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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Software Verification Toolkit (SVT): Survey on Available Software Verification Tools and Future Direction

Writing software is difficult. However, writing complex, well tested and designed, and functionally correct software is incredibly difficult. An entire field of study is devoted to the validation and verification of software to address this problem, and in this paper we analyze the landscape of currently available third party software. We have divided our analyses into three separate subsections with regards to software validation: formal methods, static analysis, and test generation. Formal verification is the most complex method in which to validate software correctness, but also the most thorough as it truly validates the mathematical validity of the source code. Static analysis generally is relegated to abstract syntax tree traversal techniques to find errors related to faulty software such as memory leaks or stack overflow issues. Automatic test generation is similar in implementation to static analysis, but pushes a bit further in verifying the boundedness of function inputs and outputs with regards to annotated or parsed criteria. The crux of this report is to analyze and describe the software tools that implement these techniques to validate and verify software. Pros and cons related to installation, utilization, and capabilities of the frameworks are described, and reproducible examples are provided with a focus on usability. The initial survey concluded that the most interesting tools of note are Z3, Isabelle/HOL, and TLA+ with regards to formal verification; and Infer, Frama-C, and SonarQube with regards to static analysis. With these tools in mind, a final conjecture is provided that describes future avenues of utilizing these tools for developing a verification framework to assist in validating existing software at Sandia National Laboratories.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A multidimensional study of the structure function ratio $\sigma_{LT'}$/$\sigma_0$ from hard exclusive $\pi^+$ electro-production off protons in the GPD regime

A multidimensional extraction of the structure function ratio σ LT' /σ 0 from the hard exclusive $\vec{e}$p → e'nπ+ reaction above the resonance region has been performed. The study was done based on beam-spin asymmetry measurements using a 10.6 GeV incident electron beam on a liquid-hydrogen target and the CLAS12 spectrometer at Jefferson Lab. The measurements focus on the very forward regime (t/Q 2 $\ll$ 1) with a wide kinematic range of x B in the valence regime (0.17 < x B < 0.55), and virtualities Q 2 ranging from 1.5 GeV 2 up to 6 GeV 2 . The results and their comparison to theoretical models based on Generalized Parton Distributions demonstrate the sensitivity to chiral-odd GPDs and the directly related tensor charge of the nucleon. In addition, the data is compared to an extension of a Regge formalism at high photon virtualities. It was found that the Regge model provides a better description at low Q 2 , while the GPD model is more appropriate at high Q 2 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2000

Generalizing Backtrack-Free Search: A Framework for Search-Free Constraint Satisfaction

Tractable classes of constraint satisfaction problems are of great importance in artificial intelligence. Identifying and taking advantage of such classes can significantly speed up constraint problem solving. In addition, tractable classes are utilized in applications where strict worst-case performance guarantees are required, such as constraint-based plan execution. In this work, we present a formal framework for search-free (backtrack-free) constraint satisfaction. The framework is based on general procedures, rather than specific propagation techniques, and thus generalizes existing techniques in this area. We also relate search-free problem solving to the notion of decision sets and use the result to provide a constructive criterion that is sufficient to guarantee search-free problem solving.

Jonsson, Ari K.↗
DOE OSTI2025

The Nontrivial Vacuum Structure of an Extended $t\bar{t}$ BEH (Higgs) Bound State

In a recent reformulation of top-quark condensation for the Brout-Englert-Higgs boson, we introduced an extended internal wave-function, $ϕ(r)$. We show how this leads to a manifestly Lorentz invariant formalism, where the absence of ``relative time'' is a gauge invariance of the bilocal field theory. This dictates a novel and nontrivial Lorentz invariant vacuum structure for the BEH boson, the relativistic generalization of a condensed matter state such as a BCS or Bose-Einstein condensate.

Hill, Christopher T. [Fermilab; Wisconsin U., Madi↗
DOE OSTI2022

Deformations, relaxation, and broken symmetries in liquids, solids, and glasses: A unified topological field theory

Here, we combine hydrodynamic and field theoretic methods to develop a general theory of phonons as Goldstone bosons in crystals, glasses, and liquids based on nonaffine displacements and the consequent Goldstone phase relaxation. We relate the conservation, or lack thereof, of specific higher-form currents with properties of the underlying deformation field—nonaffinity—which dictates how molecules move under an applied stress or deformation. In particular, the single-valuedness of the deformation field is associated with conservation of higher-form charges that count the number of topological defects. Our formalism predicts, from first principles, the presence of propagating shear waves above a critical wave vector in liquids, thus giving a formal derivation of the phenomenon in terms of fundamental symmetries. The same picture provides also a theoretical explanation of the corresponding “positive sound dispersion” phenomenon for longitudinal sound. Importantly, accordingly to our theory, the main collective relaxation timescale of a liquid or a glass (known as the α relaxation for the latter) is given by the phase relaxation time, which is not necessarily related to the Maxwell time. Finally, we build a nonequilibrium effective action using the in-in formalism defined on the Schwinger-Keldysh contour, that further supports the emerging picture. In summary, our work suggests that the fundamental difference between solids, fluids, and glasses has to be identified with the associated generalized higher-form global symmetries and their topological structure, and that the Burgers vector for the displacement fields serves as a suitable topological order parameter distinguishing the solid (ordered) phase and the amorphous ones (fluids, glasses).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Casimir effect in Very Special Relativity at finite temperature

