Self-adjoint extensions for confined electrons: From a particle in a spherical cavity to the hydrogen atom in a sphere and on a cone

In a recent study of the self-adjoint extensions of the Hamiltonian of a particle confined to a finite region of space, in which we generalized the Heisenberg uncertainty relation to a finite volume, we encountered bound states localized at the wall of the cavity. In this paper, we study this situation in detail both for a free particle and for a hydrogen atom centered in a spherical cavity. For appropriate values of the self-adjoint extension parameter, the bound states localized at the wall resonate with the standard hydrogen bound states. We also examine the accidental symmetry generated by the Runge–Lenz vector, which is explicitly broken in a spherical cavity with general Robin boundary conditions. However, for specific radii of the confining sphere, a remnant of the accidental symmetry persists. The same is true for an electron moving on the surface of a finite circular cone, bound to its tip by a 1/r1/r potential.

Self-assembling cannabinomimetics: supramolecular structures of N-alkyl amides

Certain fatty acid N-alkyl amides from the medicinal plant Echinacea activate cannabinoid type-2 (CB2) receptors. In this study we show that the CB2-binding Echinacea constituents dodeca-2E,4E-dienoic acid isobutylamide (1) and dodeca-2E,4E,8Z,10Z-tetraenoic acid isobutylamide (2) form micelles in aqueous medium. In contrast, micelle formation is not observed for undeca-2E-ene-8,10-diynoic acid isobutylamide (3), which does not bind to CB2, or structurally related endogenous cannabinoids, such as arachidonoyl ethanolamine (anandamide). The critical micelle concentration (CMC) range of 1 and 2 was determined by fluorescence spectroscopy as 200-300 and 7400-10000 nM, respectively. The size of premicelle aggregates, micelles, and supermicelles was studied by dynamic light scattering. Microscopy images show that compound 1, but not 2, forms globular and rod-like supermicelles with radii of approximately 75 nm. The self-assembling N-alkyl amides partition between themselves and the CB2 receptor, and aggregation of N-alkyl amides thus determines their in vitro pharmacological effects. Molecular mechanics by Monte Carlo simulations of the aggregation process support the experimental data, suggesting that both 1 and 2 can readily aggregate into premicelles, but only 1 spontaneously assembles into larger aggregates. These findings have important implications for biological studies with this class of compounds.

Mass spectrometry-based analytical tools for the molecular protein characterization of human plasma lipoproteins

Lipoproteins are a heterogeneous population of blood plasma particles composed of apolipoproteins and lipids. Lipoproteins transport exogenous and endogenous triglycerides and cholesterol from sites of absorption and formation to sites of storage and usage. Three major classes of lipoproteins are distinguished according to their density: high-density (HDL), low-density (LDL) and very low-density lipoproteins (VLDL). While HDLs contain mainly apolipoproteins of lower molecular weight, the two other classes contain apolipoprotein B and apolipoprotein (a) together with triglycerides and cholesterol. HDL concentrations were found to be inversely related to coronary heart disease and LDL/VLDL concentrations directly related. Although many studies have been published in this area, few have concentrated on the exact protein composition of lipoprotein particles. Lipoproteins were separated by density gradient ultracentrifugation into different subclasses. Native gel electrophoresis revealed different gel migration behaviour of the particles, with less dense particles having higher apparent hydrodynamic radii than denser particles. Apolipoprotein composition profiles were measured by matrix-assisted laser desorption/ionization-mass spectrometry on a macromizer instrument, equipped with the recently introduced cryodetector technology, and revealed differences in apolipoprotein composition between HDL subclasses. By combining these profiles with protein identifications from native and denaturing polyacrylamide gels by liquid chromatography-tandem mass spectrometry, we characterized comprehensively the exact protein composition of different lipoprotein particles. We concluded that the differential display of protein weight information acquired by macromizer mass spectrometry is an excellent tool for revealing structural variations of different lipoprotein particles, and hence the foundation is laid for the screening of cardiovascular disease risk factors associated with lipoproteins.

