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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Novel superposed kinklike and pulselike solutions for several nonlocal nonlinear equations

In this work, we show that a number of nonlocal nonlinear equations, including the Ablowitz–Musslimani and Yang variant of the nonlocal nonlinear Schrödinger (NLS) equation, the nonlocal modified Korteweg de Vries (mKdV) equation, and the nonlocal Hirota equation, admit novel kinklike and pulselike superposed periodic solutions. Furthermore, we show that the nonlocal mKdV equation also admits the superposed (hyperbolic) kink–antikink solution. In addition, we show that while the nonlocal Ablowitz–Musslimani variant of the NLS admits complex parity-time reversal-invariant kink and pulse solutions, neither the local NLS nor the Yang variant of the nonlocal NLS admits such solutions. Finally, except for the Yang variant of the nonlocal NLS, we show that the other three nonlocal equations admit both the kink and pulse solutions in the same model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Constrained Tomographic Reconstructions of Gamma Scans in AGR 5/6/7 Capsules

We demonstrate a novel approach to locate potential areas of interest within individual capsules in the Advanced Gas Reactor 5/6/7 experiment. Individual capsules from the experiment have been scanned for gamma-emitting radioisotopes using the precision gamma spectrometer at Idaho National Laboratory’s hot fuel examination facility. Only a small number of scans were available, fewer than ten scan angles as opposed to a typical three hundred, so a geometry-informed algebraic reconstruction technique was used to provide qualitative information on high-activity regions in the capsule. While results are non-quantitative, some qualitative conclusions are drawn.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Modular flow in JT gravity and entanglement wedge reconstruction

It has been shown in recent works that JT gravity with matter with two boundaries has a type II ∞ algebra on each side. As the bulk spacetime between the two boundaries fluctuates in quantum nature, we can only define the entanglement wedge for each side in a pure algebraic sense. As we take the semiclassical limit, we will have a fixed long wormhole spacetime for a generic partially entangled thermal state (PETS), which is prepared by inserting heavy operators on the Euclidean path integral. Under this limit, with appropriate assumptions of the matter theory, geometric notions of the causal wedge and entanglement wedge emerge in this background. In particular, the causal wedge is manifestly nested in the entanglement wedge. Different PETS are orthogonal to each other, and thus the Hilbert space has a direct sum structure over sub-Hilbert spaces labeled by different Euclidean geometries. The full algebra for both sides is decomposed accordingly. From the algebra viewpoint, the causal wedge is dual to an emergent type III 1 subalgebra, which is generated by boundary light operators. To reconstruct the entanglement wedge, we consider the modular flow in a generic PETS for each boundary. We show that the modular flow acts locally and is the boost transformation around the global RT surface in the semiclassical limit. It follows that we can extend the causal wedge algebra to a larger type III 1 algebra corresponding to the entanglement wedge. Within each sub-Hilbert space, the original type II ∞ reduces to type III 1 .

2D Gravity↗
DOE OSTI2025

Foams and KZ-equations in Rozansky-Witten theories

In this paper, we present a geometric description of foams, which are prevalent in topological quantum field theories (TQFTs) based on quantum algebra, and reciprocally explore the geometry of Rozansky-Witten (RW) theory from an algebraic perspective. This approach illuminates various aspects of decorated TQFTs via geometry of the target space X of RW theory. Through the formulation of the Knizhnik-Zamolodchikov (KZ) equation within this geometric framework, we derive the corresponding braiding and associator morphisms. We discuss applications where the target space of RW theory emerges as the Coulomb branch of a compactified 6d SCFT or Little String Theory, with the latter being particularly intriguing as it results in a compact X.

