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

Shock-induced transformation of nitinol shape memory alloy: Effect of stress state on transformation

Due to its numerous practical applications and intriguing phase transformation behavior, shape memory alloys (SMAs) have garnered significant research and development interests. In the past, most studies on the mechanical behavior of SMAs have been conducted under uniaxial stress loadings. Limited research on SMAs under shock loading has not provided conclusive results regarding their transformation behavior and transformation stress under such loading. Additionally, there is a lack of comprehensive understanding regarding the effects of different stress states on transformation behavior. The main objectives of this study are to address these issues. To achieve these objectives, a series of shock wave experiments were designed and conducted. Additionally, quasi-static and dynamic uniaxial stress experiments were carried out to establish a baseline for comparison. The results revealed that the transformation stress under dynamic uniaxial strain shock loading was approximately 1.92 GPa in contrast to 0.5 GPa (quasi-static) to 0.8 GPa (dynamic) observed in uniaxial stress loading. The transformation behavior exhibited noticeable rate sensitivity for both types of loading. There appeared to be a critical strain rate above which the austenite phase was driven to a metastable state. This estimated critical axial strain rate along the loading direction was approximately 2 × 10 3 /s–4 × 10 3 /s for uniaxial stress loading and approximately 2 × 10 6 /s for uniaxial strain loading. The apparent high transformation stress for uniaxial strain loading can likely be attributed to a combination of high-pressure confinement and high strain rate. Furthermore, determining their relative contributions remains an open issue.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Multipole responses in fissioning nuclei and their uncertainties

Electromagnetic multipole responses are key inputs to model the structure, decay, and reactions of atomic nuclei. With the introduction of the finite amplitude method (FAM), large-scale calculations of the nuclear linear response in heavy deformed nuclei have become possible. This work provides a detailed study of multipole responses in actinide nuclei with Skyrme energy density functionals. We quantify both systematic and statistical uncertainties induced by the functional parametrization in FAM calculations. We also extend the FAM formalism to perform blocking calculations with the equal filling approximation for odd-mass and odd-odd nuclei, and analyze the impact of blocking configurations on the response. In conclusion, by examining the entire plutonium isotopic chain from the proton to the neutron drip line, we find a large variability of the response with the neutron number and study how it correlates with the deformation of the nuclear ground state.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Pulse shape measurements for neutron/gamma discrimination using the TOFPET2 ASIC

Many highly pixelated organic scintillator detection systems would benefit from independent readout of each scintillator pixel. Recent advances in Silicon Photomultiplier (SiPM) technology makes this goal feasible, however the data acquisition from potentially hundreds or thousands of channels requires a low-cost and compact solution. For pixelated neutron detection with organic scintillators, the capability to distinguish between neutron and gamma interactions using Pulse Shape Discrimination (PSD) is required along with pulse charge and time of arrival. The TOFPET2 ASIC from PETsys Electronics is a 64-channel readout chip providing pulse time and charge integration measurements from SiPMs, and is specifically designed for time-of-flight positron-emission tomography. Using an 8 × 8 array of 6 mm × 6 mm J-series SiPMs from SensL/OnSemi (ArrayJ-60035-64P-PCB), we have studied the energy and PSD performance of the TOFPET2 ASIC using a 4 × 4 array of 6 mm × 6 mm × 30 mm trans -Stilbene crystals from Inrad Optics and a custom SiPM routing board from PETsys Electronics. In conclusion, using a time-over-threshold method, we measure a maximum PSD figure-of-merit of approximately 1.2 at 478 keV (the Compton edge of 662 keV) for a J-series SiPM operating at an over-voltage of 3V.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Sustainable Shape Memory Elastomers with Reduced Melt Viscosity and Enhanced Stiffness

