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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Quantum simulations of SO(5) many-fermion systems using qudits

The structure and dynamics of many-body systems are the result of a delicate interplay between underlying interactions. Fermionic pairing, for example, plays a central role in various physical systems, ranging from condensed matter to nuclear systems, where it can lead to collective phenomena such as superconductivity and superfluidity. In atomic nuclei, the interplay between pairing and particle-hole interactions leads to a high degree of complexity and intricate entanglement structures. Despite this apparent complexity, symmetries emerge and manifest themselves in observable regular patterns. These symmetries and their breakings have long been used to determine relevant degrees of freedom and simplify classical descriptions of many-body systems. Here, this work explores the potential utility of quantum computers with arrays of qudits in simulating interacting fermionic systems, when the qudits can naturally map the relevant degrees of freedom determined by an underlying symmetry group. The Agassi model of fermions interacting via particle-hole and pairing interactions is based on an underlying so(5) algebra. Such systems can intuitively be partitioned into pairs of modes with five basis states, which thus naturally map to arrays of d = 5 qudits (qu5its). Classical noiseless simulations of the time evolution of systems with up to twelve qu5its are performed, by implementing quantum circuits that are developed herein, using PYTHON codes invoking Google's CIRQ software. The resource requirements of the qu5it circuits are analyzed and compared with two different mappings to qubit systems: a physics-aware Jordan-Wigner mapping requiring four qubits per mode pair and a state-to-state mapping requiring three qubits per mode pair. While the dimensionality of Hilbert spaces in mappings to qu5it systems are less than those for the corresponding qubit systems, the number of entangling operations, depending on the available hardware, can either be greater or smaller than for the physics-aware Jordan-Wigner mapping. The state-to-state mapping, while having a smaller Hilbert space than Jordan-Wigner mappings, appears to be the least efficient in gate counts. Further, a previously unknown sign problem has been identified from Trotterization errors in time evolving high-energy excitations. There appear to be advantages in employing quantum computers with arrays of qudits to perform simulations of many-body dynamics that exploit the role of underlying symmetries, specifically in lowering the required quantum resources and in reducing anticipated errors that take the simulation out of the physical space. If the necessary entangling gates are not directly supported by the hardware, physics-aware mappings to qubits may, however, be advantageous for other aspects.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2013

Clinical Evaluation of a Laser Surface Scanning System in 120 Patients for Improving Daily Setup Accuracy in Fractionated Radiation Therapy

Purpose: To evaluate the clinical suitability of a specific optical surface imaging system to detect setup errors in fractionated radiation therapy. Methods and Materials: The setup correction accuracy of a 3-dimensional laser imaging system was analyzed for 6 different tumor locations with 20 patients each. For each patient, the setup corrections of the megavoltage computed tomography (MVCT) images of a TomoTherapy unit (TomoTherapy, Madison, WI) were compared with those of the laser system for the first 10 fractions. For the laser system, the reference surface either was obtained from the DICOM (Digital Imaging and Communications in Medicine) surface structure delineated on the planning computed tomography images or was acquired with the system itself at the first fraction after the MVCT-based setup correction. Data analysis was performed for both reference types. Results: By use of the DICOM reference image, systematic shifts between 3 and 9 mm were found, depending on the tumor location. For the optical reference, no clinically relevant systematic shifts were found. MVCT-based setup corrections were detected with high accuracy, and only small movements were observed during treatment. Conclusions: Using a reference image acquired with the laser system itself after MVCT-based setup correction appears more reliable than importing the DICOM reference surface. After generation of the optical reference, the laser system may be used to derive setup corrections over a certain number of fractions, but additional radiologic imaging may still be necessary on a regular basis (eg, weekly) or if the corrections of the optical system appear implausibly large. Nevertheless, such a combined application may help to reduce the imaging dose for the patient.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2021

MFNets: data efficient all-at-once learning of multifidelity surrogates as directed networks of information sources

We present an approach for constructing a surrogate from ensembles of information sources of varying cost and accuracy. The multifidelity surrogate encodes connections between information sources as a directed acyclic graph, and is trained via gradient-based minimization of a nonlinear least squares objective. While the vast majority of state-of-the-art assumes hierarchical connections between information sources, our approach works with flexibly structured information sources that may not admit a strict hierarchy. The formulation has two advantages: (1) increased data efficiency due to parsimonious multifidelity networks that can be tailored to the application; and (2) no constraints on the training data—we can combine noisy, non-nested evaluations of the information sources. Finally, numerical examples ranging from synthetic to physics-based computational mechanics simulations indicate the error in our approach can be orders-of-magnitude smaller, particularly in the low-data regime, than single-fidelity and hierarchical multifidelity approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Life cycle assessment based environmental impact estimation model for pre-stressed concrete beam bridge in the early design phase

