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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 811 records · Page 45
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Direct S{sub N} Treatment of the Scattering Source with Phase Functions

In deterministic transport, the angular dependency of the scattering source is described using a so-called phase function. The scattering operator is commonly expressed using a spherical harmonics (P{sub N}) expansion of this phase function. Not only does this require minimal modifications if the problem dimensionality is changed, but it also contains little to no approximation whenever the scattering anisotropy degree is small. An alternative method relying on a discrete ordinates (S{sub N}) approach - essentially computing the angular integral of the phase function with a finite number of weighted directions - is theoretically possible and has shown some advantages. In particular, this method was introduced for neutron elastic scattering and was shown to be more accurate for highly anisotropic group-to-group transfer cross-sections. Benefits were further shown in the case of a collimated beam in highly forward peaked scattering media, particularly reducing the memory usage by storing an angle-to-angle collision matrix rather than a large number of angular moments. In addition, the scattering source was expressed using that same method, the phase function having been previously expanded using Legendre polynomials, in the context of achieving extreme precision while solving the 1D radiative transfer equation. Based on these previous works, we aim at exploring two questions. First, we wish to derive an expression of the phase function in reduced geometries that does not require any more angular quadrature points than for a standard S N calculation. This is particularly relevant because the reduced phase function does not solely depend on the product of the incoming and outgoing directions. Second, we wish to better understand the relationship between the S{sub N} and P{sub N} treatments. We in particular show equivalence if the phase function in the former case is expanded Legendre polynomials. This equivalence is verified numerically and the computational costs of the methods are compared on a test problem involving a Dirac delta phase function.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Resonant acoustic monitoring of damage in plug‐screw feeders

Abstract Plug‐screw feeders are critical in many industrial processes for compressing slurry materials via a rotating plug‐screw feeder. Over time, increasing plug‐screw feeder wear will eventually lead to catastrophic mechanical failure. Early detection of the wear state can prevent unplanned catastrophic failures resulting in operational shut‐downs, costly repairs, and most importantly the health and safety of workers. We present a theoretical basis for a noninvasive, in operando acoustic resonant technique to monitor the wear state of plug‐screw feeders. The technique is based on tracking the resonant acoustic modes of the plug‐screw feeder, which are sensitive to the plug‐screw feeder geometry, material, and operating conditions. We implemented a multivariate polynomial model to estimate the plug‐screw feeder wear state using multiple acoustic resonances by simulating the acoustic resonant modes for two categories of wear (tip and thread damage) that are common in plug‐screw feeders. Fitting multiple resonances to the polynomial model, we demonstrate accurate estimation of the total mass loss, as well as characterization of the type of damage (i.e., tip vs. thread). Current approaches for monitoring plug‐screw feeder wear rely on shutting down the operation and visually inspecting the plug‐screw feeder. The presented acoustic technique offers a noninvasive, in operando measurement approach that mitigates unplanned catastrophic failures. The acoustic resonance technique presented in the paper has a broad range of industrial applications including the Pharmaceutical, Mining, Integrated Biorefineries (IBR), and Additive Manufacturing industries, to name a few.

36 MATERIALS SCIENCE↗
DOE OSTI2014

From h to p efficiently: optimal implementation strategies for explicit time-dependent problems using the spectral/ hp element method: FROM h TO p EFFICIENTLY

We investigate the relative performance of a second-order Adams–Bashforth scheme and second-order and fourth-order Runge–Kutta schemes when time stepping a 2D linear advection problem discretised using a spectral/hp element technique for a range of different mesh sizes and polynomial orders. Numerical experiments explore the effects of short (two wavelengths) and long (32 wavelengths) time integration for sets of uniform and non-uniform meshes. The choice of time-integration scheme and discretisation together fixes a CFL limit that imposes a restriction on the maximum time step, which can be taken to ensure numerical stability. The number of steps, together with the order of the scheme, affects not only the runtime but also the accuracy of the solution. Through numerical experiments, we systematically highlight the relative effects of spatial resolution and choice of time integration on performance and provide general guidelines on how best to achieve the minimal execution time in order to obtain a prescribed solution accuracy. The significant role played by higher polynomial orders in reducing CPU time while preserving accuracy becomes more evident, especially for uniform meshes, compared with what has been typically considered when studying this type of problem.