Melt reactive processing of lignin with nitrile rubber is a promising approach to synthesizing shape memory materials. The strong intramolecular interactions in lignin macromolecular structures, caused by π–π stacking in aromatic rings and hydrogen bonding, often result in large phase separation or low miscibility with rubbers. In this study, we investigated the chemical and molecular characteristics, as well as the stiffness and complex viscosity, of modified kraft lignin melt-reacted with an acrylonitrile/butadiene copolymer containing 41% acrylonitrile (NBR41). To enhance the macromolecular compatibility of kraft lignin with NBR41, kraft lignin was cross-linked with poly(propylene glycol) diglycidyl ether (PPDE) and trimethylolpropane triglycidyl ether (TTE), both rich in epoxy reactive groups capable of forming chemical bonds with hydroxyl and carboxyl groups. Here, our findings demonstrate that the modification of kraft lignin with PPDE and TTE resulted in significantly increased stiffness of the composites. The elastic modulus of NBR41-Kraft lignin-PPDE and NBR41-Kraft lignin-TTE increased by 82 and 162%, respectively. Both the yield strength and Young’s modulus of these two samples showed dramatic improvements. Specifically, the yield strength and Young’s modulus of NBR41-Kraft lignin-TTE increased nearly 4 and 3-fold, respectively, compared to the control sample. Interestingly, despite significant improvements in mechanical properties, the viscosity of NBR41-Kraft lignin-PPDE was substantially lower than that of the control sample. At 210 °C and an angular frequency of 1 rad/s, the complex viscosity of NBR41-Kraft lignin was approximately 100.25 ± 4.77 kPa·s, while that of NBR41-Kraft lignin-PPDE was significantly lower at 56 ± 0.93 kPa·s. These findings were validated through Fourier transform infrared spectroscopy, scanning electron microscopy, dynamic mechanical analysis, thermal characterization, rheological tests, and quasi-elastic neutron scattering techniques.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Ab initio quantum scattering calculations for the CO–O 2 system and a new CO–O 2 potential energy surface: O 2 and air broadening of the R(0) line in CO

We present ab initio calculations of the collisional broadening of the R(0) pure rotational line in CO (at 115 GHz) perturbed by O 2 . Our calculations are done in a fully quantum way by solving close-coupling quantum-scattering equations without any approximations. We also report a new, highly accurate CO–O 2 potential energy surface on which we did the quantum-scattering calculations. The calculated collisional broadening agrees with the available experimental data in a wide temperature range. The calculated collisional shift is negligible compared to the broadening, which is also consistent with the experimental data. We combine this result with our previous calculations for the same line in CO perturbed by N 2 [Józwiak et al., J. Chem. Phys. 154, 054314 (2021)]; the obtained air-perturbed broadening of the R(0) pure rotational line in CO and its temperature dependence perfectly agree with the HITRAN database. This result constitutes an important step toward developing a methodology for providing accurate ab initio reference data on spectroscopic collisional line-shape parameters for molecular systems relevant to the Earth’s atmosphere and for populating spectroscopic line-by-line databases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

ComStock Measure Documentation: Thermostat and Lighting Control for Load Shedding

This report describes the modeling methodology for an upgrade package of two end-use savings shape measures - Thermostat Control for Load Shedding and Lighting Control for Load Shedding - and briefly introduces key results. The package combines thermostat control for load shedding and lighting control for load shedding measures to reduce the HVAC and lighting load during the building's electricity peak window every weekday. The measure takes daily peak load schedule inputs generated by the method "Dispatch Schedule Generation" described in the "Supplemental Documentation: Dispatch Schedule Generation for Demand Flexibility Measures" to determine the start and end times of the predicted peak window, and then relaxes the thermostat setpoints and dims the lighting level from the original schedules during the peak window to reduce the peak demand. The measure is applicable to (large, medium and small) offices, warehouses, and primary and secondary schools, which correspond to approximately 68% of the stock floor area of commercial buildings in ComStock analysis. The measure demonstrates 3%-10% daily peak demand reduction performance for applicable buildings, and 0.97% total site energy savings (0 trillion British thermal units [TBtu]) for the U.S. commercial building stock modeled in ComStock.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

Effects of Size and Shape on the Tolerances for Misalignment and Probabilities for Successful Oriented Attachment of Nanoparticles

