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DOE OSTI2023

CCN data from TAMU TRACER campaign in the Houston TX region from July to September 2022

During TRACER, the Texas A&M Rapid Onsite Atmospheric Measurements Van (ROAM-V) was deployed to capture airmasses behind (maritime) and ahead (continental) of the passage of the sea-breeze front through Houston. On select sampling days, ROAM-V sampled in the morning/mid-day on the coast and then transited to a second inland site for the afternoon/evening. The suite of instruments deployed on ROAM-V included a Condensation Particle Counter (CPC; GRIMM Model 5.403 CPC), Scanning Mobility Particle Sizer (SMPS; TSI 3750 detector, TSI 3082 classifier, TSI 3088 neutralizer, TSI 3081A Differential Mobility Analyzer), Cloud Condensation Nuclei counter (Droplet Measurement Technologies CCN Counter), micro pulse lidar (Droplet Measurement Technologies Micro Pulse LiDAR (miniMPL)), and a Davis Rotating Uniform size-cut Monitor (DRUM; DRUMAir 4-DRUM). Before sampling at each location, the latitude and longitude were recorded using the GPS on the phone application “My Altitude”. Onboard the ROAM-V, aerosol samples are drawn through a shared isokinetic inlet at a flow rate ranging from 3.5 to 7.0 LPM. A portion of this flow is directed through a cyclone impactor (Brechtel, Inc. Model SCC 0.732) and 0.5 LPM is directed to the CCN. To calculate particle losses, we used a two-step method. First, the measured SMPS size distributions were used to calculate particle loss through the inlet during sampling. Second, the corrected SMPS data was used to calculate the average of the total losses per scan down the CCN line. Then, the correction was applied to the CCN data. This calculation was done separately for each deployment location due to changes in the measured size distributions between locations. Particle loss from diffusion (based on Kesten, 1991 and Gormley, 1949), inertial impaction in 90-degree bends (based on Aerosol Measurement, 2011 and Crane, 1977), and cyclone impactor efficiency (based on Dirgo, 1985) were included in the loss calculation. When the SMPS was not sampling at a location (in the case of an instrument malfunction or operator error), the reported CPC data was corrected with an average of the total losses for the entire campaign at the specified deployment location (e.g., if we needed to correct Galveston data, then the average of all calculated losses at Galveston was taken). These flatline corrections were used for all data on 22/07/13, 22/07/20, 22/07/22, and the data from Galveston on 22/08/09. The supersaturation uncertainty is estimated conservatively at +/- 0.03%, where variation in the inlet temperature, pressure, and calibration technique prevents a more accurate measurement. Confidence in the reported supersaturation measurements is based on a pre-campaign calibration (following the methods from our previous work and Deng, 2014 based on Rose, 2008) in addition to inter-comparisons with the DOE for two days (22/08/18 and 22/09/01) where TAMU was co-located with AMF1. The inter-comparisons show good agreement between our instrument and the DOEs instrument on both days at all supersaturations. After the last inter-comparison on 22/09/01, there was no indication of a malfunction by our instrument through the rest of the campaign. Unfortunately, the instrument was dropped during demobilization. A post-campaign calibration was conducted, which showed a substantial departure from the pre-campaign calibration. The drop may have damaged the instrument’s ability to produce the desired supersaturations. Therefore, we do consider the data after 22/09/01 to be correct, but it should be used with caution. The CCN counter sampled for 3 minutes at each supersaturation setpoint (0.2, 0.4, 0.6, 0.8, 1.0, and 1.2%). At the end of a cycle, the instrument was set to 0.01% supersaturation for 5 minutes. The data is comprised of the last 60 seconds of each supersaturation set point (0.2, 0.4, 0.6, 0.8, 1.0, and 1.2%) to ensure the instrument stabilized and was able to reach thermal equilibrium. We removed the data during the periods where there were operational difficulties, setup, or maintenance. This data was collected for ARM Field Campaign AFC07055 and supported by DOE ASR grant DE-SC0021047. For any further questions, please feel free to contact the instrument PI, Sarah D. Brooks, sbrooks@tamu.edu. Rose et. al. Calibration and Measurement Uncertainties of a Continuous-Flow Cloud Condensation Nuclei Counter (DMT-CCNC): CCN Activation of Ammonium Sulfate and Sodium Chloride Aerosol Particles in Theory and Experiment. Atmos. Chem. Phys., 8, 1153-1179, 2008. Deng et. al. Using Raman Microspectroscopy to Determine Chemical Composition and Mixing State of Airborne Marine Aerosols over the Pacific Ocean. Aerosol Science and Technology, Vol 48, Issue 2, 2014. Kesten et. al. Calibration of a TSI Model 3025 Ultrafine Condensation Particle Counter. Aerosol Science and Technology, 15:2, 107-111, 1991. Gormley et. al. Diffusion from a Stream Flowing through a Cylindrical Tube. Proceedings of the Royal Irish Academy, Vol 52, 163-169, 1948. Aerosol Measurement: Principles, Techniques, and Applications, Third Edition. John Wiley & Sons, Inc, 2011. Crane et. al. Inertial Deposition of Particles in a Bent Pipe. Journal of Aerosol Science, Vol 8, 161-170, 1977. Dirgo et. al. Cyclone Collection Efficiency: Comparison of Experimental Results with Theoretical Predictions. Aerosol Science and Technology, 4:4, 401-415, 1985.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

