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Results for “higher-order integration”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Lyapunov controlled counterdiabatic quantum optimization

We introduce a quantum algorithm that integrates counterdiabatic (CD) protocols with quantum Lyapunov control (QLC) to address combinatorial optimization problems. This approach offers versatility, allowing implementation as either a digital-analog or purely digital algorithm based on selected control strategies. By examining spin-glass Hamiltonians, we illustrate how the algorithm can explore alternative paths to enhance solution outcomes compared to conventional CD techniques. This method reduces dependence on extensive higher-order CD terms and on classical optimization techniques, making it more suitable for existing quantum computing platforms. The combination of digital compression via CD protocols and the adaptable nature of QLC methods positions this approach as a promising candidate for near-term quantum devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

The soaring kite: a tale of two punctured tori

We consider the 5-mass kite family of self-energy Feynman integrals and present a systematic approach for constructing an ε-form basis, along with its differential equation pulled back onto the moduli space of two tori. Each torus is associated with one of the two distinct elliptic curves this family depends on. We demonstrate how the locations of relevant punctures, which are required to parametrize the full image of the kinematic space onto this moduli space, can be extracted from integrals over maximal cuts. A boundary value is provided such that the differential equation is systematically solved in terms of iterated integrals over g-kernels and modular forms. Then, the numerical evaluation of the master integrals is discussed, and important challenges in that regard are emphasized. In an appendix, we introduce new relations between g-kernels.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Semi-inclusive single-jet production in DIS at next-to-leading order in the Color Glass Condensate

Within the Color Glass Condensate (CGC) effective field theory, we derive the next-to-leading order (NLO) cross-section for the single-jet semi-inclusive cross-section in deep inelastic scattering (DIS) at small x, for both longitudinally and transversely polarized virtual photons. We provide analytic expressions, valid at finite N c and suitable for numerical evaluation, for both the cross-section differential in rapidity and transverse momentum and the cross-section differential in rapidity only. Our NLO formulae demonstrate that the very forward rapidity regime is plagued by large double logarithmic corrections coming from phase space constraints on soft gluons close to the kinematic threshold for jet production. A joint resummation of small-x and threshold logarithms at single logarithmic accuracy is proposed to remedy the instability of the cross-section in this regime. By integrating over the single-jet phase space, we recover known results for the NLO DIS structure functions at small x, previously obtained using the optical theorem.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Multidimensional Coherent Spectroscopy of van der Waals materials and heterostructures (Final Technical Report)

This project advanced multidimensional coherent spectroscopy (MDCS) and related spectroscopic-imaging methods as quantitative probes of many-body optical excitations in two-dimensional (2D) van der Waals (vdW) semiconductors and their heterostructures. Monolayer transition-metal dichalcogenides (TMDs) such as MoSe 2 and WSe 2 provide a uniquely strong platform for excitonic physics due to reduced dielectric screening, which enhances Coulomb interactions and makes higher-order correlated states (e.g., biexcitons and exciton–trion correlations) more prominent than in conventional bulk semiconductors. At the same time, the same sensitivity that enables strong interactions also increases susceptibility to spatial inhomogeneity—e.g., strain gradients, wrinkles, nanoscale disorder potentials, and charge puddling—which can broaden resonances, obscure interaction signatures, and complicate device-to-device reproducibility. The work reported here addressed this dual opportunity and challenge by: (i) developing and deploying coherent multidimensional methods (including double-quantum MDCS) capable of isolating interaction signals with reduced background, (ii) integrating electrostatic control to tune carrier populations and interaction strengths in situ, and (iii) introducing complementary spatially resolved photoluminescence (PL) techniques—hyperspectral PL imaging and polarization-/field-dependent PL lineshape analysis—to directly quantify disorder, strain, and localization that govern the coherent response.

