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

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

RRab variables with identical light-curve shapes at different pulsation periods

In this paper, we report on the detection of RRab stars with quasi-identical-shape light curves but period differences as large as 0.05–0.21 d using the Galactic bulge data of the OGLE-IV survey. We have examined stars with shorter periods than the Oosterhoff I ridge of the bulge. These stars generally have smaller amplitudes and larger Fourier phase-differences than the typical bulge RRab stars have at the same period. Many of these ‘anomalous’ stars have good-quality light curves without any sign of the Blazhko modulation. Examining their Fourier parameters revealed that several of these stars show very similar light curve to the typical bulge RR Lyrae. We found hundreds of quasi-identical-shape light-curve pairs with different periods between the ‘anomalous’- and the ‘normal’-position RRab stars based on the OGLE I-band data. The OGLE V-band, and the archive VVV and MACHO surveys K s -, b- and r -band data of these stars were also checked for light-curve-shape similarity. Finally, 149 pairs with identical-shape light curves in each available photometric band were identified. Calculating the physical properties of the variables using empirical formulae, on average, −0.5 dex, −0.13 mag, 0.67, and 165 K differences between the [Fe/H], M V , R/R ⊙ , and T eff values of the members of the pairs are derived, being the short-period stars less metal-poor, fainter, smaller, and hotter than the long-period variables. To explain the existence of variables with different physical properties and pulsation periods but with identical-shape light curves is a challenging task for modelling.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Higher-order correlations between different moments of two flow amplitudes in Pb-Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV

The correlations between different moments of two flow amplitudes, extracted with the recently developed asymmetric cumulants, are measured in Pb-Pb collisions at $\sqrt {s_{NN}}$ = 5.02 TeV recorded by the ALICE detector at the CERN Large Hadron Collider. The magnitudes of the measured observables show a dependence on the different moments as well as on the collision centrality, indicating the presence of nonlinear response in all even moments up to the eighth. Furthermore, the higher-order asymmetric cumulants show different signatures than the symmetric and lower-order asymmetric cumulants. Comparisons with state-of-the-art event generators using two different parametrizations obtained from Bayesian optimization show differences between data and simulations in many of the studied observables, indicating a need for further tuning of the models behind those event generators. These results provide new and independent constraints on the initial conditions and transport properties of the system created in heavy-ion collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Numerical and Visual Representations of Uncertainty Lead to Different Patterns of Decision Making

Although visualizations are a useful tool for helping people to understand information, they can also have unintended effects on human cognition. This is especially true for uncertain information, which is difficult for people to understand. Prior work has found that different methods of visualizing uncertain information can produce different patterns of decision making from users. However, uncertainty can also be represented via text or numerical information, and few studies have systematically compared these types of representations to visualizations of uncertainty. We present two experiments that compared visual representations of risk (icon arrays) to numerical representations (natural frequencies) in a wildfire evacuation task. Like prior studies, we found that different types of visual cues led to different patterns of decision making. In addition, our comparison of visual and numerical representations of risk found that people were more likely to evacuate when they saw visualizations than when they saw numerical representations. These experiments reinforce the idea that design choices are not neutral: seemingly minor differences in how information is represented can have important impacts on human risk perception and decision making.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Different CT slice thickness and contrast‐enhancement phase in radiomics models on the differential performance of lung adenocarcinoma

Abstract Background To investigate the effects of computed tomography (CT) reconstruction slice thickness and contrast‐enhancement phase on the differential diagnosis performance of radiomic signature in lung adenocarcinoma. Methods A total of 187 patients who had been pathologically confirmed with lung adenocarcinoma and nonadenocarcinoma were divided into a training cohort ( n = 149) and validation cohort ( n = 38). All the patients underwent contrast‐enhanced CT and the images were reconstructed with different slice thickness. The radiomic features were extracted from different slice thickness and scan phase. The logistic regression (LR) algorithm was used to build a machine learning model for each group. The area under the curve (AUC) obtained from the receiver operating characteristic (ROC) curve and DeLong test was used to evaluate its discriminating performance. Results Finally, 34 image features and five semantic features were selected to establish a radiomics model. Based on the three contrast‐enhanced CT phases and four reconstruction slice thickness, 12 groups of radiomics models showed good discrimination ability with the AUCs range from 0.9287 to 0.9631, sensitivity range from 0.8349 to 0.9083, specificity range from 0.825 to 0.925 in the training group. Similar results were observed in the validation group. However, there was no statistical significance between the different CT scan phase groups and different slice thickness ( p > 0.05). Conclusions The radiomic analysis of contrast‐enhanced CT can be used for the differential diagnosis of lung adenocarcinoma. Moreover, different slice thickness and contrast‐enhanced scan phase did not affect the discriminating ability in the radiomics models.