Gukov, Sergei [California Institute of Technology,↗
DOE OSTI2024

Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints

The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. Open-source implementations of our methods accompany this work to facilitate reproduction and broader adoption.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Chiral algebra, localization, modularity, surface defects, and all that

We study the 2D vertex operator algebra (VOA) construction in 4D N = 2 superconformal field theories on S 3 × S 1 , focusing on both old puzzles and new observations. The VOA lives on a two-torus T 2 ⊂ S 3 × S 1 , it is 1 2 Z -graded, and this torus is equipped with the natural choice of spin structure (1,0) for the Z + 1 2 -graded operators, corresponding to the NS sector vacuum character. By analyzing the possible refinements of the Schur index that preserves the VOA, we find that it admits discrete deformations, which allows access to the remaining spin structures (1,1), (0,1), and (0,0), of which the latter two involve the inclusion of a particular surface defect. For Lagrangian theories, we perform the detailed analysis: we describe the natural supersymmetric background, perform localization, and derive the gauged symplectic boson action on a torus in any spin structure. In the absence of flavor fugacities, the 2D and 4D path integrals precisely match, including the Casimir factors. We further analyze the 2D theory: we identify its integration cycle and the two-point functions and interpret flavor holonomies as screening charges in the VOA. Next, we make some observations about modularity; the T-transformation acts on our four partition functions and lifts to a large diffeomorphism on S 3 × S 1 . More interestingly, we generalize the four partition functions on the torus to an infinite family labeled by both the spin structure and the integration cycle inside the complexified maximal torus of the gauge group. Members of this family transform into one another under the full modular group, and we confirm the recent observation that the S-transform of the Schur index in Lagrangian theories exhibits logarithmic behavior. Finally, we comment on how locally our background reproduces the Ω-background.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A new form of the Saint-Venant equations for variable topography

The solution stability of river models using the one-dimensional (1D) Saint-Venant equations can be easily undermined when source terms in the discrete equations do not satisfy the Lipschitz smoothness condition for partial differential equations. Although instability issues have been previously noted, they are typically treated as model implementation issues rather than as underlying problems associated with the form of the governing equations. This study proposes a new reference slope form of the Saint-Venant equations to ensure smooth slope source terms and eliminate one source of potential numerical oscillations. It is shown that a simple algebraic transformation of channel geometry provides a smooth reference slope while preserving the correct cross-section flow area and the total Piezometric pressure gradient that drives the flow. The reference slope method ensures the slope source term in the governing equations is Lipschitz continuous while maintaining all the underlying complexity of the real-world geometry. The validity of the mathematical concept is demonstrated with the open-source Simulation Program for River Networks (SPRNT) model in a series of artificial test cases and a simulation of a small urban creek. Validation comparisons are made with analytical solutions and the Hydrologic Engineering Center's River Analysis System (HEC-RAS) model. The new method reduces numerical oscillations and instabilities without requiring ad hoc smoothing algorithms.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Loop-by-loop differential equations for dual (elliptic) Feynman integrals

We present a loop-by-loop method for computing the differential equations of Feynman integrals using the recently developed dual form formalism. We give explicit prescriptions for the loop-by-loop fibration of multi-loop dual forms. Then, we test our formalism on a simple, but non-trivial, example: the two-loop three-mass elliptic sunrise family of integrals. We obtain an ε-form differential equation within the correct function space in a sequence of relatively simple algebraic steps. In particular, none of these steps relies on the analysis of q-series. Then, we discuss interesting properties satisfied by our dual basis as well as its simple relation to the known ε-form basis of Feynman integrands. The underlying K3-geometry of the three-loop four-mass sunrise integral is also discussed. Finally, we speculate on how to construct a “good” loop-by-loop basis at three-loop.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Commutative Algebra Modeling in Materials Science – A Case Study on Metal–Organic Frameworks (MOFs)

Metal-organic frameworks (MOFs) are a class of important crystalline and highly porous materials whose hierarchical geometry and chemistry hinder interpretable predictions in materials properties. Commutative algebra is a branch of abstract algebra that has been rarely applied in data and material sciences. We introduce the first ever commutative algebra modeling and prediction in materials science. Specifically, category-specific commutative algebra (CSCA) is proposed as a new framework for MOF representation and learning. It integrates element-based categorization with multiscale algebraic invariants to encode both local coordination motifs and global network organization of MOFs. These algebraically consistent, chemically aware representations enable compact, interpretable, and data efficient modeling of MOF properties such as Henry’s constants and uptake capacities for common gases. Compared to traditional geometric and graph-based approaches, CSCA achieves comparable or superior predictive accuracy while substantially improving interpretability and stability across data sets. By aligning commutative algebra with the chemical hierarchy, the CSCA establishes a rigorous and generalizable paradigm for understanding structure and property relationships in porous materials and provides a nonlinear algebra-based framework for data-driven material discovery.