36 MATERIALS SCIENCE↗
DOE OSTI2024

On gauge amplitudes first appearing at two loops

We study scattering amplitudes in massless non-abelian gauge theory where all outgoing gluons have positive helicity. It has been argued recently by Costello that for a particular fermion representation (8 fundamentals plus one antisymmetric-tensor representation in SU(N)) the one-loop amplitudes vanish identically. We show that this vanishing leads to previously-observed identities among one-loop color-ordered partial amplitudes. We then turn to two loops, where Costello has computed the all-plus amplitudes for this theory, as rational functions of the kinematics for any number of gluons using the celestial chiral algebra (CCA) bootstrap. We show that in dimensional regularization, these two-loop amplitudes are not rational, and they are not even finite as ϵ → 0. However, the finite remainder for four gluons agrees with the formula by Costello. In addition, we provide a mass regulator for the infrared-divergent loop integrals; with this regulator, the CCA bootstrap formula is recovered exactly. Finally, we use the CCA bootstrap to compute the double-trace terms in the theory at two loops for an arbitrary number of gluons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Manipulating the 3D organization of the largest synthetic yeast chromosome

Whether synthetic genomes can power life has attracted broad interest in the synthetic biology field. Here, we report de novo synthesis of the largest eukaryotic chromosome thus far, synIV, a 1,454,621-bp yeast chromosome resulting from extensive genome streamlining and modification. We developed megachunk assembly combined with a hierarchical integration strategy, which significantly increased the accuracy and flexibility of synthetic chromosome construction. Besides the drastic sequence changes, we further manipulated the 3D structure of synIV to explore spatial gene regulation. Surprisingly, we found few gene expression changes, suggesting that positioning inside the yeast nucleoplasm plays a minor role in gene regulation. Lastly, we tethered synIV to the inner nuclear membrane via its hundreds of loxPsym sites and observed transcriptional repression of the entire chromosome, demonstrating chromosome-wide transcription manipulation without changing the DNA sequences. Our manipulation of the spatial structure of synIV sheds light on higher-order architectural design of the synthetic genomes.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Analysis of Power-Maximizing Region 2 Controllers for Wind and Marine Turbines

Wind and marine energy are rapidly growing and complementary technologies that share some techniques for simplified modeling and control, particularly in below-rated flow speeds. A turbine operator has several choices of controller for maximizing power in Region 2. The simple and ubiquitous KΩ 2 control law is often effective but limited in its flexibility. Alternative controllers use reference tracking to split the control objectives into a low-bandwidth optimal tip-speed ratio tracking loop to maximize steady-state power and a higher-bandwidth proportional-integral control loop to reject inflow turbulence. Several options exist for identifying the slowly varying optimal set point during operation, based on estimating the inflow velocity or filtering the power or torque signals. This study compares the trade-offs between performance and other design priorities for a few choices of reference-tracking controller in the literature for reference wind and marine turbines. Analysis is performed in the frequency domain using the linearization of each controller, and the impact of turbulent disturbances on the closed-loop system is described. The controllers are simulated in OpenFAST to analyze their performance with higher-order nonlinear turbine dynamics.

17 WIND ENERGY↗
DOE OSTI2025

SDA: a symbolic differential algebra package in C++

Truncated Power Series Algebra (TPSA), or Differential Algebra (DA), is a well-established tool in accelerator physics, commonly used for generating high-order maps of dynamic systems, as well as in symplectic tracking, normal form analysis, verified integration, optimization, and fast multipole methods. This package is the first to perform symbolic DA computations, enabling traceability of initial condition contributions and runtime reduction for repeated DA calculations, potentially expanding DA’s applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Efficiently evaluating loop integrals in the EFTofLSS using QFT integrals with massive propagators

We develop a new way to analytically calculate loop integrals in the Effective Field Theory of Large Scale-Structure. Previous available methods show severe limitations beyond the one-loop power spectrum due to analytical challenges and computational and memory costs. Our new method is based on fitting the linear power spectrum with cosmology-independent functions that resemble integer powers of quantum field theory massive propagators with complex masses. A remarkably small number of them is sufficient to reach enough accuracy. Similarly to former approaches, the cosmology dependence is encoded in the coordinate vector of the expansion of the linear power spectrum in our basis. We first produce cosmology-independent tensors where each entry is the loop integral evaluated on a given combination of basis vectors. For each cosmology, the evaluation of a loop integral amounts to contracting this tensor with the coordinate vector of the linear power spectrum. The 3-dimensional loop integrals for our basis functions can be evaluated using techniques familiar to particle physics, such as recursion relations and Feynman parametrization. We apply our formalism to evaluate the one-loop bispectrum of galaxies in redshift space. The final analytical expressions are quite simple and can be evaluated with little computational and memory cost. We show that the same expressions resolve the integration of all one-loop N-point function in the EFTofLSS. This method, which is originally presented here, has already been applied in the first one-loop bispectrum analysis of the BOSS data to constraint ΛCDM parameters and primordial non-Gaussianities [1, 2].