CPC data from TAMU TRACER campaign in the Houston, TX region from July to September 2022

During TRACER, the Texas A&M Rapid Onsite Atmospheric Measurements Van (ROAM-V) was deployed to capture airmasses behind (maritime) and ahead (continental) of the passage of the sea-breeze front through Houston. On select sampling days, ROAM-V sampled in the morning/mid-day on the coast and then transited to a second inland site for the afternoon/evening. The suite of instruments deployed on ROAM-V included a Condensation Particle Counter (CPC; GRIMM Model 5.403 CPC), Scanning Mobility Particle Sizer (SMPS; TSI 3750 detector, TSI 3082 classifier, TSI 3088 neutralizer, TSI 3081A Differential Mobility Analyzer), Cloud Condensation Nuclei counter (Droplet Measurement Technologies CCN Counter), micro pulse lidar (Droplet Measurement Technologies Micro Pulse LiDAR (miniMPL)), and a Davis Rotating Uniform size-cut Monitor (DRUM; DRUMAir 4-DRUM). Before sampling at each location, the latitude and longitude were recorded using the GPS on the phone application “My Altitude”. Onboard the ROAM-V, aerosol samples are drawn through a shared isokinetic inlet at a flow rate ranging from 3.5 to 7.0 LPM. A portion of this flow is directed through a cyclone impactor (Brechtel, Inc. Model SCC 0.732) and 0.3 LPM is directed to the CPC. To correct the data for particle losses, we used a two-step method. First, the measured SMPS size distributions were used to calculate total particle loss through the inlet for every SMPS scan at a single deployment location. Second, the CPC data was corrected for particle losses using the average of the total losses per scan. This calculation was done separately for each deployment location due to changes in the measured size distributions between locations. Particle loss from diffusion (based on Kesten, 1991 and Gormley, 1949), inertial impaction in 90-degree bends (based on Aerosol Measurement, 2011 and Crane, 1977), and cyclone impactor efficiency (based on Dirgo, 1985) were included in the loss calculation. When the SMPS was not sampling at a location (in the case of an instrument malfunction or operator error), the reported CPC data was corrected with an average of the total losses for the entire campaign at the specified deployment location (e.g., if we needed to correct Galveston data, then the average of all calculated losses at Galveston was taken). These flatline corrections were used for all data on 22/07/13, 22/07/20, 22/07/22, and the data from Galveston on 22/08/09. An additional flatline correction of 14% was applied to all CPC data based on laboratory calibration prior to and after the campaign. In laboratory calibrations, we identified that for the same sample of air the field CPC (GRIMM Model 5.403 CPC) undercounted the total concentration of particles by 14% compared to the ground truth laboratory CPC (TSI Model 3750). This data was collected for ARM Field Campaign AFC07055 and supported by DOE ASR grant DE-SC0021047. For any further questions, please feel free to contact the instrument PI, Sarah D. Brooks, sbrooks@tamu.edu. Kesten et. al. Calibration of a TSI Model 3025 Ultrafine Condensation Particle Counter. Aerosol Science and Technology, 15:2, 107-111, 1991. Gormley et. al. Diffusion from a Stream Flowing through a Cylindrical Tube. Proceedings of the Royal Irish Academy, Vol 52, 163-169, 1948. Aerosol Measurement: Principles, Techniques, and Applications, Third Edition. John Wiley & Sons, Inc, 2011. Crane et. al. Inertial Deposition of Particles in a Bent Pipe. Journal of Aerosol Science, Vol 8, 161-170, 1977. Dirgo et. al. Cyclone Collection Efficiency: Comparison of Experimental Results with Theoretical Predictions. Aerosol Science and Technology, 4:4, 401-415, 1985.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Rapid estimation of earthquake locations using waveform traveltimes

