymict impact breccia at 471.4 mblf, and three impact melt rock fragments. However, the measured Os isotope ratios and slightly elevated PGE content (up to 0.262 ng g(-1) Ir) of certain impactite samples, for which the CI-normalized logarithmic PGE signature displays a relatively flat (i.e., chondritic) pattern, can only be explained by the incorporation of a small meteoritic contribution. This component is also required to explain the exceptionally high siderophile element contents and corresponding Ni/Cr, Ni/Co, and Cr/Co ratios of impact glass spherules and spherule fragments that were recovered from the reworked fallout deposits and from terrace outcrops of the Enmyvaam River approximately 10 km southeast of the crater center. Mixing calculations support the presence of approximately 0.05 wt% and 0.50-18 wt% of ordinary chondrite (possibly type-LL) in several impactites and in the glassy spherules, respectively. The heterogeneous distribution of the meteoritic component provides clues for emplacement mechanisms of the various impactite units

Effect of Re-impacting Debris on the Solidification of the Lunar Magma Ocean

Anorthosites that comprise the bulk of the lunar crust are believed to have formed during solidification of a Lunar Magma Ocean (LMO) in which these rocks would have floated to the surface. This early flotation crust would have formed a thermal blanket over the remaining LMO, prolonging solidification. Geochronology of lunar anorthosites indicates a long timescale of LMO cooling, or re-melting and re-crystallization in one or more late events. To better interpret this geochronology, we model LMO solidification in a scenario where the Moon is being continuously bombarded by returning projectiles released from the Moon-forming giant impact. More than one lunar mass of material escaped the Earth-Moon system onto heliocentric orbits following the giant impact, much of it to come back on returning orbits for a period of 100 Myr. If large enough, these projectiles would have punctured holes in the nascent floatation crust of the Moon, exposing the LMO to space and causing more rapid cooling. We model these scenarios using a thermal evolution model of the Moon that allows for production (by cratering) and evolution (solidification and infill) of holes in the flotation crust that insulates the LMO. For effective hole production, solidification of the magma ocean can be significantly expedited, decreasing the cooling time by more than a factor of 5. If hole production is inefficient, but shock conversion of projectile kinetic energy to thermal energy is efficient, then LMO solidification can be somewhat prolonged, lengthening the cooling time by 50% or more