Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Classical solutions in field theory”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

An extended UTD analysis for the scattering and diffraction from cubic polynomial strips

Spline and polynomial type surfaces are commonly used in high frequency modeling of complex structures such as aircraft, ships, reflectors, etc. It is therefore of interest to develop an efficient and accurate solution to describe the scattered fields from such surfaces. An extended Uniform Geometrical Theory of Diffraction (UTD) solution for the scattering and diffraction from perfectly conducting cubic polynomial strips is derived and involves the incomplete Airy integrals as canonical functions. This new solution is universal in nature and can be used to effectively describe the scattered fields from flat, strictly concave or convex, and concave convex boundaries containing edges. The classic UTD solution fails to describe the more complicated field behavior associated with higher order phase catastrophes and therefore a new set of uniform reflection and first-order edge diffraction coefficients is derived. Also, an additional diffraction coefficient associated with a zero-curvature (inflection) point is presented. Higher order effects such as double edge diffraction, creeping waves, and whispering gallery modes are not examined. The extended UTD solution is independent of the scatterer size and also provides useful physical insight into the various scattering and diffraction processes. Its accuracy is confirmed via comparison with some reference moment method results.

Constantinides, E. D.↗
NASA NTRS2008

Effects of Solute Concentrations on Kinetic Pathways in Ni-Al-Cr Alloys

The kinetic pathways resulting from the formation of coherent gamma'-precipitates from the gamma-matrix are studied for two Ni-Al-Cr alloys with similar gamma'-precipitate volume fractions at 873 K. The details of the phase decompositions of Ni-7.5Al-8.5Cr at.% and Ni-5.2Al-14.2Cr at.% for aging times from 1/6 to 1024 h are investigated by atom-probe tomography, and are found to differ significantly from a mean-field description of coarsening. The morphologies of the gamma'-precipitates of the alloys are similar, though the degrees of gamma'-precipitate coagulation and coalescence differ. Quantification within the framework of classical nucleation theory reveals that differences in the chemical driving forces for phase decomposition result in differences in the nucleation behavior of the two alloys. The temporal evolution of the gamma'-precipitate average radii and the gamma-matrix supersaturations follow the predictions of classical coarsening models. The compositional trajectories of the gamma-matrix phases of the alloys are found to follow approximately the equilibrium tie-lines, while the trajectories of the gamma'-precipitates do not, resulting in significant differences in the partitioning ratios of the solute elements.

Booth-Morrison, Christopher↗
NASA NTRS1994

Quantum propagation in single mode fiber

This paper presents a theory for quantum light propagation in a single-mode fiber which includes the effects of the Kerr nonlinearity, group-velocity dispersion, and linear loss. The theory reproduces the results of classical self-phase modulation, quantum four-wave mixing, and classical solution physics, within their respective regions of validity. It demonstrates the crucial role played by the Kerr-effect material time constant, in limiting the quantum phase shifts caused by the broadband zero-point fluctuations that accompany any quantized input field. Operator moment equations - approximated, numerically, via a terminated cumulant expansion - are used to obtain results for homodyne-measurement noise spectra when dispersion is negligible. More complicated forms of these equations can be used to incorporate dispersion into the noise calculations.

Joneckis, Lance G.↗
DOE OSTI2022

Landau discriminants

Scattering amplitudes in quantum field theories have intricate analytic properties as functions of the energies and momenta of the scattered particles. In perturbation theory, their singularities are governed by a set of nonlinear polynomial equations, known as Landau equations, for each individual Feynman diagram. The singularity locus of the associated Feynman integral is made precise with the notion of the Landau discriminant, which characterizes when the Landau equations admit a solution. In order to compute this discriminant, we present approaches from classical elimination theory, as well as a numerical algorithm based on homotopy continuation. These methods allow us to compute Landau discriminants of various Feynman diagrams up to 3 loops, which were previously out of reach. For instance, the Landau discriminant of the envelope diagram is a reducible surface of degree 45 in the three-dimensional space of kinematic invariants. We investigate geometric properties of the Landau discriminant, such as irreducibility, dimension and degree. In particular, we find simple examples in which the Landau discriminant has codimension greater than one. Furthermore, we describe a numerical procedure for determining which parts of the Landau discriminant lie in the physical regions. In order to study degenerate limits of Landau equations and bounds on the degree of the Landau discriminant, we introduce Landau polytopes and study their facet structure. Finally, we provide an efficient numerical algorithm for the computation of the number of master integrals based on the connection to algebraic statistics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Conformal bootstrap deformations

