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At least 163 records · Page 9

Numerical methods and hypoexponential approximations for gamma distributed delay differential equations

Abstract Gamma distributed delay differential equations (DDEs) arise naturally in many modelling applications. However, appropriate numerical methods for generic gamma distributed DDEs have not previously been implemented. Modellers have therefore resorted to approximating the gamma distribution with an Erlang distribution and using the linear chain technique to derive an equivalent system of ordinary differential equations (ODEs). In this work, we address the lack of appropriate numerical tools for gamma distributed DDEs in two ways. First, we develop a functional continuous Runge–Kutta (FCRK) method to numerically integrate the gamma distributed DDE without resorting to Erlang approximation. We prove the fourth-order convergence of the FCRK method and perform numerical tests to demonstrate the accuracy of the new numerical method. Nevertheless, FCRK methods for infinite delay DDEs are not widely available in existing scientific software packages. As an alternative approach to solving gamma distributed DDEs, we also derive a hypoexponential approximation of the gamma distributed DDE. This hypoexponential approach is a more accurate approximation of the true gamma distributed DDE than the common Erlang approximation but, like the Erlang approximation, can be formulated as a system of ODEs and solved numerically using standard ODE software. Using our FCRK method to provide reference solutions, we show that the common Erlang approximation may produce solutions that are qualitatively different from the underlying gamma distributed DDE. However, the proposed hypoexponential approximations do not have this limitation. Finally, we apply our hypoexponential approximations to perform statistical inference on synthetic epidemiological data to illustrate the utility of the hypoexponential approximation.

97 MATHEMATICS AND COMPUTING↗

Improved time-delay lens modelling and H 0 inference with transient sources

ABSTRACT Strongly lensed explosive transients such as supernovae, gamma-ray bursts, fast radio bursts, and gravitational waves are very promising tools to determine the Hubble constant (H0) in the near future in addition to strongly lensed quasars. In this work, we show that the transient nature of the point source provides an advantage over quasars: The lensed host galaxy can be observed before or after the transient’s appearance. Therefore, the lens model can be derived from images free of contamination from bright point sources. We quantify this advantage by comparing the precision of a lens model obtained from the same lenses with and without point sources. Based on Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) observations with the same sets of lensing parameters, we simulate realistic mock data sets of 48 quasar lensing systems (i.e. adding AGN in the galaxy centre) and 48 galaxy–galaxy lensing systems (assuming the transient source is not visible but the time delay and image positions have been or will be measured). We then model the images and compare the inferences of the lens model parameters and H0. We find that the precision of the lens models (in terms of the deflector mass slope) is better by a factor of 4.1 for the sample without lensed point sources, resulting in an increase of H0 precision by a factor of 2.9. The opportunity to observe the lens systems without the transient point sources provides an additional advantage for time-delay cosmography over lensed quasars. It facilitates the determination of higher signal-to-noise stellar kinematics of the main deflector, and thus its mass density profile, which, in turn plays a key role in breaking the mass-sheet degeneracy and constraining H0.

Ding, Xuheng↗

Time delay lens modelling challenge

ABSTRACT In recent years, breakthroughs in methods and data have enabled gravitational time delays to emerge as a very powerful tool to measure the Hubble constant H0. However, published state-of-the-art analyses require of order 1 yr of expert investigator time and up to a million hours of computing time per system. Furthermore, as precision improves, it is crucial to identify and mitigate systematic uncertainties. With this time delay lens modelling challenge, we aim to assess the level of precision and accuracy of the modelling techniques that are currently fast enough to handle of order 50 lenses, via the blind analysis of simulated data sets. The results in Rungs 1 and 2 show that methods that use only the point source positions tend to have lower precision ($10\!-\!20{{\ \rm per\ cent}}$) while remaining accurate. In Rung 2, the methods that exploit the full information of the imaging and kinematic data sets can recover H0 within the target accuracy (|A| < 2 per cent) and precision (<6 per cent per system), even in the presence of a poorly known point spread function and complex source morphology. A post-unblinding analysis of Rung 3 showed the numerical precision of the ray-traced cosmological simulations to be insufficient to test lens modelling methodology at the percent level, making the results difficult to interpret. A new challenge with improved simulations is needed to make further progress in the investigation of systematic uncertainties. For completeness, we present the Rung 3 results in an appendix and use them to discuss various approaches to mitigating against similar subtle data generation effects in future blind challenges.