Finite element analysis for prediction of bone strength

Article preview View full access options BoneKEy Reports | Review Print Email Share/bookmark Finite element analysis for prediction of bone strength Philippe K Zysset, Enrico Dall'Ara, Peter Varga & Dieter H Pahr Affiliations Corresponding author BoneKEy Reports (2013) 2, Article number: 386 (2013) doi:10.1038/bonekey.2013.120 Received 03 January 2013 Accepted 25 June 2013 Published online 07 August 2013 Article tools Citation Reprints Rights & permissions Abstract Abstract• References• Author information Finite element (FE) analysis has been applied for the past 40 years to simulate the mechanical behavior of bone. Although several validation studies have been performed on specific anatomical sites and load cases, this study aims to review the predictability of human bone strength at the three major osteoporotic fracture sites quantified in recently completed in vitro studies at our former institute. Specifically, the performance of FE analysis based on clinical computer tomography (QCT) is compared with the ones of the current densitometric standards, bone mineral content, bone mineral density (BMD) and areal BMD (aBMD). Clinical fractures were produced in monotonic axial compression of the distal radii, vertebral sections and in side loading of the proximal femora. QCT-based FE models of the three bones were developed to simulate as closely as possible the boundary conditions of each experiment. For all sites, the FE methodology exhibited the lowest errors and the highest correlations in predicting the experimental bone strength. Likely due to the improved CT image resolution, the quality of the FE prediction in the peripheral skeleton using high-resolution peripheral CT was superior to that in the axial skeleton with whole-body QCT. Because of its projective and scalar nature, the performance of aBMD in predicting bone strength depended on loading mode and was significantly inferior to FE in axial compression of radial or vertebral sections but not significantly inferior to FE in side loading of the femur. Considering the cumulated evidence from the published validation studies, it is concluded that FE models provide the most reliable surrogates of bone strength at any of the three fracture sites.

Micrometer-sized ice particles for planetary-science experiments – II. Bidirectional reflectance

We have measured the bidirectional reflectance of spherical micrometer-sized water-ice particles in the visible spectral range over a wide range of incidence and emission angles. The small ice spheres were produced by spraying fine water droplets directly into liquid nitrogen. The resulting mean particle radii are 1.47 + 0.96 - 0.58 μm. Such a material shares many properties with ice in comets and at the surface of icy satellites. Measurements show that the fresh sample material is highly backscattering, contrasting with natural terrestrial snow and frost. The formation of agglomerates of particles during the sample production results in a noticeable variability of the photometric properties of the samples in their initial state. We have also observed significant temporal evolutions of the scattering behavior of the samples, shifting towards more forward scattering within some tens of hours, resulting most likely from sintering processes. All reflectance data are fitted by the Hapke photometric model (1993 and 2002 formulation) with a one/two/three-parameter Henyey-Greenstein phase function and the resulting Hapke parameters are provided. These parameters can be used to compare laboratory results with the observed photometric behaviors of astronomical objects. We show, in particular, that the optical properties of the fresh micrometer-sized ice samples can be used to reproduce the predominant backscattering in the phase curves of Enceladus and Europa.

Calibration of cosmogenic noble gas production in ordinary chondrites based on 36 Cl- 36 Ar ages. Part 1: Refined produced rates for cosmogenic 21 Ne and 38 Ar

We measured the concentrations and isotopic compositions of He, Ne, and Ar in bulk samples and metal separates of 14 ordinary chondrite falls with long exposure ages and high metamorphic grades. In addition, we measured concentrations of the cosmogenic radionuclides 10Be, 26Al, and 36Cl in metal separates and in the nonmagnetic fractions of the selected meteorites. Using cosmogenic 36Cl and 36Ar measured in the metal separates, we determined 36Cl-36Ar cosmic-ray exposure (CRE) ages, which are shielding-independent and therefore particularly reliable. Using the cosmogenic noble gases and radionuclides, we are able to decipher the CRE history for the studied objects. Based on the correlation 3He/21Ne versus 22Ne/21Ne, we demonstrate that, among the meteorites studied, only one suffered significant diffusive losses (about 35%). The data confirm that the linear correlation 3He/21Ne versus 22Ne/21Ne breaks down at high shielding. Using 36Cl-36Ar exposure ages and measured noble gas concentrations, we determine 21Ne and 38Ar production rates as a function of 22Ne/21Ne. The new data agree with recent model calculations for the relationship between 21Ne and 38Ar production rates and the 22Ne/21Ne ratio, which does not always provide unique shielding information. Based on the model calculations, we determine a new correlation line for 21Ne and 38Ar production rates as a function of the shielding indicator 22Ne/21Ne for H, L, and LL chondrites with preatmospheric radii less than about 65 cm. We also calculated the 10Be/21Ne and 26Al/21Ne production rate ratios for the investigated samples, which show good agreement with recent model calculations.

