Density Discontinuity Research Articles

Broken into Pieces: ATLAS and Aliqa Uma as One Single Stream

Abstract We present the first spectroscopic measurements of the ATLAS and Aliqa Uma streams from the Southern Stellar Stream Spectroscopic Survey (S 5), in combination with the photometric data from the Dark Energy Survey and astrometric data from Gaia. From the coherence of spectroscopic members in radial velocity and proper motion, we find that these two systems are extremely likely to be one stream with discontinuity in morphology and density on the sky (the “kink” feature). We refer to this entire stream as the ATLAS-Aliqa Uma stream, or the AAU stream. We perform a comprehensive exploration of the effect of baryonic substructures and find that only an encounter with the Sagittarius dwarf ∼0.5 Gyr ago can create a feature similar to the observed “kink.” In addition, we also identify two gaps in the ATLAS component associated with the broadening in the stream width (the “broadening” feature). These gaps have likely been created by small mass perturbers, such as dark matter halos, as the AAU stream is the most distant cold stream known with severe variations in both the stream surface density and the stream track on the sky. With the stream track, stream distance, and kinematic information, we determine the orbit of the AAU stream and find that it has been affected by the Large Magellanic Cloud, resulting in a misalignment between the proper motion and stream track. Together with the Orphan-Chenab Stream, AAU is the second stream pair that has been found to be a single stream separated into two segments by external perturbation.

Supermassive neutron stars rule out twin stars

We investigate the implications of a hypothetical $2.5\text{ }\text{ }{\mathrm{M}}_{\ensuremath{\bigodot}}$ neutron star in regard to the possibility of a first order phase transition to quark matter. We use equations of state (EoS) of varying stiffness provided by a parametrizable relativistic mean field model transitioning to a constant speed of sound EoS. We find a strong connection between the discontinuity in energy density and the maximal neutron star mass. We demonstrate, that high maximal masses cannot be realized for large discontinuities. As a result visible mass gaps, i.e., twin stars, and masses of ${M}_{\mathrm{max}}\ensuremath{\gtrsim}2.2\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ are mutually exclusive.

The ocean in a box: water density gradients and discontinuities in water masses are important cues guiding fish larvae towards estuarine nursery grounds

The ocean in a box: water density gradients and discontinuities in water masses are important cues guiding fish larvae towards estuarine nursery grounds

Neuroevolution-enabled adaptation of the Jacobi method for Poisson’s equation with density discontinuities

Lacking labeled examples of working numerical strategies, adapting an iterative solver to accommodate a numerical issue, e.g., density discontinuities in the pressure Poisson equation, is non-trivial and usually involves a lot of trial and error. Here, we resort to evolutionary neural network. A evolutionary neural network observes the outcome of an action and adapts its strategy accordingly. The process requires no labeled data but only a measure of a network’s performance at a task. Applying neuro-evolution and adapting the Jacobi iterative method for the pressure Poisson equation with density discontinuities, we show that the adapted Jacobi method is able to accommodate density discontinuities.

Connecting the Gravity Field, Moment of Inertia, and Core Properties in Jupiter through Empirical Structural Models

Abstract Constraining Jupiter’s internal structure is crucial for understanding its formation and evolution history. Recent interior models of Jupiter that fit Juno’s measured gravitational field suggest an inhomogeneous interior and potentially the existence of a diluted core. These models, however, strongly depend on the model assumptions and the equations of state used. A complementary modeling approach is to use empirical structural models. These can later be used to reveal new insights into the planetary interior and be compared to standard models. Here we present empirical structural models of Jupiter where the density profile is constructed by piecewise-polytropic equations. With these models we investigate the relation between the normalized moment of inertia (MoI) and the gravitational moments J 2 and J 4. Given that only the first few gravitational moments of Jupiter are measured with high precision, we show that an accurate and independent measurement of the MoI value could be used to further constrain Jupiter’s interior. An independent measurement of the MoI with an accuracy better than ∼0.1% could constrain Jupiter’s core region and density discontinuities in its envelope. We find that models with a density discontinuity at ∼1 Mbar, as would produce a presumed hydrogen–helium separation, correspond to a fuzzy core in Jupiter. We next test the appropriateness of using polytropes, by comparing them with empirical models based on polynomials. We conclude that both representations result in similar density profiles and ranges of values for quantities like core mass and MoI.