42 ENGINEERING↗
DOE OSTI2020

Matrix-free preconditioning for high-order H (curl) discretizations

The greater arithmetic intensity of high-order finite element discretizations makes them attractive for implementation on next-generation hardware, but assembly of high-order finite element operators as matrices is prohibitively expensive. As a result, the development of general algebraic solvers for such operators has been an open research challenge. Fast matrix-free application of high-order operators has received significant attention in the literature in the context of Poisson-type problems, but preconditioners and solvers for inverting more general operators are not very well-developed. In this paper, we consider the problem of preconditioning a definite Maxwell operator at high polynomial order without assembling a matrix. We show that given efficient preconditioners for high-order H 1 finite element problems on the same mesh, efficient H(curl) preconditioners can be constructed in an auxiliary space framework. We demonstrate the resulting preconditioners in a practical setting with tensor-product basis functions on an unstructured mesh of quadrilaterals. Overall, our approach uses a sparsified H 1 solver constructed on a low-order mesh of the nodal points of the underlying high-order space, and we show that the resulting H(curl) preconditioner is effective at very high polynomial orders for two-dimensional model problems with complicated geometry, varying piecewise constant coefficients, and curved elements. The resulting preconditioner scales with nearly optimal O(p d+1 ) floating point operation count and optimal O(p d ) memory transfer requirements, outperforming existing Maxwell preconditioners in the high-order regime.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Overcoming element quality dependence of finite elements with adaptive extended stencil FEM (AES‐FEM)

Summary The finite element methods (FEMs) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the Adaptive Extended Stencil Finite Element Method (AES‐FEM) as a means for overcoming this dependence on element shape quality. Our method replaces the traditional basis functions with a set of generalized Lagrange polynomial basis functions , which we construct using local weighted least‐squares approximations. The method preserves the theoretical framework of FEM and allows imposing essential boundary conditions and integrating the stiffness matrix in the same way as the classical FEM. In addition, AES‐FEM can use higher‐degree polynomial basis functions than the classical FEM, while virtually preserving the sparsity pattern of the stiffness matrix. We describe the formulation and implementation of AES‐FEM and analyze its consistency and stability. We present numerical experiments in both 2D and 3D for the Poisson equation and a time‐independent convection–diffusion equation. The numerical results demonstrate that AES‐FEM is more accurate than linear FEM, is also more efficient than linear FEM in terms of error versus runtime, and enables much better stability and faster convergence of iterative solvers than linear FEM over poor‐quality meshes. Copyright © 2016 John Wiley & Sons, Ltd.

Conley, Rebecca↗
DOE OSTI2020

High‐order symmetric cubature rules for tetrahedra and pyramids

Abstract In this article, we present an algorithm to construct high‐order fully symmetric cubature rules for tetrahedral and pyramidal elements, with positive weights and integration points that are in the interior of the domain. Cubature rules are fully symmetric if they are invariant to affine transformations of the domain. We divide the integration points into symmetry orbits where each orbit contains all the points generated by the permutation stars. These relations are represented by equality constraints. The construction of symmetric cubature rules require the solution of nonlinear polynomial equations with both inequality and equality constraints. For higher orders, we use an algorithm that consists of five sequential phases to produce the cubature rules. In the literature, symmetric numerical integration rules are available for the tetrahedron for orders p = 1 – 10, 14 , and for the pyramid up to p = 10 . We have obtained fully symmetric cubature rules for both of these elements up to order p = 20 . Numerical tests are presented that verify the polynomial‐precision of the cubature rules. Convergence studies are performed for the integration of exponential, weakly singular, and trigonometric test functions over both elements with flat and curved faces. With increase in p , improvements in accuracy is realized, though nonmonotonic convergence is observed.

Jaśkowiec, Jan↗
DOE OSTI2025

Kernel Manifolds: Nonlinear‐Augmentation Dimensionality Reduction Using Reproducing Kernel Hilbert Spaces

This paper generalizes recent advances on quadratic manifold (QM) dimensionality reduction by developing kernel methods-based nonlinear-augmentation dimensionality reduction. QMs, and more generally feature map-based nonlinear corrections, augment linear dimensionality reduction with a nonlinear correction term in the reconstruction map to overcome approximation accuracy limitations of purely linear approaches. While feature map-based approaches typically learn a least squares optimal polynomial correction term, we generalize this approach by learning an optimal nonlinear correction from a user-defined reproducing kernel Hilbert space. Our approach allows one to impose arbitrary nonlinear structure on the correction term, including polynomial structure, and includes feature map and radial basis function-based corrections as special cases. Furthermore, our method has relatively low training cost and has monotonically decreasing error as the latent space dimension increases. In conclusion, we compare our approach to proper orthogonal decomposition and several recent QM approaches on data from several example problems.

kernel methods↗
DOE OSTI2016

Parameterized complex dielectric functions of CuIn 1−x Ga x Se 2 : applications in optical characterization of compositional non‐uniformities and depth profiles in materials and solar cells