We explore the space of extremal functionals in the conformal bootstrap. By recasting the bootstrap problem as a set of non-linear equations parameterized by the CFT data, we find an efficient algorithm for converging to the extremal solution corresponding to the boundary of allowed regions in the parameter space of CFTs. Furthermore, by deforming these solutions, we demonstrate that certain solutions corresponding to known theories are continuously connected. Employing these methods, we will explore the space of non-unitary CFTs in the context of modular as well as correlation function bootstrap. In two dimensions, we show that the extremal solution corresponding to the Ising model is connected to that of the Yang-Lee minimal model. By deforming this solution to three dimensions, we provide evidence that the CFT data obtained in this way is compatible with the E-expansion for a non-unitary theory

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Microstructure modeling of nuclear structural materials: Recent progress and future directions

Modeling and simulation of microstructures are essential to understand the complex responses and behaviors of nuclear materials in extreme environments. The needs to assess the extended life operation as well as the growing interest in accelerating nuclear materials development and qualification have stimulated the use of high-fidelity multiscale models aided by empirical and ab initio data. This paper reviews the role of various models across different length and time scales in investigating irradiation effects on microstructure evolution and degradation, in particular the embrittlement caused by radiation induced or enhanced formation of nanoscale chemical heterogeneities. The strength and limitations of these models, including classical rate theories, cluster dynamics, phase-field methods, and atomistic models informed by ab initio energies, are discussed with seminal examples. Challenges regarding the lack of thermo-kinetic data and theoretical treatments considering chemical complexities and magnetic excitations, as well as the stabilizing effect by excess point defects in nuclear structural materials are presented, along with potential solutions based on ab initio informed surrogate energy models and statistical sampling by Monte Carlo simulations. Further, the review then highlights the opportunities to leverage the advantages of different methods by establishing hybrid models by shared variables or coupled codes and applications. Finally, the review concludes with forward-looking remarks on how the use of physics-based models can aid the improvement of machine-learning models of property degradation and vice versa.

36 MATERIALS SCIENCE↗
NASA NTRS1994

A uniform geometrical optics and an extended uniform geometrical theory of diffraction for evaluating high frequency EM fields near smooth caustics and composite shadow boundaries

A uniform geometrical optics (UGO) and an extended uniform geometrical theory of diffraction (EUTD) are developed for evaluating high frequency electromagnetic (EM) fields within transition regions associated with a two and three dimensional smooth caustic of reflected rays and a composite shadow boundary formed by the caustic termination or the confluence of the caustic with the reflection shadow boundary (RSB). The UGO is a uniform version of the classic geometrical optics (GO). It retains the simple ray optical expressions of classic GO and employs a new set of uniform reflection coefficients. The UGO also includes a uniform version of the complex GO ray field that exists on the dark side of the smooth caustic. The EUTD is an extension of the classic uniform geometrical theory of diffraction (UTD) and accounts for the non-ray optical behavior of the UGO reflected field near caustics by using a two-variable transition function in the expressions for the edge diffraction coefficients. It also uniformly recovers the classic UTD behavior of the edge diffracted field outside the composite shadow boundary transition region. The approach employed for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the fields which is then reduced using uniform asymptotic procedures. The UGO/EUTD analysis is also employed to investigate the far-zone RCS problem of plane wave scattering from two and three dimensional polynomial defined surfaces, and uniform reflection, zero-curvature, and edge diffraction coefficients are derived. Numerical results for the scattering and diffraction from cubic and fourth order polynomial strips are also shown and the UGO/EUTD solution is validated by comparison to an independent moment method (MM) solution. The UGO/EUTD solution is also compared with the classic GO/UTD solution. The failure of the classic techniques near caustics and composite shadow boundaries is clearly demonstrated and it is shown that the UGO/EUTD results remain valid and uniformly reduce to the classic results away from the transition regions. Mathematical details on the asymptotic properties and efficient numerical evaluation of the canonical functions involved in the UGO/EUTD expressions are also provided.