Urban sprawl and air quality in European Cities: an empirical assessment

In this paper we estimate the relationship between urban sprawl and a measure of air quality, namely the number of days in which the PM10 concentration exceeds safeguard limits in European Union cities. Building on a multidimensional representation of sprawl, the paper employs several indicators to account for built-up area development, population density, and residential discontinuity. The paper employs generalised additive models to disentangle the non-linear effects in the variables and the interaction effects of the three sprawl dimensions. A significant and robust effect of urban morphology emerges after controlling for socio-economic, demographic, and climatic factors and the geographical location of the city. We find that urban sprawl impacts positively on pollutant concentration, but the effect is highly context-specific because of threshold effects and interactions.

Gender identity and wives’ labor market outcomes in West and East Germany between 1983 and 2016

Abstract We exploit the natural experiment of German reunification in 1990 to investigate if the institutional regimes of the formerly socialist (rather gender-equal) East Germany and the capitalist (rather gender-traditional) West Germany resulted in differing gender norms regarding who should be the family breadwinner. We use data for three periods between 1983 and 2016 from the German Socio-Economic Panel. Density discontinuity tests and fixed-effects regressions suggest that married couples in West (but not East) Germany diminished the wife’s labor market outcomes in order to avoid situations where she would earn more than him. However, the significance of the male breadwinner norm seems to decline in West Germany since reunification, converging to the more gender egalitarian East Germany. Our work provides evidence that political and institutional frameworks can shape fairly persistent gender identity norms that influence household economic decisions for some time, even when these frameworks change.

Fast multigrid solution of high-order accurate multiphase Stokes problems

A fast multigrid solver is presented for high-order accurate Stokes problems discretised by local discontinuous Galerkin (LDG) methods. The multigrid algorithm consists of a simple V-cycle, using an element-wise block Gauss-Seidel smoother. The efficacy of this approach depends on the LDG pressure penalty stabilisation parameter -- provided the parameter is suitably chosen, numerical experiment shows that: (i) for steady-state Stokes problems, the convergence rate of the multigrid solver can match that of classical geometric multigrid methods for Poisson problems; (ii) for unsteady Stokes problems, the convergence rate further accelerates as the effective Reynolds number is increased. An extensive range of two- and three-dimensional test problems demonstrates the solver performance as well as high-order accuracy -- these include cases with periodic, Dirichlet, and stress boundary conditions; variable-viscosity and multi-phase embedded interface problems containing density and viscosity discontinuities several orders in magnitude; and test cases with curved geometries using semi-unstructured meshes.

Multiphase smoothed particle hydrodynamics modeling of forced liquid sloshing

AbstractIn the present paper, an improved multiphase weakly compressible smoothed particle hydrodynamics model for balancing the accuracy and stability of the long‐term simulations is proposed to model the forced liquid sloshing in a tank. The governing equations of the multiphase flow are discretized by considering the density discontinuity over the interface. To suppress the pressure oscillation, a previous density correction term suitable only for single‐phase problems is modified and incorporated into the discrete continuity equation to suit multiphase problems. The modified density reinitialization algorithm is implemented to calculate the pressure of the boundary particles, and the coupled dynamic solid boundary treatment (SBT) is employed to determine the rigid wall condition. For convenience, a numerical probe algorithm is also proposed to accurately measure the wave height. The present model exhibits a better numerical stability than the previous multiphase smoothed particle hydrodynamics model, and its results well confirm with the experimental data of the forced sloshing of liquid excited by swaying or rolling.