SUMMARY We introduce a new approach for locating earthquakes using arrival times derived from waveforms. The most costly computational step of the algorithm scales as the number of stations in the active seismographic network. In this approach, a variation on existing grid search methods, a series of full waveform simulations are conducted for all receiver locations, with sources positioned successively at each station. The traveltime field over the region of interest is calculated by applying a phase picking algorithm to the numerical wavefields produced from each simulation. An event is located by subtracting the stored traveltime field from the arrival time at each station. This provides a shifted and time-reversed traveltime field for each station. The shifted and time-reversed fields all approach the origin time of the event at the source location. The mean or median value at the source location thus approximates the event origin time. Measures of dispersion about this mean or median time at each grid point, such as the sample standard error and the average deviation, are minimized at the correct source position. Uncertainty in the event position is provided by the contours of standard error defined over the grid. An application of this technique to a synthetic data set indicates that the approach provides stable locations even when the traveltimes are contaminated by additive random noise containing a significant number of outliers and velocity model errors. It is found that the waveform-based method out-performs one based upon the eikonal equation for a velocity model with rapid spatial variations in properties due to layering. A comparison with conventional location algorithms in both a laboratory and field setting demonstrates that the technique performs at least as well as existing techniques.

58 GEOSCIENCES↗
DOE OSTI2016

The hadronic corrections to muonic hydrogen Lamb shift from ChPT and the proton radius

We obtain a model independent expression for the muonic hydrogen Lamb shift. The leading hadronic effects are controlled by the chiral theory, which allows for their model independent determination. We give their complete expression including the pion and Delta particles. Out of this analysis and the experimental measurement of the muonic hydrogen Lamb shift we determine the electromagnetic proton radius: r{sub p} = 0.8412(15) fm. This number is at 6.8σ variance with respect to the CODATA value. The parametric control of the uncertainties allows us to obtain a model independent determination of the error, which is dominated by hadronic effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

First evaluation of the feasibility of MLC tracking using ultrasound motion estimation

Purpose: To quantify the performance of the Clarity ultrasound (US) imaging system (Elekta AB, Stockholm, Sweden) for real-time dynamic multileaf collimator (MLC) tracking. Methods: The Clarity calibration and quality assurance phantom was mounted on a motion platform moving with a periodic sine wave trajectory. The detected position of a 30 mm hypoechogenic sphere within the phantom was continuously reported via Clarity’s real-time streaming interface to an in-house tracking and delivery software and subsequently used to adapt the MLC aperture. A portal imager measured MV treatment field/MLC apertures and motion platform positions throughout each experiment to independently quantify system latency and geometric error. Based on the measured range of latency values, a prostate stereotactic body radiation therapy (SBRT) delivery was performed with three realistic motion trajectories. The dosimetric impact of system latency on MLC tracking was directly measured using a 3D dosimeter mounted on the motion platform. Results: For 2D US imaging, the overall system latency, including all delay times from the imaging and delivery chain, ranged from 392 to 424 ms depending on the lateral sector size. For 3D US imaging, the latency ranged from 566 to 1031 ms depending on the elevational sweep. The latency-corrected geometric root-mean squared error was below 0.75 mm (2D US) and below 1.75 mm (3D US). For the prostate SBRT delivery, the impact of a range of system latencies (400–1000 ms) on the MLC tracking performance was minimal in terms of gamma failure rate. Conclusions: Real-time MLC tracking based on a noninvasive US input is technologically feasible. Current system latencies are higher than those for x-ray imaging systems, but US can provide full volumetric image data and the impact of system latency was measured to be small for a prostate SBRT case when using a US-like motion input.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Density functional theory and chromium: Insights from the dimers