Wang, Yang↗
DOE OSTI2021

Characterisation of motor cortex organisation in patients with different presentations of persistent low back pain

Abstract Persistence of low back pain is thought to be associated with different underlying pain mechanisms, including ongoing nociceptive input and central sensitisation. We hypothesised that primary motor cortex (M1) representations of back muscles (a measure of motor system adaptation) would differ between pain mechanisms, with more consistent observations in individuals presumed to have an ongoing contribution of nociceptive input consistently related to movement/posture. We tested 28 participants with low back pain sub‐grouped by the presumed underlying pain mechanisms: nociceptive pain, nociplastic pain and a mixed group with features consistent with both. Transcranial magnetic stimulation was used to study M1 organisation of back muscles. M1 maps of multifidus (deep and superficial) and longissimus erector spinae were recorded with fine‐wire electromyography and thoracic erector spinae with surface electromyography. The nociplastic pain group had greater variability in M1 map location (centre of gravity) than other groups ( p < .01), which may suggest less consistency, and perhaps relevance, of motor cortex adaptation for that group. The mixed group had greater overlap of M1 representations between deep/superficial muscles than nociceptive pain (deep multifidus/longissimus: p = .001, deep multifidus/thoracic erector spinae: p = .008) and nociplastic pain (deep multifidus/longissimus: p = .02, deep multifidus/thoracic erector spinae: p = .02) groups. This study provides preliminary evidence of differences in M1 organisation in subgroups of low back pain classified by likely underlying pain mechanisms. Despite the sample size, differences in cortical re‐organisation between subgroups were detected. Differences in M1 organisation in subgroups of low back pain supports tailoring of treatment based on pain mechanism and motor adaptation.

Elgueta‐Cancino, Edith↗
DOE OSTI2020

The Frequency of Sex: Population Genomics Reveals Differences in Recombination and Population Structure of the Aflatoxin-Producing Fungus Aspergillus flavus

The apparent rarity of sex in many fungal species has raised questions about how much sex is needed to purge deleterious mutations and how differences in frequency of sex impact fungal evolution. We sought to determine how differences in the extent of recombination between populations of Aspergillus flavus impact the evolution of genes associated with the synthesis of aflatoxin, a notoriously potent carcinogen. We sequenced the genomes of, and quantified aflatoxin production in, 94 isolates of A. flavus sampled from seven states in eastern and central latitudinal transects of the United States. The overall population is subdivided into three genetically differentiated populations (A, B, and C) that differ greatly in their extent of recombination, diversity, and aflatoxin-producing ability. Estimates of the number of recombination events and linkage disequilibrium decay suggest relatively frequent sex only in population A. Population B is sympatric with population A but produces significantly less aflatoxin and is the only population where the inability of nonaflatoxigenic isolates to produce aflatoxin was explained by multiple gene deletions. Population expansion evident in population B suggests a recent introduction or range expansion. Population C is largely nonaflatoxigenic and restricted mainly to northern sampling locations through restricted migration and/or selection. Despite differences in the number and type of mutations in the aflatoxin gene cluster, codon optimization and site frequency differences in synonymous and nonsynonymous mutations suggest that low levels of recombination in some A. flavus populations are sufficient to purge deleterious mutations.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