The gravimetric contribution to the Moho estimation in the presence of vertical density variations

The Moho surface, namely the density discontinuity between crust and mantle, is traditionally studied by seismic methods. However, gravity information can contribute to the Moho estimation and, more generally, to the crustal modeling. The contribution is twofold. First, gravimetry generally provides observations with much lower errors than those implied by the mass density uncertainty and other geophysical assumptions. This means that it can be used to validate existing Moho and/or crustal models by forward modeling. Second, gravity inversion is able to provide diffused (not localized) information on the mass distribution, both regionally and globally (thanks to dedicated satellite gravity missions). However, this information is weak due to its intrinsic ill-posedness. This means that it can be used to correct and spatially interpolate existing models, and to complement seismic, magnetic and geological information to create new models. In this work, the problem of estimating the Moho surface by gravity inversion assuming a two-layer model with lateral and vertical density variations is treated at a regional level. The approach consists in linearizing the forward modeling around a reference Moho at a constant depth and then inverting it through a Wiener filter. This is standard in case of two layers with homogeneous density distributions (or with lateral density variations), while it requires some additional considerations and algorithm modifications in case of vertical density variations. The basic idea is to “condensate” the masses inside the Moho undulation on the reference surface used for the linearization, thus requiring the setup of an iterative procedure. A strategy to introduce seismic information into this inversion procedure is proposed too, with the aim of improving the a priori density modeling. A closed loop test is presented for the algorithm assessment, showing the improvement with respect to a standard approach and the capability of the proposed algorithm to reconstruct the originally simulated Moho undulation by also fitting the gravity and seismic data at a level that is consistent with their observation noise.

Comment on “Tidal Love numbers of neutron and self-bound quark stars”

We comment on the paper of S. Postnikov et al. in Phys. Rev. D 82, 024016 (2010) and give a modified formula that needs to be taken into account when calculating the tidal Love number of neutron stars in case a first order phase-transition occurs at non-zero pressure. We show that the error made when using the original formula tends to zero as $p \rightarrow 0$ and we estimate the maximum relative error to be $\sim 5\%$ if the density discontinuity is at larger densities.

Smoothed particle magnetohydrodynamics with the geometric density average force expression

We present a novel method of magnetohydrodynamics (MHD) within the smoothed particle hydrodynamics scheme (SPMHD) using the geometric density average force expression. Geometric density average within smoothed particle hydrodynamics (GDSPH) has recently been shown to reduce the leading order errors and greatly improve the accuracy near density discontinuities, eliminating surface tension effects. Here, we extend the study to investigate how SPMHD benefits from this method. We implement ideal MHD in the GASOLINE2 and CHANGA codes with both GDSPH and traditional smoothed particle hydrodynamics (TSPH) schemes. A constrained hyperbolic divergence cleaning scheme was employed to control the divergence error and a switch for artificial resistivity with minimized dissipation was also used. We tested the codes with a large suite of MHD tests and showed that in all problems, the results are comparable or improved over previous SPMHD implementations. While both GDSPH and TSPH perform well with relatively smooth or highly supersonic flows, GDSPH shows significant improvements in the presence of strong discontinuities and large dynamic scales. In particular, when applied to the astrophysical problem of the collapse of a magnetized cloud, GDSPH realistically captures the development of a magnetic tower and jet launching in the weak-field regime, while exhibiting fast convergence with resolution, whereas TSPH failed to do so. Our new method shows qualitatively similar results to those of the meshless finite mass/volume schemes within the GIZMO code, while remaining computationally less expensive.