The binding in small Cr clusters is re-investigated, where the correct description of the dimer in three charge states is used as criterion to assign the most suitable density functional theory approximation. The difficulty in chromium arises from the subtle interplay between energy gain from hybridization and energetic cost due to exchange between s and d based molecular orbitals. Variations in published bond lengths and binding energies are shown to arise from insufficient numerical representation of electron density and Kohn-Sham wave-functions. The best functional performance is found for gradient corrected (GGA) functionals and meta-GGAs, where we find severe differences between functionals from the same family due to the importance of exchange. Only the “best fit” from Bayesian error estimation is able to predict the correct energetics for all three charge states unambiguously. With this knowledge, we predict small bond-lengths to be exclusively present in Cr{sub 2} and Cr{sub 2}{sup −}. Already for the dimer cation, solely long bond-lengths appear, similar to what is found in the trimer and in chromium bulk.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Development of ion beam figuring system with electrostatic deflection for ultraprecise X-ray reflective optics

We developed an ion beam figuring system that utilizes electrostatic deflection. The system can produce an arbitrary shape by deterministically scanning the ion beam. The scan of the ion beam, which can be precisely controlled using only an electrical signal, enables us to avoid degradation of the mirror shape caused by imperfect acceleration or deceleration of a mechanically scanning stage. Additionally, this surface figuring method can easily be combined with X-ray metrology because the workpiece remains fixed during the figuring. We evaluated the figuring accuracy of the system by fabricating a plano-elliptical mirror for X-ray focusing. A mirror with a shape error of 1.4 nm root mean square (RMS) with a maximum removal depth of 992 nm, which corresponds to figuring accuracy of 0.14% RMS, was achieved. After the second shape corrections, an elliptical shape with a shape error of approximately 1 nm peak-to-valley, 0.48 nm RMS could be fabricated. Then, the mirror surface was smoothed by a low-energy ion beam. Consequently, a micro-roughness of 0.117 nm RMS, measured by atomic force microscopy, was achieved over an area of 1 × 1 μm{sup 2}.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2015

Theory of Lamb Shift in Muonic Hydrogen

There has been for a while a large discrepancy between the values of the proton charge radius measured by the Lamb shift in muonic hydrogen and by other methods. It has already been clear that theory of muonic hydrogen is reliable at the level of this discrepancy and an error there cannot be a reason for the contradiction. Still the status of theory at the level of the uncertainty of the muonic-hydrogen experiment (which is two orders of magnitude below the discrepancy level) requires an additional clarification. Here, we revisit theory of the 2p − 2s Lamb shift in muonic hydrogen. We summarize all the theoretical contributions in order α{sup 5}m, including pure quantum electrodynamics (QED) ones as well as those which involve the proton-structure effects. Certain enhanced higher-order effects are also discussed. We basically confirm former QED calculations of other authors, present a review of recent calculations of the proton-structure effects, and treat self-consistently higher-order proton-finite-size corrections. We also overview theory of the 2p states. Eventually, we derive a value of the root-mean-square proton charge radius. It is found to be 0.840 29(55) fm, which is slightly different from that previously published in the literature (0.840 87(39) fm [Antognini et al., Science 339, 417 (2013)])

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Improving Solution Accuracy and Convergence for Stochastic Physics Parameterizations with Colored Noise

