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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Singular value decomposition and similarity renormalization group evolution of nuclear interactions

One of the main challenges for ab initio nuclear many-body theory is the growth of computational and storage costs as calculations are extended to heavy, exotic, and structurally complex nuclei. Here, we investigate the factorization of nuclear interactions as a means to address this issue. We perform Singular Value Decompositions of nucleon-nucleon interactions in partial wave representation and study the dependence of the singular value spectrum on interaction characteristics like regularization scheme and resolution scales. We develop and implement the Similarity Renormalization Group (SRG) evolution of the factorized interaction, and demonstrate that this SVD-SRG approach accurately preserves two-nucleon observables. We find that low-resolution interactions allow the truncation of the SVD at low rank, and that a small number of relevant components is sufficient to capture the nuclear interaction and perform an accurate SRG evolution, while the Coulomb interaction requires special consideration. The rank is uniform across all partial waves, and almost independent of the basis choice in the tested cases. This suggests an interpretation of the relevant singular components as mere representations of a small set of abstract operators that can describe the interaction and its SRG flow. Following the traditional workflow for nuclear interactions, we discuss how the transformation between the center-of-mass and laboratory frames creates redundant copies of the partial wave components when implemented in matrix representation, and we discuss strategies for mitigation. Lastly, we test the low-rank approximation to the SRG-evolved interactions in many-body calculations using the In-Medium SRG. By including nuclear radii in our analysis, we verify that the implementation of the SRG using the singular vectors of the interaction does not spoil the evolution of other observables.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Code verification for practically singular equations

We report the method-of-moments implementation of the electric-field integral equation (EFIE) yields many code-verification challenges due to the various sources of numerical error and their possible interactions. Matters are further complicated by singular integrals, which arise from the presence of a Green's function. To address these singular integrals, an approach is presented in wherein both the solution and Green's function are manufactured. Because the arising equations are poorly conditioned, they are reformulated as a set of constraints for an optimization problem that selects the solution closest to the manufactured solution. In this paper, we demonstrate how, for such practically singular systems of equations, computing the truncation error by inserting the exact solution into the discretized equations cannot detect certain orders of coding errors. On the other hand, the discretization error from the optimal solution is a more sensitive metric that can detect orders less than those of the expected convergence rate.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

The infinite level normal forms for non-resonant double Hopf singularities

Here, in this paper, we explore hypernormal forms of vector fields that have non-resonant double Hopf singularities with a non-zero radial cubic part. Our primary focus is on investigating the infinite-level normal form classification of this type of singularities. We provide a normal form decomposition in terms of planar-rotating and planar-radial vector fields, which greatly facilitate the pattern recognition and analysis of the corresponding generalized homological maps. Notably, our paper represents the first instance of the normal form classification for general non-resonant double Hopf singularities without structural symmetry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Unified wavefront singularity characterization of three-dimensional elastodynamic time-domain half-space Green's function under impulsive boundary and internal loads

Founded on a novel analytical formulation that led to a rigorous yet compact path-integral representation of the time-domain elastodynamic half-space Green's function, a unified analysis of the possible occurrence of different singular wavefront behaviour in the response under arbitrary impulsive internal or surface point loads at arbitrary source-receiver locations is presented. With the decomposition of the general solution into distinct initiating and reflected wave group integrals that share a common factored format and simple contour definitions, the mathematical framework is shown to allow a straightforward identification of the specific conditions and the particular wave groups that are responsible for the singular wavefront phenomena without resorting to advanced analytic function theories or asymptotic methods. Analytic characterizations of the nature, strength and direction of all intrinsic singular wavefront behaviours of the three-dimensional Green's function in three canonical cases of source-receiver configurations are given in a dual integral-closed form format to facilitate their theoretical understanding as well as computational applications. Graphical illustrations of their variation with the source-receiver configuration and the medium's Poisson's ratio together with relevant comparison and clarifications of some classical treatments are included.