ESTIMATION OF THE WAKEFIELD RESONANT FREQUENCY USING DIFFERENT SIMULATION TOOLS

Reliable and fast wakefield calculations are important for beam dynamics and THz generation in accelerators. We compare approaches and limitations with different available simulation tools and compare results. As an example, we analyse a cylindrical corrugated waveguide with narrower and wider radii of 5 and 6 mm, and aperture width and periodicity of 1 and 2 mm using ABCI by KEK and ANSYS HFSS simulation software. First, ABCI was used to determine the resonant frequency of the cylindri-cal corrugated waveguide with different lengths. The corresponding results were taken as a reference to exam-ine the simulation method in the ANSYS HFSS environ-ment. The eigenmode solver of ANSYS HFSS was used to determine different resonant frequencies. This was fol-lowed by examining a cylindrical corrugated waveguide that was implemented having a length of 17 mm for dif-ferent conductor settings. The corresponding waveguide was fed by a plane wave having a resonant frequency that satisfies the intersection of the light line and dispersion curve of the corresponding mode. The analysis showed that the maximum loss factor was achieved at 39.20 and 40.07 GHz using ANSYS HFSS simulation data for differ-ent conductors, whereas ABCI resulted in 38.50 GHz. The talk will present the results gathered by different simula-tion setups implemented in ANSYS HFSS.

Unutmaz, Muhammed [SLAC National Accelerator Labor↗
DOE OSTI2023

Risk Ratio and Risk Difference Estimation in Case-cohort Studies

Background: In case-cohort studies with binary outcomes, ordinary logistic regression analyses have been widely used because of their computational simplicity. However, the resultant odds ratio estimates cannot be interpreted as relative risk measures unless the event rate is low. The risk ratio and risk difference are more favorable outcome measures that are directly interpreted as effect measures without the rare disease assumption. Methods: We provide pseudo-Poisson and pseudo-normal linear regression methods for estimating risk ratios and risk differences in analyses of case-cohort studies. These multivariate regression models are fitted by weighting the inverses of sampling probabilities. Also, the precisions of the risk ratio and risk difference estimators can be improved using auxiliary variable information, specifically by adapting the calibrated or estimated weights, which are readily measured on all samples from the whole cohort. Finally, we provide computational code in R (R Foundation for Statistical Computing, Vienna, Austria) that can easily perform these methods. Results: Through numerical analyses of artificially simulated data and the National Wilms Tumor Study data, accurate risk ratio and risk difference estimates were obtained using the pseudo-Poisson and pseudo-normal linear regression methods. Also, using the auxiliary variable information from the whole cohort, precisions of these estimators were markedly improved. Conclusion: The ordinary logistic regression analyses may provide uninterpretable effect measure estimates, and the risk ratio and risk difference estimation methods are effective alternative approaches for case-cohort studies. These methods are especially recommended under situations in which the event rate is not low.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Uncertainty in Atlantic Multidecadal Oscillation derived from different observed datasets and their possible causes

As a leading mode of sea surface temperature (SST) variability over the North Atlantic in both observations and model simulations, the Atlantic Multidecadal Oscillation (AMO) can have a substantial influence on regional and global climate. By using Low-Frequency Component Analysis, we explore the uncertainties of the resulting AMO indices and the corresponding spatial patterns derived from three observational SST datasets. We found that the known coherent spatial pattern of the AMO at the basin scale over the North Atlantic appears in two out of the three datasets. Further analysis indicates that both the warming trend and the different techniques used to construct these observed gridded SSTs contribute to the AMO’s spatial coherence over the North Atlantic, especially during periods of sparse data sampling. The SST in the Extended Reconstructed SST dataset version 5 (ERSSTv5), changes from being systematically below the other datasets during the dense sampling periods on either side of the Second World War (WWII), to systematically above the other datasets during WWII, thereby introducing an artificial 10–20-year variability that affects the AMO’s spatial coherence. This coherence in the AMO’s spatial pattern is also affected by bias adjustment in ERSSTv5 at relative cool (i.e., non-summer) seasons, and by the heterogeneous North Atlantic warming pattern. The different AMO patterns can induce the different effects of wind, surface heat fluxes, and then drive ocean circulation and its heat transport convergence, especially for some seasons. For AMO indices, both the different detrending methods and different observational data result in uncertainty for the period 1935–1950. Such SST uncertainty is important to detect the relative role of the atmosphere and ocean in shaping the AMO.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Effects of different cultivation media on root bacterial community characteristics of greenhouse tomatoes

