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At least 1,081 records · Page 60
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Analyzing the Validity of Brazilian Testing Using Digital Image Correlation and Numerical Simulation Techniques

Characterizing the mechanical behavior of rocks plays a crucial role to optimize the fracturing process in unconventional reservoirs. However, due to the intrinsic anisotropy and heterogeneity in unconventional resources, fracture process prediction remains the most significant challenge for sustainable and economic hydrocarbon production. During the deformation tracking under compression, deploying conventional methods (strain gauge, extensometer, etc.) is insufficient to measure the deformation since the physical attachment of the device is restricted to the size of the sample, monitoring limited point-wise deformation, producing difficulties in data retrieval, and a tendency to lose track in failure points, etc. Where conventional methods are limited, the application of digital image correlation (DIC) provides detailed and additional information of strain evolution and fracture patterns under loading. DIC is an image-based optical method that records an object with a camera and monitors the random contrast speckle pattern painted on the facing surface of the specimen. To overcome the existing limitations, this paper presents numerical modeling of Brazilian disc tests under quasi-static conditions to understand the full-field deformation behaviors and finally, it is validated by DIC. As the direct tensile test has limitations in sample preparation and test execution, the Brazilian testing principle is commonly used to evaluate indirectly the tensile strength of rocks. The two-dimensional numerical model was built to predict the stress distribution and full-field deformation on Brazilian disc under compression based on the assumptions of a homogenous, isotropic and linear elastic material. The uniaxial compression test was conducted using the DIC technique to determine the elastic properties of Spider Berea sandstone, which were used as inputs for the simulation model. The model was verified by the analytical solution and compared with the digital image correlation. The numerical simulation results showed that the solutions matched reasonably with the analytical solutions where the maximum deviation of stress distribution was obtained as 14.59%. The strain evolution (normal and shear strains) and displacements along the central horizontal and vertical planes were investigated in three distinguishable percentages of peak loads (20%, 40%, and 90%) to understand the deformation behaviors in rock. The simulation results demonstrated that the strain evolution contours consistently matched with DIC generated contours with a reasonable agreement. The changes in displacement along the central horizontal and vertical planes showed that numerical simulation and DIC generated experimental results were repeatable and matched closely. In terms of validation, Brazilian testing to measure the indirect tensile strength of rocks is still an issue of debate. The numerical model of fracture propagation supported by digital image correlation from this study can be used to explain the fracturing process in the homogeneous material and can be extended to non-homogeneous cases by incorporating heterogeneity, which is essential for rock mechanics field applications.

58 GEOSCIENCES↗
DOE OSTI2022

Understanding Uncertainty in Microstructure Evolution and Constitutive Properties in Additive Process Modeling

Coupled process–microstructure–property modeling, and understanding the sources of uncertainty and their propagation toward error in part property prediction, are key steps toward full utilization of additive manufacturing (AM) for predictable quality part development. The OpenFOAM model for process conditions, the ExaCA model for as-solidified grain structure, and the ExaConstit model for constitutive mechanical properties are used as part of the ExaAM modeling framework to examine a few of the various sources of uncertainty in the modeling workflow. In addition to “random” uncertainty (due to random number generation in the orientations and locations of grains present), the heterogeneous nucleation density N 0 and the mean substrate grain spacing S 0 are varied to examine their impact of grain area development as a function of build height in the simulated microstructure. While mean grain area after 1 mm of build is found to be sensitive to N 0 and S 0 , particularly at small N 0 and large S 0 (despite some convergence toward similar values), the resulting grain shapes and overall textures develop in a reasonably similar manner. As a result of these similar textures, ExaConstit simulation using ExaCA representative volume elements (RVEs) from various permutations of N 0 , S 0 , and location within the build resulted in similar yield stress, stress–strain curve shape, and stress triaxiality distributions. It is concluded that for this particular material and scan pattern, 15 layers is sufficient for ExaCA texture and ExaConstit predicted properties to become relatively independent of additional layer simulation, provided that reasonable estimates for N 0 and S 0 are used. However, additional layers of ExaCA will need to be run to obtain mean grain areas independent of build height and baseplate structure.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Utility of Physiologically Based Pharmacokinetic Modeling to Investigate the Impact of Physiological Changes of Pregnancy and Cancer on Oncology Drug Pharmacokinetics