New gravity data and 3-D density model constraints on the Ivrea Geophysical Body (Western Alps)

SUMMARY We provide a high-resolution image of the Ivrea Geophysical Body (IGB) in the Western Alps with new gravity data and 3-D density modelling, integrated with surface geological observations and laboratory analyses of rock properties. The IGB is a sliver of Adriatic lower lithosphere that is located at shallow depths along the inner arc of the Western Alps, and associated with dense rocks that are exposed in the Ivrea-Verbano Zone (IVZ). The IGB is known for its high seismic velocity anomaly at shallow crustal depths and a pronounced positive gravity anomaly. Here, we investigate the IGB at a finer spatial scale, merging geophysical and geological observations. We compile existing gravity data and we add 207 new relative gravity measurements, approaching an optimal spatial coverage of 1 data point per 4–9 km2 across the IVZ. A compilation of tectonic maps and rock laboratory analyses together with a mineral properties database is used to produce a novel surface rock-density map of the IVZ. The density map is incorporated into the gravity anomaly computation routine, from which we defined the Niggli gravity anomaly. This accounts for Bouguer Plate and terrain correction, both considering the in situ surface rock densities, deviating from the 2670 kg m–3 value commonly used in such computations. We then develop a 3-D single-interface crustal density model, which represents the density distribution of the IGB, including the above Niggli-correction. We retrieve an optimal fit to the observations by using a 400 kg m–3 density contrast across the model interface, which reaches as shallow as 1 km depth below sea level. The model sensitivity tests suggest that the ∼300–500 kg m–3 density contrast range is still plausible, and consequently locates the shallowest parts of the interface at 0 km and at 2 km depth below sea level, for the lowest and the highest density contrast, respectively. The former model requires a sharp density discontinuity, the latter may feature a vertical transition of densities on the order of few kilometres. Compared with previous studies, the model geometry reaches shallower depths and suggests that the width of the anomaly is larger, ∼20 km in west–east direction and steeply E–SE dipping. Regarding the possible rock types composing the IGB, both regional geology and standard background crustal structure considerations are taken into account. These exclude both felsic rocks and high-pressure metamorphic rocks as suitable candidates, and point towards ultramafic or mantle peridotite type rocks composing the bulk of the IGB.

Bilateral Boundary Control of Moving Shockwave in LWR Model of Congested Traffic

We develop backstepping state feedback control to stabilize a moving shockwave in a freeway segment under bilateral boundary actuations of traffic flow. A moving shockwave, consisting of light traffic upstream of the shockwave and heavy traffic downstream, is usually caused by changes of local road situations. The density discontinuity travels upstream and drivers caught in the shockwave experience transitions from free to congested traffic. Boundary control design in this paper brings the moving shockwave front to a static setpoint position, hindering the upstream propagation of traffic congestion. The traffic dynamics are described with Lighthill-Whitham-Richard (LWR) model, leading to a system of two first-order hyperbolic partial differential equations (PDEs). Each represents the traffic density of a spatial domain segregated by the moving interface. By Rankine-Hugoniot condition, the interface position is driven by flux discontinuity and thus governed by a PDE state dependent ordinary differential equation (ODE). For the PDE-ODE coupled system. the control objective is to stabilize both the PDE states of traffic density and the ODE state of moving shock position to setpoint values. Using delay representation and backstepping method, we design predictor feedback controllers to cooperatively compensate state-dependent input delays to the ODE. From Lyapunov stability analysis, we show local stability of the closed-loop system in $H^1$ norm. The performance of controllers is demonstrated by numerical simulation.

Potential deep-buried petroleum systems in Meso-Neoproterozoic rifts of the southwestern North China Craton revealed by gravity anomalies

