Search NASA⌕ Search

SEARCH · Search NASA

Results for “Higher-Order”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9

On the use of residue theory for treating the subsonic flow of a compressible fluid

A new mathematical technique, due to Milne-Thomson, is used to obtain an improved form of the method of Poggi for calculating the effect of compressibility on the subsonic flow past an obstacle. By means of this new method, the difficult surface integrals of the original Poggi method can be replaced by line integrals. These line integrals are then solved by the use of residue theory. In this way an equation is obtained giving the second-order effect of compressibility on the velocity of the fluid. The method is practicable for obtaining the higher-order effects of compressibility on the velocity field. As an illustration of the general result, the flow past an elliptic cylinder is discussed.

Kaplan, Carl↗

Technology Assessment and Modelling of Three Terminal Tandem Solar Cells for In-Space Utilization

NASA seeks a sustained human presence on the lunar surface. High-efficiency and resilient energy systems are critical to supporting habitats, scientific outposts, and lunar surface operations. Photovoltaics have long been the backbone of space power systems, transitioning from silicon solar cells to multi-junction III-V solar cells, which now dominate state-of-the-art (SOA) technology. Multi-junction cells achieve high efficiency by layering semiconductors, each absorbing a specific portion of the solar spectrum. However, efficiency gains are increasingly constrained by device physics and manufacturing complexity. Additionally, higher-order junctions pose challenges for accurate modelling and performance characterization due to difficulties in replicating the AM0 spectrum.

solar cells↗

Mathematical Model of a Regenerative Fuel Cell for System Optimization

This thesis developed a system-level optimization model of a regenerative fuel cell (RFC) system for long-duration, off-world energy storage applications. Prior RFC design studies have typically been limited to reduced parameter sets and simplified constraints due to computational limitations relative to the number of relevant degrees of freedom. As a result, important nonlinear interactions between subsystems have not been fully captured. This work began to address that gap by developing a higher-fidelity, nonlinear optimization framework that incorporates a broader set of design variables and coupled constraints, enabling a multidimensional model that captures the coupled behavior of RFC subsystems and demonstrates the feasibility of applying optimization to such systems. An expanded system-level optimization approach was established that captures interactions between electrochemical performance, structural requirements, and storage design. This enabled a more comprehensive evaluation of trade-offs than conventional formulations. The model integrates four coupled subsystems: a fuel cell, an electrolyzer, reactant gas, and high-pressure storage tanks, and was formulated to accommodate a wide range of mission parameters, including operational time and required output power. It incorporates constraints on available solar array power, reactant mass balance between production and consumption, and pressure-dependent storage requirements. To enable reliable convergence, the optimization problem was reformulated to reduce dimensionality and improve numerical stability, with subsystem models organized for efficient evaluation. Problem dimensionality was reduced by consolidating lower-level design variables into higher-level representative quantities, and subsystem behavior was evaluated within the optimization loop. A multi-start initialization strategy was employed to mitigate sensitivity to local minima and improve solution quality, while nonlinear relationships were solved using robust numerical methods. The results showed that convergence was achieved across a range of required output power values. Specific energy reached a maximum at a critical mission power level, where the electrolyzer power matched the available solar input and operated near its voltage and current density limits. Beyond this point, further increases in required power resulted in less mass-efficient operation, increasing total system mass and reducing overall performance. The developed model represents an advancement in RFC system-level optimization by enabling analysis of a broader and more tightly coupled design space than previous considerations. While convergence behavior and computational cost remain challenges, the methods introduced improve solvability and allow inclusion of additional design variables with minimal loss of physical fidelity. However, the numerical results should not be interpreted as definitive design recommendations, as the model includes simplifying assumptions and omits several higher-order effects. Future work should extend this framework by incorporating additional subsystems and loss mechanisms, such as thermal management, parasitic power consumption, and reactant losses, to improve fidelity and ensure more representative design conclusions.

Electrochemistry↗

In-Band Scattering and Absorption of Infrared Blocking Foam Filters for Millimeter-wave Cameras

Expanded closed-cell polymer foams are widely used as thermal infrared (IR) blocking filters in millimeter-wave cameras, particularly for Cosmic Microwave Background observations. Precise knowledge of their millimeter-wave properties is essential for optimizing sensitivity. We present broadband (150 GHz - 2 THz) transmittance spectroscopy of Styroace-II and several Zotefoam filters, fitting their spectra with a radiative transfer model incorporating dielectric absorption and Rayleigh, Mie, and higher-order scattering. For a typical 5~cm thick filter stack at 280~GHz, Styroace-II exhibits ${\sim}10\%$ scattering with absorption estimated as ${\lesssim}5\%$ by effective-medium theory, while Zotefoam HD30 offers superior performance at ${\sim}3\%$ scattering and absorption likewise bounded to ${{\lesssim}0.3\%}$. Each model component is constrained at the ${\sim}0.1\%$ transmittance level for millimeter wavelengths. We observe batch-to-batch scattering variability of up to 2 percentage points in foams with multiple tested batches. Less commonly used Zotefoam formulations (LD15 and LD24) can further reduce in-band scattering to ${<}1\%$ while maintaining negligible in-band absorption and likely comparable IR blocking due to shared polyethylene absorption features and similar cell sizes. Based on this work, a filter constructed from the best measured LD24 batch has replaced the Styroace-II filter in a Simons Observatory 220/280 GHz Small Aperture Telescope.

