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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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6 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

The hyperplane of early-type galaxies: using stellar population properties to increase the precision and accuracy of the fundamental plane as a distance indicator

ABSTRACT We use deep spectroscopy from the SAMI (Sydney-AAO Multi-object Integral) Galaxy Survey to explore the precision of the fundamental plane (FP) of early-type galaxies as a distance indicator for future single-fibre spectroscopy surveys. We study the optimal trade-off between sample size and signal-to-noise ratio (SNR), and investigate which additional observables can be used to construct hyperplanes with smaller intrinsic scatter than the FP. We add increasing levels of random noise (parametrized as effective exposure time) to the SAMI spectra to study the effect of increasing measurement uncertainties on the FP- and hyperplane-inferred distances. We find that, using direct-fit methods, the values of the FP and hyperplane best-fitting coefficients depend on the spectral SNR, and reach asymptotic values for a mean $\langle \mathrm{ SNR} \rangle =40\, \mathrm{\mathring{\rm A}}^{-1}$. As additional variables for the FP we consider three stellar-population observables: light-weighted age, stellar mass-to-light ratio, and a novel combination of Lick indices ($I_\mathrm{age}$). For an $\langle \mathrm{ SNR} \rangle =45~\mathrm{\mathring{\rm A}}^{-1}$ (equivalent to 1-h exposure on a 4-m telescope), all three hyperplanes outperform the FP as distance indicators. Being an empirical spectral index, $I_\mathrm{age}$ avoids the model-dependent uncertainties and bias underlying age and mass-to-light ratio measurements, yet yields a 10 per cent reduction of the median distance uncertainty compared to the FP. We also find that, as a by-product, the $I_\mathrm{age}$ hyperplane removes most of the reported environment bias of the FP. After accounting for the different SNR, these conclusions also apply to a 50 times larger sample from SDSS-III (Sloan Digital Sky Survey). However, in this case, only $\mathrm{ age}$ removes the environment bias.

D’Eugenio, Francesco (ORCID:0000000323888172)↗
DOE OSTI2025

Hyperplane decision trees as piecewise linear surrogate models for chemical process design

Recent trends in chemical engineering research point towards an increasing reliance on data-driven modeling approaches. Neural networks, for instance, have proven to be accurate when data is plentiful and high-dimensional, but in many cases, they require computationally-intensive training procedures. Here, in this work, we describe hyperplane decision trees (HT) as a highly expressive and low-compute machine learning model architecture. These models are locally linear and have linear decision boundaries, resulting in a piecewise linear model of the data. This property allows them to be converted into mixed-integer linear constraints which can be globally optimized. Our open-source PyTorch implementation of this method is a fast, flexible, and accessible way to build accurate piecewise linear models of data.

Decision trees↗
DOE OSTI2025

A physical basis for cosmological correlators from cuts

Significant progress has been made in our understanding of the analytic structure of FRW wavefunction coefficients, facilitated by the development of efficient algorithms to derive the differential equations they satisfy. Moreover, recent findings indicate that the twisted cohomology of the associated hyperplane arrangement defining FRW integrals overestimates the number of integrals required to define differential equations for the wave-function coefficient. We demonstrate that the associated dual cohomology is automatically organized in a way that is ideal for understanding and exploiting the cut/residue structure of FRW integrals. Utilizing this understanding, we develop a systematic approach to organize compatible sequential residues, which dictates the physical subspace of FRW integrals for any n -site, ℓ-loop graph. In particular, the physical subspace of tree-level FRW wavefunction coefficients is populated by differential forms associated to cuts/residues that factorize the integrand of the wavefunction coefficient into only flat space amplitudes. After demonstrating the validity of our construction using intersection theory, we develop simple graphical rules for cut tubings that enumerate the space of physical cuts and, consequently, differential forms without any calculation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Spatial Correlations of the Poisson Model for Radiation Transport

Characterizing the relationship between bulk physical properties and mixing in randomly heterogeneous media is a central challenge across many areas of science and engineering. A benchmark model for such studies is the Poisson model, a random tessellation of space by a Poisson process of hyperplanes. In radiation transport studies, the lack of exact expressions for the Poisson model’s spatial multipoint functions has led to approximate methods being used, introducing unquantified sources of error. Here, we recently introduced an exact solution for the Poisson model’s multipoint functions and closely related conditional probability functions (CPFs), providing a new opportunity to understand and reduce these sources of error. In this paper, we enable a more rigorous investigation of radiation transport in stochastic media by applying the recently introduced exact solution for the Poisson model’s CPFs. This paper consists of three main contributions. First, we introduce a unified framework for CPFs of the Poisson model, encompassing the recently introduced exact CPFs as well as the previously introduced atomic mix, nearest-neighbor, and combination CPFs. This framework also includes existing pruning techniques for the approximate CPFs, such as angular exclusion, as well as a novel form of angular exclusion suitable for the exact CPFs. Second, we use the exact CPFs to characterize the spatial regions where each approximate three-point CPF is most accurate, thereby explaining the observed hierarchy of accuracy among the approximate models. Finally, we evaluate material transmittance, reflectance, and flux in a three-dimensional test problem using conditional point sampling, demonstrating the relationship between CPF accuracy and transport simulation accuracy.

Poisson model↗
DOE OSTI2025

Multipoint Correlations in Poisson Media

Multipoint correlations in randomly heterogeneous composite media are determined by the probability that a set of points belong to specific phases. They determine a wide range of macroscopic transport properties such as conductivity, dielectric constant, diffusion coefficient, and transmittance. The Poisson model—a random tesselation of space by hyperplanes—provides realistic descriptions of heterogeneous media in, e.g., radiation-transport applications; yet, until now, it has lacked closed-form expressions for its multipoint correlations. We resolve this problem by presenting an exact solution for the multipoint correlations in the Poisson model. By comparing it to Monte Carlo simulations of four-point correlations in three dimensions, we demonstrate the accuracy of our solution. In conclusion, we visualize the multipoint correlations and discuss their features.

Amorphous materials↗
DOE OSTI2025

Kinematic flow from the flow of cuts

The wavefunction coefficients of conformally coupled scalars in power-law FRW cosmologies satisfy differential equations governed by a set of simple combinatorial rules known as the kinematic flow. In this paper we derive the kinematic flow, expressed using a set of differential forms referred to as the cut basis, from a geometric perspective, relying solely on the cosmological hyperplane arrangement and without invoking bulk physics. Each element of the cut basis corresponds to the positive geometry associated to an independent cut of the physical FRW-form and can be labeled by decorating (minors of) the truncated Feynman graph with an acyclic orientation. We provide a straightforward prescription to associate a logarithmic differential form to each element of the cut basis by considering its corresponding decorated graph. Moreover, we show that the residues of the physical FRW-form are canonical forms of certain graphical zonotopes labeled by the same set of decorated graphs. These zonotopes control the cut combinatorics -- flow of cuts -- of the physical FRW-form and the cut basis (by construction). Using the theory of relative twisted cohomology and intersection theory, we derive a closed form formula for the differential equations of the cut basis. We also introduce combinatorial rules that compute the kinematic differential of any basis element without explicit calculation. The combinatorics of our differential equations is a natural consequence of the flow of cuts and is equivalent (up to rescaling) to the kinematic flow for the recently studied time integral basis. In particular, our differential equations decouple into exponentially many sectors, one for each way of cutting a subset of edges of the graph.

General Relativity and Quantum Cosmology↗