A Compensating Anastigmatic Submillimeter Array Imaging System for STEAMR

In this paper, we present a novel technique for the removal of astigmatism in submillimeter-wave optical systems through employment of a specific combination of so-called astigmatic off-axis reflectors. This technique treats an orthogonally astigmatic beam using skew Gaussian beam analysis, from which an anastigmatic imaging network is derived. The resultant beam is considered truly stigmatic, with all Gaussian beam parameters in the orthogonal directions being matched. This is thus considered an improvement over previous techniques wherein a beam corrected for astigmatism has only the orthogonal beam amplitude radii matched, with phase shift and phase radius of curvature not considered. This technique is computationally efficient, negating the requirement for computationally intensive numerical analysis of shaped reflector surfaces. The required optical surfaces are also relatively simple to implement compared to such numerically optimized shaped surfaces. This technique is implemented in this work as part of the complete optics train for the STEAMR antenna. The STEAMR instrument is envisaged as a mutli-beam limb sounding instrument operating at submillimeter wavelengths. The antenna optics arrangement for this instrument uses multiple off-axis reflectors to control the incident radiation and couple them to their corresponding receiver feeds. An anastigmatic imaging network is successfully implemented into an optical model of this antenna, and the resultant design ensures optimal imaging of the beams to the corresponding feed horns. This example also addresses the challenges of imaging in multi-beam antenna systems.

Evidence of species-specific neighborhood effects in the dipterocarpaceae of a Bornean rain forest

Although accumulating evidence indicates that local intraspecific density-dependent effects are not as rare in species-rich communities as previously suspected, there are still very few detailed and systematic neighborhood analyses of species-rich communities. Here, we provide such an analysis with the overall goal of quantifying the relative importance of inter- and intraspecific interaction strength in a primary, lowland dipterocarp forest located at Danum, Sabah, Malaysia. Using data on 10 abundant overstory dipterocarp species from two 4-ha permanent plots, we evaluated the effects of neighbors on the absolute growth rate of focal trees (from 1986 to 1996) over increasing neighborhood radii (from 1 to 20 m) with multiple regressions. Only trees 10 cm to < 100 cm girth at breast height in 1986 were considered as focal trees. Among neighborhood models with one neighbor term, models including only conspecific larger trees performed best in five out of 10 species. Negative effects of conspecific larger neighbors were most apparent in large overstory species such as those of the genus Shorea. However, neighborhood models with separate terms and radii for heterospecific and conspecific neighbors accounted for more variability in absolute growth rates than did neighborhood models with one neighbor term. The conspecific term was significant for nine out of 10 species. Moreover, in five out of 10 species, trees without conspecific neighbors had significantly higher absolute growth rates than trees with conspecific neighbors. Averaged over the 10 species, trees without conspecific neighbors grew 32.4 cm(2) in basal area from 1986 to 1996, whereas trees with conspecific neighbors only grew 14.7 cm(2) in basal area, although there was no difference in initial basal area between trees in the two groups. Averaged across the six species of the genus Shorea, negative effects of conspecific larger trees were significantly stronger than for heterospecific larger neighbors. Thus, high local densities within neighborhoods of 20 m may lead to strong intraspecific negative and, hence, density-dependent, effects even in species rich communities with low overall densities at larger spatial scales. We conjecture that the strength of conspecific effects may be correlated with the degree of host specificity of ectomycorrhizae.