Thomas, Alex [Chicago U., Astron. Astrophys. Ctr.;↗

QuadSync: Quadrifocal tensor synchronization via Tucker decomposition

In structure from motion, quadrifocal tensors capture more information than their pairwise counterparts (essential matrices), yet they have often been thought of as impractical and only of theoretical interest. In this work, we challenge such beliefs by providing a new framework to recover n cameras from the corresponding collection of quadrifocal tensors. We form the block quadrifocal tensor and show that it admits a Tucker decomposition whose factor matrices are the stacked camera matrices, and which thus has a multilinear rank of (4,4,4,4) independent of n. We develop the first synchronization algorithm for quadrifocal tensors, using Tucker decomposition, alternating direction method of multipliers, and iteratively reweighted least squares. We further establish relationships between the block quadrifocal, trifocal, and bifocal tensors, and introduce an algorithm that jointly synchronizes these three entities. Numerical experiments demonstrate the effectiveness of our methods on modern datasets, indicating the potential and importance of using higher-order information in synchronization.

Miao, Daniel [University of Minnesota]↗

Splitting amplitudes at N 3 LO in QCD

In the limit where partons become collinear to each other, scattering amplitudes factorize into a product of universal, process-independent building blocks and scattering amplitudes involving fewer partons. We compute these universal building blocks — known as splitting amplitudes — for two collinear QCD partons up to third loop order in QCD. Our results describe arbitrary time-like splitting processes. Due to the violation of strict collinear factorization in space-like splitting processes, we specifically present space-like splitting amplitudes for three-parton QCD scattering amplitudes at third loop order. To achieve our results, we perform a collinear expansion of three-loop scattering amplitudes using a new expansion-by-subgraph technology, which is based on the method of regions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

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↗

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↗

Investigating the universality of five-point QCD scattering amplitudes at high energy

We investigate 2 → 3 QCD scattering amplitudes in multi-Regge kinematics, i.e. where the final partons are strongly ordered in rapidity. In this regime amplitudes exhibit intriguing factorisation properties which can be understood in terms of effective degrees of freedom called reggeons. Working within the Balitsky/JIMWLK framework, we predict these amplitudes for the first time to next-to-next-to-leading logarithmic order, and compare against the limit of QCD scattering amplitudes in full colour and kinematics. We find that the latter can be described in terms of universal objects, and that the apparent non-universality arising at NNLL comes from well-defined and under-control contributions that we can predict. Thanks to this observation, we extract for the first time the universal vertex that controls the emission of the central-rapidity gluon, both in QCD and $\mathcal{N}$ = 4 super Yang-Mills.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Rational QCD loop amplitudes and quantum theories on twistor space

We show how curing an anomaly of the twistor uplift of self-dual Yang-Mills theory implies linear relations among one-loop, n-gluon, color-ordered subamplitudes in QCD, when all n gluon helicities are positive, or when exactly one is negative. We compute the number of linearly independent subamplitudes as determined by these relations, in terms of unsigned Stirling numbers. Then we use a momentum-twistor parametrization to show that there are no further linear dependencies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Projection-to-Born-improved subtractions at NNLO

While the current frontier in fixed-order precision for collider observables is N 3 LO, important steps are necessary to consolidate NNLO cross-section predictions with improved stability and efficiency. Slicing methods have been successfully applied to obtain NNLO and N 3 LO predictions, but have shown poor performance in the presence of fiducial cuts due to large kinematical power corrections. In this paper we implement Projection-to-Born-improved q T (P2B q T ) and jettiness (P2Bτ 0 ) subtractions for a large class of color singlet processes in MCFM. This method allows for the efficient evaluation of fiducial power corrections in any non-local subtraction scheme using a Projection-to-Born subtraction. We demonstrate the significant numerical improvements of this method based on fiducial Drell-Yan and Higgs cross-sections. Moreover, with fiducial power corrections removed via this method, the leading-logarithmic power corrections that have only been calculated without fiducial cuts can be included, further improving the calculations. For di-photon production with photon isolation, we devise a novel method in combination with P2B-improved subtractions, which we name P2B γ τ 0 , and P2B γ q T for the two subtraction schemes, respectively. This method allows the inclusion of both fiducial power corrections due to kinematic cuts on the photons and a set of isolation power corrections in the fragmentation channel where a quark may enter the isolation cone. We find significant improvements in the convergence of NNLO di-photon cross-sections with photon isolation cuts, demonstrating that it is possible to achieve a stable and efficient calculation of di-photon cross-sections using slicing methods.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Heavy-quark contributions to the DIS structure functions F 4 and F 5 at NLO in the ACOT scheme