The treatment of cancer during pregnancy remains challenging with knowledge gaps in drug dosage, safety, and efficacy due to the under-representation of this population in clinical trials. Our aim was to investigate physiological changes reported in both pregnancy and cancer populations into a PBPK modeling framework that allows for a more accurate estimation of PK changes in pregnant patients with cancer. Methods: Paclitaxel and docetaxel were selected to validate a population model using clinical data from pregnant patients with cancer. The validated population model was subsequently used to predict the PK of acalabrutinib in pregnant patients with cancer. Results: The Simcyp pregnancy population model reasonably predicted the PK of docetaxel in pregnant patients with cancer, while a modified model that included a 2.5-fold increase in CYP2C8 abundance, consistent with the increased expression during pregnancy, was needed to reasonably predict the PK of paclitaxel in pregnant patients with cancer. Changes in protein binding levels of patients with cancer had a minimal impact on the predicted clearance of paclitaxel and docetaxel. PBPK modeling predicted approximately 60% lower AUC and Cmax for acalabrutinib in pregnant versus non-pregnant patients with cancer. Conclusions: Our results suggest that PBPK modeling is a promising approach to investigate the effects of pregnancy and cancer on the PK of oncology drugs and potentially inform dosing for pregnant patients with cancer. Further evaluation and refinement of the population model are needed for pregnant patients with cancer with additional compounds and clinical PK data.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

QED Meson Description of the Anomalous Particles at ∼17 and ∼38 MeV

The Schwinger confinement mechanism stipulates that a massless fermion and a massless antifermion are confined as a massive boson when they interact in the Abelian QED interaction in (1+1)D.If we approximate light quarks as massless and apply the Schwinger confinement mechanism to quarks, we can infer that a light quark and a light antiquark interacting in the Abelian QED interaction are confined as a QED meson in (1+1)D. Similarly, a light quark and a light antiquark interacting in the QCD interaction in the quasi-Abelian approximation will be confined as a QCD meson in (1+1)D. The QED and QCD mesons in (1+1)D can represent physical mesons in (3+1)D when the flux tube radius is properly taken into account. Such a theory leads to a reasonable description of the masses of π0,η, and η′, and its extrapolation to the unknown QED sector yields an isoscalar QED meson at about 17 MeV and an isovector QED meson at about 38 MeV. The observations of the anomalous soft photons, the hypothetical X17 particle, and the hypothetical E38 particle bear promising evidence for the possible existence of the QED mesons. Pending further confirmation, they hold important implications on the properties on the quarks and their interactions.

Wong, Cheuk-Yin (ORCID:0000000182230659)↗
DOE OSTI2016

Modelling economic losses of historic and present-day high-impact winter windstorms in Switzerland

This study investigates the wind gusts and associated economic loss patterns of high-impact winter windstorms in Switzerland between 1871 and 2011. A novel approach for simulating windstorm-related gusts and losses at regional to local scales is applied to a sample of 84 windstorms. The approach involves the dynamical downscaling of the Twentieth Century Reanalysis (20CR) ensemble mean to 3-km horizontal grid size using the Weather Research and Forecasting (WRF) model. Economic losses are simulated at municipal level for present-day asset distribution based on the downscaled (parameterised) wind gusts at high spatiotemporal resolution using the open-source impact model climada. A comparison with insurance loss data for two recent windstorms (“Lothar” in 1999, “Joachim” in 2011) indicates that the loss simulation allows to realistically simulate the spatial patterns of windstorm losses. The loss amplitude is strongly underestimated for ‘Lothar’, while it is in reasonable agreement for ‘Joachim’. Possible reasons are discussed. Uncertainties concerning the loss simulation arise from the wind gust estimation method applied; estimates can differ considerably among the different methods, in particular over high orography. Furthermore, the quality of the loss simulation is affected by the underlying simplified assumptions regarding the distribution of assets and their susceptibilities to damage. For the whole windstorm sample, composite averages of simulated wind gust speed and loss are computed. Both composites reveal high values for the densely populated Swiss Plateau and lower values for south-eastern Switzerland; metropolitan areas stand out in the loss composite. Eight of the top 10 events concerning the losses simulated for present-day asset distribution and summed over all Swiss municipalities occurred after 1950. It remains uncertain whether this is due to decadal-scale changes of winter windstorms in Switzerland or merely due to a possible bias of the 20CR ensemble mean towards lower wind speeds in the period before around 1950.

