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Results for “Integrable Field Theories”

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 OSTI2024

Infinite Family of Integrable Sigma Models Using Auxiliary Fields

We introduce a class of 2D sigma models which are parametrized by a function of one variable. In addition to the physical field g , these models include an auxiliary field v α which mediates interactions in a prescribed way. We prove that every theory in this family is classically integrable, in that it possesses an infinite set of conserved charges in involution, which can be constructed from a Lax representation for the equations of motion. This class includes the principal chiral model (PCM) and all deformations of the PCM by functions of the energy-momentum tensor. Published by the American Physical Society 2024

Physics↗
DOE OSTI2025

LLM Generation of Online Courses from a Curated Set of Documents in the Nuclear Safeguards Domain

A multidisciplinary team at Argonne National Laboratory explores the application of advanced technologies to enhance knowledge transfer and retention within the nuclear safeguards domain. Specifically, it examines the feasibility of leveraging secure large language models (LLMs) to streamline the creation of e-learning modules for the U.S. National Nuclear Security Administration (NNSA) Office of International Nuclear Safeguards (NA-241). The initiative addresses the critical need for preserving institutional memory and accelerating skill development amidst the imminent retirement of senior professionals in the field in addition to supporting good knowledge management practices. The project integrates instructional design theory with cutting-edge AI technologies to transform curated document sets from the Safeguards Knowledge Repository (SKR) into modular online courses. By automating the generation of learning objectives and instructional content, the effort aims to reduce manual effort while maintaining high-quality educational outcomes. A limited measure of human supervision, however, ensures accuracy, relevance, and alignment with NNSA’s strategic priorities. Key findings highlight the potential of AI-assisted course generation to support safeguards professionals by creating structured, interactive learning experiences. The report underscores the importance of SME validation to address limitations in AI-generated content, such as terminology errors and gaps in coverage. Recommendations include adopting a structured workflow combining LLM acceleration with expert oversight to ensure accuracy, usability, and alignment with learner needs. This work demonstrates Argonne’s commitment to advancing national security and scientific excellence through innovative knowledge management solutions.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2024

Thermodynamic stability of a spin microemulsion in Rashba spin-orbit-coupled bosons

Recent finite-temperature numerical simulations have unveiled a quantum “spin” microemulsion analog, found by raising the temperature of a stripe supersolid phase in a Rashba spin-orbit coupled Bose gas. This microemulsion state is a highly correlated, isotropic normal fluid where atoms self-arrange based on their internal pseudospin into patterns that resemble bicontinuous microemulsions. This finding leaves several open questions regarding the broader accessibility of this phase in experiments. Here, we use equilibrium finite-temperature numerical simulations based on a coherent-state path integral representation to perform a computational investigation into the thermodynamic stability of the spin microemulsion state. Numerical simulations emphasize the requirement of a nearly, but not perfectly, isotropic spin-orbit coupling in order to achieve the microemulsion phase in cold-atom experiments. Moreover, the microemulsion state exists independent of miscibility of the pseudospin components and for a wide range of pseudospin population imbalance, suggesting a high degree of flexibility in choosing the atom and hyperfine states in an experimental realization. Lastly, we demonstrate this feasibility by mimicking a Rashba spin-orbit-coupled 87 Rb experiment in an isotropic harmonic trap, where we confirm the microemulsion's existence via its density profile and equilibrium quasimomentum distribution.

Complex Langevin dynamics↗
NASA NTRS1992

MOM3D method of moments code theory manual

MOM3D is a FORTRAN algorithm that solves Maxwell's equations as expressed via the electric field integral equation for the electromagnetic response of open or closed three dimensional surfaces modeled with triangle patches. Two joined triangles (couples) form the vector current unknowns for the surface. Boundary conditions are for perfectly conducting or resistive surfaces. The impedance matrix represents the fundamental electromagnetic interaction of the body with itself. A variety of electromagnetic analysis options are possible once the impedance matrix is computed including backscatter radar cross section (RCS), bistatic RCS, antenna pattern prediction for user specified body voltage excitation ports, RCS image projection showing RCS scattering center locations, surface currents excited on the body as induced by specified plane wave excitation, and near field computation for the electric field on or near the body.