The late rise in global concern for environmental issues such as global warming and air pollution is accentuating the need for environmental assessments in the construction industry. Promptly evaluating the environmental loads of the various design alternatives during the early stages of a construction project and adopting the most environmentally sustainable candidate is therefore of large importance. Yet, research on the early evaluation of a construction project's environmental load in order to aid the decision making process is hitherto lacking. In light of this dilemma, this study proposes a model for estimating the environmental load by employing only the most basic information accessible during the early design phases of a project for the pre-stressed concrete (PSC) beam bridge, the most common bridge structure. Firstly, a life cycle assessment (LCA) was conducted on the data from 99 bridges by integrating the bills of quantities (BOQ) with a life cycle inventory (LCI) database. The processed data was then utilized to construct a case based reasoning (CBR) model for estimating the environmental load. The accuracy of the estimation model was then validated using five test cases; the model's mean absolute error rates (MAER) for the total environmental load was calculated as 7.09%. Such test results were shown to be superior compared to those obtained from a multiple-regression based model and a slab area base-unit analysis model. Henceforth application of this model during the early stages of a project is expected to highly complement environmentally friendly designs and construction by facilitating the swift evaluation of the environmental load from multiple standpoints. - Highlights: • This study is to develop the model of assessing the environmental impacts on LCA. • Bills of quantity from completed designs of PSC Beam were linked with the LCI DB. • Previous cases were used to estimate the environmental load of new case by CBR model. • CBR model produces more accurate estimations (7.09%) than other conventional models. • This study supports decision making process in the early stage of a new construction case.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Density functional study on redox energetics of LaMO{sub 3−δ} (M=Sc–Cu) perovskite-type oxides

This study evaluates the redox energetics of LaMO{sub 3−δ} (M=Sc–Cu) perovskite-type oxides via generalized gradient approximation (GGA) to DFT. Two different approaches to redox energetics of oxygen deficient perovskites of strongly non-stoichiometric (δ=0.5) and dilute defect limits (δ→0) are studied. In the first approach the enthalpies of oxidation are calculated using the stoichiometric end-compounds of LaMO{sub 3} and LaMO{sub 2.5}. The most common structures for the reduced lanthanides and strontides similar to the ones experimentally reported for SrMnO{sub 2.5}, SrFeO{sub 2.5}, and LaNiO{sub 2.5} are considered. The second approach to the oxidation enthalpies termed (δ→0) follow the trend observed experimentally. This approach represents the experimental conditions of the measured oxygen enthalpies, and is hampered less by the artificial features due to spurious self-interaction errors in GGA.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Design, development, and acceleration trials of radio-frequency quadrupole

A deuteron radio frequency quadrupole (RFQ) accelerator has been designed, fabricated, and tested at BARC, which will be used for neutron generation. The RFQ operates at a frequency of 350 MHz and needs an inter-vane voltage of 44 kV to accelerate the deuteron beam to 400 keV within a length of 1.03 m. The error analysis shows that the offset of two opposite vanes in the same direction by 100 μm leads to a change in resonant frequency by 1.3 MHz and a significant change of fields in the quadrants (∼±40% with respect to average field). From the 3D analysis, we have observed that the unwanted dipole mode frequencies are very near to the quadrupole mode frequency which will make structure sensitive to the perturbations. In order to move the dipole modes away from the quadrupole modes, we have used the dipole stabilizer rods. The 5 wire transmission line theory was used to study the perturbative analysis of the RFQ and based on this a computer program has been written to tune the cavity to get required field distribution. Based on these studies, a 1.03 m long RFQ made of OFE copper has been fabricated and tested. Even though the RFQ was designed for deuteron (D{sup +}) beam, we tested it by accelerating both the proton (H{sup +}) and D{sup +} beams. The RFQ was operated in pulsed mode and accelerated both H{sup +} and D{sup +} beams to designed values of 200 and 400 keV, respectively. The measured parameters are in good agreement with the designed values validating our simulations and fabrication processes. In this paper, simulations, RF measurements, and beam commissioning results are presented.

