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DOE OSTI2026

An analytic result for the 0 → ggHHH amplitude

We present a fully analytic calculation of the leading-order one-loop amplitude for triple Higgs production via gluon fusion, gg → HHH, retaining full dependence on the mass of the heavy quark circulating in the loop. This amplitude provides a direct probe of the triple and quartic Higgs self-couplings, the measurement of which is a central goal of current and future colliders. The amplitude can be presented in compact form thanks to the use of analytic reconstruction techniques, based on finite-field and p-adic evaluations, multivariate partial fraction decompositions, and primary decompositions to identify common numerator factors. Although full analytic results are given in the text and in the supplementary material, the main thrust of this paper is to further test and illustrate these analytic reconstruction techniques in a concrete physical example. Our results provide a compact and efficient representation of the matrix element for this process, enabling evaluations that are more than an order of magnitude faster than existing numerical alternatives. Full analytic control of the leading-order, loop-induced amplitude is an important step towards handling more complex 2-loop or real-radiation corrections to this and related processes.

Campbell, John M. [Fermilab] (ORCID:00000002136193↗

DOE OSTI2026

Toward the analytic bootstrap of energy correlators

In this paper, we present a framework for the analytic bootstrap of three-point energy correlators, a crucial observable in $\mathcal{N}$ = 4 super Yang-Mills theory and quantum chromodynamics (QCD). Our approach combines spherical contour techniques, general physical constraints such as pole cancellations, and power correction data in the singular limits to determine its analytic expression. In contrast to previous bootstrap studies restricted to scattering amplitudes for supersymmetric theories, our framework makes use of the properties of Feynman integrals, marking a significant step toward bootstrapping realistic QCD observables. Using this method, we derive analytic expressions for leading-order three-point energy correlators in the multi-collinear limit with equal and unequal energy weights, where the latter are crucial ingredients for projected N -point energy correlators. We also apply the recently developed technique of analytic regression with lattice reduction as a way to bypass needing explicit expressions for the singular limits. Bridging theoretical advances in scattering amplitudes with the renewed interest in weighted cross-sections, our work opens the door to precision tests of QCD dynamics through analytic event-shape predictions.

jet substructure↗

DOE OSTI2021

Analytical models of the strength and ductility of CNT reinforced metal matrix nano composites under elevated temperatures

Carbon nanotubes (CNTs) can greatly enhance the strength of metal matrix composites while resulting in ductility loss. This strength-ductility tradeoff dilemma always confines the development of material design and real-life applications. Here in this work, a temperature dependent strengthening analytical model is proposed for CNT reinforced metal matrix composites which considers three common strengthening mechanisms: Orowan looping effect, thermal expansion mismatch effect, and load bearing effect. The proposed model can predict composite material strength with different volume fractions of CNTs and under different temperatures. Combining the strengthening model with the stress based modified Mohr-Coulomb (sMMC) ductile fracture model, a ductility analytical model is then derived. This ductility analytical model includes the influences of temperature, multi-axial stress loading conditions, as well as the aforementioned three strengthening mechanisms. A good agreement has been achieved between literature published experimental data and analytical predictions for both composite material strength and ductility loss. The proposed two analytical models can provide a straightforward way to study the strength-ductility relationship for CNT reinforced metal matrix composites over a wide range of temperatures and different stress states, and then provide guidance on new material design and processing.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Metall: A persistent memory allocator for data-centric analytics

Data analytics applications transform raw input data into analytics-specific data structures before performing analytics. Unfortunately, such data ingestion steps are often more expensive than analytics. In addition, various types of NVRAM devices are already used in many HPC systems today. Such devices will be useful for storing and reusing data structures beyond a single process life cycle. We developed Metall, a persistent memory allocator built on top of the memory-mapped file mechanism. Metall enables applications to transparently allocate custom C++ data structures into various types of persistent memories. Metall incorporates a concise and high-performance memory management algorithm inspired by Supermalloc and the rich C++ interface developed by Boost.Interprocess library. On a dynamic graph construction workload, Metall achieved up to 11.7x and 48.3x performance improvements over Boost.Interprocess and memkind (PMEM kind), respectively. We also demonstrate Metall’s high adaptability by integrating Metall into a graph processing framework, GraphBLAS Template Library. Here this study’s outcomes indicate that Metall will be a strong tool for accelerating future large-scale data analytics by allowing applications to leverage persistent memory efficiently.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Advanced Health Information Technology Analytic Framework and Application to Hazard Detection