20CR↗
DOE OSTI2016

PHOTOIONIZATION MODELS OF THE INNER GASEOUS DISK OF THE HERBIG BE STAR BD+65 1637

We attempt to constrain the physical properties of the inner, gaseous disk of the Herbig Be star BD+65 1637 using non-LTE, circumstellar disk codes and observed spectra (3700–10500 Å) from the ESPaDOnS instrument on the Canada–France–Hawaii Telescope. The photoionizing radiation of the central star is assumed to be the sole source of input energy for the disk. We model optical and near-infrared emission lines that are thought to form in this region using standard techniques that have been successful in modeling the spectra of classical Be stars. By comparing synthetic line profiles of hydrogen, helium, iron, and calcium with the observed line profiles, we try to constrain the geometry, density structure, and kinematics of the gaseous disk. Reasonable matches have been found for all line profiles individually; however, no disk density model based on a single power law for the equatorial density was able to simultaneously fit all of the observed emission lines. Among the emission lines, the metal lines, especially the Ca ii IR triplet, seem to require higher disk densities than the other lines. Excluding the Ca ii lines, a model in which the equatorial disk density falls as 10{sup −10} (R{sub *}/R){sup 3} g cm{sup −3} seen at an inclination of 45° for a 50 R{sub *} disk provides reasonable matches to the overall line shapes and strengths. The Ca ii lines seem to require a shallower drop-off as 10{sup −10} (R{sub *}/R){sup 2} g cm{sup −3} to match their strength. More complex disk density models are likely required to refine the match to the BD+65 1637 spectrum.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

A NEW GENERATION OF LOS ALAMOS OPACITY TABLES

We present a new, publicly available set of Los Alamos OPLIB opacity tables for the elements hydrogen through zinc. Our tables are computed using the Los Alamos ATOMIC opacity and plasma modeling code, and make use of atomic structure calculations that use fine-structure detail for all the elements considered. Our equation of state model, known as ChemEOS, is based on the minimization of free energy in a chemical picture and appears to be a reasonable and robust approach to determining atomic state populations over a wide range of temperatures and densities. In this paper we discuss in detail the calculations that we have performed for the 30 elements considered, and present some comparisons of our monochromatic opacities with measurements and other opacity codes. We also use our new opacity tables in solar modeling calculations and compare and contrast such modeling with previous work.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

MODELING DUST EMISSION OF HL TAU DISK BASED ON PLANET–DISK INTERACTIONS

We use extensive global two-dimensional hydrodynamic disk gas+dust simulations with embedded planets, coupled with three-dimensional radiative transfer calculations, to model the dust ring and gap structures in the HL Tau protoplanetary disk observed with the Atacama Large Millimeter/Submillimeter Array (ALMA). We include the self-gravity of disk gas and dust components and make reasonable choices of disk parameters, assuming an already settled dust distribution and no planet migration. We can obtain quite adequate fits to the observed dust emission using three planets with masses of 0.35, 0.17, and 0.26 M{sub Jup} at 13.1, 33.0, and 68.6 AU, respectively. Implications for the planet formation as well as the limitations of this scenario are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