43 PARTICLE ACCELERATORS↗
DOE OSTI2015

Long-range correction for tight-binding TD-DFT

We present two improvements to the tight-binding approximation of time-dependent density functional theory (TD-DFTB): First, we add an exact Hartree-Fock exchange term, which is switched on at large distances, to the ground state Hamiltonian and similarly to the coupling matrix that enters the linear response equations for the calculation of excited electronic states. We show that the excitation energies of charge transfer states are improved relative to the standard approach without the long-range correction by testing the method on a set of molecules from the database in Peach et al. [J. Chem. Phys. 128, 044118 (2008)] which are known to exhibit problematic charge transfer states. The degree of spatial overlap between occupied and virtual orbitals indicates where TD-DFTB and long-range corrected TD-DFTB (lc-TD-DFTB) can be expected to produce large errors. Second, we improve the calculation of oscillator strengths. The transition dipoles are obtained from Slater Koster files for the dipole matrix elements between valence orbitals. In particular, excitations localized on a single atom, which appear dark when using Mulliken transition charges, acquire a more realistic oscillator strength in this way. These extensions pave the way for using lc-TD-DFTB to describe the electronic structure of large chromophoric polymers, where uncorrected TD-DFTB fails to describe the high degree of conjugation and produces spurious low-lying charge transfer states.

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

Many-body expansion based machine learning models for octahedral transition metal complexes

Abstract Graph-based machine learning (ML) models for material properties show great potential to accelerate virtual high-throughput screening of large chemical spaces. However, in their simplest forms, graph-based models do not include any 3D information and are unable to distinguish stereoisomers such as those arising from different orderings of ligands around a metal center in coordination complexes. In this work we present a modification to revised autocorrelation descriptors, a molecular graph featurization method, for predicting spin state dependent properties of octahedral transition metal complexes (TMCs). Inspired by analytical semi-empirical models for TMCs, the new modeling strategy is based on the many-body expansion (MBE) and allows one to tune the captured stereoisomer information by changing the truncation order of the MBE. We present the necessary modifications to include this approach in two commonly used ML methods, kernel ridge regression and feed-forward neural networks. On a test set composed of all possible isomers of binary TMCs, the best MBE models achieve mean absolute errors (MAEs) of 2.75 kcal mol −1 on spin-splitting energies and 0.26 eV on frontier orbital energy gaps, a 30%–40% reduction in error compared to models based on our previous approach. We also observe improved generalization to previously unseen ligands where the best-performing models exhibit MAEs of 4.00 kcal mol −1 (i.e. a 0.73 kcal mol −1 reduction) on the spin-splitting energies and 0.53 eV (i.e. a 0.10 eV reduction) on the frontier orbital energy gaps. Because the new approach incorporates insights from electronic structure theory, such as ligand additivity relationships, these models exhibit systematic generalization from homoleptic to heteroleptic complexes, allowing for efficient screening of TMC search spaces.

Meyer, Ralf (ORCID:0000000322360261)↗
DOE OSTI2020

Testing general relativity on cosmological scales at redshift z ∼ 1.5 with quasar and CMB lensing

ABSTRACT We test general relativity (GR) at the effective redshift $\bar{z} \sim 1.5$ by estimating the statistic EG, a probe of gravity, on cosmological scales $19 - 190\, h^{-1}{\rm Mpc}$. This is the highest redshift and largest scale estimation of EG so far. We use the quasar sample with redshifts 0.8 < z < 2.2 from Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey Data Release 16 as the large-scale structure (LSS) tracer, for which the angular power spectrum $C_\ell ^{qq}$ and the redshift-space distortion parameter β are estimated. By cross-correlating with the Planck 2018 cosmic microwave background (CMB) lensing map, we detect the angular cross-power spectrum $C_\ell ^{\kappa q}$ signal at $12\, \sigma$ significance. Both jackknife resampling and simulations are used to estimate the covariance matrix (CM) of EG at five bins covering different scales, with the later preferred for its better constraints on the covariances. We find EG estimates agree with the GR prediction at $1\, \sigma$ level over all these scales. With the CM estimated with 300 simulations, we report a best-fitting scale-averaged estimate of $E_G(\bar{z})=0.30\pm 0.05$, which is in line with the GR prediction $E_G^{\rm GR}(\bar{z})=0.33$ with Planck 2018 CMB + BAO matter density fraction Ωm = 0.31. The statistical errors of EG with future LSS surveys at similar redshifts will be reduced by an order of magnitude, which makes it possible to constrain modified gravity models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Modelling the BAO feature in bispectrum