Health Information Technology (HIT) aims to improve healthcare outcomes by organizing and analyzing various health-related data. With data accumulating at a staggering rate, the importance of real-time analytics has been increasing dramatically, shifting the focus of informatics from batch processing to streaming analytics. HIT is also facing unprecedented challenges in adapting to this new requirement and leveraging advanced IT technologies. This paper introduces a HIT data and compute platform that supports multi-granularity real-time analytics from heterogeneous data sources. The paper first identifies functional requirements and proposes a framework that satisfies the requirements using state-of-the-art big data technologies including Apache Kafka, Spark Structured Streaming Engine, and Delta Lake. To demonstrate its capability to support data analytics in multiple time granularities analytics, a statistical process control-based hazard detection algorithm has been implemented on top of the framework to detect unexpected hazards from order cancellation data of the Department of US Veterans Affairs (VA) in near real-time.

Kumar, Mohit↗

DOE OSTI2023

Continental Scale Hydrostratigraphy: Comparing Geologically Informed Data Products to Analytical Solutions

Abstract This study synthesizes two different methods for estimating hydraulic conductivity (K) at large scales. We derive analytical approaches that estimate K and apply them to the contiguous United States. We then compare these analytical approaches to three‐dimensional, national gridded K data products and three transmissivity (T) data products developed from publicly available sources. We evaluate these data products using multiple approaches: comparing their statistics qualitatively and quantitatively and with hydrologic model simulations. Some of these datasets were used as inputs for an integrated hydrologic model of the Upper Colorado River Basin and the comparison of the results with observations was used to further evaluate the K data products. Simulated average daily streamflow was compared to daily flow data from 10 USGS stream gages in the domain, and annually averaged simulated groundwater depths are compared to observations from nearly 2000 monitoring wells. We find streamflow predictions from analytically informed simulations to be similar in relative bias and Spearman's rho to the geologically informed simulations. R ‐squared values for groundwater depth predictions are close between the best performing analytically and geologically informed simulations at 0.68 and 0.70 respectively, with RMSE values under 10 m. We also show that the analytical approach derived by this study produces estimates of K that are similar in spatial distribution, standard deviation, mean value, and modeling performance to geologically‐informed estimates. The results of this work are used to inform a follow‐on study that tests additional data‐driven approaches in multiple basins within the contiguous United States.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Analytical Sensitivity Analysis of a Spent Nuclear Fuel Cask

Here, we report nuclear science and engineering is a field increasingly dominated by computational studies resulting from increasingly powerful computational tools. As a result, analytical studies, which previously pioneered nuclear engineering, are increasingly viewed as secondary or unnecessary. However, analytical solutions to reduced-fidelity models can provide important information concerning the underlying physics of a problem and aid in guiding computational studies. Similarly, there is increased interest in sensitivity analysis studies. These studies commonly use computational tools. However, providing a complementary sensitivity study of relevant analytical models can lead to a deeper analysis of a problem. This work provides the analytical sensitivity analysis of the one-dimensional (1D) cylindrical mono-energetic neutron diffusion equation using the forward sensitivity analysis procedure (FSAP) developed by Cacuci. Further, these results are applied to a reduced-fidelity model of a spent nuclear fuel cask, demonstrating how computational analysis might be improved with a complementary analytic sensitivity analysis.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2025

Toward the Analytic Bootstrap of Energy Correlators

In this paper, we present a framework for the analytic bootstrap of three-point energy correlators, a crucial observable in N = 4 N=4 super Yang-Mills theory and quantum chromodynamics (QCD). Our approach combines spherical contour techniques, general physical constraints such as pole cancellations, and power correction data in the singular limits to determine its analytic expression. In contrast to previous bootstrap studies restricted to scattering amplitudes for supersymmetric theories, our framework makes use of the properties of Feynman integrals, marking a significant step toward bootstrapping realistic QCD observables. Using this method, we derive analytic expressions for leading-order three-point energy correlators with equal and unequal energy weights, where the latter are crucial ingredients for projected N N-point energy correlators. We also apply the recently developed technique of analytic regression with lattice reduction as a way to bypass needing explicit expressions for the singular limits. Bridging theoretical advances in scattering amplitudes with the renewed interest in weighted cross-sections, our work opens the door to precision tests of QCD dynamics through analytic event-shape predictions.