Recently a great deal of interest in field theories formulated in a Lorentz violating framework has been developed. Here the Very Special Relativity (VSR) is considered. The main aspect in the VSR proposal is that laws of physics are invariant under the subgroups of the Poincaré group preserving the basic elements of special relativity. An important point is that the photon acquires a mass. In this context, the energy–momentum tensor for the electromagnetic field is calculated. From this, the Stefan–Boltzmann law and Casimir effect at finite temperature in VSR are obtained. The effects of temperature are introduced using the Thermo Field Dynamics (TFD) formalism. A comparative analysis with the Casimir effect for the standard electromagnetic case is developed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Developing a predictive science of the biosphere requires the integration of scientific cultures

Increasing the speed of scientific progress is urgently needed to address the many challenges associated with the biosphere in the Anthropocene. Consequently, the critical question becomes: How can science most rapidly progress to address large, complex global problems? We suggest that the lag in the development of a more predictive science of the biosphere is not only because the biosphere is so much more complex, or because we do not have enough data, or are not doing enough experiments, but, in large part, because of unresolved tension between the three dominant scientific cultures that pervade the research community. We introduce and explain the concept of the three scientific cultures and present a novel analysis of their characteristics, supported by examples and a formal mathematical definition/representation of what this means and implies. The three cultures operate, to varying degrees, across all of science. However, within the biosciences, and in contrast to some of the other sciences, they remain relatively more separated, and their lack of integration has hindered their potential power and insight. Our solution to accelerating a broader, predictive science of the biosphere is to enhance integration of scientific cultures. The process of integration—Scientific Transculturalism—recognizes that the push for interdisciplinary research, in general, is just not enough. Unless these cultures of science are formally appreciated and their thinking iteratively integrated into scientific discovery and advancement, there will continue to be numerous significant challenges that will increasingly limit forecasting and prediction efforts.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1980

The fate of the downgoing slab - A study of the moment tensors from body waves of complex deep-focus earthquakes

Two large, complex deep-focus earthquakes are analyzed, using body waves, to determine the relative locations and equivalent forces of the component events. Details of the source mechanism determination are given, with special emphasis on the means of comparing results for double-couple and more general models. The formalism includes a description of a method for calculating the confidence ellipses around the principal axes of the moment tensor. An interpretation of the results suggests that the mechanism of deep-focus earthquakes is controlled by the buoyancy of the slab and the change in viscosity at the 650 km discontinuity.

Strelitz, R. A.↗
DOE OSTI2022

Role of electromagnetic gauge-field fluctuations in the selection between chiral and nematic superconductivity

Motivated by the observation of nematic superconductivity in several systems, we revisit the problem of the leading pairing instability of two-component unconventional superconductors on the triangular lattice—such as (p x , p y )-wave and (d x 2 –y 2 , d xy )-wave superconductors. Such a system has two possible superconducting states: the chiral state (e.g., p + ip or d + id), which breaks time-reversal symmetry, and the nematic state (e.g., p + p or d + d), which breaks the threefold rotational symmetry of the lattice. Weak-coupling calculations generally favor the chiral over the nematic superconducting state, raising the question of what mechanism can stabilize the latter. Here, we show that the electromagnetic field fluctuations can play a crucial role in selecting between these two states. Specifically, we derive and analyze the effective free energy for the two-component superconducting order parameter after integrating out the gauge-field fluctuations, which is formally justified if the spatial order parameter fluctuations can be neglected. A nonanalytic cubic term arises, as in the case of a conventional s -wave superconductor. However, unlike the latter, the cubic term depends on the relative phase and on the relative amplitudes between the two order parameter components, in such a way that it generally favors the nematic state. This result is a direct consequence of the fact that the stiffness of the superconducting order parameter is not isotropic. Competition with the quartic term, which favors the chiral state, leads to a renormalized phase diagram in which the nematic state displaces the chiral state over a wide region in the parameter space. Here, we analyze the stability of the fluctuation-induced nematic phase, generalize our results to tetragonal lattices, and discuss their applicability to candidate nematic superconductors, including twisted bilayer graphene.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Gravitational waveforms: A tale of two formalisms