FERMI LAT DISCOVERY OF EXTENDED GAMMA-RAY EMISSIONS IN THE VICINITY OF THE HB 3 SUPERNOVA REMNANT

We report the discovery of extended gamma-ray emission measured by the Large Area Telescope (LAT) onboard the Fermi Gamma-ray Space Telescope in the region of the supernova remnant (SNR) HB 3 (G132.7+1.3) and the W3 II complex adjacent to the southeast of the remnant. W3 is spatially associated with bright {sup 12}CO (J = 1–0) emission. The gamma-ray emission is spatially correlated with this gas and the SNR. We discuss the possibility that gamma rays originate in interactions between particles accelerated in the SNR and interstellar gas or radiation fields. The decay of neutral pions produced in nucleon–nucleon interactions between accelerated hadrons and interstellar gas provides a reasonable explanation for the gamma-ray emission. The emission from W3 is consistent with irradiation of the CO clouds by the cosmic rays accelerated in HB 3.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Atomic chemistry in turbulent astrophysical media II: Effect of the redshift zero metagalactic background

Here, we carry out direct numerical simulations of turbulent astrophysical media exposed to the redshift zero metagalactic background. The simulations assume solar composition and explicitly track ionizations, recombinations, and ion-by-ion radiative cooling for hydrogen, helium, carbon, nitrogen, oxygen, neon, sodium, magnesium, silicon, sulfur, calcium, and iron. Each run reaches a global steady state that depends not only on the ionization parameter, $U,$ and mass-weighted average temperature, ${T}_{{\rm{MW}}},$ but also on the one-dimensional turbulent velocity dispersion, ${\sigma }_{{\rm{1D}}}$. We carry out runs that span a grid of models with U ranging from 0 to 10 –1 and ${\sigma }_{{\rm{1D}}}$ ranging from 3.5 to 58 km s –1 , and we vary the product of the mean density and the driving scale of the turbulence, ${nL},$ which determines the average temperature of the medium, from ${nL}={10}^{16}$ to ${nL}={10}^{20}$ cm –2 . The turbulent Mach numbers of our simulations vary from $M\approx 0.5$ for the lowest velocity dispersion cases to $M\approx 20$ for the largest velocity dispersion cases. When $M\lesssim 1,$ turbulent effects are minimal, and the species abundances are reasonably described as those of a uniform photoionized medium at a fixed temperature. On the other hand, when $M\gtrsim 1,$ dynamical simulations such as the ones carried out here are required to accurately predict the species abundances. We gather our results into a set of tables to allow future redshift zero studies of the intergalactic medium to account for turbulent effects.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

SIX NEW MILLISECOND PULSARS FROM ARECIBO SEARCHES OF FERMI GAMMA-RAY SOURCES

We have discovered six radio millisecond pulsars (MSPs) in a search with the Arecibo telescope of 34 unidentified gamma-ray sources from the Fermi Large Area Telescope (LAT) four year point source catalog. Among the 34 sources, we also detected two MSPs previously discovered elsewhere. Each source was observed at a center frequency of 327 MHz, typically at three epochs with individual integration times of 15 minutes. The new MSP spin periods range from 1.99 to 4.66 ms. Five of the six pulsars are in interacting compact binaries (period ≤ 8.1 hr), while the sixth is a more typical neutron star-white dwarf binary with an 83 day orbital period. This is a higher proportion of interacting binaries than for equivalent Fermi-LAT searches elsewhere. The reason is that Arecibo's large gain afforded us the opportunity to limit integration times to 15 minutes, which significantly increased our sensitivity to these highly accelerated systems. Seventeen of the remaining 26 gamma-ray sources are still categorized as strong MSP candidates, and will be re-searched.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Core-collapse supernovae from 9 to 120 solar masses based on neutrino-powered explosions

Nucleosynthesis, light curves, explosion energies, and remnant masses are calculated for a grid of supernovae (SNe) resulting from massive stars with solar metallicity and masses from 9.0 to 120 M{sub ⊙}. The full evolution is followed using an adaptive reaction network of up to 2000 nuclei. A novel aspect of the survey is the use of a one-dimensional neutrino transport model for the explosion. This explosion model has been calibrated to give the observed energy for SN 1987A, using five standard progenitors, and for the Crab SN using a 9.6 M{sub ⊙} progenitor. As a result of using a calibrated central engine, the final kinetic energy of the SN is variable and sensitive to the structure of each pre-SN star. Many progenitors with extended core structures do not explode, but become black holes (BHs), and the masses of exploding stars do not form a simply connected set. The resulting nucleosynthesis agrees reasonably well with the Sun provided that a reasonable contribution from SNe Ia is also allowed, but with a deficiency of light s-process isotopes. The resulting neutron star initial mass function has a mean gravitational mass near 1.4 M{sub ⊙}. The average BH mass is about 9 M{sub ⊙} if only the helium core implodes, and 14 M{sub ⊙} if the entire pre-SN star collapses. Only ∼10% of SNe come from stars over 20 M{sub ⊙}, and some of these are Type Ib or Ic. Some useful systematics of Type IIp light curves are explored.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