Green’s functions↗
DOE OSTI2024

Landau singularities of the 7-point ziggurat. Part II

We solve the Landau equations to find the singularities of nine three-loop 7-point graphs that arise as relaxations of the graph studied in [22]. Along the way we establish that Y – Δ equivalence fails for certain branches of solutions to the Landau equations. We find two graphs with singularities outside the heptagon symbol alphabet; in particular they are not cluster variables of Gr(4, 7). We compare maximal residues of scalar graphs exhibiting these singularities to those in $\mathcal{N}$ = 4 super-Yang-Mills theory in order to probe their cancellation from its amplitudes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Immersion Freezing in Particle-Based Aerosol-Cloud Microphysics: A Probabilistic Perspective on Singular and Time-Dependent Models

Cloud droplets containing immersed ice-nucleating particles (INPs) may freeze at temperatures above the homogeneous freezing threshold temperature in a process referred to as immersion freezing. In modeling studies, immersion freezing is often described using either so-called “singular” or “time-dependent” parameterizations. Here, we compare both approaches and discuss them in the context of probabilistic particle-based (super-droplet) cloud microphysics modeling. First, using a box model, we contrast how both parameterizations respond to idealized ambient cooling rate profiles and quantify the impact of the polydispersity of the immersed surface spectrum on the frozen fraction evolution. Presented simulations highlight that the singular approach, constituting a time-integrated form of a more general time-dependent approach, is only accurate under a limited range of ambient cooling rates. The time-dependent approach is free from this limitation. Second, using a prescribed-flow two-dimensional cloud model, we illustrate the macroscopic differences in the evolution in time of ice particle concentrations in simulations with flow regimes relevant to ambient cloud conditions. The flow-coupled aerosol-budget-resolving simulations highlight the benefits and challenges of modeling cloud condensation nuclei activation and immersion freezing on insoluble ice nuclei with super-particle methods. The challenges stem, on the one hand, from heterogeneous ice nucleation being contingent on the presence of relatively sparse immersed INPs, and on the other hand, from the need to represent a vast population of particles with relatively few so-called super particles (each representing a multiplicity of real particles). We discuss the critical role of the sampling strategy for particle attributes, including the INP size, the freezing temperature (for singular scheme) and the multiplicity.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Quasi-particle interference of the van Hove singularity in Sr2RuO4

Abstract The single-layered ruthenate Sr 2 RuO 4 is one of the most enigmatic unconventional superconductors. While for many years it was thought to be the best candidate for a chiral p -wave superconducting ground state, desirable for topological quantum computations, recent experiments suggest a singlet state, ruling out the original p -wave scenario. The superconductivity as well as the properties of the multi-layered compounds of the ruthenate perovskites are strongly influenced by a van Hove singularity in proximity of the Fermi energy. Tiny structural distortions move the van Hove singularity across the Fermi energy with dramatic consequences for the physical properties. Here, we determine the electronic structure of the van Hove singularity in the surface layer of Sr 2 RuO 4 by quasi-particle interference imaging. We trace its dispersion and demonstrate from a model calculation accounting for the full vacuum overlap of the wave functions that its detection is facilitated through the octahedral rotations in the surface layer.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Hybridization of colloidal handlebodies with singular defects and topological solitons in chiral liquid crystals

Topology can manifest itself in colloids when quantified by invariants like Euler characteristics of nonzero-genus colloidal surfaces, albeit spherical colloidal particles are most often studied, and colloidal particles with complex topology are rarely considered. On the other hand, singular defects and topological solitons often define the physical behavior of the molecular alignment director fields in liquid crystals. Interestingly, nematic liquid crystalline dispersions of colloidal particles allow for probing the interplay between topologies of surfaces and fields, but only a limited number of such cases have been explored so far. Here, we study the hybridization of topological solitons, singular defects, and topologically nontrivial colloidal particles with the genus of surfaces different from zero in a chiral nematic liquid crystal phase. Hybridization occurs when distortions separately induced by colloidal particles and LC solitons overlap, leading to energy minimization-driven redistribution of director field deformations and defects. As a result, hybrid director configurations emerge, combining topological features from both components. We uncover a host of director field configurations complying with topological theorems, which can be controlled by applying electric fields. Rotational and translational dynamics arise due to the nonreciprocal evolution of the director fields in response to alternating electric fields of different frequencies. These findings help define a platform for controlling topologically hyper-complex colloidal structures and dynamics with electrically reconfigurable singular defects and topological solitons induced by colloidal handlebodies.

