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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Analytic solutions of the DGLAP evolution and theoretical uncertainties

The energy dependence for the singlet sector of Parton Distributions Functions (PDFs) is described by an entangled pair of ordinary linear differential equations. Although there are no exact analytic solutions, it is possible to provide approximated results depending on the assumptions and the methodology adopted. These results differ in their sub-leading, neglected terms and ultimately they are associated with different treatments of the theoretical uncertainties. In this work, a novel analytic approach in Mellin space is presented and a new methodology for obtaining closed and exponentiated analytic solutions is devised. Different results for the DGLAP evolution at Next-Leading-Order are compared, discussing advantages and disadvantages for each solution. The generalizations to higher orders are addressed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Universality aspects of quantum corrections to transverse momentum broadening in QCD media

We study non-linear quantum corrections to transverse momentum broadening (TMB) of a fast parton propagating in dense QCD matter in the leading logarithmic approximation. These non-local corrections yield an anomalous super-diffusive behavior characterized by a heavy tailed distribution which is associated with Lévy random walks. Using a formal analogy with the physics of traveling waves, we show that at late times the transverse momentum distribution tends to a universal scaling regime. We derive analytic solutions in terms of an asymptotic expansion around the scaling limit for both fixed and running coupling. We note that our analytic approach yields a good agreement with the exact numerical solutions down to realistic values of medium length. Finally, we discuss the interplay between system size and energy dependence of the diffusion coefficient $\hat{q}$ and its connection with the gluon distribution function that is manifest at large transverse momentum transfer.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

A note on the reliability of goal-oriented error estimates for Galerkin finite element methods with nonlinear functionals

Here, we consider estimating the discretization error in a nonlinear functional J (u) in the setting of an abstract variational problem: find u ϵ $\mathscr{V}$ such that B (u, φ) = L (φ) ∀φ ϵ $\mathscr{V}$, as approximated by a Galerkin finite element method. Here, $\mathscr{V}$ is a Hilbert space, B (. , .) is a bilinear form, and L (∙) is a linear functional. We consider well-known error estimates η of the form J (u) - J (u h ) ≈ η = L (z) - B (u h , z), where u h denotes a finite element approximation to u, and z denotes the solution to an auxiliary adjoint variational problem. We show that there exist nonlinear functionals for which error estimates of this form are not reliable, even in the presence of an exact adjoint solution z. An estimate η is said to be reliable if there exists a constant C ϵ $\mathbb{R}$ >0 independent of u h such that |J (u) - J (u h )| ≤ C|η|. We present several example pairs of bilinear forms and nonlinear functionals where reliability of η is not achieved.

A posteriori↗
DOE OSTI2022

An Asymptotically Compatible Coupling Formulation for Nonlocal Interface Problems with Jumps

Here, we introduce a mathematically rigorous formulation for a nonlocal interface problem with jumps and propose an asymptotically compatible finite element discretization for the weak form of the interface problem. After proving the well-posedness of the weak form, we demonstrate that solutions to the nonlocal interface problem converge to the corresponding local counterpart when the nonlocal data are appropriately prescribed. Several numerical tests in one and two dimensions show the applicability of our technique, its numerical convergence to exact nonlocal solutions, its convergence to the local limit when the horizons vanish, and its robustness with respect to the patch test.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Theoretical Analysis of Fractional Viscoelastic Flow in Circular Pipes: General Solutions

Fractional calculus is a relatively old yet emerging field of mathematics with the widest range of engineering and biomedical applications. Despite being an incredibly powerful tool, it, however, requires promotion in the engineering community. Rheology is undoubtedly one of the fields where fractional calculus has become an integral part of cutting-edge research. There exists extensive literature on the theoretical, experimental, and numerical treatment of various fractional viscoelastic flows in constraint geometries. However, the general theoretical approach that unites several most commonly used models is missing. Here we present exact analytical solutions for fractional viscoelastic flow in a circular pipe. We find velocity profiles and shear stresses for fractional Maxwell, Kelvin–Voigt, Zener, Poynting–Thomson, and Burgers models. The dynamics of these quantities are studied with respect to normalized pipe radius, fractional orders, and elastic moduli ratio. Three different types of behavior are identified: monotonic increase, resonant, and aperiodic oscillations. The models developed are applicable in the widest material range and allow for the alteration of the balance between viscous and elastic properties of the materials.