We revisit the quantum-amplitude-based derivation of the gravitational waveform emitted by the scattering of two spinless massive bodies at the third order in Newton’s constant, ℎ ∼ 𝐺 + 𝐺 2 + 𝐺 3 (one-loop level), and correspondingly update its comparison with its classically derived multipolar-post-Minkowskian counterpart. A spurious-pole-free reorganization of the one-loop five-point amplitude substantially simplifies the post-Newtonian expansion. We find complete agreement between the two results up to the fifth order in the small velocity expansion after taking into account three subtle aspects of the amplitude derivation: (1) in agreement with [A. Georgoudis et al., J. High Energy Phys. 03 (2024) 089], the term quadratic in the amplitude in the observable-based formalism [D. A. Kosower et al., J. High Energy Phys. 02 (2019) 137] generates a frame rotation by half the classical scattering angle; (2) the dimensional regularization of the infrared divergences of the amplitude introduces an additional (𝑑 − 4)/(𝑑 − 4) finite term; and (3) zero-frequency gravitons are found to contribute additional terms both at order ℎ ∼ 𝐺 1 and at order ℎ ∼ 𝐺 3 when including disconnected diagrams in the observable-based formalism.

Astronomy & Astrophysics↗
DOE OSTI2022

Surface stress tensor and junction conditions on a rotating null horizon

The general form of the surface stress tensor of an infinitesimally thin shell located on a rotating null horizon is derived, when different interior and exterior geometries are joined there. Even though the induced metric on the surface must be the same approached from either side, the first derivatives of the metric need not be. Such discontinuities lead to a Dirac δ-distribution in the Einstein tensor localized on the horizon. For a general stationary axisymmetric geometry the surface stress tensor can be expressed in terms of two geometric invariants that characterize the surface, namely the discontinuities [κ] and [J] of the surface gravity κ and angular momentum density J. The Komar energy and angular momentum are given in coordinates adapted to the Killing symmetries, and the surface contributions to each determined in terms of [κ] and [J] . Guided by these, a simple modification of the original Israel junction conditions is verified directly from the Einstein tensor density to give the correct finite result for the surface stress, when the normal n to the surface is allowed to tend continuously to a null vector. The relation to Israel’s original junction conditions, which fail on null surfaces, is given. The modified junction conditions are suitable to the matching of a rotating “black hole” exterior to any interior geometry joined at the Kerr null horizon surface, even when the surface normal is itself discontinuous and the Barrabès-Israel formalism is also inapplicable. This joining on a rotating null horizon is purely of the matter shell type and does not contain a propagating gravitational shock wave.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Surrogate Distributed Radiological Sources—Part II: Aerial Measurement Campaign

In this second part of a multipaper series, we present results from outdoor aerial measurements of surrogate distributed gamma-ray sources. Here we detail the design, manufacture, and testing of 300 individual ~7 mCi Cu-64 sealed sources at the Washington State University (WSU) research reactor and their deployment in various source patterns (each comprising up to 100 point sources) during the aerial measurement campaign. We show the results of two such measurements, in which approximate source shapes and qualitative source intensities can be seen from the count rate versus position plots, even without performing reconstructions. We also detail our efforts in ground-truthing the deployed sources and comparing measured gamma-ray data to model predictions. In particular, we compare measured versus expected count data using the Poisson deviance formalism of Part I to evaluate whether the fielded surrogate point-source arrays “look like” their truly continuous distributed source analogs. More generally, we find that the point-source array technique provides high source placement accuracy, relative ease of quantifying the true source configuration, scalability to source dimensions of ≲100 m, ease of reconfiguration and removal, and relatively low dose to personnel. Finally, we consider potential improvements and generalizations of the point-source array technique for future measurement campaigns.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS2003

On the Applicability of High-frequency Approximations to Lilley's Equation

Three forms of the high-frequency asymptotic Green's function for Lilley's equation are reviewed and compared to the exact solution over wide range of Strouhal numbers. The asymmetric approximation, which applies to sources away form the jet axis, and the quasi-symmetric approximation, which is arrived at by making a near-axis source assumption, are both obtained for parallel round jets from a formal Fourier-transform solution. The ray-theory solution, which is the only high-frequency approximation that can be applied to more general mean flows, follows from a WKB ansatz and is shown to be closely related to the asymmetric approximation. The comparisons show that the best overall prediction of the exact Green's function is given by the asymmetric approximation which remains accurate down to a Strouhal number of 1/2. The close relationship between the asymmetric and ray-theory approximations suggests that the high-frequency asymptotic Green's function for more general mean flows would be similarly successful.