Ding, X.↗

Reversible electron spirals by chirped attopulses at zero time delay

A class of linear, spiral phenomena is discovered in the photoelectron momentum distribution when studying photoionization of S -state atoms by a pair of linearly chirped, oppositely circularly polarized attosecond pulses eventually delayed in time by $\tau$. This controllable effect, dubbed. reversible electron spirals because of its energy-dependent sense of rotation, is identified and can be isolated in the absence of time delay for the case of opposite chirp rates. Further, the astrophysical concept of spiral arm pitch angle is borrowed to gain a better insight into the energy dependence of the reversible spiral rotation, to determine the attochirp as well as the binding energy characteristic of an atomic target. Our results indicate potential applications in attochirpmetry and polarimetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

β -delayed neutron emission of Mn 64 , Cr 62 , and Fe 65

The β-decay properties of nuclei near the second nuclear “island of inversion” around neutron rich nuclei with neutron number 40 are important tests of nuclear structure models and interactions. In particular, the β-delayed neutron emission branch (Ρ n ), is useful for investigating β-strength and neutron-γ competition above the neutron separation energies of the daughter nuclei. We report new constraints for Ρ n values for three nuclei in the region: 62 Cr (Ρ n <1%), 64 Mn (Ρ n = 1.5⁢(6)%), and 65 Fe (Ρ n < 1%), measured with the Neutron Emission Ratio Observer (NERO) neutron long counter system and the Beta Counting Station (BCS) at the National Superconducting Cyclotron Laboratory (NSCL). Our results resolve the large discrepancy between previous direct and indirect measurements for 64 Mn and confirm the predictions of global theoretical models when a statistical treatment of the γ and neutron decays of the daughter states is included. Here we also obtain improved half-lives for 62 Cr [206(5) ms] and the short-lived isomer in the 62 Fe daughter [112(7) ms] from β-delayed γ emission data obtained in the same experiment with the Summing NaI (SuN) total absorption spectrometer. Finally, we use γ emission data to obtain a new upper limit for the 62 Cr β-decay population of the long-lived isomeric state in 62 Mn.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Superexponential primordial black hole production via delayed vacuum decay

If a cosmological first-order phase transition occurs sufficiently slowly, delayed vacuum decay may lead to the formation of primordial black holes. Here we consider a simple model as a case study of how the abundance of the produced black holes depends on the model’s input parameters. We demonstrate, using both numerical and analytical arguments and methods, that the black hole abundance is controlled by a double, “super”-exponential dependence on the three-dimensional Euclidean action over temperature at its minimal value. We show that a modified expansion rate during the phase transition, such as one driven by an additional energy density component, leads to a weaker dependence on the underlying model parameters, but maintains the same superexponential structure. We argue that our findings generalize to any framework of black hole production via delayed vacuum decay. Published by the American Physical Society 2025

Wu, Yanda (ORCID:000000034487305X)↗

Attosecond Intramolecular Scattering and Vibronic Delays

We study the temporal and vibrational signature of the universal nuclear recoil associated with the electron emission and intramolecular scattering that accompanies the photoelectric effect. We illustrate these phenomena in the photoionization of the CO molecule from the C-1s orbital using an analytical model that reproduces the entangled character of the nuclear and electronic motion in this process. We show that the photoelectron emission delay can be decomposed into its localization and resonant-confinement components. Photoionization by a broadband x-ray pulse results in a coherent vibrational ionic state delayed compared to the classical sudden-photoemission limit.

74 ATOMIC AND MOLECULAR PHYSICS↗

Constraining the P 30 ( p , γ ) S 31 Reaction Rate in ONe Novae via the Weak, Low-Energy, β -Delayed Proton Decay of Cl 31

The 30 P(p,γ) 31 S reaction plays an important role in understanding the nucleosynthesis of A ≥ 30 nuclides in oxygen-neon novae. The Gaseous Detector with Germanium Tagging was used to measure 31 Cl β-delayed proton decay through the key J π = 3/2 + , 260-keV resonance. The intensity $I$$^{260}_{βp}$ = $8.3$$^{+1.2}_{–0.9}$ × 10 –6 represents the weakest β-delayed, charged-particle emission ever measured below 400 keV, resulting in a proton branching ratio of Γ p /Γ = $2.5$$^{+0.4}_{–0.3}$ × 10 –4 . Here, by combining this measurement with shell-model calculations for Γγ and past work on other resonances, the total 30 P(p,γ) 31 S rate has been determined with reduced uncertainty. The new rate has been used in hydrodynamic simulations to model the composition of nova ejecta, leading to a concrete prediction of 30 Si: 28 Si excesses in presolar nova grains and the calibration of nuclear thermometers.