Stochastic parameterizations are used in numerical weather prediction and climate modeling to help capture the uncertainty in the simulations and improve their statistical properties. Convergence issues can arise when time integration methods originally developed for deterministic differential equations are applied naively to stochastic problems. In previous studies, it has been demonstrated that a correction term, known in stochastic analysis as the Itô correction, can help improve solution accuracy for various deterministic numerical schemes and ensure convergence to the physically relevant solution without substantial computational overhead. The usual formulation of the Itô correction is valid only when the stochasticity is represented by white noise. In this study, a generalized formulation of the Itô correction is derived for noises of any color. The formulation is applied to a test problem described by an advection–diffusion equation forced with a spectrum of fast processes. We present numerical results for cases with both constant and spatially varying advection velocities to show that, for the same time step sizes, the introduction of the generalized Itô correction helps to substantially reduce time integration error and significantly improve the convergence rate of the numerical solutions when the forcing term in the governing equation is rough (fast varying); alternatively, for the same target accuracy, the generalized Itô correction allows for the use of significantly longer time steps and, hence, helps to reduce the computational cost of the numerical simulation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

A Predictor-Corrector Strategy for Adaptivity in Dynamical Low-Rank Approximations

Here, in this paper, we present a predictor-corrector strategy for constructing rank-adaptive, dynamical low-rank approximations (DLRAs) of matrix-valued ODE systems. The strategy is a compromise between (i) low-rank step-truncation approaches that alternately evolve and compress solutions and (ii) strict DLRA approaches that augment the low-rank manifold using subspaces generated locally in time by the DLRA integrator. The strategy is based on an analysis of the error between a forward temporal update into the ambient full-rank space, which is typically computed in a step-truncation approach before recompressing, and the standard DLRA update, which is forced to live in a low-rank manifold. We use this error, without requiring its full-rank representation, to correct the DLRA solution. A key ingredient for maintaining a low-rank representation of the error is a randomized SVD, which introduces some degree of stochastic variability into the implementation. The strategy is formulated and implemented in the context of discontinuous Galerkin spatial discretizations of PDEs and applied to several versions of DLRA methods found in the literature as well as a new variant. Numerical experiments comparing the predictor-corrector strategy to other methods demonstrate robustness to overcome shortcomings of step truncation or strict DLRA approaches: The former may require more memory than is strictly needed, while the latter may miss transients solution features that cannot be recovered. The effect of randomization, tolerances, and other implementation parameters is also explored.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Fermi-Löwdin orbital self-interaction correction to magnetic exchange couplings

We analyze the effect of removing self-interaction error on magnetic exchange couplings using the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method in the framework of density functional theory (DFT). We compare magnetic exchange couplings obtained from self-interaction-free FLOSIC calculations with the local spin density approximation (LSDA) with several widely used DFT realizations and wave function based methods. To this end, we employ the linear H–He–H model system, six organic radical molecules, and [Cu 2 Cl 6 ] 2- as representatives of different types of magnetic interactions. Finally, we show that the simple self-interaction-free version of LSDA improves calculated couplings with respect to LSDA in all cases, even though the nature of the exchange interaction varies across the test set, and in most cases, it yields results comparable to modern hybrids and range-separated approximate functionals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

High-throughput determination of Hubbard $U$ and Hund $J$ values for transition metal oxides via the linear response formalism

DFT+U provides a convenient, cost-effective correction for the self-interaction error (SIE) that arises when describing correlated electronic states using conventional approximate density functional theory (DFT). The success of a DFT+U(+J) calculation hinges on the accurate determination of its Hubbard U and Hund J parameters, and the linear response (LR) methodology has proven to be computationally effective and accurate for calculating these parameters. This study provides a high-throughput computational analysis of the U and J values for transition metal d-electron states in a representative set of over 1000 magnetic transition metal oxides (TMOs), providing a frame of reference for researchers who use DFT+U to study transition metal oxides. In order to perform this high-throughput study, an ATOMATE workflow is developed for calculating U and J values automatically on massively parallel supercomputing architectures. Here, to demonstrate an application of this workflow, the spin-canting magnetic structure and unit cell parameters of the multiferroic olivine LiNiPO4 are calculated using the computed Hubbard U and Hund J values for Ni-d and O-p states, and are compared with experiment. Both the Ni-d U and J corrections have a strong effect on the Ni-moment canting angle. Additionally, including a O-pU value results in a significantly improved agreement between the computed lattice parameters and experiment

36 MATERIALS SCIENCE↗
DOE OSTI2016

Comment on “Breakdown of the expansion of finite-size corrections to the hydrogen Lamb shift in moments of charge distribution”