Tomato, as a typical greenhouse crop, is commonly first planted as seedlings in a variety of substrates before being transplanted into soil. However, there is rare research on the characteristics of the bacterial community in tomato roots under this planting mode. In this study, tomatoes were planted in pots containing three different cultivation media, including soil and two types of substrates in a greenhouse, followed by a transplanting treatment. After collecting tomato root samples, high-throughput sequencing and bioinformatic analysis were used to compare the differences in bacterial diversity and functions between tomato roots before and after transplanting in different cultivation media. In total, 702776 sequences were obtained, and the OTUs were belonging to 109 genera, 58 families, 41 orders, 14 classes, and 12 phyla. Among the three cultivation media, the β -diversity was significant, and there was a slight difference in bacterial species diversity along with a large difference in their abundance at the genus level. Soil and both substrates had 79 bacterial genera in common, these genera accounted for 68.70%, 76.70%, and 71.17% of the total genera found in the soil, substrate 1, and substrate 2, respectively. After being transplanted from the two substrates to the soil, the bacterial community structure and abundance exhibited similarities with those found in the soil. Furthermore, based on microbial function prediction, the microbial communities in the two-substrate environment demonstrated a greater potential for promoting growth, while the microbial communities in the soil exhibited a greater tendency to exert their antibacterial potential. Our findings offer theoretical support for the creation of artificially reconstructed microbial communities in greenhouse cultivation.

Zhang, Xinjian↗
DOE OSTI2019

Vehicle Electrification Impacts on Energy Consumption for Different Connected-Autonomous Vehicle Scenario Runs

Transportation system simulation is a widely accepted approach to evaluate the impact of transport policy deployment. In developing a transportation system deployment model, the energy impact of the model is extremely valuable for sustainability and validation. It is expected that different penetration levels of Connected-Autonomous Vehicles (CAVs) will impact travel behavior due to changes in potential factors such as congestion, miles traveled, etc. Along with such impact analyses, it is also important to further quantify the regional energy impact of CAV deployment under different factors of interest. The objective of this paper is to study the energy consumption of electrified vehicles in the future for different penetration levels of CAVs deployment in the City of Chicago. The paper will further provide a statistical analysis of the results to evaluate the impact of the different penetration levels on the different electrified powertrains used in the study.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

The mechanisms and seasonal differences of the impact of aerosols on daytime surface urban heat island effect

The urban heat island intensity (UHII) is the temperature difference between urban areas and their rural surroundings. It is commonly attributed to changes in the underlying surface structure caused by urbanization. Air pollution caused by aerosol particles can affect the UHII through changing (1) the surface energy balance by the aerosol radiative effect (ARE) and (2) planetary-boundary-layer (PBL) stability and airflow intensity by modifying thermodynamic structure, which is referred to as the aerosol dynamic effect (ADE). By analyzing satellite data and ground-based observations collected from 2001 to 2010 at 35 cities in China and using the WRF-Chem model, we find that the impact of aerosols on UHII differs considerably: reducing the UHII in summer but increasing the UHII in winter. This seasonal contrast is proposed to be caused by the different strengths of the ARE and ADE between summer and winter. In summer, the ARE on UHII is dominant over the ADE, cooling down surface temperature more strongly in urban areas than in rural areas because of much higher aerosol loading, and offsets the urban heating, therefore weakening UHII. In winter, however, the ADE is more dominant, because aerosols stabilize the PBL more in the polluted condition, weakening the near-surface heat transport over urban areas in both vertical and horizontal directions. This means that the heat accumulated in urban areas is dispersed less effectively, and thus the UHII is enhanced. These findings shed new light on the impact of the interaction between urbanization-induced surface changes and air pollution on urban climate.urban areas and their rural surroundings. It is commonly attributed to changes in the underlying surface structure caused by urbanization. Air pollution caused by aerosol particles can affect the UHII through changing (1) the surface energy balance by the aerosol radiative effect (ARE) and (2) planetary-boundary-layer (PBL) stability and airflow intensity by modifying thermodynamic structure, which is referred to as the aerosol dynamic effect (ADE). By analyzing satellite data and ground-based observations collected from 2001 to 2010 at 35 cities in China and using the WRF-Chem model, we find that the impact of aerosols on UHII differs considerably: reducing the UHII in summer but increasing the UHII in winter. This seasonal contrast is proposed to be caused by the different strengths of the ARE and ADE between summer and winter. In summer, the ARE on UHII is dominant over the ADE, cooling down surface temperature more strongly in urban areas than in rural areas because of much higher aerosol loading, and offsets the urban heating, therefore weakening UHII. In winter, however, the ADE is more dominant, because aerosols stabilize the PBL more in the polluted condition, weakening the near-surface heat transport over urban areas in both vertical and horizontal directions. This means that the heat accumulated in urban areas is dispersed less effectively, and thus the UHII is enhanced. These findings shed new light on the impact of the interaction between urbanization-induced surface changes and air pollution on urban climate.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

