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Gerald Schubert

Publications and source records attributed to Gerald Schubert.

At least 19 recordsLinked to original sources
arXiv2021

Venus upper atmosphere revealed by a GCM: II. Model validation with temperature and density measurements

An improved high-resolution ground-to-thermosphere version of the Institut Pierre-Simon Laplace (IPSL) Venus General Circulation Model (VGCM), including non-orographic gravity waves (GW) parameterization and fine-tuned non-LTE parameters, is presented here. We focus on the validation of the model built from a collection of data mostly from Venus Express experiments and coordinated ground-based telescope campaigns, in the upper mesosphere/lower thermosphere of Venus. These simulations result in an overall better agreement with temperature observations above 90 km, compared with previous versions of the VGCM. Density of CO2 and light species (CO and O) are also comparable with observations in terms of trend and order of magnitude. Systematic biases in the temperature structure are found at about 80-100 km and above 130 km at the terminator, possibly due to assumptions on the CO2 mixing ratio made for stellar/solar occultation retrievals and uncertainties on the collisional rate coefficients used in the non-LTE parameterization, respectively. Diurnal and latitudinal distribution of dynamical tracers are also analyzed. Overall, our simulations indicate that a weak westward retrograde wind is present up to about 120 km, producing the CO bulge displacement toward 2h-3h in the morning, instead of piling up at the anti-solar point, as for an idealised SS-AS circulation. This retrograde imbalance is suggested to be produced by perturbations of about 5 days Kelvin wave impacting the mesosphere up to 110 km (see the companion paper Navarro et al. 2021), combined with GW westward acceleration mostly above 110 km. On the whole, these model developments point to the importance of the inclusion of the lower atmosphere, higher resolution and finely tuned parameterizations in GCM of the Venusian upper atmosphere, in order to shed light on existing observations.

astro-ph.EP↗
arXiv2019

Effect of Non-Adiabatic Thermal Profiles on the Inferred Compositions of Uranus and Neptune

It has been a common assumption of interior models that the outer planets of our solar system are convective, and that the internal temperature distributions are therefore adiabatic. This assumption is also often applied to exoplanets. However, if a large portion of the thermal flux can be transferred by conduction, or if convection is inhibited, the thermal profile could be substantially different and would therefore affect the inferred planetary composition. Here we investigate how the assumption of non-adiabatic temperature profiles in Uranus and Neptune affects their internal structures and compositions. We use a set of plausible temperature profiles together with density profiles that match the measured gravitational fields to derive the planets' compositions. We find that the inferred compositions of both Uranus and Neptune are quite sensitive to the assumed thermal profile in the outer layers, but relatively insensitive to the thermal profile in the central, high pressure region. The overall value of the heavy element mass fraction, $Z$, for these planets is between 0.8 and 0.9. Finally, we suggest that large parts of Uranus' interior might be conductive, a conclusion that is consistent with Uranus dynamo models and a hot central inner region.

astro-ph.EP↗
arXiv2017

The Contraction/Expansion History of Charon with implication for its Planetary Scale Tectonic Belt

The New Horizons mission to the Kuiper Belt has recently revealed intriguing features on the surface of Charon, including a network of chasmata, cutting across or around a series of high topography features, conjoining to form a belt. It is proposed that this tectonic belt is a consequence of contraction/expansion episodes in the moon's evolution associated particularly with compaction, differentiation and geochemical reactions of the interior. The proposed scenario involves no need for solidification of a vast subsurface ocean and/or a warm initial state. This scenario is based on a new, detailed thermo-physical evolution model of Charon that includes multiple processes. According to the model, Charon experiences two contraction/expansion episodes in its history that may provide the proper environment for the formation of the tectonic belt. This outcome remains qualitatively the same, for several different initial conditions and parameter variations. The precise orientation of Charon's tectonic belt, and the cryovolcanic features observed south of the tectonic belt may have involved a planetary-scale impact, that occurred only after the belt had already formed.

astro-ph.EP↗
arXiv2016

Deep space experiment to measure $G$

Responding to calls from the National Science Foundation (NSF) for new proposals to measure the gravitational constant $G$, we offer an interesting experiment in deep space employing the classic gravity train mechanism. Our setup requires three bodies: a larger layered solid sphere with a cylindrical hole through its center, a much smaller retroreflector which will undergo harmonic motion within the hole and a host spacecraft with laser ranging capabilities to measure round trip light-times to the retroreflector but ultimately separated a significant distance away from the sphere-retroreflector apparatus. Measurements of the period of oscillation of the retroreflector in terms of host spacecraft clock time using existing technology could give determinations of $G$ nearly three orders of magnitude more accurate than current measurements here on Earth. However, significant engineering advances in the release mechanism of the apparatus from the host spacecraft will likely be necessary. Issues with regard to the stability of the system are briefly addressed.

