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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

An experimental and computational analysis of combustion heat release transformation in dual fuel combustion

Dual fuel (DF) diesel-methane combustion, which employs a high-reactivity fuel (diesel) to ignite a low-reactivity fuel (methane), is a widely studied combustion strategy for internal combustion engines, with significant potential for engine-out emissions reductions without the need for major hardware modifications. A phenomenon, which has been reported in the DF literature, but not explained fully, is the transformation of the shape of the apparent heat release rate (AHRR) curve as the start of injection (SOI) of diesel is advanced beyond a certain threshold; coincidentally, this AHRR transformation is usually accompanied by a sharp decrease in engine-out emissions of oxides of nitrogen (NOx). The goal of the present work is to establish the underlying physical reason(s) that cause the AHRR transformation. The AHRR transformation was observed on a single cylinder research engine (SCRE) at an indicated mean effective pressure (IMEP) of 5 bar at a speed of 1500 rev/min. The transformation occurred over a range of SOIs from 330 to 320 crank angle degrees (CAD). While the 330 CAD SOI exhibited a typical two-stage AHRR curve, with a clearly definable first-stage peak followed by a second-stage AHRR with little-to-no low temperature heat release (LTHR) present and high engine-out NOx, the 320 CAD SOI exhibited a single-stage, Gaussian-like AHRR curve, with noticeable LTHR and at least one order-of-magnitude lower NOx emissions. Here, leveraging analysis of experimental data and three-dimensional computational fluid dynamic simulations, the authors show that the AHRR transformation is impacted mainly by differences in local equivalence ratio distributions within the cylinder at ignition onset for different diesel SOIs.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2025

Equilibrium expectations for non-Gaussian fluctuations near a QCD critical point

With the highly anticipated results from the Beam Energy Scan II program at RHIC being recently revealed, an understanding of particle-number fluctuations and their significance as a potential signature of a possible QCD critical point is crucial. Early works that embarked on this endeavor sought to estimate the fluctuations due to the presence of a critical point assuming they stay in equilibrium. From these results came the proposal to focus efforts on higher, non-Gaussian, moments of the event-by-event distributions, in particular of the number of protons. These non-Gaussian moments are especially sensitive to critical fluctuations, as their magnitudes are proportional to high powers of the critical correlation length. As the equation of state provides key input for hydrodynamical simulations of heavy-ion collisions, we estimate equilibrium fluctuations from the BEST equation of state (EoS) that includes critical features from the 3D Ising Model. In particular, the proton factorial cumulants and their dependence on non-universal mapping parameters is investigated within the BEST EoS. Furthermore, the correlation length, as a central quantity for the assessment of fluctuations in the vicinity of a critical point, is also calculated in a consistent manner with the scaling equation of state. An understanding of the equilibrium estimates of proton factorial cumulants will be useful for further comparison to estimates of out-of-equilibrium fluctuations in order to determine the magnitude of the observable fluctuations to be expected in heavyion collision experiments, in which the time spent near a critical point is short.

Karthein, Jamie M. [Massachusetts Institute of Tec↗
DOE OSTI2021

An accurate, non-empirical method for incorporating decoherence into Ehrenfest dynamics

In mixed quantum-classical nonadiabatic molecular dynamics methods, the anchoring of the electronic wave function to a single nuclear geometry results in both quantitative and qualitative errors in the dynamics. In the context of both Ehrenfest and trajectory surface hopping methods, methods for incorporating decoherence are widely used to eliminate these errors. However, the accuracy of these methods often depends strongly on the parameterization of the decoherence time and/or other related quantities. Here, we present a refinement of the recently introduced collapse to a block (TAB) scheme for incorporating decoherence into Ehrenfest dynamics. The proposed approach incorporates an approximation to the history of the population dynamics and treats the coherence decay as Gaussian, rather than exponential. This method uses parameters that can be obtained from first principles, rather than empirical fitting. Application to one-dimensional models indicates excellent agreement with numerically exact simulations. We also introduce a second refinement to the TAB method: a robust linear least-squares algorithm for determining collapse probabilities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Biases to primordial non-Gaussianity measurements from CMB secondary anisotropies