The PLATO 2.0 mission

PLATO 2.0 has recently been selected for ESA’s M3 launch opportunity (2022/24). Providing accurate key planet parameters (radius, mass, density and age) in statistical numbers, it addresses fundamental questions such as: How do planetary systems form and evolve? Are there other systems with planets like ours, including potentially habitable planets? The PLATO 2.0 instrument consists of 34 small aperture telescopes (32 with 25 s readout cadence and 2 with 2.5 s candence) providing a wide field-of-view (2232 deg 2) and a large photometric magnitude range (4–16 mag). It focusses on bright (4–11 mag) stars in wide fields to detect and characterize planets down to Earth-size by photometric transits, whose masses can then be determined by ground-based radial-velocity follow-up measurements. Asteroseismology will be performed for these bright stars to obtain highly accurate stellar parameters, including masses and ages. The combination of bright targets and asteroseismology results in high accuracy for the bulk planet parameters: 2 %, 4–10 % and 10 % for planet radii, masses and ages, respectively. The planned baseline observing strategy includes two long pointings (2–3 years) to detect and bulk characterize planets reaching into the habitable zone (HZ) of solar-like stars and an additional step-and-stare phase to cover in total about 50 % of the sky. PLATO 2.0 will observe up to 1,000,000 stars and detect and characterize hundreds of small planets, and thousands of planets in the Neptune to gas giant regime out to the HZ. It will therefore provide the first large-scale catalogue of bulk characterized planets with accurate radii, masses, mean densities and ages. This catalogue will include terrestrial planets at intermediate orbital distances, where surface temperatures are moderate. Coverage of this parameter range with statistical numbers of bulk characterized planets is unique to PLATO 2.0. The PLATO 2.0 catalogue allows us to e.g.: - complete our knowledge of planet diversity for low-mass objects, - correlate the planet mean density-orbital distance distribution with predictions from planet formation theories,- constrain the influence of planet migration and scattering on the architecture of multiple systems, and - specify how planet and system parameters change with host star characteristics, such as type, metallicity and age. The catalogue will allow us to study planets and planetary systems at different evolutionary phases. It will further provide a census for small, low-mass planets. This will serve to identify objects which retained their primordial hydrogen atmosphere and in general the typical characteristics of planets in such low-mass, low-density range. Planets detected by PLATO 2.0 will orbit bright stars and many of them will be targets for future atmosphere spectroscopy exploring their atmosphere. Furthermore, the mission has the potential to detect exomoons, planetary rings, binary and Trojan planets. The planetary science possible with PLATO 2.0 is complemented by its impact on stellar and galactic science via asteroseismology as well as light curves of all kinds of variable stars, together with observations of stellar clusters of different ages. This will allow us to improve stellar models and study stellar activity. A large number of well-known ages from red giant stars will probe the structure and evolution of our Galaxy. Asteroseismic ages of bright stars for different phases of stellar evolution allow calibrating stellar age-rotation relationships. Together with the results of ESA’s Gaia mission, the results of PLATO 2.0 will provide a huge legacy to planetary, stellar and galactic science.

CHEOPS: a space telescope for ultra-high precision photometry of exoplanet transits

The CHaracterising ExOPlanet Satellite (CHEOPS) is a joint ESA-Switzerland space mission (expected to launch in 2017) dedicated to search for exoplanet transits by means of ultra-high precision photometry. CHEOPS will provide accurate radii for planets down to Earth size. Targets will mainly come from radial velocity surveys. The CHEOPS instrument is an optical space telescope of 30 cm clear aperture with a single focal plane CCD detector. The tube assembly is passively cooled and thermally controlled to support high precision, low noise photometry. The telescope feeds a re-imaging optic, which supports the straylight suppression concept to achieve the required Signal to Noise. © (2014) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

Measurement of inclusive jet charged-particle fragmentation functions in Pb+Pb collisions at √sNN = 2.76 TeV with the ATLAS detector

Measurements of charged-particle fragmentation functions of jets produced in ultra-relativistic nuclear collisions can provide insight into the modification of parton showers in the hot, dense medium created in the collisions. ATLAS has measured jets in √sNN=2.76 TeV Pb+Pb collisions at the LHC using a data set recorded in 2011 with an integrated luminosity of 0.14 nb−1. Jets were reconstructed using the anti-kt algorithm with distance parameter values R = 0.2, 0.3, and 0.4. Distributions of charged-particle transverse momentum and longitudinal momentum fraction are reported for seven bins in collision centrality for R=0.4 jets with pjetT>100 GeV. Commensurate minimum pT values are used for the other radii. Ratios of fragment distributions in each centrality bin to those measured in the most peripheral bin are presented. These ratios show a reduction of fragment yield in central collisions relative to peripheral collisions at intermediate z values, 0.04≲z≲0.2 and an enhancement in fragment yield for z≲0.04. A smaller, less significant enhancement is observed at large z and large pT in central collisions.