Constantinides, E. D.↗
DOE OSTI2022

Supergravity black holes, Love numbers, and harmonic coordinates

A problem which has now come to a head in general relativity, primarily as a result of the many recent detections of gravitational waves from the coalescence of compact binaries, is that there are very few viable theories against which to “test” it. To perform realistic tests of theories of gravity, we need to be able to look beyond general relativity and evaluate the consistency of a parametrized, physically acceptable, family of black hole metric alternatives with observational data from, especially, gravitational wave detections using, for example, an agnostic Bayesian approach. In this paper we further examine properties of one class of such metrics, which in fact arise as solutions of ungauged supergravity. In particular, we examine the massless, neutral, minimally coupled scalar wave equation in a general stationary, axisymmetric background metric such as that of a charged rotating black hole, when the scalar field is either time independent or in the low-frequency, near-zone limit, with a view to calculating the Love numbers of tidal perturbations, and of obtaining harmonic coordinates for the background metric. For a four-parameter family of charged asymptotically flat rotating black hole solutions of ungauged supergravity theory known as STU black holes, which includes Kaluza-Klein black holes and the Kerr-Sen black hole as special cases, we find that all time-independent solutions, and hence the harmonic coordinates of the metrics, are identical to those of the Kerr solution. In the low-frequency limit we find the scalar fields exhibit the same SL(2,R) symmetry as holds in the case of the Kerr solution. We point out extensions of our results to a wider class of metrics, which includes solutions of Einstein-Maxwell-dilaton theory.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Demystifying the Stern layer at a metal–electrolyte interface: Local dielectric constant, specific ion adsorption, and partial charge transfer

Electric double layer (EDL) represents one of the most basic concepts in electrochemistry and is pertinent to diverse engineering applications ranging from electrocatalysis to energy storage. Whereas phenomenological and coarse-grained models have been long established to describe ionic distributions in the diffuse layer, a faithful prediction of the physicochemical properties of the electrode–electrolyte interface from a molecular perspective remains a daunting challenge. In this work, we investigate the charging behavior of an Ag (111) electrode in NaF aqueous solutions leveraging experimental results and theoretical calculations based on the classical density functional theory for ion distributions in the diffuse layer and on the joint density functional theory (JDFT) for the electronic structure. When the Ag electrode is applied with a negative voltage, the surface charge density can be reasonably described by assuming a neutral Stern layer with the dielectric constant dependent on the local electric field as predicted by the Kirkwood equation. However, the specific adsorption of F− ions must be considered when the electrode is positively charged and the fluoride adsorption can be attributed to both physical and chemical interactions. Qualitatively, F− binding and partial charge transfer are supported by JDFT calculations, which predict an increased binding energy as the voltage increases. Our findings shed insight on the molecular characteristics of the Stern layer and the charge behavior of adsorbed species not specified by conventional EDL models.

Wang, Xuepeng (ORCID:0000000285704546)↗
NASA NTRS2003

Analysis Method for Inelastic, Adhesively Bonded Joints with Anisotropic Adherends

A one-dimensional analysis method for evaluating adhesively bonded joints composed of anisotropic adherends and adhesives with nonlinear material behavior is presented in the proposed paper. The strain and resulting stress field in a general, bonded joint overlap are determined by using a variable-step, finite-difference solution algorithm to iteratively solve a system of first-order differential equations. Applied loading is given by a system of combined extensional, bending, and shear forces that are applied to the edge of the joint overlap. Adherends are assumed to behave as linear, cylindrically bent plates using classical laminated plate theory that includes the effects of first-order transverse shear deformation. Using the deformation theory of plasticity and a modified von-Mises yield criterion, inelastic material behavior is modeled in the adhesive layer. Results for the proposed method are verified against previous results from the literature and shown to be in excellent agreement. An additional case that highlights the effects of transverse shear deformation between similar adherends is also presented.

Smeltzer, Stanley S., III↗
DOE OSTI2020

Resonating AdS soliton

The AdS soliton is a nonsingular spacetime that has a flat conformal boundary with a compact S 1 direction. We find a horizonless cohomogeneity-1 metric that describes nonlinear gravitational oscillations of the AdS soliton in five dimensions. We call this spacetime the resonating AdS soliton. This solution is obtained as the nonlinear extension of normal modes of the AdS soliton dual to spin-2 glueball excitations. The boundary energy momentum tensor of the resonating AdS soliton has time periodic components, and it is interpreted as a coherently excited state in the dual field theory. Physical quantities of the resonating AdS soliton are multivalued at a fixed energy, suggesting a transition between different frequency solutions. The energy of the resonating AdS soliton is higher than that of the undeformed AdS soliton, in accordance with the positive energy conjecture proposed by Horowitz and Myers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Quadrupole-mediated dielectric response and the charge-asymmetric solvation of ions in water