ABSTRACT Our view of the last-scattering surface in the cosmic microwave background (CMB) is obscured by secondary anisotropies, sourced by scattering, extragalactic emission, and gravitational processes between recombination and observation. Whilst it is established that non-Gaussianity from the correlation between the integrated-Sachs–Wolfe (ISW) effect and gravitational lensing can significantly bias primordial non-Gaussianity (PNG) searches, recent work by Hill suggests that other combinations of secondary anisotropies can also produce significant biases. Building on that work, we use the WebSky and Sehgal et al. simulations to perform an extensive examination of possible biases to PNG measurements for the local, equilateral and orthogonal shapes. For a Planck-like CMB experiment, without foreground cleaning, we find significant biases from cosmic infrared background (CIB)-lensing and thermal Sunyaev–Zel’dovich (tSZ)-lensing bispectra for the local and orthogonal templates, and from CIB and tSZ bispectra for the equilateral template. For future experiments, such as the Simons Observatory, biases from correlations between the ISW effect and the tSZ and CIB will also become important. Finally, we investigate the effectiveness of foreground-cleaning techniques to suppress these biases. We find that the majority of these biases are effectively suppressed by the internal-linear combination method with a total bias below the $1\, \sigma$ statistical error for both experiments. However, the small total bias arises from the cancellation of several $1\, \sigma$ biases for Planck-like experiments and $2\, \sigma$ biases for SO-like. As this cancellation is likely sensitive to the modelling, to ensure robustness against these biases, we recommend that explicit removal methods should be used.

Astronomy & Astrophysics↗
DOE OSTI2020

Forecasting cosmological constraints from the weak lensing magnification of type Ia supernovae measured by the Nancy Grace Roman Space Telescope

We report that the weak lensing magnification of type Ia supernovae (SNe Ia) is sensitive to the clustering of matter and provides an independent cosmological probe complementary to SN Ia distance measurements. The Nancy Grace Roman Space Telescope is uniquely sensitive to this measurement as it can discover high redshift SNe Ia and measure them with high precision. We present a methodology for reconstructing the probability distribution of the weak lensing magnification μ of SNe Ia, p(μ), from observational data, and using it to constrain cosmological parameters. We find that the reconstructed p(μ) can be fitted accurately by a stretched Gaussian distribution and used to measure the variance of μ, ξ μ , which can be compared to theoretical predictions in a likelihood analysis. Applying our methodology to a set of realistically simulated SNe Ia expected from the Roman Space Telescope, we find that using the weak lensing magnification of the SNe Ia constrains a combination of matter density Ω m and matter clustering amplitude σ 8 . SN Ia distances alone lead to a better than 1% measurement of Ωm. The combination of SN Ia weak lensing magnification and distance measurements result in a ~10 % measurement on σ 8 . The SNe Ia from Roman will be powerful in constraining the cosmological model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Fingerprinting Brownian Motions of Polymers under Flow

Here, we present a quantitative approach to the self-dynamics of polymers under steady flow by employing a set of complementary reference frames and extending the spherical harmonic expansion technique to dynamic density correlations. Application of this method to nonequilibrium molecular dynamics simulations of polymer melts reveals a number of universal features. For both unentangled and entangled melts, the center-of-mass motions in the flow frame are described by superdiffusive, anisotropic Gaussian distributions, whereas the isotropic component of monomer self-dynamics in the center-of-mass frame is strongly suppressed. Spatial correlation analysis shows that the heterogeneity of monomer self-dynamics increases significantly under flow.

36 MATERIALS SCIENCE↗
DOE OSTI2023

The Atacama Cosmology Telescope: map-based noise simulations for DR6

Abstract The increasing statistical power of cosmic microwave background (CMB) datasets requires a commensurate effort in understanding their noise properties. The noise in maps from ground-based instruments is dominated by large-scale correlations, which poses a modeling challenge. This paper develops novel models of the complex noise covariance structure in the Atacama Cosmology Telescope Data Release 6 (ACT DR6) maps. We first enumerate the noise properties that arise from the combination of the atmosphere and the ACT scan strategy. We then prescribe a class of Gaussian, map-based noise models, including a new wavelet-based approach that uses directional wavelet kernels for modeling correlated instrumental noise. The models are empirical, whose only inputs are a small number of independent realizations of the same region of sky. We evaluate the performance of these models against the ACT DR6 data by drawing ensembles of noise realizations. Applying these simulations to the ACT DR6 power spectrum pipeline reveals a ∼ 20% excess in the covariance matrix diagonal when compared to an analytic expression that assumes noise properties are uniquely described by their power spectrum. Along with our public code,mnms, this work establishes a necessary element in the science pipelines of both ACT DR6 and future ground-based CMB experiments such as the Simons Observatory (SO).

