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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Threshold progressions in covering and packing contexts

Here, using standard methods (due to Janson, Stein–Chen, and Talagrand) from probabilistic combinatorics, we explore the following general theme: As one progresses from each member of a family of objects $\mathcal{A}$ being “covered” by at most one object in a random collection $\mathcal{C}$, to being covered at most λ times, to being covered at least once, to being covered at least λ times, a hierarchy of thresholds emerge. We will use examples from extremal set theory, combinatorics, and additive number theory to see how these results vary according to the context, and level of dependence introduced.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Beurling-Selberg extremization and modular bootstrap at high energies

We consider previously derived upper and lower bounds on the number of operators in a window of scaling dimensions [\Delta - \delta,\Delta + \delta] [ Δ − δ , Δ + δ ] at asymptotically large \Delta Δ in 2d unitary modular invariant CFTs. These bounds depend on a choice of functions that majorize and minorize the characteristic function of the interval [\Delta - \delta,\Delta + \delta] [ Δ − δ , Δ + δ ] and have Fourier transforms of finite support. The optimization of the bounds over this choice turns out to be exactly the Beurling-Selberg extremization problem, widely known in analytic number theory. We review solutions of this problem and present the corresponding bounds on the number of operators for any \delta \geq 0 δ ≥ 0 . When 2\delta \in \mathbb Z_{\geq 0} 2 δ ∈ ℤ ≥ 0 the bounds are saturated by known partition functions with integer-spaced spectra. Similar results apply to operators of fixed spin and Virasoro primaries in c>1 c > 1 theories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Nucleation Rate Theory for Coordination Number: Elucidating Water-Mediated Formation of a Zigzag Na 2 SO 4 Morphology

Predicting and controlling nanostructure formation during nucleation can pave the way to synthesizing novel energy materials via crystallization. However, such control over nucleation and crystallization remains challenging due to an inadequate understanding of critical factors that govern evolving atomistic structures and dynamics. Here, in this paper, we utilize coordination number as a reaction coordinate and rate theory to investigate how sodium sulfate, commonly known as a phase-change energy material, nucleates in a supersaturated aqueous solution. In conjunction with ab initio and force field-based molecular dynamics simulation, the rate theoretical analysis reveals that sodium sulfate from an initially dissolved metastable state transits to a heterogeneous mixture of prenucleated clusters and finally to a large cylindrical zigzag morphology. Measurements of Raman spectra and their ab initio modeling confirm that this nucleated morphology contains a few waters for every sulfate. Rate processes such as solvent exchange and desolvation exhibit high sensitivity to the evolving prenucleation/nucleation structures, providing a means to distinguish between critical nucleation precursors. Desolvation and forming the first-shell interionic coordination structure via monomer-by-monomer addition around sulfates are found to explain the formation of large nuclei. Thus, a detailed understanding of the step-by-step structure formation across scales has been achieved. This can be leveraged to predict nucleation-related structures and dynamics and potentially control the synthesis of novel phase-change materials for energy applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Vector boson pair production at one loop: analytic results for the process $q\bar{q}$$ℓ\bar{ℓ}$$ℓ'\bar{ℓ}'g$

We present compact analytic results for the one-loop amplitude for the process 0 → $q\bar{q}$$ℓ\bar{ℓ}$$ℓ'\bar{ℓ}'g$, relevant for both the production of a pair of Z and W-bosons in association with a jet. We focus on the gauge-invariant contribution mediated by a loop of quarks. We explicitly include all effects of the loop-quark mass m, appropriate for the production of a pair of Z-bosons. In the limit m → 0, our results are also applicable to the production of W-boson pairs, mediated by a loop of massless quarks. Implemented in a numerical code, the results are fast. The calculation uses novel advancements in spinor-helicity simplification techniques, for the first time applied beyond five-point massless kinematics. We make use of primary decompositions from algebraic-geometry, which now involve non-radical ideals, and p-adic numbers from number theory. We show how to infer whether numerator polynomials belong to symbolic powers of non-radical ideals through numerical evaluations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Perovskite neural trees

Trees are used by animals, humans and machines to classify information and make decisions. Natural tree structures displayed by synapses of the brain involves potentiation and depression capable of branching and is essential for survival and learning. Demonstration of such features in synthetic matter is challenging due to the need to host a complex energy landscape capable of learning, memory and electrical interrogation. We report experimental realization of tree-like conductance states at room temperature in strongly correlated perovskite nickelates by modulating proton distribution under high speed electric pulses. This demonstration represents physical realization of ultrametric trees, a concept from number theory applied to the study of spin glasses in physics that inspired early neural network theory dating almost forty years ago. We apply the tree-like memory features in spiking neural networks to demonstrate high fidelity object recognition, and in future can open new directions for neuromorphic computing and artificial intelligence.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Topological aspects of matters and Langlands program

The Langlands program is a vast mathematical projection linking number theory and geometry. In high-energy physics, a connection with mirror symmetry has been suggested in string theory, but it has been little studied in low-energy physics. In the framework of the Langlands program, we present a unified description of the integer and fractional quantum Hall effect and the duality found in the fractal nature of the energy spectrum of two-dimensional Bloch electrons, statistical physics, and quantum computation. The new unified view of existing dualism presented in this paper raises the entirely new question of how each theory of physics is connected as a piece of the Langlands program.