Wundrow, David W.↗
DOE OSTI2023

Parameterization of Direct and Doorway Processes in R-Matrix Formalism

R-matrix formalism is extended beyond compound nuclear (CN) resonant reactions to include parameterization of direct as well as doorway processes. Direct processes in the R-matrix exterior are parameterized by a unitary matrix that introduces mixing among wave function coefficients of the incoming and outgoing wave function components at the R-matrix channel surface. Doorway processes are parameterized by separating the Hilbert space of the interior R-matrix region into its doorway and CN subspaces, from which doorway state eigenenergies, reduced width amplitudes, and the strengths of their coupling to CN levels appear as new R-matrix parameters. Parameterization of generalized as well as the conventional Reich–Moore approximation for eliminated capture channels in the presence of direct, doorway, and CN processes is presented along with a complex-valued scattering length with contributions from direct, doorway, and CN capture processes. Derivation of Brune’s alternative R-matrix parameters is extended to include doorway states. This work suggests how R-matrix formalism could be extended further by adopting the concepts from related reaction formalisms.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Computational Aspects of Single-Molecule Kinetics for Coupled Catalytic Cycles: A Spectral Analysis

Catalysis from single active sites is analyzed using methods developed from single molecule kinetics. Using a stochastic Markov state description, the observable properties of general catalytic networks of reactions are expressed using an eigenvalue decomposition of the transition matrix for the Markov process. By the use of a sensitivity analysis, the necessary eigenvalues and eigenvectors are related to the energies of controlling barriers and wells located along the reaction routes. A generalization of the energetic span theory allows the eigenvalues to be computed from several activation energies corresponding to distinct barrier-well pairings. The formalism is demonstrated accurately for model problems for a physically realistic mechanism for an alkene hydrogenation reaction on a single atom catalyst.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Exclusive QCD Factorization and Single Transverse Polarization Phenomena at High-Energy Colliders

This Ph.D. thesis is divided into two distinct parts. The first part focuses on hard exclusive scattering processes in Quantum Chromodynamics (QCD) at high energies, while the second part delves into spin phenomena at the Large Hadron Collider (LHC). Hard exclusive scattering processes play a crucial role in QCD at high energies, providing unique insights into the confined partonic dynamics within hadrons, complementing inclusive processes. Studying these processes within the QCD factorization approach yields the generalized parton distribution (GPD), a nonperturbative parton correlation function that offers a three-dimensional tomographic parton image within a hadron. However, the experimental measurement of these processes poses significant challenges. This thesis will review the factorization formalism for related processes, examine the limitations of some widely used processes, and introduce two novel processes that enhance the sensitivity to GPD, particularly its dependence on the parton momentum fraction x. The second part of the thesis centers on spin phenomena, specifically single spin production, at the LHC. Noting that a single transverse polarization can be generated even in an unpolarized collision, this research proposes two new jet substructure observables: one for boosted top quark jets and another for high-energy gluon jets. The observation of these phenomena paves the way for innovative tools in LHC phenomenology, enabling both precision measurements and the search for new physics.

Yu, Zhite↗
DOE OSTI2020

Effective field theory for quasicrystals and phasons dynamics

We build an effective field theory (EFT) for quasicrystals -- aperiodic incommensurate lattice structures -- at finite temperature, entirely based on symmetry arguments and a well-define action principle. By means of Schwinger-Keldysh techniques, we derive the full dissipative dynamics of the system and we recover the experimentally observed diffusion-to-propagation crossover of the phason mode. From a symmetry point of view, the diffusive nature of the phason at long wavelengths is due to the fact that the internal translations, or phason shifts, are symmetries of the system with no associated Noether currents. The latter feature is compatible with the EFT description only because of the presence of dissipation (finite temperature) and the lack of periodic order. Finally, we comment on the similarities with certain homogeneous holographic models and we formally derive the universal relation between the pinning frequency of the phonons and the damping and diffusion constant of the phason.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1987

A structure-based model of semantic integrity constraints for relational data bases

Data base management systems (DBMSs) are in widespread use because of the ease and flexibility with which users access large volumes of data. Ensuring data accuracy through integrity constraints is a central aspect of DBMS use. However, many DBMSs still lack adequate integrity support. In additon, a comprehensive theoretical basis for such support the role of a constraint classification system - has yet to be developed. This paper presents a formalism that classifies semantic integrity constraints based on the structure of the relational model. Integrity constraints are characterized by the portion of the data base structure they access, whether one or more relations, attributes, or tuples. Thus, the model is completely general, allowing the arbitrary specification of any constraint. Examples of each type of constraint are illustrated using a small engineering data base, and various implementation issues are discussed.

Rasdorf, William J.↗