Astronomy & Astrophysics↗
DOE OSTI2025

Simulations of Attosecond Metallization in Quartz and Diamond Probed with Inner-Shell Transient Absorption Spectroscopy

When dielectrics are hit with intense infrared (IR) laser pulses, transient metalization can occur. The initial attosecond dynamics behind this metallization are not entirely understood. Therefore, simulations are needed to understand this process and to help interpret experimental observations of it, such as with attosecond transient absorption (ATA). In this paper, we present first-principles simulations of ATA based on bulk-mimicking clusters and real-time time-dependent density functional theory (RT-TDDFT), with Koopmans-tuned range-separated hybrid functionals and Gaussian basis sets. Our method gives good agreement with the experiment for the breakdown threshold in silica and diamond. This breakdown voltage corresponds to a Keldysh parameter of approximately one and thus involves a transition to a regime where the dynamics are driven by tunneling. Pumping at an amplitude just below this value causes a mixture of multiphoton and tunneling excitations across the band gap to occur. The computed extreme ultraviolet and X-ray attosecond transient spectra also agree well with the experiment and show a decrease in optical density due to the transient population of the conduction band from the IR field. First-principles approaches such as this are valuable for interpreting the complicated modulations in a spectrum and for guiding future attosecond experiments on solids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Reflectivity and spectrum of relativistic flying plasma mirrors

Flying plasma mirrors induced by intense lasers via laser wake field acceleration scheme have been proposed as a promising way to generate few-cycle EUV or x-ray lasers. In addition, if such a relativistic plasma mirror can accelerate, then it would serve as an analog black hole to investigate the information loss paradox associated with the black hole Hawking evaporation. Among these applications, the reflectivity, which is usually frequency-dependent, would affect the outgoing photon spectrum and, therefore, impact on the analysis of the physics under investigation. In this paper, these two issues are investigated analytically and numerically with one-dimensional particle-in-cell simulations. Based on our simulation results, we propose a new model that provides a better estimate of the reflectivity than those studied previously. Moreover, we found that the peak frequency of the reflected spectrum of a Gaussian incident wave deviates from the expected value, 4γ 2 ω, due to the dependence of reflectivity on the frequency of the incident wave.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Inferring performance metrics for laser direct drive experiments on OMEGA

Quantifying performance improvements on the OMEGA laser facility requires robust inference of established no-alpha performance metrics, which requires, at minimum, a model to infer the shocked fuel mass and pressure of the confined fusion plasma. In this work, we describe the methodology used to infer performance metrics on OMEGA and present the current state-of-the art model used to infer these metrics from OMEGA experiments. In particular, since neutron images of cryogenic implosions are not available on OMEGA at present, we present how x-ray sizes are determined on OMEGA using a Gaussian Process regression model and how the neutron production region's size is inferred from them. As a result, we end by benchmarking the model using synthetic data and 1-D LILAC simulations and test its experimental self-consistency across available x-ray diagnostic channels.