Shaeffer, John F.↗
DOE OSTI2025

16 O Electroweak Response Functions from First Principles

We present calculations of various electroweak response functions for the 16 O nucleus obtained using coupled-cluster theory in conjunction with the Lorentz integral transform method. We employ nuclear forces derived at next-to-leading order and next-to-next-to-leading order in chiral effective field theory and perform a Bayesian analysis to assess uncertainties. Our results are in good agreement with available electron-scattering data at |𝐪|≈326 MeV/c. Additionally, we provide several predictions for the weak response functions in the quasielastic peak region at |𝐪| =300 and 400 MeV/c, which are critical for long-baseline neutrino experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1971

Numerical solution of stiff systems of ordinary differential equations with applications to electronic circuits

Systems of ordinary differential equations in which the magnitudes of the eigenvalues (or time constants) vary greatly are commonly called stiff. Such systems of equations arise in nuclear reactor kinetics, the flow of chemically reacting gas, dynamics, control theory, circuit analysis and other fields. The research reported develops an A-stable numerical integration technique for solving stiff systems of ordinary differential equations. The method, which is called the generalized trapezoidal rule, is a modification of the trapezoidal rule. However, the method is computationally more efficient than the trapezoidal rule when the solution of the almost-discontinuous segments is being calculated.

Rosenbaum, J. S.↗
NASA NTRS1994

The transition from diapirism to dike intrusion: Implications for planetary volcanism

Magma transport processes influence the rate of magma transport and how far the magma travels before it freezes, the degree to which the magma communicates chemically with the host rock, the morphology of volcanic landforms on planetary surfaces, the interplay between magmatism and regional tectonics, and even the direction the magma moves. The primary question motivating this research is: How does magma rheology influence the mechanisms by which it is transported through planetary lithospheres? It is widely recognized that on Earth basaltic intrusions typically take the form of narrow dikes, while granites are typically found in more equidimensional plutons. Several explanations for this observation were offered over the last 50 years. While basalts and rhyolites vary somewhat in temperature and density, the major difference is the 2 to 8 orders of magnitude contrast in viscosity. The significant ductile strains associated with many granitic plutons has led to the statement that the occurrence of granites in diapirs rather than dikes results from the fact that there is insufficient viscosity contrast between the magma and wall rock for the granite to intrude narrow cracks. A second explanation states that granites are so viscous that they cannot propagate far before freezing. Despite the length of time these explanations have been around, there has been relatively little effort to investigate them quantitatively. My goal has been to evaluate these explanations through a series of well-posed numerical models. These models can be tested by the decades of field data collected by structural geologists that have yet to be integrated into any coherent theory, and the results should have important implications for volcanism on the terrestrial planets.

Rubin, Allan M.↗
NASA NTRS1985

A multiple scattering theory for EM wave propagation in a dense random medium

For a dense medium of randomly distributed scatterers an integral formulation for the total coherent field has been developed. This formulation accounts for the multiple scattering of electromagnetic waves including both the twoand three-particle terms. It is shown that under the Markovian assumption the total coherent field and the effective field have the same effective wave number. As an illustration of this theory, the effective wave number and the extinction coefficient are derived in terms of the polarizability tensor and the pair distribution function for randomly distributed small spherical scatterers. It is found that the contribution of the three-particle term increases with the particle size, the volume fraction, the frequency and the permittivity of the particle. This increase is more significant with frequency and particle size than with other parameters.