We investigate how well a simple leading order perturbation theory model of the bispectrum can fit the baryon acoustic oscillation (BAO) feature in the measured bispectrum monopole of galaxies. Previous works showed that perturbative models of the galaxy bispectrum start failing at the wavenumbers of k ∼ 0.1 h Mpc −1 . We show that when the BAO feature in the bispectrum is separated, it can be successfully modelled up to much higher wavenumbers. We validate our modelling on GLAM simulations that were run with and without the BAO feature in the initial conditions. We also quantify the amount of systematic error due to BAO template being offset from the true cosmology. We find that the systematic errors do not exceed 0.3 per cent for reasonable deviations of up to 3 per cent from the true value of the sound horizon.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Subregion-subalgebra duality: Emergence of space and time in holography

In holographic duality, a higher dimensional quantum gravity system emerges from a lower dimensional conformal field theory (CFT) with a large number of degrees of freedom. We propose a formulation of duality for a general causally complete bulk spacetime region, called subregion-subalgebra duality, which provides a framework to describe how geometric notions in the gravity system, such as spacetime subregions, different notions of times, and causal structure, emerge from the dual CFT. Subregion-subalgebra duality generalizes and brings new insights into subregion-subregion duality (or equivalently entanglement wedge reconstruction). It provides a mathematically precise definition of subregion-subregion duality and gives an independent definition of entanglement wedges without using entropy. Geometric properties of entanglement wedges, including those that play a crucial role in interpreting the bulk as a quantum error correcting code, can be understood from the duality as the geometrization of the superadditivity of certain algebras. Using general boundary subalgebras rather than those associated with geometric subregions makes it possible to find duals for general bulk spacetime regions, including those not touching the boundary. Applying subregion-subalgebra duality to a boundary state describing a single-sided black hole also provides a precise way to define mirror operators. Published by the American Physical Society 2025

Leutheusser, Sam (ORCID:0000000339228128)↗
DOE OSTI2012

XCOM intrinsic dimensionality for low-Z elements at diagnostic energies

Purpose: To determine the intrinsic dimensionality of linear attenuation coefficients (LACs) from XCOM for elements with low atomic number (Z = 1-20) at diagnostic x-ray energies (25-120 keV). H{sub 0}{sup q}, the hypothesis that the space of LACs is spanned by q bases, is tested for various q-values. Methods: Principal component analysis is first applied and the LACs are projected onto the first q principal component bases. The residuals of the model values vs XCOM data are determined for all energies and atomic numbers. Heteroscedasticity invalidates the prerequisite of i.i.d. errors necessary for bootstrapping residuals. Instead wild bootstrap is applied, which, by not mixing residuals, allows the effect of the non-i.i.d residuals to be reflected in the result. Credible regions for the eigenvalues of the correlation matrix for the bootstrapped LAC data are determined. If subsequent credible regions for the eigenvalues overlap, the corresponding principal component is not considered to represent true data structure but noise. If this happens for eigenvalues l and l + 1, for any l{<=}q, H{sub 0}{sup q} is rejected. Results: The largest value of q for which H{sub 0}{sup q} is nonrejectable at the 5%-level is q = 4. This indicates that the statistically significant intrinsic dimensionality of low-Z XCOM data at diagnostic energies is four. Conclusions: The method presented allows determination of the statistically significant dimensionality of any noisy linear subspace. Knowledge of such significant dimensionality is of interest for any method making assumptions on intrinsic dimensionality and evaluating results on noisy reference data. For LACs, knowledge of the low-Z dimensionality might be relevant when parametrization schemes are tuned to XCOM data. For x-ray imaging techniques based on the basis decomposition method (Alvarez and Macovski, Phys. Med. Biol. 21, 733-744, 1976), an underlying dimensionality of two is commonly assigned to the LAC of human tissue at diagnostic energies. The finding of a higher statistically significant dimensionality thus raises the question whether a higher assumed model dimensionality (now feasible with the advent of multibin x-ray systems) might also be practically relevant, i.e., if better tissue characterization results can be obtained.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