Gopalaswamy, V. [Laboratory for Laser Energetics, ↗
DOE OSTI2021

Dark Energy Survey Year 3 results: Curved-sky weak lensing mass map reconstruction

ABSTRACT We present reconstructed convergence maps, mass maps, from the Dark Energy Survey (DES) third year (Y3) weak gravitational lensing data set. The mass maps are weighted projections of the density field (primarily dark matter) in the foreground of the observed galaxies. We use four reconstruction methods, each is a maximum a posteriori estimate with a different model for the prior probability of the map: Kaiser–Squires, null B-mode prior, Gaussian prior, and a sparsity prior. All methods are implemented on the celestial sphere to accommodate the large sky coverage of the DES Y3 data. We compare the methods using realistic ΛCDM simulations with mock data that are closely matched to the DES Y3 data. We quantify the performance of the methods at the map level and then apply the reconstruction methods to the DES Y3 data, performing tests for systematic error effects. The maps are compared with optical foreground cosmic-web structures and are used to evaluate the lensing signal from cosmic-void profiles. The recovered dark matter map covers the largest sky fraction of any galaxy weak lensing map to date.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Constraining cosmological parameters using the pairwise kinematic Sunyaev-Zel’dovich effect with CMB-S4 and future galaxy cluster surveys

We present a forecast of the pairwise kinematic Sunyaev-Zel’dovich (kSZ) measurement that will be achievable with the future CMB-S4 experiment. CMB-S4 is the next stage for ground-based cosmic microwave background experiments, with a planned wide-area survey that will observe approximately 50% of the sky. We construct a simulated sample of galaxy clusters that have been optically selected in a Legacy Survey of Space and Time–like survey and have spectroscopic redshifts. For this cluster sample, assuming the likelihood is Gaussian, we predict that CMB-S4 will reject the null hypothesis of zero pairwise kSZ signal at 36⁢𝜎. We estimate the effects of systematic uncertainties such as scatter in the mass-richness scaling relation and cluster miscentering. We find that these effects can reduce the signal-to-noise ratio of the CMB-S4 pairwise kSZ measurement by 20%. We explore the constraining power of the measured kSZ signal in combination with measurements of the galaxy clusters’ thermal SZ emission on two extensions to the standard cosmological model. The first extension allows the dark energy equation of state 𝑤 to vary. We find the CMB-S4 pairwise kSZ measurement yields a modest reduction in the uncertainty on 𝑤 by a factor of 1.36 over the Planck’s 2018 uncertainty. The second extension tests general relativity by varying the growth index 𝛾. In conclusion, we find that CMB-S4’s pairwise kSZ measurement will yield a 28⁢𝜎 constraint on 𝛾 and strongly constrain alternative theories of gravity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

On the Properties of Cosmological Ionization Fronts

We investigate the properties of cosmological ionization fronts during the epoch of reionization using the Cosmic Reionization on Computers simulations. By analyzing reionization timing maps, we characterize ionization front velocities and curvatures and their dependence on the density structure of the intergalactic medium (IGM). The velocity distribution of ionization fronts in the simulations indicates that while the barrier-crossing analytical model captures the overall shape in high-velocity regions, it fails to reproduce the low-velocity tail, highlighting the non-Gaussian nature of the IGM’s density field. Ionization front velocities are inversely correlated with local density, propagating faster in underdense regions and more slowly in overdense environments. Faster ionization fronts also lead to higher postionization temperatures, reaching a plateau at ∼2 × 10$^{4}$ K for velocities exceeding 3000 km s$^{−1}$. Examining curvature statistics further establishes a connection between ionization front structure and the normalized density contrast ν, with trends in overdense regions aligning well with barrier-crossing model predictions, while deviations appear in underdense environments due to model limitations. These results provide a detailed characterization of ionization front dynamics and their interaction with the underlying density field, bridging small-scale reionization physics with large-scale observables such as the 21 cm signal and the IGM’s thermal history.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