Gong, Jianyu [State Key Laboratory]↗

NASA NTRS1974

Analytical and experimental investigation of flow fields of annular jets with and without swirling flow

Analytical and experimental studies were performed to define the flowfield of annular jets, with and, without swirling flow. The analytical model treated configurations with variations of flow angularities, radius ratio, and swirl distributions. Swirl distributions characteristic of stator vanes and rotor blade rows, where the total pressure and swirl distributions are related were incorporated in the mathematical model. The experimental studies included tests of eleven nozzle models, both with and, without swirling exhaust flow. Flowfield surveys were obtained and used for comparison with the analytical model. This comparison of experimental and analytical studies served as the basis for evaluation of several empirical constants as required for application of the analysis to the general flow configuration. The analytical model developed during these studies is applicable to the evaluation of the flowfield and overall performance of the exhaust of statorless lift fan systems that contain various levels of exhaust swirl.

Simonson, M. R.↗

NASA NTRS1978

TDRSS performance evaluation for Shuttle services using analytical simulation

A recently developed analytical simulation package makes it possible to obtain an analytical verification of data transmission performance through Tracking and Data Relay Satellite System (TDRSS) satellites. The development of this simulation package has required performing an analytical evaluation of several key communication features of the TDRSS services in order to ensure the consistency of TDRSS and Shuttle user spacecraft transponder performance specifications. Analytical models of the Shuttle transponder, TDRS, TDRSS ground terminal, and link dynamics have been developed for the forward and return links. The models used for the signals and the transmission path are discussed, giving attention to the general set-up of the program and the analytical approach used. Some of the results obtained by using the program are also considered.

Lindsey, W. C.↗

NASA NTRS1981

Flight test results for the F-8 digital fly-by-wire aircraft control sensor analytic redundancy management technique

This paper reviews the formulation and flight test results of an algorithm to detect and isolate the first failure of any one of twelve duplex control sensor signals being monitored. The technique uses like-signal differences for fault detection while relying upon analytic redundancy relationships among unlike quantities to isolate the faulty sensor. The fault isolation logic utilizes the modified sequential probability ratio test, which explicitly accommodates the inevitable irreducible low frequency errors present in the analytic redundancy residuals. In addition, the algorithm uses sensor output selftest, which takes advantage of the duplex sensor structure by immediately removing a highly erratic sensor from control calculations and analytic redundancy relationships while awaiting a definitive fault isolation decision via analytic redundancy. This study represents a proof of concept demonstration of a methodology that can be applied to duplex or higher flight control sensor configurations and, in addition, can monitor the health of one simplex signal per analytic redundancy relationship.

Deckert, J. C.↗

NASA NTRS1983

Analytic redundance management for flight control sensors

The formulation and flight test results of an algorithm to detect and isolate the first failure of any one of 12 duplex control sensor signals (24 in all) being monitored are reviewed. The technique uses like signal differences for fault detection while relying upon analytic redundancy relationships among unlike quantities to isolate the faulty sensor. The fault isolation logic utilizes the modified sequential probability ratio test, which explicitly accommodates the inevitable, irreducible low frequency errors present in the analytic redundancy residuals. In addition, the algorithm used sensor output selftest, which takes advantage of the duplex sensor structure by immediately removing a hard failed sensor from control calculations and analytic redundancy relationships while awaiting a definitive fault isolation decision via analytic redundancy. This study represents a proof of concept demonstration of a methodology that is applied to duplex or higher flight control sensor configurations and, in addition, can monitor the health of one simplex signal per analytic redundancy relationship.

Deckert, J. C.↗

NASA NTRS1984

Comparison of an analytical approximation for particle motion in a current sheet with precise numerical calculations

Approximate analytic solutions exist for particle motion in a one-dimensional current sheet with a constant normal magnetic field component. These solutions are tested against precise numerical calculations, and a range of validity of the analytic solutions is inferred. For example, in the geomagnetic tail neutral sheet, for a dawn-dusk electric field of 0.1-1 mV/m, lobe field of 10-40 nT, and sheet thickness of 1000 km, the analytic solutions serve as a good predictor of particle motion when the normal magnetic field component is less than 3 or 4 nT. By using the analytic solutions, initial distribution functions are mapped into final (accelerated) distributions, and the analytic mappings are compared with numerical mappings.

Speiser, T. W.↗

NASA NTRS1989

Error analysis for semi-analytic displacement derivatives with respect to shape and sizing variables

Sensitivity analysis is fundamental to the solution of structural optimization problems. Consequently, much research has focused on the efficient computation of static displacement derivatives. As originally developed, these methods relied on analytical representations for the derivatives of the structural stiffness matrix (K) with respect to the design variables (b sub i). To extend these methods for use with complex finite element formulations and facilitate their implementation into structural optimization programs using the general finite element method analysis codes, the semi-analytic method was developed. In this method the matrix the derivative of K/the derivative b sub i is approximated by finite difference. Although it is well known that the accuracy of the semi-analytic method is dependent on the finite difference parameter, recent work has suggested that more fundamental inaccuracies exist in the method when used for shape optimization. Another study has argued qualitatively that these errors are related to nonuniform errors in the stiffness matrix derivatives. The accuracy of the semi-analytic method is investigated. A general framework was developed for the error analysis and then it is shown analytically that the errors in the method are entirely accounted for by errors in delta K/delta b sub i. Furthermore, it is demonstrated that acceptable accuracy in the derivatives can be obtained through careful selection of the finite difference parameter.