Oriented attachment (OA) of nanoparticles is an important pathway of crystal growth, but tools for quantitatively modeling OA are lacking. Here we present several simple models that relate the probability of achieving OA to basic geometric parameters such as particle size, shape, and lattice periodicity. A Moiré-domain model is applied to understand twist-misorientations between parallel surfaces, and it predicts that the range of twist angles yielding perfect OA is inversely related to the width of the contact area. This is confirmed and further developed using a surface functional model, which predicts how crystallographic registration forces drive the emergence of complex orientational energy landscapes. The energy landscapes are predicted to possess local minima that can trap particles in imperfect alignments, and these local minima become deeper and more numerous as the contact area increases, making OA more challenging for large particles. Further, a second set of models is presented to understand the sequence of events by which two crystallographic faces become co-planer after collision. We use a ‘central force approximation’ to quantitatively predict the odds of attaining coalignment between various faces when particles collide with random misalignments, and we show that in the absence of biasing forces, the probability of attaining alignment on a given face is roughly proportional to its solid angle as viewed from the center of the particle. The model predicts that OA is most favorable between well-faceted particles and becomes exceedingly unlikely for large spherical particles that express many microfacets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Large-d phase transitions in holographic mutual information

In the AdS/CFT correspondence, the entanglement entropy of subregions in the boundary CFT is conjectured to be dual to the area of a bulk extremal surface at leading order in G N in the holographic limit. Under this dictionary, distantly separated regions in the CFT vacuum state have zero mutual information at leading order, and only attain nonzero mutual information at this order when they lie close enough to develop significant classical and quantum correlations. Previously, the separation at which this phase transition occurs for equal-size ball-shaped regions centered at antipodal points on the boundary was known analytically only in 3 spacetime dimensions. Inspired by recent explorations of general relativity at large- d , we compute the separation at which the phase transition occurs analytically in the limit of infinitely many spacetime dimensions, and find that distant regions cannot develop large correlations without collectively occupying the entire volume of the boundary theory. We interpret this result as illustrating the spatial decoupling of holographic correlations in the large- d limit, and provide intuition for this phenomenon using results from quantum information theory. We also compute the phase transition separation numerically for a range of bulk spacetime dimensions from 4 to 21, where analytic results are intractable but numerical results provide insight into the dimension-dependence of holographic correlations. For bulk dimensions above 5, our exact numerical results are well approximated analytically by working to next-to-leading order in the large- d expansion.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Coil optimization for quasi-helically symmetric stellarator configurations

Filament-based coil optimizations are performed for several quasi-helical stellarator configurations, beginning with the one from Landreman & Paul ( Phys. Rev. Lett. , vol. 128, 2022, 035001), demonstrating that precise quasi-helical symmetry can be achieved with realistic coils. Several constraints are placed on the shape and spacing of the coils, such as low curvature and sufficient plasma–coil distance for neutron shielding. The coils resulting from this optimization have a maximum curvature 0.8 times that of the coils of the Helically Symmetric eXperiment (HSX) and a mean squared curvature 0.4 times that of the HSX coils when scaled to the same plasma minor radius. When scaled up to reactor size and magnetic field strength, no fast particle losses were found in the free-boundary configuration when simulating 5000 alpha particles launched at $3.5\,\mathrm {MeV}$ on the flux surface with a normalized toroidal flux of $s=0.5$ . An analysis of the tolerance of the coils to manufacturing errors is performed using a Gaussian process model, and the coils are found to maintain low particle losses for smooth, large-scale errors up to amplitudes of approximately $0.15\,\mathrm {m}$ . Another coil optimization is performed for the Landreman–Paul configuration with the additional constraint that the coils are purely planar. Visual inspection of the Poincaré plot of the resulting magnetic field-lines reveal that the planar modular coils alone do a poor job of reproducing the target equilibrium. Additional non-planar coil optimizations are performed for the quasi-helical configuration with $5\,\%$ volume-averaged plasma beta from Landreman et al. ( Phys. Plasma , vol. 29, issue 8, 2022, 082501), and a similar configuration also optimized to satisfy the Mercier criterion. The finite beta configurations had larger fast-particle losses, with the free-boundary Mercier-optimized configuration performing the worst, losing approximately $5.5\,\%$ of alpha particles launched at $s=0.5$ .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Spherical Congeners of Polyaromatic Compounds Approaching C 20 - and C 60 -Fullerene-Type Structures