SU-E-J-192: Verification of 4D-MRI Internal Target Volume Using Cine MRI

Purpose: To investigate the accuracy of 4D-MRI in determining the Internal Target Volume (ITV) used in radiation oncology treatment planning of liver cancers. Cine MRI is used as the standard baseline in establishing the feasibility and accuracy of 4D-MRI tumor motion within the liver. Methods: IRB approval was obtained for this retrospective study. Analysis was performed on MR images from four patients receiving external beam radiation therapy for liver cancer at our institution. Eligible patients received both Cine and 4D-MRI scans before treatment. Cine images were acquired sagittally in real time at a slice bisecting the tumor, while 4D images were acquired volumetrically. Cine MR DICOM headers were manipulated such that each respiratory frame was assigned a unique slice location. This approach permitted the treatment planning system (Eclipse, Varian Medical Systems) to recognize a complete respiratory cycle as a “volume”, where the gross tumor was contoured temporally. Software was developed to calculate the union of all frame contours in the structure set, resulting in the corresponding plane of the ITV projecting through the middle of the tumor, defined as the Internal Target Area (ITA). This was repeated for 4D-MRI, at the corresponding slice location, allowing a direct comparison of ITAs obtained from each modality. Results: Four patients have been analyzed. ITAs contoured from 4D-MRI correlate with contours from Cine MRI. The mean error of 4D values relative to Cine values is 7.67 +/− 2.55 %. No single ITA contoured from 4D-MRI demonstrated more than 10.5 % error compared to its Cine MRI counterpart. Conclusion: Motion management is a significant aspect of treatment planning within dynamic environments such as the liver, where diaphragmatic and cardiac activity influence plan accuracy. This small pilot study suggests that 4D-MRI based ITA measurements agree with Cine MRI based measurements, an important step towards clinical implementation. NIH 1R21CA165384-01A1.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

Quantifying Environmental and Line-of-sight Effects in Models of Strong Gravitational Lens Systems

Matter near a gravitational lens galaxy or projected along the line of sight (LOS) can affect strong lensing observables by more than contemporary measurement errors. We simulate lens fields with realistic three-dimensional mass configurations (self-consistently including voids), and then fit mock lensing observables with increasingly complex lens models to quantify biases and uncertainties associated with different ways of treating the lens environment (ENV) and LOS. We identify the combination of mass, projected offset, and redshift that determines the importance of a perturbing galaxy for lensing. Foreground structures have a stronger effect on the lens potential than background structures, due to nonlinear effects in the foreground and downweighting in the background. There is dramatic variation in the net strength of ENV/LOS effects across different lens fields; modeling fields individually yields stronger priors for H {sub 0} than ray tracing through N-body simulations. Models that ignore mass outside the lens yield poor fits and biased results. Adding external shear can account for tidal stretching from galaxies at redshifts z⩾z{sub lens}, but it requires corrections for external convergence and cannot reproduce nonlinear effects from foreground galaxies. Using the tidal approximation is reasonable for most perturbers as long as nonlinear redshift effects are included. Even then, the scatter in H {sub 0} is limited by the lens profile degeneracy. Asymmetric image configurations produced by highly elliptical lens galaxies are less sensitive to the lens profile degeneracy, so they offer appealing targets for precision lensing analyses in future surveys like LSST and Euclid.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