In order to evaluate the potential petroleum system within the Meso-Neoproterozoic strata of the southwest North China Craton (NCC), we explored the deep-buried basal tectonics on the Precambrian basement and the residual sedimentary thickness of the Meso-Neoproterozoic in the Ordos Basin. A combination of geophysical processing methodologies has been conducted. Based on regional seismic exploration, the shallow gravity effects caused by the undulation of the Cenozoic, Jurassic, Carboniferous and Cambrian sedimentary formations were calculated through forward modeling, and eliminated the free-air gravity anomaly by a gravity stripping technique. Subsequently, by using the wavelet multi-scale decomposition method, the deeper gravity effect sourcing from underneath the Meso-Neoproterozoic base was calculated and then eliminated, including the undulation of Paleoproterozoic-Archaean crystalline basement and the lateral density discontinuity of the lower crust. As a result, the residual gravity anomalies caused by the Meso-Neoproterozoic sedimentary formations and the Moho discontinuity of the Ordos Block were both obtained, which was then used for inversion. The inversion results show that the residual Meso-Neoproterozoic strata are mainly distributed in the southwest and northern part of the Ordos Block, and the Moho depth of the Ordos Block averages about 42 km. It ranges from 38 to 42 km in the eastern part and deepens to over 44 km in the west. In addition, there are some detailed deep-structure reflections on the Moho discontinuity. For instance, the parallel-arranged NE-trending anomalous belts in southwest Ordos Block indicate strong crustal extension and mantle uplift. The regional geology indicates that the NE-trending crustal extension is not related to the Cenozoic strike-slip pull-apart process around the Ordos Block, nor the Indosinian Movement in Early Mesozoic, or the cratonic depression in the Paleozoic. However, it highly resembles the NE-oriented paleo-rifts that developed in the Meso-Neoproterozic aulacogens. The residual crustal gravity anomaly eliminates both the shallow disturbance from the sediments and the deep shadow from the mantle. It shows very good consistency with the undulation of the Meso-Neoproterozoic sedimentary basement along a classical interpreted seismic survey line, which validates the correlation between the NE-trending anomalous belts with the basal aulacogen tectonics. According to seismic interpretation, the paleo-rifts within the Precambrian aulacogens occurred during the Mesoproterozoic and continued into the early Neoproterozoic. Huge volumes of sediment filled the rift troughs during the Meso-Neoproterozoic, causing a significant gravity loss on the gravity field, and formed considerable oil–gas exploration potential. Given suitable paleoclimatic conditions, the grabens would have provided a favorable environment for organic-rich shales and source rocks to develop. While the faults controlling the grabens and horsts would have played an important role in the migration and accumulation of hydrocarbons in the potential petroleum system. Combined with paleoclimate and lithofacies paleogeography analysis, five favorable areas are speculated for Meso-Neoproterozoic potential petroleum systems, which are the northwest Yimeng Uplift, the northern Tianhuan Depression, the southern Tianhuan Depression, the southwestern to central Yishaan Slope and the western Weibei Uplift, respectively. Based on lithofacies paleogeography, source rock maturity and organic carbon abundance, it suggests that the favorable petroleum systems within the Proterozoic strata of the Ordos Block were obviously controlled or influenced by the deep paleo-rifts and block faults, which resulted in forming three types of play, called the Weathering Model, the Tilting Model and the Transition Model. In particular, the central to western parts of the Yimeng Uplift and the southern Tianhuan Depression, where the Weathering Model developed, as the Upper Paleozoic coal-bearing source rocks have large hydrocarbon generation potential and good preservation conditions, these two areas should be regarded as important favorable prospecting regions in the Ordos Basin.

Length of standing jumps along granular flows down smooth inclines

Predicting the flows of dense granular media is still a challenging issue. Here, numerical discrete element method simulations are used to investigate the diversity of patterns within granular jumps that accompany height, velocity, and density discontinuities in gravity-driven free-surface flows. It is demonstrated that standing granular jumps can serve as a useful gauge for evaluating the dissipation mechanisms that govern the flowability of granular media.