A cross-sectional study of the nasal and fecal microbiota of sows from different health status within six commercial swine farms

Cull sows are a unique population on swine farms, often representing poor producing or compromised animals, and even though recent studies have reported that the microbiome is associated with susceptibility to diseases, the microbiome of the cull sow population has not been explored. The main objective of this study was to investigate whether there were differences in fecal and upper respiratory tract microbiota composition for groups of sows of different health status (healthy, cull, and compromised/ clinical sows) and from different farms (1 to 6). Six swine farms were visited once. Thirty individual fecal samples and nasal swabs were obtained at each farm and pooled by five across health status and farm. Samples underwent 16S rRNA gene amplicon sequencing and nasal and fecal microbiota were analyzed using QIIME2 v.2021.4. Overall, the diversity of the nasal microbiota was lower than the fecal microbiota (p < 0.01). No significant differences were found in fecal or nasal alpha diversity by sow’s health status or by farm. Furthermore, there were significant differences in nasal microbial composition by farm and health status (PERMANOVA, p < 0.05), and in fecal microbiota by farm (PERMANOVA, p < 0.05), but not by health status. Lastly, at the L7 level, there was one differentially abundant taxa across farms for each nasal and fecal pooled samples. This study provided baseline information for nasal and fecal microbiota of sows under field conditions, and results suggest that farm of origin can affect microbial diversity and composition. Furthermore, sow’s health status may have an impact on the nasal microbiota composition.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

DIFFERENTIAL CANID PREDATION OF TRANSLOCATED JUVENILE DESERT TORTOISES AND CHEMICAL SIGNATURE DIFFERENCES BETWEEN FEMALE AND MALE ADULT AND JUVENILE DESERT TORTOISES

Differential predation was observed in a population of 59 translocated juvenile Desert Tortoises (Gopherus agassizii) of known sex during a juvenile translocation survival study between September 2012 and November 2017. The main source of mortality (77%; 24 of 31 deaths) was attributed to Coyote (Canis latrans) and Kit Fox (Vulpes macrotis) predation. Predation was skewed with 71% (n = 17) female mortality versus 29% (n = 7) male mortality. We tested the hypothesis that juvenile females smell different than males which leads to increased canid predation. We also explored differences in chemical signatures of resident adult female and male Desert Tortoises. We collected oral, cloacal and chin/forelimb swabs from translocated juvenile and resident adult female and male tortoises during fall 2015 and fall 2017 and analyzed them using headspace gas chromatography/mass spectrometry to determine potential differences in the chemical signatures among the four groups. Standardized chromatographic peak responses were subjected to repeated analyses of variance (ANOVA). For development of artificial scents, mean responses were calculated for each juvenile tortoise from standardized responses representing all collections (i.e., oral, cloacal, and chin/forelimb swabs) and grand means were determined for males and females. Repeated measures ANOVAs clearly demonstrated that the collections of volatiles differed according to age and/or sex depending on the body location of collection. Among the plausibly endogenous volatiles that differed by age, many of them are alcohols. Two field trials using captive Coyotes and one field trial partially within the translocation area were conducted to test if Coyotes showed a preference for female or bias against male synthesized scent. No consistent preference or bias was shown, suggesting that no innate preference for female odor was evident.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Investigating Similarity Differences for Light-Water-Moderated and Polyethylene-Moderated Systems

Oak Ridge National Laboratory has performed validation studies in support of Pacific Northwest Laboratory’s analysis of the Sum-of-Fractions method. Work in a companion paper examines the validation methods and results for various mixtures of fissile isotopes in various concentrations moderated and reflected by light-water and polyethylene. Those results indicate a greater coverage of critical experiments for validating light water moderated and reflected systems vs. those with polyethylene. The work presented here details the analysis of differences between light-water and polyethylene systems developed from the different concentration mixtures utilized in the Sum-of-Fractions validation study. Differences in actinide contributions are detailed, explaining the differences in ck for the various systems. The available tools and analysis techniques in TSUNAMI are described to illustrate how these types of differences can be understood by practitioners.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2024

