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Results for “factorisation methods”

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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NASA NTRS2021

Multi-Variate Factorisation of Numerical Simulations

Factorisation (also known as “factor separation”) is widely used in the analysis of numerical simulations. It allows changes in properties of a system to be attributed to changes in multiple variables associated with that system. There are many possible factorisation methods; here we discuss three previously proposed factorisations that have been applied in the field of climate modelling: the linear factorisation, the Stein and Alpert (1993) factorisation, and the Lunt et al. (2012) factorisation. We show that, when more than two variables are being considered, none of these three methods possess all four properties of “uniqueness”, “symmetry”, “completeness”, and “purity”. Here, we extend each of these factorisations so that they do possess these properties for any number of variables, resulting in three factorisations – the “linear-sum” factorisation, the “shared-interaction” factorisation, and the “scaled-residual” factorisation. We show that the linear-sum factorisation and the shared-interaction factorisation reduce to be identical in the case of four or fewer variables, and we conjecture that this holds for any number of variables. We present the results of the factorisations in the context of three past studies that used the previously proposed factorisations.

Numerical simulations↗
NASA NTRS2022

Multi-variate Factorisation of Numerical Simulations

Factorisation is widely used in the analysis of numerical simulations. It allows changes in properties of a system to be attributed to changes in multiple variables associated with that system. There are many possible factorisation methods; here we discuss three previously-proposed factorisations that have been applied in the field of climate modelling: the linear factorisation, the Stein and Alpert (1993) factorisation, and the Lunt et al (2012) factorisation. We show that, when more than two variables are being considered, none of these three methods possess all three properties of "uniqueness", "symmetry", and "completeness". Here, we extend each of these factorisations so that they do possess these properties for any number of variables, resulting in three factorisations – the "linear-sum" factorisation, the "shared-interaction" factorisation, and the "scaled-total" factorisation. We show that the linear-sum factorisation and the shared-interaction factorisation reduce to be identical. We present the results of the factorisations in the context of studies that used the previously-proposed factorisations. This reveals that only the linear-sum/shared-interaction factorisation possesses a fourth property – "boundedness", and as such we recommend the use of this factorisation in applications for which these properties are desirable.

Numerican simulations↗
NASA NTRS2012

On the Causes of Mid-Pliocene Warmth and Polar Amplification

The mid-Pliocene (approximately 3 to 3.3 Ma ago), is a period of sustained global warmth in comparison to the late Quaternary (0 to approximately 1 Ma ago), and has potential to inform predictions of long-term future climate change. However, given that several processes potentially contributed, relatively little is understood about the reasons for the observed warmth, or the associated polar amplification. Here, using a modelling approach and a novel factorisation method, we assess the relative contributions to mid-Pliocene warmth from: elevated CO2, lowered orography, and vegetation and ice sheet changes. The results show that on a global scale, the largest contributor to mid-Pliocene warmth is elevated CO2. However, in terms of polar amplification, changes to ice sheets contribute significantly in the Southern Hemisphere, and orographic changes contribute significantly in the Northern Hemisphere. We also carry out an energy balance analysis which indicates that that on a global scale, surface albedo and atmospheric emmissivity changes dominate over cloud changes. We investigate the sensitivity of our results to uncertainties in the prescribed CO2 and orographic changes, to derive uncertainty ranges for the various contributing processes.

Lunt, Daniel J.↗
DOE OSTI2025

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↗
DOE OSTI2026

Soft factorisation and exponentiation from Schwinger-space geometry

Infrared divergences in Quantum Field Theory govern the low-energy dynamics of many physical theories, and their understanding is a crucial ingredient in predicting the outcomes of collider experiments. We present a novel approach to deriving the structure of these divergences by employing the Schwinger parametrization of Feynman integrals. After using tropical geometry to identify divergent limits, we study the all-orders asymptotic properties of Feynman diagrams via matrix manipulations of graph Laplacians, which allows us to analyse their IR behaviour systematically. We explicitly demonstrate the soft-hard factorization of the integrand for a broad class of diagrams, and reveal that when written in terms of worldline distances, topologically distinct diagrams asymptote to the same integrand at leading order in the soft limit. In particular, for the case of Quantum Electrodynamics (with massive fermions), we use this fact to show how ladder-type diagrams combine in Schwinger-parameter space to yield the correct exponentiated soft anomalous dimension. This framework provides a foundation for extending these methods to more complex theories like Quantum Chromodynamics and offers a pathway towards a systematic understanding of infrared divergences in perturbative amplitudes.

Factorization↗
DOE OSTI2025

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↗