Karam, M. A.↗
NASA NTRS1996

Artificial Boundary Conditions Based on the Difference Potentials Method

While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears to be most significant in many areas of scientific computing, for example, in problems originating from acoustics, electrodynamics, solid mechanics, and fluid dynamics. In particular, in computational fluid dynamics (where external problems present a wide class of practically important formulations) the proper treatment of external boundaries may have a profound impact on the overall quality and performance of numerical algorithms. Most of the currently used techniques for setting the ABC's can basically be classified into two groups. The methods from the first group (global ABC's) usually provide high accuracy and robustness of the numerical procedure but often appear to be fairly cumbersome and (computationally) expensive. The methods from the second group (local ABC's) are, as a rule, algorithmically simple, numerically cheap, and geometrically universal; however, they usually lack accuracy of computations. In this paper we first present a survey and provide a comparative assessment of different existing methods for constructing the ABC's. Then, we describe a relatively new ABC's technique of ours and review the corresponding results. This new technique, in our opinion, is currently one of the most promising in the field. It enables one to construct such ABC's that combine the advantages relevant to the two aforementioned classes of existing methods. Our approach is based on application of the difference potentials method attributable to V. S. Ryaben'kii. This approach allows us to obtain highly accurate ABC's in the form of certain (nonlocal) boundary operator equations. The operators involved are analogous to the pseudodifferential boundary projections first introduced by A. P. Calderon and then also studied by R. T. Seeley. The apparatus of the boundary pseudodifferential equations, which has formerly been used mostly in the qualitative theory of integral equations and PDE'S, is now effectively employed for developing numerical methods in the different fields of scientific computing.

Tsynkov, Semyon V.↗
NASA NTRS1997

The Reduction of Ducted Fan Engine Noise Via A Boundary Integral Equation Method

The development of a Boundary Integral Equation Method (BIEM) for the prediction of ducted fan engine noise is discussed. The method is motivated by the need for an efficient and versatile computational tool to assist in parametric noise reduction studies. In this research, the work in reference 1 was extended to include passive noise control treatment on the duct interior. The BEM considers the scattering of incident sound generated by spinning point thrust dipoles in a uniform flow field by a thin cylindrical duct. The acoustic field is written as a superposition of spinning modes. Modal coefficients of acoustic pressure are calculated term by term. The BEM theoretical framework is based on Helmholtz potential theory. A boundary value problem is converted to a boundary integral equation formulation with unknown single and double layer densities on the duct wall. After solving for the unknown densities, the acoustic field is easily calculated. The main feature of the BIEM is the ability to compute any portion of the sound field without the need to compute the entire field. Other noise prediction methods such as CFD and Finite Element methods lack this property. Additional BIEM attributes include versatility, ease of use, rapid noise predictions, coupling of propagation and radiation both forward and aft, implementable on midrange personal computers, and valid over a wide range of frequencies.

Tweed, J.↗
NASA NTRS1982

Utilizing numerical techniques in turbofan inlet acoustic suppressor design

Numerical theories in conjunction with previously published analytical results are used to augment current analytical theories in the acoustic design of a turbofan inlet nacelle. In particular, a finite element-integral theory is used to study the effect of the inlet lip radius on the far field radiation pattern and to determine the optimum impedance in an actual engine environment. For some single mode JT15D data, the numerical theory and experiment are found to be in a good agreement.

Baumeister, K. J.↗
NASA NTRS1992

Electron acceleration in Tycho's and Kepler's supernova remnants - Spectral evidence of Fermi shock acceleration

First model synchrotron spectra calculated with a self-consistent nonlinear shock model of first order Fermi acceleration are presented and compared with the observed radio spectra of Tycho's and Kepler's SNR. Excellent agreement is obtained, and the correct mean spectral indices of about -0.64 are easily reproduced. The model spectra are slightly concave, with hardening toward higher energies, and there is evidence for such an effect in the data, allowing the mean magnetic field strength to be estimated in each remnant. Improvements in both theory and observation could allow accurate values of magnetic fields to be inferred from sufficiently precise integrated synchrotron spectra.

Reynolds, Stephen P.↗
DOE OSTI2026

Global anomalies of Green's function zeros.