79 ASTRONOMY AND ASTROPHYSICS↗

Impact of Newly Measured 𝛽-Delayed Neutron Emitters around 78 Ni on Light Element Nucleosynthesis in the Neutrino Wind Following a Neutron Star Merger

Neutron emission probabilities and half-lives of 37 𝛽-delayed neutron emitters from 75 Ni to 92 Br were measured at the RIKEN Nishina Center in Japan, including 11 one-neutron and 13 two-neutron emission probabilities and six half-lives for the first time that supersede theoretical estimates. These nuclei lie in the path of the weak 𝑟 process occurring in neutrino-driven winds from the accretion disk formed after the merger of two neutron stars synthesizing elements in the 𝐴∼80 abundance peak. The presence of such elements dominates the accompanying kilonova emission over the first few days and have been identified in the AT2017gfo event, associated to the gravitational wave detection GW170817. Abundance calculations based on over 17,000 simulated trajectories describing the evolution of matter properties in the merger outflows show that the new data lead to an increase of 50%–70% in the abundance of Y, Zr, Nb, and Mo. This enhancement is large compared to the scatter of relative abundances observed in old very metal poor stars and thus is significant in the comparison with other possible astrophysical processes contributing to the light-element production. These results underline the importance of including experimental decay data for very neutron-rich 𝛽 -delayed neutron emitters into 𝑟 -process models.

59 ≤ A ≤ 89↗

Hybrid Recurrent Neural Network Modeling for Traffic Delay Prediction at Signalized Intersections Along an Urban Arterial

This paper studies the traffic delay prediction modeling for multiple signalized intersections along the Ala Moana Boulevard and Nimitz Highway in Hawaii. Several machine learning (ML) based approaches have been studied in the literature, and most of them focused on prediction accuracy rather than the end use of real-time control and implementation. These ML models tend to be very complex and non-linear in nature, making it challenging to achieve fast inferences and are computationally heavy for real-time signal control implementation. As such, in this paper, a simple yet accurate hybrid modeling method is proposed to predict traffic delay one-step ahead with the model made suitable for real-time implementation to control traffic flow. Since real-time road-side measurements are recorded in unstructured form, the paper also discusses other issues related to data extraction and the pre-processing process. Finally, a simple signal control loop is developed to demonstrate the proposed modeling approach, which has shown advantages in model accuracy and computation efficiency compared against several existing modeling methods.

42 ENGINEERING↗

Hydrogen and Ammonia Blending With Natural Gas: Ignition Delay Times and Chemical Kinetic Model Validation at Gas Turbine Relevant Conditions

Abstract Ignition delay times from undiluted mixtures of natural gas (NG)/H2/Air and NG/NH3/Air were measured using a high-pressure shock tube at the University of Central Florida. The combustion temperatures were experimentally tested between 1000–1500 K near a constant pressure of 25 bar. As mentioned, mixtures were kept undiluted to replicate the same chemistry pathways seen in gas turbine combustion chambers. Recorded combustion pressures exceeded 200 bar due to the large energy release, hence why these were performed at the high-pressure shock tube facility. The data is compared to the predictions of the NUIGMech 1.1 mechanism for chemical kinetic model validation and refinement. An exceptional agreement was shown for stoichiometric conditions in all cases but strayed at lean and rich equivalence ratios, especially in the lower temperature regime of H2 addition and all temperature ranges of the baseline NG mixture. Hydrogen addition also decreased ignition delay times by nearly 90%, while NH3 fuel addition made no noticeable difference in ignition time. NG/NH3 exhibited similar chemistry to pure NG under the same conditions, which is shown in a sensitivity analysis. The reaction CH3 + O2 = CH3O + O is identified and suggested as a possible modification target to improve model performance. Increasing the robustness of chemical kinetic models via experimental validation will directly aid in designing next-generation combustion chambers for use in gas turbines, which in turn will greatly lower global emissions and reduce greenhouse effects.