The triplite–triploidite supergroup: structural modulation in wagnerite, discreditation of magniotriplite, and the new mineral hydroxylwagnerite

Electron-microprobe analysis, single-crystal X-ray diffraction with an area detector, and high-resolution transmission electron microscopy show that minerals related to wagnerite, triplite and triploidite, which are monoclinic Mg, Fe and Mn phosphates with the formula Me2+ 2PO4(F,OH), constitute a modulated series based on the average triplite structure. Modulation occurs along b and may be commensurate with (2b periodicity) or incommensurate but generally close to integer values (∼3b, ∼5b, ∼7b, ∼9b), i.e. close to polytypic behaviour. As a result, the Mg- and F-dominant minerals magniotriplite and wagnerite can no longer be considered polymorphs of Mg2PO4F, i.e., there is no basis for recognizing them as distinct species. Given that wagnerite has priority (1821 vs. 1951), the name magniotriplite should be discarded in favour of wagnerite. Hydroxylwagnerite, end-member Mg2PO4OH, occurs in pyrope megablasts along with talc, clinochlore, kyanite, rutile and secondary apatite in two samples from lenses of pyrope–kyanite–phengite–quartz-schist within metagranite in the coesite-bearing ultrahigh-pressure metamorphic unit of the Dora-Maira Massif, western Alps, Vallone di Gilba, Val Varaita, Piemonte, Italy. Electron microprobe analyses of holotype hydroxylwagnerite and of the crystal with the lowest F content gave in wt%: P2O5 44.14, 43.99; SiO2 0.28, 0.02; SO3 –, 0.01; TiO2 0.20, 0.16; Al2O3 0.06, 0.03; MgO 48.82, 49.12; FeO 0.33, 0.48; MnO 0.01, 0.02; CaO 0.12, 0.10; Na2O 0.01, –; F 5.58, 4.67; H2O (calc) 2.94, 3.36; –O = F 2.35, 1.97; Sum 100.14, 99.98, corresponding to (Mg1.954Fe0.007Ca0.003Ti0.004Al0.002Na0.001)Σ=1.971(P1.003Si0.008)Σ=1.011O4(OH0.526F0.474)Σ=1 and (Mg1.971Fe0.011Ca0.003Ti0.003Al0.001)Σ=1.989(P1.002Si0.001)Σ=1.003O4(OH0.603F0.397)Σ=1, respectively. Due to the paucity of material, H2O could not be measured, so OH was calculated from the deficit in F assuming stoichiometry, i.e., by assuming F + OH = 1 per formula unit. Holotype hydroxylwagnerite is optically biaxial (+), α 1.584(1), β 1.586(1), γ 1.587(1) (589 nm); 2V Z(meas.) = 43(2)°; orientation Y = b. Single-crystal X-ray diffraction gives monoclinic symmetry, space group P21/c, a = 9.646(3) Å, b = 12.7314(16) Å, c = 11.980(4) Å, β = 108.38(4) , V = 1396.2(8) Å3, Z = 16, i.e., hydroxylwagnerite is the OH-dominant analogue of wagnerite [β-Mg2PO4(OH)] and a high-pressure polymorph of althausite, holtedahlite, and α- and ε-Mg2PO4(OH). We suggest that the group of minerals related to wagnerite, triplite and triploidite constitutes a triplite–triploidite super-group that can be divided into F-dominant phosphates (triplite group), OH-dominant phosphates (triploidite group), O-dominant phosphates (staněkite group) and an OH-dominant arsenate (sarkinite). The distinction among the three groups and a potential fourth group is based only on chemical features, i.e., occupancy of anion or cation sites. The structures of these minerals are all based on the average triplite structure, with a modulation controlled by the ratio of Mg, Fe2+, Fe3+ and Mn2+ ionic radii to (O,OH,F) ionic radii.