R and DE Robotic Sensor Intern Team: Sensor Suite Mock Up Testing

Assess sensor suite performance: - Mounted on crawler typical to what would be used in tunnel; - In test bed simulating the tunnel environment. The SuperDroid fiber tethered LT-F crawler is a general-purpose surveillance robot that our team has refurbished as a testing platform for the sensor suite. This crawler was selected because its dimensions are similar to the actual crawler that will be deployed in the field. Crawler preparation included: - Communicating with vendor to resolve software and platform issues; - Configuring a laptop with the crawler control software; - Reconfiguration of communication protocol between computer and crawler; - Resolution of control board checksum errors; - Installation of a mounting fixture on the base; - In progress: addition of lighting needed for total darkness. A solution for hosting the selected sensors onto a single unit that could function standalone or be mounted on the crawler was needed. Sensor mount requirements included: - Host Lidar, panospheric cameras and IMU sensors; - Cable management for rotating Lidar; - House on-board crawler computer; - Method for affixing to crawler; - Robust and vibration proof. The Lidar sensor required a sturdy mount that ensured the axis of rotation be centered with the LiDAR's desired laser path and included a slender profile in order to not block the scanning FOV. The mounting plate holds two 180-degree cameras on either side and the servo on the center. The servo mount is located so the axis of rotation is in the center of the plate. The mount features a set of guides that hold the wires and ensure they wrap around the spool area properly. The sensor box design features thick walls for added strength, holes for mounting the sensor suite to the crawler, notches on the bottom for the different components and holes for cable routing and management. The sensor mounts were designed using CREO and printed in the R and DE Additive Manufacturing Lab. To test the performance of the sensor suite for our application it was desired to design and build a test bed simulating the H-Canyon tunnel environment. Requirements included: - Dimensions similar to the tunnel; - Wall surfaces simulating the eroded tunnel walls; - Complete darkness; - Even and uneven crawler path; - Ability to change the tunnel width to simulate erosion. The HCAEX tunnel changes in height and includes several bends ranging from approximately 30 to 80 degrees, for that reason a test bed capable of easily being changed was needed. The final design includes two sections that can be connected to provide a 16' tunnel or placed at an angle to create a tunnel bend. The test bed features caster wheels for easy movement and has a sliding inner wall that enables tunnel width to be controlled. In order to simulate the tunnel walls without adding a lot of weight to the test bed, sheets of faux stone are to be used on the inner walls. To create a completely dark tunnel, 100% black-out film will be draped over the tunnel structure. Carpet remnants in the lab will enable folds to be introduced in the floor to generate uneven surface data.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2015

Comparison of algorithms for determination of rotation measure and Faraday structure. I. 1100–1400 MHz

Faraday rotation measures (RMs) and more general Faraday structures are key parameters for studying cosmic magnetism and are also sensitive probes of faint ionized thermal gas. A definition of which derived quantities are required for various scientific studies is needed, as well as addressing the challenges in determining Faraday structures. A wide variety of algorithms has been proposed to reconstruct these structures. In preparation for the Polarization Sky Survey of the Universe's Magnetism (POSSUM) to be conducted with the Australian Square Kilometre Array Pathfinder and the ongoing Galactic Arecibo L-band Feeds Array Continuum Transit Survey (GALFACTS), we run a Faraday structure determination data challenge to benchmark the currently available algorithms, including Faraday synthesis (previously called RM synthesis in the literature), wavelet, compressive sampling, and QU-fitting. The input models include sources with one Faraday thin component, two Faraday thin components, and one Faraday thick component. The frequency set is similar to POSSUM/GALFACTS with a 300 MHz bandwidth from 1.1 to 1.4 GHz. We define three figures of merit motivated by the underlying science: (1) an average RM weighted by polarized intensity, RM{sub wtd}, (2) the separation Δϕ of two Faraday components, and (3) the reduced chi-squared χ{sub r}{sup 2}. Based on the current test data with a signal-to-noise ratio of about 32, we find the following. (1) When only one Faraday thin component is present, most methods perform as expected, with occasional failures where two components are incorrectly found. (2) For two Faraday thin components, QU-fitting routines perform the best, with errors close to the theoretical ones for RM{sub wtd} but with significantly higher errors for Δϕ. All other methods, including standard Faraday synthesis, frequently identify only one component when Δϕ is below or near the width of the Faraday point-spread function. (3) No methods as currently implemented work well for Faraday thick components due to the narrow bandwidth. (4) There exist combinations of two Faraday components that produce a large range of acceptable fits and hence large uncertainties in the derived single RMs; in these cases, different RMs lead to the same Q, U behavior, so no method can recover a unique input model. Further exploration of all these issues is required before upcoming surveys will be able to provide reliable results on Faraday structures.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

A family of second-order fully explicit time integration schemes

A new family of fully explicit time integration methods is proposed, which has second-order accuracy for structures with and without damping. Using a diagonal mass matrix, the suggested scheme remains fully explicit not only for structures with a non-diagonal damping matrix, but also when the internal force vector is a nonlinear function of velocity. The present algorithm has an acceptable domain of stability, and it is self-starting. This technique introduces effectively numerical dissipation to suppress the high-frequency spurious modes, while at the same time the lower modes are not affected too much. In addition, numerical dispersion error of the scheme is considerably smaller than that of the central difference method. Solving several linear and nonlinear problems highlights the superior performance of the authors’ approach. Findings demonstrate that solution time for the suggested scheme is much less than that of the central difference technique. The related algorithm can be easily implemented into programs, which already contain the central difference method.

97 MATHEMATICS AND COMPUTING↗