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.

The influence of yield surface shape and damage in the depth-dependent response of bone tissue to nanoindentation using spherical and Berkovich indenters

Prevention and treatment of osteoporosis rely on understanding of the micromechanical behaviour of bone and its influence on fracture toughness and cell-mediated adaptation processes. Postyield properties may be assessed by nonlinear finite element simulations of nanoindentation using elastoplastic and damage models. This computational study aims at determining the influence of yield surface shape and damage on the depth-dependent response of bone to nanoindentation using spherical and conical tips. Yield surface shape and damage were shown to have a major impact on the indentation curves. Their influence on indentation modulus, hardness, their ratio as well as the elastic-to-total work ratio is well described by multilinear regressions for both tip shapes. For conical tips, indentation depth was not statistically significant (p<0.0001). For spherical tips, damage was not a significant parameter (p<0.0001). The gained knowledge can be used for developing an inverse method for identification of postelastic properties of bone from nanoindentation.

Combined LARES-LAGEOS Solutions

LARES is a new spherical geodetic satellite designed for SLR observations. It is made of solid tungsten alloy covered with 92 corner cubes. Due to a very small area-to-mass ratio, the sensitivity of LARES orbits to non-gravitational forces is greatly minimized. We processed 82 weeks (Feb12-Aug13) of LARES observations from a global SLR network and we analyzed the contribution of LARES data to the current SLR products (e.g., global scale and geocenter coordinates). The quality of the combined LARES+LAGEOS-1/2 solutions is also addressed in the paper. Introduction LARES

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.

Coupled W–Os–Pt isotope systematics in IVB iron meteorites: In situ neutron dosimetry for W isotope chronology

Tungsten isotope compositions of magmatic iron meteorites yield ages of differentiation that are within ±2 Ma of the formation of CAIs, with the exception of IVB irons that plot to systematically less radiogenic compositions yielding erroneously old ages. Secondary neutron capture due to galactic cosmic ray (GCR) irradiation is known to lower the ε182W of iron meteorites, adequate correction of which requires a measure of neutron dosage which has not been available, thus far. The W, Os and Pt isotope systematics of 12 of the 13 known IVB iron meteorites were determined by MC-ICP-MS (W, Os, Pt) and TIMS (Os). On the same dissolutions that yield precise ε182W, stable Os and Pt isotopes were determined as in situ neutron dosimeters for empirical correction of the ubiquitous cosmic-ray induced burn-out of 182W in iron meteorites. The W isotope data reveal a main cluster with ε182W of ∼−3.6, but a much larger range than observed in previous studies including irons (Weaver Mountains and Warburton Range) that show essentially no cosmogenic effect on their ε182W. The IVB data exhibits resolvable negative anomalies in ε189Os (−0.6ε) and complementary ε190Os anomalies (+0.4ε) in Tlacotepec due to neutron capture on 189Os which has approximately the same neutron capture cross section as 182W, and captures neutrons to produce 190Os. The least irradiated IVB iron, Warburton Range, has ε189Os and ε190Os identical to terrestrial values. Similarly, Pt isotopes, which are presented as ε192Pt, ε194Pt and ε196Pt range from +4.4ε to +53ε, +1.54ε to −0.32ε and +0.73ε to −0.20ε, respectively, also identify Tlacotepec and Dumont as the most GCR-damaged samples. In W–Os and W–Pt isotope space, the correlated isotope data back-project toward a 0-epsilon value of ε192Pt, ε189Os and ε190Os from which a pre-GCR irradiation ε182W of −3.42±0.09 (2σ) is derived. This pre-GCR irradiation ε182W is within uncertainty of the currently accepted CAI initial ε182W. The Pt and Os isotope correlations in the IVB irons are in good agreement with a nuclear model for spherical irons undergoing GCR spallation, although this model over-predicts the change of ε182W by ∼2×, indicating a need for better W neutron capture cross section determinations. A nucleosynthetic effect in ε184W in these irons of −0.14±0.08 is confirmed, consistent with the presence of Mo and Ru isotope anomalies in IVB irons. The lack of a non-GCR Os isotope anomaly in these irons requires more complex explanations for the production of W, Ru and Mo anomalies than nebular heterogeneity in the distribution of s-process to r-process nuclides.