We study global anomalies of nonlocal effective theories proposed to describe symmetry-preserving Luttinger surfaces, i.e., the momentum-space manifolds of Green’s function zeros (GFZs) at zero energy, in strongly interacting fermionic systems. In particular, we focus on the simplest possible cases associated with a gapless Dirac zero, which is the counterpart of the gapless Dirac quasiparticle in weakly interacting systems. These theories may be derived by integrating out low-energy degrees of freedom that do not couple to the relevant gauge field. We discuss the global anomaly, the bulk-boundary correspondence, and the constraint on phases consistent with the anomaly, such as non-Fermi liquids and emergent gapless quasiparticles on Luttinger surfaces. Failing to avoid spontaneous symmetry breaking in the thermodynamical limit inevitably leads to unstable GFZs. We also provide some perspective on why the related nonlocal fermionic effective theory studied recently is not a suitable starting point for a symmetrically gapped phase

Su, Lei↗
DOE OSTI2024

Improving modular bootstrap bounds with integrality

We propose methods that efficiently impose integrality — i.e., the condition that the coefficients of characters in the partition function must be integers — into numerical modular bootstrap. We demonstrate the method with a number of examples where it can be used to strengthen modular bootstrap results. First, we show that, with a mild extra assumption, imposing integrality improves the bound on the maximal allowed gap in dimensions of operators in theories with a U(1) c symmetry at c = 3, and reduces it to the value saturated by the SU(4) 1 WZW model point of c = 3 Narain lattices moduli space. Second, we show that our method can be used to eliminate all but a discrete set of points saturating the bound from previous Virasoro modular bootstrap results. Finally, when central charge is close to 1, we can slightly improve the upper bound on the scaling dimension gap.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1980

Vector analogues of the Maggi-Rubinowicz theory of edge diffraction

The Maggi-Rubinowicz technique for scalar and electromagnetic fields is interpreted as a transformation of an integral over an open surface to a line integral around its rim. Maggi-Rubinowicz analogues are found for several vector physical optics representations. For diffraction from a circular aperture, a numerical comparison between these formulations shows the two methods are in agreement. To circumvent certain convergence difficulties in the Maggi-Rubinowicz integrals that occur as the observer approaches the shadow boundary, a variable mesh integration is used. For the examples considered, where the ratio of the aperture diameter to wavelength is about ten, the Maggi-Rubinowicz formulation yields an 8 to 10 fold decrease in computation time relative to the physical optics formulation.

Meneghini, R.↗
NASA NTRS1989

Designing ceramic components with the CARES computer program

NASA-Lewis has developed a public-domain computer program, designated 'Ceramic Analysis and Reliability Evaluation of Structures' (CARES) for calculating the fast-fracture reliability of macroscopically isotropic ceramic components subjected to the complex thermomechanical loadings typical of heat engines. The design methodology employed by CARES encompasses linear elastic fracture mechanics theory, extreme value statistics, and material microstructures; component integrity is conceived as a function of the entire field solution of the stresses, rather than being based solely on the most highly stressed point.

Nemeth, Noel N.↗
NASA NTRS1993

A theory for the fracture of thin plates subjected to bending and twisting moments

Stress fields near the tip of a through crack in an elastic plate under bending and twisting moments are reviewed assuming both Kirchhoff and Reissner plate theories. The crack tip displacement and rotation fields based on the Reissner theory are calculated. These results are used to calculate the J-integral (energy release rate) for both Kirchhoff and Reissner plate theories. Invoking Simmonds and Duva's (1981) result that the value of the J-integral based on either theory is the same for thin plates, a universal relationship between the Kirchhoff theory stress intensity factors and the Reissner theory stress intensity factors is obtained for thin plates. Calculation of Kirchhoff theory stress intensity factors from finite elements based on energy release rate is illustrated. It is proposed that, for thin plates, fracture toughness and crack growth rates be correlated with the Kirchhoff theory stress intensity factors.

Hui, C. Y.↗