SANTA BARBARA CLUSTER COMPARISON TEST WITH DISPH

The Santa Barbara cluster comparison project revealed that there is a systematic difference between entropy profiles of clusters of galaxies obtained by Eulerian mesh and Lagrangian smoothed particle hydrodynamics (SPH) codes: mesh codes gave a core with a constant entropy, whereas SPH codes did not. One possible reason for this difference is that mesh codes are not Galilean invariant. Another possible reason is the problem of the SPH method, which might give too much “protection” to cold clumps because of the unphysical surface tension induced at contact discontinuities. In this paper, we apply the density-independent formulation of SPH (DISPH), which can handle contact discontinuities accurately, to simulations of a cluster of galaxies and compare the results with those with the standard SPH. We obtained the entropy core when we adopt DISPH. The size of the core is, however, significantly smaller than those obtained with mesh simulations and is comparable to those obtained with quasi-Lagrangian schemes such as “moving mesh” and “mesh free” schemes. We conclude that both the standard SPH without artificial conductivity and Eulerian mesh codes have serious problems even with such an idealized simulation, while DISPH, SPH with artificial conductivity, and quasi-Lagrangian schemes have sufficient capability to deal with it.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

MODELING THE Ly α FOREST IN COLLISIONLESS SIMULATIONS

Cosmological hydrodynamic simulations can accurately predict the properties of the intergalactic medium (IGM), but only under the condition of retaining the high spatial resolution necessary to resolve density fluctuations in the IGM. This resolution constraint prohibits simulating large volumes, such as those probed by BOSS and future surveys, like DESI and 4MOST. To overcome this limitation, we present “Iteratively Matched Statistics” (IMS), a novel method to accurately model the Ly α forest with collisionless N -body simulations, where the relevant density fluctuations are unresolved. We use a small-box, high-resolution hydrodynamic simulation to obtain the probability distribution function (PDF) and the power spectrum of the real-space Ly α forest flux. These two statistics are iteratively mapped onto a pseudo-flux field of an N -body simulation, which we construct from the matter density. We demonstrate that our method can reproduce the PDF, line of sight and 3D power spectra of the Ly α forest with good accuracy (7%, 4%, and 7% respectively). We quantify the performance of the commonly used Gaussian smoothing technique and show that it has significantly lower accuracy (20%–80%), especially for N -body simulations with achievable mean inter-particle separations in large-volume simulations. In addition, we show that IMS produces reasonable and smooth spectra, making it a powerful tool for modeling the IGM in large cosmological volumes and for producing realistic “mock” skies for Ly α forest surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Data assimilation in a solar dynamo model using Ensemble Kalman Filters: sensitivity and robustness in reconstruction of meridional flow speed

We implement an Ensemble Kalman Filter procedure using the Data Assimilation Research Testbed for assimilating “synthetic” meridional flow-speed data in a Babcock–Leighton-type flux-transport solar dynamo model. By performing several “observing system simulation experiments,” we reconstruct time variation in meridional flow speed and analyze sensitivity and robustness of reconstruction. Using 192 ensemble members including 10 observations, each with 4% error, we find that flow speed is reconstructed best if observations of near-surface poloidal fields from low latitudes and tachocline toroidal fields from midlatitudes are assimilated. If observations include a mixture of poloidal and toroidal fields from different latitude locations, reconstruction is reasonably good for ⩽40% error in low-latitude data, even if observational error in polar region data becomes 200%, but deteriorates when observational error increases in low- and midlatitude data. Solar polar region observations are known to contain larger errors than those in low latitudes; our forward operator (a flux-transport dynamo model here) can sustain larger errors in polar region data, but is more sensitive to errors in low-latitude data. An optimal reconstruction is obtained if an assimilation interval of 15 days is used; 10- and 20-day assimilation intervals also give reasonably good results. Assimilation intervals <5 days do not produce faithful reconstructions of flow speed, because the system requires a minimum time to develop dynamics to respond to flow variations. Reconstruction also deteriorates if an assimilation interval >45 days is used, because the system’s inherent memory interferes with its short-term dynamics during a substantially long run without updating.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