Treating water as a linearly responding dielectric continuum on molecular length scales allows very simple estimates of the solvation structure and thermodynamics for charged and polar solutes. While this approach can successfully account for basic length and energy scales of ion solvation, computer simulations indicate not only its quantitative inaccuracies but also its inability to capture some basic and important aspects of microscopic polarization response. Here, we consider one such shortcoming, a failure to distinguish the solvation thermodynamics of cations from that of otherwise-identical anions, and we pursue a simple, physically inspired modification of the dielectric continuum model to address it. The adaptation is motivated by analyzing the orientational response of an isolated water molecule whose dipole is rigidly constrained. Its free energy suggests a Hamiltonian for dipole fluctuations that accounts implicitly for the influence of higher-order multipole moments while respecting constraints of molecular geometry. Finally, we propose a field theory with the suggested form, whose nonlinear response breaks the charge symmetry of ion solvation. An approximate variational solution of this theory, with a single adjustable parameter, yields solvation free energies that agree closely with simulation results over a considerable range of solute size and charge.

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

Low-energy effective quantum field theoretic description of excitations about soliton configurations

Solitons are the classical field configurations connecting two trivial vacua. These are also the solutions of classical field equations of motion with particle-like properties. Moreover, they are localized in space, having finite energy, and are stable against decay into radiation. The coherent state description of kink-solitons is discussed in the present article. Further, the relation between topological solitons and occupation numbers corresponding to low momentum excitations are also discussed coherently. The description of the low energy excitations about solitons in quantum field theory is the main theme of this article. Further, a few physical observables, namely some low order correlation functions, are computed up to certain integral forms. Furthermore, we have shown that it is possible to detect the presence of soliton-like classical configurations in many-particle systems from the nature of the one-point function and non-conservation of momentum feature of one-point, two-point and three-point functions in this low-energy effective field theory of these excitations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2003

Fundamentals of Polarized Light

The analytical and numerical basis for describing scattering properties of media composed of small discrete particles is formed by the classical electromagnetic theory. Although there are several excellent textbooks outlining the fundamentals of this theory, it is convenient for our purposes to begin with a summary of those concepts and equations that are central to the subject of this book and will be used extensively in the following chapters. We start by formulating Maxwell's equations and constitutive relations for time- harmonic macroscopic electromagnetic fields and derive the simplest plane-wave solution that underlies the basic optical idea of a monochromatic parallel beam of light. This solution naturally leads to the introduction of such fundamental quantities as the refractive index and the Stokes parameters. Finally, we define the concept of a quasi-monochromatic beam of light and discuss its implications.

Mishchenko, Michael↗
DOE OSTI2021

Fast and robust all-electron density functional theory calculations in solids using orthogonalized enriched finite elements

Here, we present a computationally efficient approach to perform systematically convergent real-space all-electron Kohn-Sham density functional theory calculations for solids using an enriched finite element (FE) basis. The enriched FE basis is constructed by augmenting the classical FE basis with atom-centered numerical basis functions, comprising of atomic solutions to the Kohn-Sham problem. Notably, to improve the conditioning, we orthogonalize the enrichment functions with respect to the classical FE basis, without sacrificing the locality of the resultant basis. In addition to improved conditioning, this orthogonalization procedure also renders the overlap matrix block diagonal, greatly simplifying its inversion. Subsequently, we use a Chebyshev polynomial based filtering technique to efficiently compute the occupied eigenspace in each self-consistent field iteration. We demonstrate the accuracy and efficiency of the proposed approach on periodic unit cells and supercells. The benchmark studies show a staggering 130× speedup of the orthogonalized enriched FE basis over the classical FE basis. We also present a comparison of the orthogonalized enriched FE basis with the linearized augmented plane-wave + local orbitals basis, both in terms of accuracy and efficiency. Notably, we demonstrate that the orthogonalized enriched FE basis can handle large system sizes of ~10 000 electrons. Finally, we observe good parallel scalability of our implementation with 92% efficiency at 22× speedup for a system with 620 electrons

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Holographic interfaces in $ \mathcal{N} $ = 4 SYM: Janus and J-folds

We find the holographic dual to the three classes of superconformal Janus interfaces in N = 4 SYM that preserve three-dimensional N = 4, N = 2, and N = 1 supersymmetry. The solutions are constructed in five-dimensional SO(6) maximal gauged supergravity and are then uplifted to type IIB supergravity. Corresponding to each of the three classes of Janus solutions, there are also AdS 4 × S 1 × S 5 J-fold backgrounds. These J-folds have a non-trivial SL(2, Z) monodromy for the axio-dilaton on the S 1 and are dual to three dimensional superconformal field theories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2022