ANALYTICAL MODELS OF EXOPLANETARY ATMOSPHERES. I. ATMOSPHERIC DYNAMICS VIA THE SHALLOW WATER SYSTEM

Within the context of exoplanetary atmospheres, we present a comprehensive linear analysis of forced, damped, magnetized shallow water systems, exploring the effects of dimensionality, geometry (Cartesian, pseudo-spherical, and spherical), rotation, magnetic tension, and hydrodynamic and magnetic sources of friction. Across a broad range of conditions, we find that the key governing equation for atmospheres and quantum harmonic oscillators are identical, even when forcing (stellar irradiation), sources of friction (molecular viscosity, Rayleigh drag, and magnetic drag), and magnetic tension are included. The global atmospheric structure is largely controlled by a single key parameter that involves the Rossby and Prandtl numbers. This near-universality breaks down when either molecular viscosity or magnetic drag acts non-uniformly across latitude or a poloidal magnetic field is present, suggesting that these effects will introduce qualitative changes to the familiar chevron-shaped feature witnessed in simulations of atmospheric circulation. We also find that hydrodynamic and magnetic sources of friction have dissimilar phase signatures and affect the flow in fundamentally different ways, implying that using Rayleigh drag to mimic magnetic drag is inaccurate. We exhaustively lay down the theoretical formalism (dispersion relations, governing equations, and time-dependent wave solutions) for a broad suite of models. In all situations, we derive the steady state of an atmosphere, which is relevant to interpreting infrared phase and eclipse maps of exoplanetary atmospheres. We elucidate a pinching effect that confines the atmospheric structure to be near the equator. Our suite of analytical models may be used to develop decisively physical intuition and as a reference point for three-dimensional magnetohydrodynamic simulations of atmospheric circulation.

Analytical Models of Exoplanetary Atmospheres. II. Radiative Transfer via the Two-Stream Approximation

We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and solutions describing two-stream radiative transfer (which approximates the passage of radiation as a pair of outgoing and incoming fluxes), flux-limited diffusion (which describes radiative transfer in the deep interior) and solutions for the temperature-pressure profiles. Generally, the problem is mathematically under-determined unless a set of closures (Eddington coefficients) is specified. We demonstrate that the hemispheric (or hemi-isotropic) closure naturally derives from the radiative transfer equation if energy conservation is obeyed, while the Eddington closure produces spurious enhancements of both reflected light and thermal emission. We concoct recipes for implementing two-stream radiative transfer in stand-alone numerical calculations and general circulation models. We use our two-stream solutions to construct toy models of the runaway greenhouse effect. We present a new solution for temperature-pressure profiles with a non-constant optical opacity and elucidate the effects of non-isotropic scattering in the optical and infrared. We derive generalized expressions for the spherical and Bond albedos and the photon deposition depth. We demonstrate that the value of the optical depth corresponding to the photosphere is not always 2/3 (Milne's solution) and depends on a combination of stellar irradiation, internal heat and the properties of scattering both in optical and infrared. Finally, we derive generalized expressions for the total, net, outgoing and incoming fluxes in the convective regime.

Comparison of GOCE-GPS gravity fields derived by different approaches

Several techniques have been proposed to exploit GNSS-derived kinematic orbit information for the determination of long-wavelength gravity field features. These methods include the (i) celestial mechanics approach, (ii) short-arc approach, (iii) point-wise acceleration approach, (iv) averaged acceleration approach, and (v) energy balance approach. Although there is a general consensus that—except for energy balance—these methods theoretically provide equivalent results, real data gravity field solutions from kinematic orbit analysis have never been evaluated against each other within a consistent data processing environment. This contribution strives to close this gap. Target consistency criteria for our study are the input data sets, period of investigation, spherical harmonic resolution, a priori gravity field information, etc. We compare GOCE gravity field estimates based on the aforementioned approaches as computed at the Graz University of Technology, the University of Bern, the University of Stuttgart/Austrian Academy of Sciences, and by RHEA Systems for the European Space Agency. The involved research groups complied with most of the consistency criterions. Deviations only occur where technical unfeasibility exists. Performance measures include formal errors, differences with respect to a state-of-the-art GRACE gravity field, (cumulative) geoid height differences, and SLR residuals from precise orbit determination of geodetic satellites. We found that for the approaches (i) to (iv), the cumulative geoid height differences at spherical harmonic degree 100 differ by only ≈10 % ; in the absence of the polar data gap, SLR residuals agree by ≈96 % . From our investigations, we conclude that real data analysis results are in agreement with the theoretical considerations concerning the (relative) performance of the different approaches.