gr-qc↗
arXiv2015

Measurements of Newton's gravitational constant and the length of day

About a dozen measurements of Newton's gravitational constant, G, since 1962 have yielded values that differ by far more than their reported random plus systematic errors. We find that these values for G are oscillatory in nature, with a period of P = 5.899 +/- 0.062 yr, an amplitude of (1.619 +/- 0.103) x 10^{-14} m^3 kg^{-1} s^{-2}, and mean-value crossings in 1994 and 1997. However, we do not suggest that G is actually varying by this much, this quickly, but instead that something in the measurement process varies. Of other recently reported results, to the best of our knowledge, the only measurement with the same period and phase is the Length of Day (LOD - defined as a frequency measurement such that a positive increase in LOD values means slower Earth rotation rates and therefore longer days). The aforementioned period is also about half of a solar activity cycle, but the correlation is far less convincing. The 5.9 year periodic signal in LOD has previously been interpreted as due to fluid core motions and inner-core coupling. We report the G/LOD correlation, whose statistical significance is 0.99764 assuming no difference in phase, without claiming to have any satisfactory explanation for it. Least unlikely, perhaps, are currents in the Earth's fluid core that change both its moment of inertia (affecting LOD) and the circumstances in which the Earth-based experiments measure G. In this case, there might be correlations with terrestrial magnetic field measurements.

gr-qc↗
arXiv2012

The fate of topological-insulator surface states under strong disorder

Three-dimensional topological insulators feature Dirac-like surface states which are topologically protected against the influence of weak quenched disorder. Here we investigate the effect of surface disorder beyond the weak-disorder limit using large-scale numerical simulations. We find two qualitatively distinct regimes: Moderate disorder destroys the Dirac cone and induces diffusive metallic behavior at the surface. Even more remarkably, for strong surface disorder a Dirac cone reappears, as new weakly disordered "surface" states emerge in the sample beneath the disordered surface layer, which can be understood in terms of an interface between a topological and an Anderson insulator. Together, this demonstrates the drastic effect of disorder on topological surface states, which cannot be captured within effective two-dimensional models for the surface states alone.

cond-mat.str-el↗
arXiv2012

Charge carrier localisation in disordered graphene nanoribbons

We study the electronic properties of actual-size graphene nanoribbons subjected to substitutional disorder particularly with regard to the experimentally observed metal-insulator transition. Calculating the local, mean and typical density of states, as well as the time-evolution of the particle density we comment on a possible disorder-induced localisation of charge carriers at and close to the Dirac point within a percolation transition scenario.

cond-mat.str-el↗
arXiv2011

Metal-to-insulator transition and electron-hole puddle formation in disordered graphene nanoribbons

The experimentally observed metal-to-insulator transition in hydrogenated graphene is numerically confirmed for actual sized graphene samples and realistic impurity concentrations. The eigenstates of our tight-binding model with substitutional disorder corroborate the formation of electron-hole-puddles with characteristic length scales comparable to the ones found in experiments. The puddles cause charge inhomogeneities and tend to suppress Anderson localization. Even though, monitoring the charge carrier quantum dynamics and performing a finite-size scaling of the local density of states distribution, we find strong evidence for the existence of localized states in graphene nanoribbons with short-range but also correlated long-range disorder.

cond-mat.str-el↗
arXiv2011

Jupiter's Moment of Inertia: A Possible Determination by JUNO

The moment of inertia of a giant planet reveals important information about the planet's internal density structure and this information is not identical to that contained in the gravitational moments. The forthcoming Juno mission to Jupiter might determine Jupiter's normalized moment of inertia NMoI=C/MR^2 by measuring Jupiter's pole precession and the Lense-Thirring acceleration of the spacecraft (C is the axial moment of inertia, and M and R are Jupiter's mass and mean radius, respectively). We investigate the possible range of NMoI values for Jupiter based on its measured gravitational field using a simple core/envelope model of the planet assuming that J_2 and J_4 are perfectly known and are equal to their measured values. The model suggests that for fixed values of J_2 and J_4 a range of NMOI values between 0.2629 and 0.2645 can be found. The Radau-Darwin relation gives a NMoI value that is larger than the model values by less than 1%. A low NMoI of ~ 0.236, inferred from a dynamical model (Ward & Canup, 2006, ApJ, 640, L91) is inconsistent with this range, but the range is model dependent. Although we conclude that the NMoI is tightly constrained by the gravity coefficients, a measurement of Jupiter's NMoI to a few tenths of percent by Juno could provide an important constraint on Jupiter's internal structure. We carry out a simplified assessment of the error involved in Juno's possible determination of Jupiter's NMoI.