Pierro, Michael↗

Background identification in cryogenic calorimeters through $\alpha -\alpha$ delayed coincidences

Localization and modeling of radioactive contaminations is a challenge that ultra-low background experiments are constantly facing. These are fundamental steps both to extract scientific results and to further reduce the background of the detectors. Here we present an innovative technique based on the analysis of $\alpha -\alpha$ delayed coincidences in 232 Th and 238 U decay chains, developed to investigate the contaminations of the ZnSe crystals in the CUPID-0 experiment. This method allows to disentangle surface and bulk contaminations of the detectors relying on the different probability to tag delayed coincidences as function of the $\alpha$ decay position.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Correcting for reporting delay: an example using dengue fever data

One complication to infectious disease forecasting efforts is delay in reporting of cases, where real-time data often under-report the true disease burden. This pair of R scripts (1) provides example code demonstrating several strategies to account for the reporting delay and improve disease forecasts and (2) applies these methods using publicly-available data on dengue fever case reporting in Puerto Rico from 1990 to 2009.

Joann VanDervort, Lauren↗

Nonlocal subpicosecond delay metrology using spectral quantum interference

Precise knowledge of position and timing information is critical to support elementary protocols such as entanglement swapping on quantum networks. While approaches have been devised to use quantum light for such metrology, they largely rely on time-of-flight (ToF) measurements with single-photon detectors and, therefore, are limited to picosecond-scale resolution owing to detector jitter. In this work, we demonstrate an approach to distributed sensing that leverages phase modulation to map changes in the spectral phase to coincidence probability, thereby overcoming the limits imposed by single-photon detection. By extracting information about the joint biphoton phase, we measure a generalized delay—the difference in signal–idler arrival, relative to local radio frequency (RF) phase modulation. For nonlocal ranging measurements, we achieve (2$σ$) precision of ±0.04 ps and for measurements of the relative RF phase, (2$σ$) precision of ±0.7°. We complement this fine timing information with ToF data from single-photon time-tagging to demonstrate absolute measurement of time delay. By relying on off-the-shelf telecommunications equipment and standard quantum resources, this approach has the potential to reduce overhead in practical quantum networks.

42 ENGINEERING↗

Chelation Modeling of a Plutonium-238 Inhalation Incident Treated with Delayed DTPA

This work describes an analysis, using a previously established chelation model, of the bioassay data collected from a worker who received delayed chelation therapy following a plutonium-238 inhalation. The details of the case have already been described in two publications. The individual was treated with Ca-DTPA via multiple intravenous injections and then nebulizations beginning several months after the intake and continuing for four years. The exact date and circumstances of the intake are unknown. However, interviews with the worker suggested that the intake occurred via inhalation of a soluble plutonium compound. The worker provided daily urine and fecal bioassay samples throughout the chelation treatment protocol, including samples collected before, during, and after the administration of Ca-DTPA. Unlike the previous two publications presenting this case, the current analysis explicitly models the combined biokinetics of the plutonium-DTPA chelate. Further, using the previously established chelation model, it was possible to fit the data through optimizing only the intake (day and magnitude), solubility, and absorbed fraction of nebulized Ca-DTPA. This work supports the hypothesis that the efficacy of the delayed chelation treatment observed in this case results mainly from chelation of cell-internalized plutonium by Ca-DTPA (intracellular chelation). It also demonstrates the validity of the previously established chelation model. As the bioassay data were modified to ensure data anonymization, the calculation of the “true” committed effective dose was not possible. However, the treatment-induced dose inhibition (in percentage) was calculated.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗

AUTOIGNITION DELAY TIMES FOR REFORMATE GAS MIXTURES FROM METHANE GAS ENGINES

Methane slip is a prominent issue in natural gas reciprocating engines that are used in transportation and marine applications. The incomplete combustion that results in methane slip can be resolved with the introduction of hydrogen within the combustion mixture to improve methane oxidation and further enable combustion within the engine crevices where methane has previously remained unreacted. Steam methane reforming (SMR) is a common method used to produce hydrogen and can be used to design an onboard device to reduce methane slip from reciprocating engines. The development of this reformer device requires the validation of high-fidelity chemical kinetic models at the low temperatures of the crevice volumes of these engines. In this work, auto-ignition data is obtained using a shock tube at lean (φ—0.714 or λ—1.4) and stoichiometric (φ, λ = 1) equivalence ratios spanning a temperature range of 1042–1234 K at the 80-bar operating pressure of the test engine. Blends of methane, hydrogen, and reformate products from the SMR reaction are shock-heated in synthetic air, with the ignition delay time measured using an OH* chemiluminescence detector at 310 nm and a CH* detector at 430 nm. The experimental results are compared to several state-of-the-art chemical kinetic mechanisms from the literature. In general, most of the mechanisms show very good agreement with experiments at higher temperatures, with simulation results showing little deviation from experiments at lower temperatures. A sensitivity analysis was conducted, and the results reveal that the reaction H2 + CH3O2 = H + CH3O2H has a very significant role in determining low-temperature ignition delay times (IDTs) of SMR mixtures. These findings provide valuable insights into the chemical kinetics governing methane reformate combustion and contribute to the optimization of onboard reformer designs aimed at mitigating methane slip in natural gas-fueled engines.