( Fermi Fermi)/LAT study of gamma-ray emission in the direction of the Monoceros Loop supernova remnant

We present an analysis of the gamma-ray measurements by the Large Area Telescope on board the Fermi Gamma-ray Space Telescope in the region of the supernova remnant (SNR) Monoceros Loop (G205.5+0.5). The brightest gamma-ray peak is spatially correlated with the Rosette Nebula, which is a molecular cloud complex adjacent to the southeast edge of the SNR. After subtraction of this emission by spatial modeling, the gamma-ray emission from the SNR emerges, which is extended and fit by a Gaussian spatial template. The gamma-ray spectra are significantly better reproduced by a curved shape than a simple power law. The luminosities between 0.2 and 300 GeV are ∼4×10{sup 34} erg s{sup −1} for the SNR and ∼3×10{sup 34} erg s{sup −1} for the Rosette Nebula, respectively. We argue that the gamma-rays likely originate from the interactions of particles accelerated in the SNR. The decay of neutral pions produced in nucleon–nucleon interactions of accelerated hadrons with interstellar gas provides a reasonable explanation for the gamma-ray emission of both the Rosette Nebula and the Monoceros SNR.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

THE GINI COEFFICIENT AS A MORPHOLOGICAL MEASUREMENT OF STRONGLY LENSED GALAXIES IN THE IMAGE PLANE

Characterization of the morphology of strongly lensed galaxies is challenging because images of such galaxies are typically highly distorted. Lens modeling and source plane reconstruction is one approach that can provide reasonably undistorted images from which morphological measurements can be made, though at the expense of a highly spatially variable telescope point-spread function (PSF) when mapped back to the source plane. Unfortunately, modeling the lensing mass is a time- and resource-intensive process, and in many cases there are too few constraints to precisely model the lensing mass. If, however, useful morphological measurements could be made in the image plane rather than the source plane, it would bypass this issue and obviate the need for a source reconstruction process for some applications. We examine the use of the Gini coefficient as one such measurement. Because it depends on the cumulative distribution of the light of a galaxy, but not the relative spatial positions, the fact that surface brightness is conserved by lensing means that the Gini coefficient may be well preserved by strong gravitational lensing. Through simulations, we test the extent to which the Gini coefficient is conserved, including by effects due to PSF convolution and pixelization, to determine whether it is invariant enough under lensing to be used as a measurement of galaxy morphology that can be made in the image plane.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

A comparison of SPH artificial viscosities and their impact on the Keplerian disk

Hydrodynamical simulations of rotating disks play important roles in the field of astrophysical and planetary science. Smoothed particle hydrodynamics (SPH) has been widely used for such simulations. However, it has been known that when using SPH, a cold and thin Kepler disk breaks up due to the unwanted angular momentum transfer. Two possible reasons have been suggested for this breaking up of the disk; the artificial viscosity (AV) and the numerical error in the evaluation of pressure gradient in SPH. Which one is dominant is still unclear. In this paper, we investigate the reason for this rapid breaking up of the disk. We implemented most of the popular formulations of AV and switches, and measured the angular momentum transfer due to both AV and the error of SPH’s estimate of the pressure gradient. We found that the angular momentum transfer due to AV at the inner edge triggers the breaking up of the disk. We also found that the classical von Neumann–Richtmyer–Landshoff type AV with a high-order estimate for ∇⋅v can maintain the disk for ∼100 orbits even when used with the standard formulation of SPH.

79 ASTRONOMY AND ASTROPHYSICS↗