astro-ph.EP↗
arXiv2011

Shapes and gravitational fields of rotating two-layer Maclaurin ellipsoids: Application to planets and satellites

The exact solution for the shape and gravitational field of a rotating two-layer Maclaurin ellipsoid of revolution is compared with predictions of the theory of figures up to third order in the small rotational parameter of the theory of figures. An explicit formula is derived for the external gravitational coefficient $J_2$ of the exact solution. A new approach to the evaluation of the theory of figures based on numerical integration of ordinary differential equations is presented. The classical Radau-Darwin formula is found not to be valid for the rotational parameter ε_2 = Ω^2/(2πGρ_2) >= 0.17 since the formula then predicts a surface eccentricity that is smaller than the eccentricity of the core-envelope boundary. Interface eccentricity must be smaller than surface eccentricity. In the formula for $ε_2$, $Ω$ is the angular velocity of the two-layer body, $ρ_2$ is the density of the outer layer, and G is the gravitational constant. For an envelope density of 3000 kg m^(-3) the failure of the Radau-Darwin formula corresponds to a rotation period of about 3 hr. Application of the exact solution and the theory of figures is made to models of Earth, Mars, Uranus, and Neptune. The two-layer model with constant densities in the layers can provide realistic approximations to terrestrial planets and icy outer planet satellites. The two-layer model needs to be generalized to allow for a continuous envelope (outer layer) radial density profile in order to realistically model a gas or ice giant planet.

astro-ph.EP↗
arXiv2011

Hybrid-parallel sparse matrix-vector multiplication with explicit communication overlap on current multicore-based systems

We evaluate optimized parallel sparse matrix-vector operations for several representative application areas on widespread multicore-based cluster configurations. First the single-socket baseline performance is analyzed and modeled with respect to basic architectural properties of standard multicore chips. Beyond the single node, the performance of parallel sparse matrix-vector operations is often limited by communication overhead. Starting from the observation that nonblocking MPI is not able to hide communication cost using standard MPI implementations, we demonstrate that explicit overlap of communication and computation can be achieved by using a dedicated communication thread, which may run on a virtual core. Moreover we identify performance benefits of hybrid MPI/OpenMP programming due to improved load balancing even without explicit communication overlap. We compare performance results for pure MPI, the widely used "vector-like" hybrid programming strategies, and explicit overlap on a modern multicore-based cluster and a Cray XE6 system.

cs.DC↗
arXiv2010

Parallel sparse matrix-vector multiplication as a test case for hybrid MPI+OpenMP programming

We evaluate optimized parallel sparse matrix-vector operations for two representative application areas on widespread multicore-based cluster configurations. First the single-socket baseline performance is analyzed and modeled with respect to basic architectural properties of standard multicore chips. Going beyond the single node, parallel sparse matrix-vector operations often suffer from an unfavorable communication to computation ratio. Starting from the observation that nonblocking MPI is not able to hide communication cost using standard MPI implementations, we demonstrate that explicit overlap of communication and computation can be achieved by using a dedicated communication thread, which may run on a virtual core. We compare our approach to pure MPI and the widely used "vector-like" hybrid programming strategy.

cs.PF↗
arXiv2010

Interior Models of Uranus and Neptune

'Empirical' models (pressure vs. density) of Uranus and Neptune interiors constrained by the gravitational coefficients J_2, J_4, the planetary radii and masses, and Voyager solid-body rotation periods are presented. The empirical pressure-density profiles are then interpreted in terms of physical equations of state of hydrogen, helium, ice (H_2O), and rock (SiO_2) to test the physical plausibility of the models. The compositions of Uranus and Neptune are found to be similar with somewhat different distributions of the high-Z material. The big difference between the two planets is that Neptune requires a non-solar envelope while Uranus is best matched with a solar composition envelope. Our analysis suggests that the heavier elements in both Uranus' and Neptune's interior might increase gradually towards the planetary centers. Indeed it is possible to fit the gravitational moments without sharp compositional transitions.