Discovery of a Giant Radio Fossil in the Ophiuchus Galaxy Cluster

Abstract The Ophiuchus galaxy cluster exhibits a curious concave gas density discontinuity at the edge of its cool core. It was discovered in the Chandra X-ray image by Werner and collaborators, who considered the possibility of it being a boundary of an active galactic nucleus (AGN)-inflated bubble located outside the core, but discounted this possibility because it required much too powerful an AGN outburst. Using low-frequency (72–240 MHz) radio data from the Murchison Widefield Array/GLEAM and the Giant Metrewave Radio Telescope, we found that the X-ray structure is, in fact, a giant cavity in the X-ray gas filled with diffuse radio emission with an extraordinarily steep radio spectrum. It thus appears to be a very aged fossil of the most powerful AGN outburst seen in any galaxy cluster (pV ∼ 5 × 1061 erg for this cavity). There is no apparent diametrically opposite counterpart either in X-ray or in the radio. It may have aged out of the observable radio band because of the cluster asymmetry. At present, the central AGN exhibits only a weak radio source, so it should have been much more powerful in the past to have produced such a bubble. The AGN is currently starved of accreting cool gas because the gas density peak is displaced by core sloshing. The sloshing itself could have been set off by this extraordinary explosion if it had occurred in an asymmetric gas core. This dinosaur may be an early example of a new class of sources to be uncovered by low-frequency surveys of galaxy clusters.

Numerically investigating the morphology of the supernova remnant SN 1006 in the ambient medium with a density discontinuity

ABSTRACT Multiband observations on the Type Ia supernova remnant SN 1006 indicate peculiar properties in its morphologies of emission in the radio, optical, and X-ray bands. In the hard X-rays, the remnant is bilateral with two opposite bright limbs with prominent protrusions. Moreover, a filament has been detected at the radio, optical, and soft X-ray wavelengths. The reason for these peculiar features in the morphologies of the remnant is investigated using 3D HD simulations. With the assumption that the supernova ejecta are evolved in the ambient medium with a density discontinuity, the radius of the remnant’s boundary is smaller in the tenuous medium, and the shell consists of two hemispheres with different radii. Along particular line of sights, protrusions appear on the periphery of the remnants since the emission from the edge of the hemisphere with a larger radius is located outside that from the shell of the small hemisphere. Furthermore, the north-west filament of SN 1006 arises as a result of the intersection of the line of sight and the shocked material near the edges of the two hemispheres. It can be concluded that the protrusions on the north-east and south-west limbs and the north-west filament in the morphologies of SN 1006 can be reproduced as the remnants interacting with the medium with a density discontinuity.

Thermodynamic anomalies and three distinct liquid-liquid transitions in warm dense liquid hydrogen

The properties of hydrogen at high pressure have wide implications in astrophysics and high-pressure physics. Its phase change in the liquid is variously described as a metallization, H2-dissociation, density discontinuity or plasma phase transition. It has been tacitly assumed that these phenomena coincide at a first-order liquid-liquid transition (LLT). In this work, the relevant pressure-temperature conditions are thoroughly explored with first-principles molecular dynamics. We show there is a large dependency on exchange-correlation functional and significant finite size effects. We use hysteresis in a number of measurable quantities to demonstrate a first-order transition up to a critical point, above which molecular and atomic liquids are indistinguishable. At higher temperature beyond the critical point, H2-dissociation becomes a smooth cross-over in the supercritical region that can be modelled by a pseudo-transition, where the H2-2H transformation is localized and does not cause a density discontinuity at metallization. Thermodynamic anomalies and counter-intuitive transport behavior of protons are also discovered even far beyond the critical point, making this dissociative transition highly relevant to the interior dynamics of Jovian planets. Below the critical point, simulation also reveals a dynamic H2-2H chemical equilibrium with rapid interconversion, showing that H2 and H are miscible. The predicted critical temperature lies well below the ionization temperature. Our calculations unequivocally demonstrate that there are three distinct regimes in the liquid-liquid transition of warm dense hydrogen.

Existence and uniqueness of low-energy weak solutions to the compressible 3D magnetohydrodynamics equations

We prove the existence and uniqueness of weak solutions of the three dimensional compressible magnetohydrodynamics (MHD) equations. We first obtain the existence of weak solutions with small L2-norm which may display codimension-one discontinuities in density, pressure, magnetic field and velocity gradient. The weak solutions we consider here exhibit just enough regularity and structure which allow us to develop uniqueness and continuous dependence theory for the compressible MHD equations. Our results generalise and extend those for the intermediate weak solutions of compressible Navier-Stokes equations.