A series of three symmetric, hollow spherical, and shape-persistent molecular organic cages analogous to C 20 and C 60 were examined by computational modeling, analyzing structural elements, strain indicators, and physical properties relevant for potential applications. The compounds are covalent aromatic cages based on 1,3,5-substituted benzene nodes linked by paraphenylene or para-pyrenylene-connectors, with diameters varying from 2.3 to 4.2 nm. The apertures in the cage interior are varied by virtue of the cage type (C 20 - or C 60 -type cage) and the linear connectors placed between the C 6 H 3 -units. NBO and MESP analyses indicate the presence of electrophilic and nucleophilic sites in the molecular skeleton. In the cages with the phenylene-connectors, the HOMO−LUMO gaps are close to 4.0 eV. In the cage coated with an enlarged polyaromatic spacer (pyrene-unit), the gap is reduced by approximately 0.4 eV.

Aromatic compounds↗
DOE OSTI2023

Controlled Self-Assembly of Gold Nanotetrahedra into Quasicrystals and Complex Periodic Supracrystals

The self-assembly of shape-anisotropic nanocrystals into large-scale structures is a versatile and scalable approach to creating multifunctional materials. The tetrahedral geometry is ubiquitous in natural and manmade materials, yet regular tetrahedra present a formidable challenge in understanding their self-assembly behavior as they do not tile space. Here, we report diverse supracrystals from gold nanotetrahedra including the quasicrystal (QC) and the dimer packing predicted more than a decade ago and hitherto unknown phases. We solve the complex three-dimensional (3D) structure of the QC by a combination of electron microscopy, tomography, and synchrotron X-ray scattering. Nanotetrahedron vertex sharpness, surface ligands, and assembly conditions work in concert to regulate supracrystal structure. We also discover that the surface curvature of supracrystals can induce structural changes of the QC tiling and eventually, for small supracrystals with high curvature, stabilize a hexagonal approximant. Finally, our findings bridge the gap between computational design and experimental realization of soft matter assemblies and demonstrate the importance of accurate control over nanocrystal attributes and the assembly conditions to realize increasingly complex nanopolyhedron supracrystals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Two-step route to size and shape controlled gibbsite nanoplates and the crystal growth mechanism

Mastery of gibbsite (α-Al(OH) 3 ) nucleation and crystal growth is significant in fundamental aluminum chemistry and also beneficial for industrial applications and the remediation of nuclear waste. Herein, we developed an additive-free two-step route to size and morphology controlled synthesis of gibbsite nanoplates. Independent temperature manipulation of nucleation and crystal growth regimes was used to control the efficacy and yield of the process, producing gibbsite nanoplates with tunable morphologies and sizes. We achieve morphologies ranging from hexagon, pseudo hexagon, truncated triangle to rhombic, and average basal plane diameters from 120 to 850 nm, with thicknesses between 8 and 45 nm. Analysis of gibbsite structure, size and morphology with techniques including powder X-ray diffraction (p-XRD), 27 Al magic angle spinning nuclear magnetic resonance spectroscopy (MAS NMR), scanning electron microscopy (SEM), and atomic force microscopy (AFM) provided key details on the nucleation and crystal growth mechanisms. The results indicate the temperature of the nucleation aging step is the most important factor controlling the final particle size. Particularly small nanoplates were obtained with a low nucleation aging temperature followed by high crystal growth temperature, suggesting that gibbsite growth can be approximated via a LaMer-type burst nucleation and crystal growth mechanism. Scalability was demonstrated by triplicate of 2 L experiments which prepared gibbsite nanoplates of ~200 nm size and with an average yield of ~55% after 84 h. Compared to existing techniques, this improved two-step route is cheaper, more efficient and environmentally friendly.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

ComStock Measure Documentation: Thermostat and Lighting Control for Load Shedding + Photovoltaics With 40% Rooftop Coverage