In a recent study, Hagelstein and Pascalutsa [F. Hagelstein and V. Pascalutsa, Phys. Rev. A 91, 040502 (2015)] examine the error associated with an expansion of proton structure corrections to the Lamb shift in terms of moments of the charge distribution. They propose a small modification to a conventional parametrization of the proton's charge form factor and show that this can resolve the proton radius puzzle. However, while the size of the bump they add to the form factor is small, it is large compared to the total proton structure effects in the initial parametrization, yielding a final form factor that is unphysical. Reducing their modification to the point where the resulting form factor is physical does not allow for a resolution of the radius puzzle.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2016

SU-C-207A-06: On-Line Beam Range Verification with Multiple Scanning Particle Beams: Initial Feasibility Study with Simulations

Purpose: To investigate the feasibility and requirement for intra-fraction on-line multiple scanning particle beam range verifications (BRVs) with in-situ PET imaging, which is beyond the current single-beam BRV with extra factors that will affect the BR measurement accuracy, such as beam diameter, separation between beams, and different image counts at different BRV positions. Methods: We simulated a 110-MeV proton beam with 5-mm diameter irradiating a uniform PMMA phantom by GATE simulation, which generated nuclear interaction-induced positrons. In this preliminary study, we simply duplicated these positrons and placed them next to the initial protons to approximately mimic the two spatially separated positron distributions produced by two beams parallel to each other but with different beam ranges. These positrons were then imaged by a PET (∼2-mm resolution, 10% sensitivity, 320×320×128 mm^3 FOV) with different acquisition times. We calculated the positron activity ranges (ARs) from reconstructed PET images and compared them with the corresponding ARs of original positron distributions. Results: Without further image data processing and correction, the preliminary study show the errors between the measured and original ARs varied from 0.2 mm to 2.3 mm as center-to-center separations and range differences were in the range of 8–12 mm and 2–8 mm respectively, indicating the accuracy of AR measurement strongly depends on the beam separations and range differences. In addition, it is feasible to achieve ≤ 1.0-mm accuracy for both beams with 1-min PET acquisition and 12 mm beam separation. Conclusion: This study shows that the overlap between the positron distributions from multiple scanning beams can significantly impact the accuracy of BRVs of distributed particle beams and need to be further addressed beyond the established method of single-beam BRV, but it also indicates the feasibility to achieve accurate on-line multi-beam BRV with further improved method.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Impact of CT attenuation correction method on quantitative respiratory-correlated (4D) PET/CT imaging

Purpose: Respiratory-correlated positron emission tomography (PET/CT) 4D PET/CT is used to mitigate errors from respiratory motion; however, the optimal CT attenuation correction (CTAC) method for 4D PET/CT is unknown. The authors performed a phantom study to evaluate the quantitative performance of CTAC methods for 4D PET/CT in the ground truth setting. Methods: A programmable respiratory motion phantom with a custom movable insert designed to emulate a lung lesion and lung tissue was used for this study. The insert was driven by one of five waveforms: two sinusoidal waveforms or three patient-specific respiratory waveforms. 3DPET and 4DPET images of the phantom under motion were acquired and reconstructed with six CTAC methods: helical breath-hold (3DHEL), helical free-breathing (3DMOT), 4D phase-averaged (4DAVG), 4D maximum intensity projection (4DMIP), 4D phase-matched (4DMATCH), and 4D end-exhale (4DEXH) CTAC. Recovery of SUV{sub max}, SUV{sub mean}, SUV{sub peak}, and segmented tumor volume was evaluated as RC{sub max}, RC{sub mean}, RC{sub peak}, and RC{sub vol}, representing percent difference relative to the static ground truth case. Paired Wilcoxon tests and Kruskal–Wallis ANOVA were used to test for significant differences. Results: For 4DPET imaging, the maximum intensity projection CTAC produced significantly more accurate recovery coefficients than all other CTAC methods (p < 0.0001 over all metrics). Over all motion waveforms, ratios of 4DMIP CTAC recovery were 0.2 ± 5.4, −1.8 ± 6.5, −3.2 ± 5.0, and 3.0 ± 5.9 for RC{sub max}, RC{sub peak}, RC{sub mean}, and RC{sub vol}. In comparison, recovery coefficients for phase-matched CTAC were −8.4 ± 5.3, −10.5 ± 6.2, −7.6 ± 5.0, and −13.0 ± 7.7 for RC{sub max}, RC{sub peak}, RC{sub mean}, and RC{sub vol}. When testing differences between phases over all CTAC methods and waveforms, end-exhale phases were significantly more accurate (p = 0.005). However, these differences were driven by the patient-specific respiratory waveforms; when testing patient and sinusoidal waveforms separately, patient waveforms were significantly different between phases (p < 0.0001) while the sinusoidal waveforms were not significantly different (p = 0.98). When considering only the subset of 4DMATCH images that corresponded to the end-exhale image phase, 4DEXH, mean and interquartile range were similar to 4DMATCH but variability was considerably reduced. Conclusions: Comparative advantages in accuracy and precision of SUV metrics and segmented volumes were demonstrated with the use of the maximum intensity projection and end-exhale CT attenuation correction. While respiratory phase-matched CTAC should in theory provide optimal corrections, image artifacts and differences in implementation of 4DCT and 4DPET sorting can degrade the benefit of this approach. These results may be useful to guide the implementation, analysis, and development of respiratory-correlated thoracic PET/CT in the radiation oncology and diagnostic settings.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