astro-ph.EP↗
arXiv2010

Uranus and Neptune: Shape and Rotation

Both Uranus and Neptune are thought to have strong zonal winds with velocities of several hundred meters per second. These wind velocities, however, assume solid-body rotation periods based on Voyager 2 measurements of periodic variations in the planets' radio signals and of fits to the planets' magnetic fields; 17.24h and 16.11h for Uranus and Neptune, respectively. The realization that the radio period of Saturn does not represent the planet's deep interior rotation and the complexity of the magnetic fields of Uranus and Neptune raise the possibility that the Voyager 2 radio and magnetic periods might not represent the deep interior rotation periods of the ice giants. Moreover, if there is deep differential rotation within Uranus and Neptune no single solid-body rotation period could characterize the bulk rotation of the planets. We use wind and shape data to investigate the rotation of Uranus and Neptune. The shapes (flattening) of the ice giants are not measured, but only inferred from atmospheric wind speeds and radio occultation measurements at a single latitude. The inferred oblateness values of Uranus and Neptune do not correspond to bodies rotating with the Voyager rotation periods. Minimization of wind velocities or dynamic heights of the 1 bar isosurfaces, constrained by the single occultation radii and gravitational coefficients of the planets, leads to solid-body rotation periods of ~16.58h for Uranus and ~17.46h for Neptune. Uranus might be rotating faster and Neptune slower than Voyager rotation speeds. We derive shapes for the planets based on these rotation rates. Wind velocities with respect to these rotation periods are essentially identical on Uranus and Neptune and wind speeds are slower than previously thought. Alternatively, if we interpret wind measurements in terms of differential rotation on cylinders there are essentially no residual atmospheric winds.

astro-ph.EP↗
arXiv2010

Distribution of the local density of states as a criterion for Anderson localization: Numerically exact results for various lattices in two and three dimensions

Numerical approaches to Anderson localization face the problem of having to treat large localization lengths while being restricted to finite system sizes. We show that by finite-size scaling of the probability distribution of the local density of states (LDOS) this long-standing problem can be overcome. To this end we reexamine the approach, propose numerical refinements, and apply it to study the dependence of the distribution of the LDOS on the dimensionality and coordination number of the lattice. Particular attention is given to the graphene lattice. We show that the system-size dependence of the LDOS distribution is indeed an unambiguous sign of Anderson localization, irrespective of the dimension and lattice structure. The numerically exact LDOS data obtained by us agree with a log-normal distribution over up to ten orders of magnitude and thereby fulfill a nontrivial symmetry relation previously derived for the non-linear $σ$-model.

cond-mat.str-el↗
arXiv2009

Performance limitations for sparse matrix-vector multiplications on current multicore environments

The increasing importance of multicore processors calls for a reevaluation of established numerical algorithms in view of their ability to profit from this new hardware concept. In order to optimize the existent algorithms, a detailed knowledge of the different performance-limiting factors is mandatory. In this contribution we investigate sparse matrix-vector multiplication, which is the dominant operation in many sparse eigenvalue solvers. Two conceptually different storage schemes and computational kernels have been conceived in the past to target cache-based and vector architectures, respectively. Starting from a series of microbenchmarks we apply the gained insight on optimized sparse MVM implementations, whose serial and OpenMP-parallel performance we review on state-of-the-art multicore systems.

cs.PF↗
arXiv2009

Jupiter and Saturn Rotation Periods

Anderson & Schubert (2007, Science,317,1384) proposed that Saturn's rotation period can be ascertained by minimizing the dynamic heights of the 100 mbar isosurface with respect to the geoid; they derived a rotation period of 10h 32m 35s. We investigate the same approach for Jupiter to see if the Jovian rotation period is predicted by minimizing the dynamical heights of its isobaric (1 bar pressure level) surface using zonal wind data. A rotation period of 9h 54m 29s is found. Further, we investigate the minimization method by fitting Pioneer and Voyager occultation radii for both Jupiter and Saturn. Rotation periods of 9h 55m 30s and 10h 32m 35s are found to minimize the dynamical heights for Jupiter and Saturn, respectively. Though there is no dynamical principle requiring the minimization of the dynamical heights of an isobaric surface, the successful application of the method to Jupiter lends support to its relevance for Saturn. We derive Jupiter and Saturn rotation periods using equilibrium theory in which the solid-body rotation period (no winds) that gives the observed equatorial and polar radii at the 100 mbar level is found. Rotation periods of 9h 55m 20s and 10h 31m 49s are found for Jupiter and Saturn, respectively. We show that both Jupiter's and Saturn's shapes can be derived using solid-body rotation, suggesting that zonal winds have a minor effect on the planetary shape for both planets. The agreement in the values of Saturn's rotation period predicted by the different approaches supports the conclusion that the planet's period of rotation is about 10h 32m.

astro-ph.EP↗