Compactified N = 1 supersymmetric Yang-Mills theory on the lattice: continuity and the disappearance of the deconfinement transition

Fermion boundary conditions play a relevant role in revealing the confinement mechanism of N=1 supersymmetric Yang-Mills theory with one compactified space-time dimension. A deconfinement phase transition occurs for a sufficiently small compactification radius, equivalent to a high temperature in the thermal theory where antiperiodic fermion boundary conditions are applied. Periodic fermion boundary conditions, on the other hand, are related to the Witten index and confinement is expected to persist independently of the length of the compactified dimension. We study this aspect with lattice Monte Carlo simulations for different values of the fermion mass parameter that breaks supersymmetry softly. We find a deconfined region that shrinks when the fermion mass is lowered. Deconfinement takes place between two confined regions at large and small compactification radii, that would correspond to low and high temperatures in the thermal theory. At the smallest fermion masses we find no indication of a deconfinement transition. These results are a first signal for the predicted continuity in the compactification of supersymmetric Yang-Mills theory.

Understanding measured water rotational temperatures and column densities in the very innermost coma of Comet 73P/Schwassmann–Wachmann 3 B

Direct sublimation of a comet nucleus surface is usually considered to be the main source of gas in the coma of a comet. However, evidence from a number of comets including the recent spectacular images of Comet 103P/Hartley 2 by the EPOXI mission indicates that the nucleus alone may not be responsible for all, or possibly at times even most, of the total amount of gas seen in the coma. Indeed, the sublimation of icy grains, which have been injected into the coma, appears to constitute an important source. We use the fully-kinetic Direct Simulation Monte Carlo model of Tenishev et al. (Tenishev, V.M., Combi, M.R., Davidsson, B. [2008]. Astrophys. J., 685, 659−677; Tenishev, V.M., Combi, M.R., Rubin, M. [2011]. Astrophys. J., 732) to reproduce the measurements of column density and rotational temperature of water in Comet 73P-B/Schwassmann–Wachmann 3 obtained with a very high spatial resolution of ∼30 km using IRCS/Subaru in May 2006 (Bonev, B.P., Mumma, M.J., Kawakita, H., Kobayashi, H., Villanueva, G.L. [2008]. Icarus, 196, 241−248). For gas released solely from the cometary nucleus at a heliocentric distance of 1 AU, modeled rotational temperatures start at 110 K close to the surface and decrease to only several tens of degrees by 10–20 nucleus radii. However, the measured decay of both rotational temperature and column density with distance from the nucleus is much slower than predicted by this simple model. The addition of a substantial (distributed) source of gas from icy grains in the model slows the decay in rotational temperature and provides a more gradual drop in column density profiles. Together with a contribution of rotational heating of water molecules by electrons, the combined effects allow a much better match to the IRCS/Subaru observations. From the spatial distributions of water abundance and temperature measured in 73P/SW3-B, we have identified and quantified multiple mechanisms of release. The application of this tool to other comets may permit such studies over a range of heliocentric and geocentric distances.

Can we constrain the interior structure of rocky exoplanets from mass and radius measurements?

Aims. We present an inversion method based on Bayesian analysis to constrain the interior structure of terrestrial exoplanets, in the form of chemical composition of the mantle and core size. Specifically, we identify what parts of the interior structure of terrestrial exoplanets can be determined from observations of mass, radius, and stellar elemental abundances. Methods. We perform a full probabilistic inverse analysis to formally account for observational and model uncertainties and obtain confidence regions of interior structure models. This enables us to characterize how model variability depends on data and associated uncertainties. Results. We test our method on terrestrial solar system planets and find that our model predictions are consistent with independent estimates. Furthermore, we apply our method to synthetic exoplanets up to 10 Earth masses and up to 1.7 Earth radii, and to exoplanet Kepler-36b. Importantly, the inversion strategy proposed here provides a framework for understanding the level of precision required to characterize the interior of exoplanets. Conclusions. Our main conclusions are (1) observations of mass and radius are sufficient to constrain core size; (2) stellar elemental abundances (Fe, Si, Mg) are principal constraints to reduce degeneracy in interior structure models and to constrain mantle composition; (3) the inherent degeneracy in determining interior structure from mass and radius observations does not only depend on measurement accuracies, but also on the actual size and density of the exoplanet. We argue that precise observations of stellar elemental abundances are central in order to place constraints on planetary bulk composition and to reduce model degeneracy. We provide a general methodology of analyzing interior structures of exoplanets that may help to understand how interior models are distributed among star systems. The methodology we propose is sufficiently general to allow its future extension to more complex internal structures including hydrogen- and water-rich exoplanets.