Physics↗
DOE OSTI2023

Hardware-Conscious Optimization of the Quantum Toffoli Gate

While quantum computing holds great potential in combinatorial optimization, electronic structure calculation, and number theory, the current era of quantum computing is limited by noisy hardware. Many quantum compilation approaches can mitigate the effects of imperfect hardware by optimizing quantum circuits for objectives such as critical path length. Few approaches consider quantum circuits in terms of the set of vendor-calibrated operations (i.e., native gates) available on target hardware. This manuscript expands the analytical and numerical approaches for optimizing quantum circuits at this abstraction level. We present a procedure for combining the strengths of analytical native gate-level optimization with numerical optimization. Although we focus on optimizing Toffoli gates on the IBMQ native gate set, the methods presented are generalizable to any gate and superconducting qubit architecture. Our optimized Toffoli gate implementation demonstrates an 18% reduction in infidelity compared with the canonical implementation as benchmarked on IBM Jakarta with quantum process tomography. Assuming the inclusion of multi-qubit cross-resonance (MCR) gates in the IBMQ native gate set, we produce Toffoli implementations with only six multi-qubit gates, a 25% reduction from the canonical eight multi-qubit implementations for linearly connected qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Evaluating one-loop string amplitudes

We evaluate one-loop open-string amplitudes at finite \alpha' α ′ for the first time. Our method involves a deformation of the integration contour over the modular parameter \tau τ to a fractal contour introduced by Rademacher in the context of analytic number theory. This procedure leads to explicit and practical formulas for the one-loop four-point amplitudes in type-I superstring theory, amenable to numerical evaluation. We plot the amplitudes as a function of the Mandelstam invariants s s and t t and directly verify long-standing conjectures about their behaviour at high energies.

Eberhardt, Lorenz↗
DOE OSTI2024

Hartree–Fock–Bogoliubov theory for number-parity-violating fermionic Hamiltonians

It is usually asserted that physical Hamiltonians for fermions must contain an even number of fermion operators. This is indeed true in electronic structure theory. However, when the Jordan–Wigner (JW) transformation is used to map physical spin Hamiltonians to Hamiltonians of spinless fermions, terms that contain an odd number of fermion operators may appear. The resulting fermionic Hamiltonian thus does not have number parity symmetry and requires wave functions that do not have this symmetry either. In this work, we discuss the extension of standard Hartree–Fock–Bogoliubov (HFB) theory to the number-parity-nonconserving case. These ideas had appeared in the literature before but, perhaps for lack of practical applications, had, to the best of our knowledge, never been employed. We here present a useful application for this more general HFB theory based on coherent states of the SO(2M + 1) Lie group, where M is the number of orbitals. Here, we also show how using these unusual mean-field states can provide significant improvements when studying the JW transformation of chemically relevant spin Hamiltonians.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Scattering matrix pole expansions for complex wave numbers in R -matrix theory

In this followup article to Ducru et al., we establish new results on scattering matrix pole expansions for complex wave numbers in R-matrix theory. In the past, two branches of theoretical formalisms emerged to describe the scattering matrix in nuclear physics: R-matrix theory and pole expansions. The two have been quite isolated from one another. Recently, our study of Brune's alternative parametrization of R-matrix theory has shown the need to extend the scattering matrix (and the underlying R-matrix operators) to complex wave numbers. Two competing ways of doing so have emerged from a historical ambiguity in the definitions of the shift S and penetration P functions: the legacy Lane and Thomas's “force closure” approach versus analytic continuation (which is the standard in mathematical physics). The R-matrix community has not yet come to a consensus as to which to adopt for evaluations in standard nuclear data libraries, such as ENDF. Here, in this article, we argue in favor of analytic continuation of R-matrix operators. We bridge R-matrix theory with the Humblet-Rosenfeld pole expansions, and discover new properties of the Siegert-Humblet radioactive poles and widths, including their invariance properties to changes in channel radii a c . We then show that analytic continuation of R-matrix operators preserves important physical and mathematical properties of the scattering matrix—canceling spurious poles and guaranteeing generalized unitarity—while still being able to close channels below thresholds.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Excitation energy of fission fragments within nuclear time-dependent density functional theory

The number and properties of the neutrons and photons emitted in nuclear fission are directly related to the excitation energy of the fission fragments when they are formed at scission. Though not observable experimentally because of the extremely short timescales, the excitation energy of fission fragments can be predicted by microscopic theory based on time-dependent density functional theory (TDDFT). Initial results on the value of the total kinetic energy of fission reactions were very promising, but could not probe all possible fragmentations. Here, in this work, we perform large-scale TDDFT calculations in 240 Pu enabled by the development of a new TDDFT solver. We obtain TDDFT trajectories covering nearly all possible fragmentations. We find that the total kinetic energy is close to experimental values only for the most likely fission while it is severely underestimated at both small and large asymmetries. This conclusion seems rather independent of the parametrization of the energy functional, both in its particle-hole and particle-particle channels.