Gritsenko, Dmitry (ORCID:0000000248181512)↗
DOE OSTI2021

Discrete Green’s functions and spectral graph theory for computationally efficient thermal modeling

Here, this work concerns solutions of the heat equation with the spectral graph method, for which the temperature is defined at discrete points in the domain and the spatial relationship among the points is described by a graph. The heat equation on the graph is solved using matrix techniques involving the eigenvectors and eigenvalues of the Laplacian matrix. The spectral graph approach precludes the computationally intensive meshing and numerous time-integration steps of the finite element method. In the present work, the spectral graph method is extended to include heat loss at the boundaries with a generalized boundary condition, and physics-based edge weights are introduced which simplify the calibration process. From this approach a discrete Green’s function is defined which allows for solutions under a variety of heating conditions including: space-varying initial conditions; time-and-space varying internal heating; and, time-and-space-varying heating at boundaries of type 1 (Dirichlet), type 2 (Neumann) and type 3 (Robin). Results are provided for benchmark heat transfer problems in one spatial dimension and in three spatial dimensions, and verification is provided by comparison with exact analytical solutions and finite difference solutions. The spectral graph method converges within 0.4% error of the analytical solution. The practical utility of the approach is demonstrated by thermal simulation of a multilayer additive manufacturing process. The spectral graph results are compared to experimentally-obtained temperature data for two metal parts, with error less than 5% of the experimental measurements, with computation time less than one minute on a desktop computer.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Bethe Ansatz solutions for certain Periodic Quantum Circuits

I derived Bethe Ansatz equations for two model Periodic Quantum Circuits: (1) XXZ model; (2) Chiral Hubbard Model. I obtained explicit expressions for the spectra of the strings of any length. These analytic results may be useful for calibration and error mitigations in modern engineered quantum platforms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Dirac systems with magnetic field and position-dependent mass: Darboux transformations and equivalence with generalized Dirac oscillators

Highlights: • We construct Darboux transformations for Dirac systems with position-dependent mass. • Our systems are either Dirac oscillators or coupled to a magnetic field. • We use our Darboux transformation to construct new solvable Dirac systems. We construct a Darboux transformation for a class of two-dimensional Dirac systems at zero energy. Our starting equation features a position-dependent mass, a matrix potential, and an additional degree of freedom that can be interpreted either as a magnetic field perpendicular to the plane or a generalized Dirac oscillator interaction. We obtain a number of Darboux-transformed Dirac equations for which the zero energy solutions are exactly known.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Cauchy data space and multisymplectic formulation of conformal classical field theories

In this article we inspect the dynamics of classical field theories with a local conformal behavior. Our interest in the multisymplectic setting comes from its suitable description of field theories, and the conformal character has been added to account for field theories that are scale invariant, flat spaces, and because some conformal fields can be exactly solved or classified. In particular, we will solve the example of a conformal scalar field using the geometric Hamilton–Jacobi theory that is explicitly proposed for conformal fields on a multisymplectic manifold. To complete the geometric approach to study field theories, we propose the Hamilton–Jacobi theory for conformal fields in a Cauchy data space, in which space and time are split separately and the dynamics is depicted in an infinite-dimensional manifold.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Adiabatic quantum decoherence in many non-interacting subsystems induced by the coupling with a common boson bath