COMPUTATIONAL MODELING OF IGNITION AND PREMIXED FLAME PROPAGATION INITIATED BY A PRE-CHAMBER TURBULENT JET

Addressing the pressing need for reduced carbon emissions, Turbulent Jet Ignition (TJI) emerges as a promising technology for ultra-lean combustion, offering enhanced thermal efficiencies and minimized cyclic variability in spark-ignited engines. To facilitate rapid testing and integration of this technology, a robust computational modeling framework is crucial. This study delves into the predictive capabilities of computational models for main-chamber ignition and premixed flame propagation using a single-cycle TJI rig measured by Biswas et al. (Applied Thermal Engineering, vol 106, 2016). Employing an open-source compressible flow simulation solver with Large Eddy Simulation (LES) for turbulence modeling, the investigation integrates the conventional Laminar Finite Rate Chemistry (LFRC) model alongside the transported Probability Density Method (PDF) for turbulence-chemistry interaction. A fully-consistent Eulerian Monte-Carlo Fields (EMCF) method is utilized to approximate the transported PDF, while Interaction by Exchange with Mean is employed to close micro-mixing terms in stochastic differential equations. A reduced chemical reaction mechanism with 21 species and 84 reactions (DRM-19) is used for solving chemical kinetics, and a double Gaussian energy deposition model is used to approximate the spark ignition in the pre-chamber. An unstructured O-grid mesh with 0.3 million cells in the prechamber and 1 million cells in the main chamber is employed. Results are divided into two phases: pre-chamber initialization and full TJI simulations. Validation of the predicted pre-chamber flame propagation and the lean ignition in the main-chamber is carried out by using available experimental data. Under quiescent conditions, both the LFRC and transported PDF methods largely underestimate the flame speed and subsequent pressure growth in the pre-chamber. A linear momentum forcing technique is applied to investigate the impact of initial turbulence in the pre-chamber, demonstrating a notable influence on flame propagation. Fine-tuning of the forcing coefficient reproduces the sudden pressure growth observed in the experiment. The experimentally validated pre-chamber simulation serves as the initial condition for the full TJI simulations. It is found that the LFRC model fails to predict lean-ignition in the main-chamber, resulting in a misfiring event. Incorporation of turbulence-chemistry interaction using the transported PDF method substantially improves the prediction of the ignition event in the main-chamber, achieving fair qualitative agreement and quantitative validation of combustion parameters within ±10% of the reported experimental data. The rich simulation results consisting of a full set of statistical description of the thermo-chemical states enable us to gain deep insights into the ignition mechanisms in the main chamber, which is limited when done experimentally. A novel dual ignition phenomenon is revealed in the TJI rig for the first time. Initially, a primary ignition kernel is formed at a downstream location which eventually detaches from the main jet. As the jet momentum decreases, a secondary ignition event follows, this time at a more upstream location which eventually combines with the primary ignition kernel to form a single connected flame front. Investigation of these ignition sequences in chemical composition space reveal distinct differences between the two. The primary ignition event in the main-chamber is followed by a large concentration of active radicals from the pre-chamber jet, accelerating the chain-branching steps, characterizing what has been referred to as flame ignition. In contrast, the secondary ignition occurs in the absence of active radicals in the pre-chamber jet, hence characterized as jet ignition. Further analysis of the effect of pre-chamber jet characteristics on lean ignition in the main-chamber is conducted by setting up cases with different initial pressure ratios (por) between the two chambers, a non-dimensional parameter, ranging from 1.2 to 3.2. As the initial pressure ratio increases, jet momentum increases, with dual ignition observed in cases above por= 2.2. Case with por= 3.2 lead to misfiring. The effect of ignition sequence on global combustion characteristics of TJI is analyzed. Dual ignition events lead to non-monotonicity in combustion characteristics such as global reaction progress variable, flame penetration, and global heat release rate. In dual ignition events, although the rate of fuel consumption and global heat release rate is initially lower, the secondary ignition leads to a sudden increase in flame surface area, resulting in a sudden jump and promoting the overall performance of the TJI system.

42 ENGINEERING↗
DOE OSTI2021

Cosmic Inference: Constraining Parameters with Observations and a Highly Limited Number of Simulations

We look at cosmological probes that pose an inverse problem where the measurement result is obtained through observations, and the objective is to infer values of model parameters that characterize the underlying physical system-our universe, from these observations and theoretical forward-modeling. The only way to accurately forward-model physical behavior on small scales is via expensive numerical simulations, which are further “emulated” due to their high cost. Emulators are commonly built with a set of simulations covering the parameter space with Latin hypercube sampling and an interpolation procedure; the aim is to establish an approximately constant prediction error across the hypercube. In this paper, we provide a description of a novel statistical framework for obtaining accurate parameter constraints. The proposed framework uses multi-output Gaussian process emulators that are adaptively constructed using Bayesian optimization methods with the goal of maintaining a low emulation error in the region of the hypercube preferred by the observational data. In this paper, we compare several approaches for constructing multi-output emulators that enable us to take possible inter-output correlations into account while maintaining the efficiency needed for inference. Using a Lyα forest flux power spectrum, we demonstrate that our adaptive approach requires considerably fewer-by a factor of a few in the Lyα P(k) case considered here-simulations compared to the emulation based on Latin hypercube sampling, and that the method is more robust in reconstructing parameters and their Bayesian credible intervals.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

aphBO-2GP-3B: a budgeted asynchronous parallel multi-acquisition functions for constrained Bayesian optimization on high-performing computing architecture

