Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “permutation”

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 73 records · Page 4

Permutation invariant potential energy surfaces for polyatomic reactions using atomistic neural networks

The applicability and accuracy of the Behler-Parrinello atomistic neural network method for fitting reactive potential energy surfaces is critically examined in three systems, H + H{sub 2} → H{sub 2} + H, H + H{sub 2}O → H{sub 2} + OH, and H + CH{sub 4} → H{sub 2} + CH{sub 3}. A pragmatic Monte Carlo method is proposed to make efficient choice of the atom-centered mapping functions. The accuracy of the potential energy surfaces is not only tested by fitting errors but also validated by direct comparison in dynamically important regions and by quantum scattering calculations. Our results suggest this method is both accurate and efficient in representing multidimensional potential energy surfaces even when dissociation continua are involved.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The signed permutation group on Feynman graphs

The Feynman rules assign to every graph an integral which can be written as a function of a scaling parameter L. Assuming L for the process under consideration is very small, so that contributions to the renormalization group are small, we can expand the integral and only consider the lowest orders in the scaling. The aim of this article is to determine specific combinations of graphs in a scalar quantum field theory that lead to a remarkable simplification of the first non-trivial term in the perturbation series. It will be seen that the result is independent of the renormalization scheme and the scattering angles. To achieve that goal we will utilize the parametric representation of scalar Feynman integrals as well as the Hopf algebraic structure of the Feynman graphs under consideration. Moreover, we will present a formula which reduces the effort of determining the first-order term in the perturbation series for the specific combination of graphs to a minimum.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Restoring permutational invariance in the Jordan–Wigner transformation

The Jordan–Wigner transformation is a powerful tool for converting systems of spins into systems of fermions, or vice versa. While this mapping is exact, the transformation itself depends on the labelling of the spins. One consequence of this dependence is that approximate solutions of a Jordan–Wigner-transformed Hamiltonian may depend on the (physically inconsequential) labelling of the spins. In this work, we turn to an extended Jordan–Wigner transformation which remedies this problem and which may also introduce some correlation atop the Hartree–Fock solution of a transformed spin Hamiltonian. We demonstrate that this extended Jordan–Wigner transformation can be thought of as arising from a unitary version of the Lie algebraic similarity transformation (LAST) theory. Here, we show how these ideas, particularly in combination with the standard (non-unitary) version of LAST, can provide a potentially powerful tool for the treatment of the XXZ and J 1 –J 2 Heisenberg Hamiltonians.

74 ATOMIC AND MOLECULAR PHYSICS↗

Split-helicity tree amplitudes and flag cluster algebras

Recent work has uncovered a connection between the symbol letters of general massless scattering and (permutations of) cluster variables of partial flag varieties. In this paper we explore the cluster adjacency of tree-level gluon amplitudes, specifically focusing on split-helicity amplitudes which can be written in closed form in terms of zigzag diagrams. We check in several cases, and conjecture in general, that the poles in each term satisfy cluster adjacency under a set of permutations that is built from arc permutations of the corresponding zigzag.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Biorefinery upgrading of herbaceous biomass to renewable hydrocarbon fuels, Part 2: Air pollutant emissions and permitting implications

The development of advanced biofuel production facilities is still at a nascent stage, and the biorefineries could face challenges in obtaining air permits required for their construction and operation because they are novel emission sources. To fill gaps in knowledge regarding potential emissions, we perform a detailed federal regulatory analysis and estimate air pollutant emissions for an advanced biorefinery that produces renewable diesel blendstock (RDB) from lignocellulosic biomass via aerobic respiration documented in Part 1 of the paper. We evaluate 12 design permutations that include two feedstocks, a uniform format blend (UFB) and corn stover; three biorefinery scales, 2,000, 5,200, and 9,100 dry metric tons per day (dmtd) of lignocellulosic biomass feed; and two lignin uses, as either a boiler fuel or for pellet production. We also evaluate 6 additional design permutations by incorporating non-emitting renewable power, which could reduce up to 63% carbon monoxide (CO) and nitrogen oxides (NO x ) each, 21% volatile organic compounds (VOC), and 43% hazardous air pollutants (HAP) as opposed to on-site power production, for biorefineries that produce pellets, using either UFB or corn stover. Our results indicate that all 18 design permutations would be classified as a major source under the Clean Air Act's New Source Review program without additional emission controls. Compared to using lignin as a boiler fuel, diverting lignin for pellet production reduces the emissions of CO up to 88%, NOx up to 73%, sulfur dioxide (SO 2 ) up to 99%, VOCs up to 72%, and HAPs up to 66%. Additionally, we explore control options that could further reduce emissions and assess whether reductions are enough to achieve minor source classification. Insights from our analysis can help biorefinery developers and regulators develop permitting strategies to mitigate investment risks.

09 BIOMASS FUELS↗