Erratum: “A high precision gas flow cell for performing in situ neutron studies of local atomic structure in catalytic materials” [Rev. Sci. Instrum. 88, 034101 (2017)]

We report that in the original paper,1 the following chemical formula was reported erroneously: Na 78-2x Ca x Al 78 Si 144 O 384 , x ≈ 38. The correct formula for the material studied is Na 86-2x Ca x Al 86 Si 106 O 384 , x ≈ 43. The difference in formula values between this corrected composition and values in Table 1 has no effect on the refinement quality (within the reported error), the subsequent analysis, or overall conclusions of the manuscript. Specifically, the neutron diffraction data and crystallographic refinement are insensitive (within the reported error) to the corresponding change in the Si/Al ratios, and the corrected number of Ca (x ≈ 43) is found to be within the error of the value reported via crystallographic refinement of the Ca occupancy [x = 46(3)].

36 MATERIALS SCIENCE↗
DOE OSTI2023

Unified analysis of finite-size error for periodic Hartree-Fock and second order Møller-Plesset perturbation theory

Despite decades of practice, finite-size errors in many widely used electronic structure theories for periodic systems remain poorly understood. For periodic systems using a general Monkhorst-Pack grid, there has been no comprehensive and rigorous analysis of the finite-size error in the Hartree-Fock theory (HF) and the second order Møller-Plesset perturbation theory (MP2), which are the simplest wavefunction based method, and the simplest post-Hartree-Fock method, respectively. Such calculations can be viewed as a multi-dimensional integral discretized with certain trapezoidal rules. Due to the Coulomb singularity, the integrand has many points of discontinuity in general, and standard error analysis based on the Euler-Maclaurin formula gives overly pessimistic results. The lack of analytic understanding of finite-size errors also impedes the development of effective finite-size correction schemes. We propose a unified analysis to obtain sharp convergence rates of finite-size errors for the periodic HF and MP2 theories. Our main technical advancement is a generalization of the result of Lyness [Math. Comp. 30 (1976), pp. 1–23] for obtaining sharp convergence rates of the trapezoidal rule for a class of non-smooth integrands. Our result is applicable to three-dimensional bulk systems as well as low dimensional systems (such as nanowires and 2D materials). Our unified analysis also allows us to prove the effectiveness of the Madelung-constant correction to the Fock exchange energy, and the effectiveness of a recently proposed staggered mesh method for periodic MP2 calculations (see X. Xing, X. Li, and L. Lin [J. Chem. Theory Comput. 17 (2021), pp. 4733–4745]). In conclusion, our analysis connects the effectiveness of the staggered mesh method with integrands with removable singularities, and suggests a new staggered mesh method for reducing finite-size errors of periodic HF calculations.

97 MATHEMATICS AND COMPUTING↗