Highlights: • System–environment quantum correlation: a main solid state NMR decoherence channel. • Non-separable system–environment model yields realistic spin decoherence rates. • New open quantum system approach explains irreversible decay of refocused NMR echoes. • Adiabatic quantum decoherence is inherently irreversible and eigen-selective. This work addresses adiabatic quantum decoherence of many-body spin systems coupled with a boson field in the framework of open quantum systems theory. We generalize the traditional spin-boson model by considering a system–environment interaction Hamiltonian that represents a partition of non-interacting subsystems and highlights the collective correlation that appears exclusively due to the coupling with a common environment. Remarkably, this simple, exactly solvable model encompasses relevant aspects of a many-body open quantum system and features the subtle quantum effects that arise when the size scales up to a macroscopic level. We derive an analytical expression for the time dependence of the density matrix elements (in the preferred basis) without assuming coarse-graining. The resulting decoherence function is eigen-selective and is a complex exponential whose exponent has a real part that introduces a decay similar to that in the spin-boson model. On the contrary, the imaginary part depends on the quantum numbers and geometry of the whole partition and does not reflect the system temperature. Motivated by decoherence in solid-state NMR, and in search of realistic numerical estimations, we apply the theoretical results to a partition of dipole-coupled spin pairs in contact with a common phonon bath, using typical parameters of hydrated salts. The proposal allows estimating the decoherence time scale in terms of the system physical constants: sound velocity and eigenvalue distribution width. As a significant novelty, the decoherence function phase depends on the eigenvalue distribution throughout the sample. It plays the leading role, overshadowing the mechanism associated with the bath thermal state. Finally, we apply the formalism to describe decoherence in the “magic echo” NMR reversal experiment. We find that the system–environment correlation explains the origin of irreversibility, and both the decoherence rate value and its dependence on the dipolar frequency, are remarkably similar to the experiment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Effects of internal swelling on residual elasticity of a quasi-brittle material through a composite sphere model

This work describes the development of a micromechanical-based constitutive model accounting for the effect of internal expansion on the residual elasticity of a Hashin composite material. This material is made of spherical inclusions that are subjected to gradual swelling within a quasi-brittle matrix. The main focus of this work is to describe and analyze the material mechanical response, with an additional focus on the internal swelling’s effect on the stress–strain response and residual elasticity. Microstructural features and parameters of major importance for the mechanical responses were identified. The innovative characteristics of the proposed approach are summarized as follows: (1) a full determination of the physics of a complete-damage problem throughout the whole process of inclusion swelling with upscaling techniques, which transfers the microcrack-related properties from the lower scale to upper scale; and (2) an evolution of the mechanical fields and the corresponding residual elasticity for various inclusion swelling levels. Concerning the matrix–inclusion composite, it was hypothesized that only the matrix was susceptible to cracking, with varied degrees of damage, whereas the inclusions behave elastically and the elastic modulus of the expanding inclusions remains constant. It is to emphasize that the gradual swelling of inclusions is modeled by an increasing strain in the current micromechanical-based constitutive model, and the microcracks are represented by a set of randomly oriented penny-shaped microcracks with identical radii (namely, closed cracks). The main contribution of the current research is to establish the exact mathematical solutions for the mechanical fields (stress, strain) caused by the swelling of the inclusions (mechanical loading) and derive the effective residual elasticity of a composite (structural response) subject to internal expansion and quasi-brittle damage. Based on the assumption of closed cracks that could be extended to open cracks in the upcoming work, the results proposed by the present paper help to understand the non-linear mechanical behavior of quasi-brittle materials subject to microcracking and provide a theoretical framework to be used as academical benchmark for numerical simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Asymptotic quasisymmetric high-beta three-dimensional magnetohydrodynamic equilibria near axisymmetry

Quasisymmetry (QS), a hidden symmetry of the magnetic field strength, is known to support nested flux surfaces and provide superior particle confinement in stellarators. In this work, we study the ideal magnetohydrodynamic (MHD) equilibrium and stability of high-beta plasma in a large-aspect-ratio stellarator. In particular, we show that the lowest-order description of a near-axisymmetric equilibrium vastly simplifies the problem of three-dimensional quasisymmetric MHD equilibria, which can be reduced to a standard elliptic Grad–Shafranov equation for the flux function. We show that any large-aspect-ratio tokamak, deformed periodically in the vertical direction, is a stellarator with approximate volumetric QS. We discuss exact analytical solutions and numerical benchmarks. Finally, we discuss the ideal ballooning and interchange stability of some of our equilibrium configurations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Reduction of the molecular hamiltonian matrix using quantum community detection