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Galerkin formulation of path integrals in lattice field theory

We present a mathematical framework for Galerkin formulations of path integrals in lattice field theory. The framework is based on using the degrees of freedom (DOFs) associated to a Galerkin discretization as the fundamental lattice variables. We formulate standard concepts in lattice field theory, such as the partition function and correlation functions, in terms of the DOFs. For example, using continuous finite element spaces, we show that the two-point spatial correlation function can be defined between any two points on the domain (as opposed to at just lattice sites) and furthermore, this two-point function satisfies a weak propagator (or Green’s function) identity, in analogy to the continuum case, as well as a convergence estimate obtained from the standard finite element techniques. Furthermore, this framework leads naturally to higher-order formulations of lattice field theories by considering higher-order finite element spaces for the Galerkin discretization. We consider analytical and numerical examples of scalar field theory to investigate how increasing the order of piecewise polynomial finite element spaces affect the approximation of lattice observables. Finally, we sketch an outline of this Galerkin framework in the context of gauge field theories.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Linearised Fokker–Planck collision model for gyrokinetic simulations

We introduce a gyrokinetic, linearised Fokker–Planck collision model that satisfies conservation laws and is accurate at arbitrary collisionalities. The differential test-particle component of the operator is exact; the integral field-particle component is approximated using a spherical harmonic and a modified Laguerre polynomial expansion developed by Hirshman and Sigmar (1976 Phys. Fluids 19 1532). The numerical methods of the implementation in the δf-gyrokinetic code stella (Barnes et al 2019 J. Comput. Phys. 391 365–80) are discussed, and conservation properties of the operator are demonstrated. The collision model is then benchmarked against the collision model of the gyrokinetic solver GS2 in the limiting cases of a reduced test-particle collision operator and energy- and momentum-conserving operator. The accuracy of the full collision model is investigated by solving the parallel Spitzer-Härm problem for the transport coefficients. It is shown that retaining collisional energy flux and higher-order terms in the field-particle operator reduces errors in the transport coefficients from 10%–25% for a simple momentum- and energy-conserving model to under 1%.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Evidential Deep Learning: Enhancing Predictive Uncertainty Estimation for Earth System Science Applications

Abstract Robust quantification of predictive uncertainty is a critical addition needed for machine learning applied to weather and climate problems to improve the understanding of what is driving prediction sensitivity. Ensembles of machine learning models provide predictive uncertainty estimates in a conceptually simple way but require multiple models for training and prediction, increasing computational cost and latency. Parametric deep learning can estimate uncertainty with one model by predicting the parameters of a probability distribution but does not account for epistemic uncertainty. Evidential deep learning, a technique that extends parametric deep learning to higher-order distributions, can account for both aleatoric and epistemic uncertainties with one model. This study compares the uncertainty derived from evidential neural networks to that obtained from ensembles. Through applications of the classification of winter precipitation type and regression of surface-layer fluxes, we show evidential deep learning models attaining predictive accuracy rivaling standard methods while robustly quantifying both sources of uncertainty. We evaluate the uncertainty in terms of how well the predictions are calibrated and how well the uncertainty correlates with prediction error. Analyses of uncertainty in the context of the inputs reveal sensitivities to underlying meteorological processes, facilitating interpretation of the models. The conceptual simplicity, interpretability, and computational efficiency of evidential neural networks make them highly extensible, offering a promising approach for reliable and practical uncertainty quantification in Earth system science modeling. To encourage broader adoption of evidential deep learning, we have developed a new Python package, Machine Integration and Learning for Earth Systems (MILES) group Generalized Uncertainty for Earth System Science (GUESS) (MILES-GUESS) ( https://github.com/ai2es/miles-guess ), that enables users to train and evaluate both evidential and ensemble deep learning. Significance Statement This study demonstrates a new technique, evidential deep learning, for robust and computationally efficient uncertainty quantification in modeling the Earth system. The method integrates probabilistic principles into deep neural networks, enabling the estimation of both aleatoric uncertainty from noisy data and epistemic uncertainty from model limitations using a single model. Our analyses reveal how decomposing these uncertainties provides valuable insights into reliability, accuracy, and model shortcomings. We show that the approach can rival standard methods in classification and regression tasks within atmospheric science while offering practical advantages such as computational efficiency. With further advances, evidential networks have the potential to enhance risk assessment and decision-making across meteorology by improving uncertainty quantification, a longstanding challenge. This work establishes a strong foundation and motivation for the broader adoption of evidential learning, where properly quantifying uncertainties is critical yet lacking.