Khaemba, Caleb S.↗
DOE OSTI2024

Soft scalars in effective field theory

We derive a soft theorem for a massless scalar in an effective field theory with generic field content using the geometry of field space. This result extends the geometric soft theorem for scalar effective field theories by allowing the massless scalar to couple to other scalars, fermions, and gauge bosons. The soft theorem keeps its geometric form, but where the field-space geometry now involves the full field content of the theory. As a bonus, we also present novel double soft theorems with fermions, which mimic the geometric structure of the double soft theorem for scalars.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Four lectures on Euler integrals

These lecture notes provide a self-contained introduction to Euler integrals, which are frequently encountered in applications. In particle physics, they arise as Feynman integrals or string amplitudes. Our four selected topics demonstrate the diverse mathematical techniques involved in the study of Euler integrals, including polyhedral geometry, very affine varieties, differential equations, and computational algebra.

Matsubara-Heo, Saiei-Jaeyeong↗
DOE OSTI2026

Nonlinear causality of Israel-Stewart theory with diffusion

We present the first fully nonlinear causality constraints in D = 3 + 1 dimensions for Israel-Stewart theory in the presence of energy and number diffusion in the Eckart and Landau hydrodynamic frames, respectively. These constraints are algebraic inequalities that make no assumption on the underlying geometry of the spacetime or the equation of state. In order to highlight the distinct physical and structural behavior of the two hydrodynamic frames, we discuss the special ultrarelativistic ideal gas equation of state considered in earlier literature in D = 1 + 1 dimensions, and show that our general D = 3 + 1 constraints reduce to their results upon an appropriate choice of angles. For this equation of state in both D = 1 + 1 and D = 3 + 1 dimensions one can show that: (i) there exists a region allowed by nonlinear causality in which the baryon current transitions into a spacelike vector in the Landau frame, and (ii) an analogous argument shows that the solutions of the Eckart frame equations of motion never violate the dominant energy condition, assuming nonlinear causality holds. Furthermore, we then compare our results with those from linearized Israel-Stewart theory and show that the linear causality bounds fail to capture the new physical constraints on energy and number diffusion that are successfully obtained through our nonlinear causality approach.

Quark-gluon plasma↗
DOE OSTI2021

Integrability, normal forms, and magnetic axis coordinates

Integrable or near-integrable magnetic fields are prominent in the design of plasma confinement devices. Such a field is characterized by the existence of a singular foliation entirely consisting of invariant submanifolds. A compact regular leaf (a flux surface) of this foliation must be diffeomorphic to the two-torus. In a neighborhood of a flux surface, it is known that the magnetic field admits several exact smooth normal forms in which the field lines are straight. However, these normal forms break down near singular leaves, including elliptic and hyperbolic magnetic axes. In this work, the existence of exact smooth normal forms for integrable magnetic fields near elliptic and hyperbolic magnetic axes is established. In the elliptic case, smooth near-axis Hamada and Boozer coordinates are defined and constructed. Ultimately, these results establish previously conjectured smoothness properties for smooth solutions of the magnetohydrodynamic equilibrium equations. The key arguments are a consequence of a geometric reframing of integrability and magnetic fields: they are presymplectic systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Bloch and Bethe Ansätze for the Harper model: A butterfly with a boundary