Fenyes, Peter A.↗

NASA NTRS1991

Experimental and analytical studies of flow through a ventral and axial exhaust nozzle system for STOVL aircraft

Flow through a combined ventral and axial exhaust nozzle system was studied experimentally and analytically. The work is part of an ongoing propulsion technology effort at NASA Lewis Research Center for short takeoff, vertical landing (STOVL) aircraft. The experimental investigation was done on the NASA Lewis Powered Lift Facility. The experiment consisted of performance testing over a range of tailpipe pressure ratios from 1 to 3.2 and flow visualization. The analytical investigation consisted of modeling the same configuration and solving for the flow using the PARC3D computational fluid dynamics program. The comparison of experimental and analytical results was very good. The ventral nozzle performance coefficients obtained from both the experimental and analytical studies agreed within 1.2 percent. The net horizontal thrust of the nozzle system contained a significant reverse thrust component created by the flow overturning in the ventral duct. This component resulted in a low net horizontal thrust coefficient. The experimental and analytical studies showed very good agreement in the internal flow patterns.

Esker, Barbara S.↗

NASA NTRS1991

Experimental and analytical studies of flow through a ventral and axial exhaust nozzle system for STOVL aircraft

Esker, Barbara S.↗

NASA NTRS1994

A simple analytical aerodynamic model of Langley Winged-Cone Aerospace Plane concept

A simple three DOF analytical aerodynamic model of the Langley Winged-Coned Aerospace Plane concept is presented in a form suitable for simulation, trajectory optimization, and guidance and control studies. The analytical model is especially suitable for methods based on variational calculus. Analytical expressions are presented for lift, drag, and pitching moment coefficients from subsonic to hypersonic Mach numbers and angles of attack up to +/- 20 deg. This analytical model has break points at Mach numbers of 1.0, 1.4, 4.0, and 6.0. Across these Mach number break points, the lift, drag, and pitching moment coefficients are made continuous but their derivatives are not. There are no break points in angle of attack. The effect of control surface deflection is not considered. The present analytical model compares well with the APAS calculations and wind tunnel test data for most angles of attack and Mach numbers.

Pamadi, Bandu N.↗

NASA NTRS1994

Theoretical investigation of wave-vector-dependent analytical and numerical formulations of the interband impact-ionization transition rate for electrons in bulk silicon and GaAs

The electron interband impact-ionization rate for both silicon and gallium arsenide is calculated using an ensemble Monte Carlo simulation with the expressed purpose of comparing different formulations of the interband ionization transition rate. Specifically, three different treatments of the transition rate are examined: the traditional Keldysh formula, a new k-dependent analytical formulation first derived by W. Quade, E. Scholl, and M. Rudan (1993), and a more exact, numerical method of Y. Wang and K. F. Brennan (1994). Although the completely numerical formulation contains no adjustable parameters and as such provides a very reliable result, it is highly computationally intensive. Alternatively, the Keldysh formular, although inherently simple and computationally efficient, fails to include the k dependence as well as the details of the energy band structure. The k-dependent analytical formulation of Quade and co-workers overcomes the limitations of both of these models but at the expense of some new parameterization. It is found that the k-dependent analytical method of Quade and co-workers produces very similar results to those obtained with the completely numerical model for some quantities. Specifically, both models predict that the effective threshold for impact ionization in GaAs and silicon is quite soft, that the majority of ionization events originate from the second conduction band in both materials, and that the transition rate is k dependent. Therefore, it is concluded that the k-dependent analytical model can qualitatively reproduce results similar to those obtained with the numerical model yet with far greater computational efficiency. Nevertheless, there exist some important drawbacks to the k-dependent analytical model of Quade and co-workers: These are that it does not accurately reproduce the quantum yield data for bulk silicon, it requires determination of a new parameter, related physically to the overlap intergrals of the Bloch state which can only be adjusted by comparison to experiment, and fails to account for any wave-vector dependence of the overlap integrals. As such the transition rate may be overestimated at those points for which 'near vertical,' small change in k, transitions occur.

Kolnik, Jan↗