Diffusion in Melts and Magmas

Diffusion results from random motion of particles and entities. Diffusion in melts and magmas is due to thermally excited random motion of atoms, ions, and clusters, and plays a critical role in magmatic and volcanic processes. In melts and magmas, diffusion is one of the two mechanisms of mass transfer; the other being bulk flow (referred to as convection or advection). When both are present, diffusion refers to the dispersive motion relative to the mean bulk flow in a given reference frame (Richter et al. 1998). Diffusion plays critical roles in controlling magma mixing (Watson 1982; Koyaguchi 1985, 1989; Lesher 1994; Huber et al. 2009; Guo and Zhang 2020), mineral growth and dissolution rates in magmas (e.g., Watson 1982; Harrison and Watson 1983; Zhang et al. 1989; Newcombe et al. 2014; Macris et al. 2018), bubble growth and dissolution rate in magmas (Sparks 1978; Proussevitch and Sahagian 1998; Liu and Zhang 2000; Zhang 2013), and elemental and isotope fractionation during mineral 2 growth and dissolution (Jambon 1980; Richter et al. 1999, 2003; Watson and Muller 2009; Chopra et al. 2012; Watkins et al. 2014, 2017; Holycross et al. 2016, 2018). As a result, diffusion also plays an essential role in explosive volcanic eruptions and magma crystallization. Furthermore, diffusion has important applications in geospeedometry (Lasaga 1983, 1998; Zhang 1994, 2008; Trail et al. 2016; Zhang and Xu 2016). Experimental investigation of diffusion in geologically relevant silicate melts began to flourish in the 1970’s when micro-analytical measurements of diffusion profiles became available. In addition to the vast number of papers published since then, numerous books and reviews are available for diffusion in silicate melts. Hofmann et al. (1974) edited a book titled “Geochemical Transport and Kinetics” published by Carnegie Institution of Washington. This was the first landmark book summarizing the field. Lasaga and Kirkpatrick (1981) edited a book “Kinetics of Geochemical Processes” as volume 8 of the Reviews in Mineralogy (later becoming Reviews in Mineralogy and Geochemistry) series. Zhang and Cherniak (2010) edited “Diffusion in Minerals and Melts” as volume 72 of Reviews of Mineralogy and Geochemistry series, in which one chapter focused on diffusion theory, five chapters on diffusion in silicate melts (Behrens 2010; Lesher 2010; Liang 2010; Zhang and Ni 2010; Zhang et al. 2010), and other chapters were on experimental, analytical, and computational methods, and diffusion in minerals. Several textbooks covered the principles and applications of diffusion theories (Kirkaldy and Young 1987; Shewmon 1989; Cussler 1997; Lasaga 1998; Zhang 2008; Vrentas and Vrentas 2016), and two classic books covered the mathematics of diffusion (Carslaw and Jaeger 1959; Crank 1975). In preparing for this review chapter, we thought carefully about what to cover for this vast field, and decided to briefly go through the fundamentals of diffusion (more complete review can be found in Chakraborty 1995; Zhang 2008, 2010) and solutions to often-encountered 3 diffusion problems, and then focus on post-2010 diffusion studies on silicate melts and magmas. Here, melts refer to (mostly natural) silicate liquid, and magmas refer to crystal-bearing and/or bubble-bearing melts in which the continuous phase is the melt. There is a large body of work on diffusion in glasses, especially in the materials science literature, which is not covered in this review.

Youxue Zhang↗
DOE OSTI2025

Quantum graph learning and algorithms applied in quantum computer sciences and image classification

Graph and network theory play a fundamental role in quantum computer sciences, including quantum information and computation. Random graphs and complex network theory are pivotal in predicting novel quantum phenomena, where entangled links are represented by edges. Quantum algorithms have been developed to enhance solutions for various network problems, giving rise to quantum graph computing and quantum graph learning (QGL). Here, in this review, we explore graph theory and graph learning methods as powerful tools for quantum computers to generate efficient solutions to problems beyond the reach of classical systems. We delve into the development of quantum complex network theory and its applications in quantum computation, materials discovery, and research. We also discuss quantum machine learning (QML) methodologies for effective image classification using qubits, quantum gates, and quantum circuits. Additionally, the paper addresses the challenges of QGL and algorithms, emphasizing the steps needed to develop flexible QGL solvers. This review presents a comprehensive overview of the fields of QGL and QML, highlights recent advancements, and identifies opportunities for future research.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