Abstract Quantum chemistry is interested in calculating ground and excited states of molecular systems by solving the electronic Schrödinger equation. The exact numerical solution of this equation, frequently represented as an eigenvalue problem, remains unfeasible for most molecules and requires approximate methods. In this paper we introduce the use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix in Slater determinant basis without chemical knowledge. Given a molecule represented by a matrix of Slater determinants, the connectivity between Slater determinants (as off-diagonal elements) is viewed as a graph adjacency matrix for determining multiple communities based on modularity maximization. A gauge metric based on perturbation theory is used to determine the lowest energy cluster. This cluster or sub-matrix of Slater determinants is used to calculate approximate ground state and excited state energies within chemical accuracy. The details of this method are described along with demonstrating its performance across multiple molecules of interest and bond dissociation cases. These examples provide proof-of-principle results for approximate solution of the electronic structure problem using quantum computing. This approach is general and shows potential to reduce the computational complexity of post-Hartree–Fock methods as future advances in quantum hardware become available.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

A forced Korteweg–de Vries model for nonlinear mixing of oscillations in a dusty plasma

Nonlinear mixing of oscillations in a dusty plasma due to the harmonic time varying modulation of a nonlinear compressional oscillation is analyzed using a simple mathematical model consisting of a forced Korteweg-de Vries equation. An exact analytic solution of this equation is found to exhibit nonlinear mixing in the system. Here, the model solution can be usefully employed to predict the existence of nonlinear mixing of oscillations in a two-dimensional dusty plasma system of a particular experimental configuration.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

An efficient random-sampling method for calculating double occupancy of Gutzwiller wave function in single-band 1D and 2D lattices

In this paper, we report a random sampling method for computing the expectation value of physical quantities based on the Gutzwiler variational wave function. As the first application, we calculated the double occupancy, which is a critical quantity for under- standing the correlation effects in many-body systems, for single-band 1D and 2D lattices. We demonstrated that the random sampling scheme is more efficient than an existing Metropolis Monte-Carlo algorithm. For the 1D Hubbard model with only nearest-neighbor hopping, our results are almost identical to the exact analytic solution. We have also studied systems to which analytic solutions are not available, including the 1D lattices with next-nearest-neighbor hopping and 2D lattices. In addition, constraints on real-space con gurations can be easily implemented in the current scheme to further improve the Gutzwiller wave function. As an example, we calculated the double occupancy for 1D Hubbard model by applying the constraint that all double-occupied sites are paired with an empty site. With enhanced correlation between double-occupied and empty sites, the constraint results in much improved ground-state energy for 1D Hubbard model with strong on-site repulsion.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Time-dependent relaxation of observables in complex quantum systems

Abstract We consider time-dependent relaxation of observables in quantum systems of chaotic and regular type. Using statistical arguments and exact numerical solutions we show that the spread of the initial wave function in the Hilbert space and the main characteristics of evolution of observables have certain generic features. The study compares examples of regular dynamics, a completely chaotic case of the Gaussian orthogonal ensemble, a bosonic system with random interactions, and a fully realistic case of the time evolution of various initial non-stationary states in the nuclear shell model. In the case of the Gaussian orthogonal ensemble we show that the survival probability obtained analytically also fully defines the relaxation timescale of observables. This is not the case in general. Using the realistic nuclear shell model and the quadrupole moment as an observable we demonstrate that the relaxation time is significantly longer than defined by the survival probability of the initial state. The full analysis does not show the presence of an analog of the Lyapunov exponent characteristic for examples of classical chaos.

Volya, Alexander (ORCID:0000000217656466)↗
DOE OSTI2020

Two-particle correlation functions in cluster perturbation theory: Hubbard spin susceptibilities

Cluster perturbation theory (CPT) is a computationally economic method commonly used to estimate the momentum- and energy-resolved single-particle Green's function. It has been used extensively in direct comparisons with experiments that effectively measure the single-particle Green's function, e.g., angle-resolved photoemission spectroscopy. However, many experimental observables are given by two-particle correlation functions. CPT can be extended to compute two-particle correlation functions by approximately solving the Bethe-Salpeter equation. We implement this method and focus on the transverse spin susceptibility, measurable via inelastic neutron scattering or with optical probes of atomic gases in optical lattices. Finally, we benchmark the method with the one-dimensional Fermi-Hubbard model by comparing with known results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