Lee, Jun-Yong [Hiroshima Univ. (Japan)]↗
DOE OSTI2021

Islands and current singularities in quasisymmetric toroidal plasmas

The presence of current singularities in a quasisymmetric magnetic field is explored. Quasisymmetry is shown effective in isolating Pfirsch–Schlüter singularities, to leading order, to a single magnetic surface resonant with the helicity of the symmetry. The effects of pressure driven currents are analyzed, indicating that exclusion of this surface from the plasma volume reduces the potential opening of islands but does not generally eliminate them completely due to higher order asymmetric geometric effects. These three-dimensional effects are contained in quasisymmetry and indicate the complexity of finding consistent solutions and their potential sensitivity. The δ-function current singularities show a distinct quasisymmetric behavior only when the higher-order Fourier content of B is relevant for the resistive stability parameter D R (not included in leading-order near-axis expansions). In such scenarios, quasisymmetry proves advantageous, both in simplicity and avoidance of amplification by low-order rational surfaces.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Resonance cones in cold plasma: Origin, singularities, and power flow

In magnetized tenuous plasma, typical at the plasma edge of fusion devices, a nearly electrostatic wave mode with relatively enhanced electric field can propagate along a specific angle with the magnetic field. For this characteristic, it is known as a “resonance cone.” For instance, these waves can be excited by radio frequency antennas in the ion-cyclotron and lower-hybrid range of frequencies. We consider the resonance cones emitted by idealized spatially extended sources. In 2D, we use a novel geometric construction which generalizes the d'Alembert solution to curved boundaries/moving sources, and show, for the first time, that singular electric fields arise under these conditions, thereby bringing the resonance cones in line with the other resonances of the cold plasma theory. Still in 2D, we give an expression for the amount of power radiated by resonance cones in terms of surface quantities on the source, which is finite despite the singular electric field. In conclusion, we generalize the conclusions regarding the presence and location of singular electric fields to the 3D electromagnetic case.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Inflation alternative via the gravitational field of a singularity

Abstract We explore the scenario that the observable Universe emerged from the vicinity of a negative mass ring singularity, and all content of the Universe travels at the same group velocity close to the speed of light on a geodesic trajectory along the axis of rotation of the singularity. In appropriate coordinate parametrization and evaluated on the trajectory, we find that the metric tensor in the vicinity of the trajectory exhibits a conformal scale factor a ( η ) with contraction and subsequent expansion properties that solve the horizon problem. We then introduce a static flow of gravitating radiation along the trajectory (perturbatively with respect to the mass scale of the singularity) to model a homogeneous radiation dominated Universe. Solving the Einstein field equations with a physically motivated ansatz of metric perturbation then reveals that the effective conformal scale factor indeed grows asymptotically with the same power law as expected in a conventional radiation dominated Universe.

Astronomy & Astrophysics↗
DOE OSTI2022

Nuclear cusps and singularities in the nonadditive kinetic potential bifunctional from analytical inversion

The non-additive kinetic potential $v^{\text{NAD}}$ is a key quantity in density-functional theory (DFT) embedding methods, such as frozen density embedding theory and partition DFT. $v^{\text{NAD}}$ is a bi-functional of electron densities $\rho_{\rm B}$ and $\rho_{\rm tot} = \rho_{\rm A} + \rho_{\rm B}$. It can be evaluated using approximate kinetic-energy functionals, but accurate approximations are challenging. The behavior of $v^{\text{NAD}}$ in the vicinity of the nuclei has long been questioned, and singularities were seen in some approximate calculations. In this article, the existence of singularities in $v^{\text{NAD}}$ is analyzed analytically for various choices of $\rho_{\rm B}$ and $\rho_{\rm tot}$, using the nuclear cusp conditions for the density and Kohn-Sham potential. It is shown that no singularities arise from smoothly partitioned ground-state Kohn-Sham densities. We confirm this result by numerical calculations on diatomic test systems HeHe, HeLi$^+$, and H$_2$, using analytical inversion to obtain a numerically exact $v^{\rm NAD}$ for the local density approximation. We examine features of $v^{\rm NAD}$ which can be used for development and testing of approximations to $v^{\rm NAD}[\rho_{\rm B},\rho_{\rm tot}]$ and kinetic-energy functionals.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Emergence of the Chern Supermetal and Pair-Density Wave through Higher-Order Van Hove Singularities in the Haldane-Hubbard Model

While advances in electronic band theory have brought to light new topological systems, understanding the interplay of band topology and electronic interactions remains a frontier question. In this work, we predict new interacting electronic orders emerging near higher-order Van Hove singularities present in the Chern bands of the Haldane model. We classify the nature of such singularities and employ unbiased renormalization group methods that unveil a complex landscape of electronic orders, which include ferromagnetism, density waves, and superconductivity. Importantly, we show that repulsive interactions can stabilize the long-sought pair-density-wave state and an exotic Chern supermetal, which is a new class of non-Fermi liquid with anomalous quantum Hall response. Further, this framework opens a new path to explore unconventional electronic phases in two-dimensional chiral bands through the interplay of band topology and higher-order Van Hove singularities.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals

We reformulate the analysis of singularities of Feynman integrals in a way that can be practically applied to perturbative computations in the standard model in dimensional regularization. After highlighting issues in the textbook treatment of Landau singularities, we develop an algorithm for classifying and computing them using techniques from computational algebraic geometry. We introduce an algebraic variety called the principal Landau determinant, which captures the singularities even in the presence of massless particles or UV/IR divergences. We illustrate this for 114 example diagrams, including a cutting-edge 2-loop 5-point nonplanar QCD process with multiple mass scales. Published by the American Physical Society 2024

Physics↗
DOE OSTI2026

Quantum critical collapse abhors a naked singularity

Classical critical collapse yields naked singularities from smooth initial data, challenging cosmic censorship, and shaping the spectrum of primordial black holes. We show that one-loop vacuum polarization near the threshold qualitatively changes this outcome by dressing the singularity with a horizon within a controlled semiclassical regime. In analytically tractable Einstein-scalar critical spacetimes, a one-loop $s$-wave treatment linearized around self-similar backgrounds shows that regularity uniquely selects an asymptotically Minkowskian, vacuum-polarization state. Its renormalized stress tensor carries a universal quantum growing mode that competes with the classical unstable mode, shifts the critical point, and generates a trapped surface along with a finite mass gap at the new threshold, thereby enforcing horizon formation even under arbitrary fine-tuning. In primordial collapse, the threshold shift enters exponentially into the formation fraction, while the mass gap truncates the low-mass tail, suggesting potentially important consequences for the predicted mass spectrum. Furthermore, these results provide a self-consistent semiclassical treatment of critical collapse and yield sharp predictions within the one-loop, near-critical, linearized regime.

Anomalies↗
DOE OSTI2024

The eXtended virtual element method for elliptic problems with weakly singular solutions

This paper introduces a novel eXtended virtual element method, an extension of the conforming virtual element method. The X-VEM is formulated by incorporating appropriate enrichment functions in the local spaces. The method is designed to handle highly generic enrichment functions, including singularities arising from fractured domains. By achieving consistency on the enrichment space, the method is proven to achieve arbitrary approximation orders even in the presence of singular solutions. The paper includes a complete convergence analysis under general assumptions on mesh regularity, and numerical experiments validating the method’s accuracy on various mesh families, demonstrating optimal convergence rates in the L 2 - and H 1 - norms on fractured or L-shaped domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Landau singularities of the 7-point ziggurat. Part I

We compute the leading (first-type Landau) singularities of a certain four-loop 7-point graph that is related to the 7-point “ziggurat” graph by the graphical moves familiar from equivalent circuit theory. We find perfect agreement with a subset of the “heptagon symbol alphabet” that has appeared in the context of planar Ν = 4 super-Yang-Mills theory. The remaining heptagon symbol letters are found in its subleading Landau singularities, which we address in a companion paper.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Geometrical optics without singularities: using the ray time as the coordinate space

Geometrical optics (GO) is widely used for reduced modelling of waves in plasmas, but it fails near reflection points, where it predicts a spurious singularity of the wave amplitude. We show how to avoid this singularity by adopting a different representation of the wave equation. Instead of the physical coordinate 𝑥 and the wavevector 𝑘, we use the ray time 𝜏 as the new canonical coordinate and the ray energy ℎ as the associated canonical momentum. To derive the envelope equation in the 𝜏-representation, we construct the Weyl symbol calculus on the (𝜏,ℎ) space and show that the corresponding Weyl symbols are related to their (𝑥,𝑘) counterparts by the Airy transform. This allows us to express the coefficients in the envelope equation through the known properties of the original dispersion operator. When necessary, solutions of this equation can be mapped to the 𝑥-space using a generalised metaplectic transform. However, the field per se might not even be needed in practice. Instead, knowing the corresponding Wigner function usually suffices for linear and quasilinear calculations. As a Weyl symbol itself, the Wigner function can be mapped analytically, using the aforementioned Airy transform. We show that the standard Airy patterns that form in regions where conventional GO fails are successfully reproduced within metaplectic GO (MGO) simply by remapping the field from the 𝜏-space to the 𝑥-space. An extension to mode-converting waves is also presented. This formulation, which we call generalised MGO, can be particularly useful, for example, for reduced modelling of the O–X conversion in inhomogeneous plasma near the critical density, an effect that is important for fusion applications and also occurs in the ionosphere. Overall, MGO can replace GO for any practical purposes, because it better handles cutoffs and is similar otherwise.

plasma waves↗