A consistent combination of GNSS and SLR with minimum constraints

In this article, the realization of a global terrestrial reference system (TRS) based on a consistent combination of Global Navigation Satellite System (GNSS) and Satellite Laser Ranging (SLR) is studied. Our input data consists of normal equation systems from 17 years (1994– 2010) of homogeneously reprocessed GPS, GLONASS and SLR data. This effort used common state of the art reduction models and the same processing software (Bernese GNSS Software) to ensure the highest consistency when combining GNSS and SLR. Residual surface load deformations are modeled with a spherical harmonic approach. The estimated degree-1 surface load coefficients have a strong annual signal for which the GNSS- and SLR-only solutions show very similar results. A combination including these coefficients reduces systematic uncertainties in comparison to the singletechnique solution. In particular, uncertainties due to solar radiation pressure modeling in the coefficient time series can be reduced up to 50 % in the GNSS+SLR solution compared to the GNSS-only solution. In contrast to the ITRF2008 realization, no local ties are used to combine the different geodetic techniques.We combine the pole coordinates as global ties and apply minimum constraints to define the geodetic datum. We show that a common origin, scale and orientation can be reliably realized from our combination strategy in comparison to the ITRF2008.

Fate of accidental symmetries of the relativistic hydrogen atom in a spherical cavity

The non-relativistic hydrogen atom enjoys an accidental SO(4) symmetry, that enlarges the rotational SO(3) symmetry, by extending the angular momentum algebra with the Runge–Lenz vector. In the relativistic hydrogen atom the accidental symmetry is partially lifted. Due to the Johnson–Lippmann operator, which commutes with the Dirac Hamiltonian, some degeneracy remains. When the non-relativistic hydrogen atom is put in a spherical cavity of radius R with perfectly reflecting Robin boundary conditions, characterized by a self-adjoint extension parameter γ, in general the accidental SO(4) symmetry is lifted. However, for R=(l+1)(l+2)a (where a is the Bohr radius and l is the orbital angular momentum) some degeneracy remains when γ=∞ or γ = 2/R. In the relativistic case, we consider the most general spherically and parity invariant boundary condition, which is characterized by a self-adjoint extension parameter. In this case, the remnant accidental symmetry is always lifted in a finite volume. We also investigate the accidental symmetry in the context of the Pauli equation, which sheds light on the proper non-relativistic treatment including spin. In that case, again some degeneracy remains for specific values of R and γ.

Photometric monitoring of non-resolved space debris and databases of optical light curves.

The population of space debris increased drastically during the last years. Collisions involving massive objects may produce large number of fragments leading to significantly growth of the space debris population. An effective remediation measure in order to stabilize the population in LEO, is therefore the removal of large, massive space debris. To remove these objects, not only precise orbits, but also more detailed information about their attitude states will be required. One important property of an object targeted for removal is its spin period and spin axis orientation. If we observe a rotating object, the observer sees different surface areas of the object which leads to changes in the measured intensity. Rotating objects will produce periodic brightness vari ations with frequencies which are related to the spin periods. Photometric monitoring is the real tool for remote diagnostics of the satellite rotation around its center of mass. This information is also useful, for example, in case of contingency. Moreover, it is also important to take into account the orientation of non-spherical body (e.g. space debris) in the numerical integration of its motion when a close approach with the another spacecr aft is predicted. We introduce the two databases of light curves: the AIUB data base, which contains about a thousand light curves of LEO, MEO and high-altitude debris objects (including a few functional objects) obtained over more than seven years, and the data base of the Astronomical Observatory of Odessa University (Ukraine), which contains the results of more than 10 years of photometric monitoring of functioning satellites and large space debris objects in low Earth orbit. AIUB used its 1m ZIMLAT telescope for all light curves. For tracking low-orbit satellites, the Astronomical Observatory of Odessa used the KT-50 telescope, which has an alt-azimuth mount and allows tracking objects moving at a high angular velocity. The diameter of the KT-50 main mirror is 0.5 m, and the focal length is 3 m. The Odessa's Atlas of light curves includes almost 5,5 thousand light curves for ~500 correlated objects from a time period of 2005-2014. The processing of light curves and the determination of the rotation period in the inertial frame is challenging. Extracted frequencies and reconstructed phases for some interesting targets, e.g. GLONASS satellites, for which also SLR data were available for confirmation, will be presented. The rotation of the Envisat satellite after its sudden failure will be analyzed. The deceleration of its rotation rate within 3 years is studied together with the attempt to determine the orientation of the rotation axis.