Fraze, Matthew↗

Delayed Critical and Subcritical Experiments with Polyethylene Moderated Unreflected Thin 15 in. Diameter HEU Metal Plates

The thin ~15 in. diameter highly enriched uranium (HEU) metal plates were assembled to delayed criticality at the Oak Ridge Critical Experiments Facility (ORCEF) in 1969 with various thicknesses of polyethylene (varying from 1/16 to 2$\frac{3}{8}$ inches) between uranium metal plates. The average 235 U enrichment was 93.27 wt. %. These unreflected critical configurations contained 4$\frac{2}{3}$ to 20$\frac{5}{6}$ thin 15 in. diameter HEU metal plates (on loan from Los Alamos National Laboratory [LANL] and shipped to Oak Ridge National Laboratory [ORNL] on June 3, 1969). Depending on the thickness of polyethylene, the enriched uranium masses varying from 28,053 to 135,148 grams. Fractional plate sections consisted of the appropriate number of 60° pie sections. In addition to the measurement at delayed criticality, subcritical measurements were also performed by the inverse kinetic rod drop method. Prompt neutron decay constant measurements were also performed by the Rossi alpha and randomly pulsed neutron method using a time-tagged spontaneous fission californium neutron source; these are briefly reported here. At the time of these measurements in 1969, the thin HEU metal plates were in near-pristine condition with extremely little oxidation, allowing better descriptions of the uranium plates than the use of these plates in a heavily oxidized and deteriorated condition in recent reflected benchmark experiments at the LANL facility at the Nevada Test Site with these same thin highly enriched uranium metal plates. This report documents the experimental information for the measurements performed so that later researchers can perform the required uncertainty and calculational analyses and documentation to use these data for an International Nuclear Criticality Safety Benchmark Evaluation Program (ICSBEP) or a Nuclear Energy Agency (NEA) benchmark. Data from the experiments described should be acceptable for use as criticality safety benchmark experiments for the ICSBEP and the NEA nuclear criticality safety benchmark program once the uncertainty analysis on the measured neutron multiplication factors is completed. Additional data—such as the dimensional inspection reports, uranium isotopic information, and other relevant particulars—should be retrieved from the Y-12 Plant or LANL and incorporated in the final ICSBEP benchmark. Based on previous ICSBEP benchmarks with this enriched uranium metal at ORCEF, the uncertainties in $k_{eff}$ could be as low as ± 0.0002 for some configurations. Other experiments with smaller-diameter than 15 in. diameter HEU metal plates have been benchmarked in HEU-METFAST-001. The prompt neutron time decay measurements could be the basis for an International Reactor Physics Benchmark Program. Preparation of the present report is part of an effort at ORNL to document more than 15 undocumented critical and subcritical experiments enumerated in ORNL/TM-2019/18 and performed by ORNL at ORCEF and other US Department of Energy critical experiments facilities using more than 500 operational days of critical facility time. This work for this report publication was supported by the Nuclear Criticality, Radiation Transport and Safety NCSP Program at ORNL.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Time-Delay Cosmography: Spectroscopy of Galaxies in the Environment of the J1537 Lensed Quasar System

Due to their sufficient distances and prevalence, lensed quasars have been a key site for research in gravitational lensing. In particular, researchers are interested in constraining Hubble's constant by measuring time delays in the arrival times of multiply imaged quasars. However, a lens model will need to be created that accounts for not just the lensing galaxy, but also any perturbers nearby that could affect the light path. Here, the J1537-3010 lensed quasar environment is investigated, and redshifts of 62 targets have been identified using Gemini IRAF and RASCAL. The success rate is roughly 45% across all four masks, less than the expected 60%-70%. We expect that masking out a bad amplifier contributed to the lower redshift measurement rates, as well as potentially poor viewing conditions during observation. With these redshifts, flexion shifts can be measured to determine if the observed target should be included in the lens model. An accurate lens model is fundament al for constraining the measurements of the time-delays of the quasar images and, thereby, constraining measurements in Hubble’s constant.

Kharchilava, George V.↗