A finite difference informed random walker (FDiRW) solver for strongly inhomogeneous diffusion problems

In nature, many complex multi-physics coupling problems exhibit strong diffusivity inhomogeneity. For instance, in the context of radionuclide absorption by porous wasteform materials within a flowing waste stream, the difference of species’ diffusivity in solid and liquid phases spans by 3~8 orders of magnitude. To solve the diffusion equations with strongly inhomogeneous diffusivity, traditional discretization-based methods, such as the Finite Difference Method (FDM), require infinitesimally small time steps (<10 -10 ) as high spatial resolutions are employed in most microstructure evolution processes, leading to prohibitively high computational costs. Here, this work developed an integrated numerical approach (FDiRW: Finite Difference informed Random Walk) to tackle this challenge. The idea is that utilizing the Random Walk concept, the fast diffusion is modeled as a superposition of point source’s solution for a concentration distribution while FDM is used to obtain the point source’s solution at each node. A mesh-coarsening algorithm is developed to generate an exclusive coarse mesh for FDiRW approach to maximize its efficiency. The effectiveness of the coarse mesh-based FDiRW approach is validated by benchmarking Finite Difference solutions. Numerical results demonstrated that FDiRW achieves a remarkable 1000x computational efficiency improvement over FDM while preserving desired accuracy for a medium-sized model of 192 × 192 × 192 grids. Finally, as models scale up, a floating-point operations (PLOPs) analysis of the FDiRW algorithm reveals that its computational complexity grows quadratically in terms of the number of nodes employed in computation.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Regional difference and related cooling electricity savings of air pollutant affected natural ventilation in commercial buildings across the US

Maintaining indoor air pollutants under acceptable levels is significant to protect occupants from exposure to excessive air pollutants in natural ventilation. In this paper, using the representative air pollutant concentration data, we present the natural ventilation usability with associated cooling energy saving potentials in different location settings (urban and city center, suburban and rural) of the US under the influence of local weather conditions and major outdoor air pollutants, i.e. PM2.5, PM10 and ozone. It is found that the impacts of air pollutants on natural ventilation are usually higher in urban/suburban areas than rural areas (up to 25% difference) with the PM2.5 being the most significant outdoor air pollutant affecting natural ventilation usage. Furthermore, ozone could become increasingly influential on natural ventilation as moving from urban to suburban/rural areas. As to the cooling energy saving considering the impacts of outdoor air pollutants, natural ventilation is estimated to save approximately 10%–40% cooling energy (800–2600 kWh per small commercial building) annually in different location settings of investigated areas across the US. The following economic analysis demonstrates that these electricity savings lead to approximately 80–540 dollars annual savings of building operation cost per building. If the time of use rate is adopted, these cost savings could further increase by approximately 20% (Los Angeles) to more than 50% (Albuquerque) depending on different rate structures, which further demonstrates the potential of adopting natural ventilation as a sustainability measurement with benefits for building owners without compromising occupants health.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

Spatial resolution of different discretizations over long-time for the Dirac equation with small potentials

In this report we compare the long-time error bounds and spatial resolution of finite difference methods with different spatial discretizations for the Dirac equation with small electromagnetic potentials characterized by $\varepsilon \in (0, 1]$ a dimensionless parameter. We begin with the simple and widely used finite difference time domain (FDTD) methods, and establish rigorous error bounds of them, which are valid up to the time at $O(1/\varepsilon)$. In the error estimates, we pay particular attention to how the errors depend explicitly on the mesh size $h$ and time step $\tau$ as well as the small parameter $\varepsilon$. Based on the results, in order to obtain "correct" numerical solutions up to the time at $O(1/\varepsilon)$, the $\varepsilon$-scalability (or meshing strategy requirement) of the FDTD methods should be taken as $h = O(\varepsilon^{1/2})$ and $\tau = O(\varepsilon^{1/2})$. To improve the spatial resolution capacity, we apply the Fourier spectral method to discretize the Dirac equation in space. Error bounds of the resulting finite difference Fourier pseudospectral (FDFP) methods show that they exhibit uniform spatial errors in the long-time regime, which are optimal in space as suggested by the Shannon's sampling theorem. Extensive numerical results are reported to confirm the error bounds and demonstrate that they are sharp.

79 ASTRONOMY AND ASTROPHYSICS↗