Based on a recent generalization of Bloch's theorem, herein we present a Bloch Ansatz for the Harper model with an arbitrary rational magnetic flux in various geometries, and solve the associated Ansatz equations analytically. In the case of a cylinder and a particular boundary condition, the energy spectrum of edge states has no dependence on the length of the cylinder, which allows us to construct a quasi-one-dimensional edge theory that is exact and describes two edges simultaneously. We prove that energies of bulk states, generating the so-called Hofstadter's butterfly, depend on a single geometry-dependent spectral parameter and have exactly the same functional form for the cylinder and the torus with general twisted boundary conditions, and argue that the (edge) bulk spectrum of a semi-infinite cylinder in an irrational magnetic field is (the complement of) a Cantor set. Finally, realizing that the bulk projection of the Harper Hamiltonian is a linear form over a deformed Weyl algebra, we introduce a Bethe Ansatz valid for both cylinder and torus geometries.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Rindler fluids from gravitational shockwaves

We study a correspondence between gravitational shockwave geometry and its fluid description near a Rindler horizon in Minkowski spacetime. Utilizing the Petrov classification that describes algebraic symmetries for Lorentzian spaces, we establish an explicit mapping between a potential fluid and the shockwave metric perturbation, where the Einstein equation for the shockwave geometry is equivalent to the incompressibility condition of the fluid, augmented by a shockwave source. Then we consider an Ansatz of a stochastic quantum source for the potential fluid, which has the physical interpretation of shockwaves created by vacuum energy fluctuations. Under such circumstance, the Einstein equation, or equivalently, the incompressibility condition for the fluid, becomes a stochastic differential equation. By smearing the quantum source on a stretched horizon in a Lorentz invariant manner with a Planckian width (similarly to the membrane paradigm), we integrate fluctuations near the Rindler horizon to find an accumulated effect of the variance in the round-trip time of a photon traversing the horizon of a causal diamond.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Deformation of Lie–Poisson algebras and chirality

Linearization of a Hamiltonian system around an equilibrium point yields a set of Hamiltonian symmetric spectra: If λ is an eigenvalue of the linearized generator, -λ and $\barλ$ (hence, -$\barλ$) are also eigenvalues—the former implies a time-reversal symmetry, while the latter guarantees the reality of the solution. However, linearization around a singular equilibrium point (which commonly exists in noncanonical Hamiltonian systems) works out differently, resulting in breaking of the Hamiltonian symmetry of spectra; time-reversal asymmetry causes chirality. This interesting phenomenon was first found in analyzing the chiral motion of the rattleback, a boat-shaped top having misaligned axes of inertia and geometry [Z. Yoshida et al., Phys. Lett. A 381, 2772–2777 (2017)]. To elucidate how chiral spectra are generated, we study the three-dimensional Lie–Poisson systems and classify the prototypes of singularities that cause symmetry breaking. The central idea is the deformation of the underlying Lie algebra; invoking Bianchi’s list of all three-dimensional Lie algebras, we show that the so-called class-B algebras, which are produced by asymmetric deformations of the simple algebra s o ( 3 ) , yield chiral spectra when linearized around their singularities. The theory of deformation is generalized to higher dimensions, including the infinite-dimensional Poisson manifolds relevant to fluid mechanics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Algebraic Structures in the Coupling of Gravity to Gauge Theories

Highlights: • Geometric foundation for Quantum General Relativity coupled to Quantum Electrodynamics. • Rigorous introduction to Hopf algebraic renormalization. • Appropriate modifications in case renormalization Hopf algebra is ill-defined. • Generalization of Furry’s Theorem to include gravitons and ghosts. • Discussion of obstructions to multiplicative renormalization. This article is an extension of the author’s second master thesis, Prinz (2017). It aims to introduce to the theory of perturbatively quantized General Relativity coupled to Spinor Electrodynamics, provide the results thereof and set the notation to serve as a starting point for further research in this direction. It includes the differential geometric and Hopf algebraic background, as well as the corresponding Lagrange density and some renormalization theory. Then, a particular problem in the renormalization of Quantum General Relativity coupled to Quantum Electrodynamics is addressed and solved by a generalization of Furry’s Theorem. Next, the restricted combinatorial Green’s functions for all two-loop propagators and all one-loop divergent subgraphs thereof are presented. Finally, relations between these one-loop restricted combinatorial Green’s functions necessary for multiplicative renormalization are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