We compute the contributions of heavy quarks to the deep-inelastic scattering structure functions F 4 and F 5 at next-to-leading order of perturbative QCD in the ACOT scheme. Both analytic results including the details of the calculation as well as numerical results for the neutral and charged current cases are presented. Our study thus lays the groundwork for future measurements of these two structure functions in experiments such as the SHiP experiment.

deep inelastic scattering↗

Analytic reconstruction with massive particles: one-loop amplitudes for $0\to \overline{q} qt\overline{t}H$

We present an analytic reconstruction of one-loop amplitudes for the process $0\to \overline{q} qt\overline{t}H$. Our calculation is a novel use of analytic reconstruction, retaining explicit covariance in the massive spin states through the massive spinor-helicity formalism. The analytic reconstruction relies on embedding the massive five-point kinematics in a fully massless eight-point phase space while still building a minimal ansatz directly in the five-point phase space. In order to obtain compact analytic expressions it is necessary to identify suitable partial fraction decompositions and extract common numerator factors, which we achieve through careful inspection of limits in which pairs of denominators vanish. We find that the resulting amplitudes are more numerically efficient than ones computed using automatic methods but that the gains are not as significant as in the massless case, at least at present. The method opens the door to applications at two-loop order, where numerical efficiency and improvements in the reconstruction methodology are more crucial, especially with regards to the number of free parameters in the ansatz.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Small radius inclusive jet production at the LHC through NNLO+NNLL

The study of hadronic jets and their substructure at hadronic colliders is crucial for improving our understanding of QCD, and searching for new physics. As such, there has been a significant effort to improve their theoretical description. In the small radius limit, inclusive jet production exhibits a universal factorization, enabling the resummation of logarithms which greatly stabilizes theoretical predictions. In this paper, we show how to combine a recently introduced framework for small-R resummation with the Stripper subtraction formalism for fragmentation, enabling next-to-next-to-leading order calculations of small-R inclusive jet production for a wide variety of processes at the LHC. We extract the two-loop constants for the jet functions, enabling for the first time next-to-next-to-leading logarithmic resummation matched to next-to-next-to-leading order perturbative calculation. We compare with CMS data for small-R jet production, and find that our results greatly improve the accuracy of the predictions at small-R, and stabilize the perturbative convergence and error estimates at larger R. Our approach is applicable to a wide class of jet substructure observables exhibiting similar factorization theorems, opening the door to an NNLO jet substructure program at the LHC.

Effective Field Theories↗

The structure of quark mass corrections in the gg → HH amplitude at high-energy

The leading and next-to-leading order QCD predictions for Higgs boson pair production at hadron colliders suffer from a significant mass renormalisation scheme uncertainty related to the choice of the top-quark mass. The functional dependence of the result on the value of the intermediate quark mass can be understood in the high-energy limit using the Method of Regions and the tools of Soft-Collinear Effective Theory. In this work, we study the origin of the sizeable logarithmic mass corrections in the gg → HH amplitudes at leading and next-to-leading power in the limit s, |t|, |u| ≫ ${m}_t^2$ ≫ ${m}_H^2$. We argue that the mass corrections follow a predictable factorised pattern that can be exploited to simplify their computation. We present results for the leading power leading logarithmic corrections, our analysis leads to a significant reduction in the theoretical uncertainty of the double Higgs production amplitudes at scattering energies ≳ 1 TeV due to the top-quark mass scheme.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Dihadron correlations in small- x DIS at NLO: transverse momentum dependent fragmentation

We compute the inclusive dihadron cross-section in Deep Inelastic Scattering at next-to-leading order (NLO) and small x in the Color Glass Condensate. We focus on the kinematic limit where the hadrons are produced at forward rapidities (in the direction of the virtual photon) and back-to-back in the transverse plane. Our calculation demonstrates that the coefficient of the Sudakov double logarithm for this process is –$\frac{αs}{2π}$ [C F + $\frac{Nc}{2}$] instead of –$\frac{αsNc}{4π}$ when back-to-back jets are measured in the final state. To preserve the universality of the Sudakov soft factor associated with the Weizsäcker-Williams transverse momentum dependent (TMD) gluon distribution, we promote the collinear fragmentation functions into TMD fragmentation functions. We then perform the resummation of the Sudakov logarithms through Collins-Soper-Sterman evolution of the TMD fragmentation functions and the Weizsäcker-Williams TMD gluon distribution. Finally, analytic expressions are obtained for the NLO coefficient functions in the $\overline{MS}$-scheme. These results pave the way towards numerically calculating dihadron correlations at small x at the future Electron-Ion Collider with full NLO accuracy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