High-fidelity complex engineering simulations are often predictive, but also computationally expensive and often require substantial computational efforts. The mitigation of computational burden is usually enabled through parallelism in high-performance cluster (HPC) architecture. Optimization problems associated with these applications is a challenging problem due to the high computational cost of the high-fidelity simulations. In this paper, an asynchronous parallel constrained Bayesian optimization method is proposed to efficiently solve the computationally expensive simulation-based optimization problems on the HPC platform, with a budgeted computational resource, where the maximum number of simulations is a constant. The advantage of this method are three-fold. Firstly, the efficiency of the Bayesian optimization is improved, where multiple input locations are evaluated parallel in an asynchronous manner to accelerate the optimization convergence with respect to physical runtime. This efficiency feature is further improved so that when each of the inputs is finished, another input is queried without waiting for the whole batch to complete. Second, the proposed method can handle both known and unknown constraints. Third, the proposed method samples several acquisition functions based on their rewards using a modified GP-Hedge scheme. The proposed framework is termed aphBO-2GP-3B, which means asynchronous parallel hedge Bayesian optimization with two Gaussian processes and three batches. The numerical performance of the proposed framework aphBO-2GP-3B is comprehensively benchmarked using 16 numerical examples, compared against other 6 parallel Bayesian optimization variants and 1 parallel Monte Carlo as a baseline, and demonstrated using two real-world high-fidelity expensive industrial applications. The first engineering application is based on finite element analysis (FEA) and the second one is based on computational fluid dynamics (CFD) simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A vortex sheet based analytical model of the curled wake behind yawed wind turbines

Motivated by the need for compact descriptions of the evolution of non-classical wakes behind yawed wind turbines, we develop an analytical model to predict the shape of curled wakes. Interest in such modelling arises due to the potential of wake steering as a strategy for mitigating power reduction and unsteady loading of downstream turbines in wind farms. We first estimate the distribution of the shed vorticity at the wake edge due to both yaw offset and rotating blades. By considering the wake edge as an ideally thin vortex sheet, we describe its evolution in time moving with the flow. Vortex sheet equations are solved using a power series expansion method, and an approximate solution for the wake shape is obtained. The vortex sheet time evolution is then mapped into a spatial evolution by using a convection velocity. Apart from the wake shape, the lateral deflection of the wake including ground effects is modelled. Our results show that there exists a universal solution for the shape of curled wakes if suitable dimensionless variables are employed. For the case of turbulent boundary layer inflow, the decay of vortex sheet circulation due to turbulent diffusion is included. Finally, we modify the Gaussian wake model by incorporating the predicted shape and deflection of the curled wake, so that we can calculate the wake profiles behind yawed turbines. Model predictions are validated against large-eddy simulations and laboratory experiments for turbines with various operating conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Self-similarity of k -nearest neighbour distributions in scale-free simulations

ABSTRACT We use the k-nearest neighbour probability distribution function (kNN-PDF; Banerjee & Abel 2021a) to assess convergence in a scale-free N-body simulation. Compared to our previous two-point analysis, the kNN-PDF allows us to quantify our results in the language of haloes and numbers of particles, while also incorporating non-Gaussian information. We find good convergence for 32 particles and greater at densities typical of haloes, while 16 particles and fewer appear unconverged. Halving the softening length extends convergence to higher densities, but not to fewer particles. Our analysis is less sensitive to voids, but we analyse a limited range of underdensities and find evidence for convergence at 16 particles and greater even in sparse voids.

79 ASTRONOMY AND ASTROPHYSICS↗