This report describes the modeling methodology for an upgrade package of two end-use savings shape measures - Thermostat Control for Load Shedding and Lighting Control for Load Shedding - and briefly introduces key results. The package combines thermostat control for load shedding, lighting control for load shedding, and PV with 40% rooftop coverage measures to reduce the net building load during the building's electricity peak window every weekday. The measure takes daily peak load schedule inputs generated by the method "Dispatch Schedule Generation" described in the "Supplemental Documentation: Dispatch Schedule Generation for Demand Flexibility Measures" to determine the start and end times of the predicted peak window, and then relaxes the thermostat setpoints and dims the lighting level from the original schedules during the peak window to reduce the peak demand, while applying the fixed rooftop PV application for onsite electricity generation. The measure is applicable to (large, medium and small) offices, warehouses, and primary and secondary schools, which correspond to approximately 68% of the stock floor area of commercial buildings in ComStock analysis. The measure demonstrates 5%-15% daily peak demand reduction performance for applicable buildings, and around 1% total site energy savings (0 trillion British thermal units [TBtu]) for the U.S. commercial building stock modeled in ComStock.

14 SOLAR ENERGY↗
DOE OSTI2022

Between Harmonic Crystal and Glass: Solids with Dimpled Potential-Energy Surfaces Having Multiple Local Energy Minima

Solids with dimpled potential-energy surfaces are ubiquitous in nature and, typically, exhibit structural (elastic or phonon) instabilities. Dimpled potentials are not harmonic; thus, the conventional quasiharmonic approximation at finite temperatures fails to describe anharmonic vibrations in such solids. At sufficiently high temperatures, their crystal structure is stabilized by entropy; in this phase, a diffraction pattern of a periodic crystal is combined with vibrational properties of a phonon glass. As temperature is lowered, the solid undergoes a symmetry-breaking transition and transforms into a lower-symmetry phase with lower lattice entropy. Here, we identify specific features in the potential-energy surface that lead to such polymorphic behavior; we establish reliable estimates for the relative energies and temperatures associated with the anharmonic vibrations and the solid–solid symmetry-breaking phase transitions. We show that computational phonon methods can be applied to address anharmonic vibrations in a polymorphic solid at fixed temperature. To illustrate the ubiquity of this class of materials, we present a range of examples (elemental metals, a shape-memory alloy, and a layered charge-density-wave system); we show that our theoretical predictions compare well with known experimental data.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Recovery and Calibration of Legacy Underground Nuclear Test Seismic Data from the Leo Brady Seismic Network

The Leo Brady Seismic Network (LBSN, originally the Sandia Seismic Network) was established in 1960 by Sandia National Laboratories to monitor underground nuclear tests (UGTs) at the Nevada National Security Site (NNSS, formerly named the Nevada Test Site). The LBSN has been in various configurations throughout its existence, but it has generally been comprised of four to six stations at regional distances (~150–400 km) from the NNSS with approximately evenly spaced azimuthal coverage. Between 1962 and the end of nuclear testing in 1992, the LBSN—and a sister network operated by Lawrence Livermore National Laboratories—was the most comprehensive United States source of regional seismic data of UGTs. Approximately 75% of all UGTs performed by the United States occurred in the predigital era. At that time, LBSN data were transmitted as frequency-modulated (FM) audio over telephone lines to a central location and recorded as analog waveforms on high-fidelity magnetic audio tapes. These tapes have been in dry temperature-stable storage for decades and contain the sole record of this irreplaceable data; full waveforms of LBSN-recorded UGTs from this era were not routinely digitized or otherwise published. We have developed a process to recover and calibrate data from these tapes. First, we play back and digitize the tapes as audio. Next, we demodulate the FM “audio” into individual waveforms. We then estimate the various instrument constants through careful measurement of “weight-lift” tests performed prior to each UGT on each instrument. Finally, these coefficients allow us to scale and shape the derived instrument response of the seismographs and compute poles and zeros. Finally, the result of this process is a digital record of the recorded seismic ground motion in a modern data format, stored in a searchable database. To date, we have digitized tapes from 592 UGTs.