Schreck, John S.↗
DOE OSTI2026

Radiative corrections to superallowed beta decays at $\mathcal{O}\left({\alpha}^2Z\right)$

We compute $\mathcal{O}\left({\alpha}^2Z\right)$ radiative corrections to superallowed β decays with a heavy-particle effective field theory that systematically describes the interactions of low-energy ultrasoft photons with nuclei. We calculate two-loop virtual and one-loop real-virtual amplitudes by reducing the Feynman integrals to a set of master integrals, which we solve analytically using a variety of techniques. These techniques can be applied to other phenomenologically interesting observables. The ultrasoft corrections can then be combined with contributions arising from the exchange of potential photons to obtain the complete $\mathcal{O}\left({\alpha}^2Z\right)$ correction to the decay rate, with resummation of large logarithms of the electron energy times the nuclear radius. We find that $\mathcal{O}\left({\alpha}^2Z\right)$ ultrasoft loops induce a relative correction to the decay rate that ranges from 0.7 ∙ 10 −3 in the decay of 10 C to 3.6 ∙ 10 −3 in the decay of 54 Co, and will thus impact the extraction of V ud at the permille level. We show that the inclusion of these corrections reduces the residual renormalization scale dependence of the decay rate to a negligible level, making missing ultrasoft perturbative corrections a subdominant source of theoretical uncertainty.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Higher-order moments of the elliptic flow distribution in PbPb collisions at $ \sqrt{s_{\textrm{NN}}}$ = 5.02 TeV

The hydrodynamic flow-like behavior of charged hadrons in high-energy lead-lead collisions is studied through multiparticle correlations. The elliptic anisotropy values based on different orders of multiparticle cumulants, v$_{2}${2k}, are measured up to the tenth order (k = 5) as functions of the collision centrality at a nucleon-nucleon center-of-mass energy of $ \sqrt{s_{\textrm{NN}}} $ = 5.02 TeV. The data were recorded by the CMS experiment at the LHC and correspond to an integrated luminosity of 0.607 nb$^{–1}$. A hierarchy is observed between the coefficients, with v$_{2}${2} > v$_{2}${4} ≳ v$_{2}${6} ≳ v$_{2}${8} ≳ v$_{2}${10}. Based on these results, centrality-dependent moments for the fluctuation-driven event-by-event v$_{2}$ distribution are determined, including the skewness, kurtosis and, for the first time, superskewness. Assuming a hydrodynamic expansion of the produced medium, these moments directly probe the initial-state geometry in high-energy nucleus-nucleus collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Tracking discontinuities in parameter space

We develop a geometric framework in Feynman-parameter space to determine constraints on the sequential discontinuities of Feynman integrals. Our method is based on tracking the deformation of the integration contour as external kinematics are analytically continued. This procedure imposes powerful constraints on the analytic structure of Feynman integrals, providing crucial inputs for their bootstrap. We demonstrate the usefulness of this framework by applying it to integrals in dimensional regularization, with higher propagator powers, and to examples with non-uniform transcendental weight. The method is illustrated with several one- and two-loop calculations.

Differential and Algebraic Geometry↗
DOE OSTI2025

Enhanced MPM framework with multipatch isogeometric analysis for geotechnical applications

Achieving stable stress solutions at large strains using the Material Point Method (MPM) is challenging due to the accumulation of errors associated with geometry discretization, cell-crossing noise, and volumetric locking. Several simplified attempts exist in the literature to mitigate these errors, including higher-order frameworks. However, the stability of the MPM solution in such frameworks has been limited to simple geometries and the single-phase formulation (i.e., neglecting pore fluid). Although never explored, multipatch isogeometric analysis offers desirable qualities to simulate complex geometries while mitigating errors in the MPM. The degree of required high-order spatial integration has also never been investigated to infer a minimum limit for the stability of the stress solution in MPM. This paper presents a general-purpose numerical framework for simulating stable stresses in porous media, capturing both near incompressibility and multiphase interactions. First, the numerical framework is presented considering Non-Uniform Rational B-splines (NURBS) to perform isogeometric analysis (IGA) in MPM. Additionally, a volumetric strain smoothing algorithm is used to alleviate errors associated with volumetric locking. Second, the manifestation of cell-crossing errors is assessed via a series of problems with orders ranging from linear to cubic interpolation functions. Third, the use of NURBS is investigated and verified for problems with circular geometries. Finally, multipatch analysis is deployed to simulate plane strain and 3D penetration in soils, considering nearly incompressible elastoplastic (total stress) analysis and fully-coupled hydro-mechanical (effective stress) analysis. The stability of the solution is also analyzed for different constitutive models. From the results, it can be concluded that the framework using cubic interpolation functions with strain smoothing is the most convenient, presenting stable stress solutions for a broad range of multiphase geotechnical applications.