Physics - Nuclear physics and radiation physics↗
DOE OSTI2025

Foaming prediction in pure liquids from dimensionless numbers inspired by the theory of fluid behavior for drops

Foaming prediction is critical for selecting materials and designing processes in industries such as bioprocessing and gas processing. Existing models lack the generality needed for a wide range of materials and overlook the foaming behavior in pure liquids. Here, this work presents a novel method for predicting foaming in pure liquids based on their density, surface tension, and viscosity, using Reynolds ( Re ) and Ohnesorge ( Oh ) numbers. A foaming prediction map, leveraging the theory of fluid drop behavior, was developed by plotting these numbers. This map delineates distinct non-foaming and foaming regions, functioning as a binary classifier for foaming predictions. The map was fitted and validated through shake test experiments on 46 liquids, demonstrating reliable predictions, except for a specific region characterized by small Oh and large Re numbers. This region corresponded to relatively low foam stability and high turbulence, making foaming predictions challenging for liquids in this category.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Emergence of the polydeterminant in QCD

A generalization of the determinant appears in particle physics in effective Lagrangian interaction terms that model the chiral anomaly in quantum chromodynamics (Giacosa et al. in Phys Rev D 97(9):091901, 2018, Phys Rev D 109(7):L071502, 2024), in particular in connection to mesons. This polydeterminant function, known in the mathematical literature as a mixed discriminant, associates N distinct N x N complex matrices into a complex number and reduces to the usual determinant when all matrices are taken as equal. Here, we explore the main properties of the polydeterminant applied to (quantum) fields by using a formalism and a language close to high-energy physics approaches. We discuss its use as a tool to write down novel chiral anomalous Lagrangian terms and present an explicit illustrative model for mesons. Finally, the extension of the polydeterminant as a function of tensors is shown.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Observation of a linked-loop quantum state in a topological magnet

Quantum phases can be classified by topological invariants, which take on discrete values capturing global information about the quantum state. Over the past decades, these invariants have come to play a central role in describing matter, providing the foundation for understanding superfluids, magnets, the quantum Hall effect, topological insulators, Weyl semimetals and other phenomena. Here we report an unusual linking-number (knot theory) invariant associated with loops of electronic band crossings in a mirror-symmetric ferromagnet. Using state-of-the-art spectroscopic methods, we directly observe three intertwined degeneracy loops in the material's three-torus, T 3 , bulk Brillouin zone. We find that each loop links each other loop twice. Through systematic spectroscopic investigation of this linked-loop quantum state, we explicitly draw its link diagram and conclude, in analogy with knot theory, that it exhibits the linking number (2, 2, 2), providing a direct determination of the invariant structure from the experimental data. Here we further predict and observe, on the surface of our samples, Seifert boundary states protected by the bulk linked loops, suggestive of a remarkable Seifert bulk-boundary correspondence. Our observation of a quantum loop link motivates the application of knot theory to the exploration of magnetic and superconducting quantum matter.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Hilbert series for covariants and their applications to minimal flavor violation

We elaborate how to apply the Hilbert series method to enumerating group covariants, which transform under any given representation, including but going beyond group invariants. Mathematically, group covariants form a module over the ring of the invariants. The number of independent covariants is given by the rank of the module, which can be computed by taking a ratio of two Hilbert series. In many cases, the rank equals the dimension of the group covariant representation. When this happens, we say that there is a rank saturation. We apply this technology to revisit the hypothesis of Minimal Flavor Violation in constructing Effective Field Theories beyond the Standard Model. We find that rank saturation is guaranteed in this case, leading to the important consequence that the MFV symmetry principle does not impose any restriction on the EFT, i.e. MFV SMEFT = SMEFT, in the absence of additional assumptions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Open momentum space method for the Hofstadter butterfly and the quantized Lorentz susceptibility

Here we develop a generic k ∙ p open momentum space method for calculating the Hofstadter butterfly of both continuum (moiré) models and tight-binding models, where the quasimomentum is directly substituted by the Landau level (LL) operators. By taking a LL cutoff (and a reciprocal lattice cutoff for continuum models), one obtains the Hofstadter butterfly with in-gap spectral flows. For continuum models such as the moiré model for twisted bilayer graphene, our method gives a sparse Hamiltonian, making it much more efficient than existing methods. The spectral flows in the Hofstadter gaps can be understood as edge states on a momentum space boundary, from which one can determine the two integers (t ν , s ν ) of a gap ν satisfying the Diophantine equation. The spectral flows can also be removed to obtain a clear Hofstadter butterfly. While t ν is known as the Chern number, our theory identifies s ν as a dual Chern number for the momentum space, which corresponds to a quantized Lorentz susceptibility γ xy = eBs ν .

2-dimensional systems↗