58 GEOSCIENCES↗
DOE OSTI2021

Surrogate approximation of the Grad–Shafranov free boundary problem via stochastic collocation on sparse grids

In magnetic confinement fusion devices, the equilibrium configuration of a plasma is determined by the balance between the hydrostatic pressure in the fluid and the magnetic forces generated by an array of external coils and the plasma itself. The location of the plasma is not known a priori and must be obtained as the solution to a free boundary problem. The partial differential equation that determines the behavior of the combined magnetic field depends on a set of physical parameters (location of the coils, intensity of the electric currents going through them, magnetic permeability, etc.) that are subject to uncertainty and variability. The confinement region is in turn a function of these stochastic parameters as well. In this work, we consider variations on the current intensities running through the external coils as the dominant source of uncertainty. This leads to a parameter space of dimension equal to the number of coils in the reactor. With the aid of a surrogate function built on a sparse grid in parameter space, a Monte Carlo strategy is used to explore the effect that stochasticity in the parameters has on important features of the plasma boundary such as the location of the x-point, the strike points, and shaping attributes such as triangularity and elongation. Furthermore, the use of the surrogate function reduces the time required for the Monte Carlo simulations by factors that range between 7 and over 30.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Analytical simulation of meander morphology from equilibrium to long-term evolution: Impacts of channel geometry and vegetation-induced coarsening

This study introduces an innovative approach to modeling meandering river morphology, integrating and investigating the effects of geometric characteristics and vegetation-induced channel coarsening. The developed comprehensive framework combines several advanced techniques: Genetic Programming for refining the scour factor of transverse bed slope, a Leaf Area Index (LAI)-enhanced analytical model for quantifying vegetative flow resistance, and an upstream-weighted moving average method for efficient approximation of the convolution integral in meander migration calculations. The model is validated against both an idealized Kinoshita meander and a natural bend of the Tumen River (China) in equilibrium, demonstrating its robustness across diverse scales and conditions. The model's ability to simulate the long-term evolution, including cutoff events, provides valuable insight for river management strategies. The current findings demonstrate that channel geometry, particularly width-to-depth ratio, plays a dominant role in meander evolution, with wider channels prone to more complex and rapid morphological changes. Vegetation effects are most pronounced in channels with moderate width-to-depth ratios, where they can significantly influence migration rates and bed topography. A combination of channel widening and deepening, coupled with strategic vegetation management, can effectively enhance navigability while maintaining channel stability in the studied Tumen River reach. Sensitivity analyses highlight the complex interplay between hydraulic conditions, sediment characteristics, and vegetation in shaping river morphology. This research advances understanding of the multifaceted nature of meandering river systems and offers practical tools for informed decision-making in river engineering and environmental management, particularly in the context of climate change and increasing anthropogenic pressures on fluvial ecosystems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Estimating the local dark matter density in a non-axisymmetric wobbling disc

The density of dark matter near the Sun, ρDM, ⊙, is important for experiments hunting for dark matter particles in the laboratory, and for constraining the local shape of the Milky Way’s dark matter halo. Estimates to date have typically assumed that the Milky Way’s stellar disc is axisymmetric and in a steady-state. Yet the Milky Way disc is neither, exhibiting prominent spiral arms and a bar, and vertical and radial oscillations. Here, we assess the impact of these assumptions on determinations of ρDM, ⊙ by applying a free-form, steady-state, Jeans method to two different N-body simulations of Milky Way-like galaxies. In one, the galaxy has experienced an ancient major merger, similar to the hypothesized Gaia–Sausage–Enceladus; in the other, the galaxy is perturbed more recently by the repeated passage and slow merger of a Sagittarius-like dwarf galaxy. We assess the impact of each of the terms in the Jeans–Poisson equations on our ability to correctly extract ρDM, ⊙ from the simulated data. We find that common approximations employed in the literature – axisymmetry and a locally flat rotation curve – can lead to significant systematic errors of up to a factor ~1.5 in the recovered surface mass density ~2 kpc above the disc plane, implying a fractional error on ρDM, ⊙ of the order of unity. However, once we add in the tilt term and the rotation curve term in our models, we obtain an unbiased estimate of ρDM, ⊙, consistent with the true value within our 95 percent confidence intervals for realistic 20 percent uncertainties on the baryonic surface density of the disc. Other terms – the axial tilt, 2nd Poisson and time-dependent terms – contribute less than 10 percent to ρDM, ⊙ (given current data) and can be safely neglected for now. In the future, as more data become available, these terms will need to be included in the analysis.

79 ASTRONOMY AND ASTROPHYSICS↗