58 GEOSCIENCES↗
DOE OSTI2024

Hidden quantum criticality and entanglement in quench dynamics

Entanglement exhibits universal behavior near the ground-state critical point where correlations are long ranged and the thermodynamic entropy is vanishing. On the other hand, a quantum quench imparts extensive energy and results in a build up of entropy, hence no critical behavior is expected at long times. In this work, we present a new paradigm in the quench dynamics of integrable spin chains which exhibit a ground-state order-disorder phase transition at a critical line. Specifically, we consider a quench along the critical line which displays a volume-law behavior of the entropy and exponentially decaying correlations; however, we show that quantum criticality is hidden in higher-order correlations and becomes manifest via measures such as the mutual information and logarithmic negativity. Furthermore, we showcase the scale invariance of the Rényi mutual information between disjoint regions as further evidence for genuine critical behavior. We attribute the emergent quantum criticality to the soft mode not getting excited in spite of the quench. Moreover, the results presented here are universal to models whose low-energy or long-wavelength dynamics are well described by a free-fermionic field theory. Our results are amenable to an experimental realization on different quantum simulator platforms, particularly the Rydberg simulators. Published by the American Physical Society 2024

Paul, Sanku↗
DOE OSTI2025

A Block-Structured Adaptive Mesh Framework to Solve Radiation Transfer Equation in Irregular Embedded Geometries

Radiation transport arises in various scientific, industrial, and medical fields, and understanding its effect in applications is needed to make accurate predictions, safety assessments and performance optimizations. Solving the Radiation Transport Equation (RTE) is challenging due to its integro-differential nature, which involves both differential and integral terms. The differential term describes the change in radiation intensity due to absorption and emission, while the integral term accounts for scattering. The accurate modeling of radiation is further complicated in many applications due to the complex, irregular geometries. Various methods exist for solving the RTE, including the zonal, Monte Carlo, spherical harmonics, discrete ordinates, and finite volume methods. Traditional mesh-based approaches, which rely on structured or unstructured meshes, struggle with irregular geometries due to: a) the difficulty of conforming structured grids to irregular domains, b) challenges in enforcing boundary conditions correctly, and c) the additional computational cost of unstructured mesh methods. This work presents a second-order accurate method for solving the RTE in irregular geometries. The radiation intensity is discretized using the finite-volume method in both spatial and angular directions on regular Cartesian grid blocks. Leveraging the block-structured adaptive mesh refinement (AMR) framework provided by AMReX, our method refines the grid locally to reduce spatial discretization error, ensuring a converged numerical solution while minimizing computational costs elsewhere. A two-stage deferred correction approach is employed: First, a first-order discretization on grid blocks is solved using an algebraic multigrid method in HYPRE. Second, a correction term is applied explicitly to achieve second-order accuracy. The correction term is calculated by approximating the radiation flux on cell faces using a Total Variation Diminishing (TVD) scheme. This approach ensures quick convergence of the multigrid method while preserving higher-order accuracy of the numerical solution. Irregular geometries are resolved as embedded boundaries (EB), resulting in both cut cells and regular cells. In cut cells, we modify the fluxes using face fractions and incorporate additional contributions from EB boundary conditions. To ensure higher-order convergence near the EB interface, the correction term is modified by interpolating the radiation intensity to fictitious ghost points. The implementation takes advantage of modern supercomputers by leveraging AMReX’sMPI/X parallelization strategy where X can be MPI or a GPU accelerator including CUDA, HIP and DPC++. We validate our solver using classical test cases, both with and without EB, demonstrating accuracy and efficiency. Additionally, we analyze the impact of adaptive mesh refinement on solution accuracy and computational cost, highlighting the advantages of our approach for high-resolution radiation transport simulations.

computational fluid dynamics (CFD)↗