Abstract In‐situ spectroscopic ellipsometry (SE) was employed to extract the complex dielectric functions ε = ε 1 + iε 2 over the spectral range of 0.75–6.5 eV for a set of polycrystalline CuIn 1− x Ga x Se 2 (CIGS) thin films with different alloy compositions x = [Ga]/{[In] + [Ga]}. For highest possible accuracy in ε for each CIGS thin film, specialized SE procedures were adopted including (i) deposition to a thickness of ~600 Å on smooth native oxide covered crystal silicon wafers, which minimizes the surface roughness on the film and thus the required corrections in data analysis, and (ii) measurement in‐situ , which minimizes ambient contamination and oxidation of the film surface. Assuming an analytical form for each of the ε spectra for these CIGS films, oscillator parameters were obtained in best fits, and these parameters were fit in turn to polynomials in x . With the resulting database of polynomial coefficients, the ε spectra for any composition of CIGS can be generated from the single parameter, x . In addition to enabling accurate contactless determination of bulk and surface roughness layer thicknesses of CIGS films by high speed multichannel SE, the database enables characterization of the composition and its profile with depth into these films, and even how the depth profile varies spatially within the plane of the films. In this study, depth profile parameters were found to correlate spatially with solar cell performance parameters. As a result, SE provides the capability of contactless compositional analysis of production‐scale CIGS photovoltaic modules at high speed. Copyright © 2016 John Wiley & Sons, Ltd.

Aryal, Puruswottam↗
DOE OSTI2018

A generalized framework for reduced-order modeling of a wind turbine wake

A reduced-order model for a wind turbine wake is sought from large eddy simulation data. Fluctuating velocity fields are combined in the correlation tensor to form the kernel of the proper orthogonal decomposition (POD). Proper orthogonal decomposition modes resulting from the decomposition represent the spatially coherent turbulence structures in the wind turbine wake; eigenvalues delineate the relative amount of turbulent kinetic energy associated with each mode. Back-projecting the POD modes onto the velocity snapshots produces dynamic coefficients that express the amplitude of each mode in time. A reduced-order model of the wind turbine wake (wakeROM) is defined through a series of polynomial parameters that quantify mode interaction and the evolution of each POD mode coefficients. The resulting system of ordinary differential equations models the wind turbine wake composed only of the large-scale turbulent dynamics identified by the POD. Tikhonov regularization is used to recalibrate the dynamical system by adding additional constraints to the minimization seeking polynomial parameters, reducing error in the modeled mode coefficients. The wakeROM is periodically reinitialized with new initial conditions found by relating the incoming turbulent velocity to the POD mode coefficients through a series of open-loop transfer functions. The wakeROM reproduces mode coefficients to within 25.2%, quantified through the normalized root-mean-square error. Furthermore, a high-level view of the modeling approach is provided as a platform to discuss promising research directions, alternate processes that could benefit stability and efficiency, and desired extensions of the wakeROM.

17 WIND ENERGY↗
DOE OSTI2019

deal.II Implementation of a Weak Galerkin Finite Element Solver for Darcy Flow

This paper presents a weak Galerkin (WG) finite element solver for Darcy flow and its implementation on the deal.II platform. The solver works for quadrilateral and hexahedral meshes in a unified way. It approximates pressure by Q-type degree $k(≥ 0)$ polynomials separately defined in element interiors and on edges/faces. In this work, numerical velocity is obtained in the unmapped Raviart-Thomas space $RT_{[k]}$ via postprocessing based on the novel concepts of discrete weak gradients. The solver is locally mass-conservative and produces continuous normal fluxes. The implementation in deal.II allows polynomial degrees up to 5. Numerical experiments show that our new WG solver performs better than the classical mixed finite element methods.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Stringy canonical forms

Canonical forms of positive geometries play an important role in revealing hidden structures of scattering amplitudes, from amplituhedra to associahedra. In this paper, we introduce “stringy canonical forms”, which provide a natural definition and extension of canonical forms for general polytopes, deformed by a parameter α'. They are defined by real or complex integrals regulated with polynomials with exponents, and are meromorphic functions of the exponents, sharing various properties of string amplitudes. As α'→ 0, they reduce to the usual canonical form of a polytope given by the Minkowski sum of the Newton polytopes of the regulating polynomials, or equivalently the volume of the dual of this polytope, naturally determined by tropical functions. At finite α', they have simple poles corresponding to the facets of the polytope, with the residue on the pole given by the stringy canonical form of the facet. There is the remarkable connection between the α'→ 0 limit of tree-level string amplitudes, and scattering equations that appear when studying the α'→ ∞ limit. We show that there is a simple conceptual understanding of this phenomenon for any stringy canonical form: the saddle-point equations provide a diffeomorphism from the integration domain to the interior of the polytope, and thus the canonical form can be obtained as a pushforward via summing over saddle points. When the stringy canonical form is applied to the ABHY associahedron in kinematic space, it produces the usual Koba-Nielsen string integral, giving a direct path from particle to string amplitudes without an a priori reference to the string worldsheet. We also discuss a number of other examples, including stringy canonical forms for finite-type cluster algebras (with type A corresponding to usual string amplitudes), and other natural integrals over the positive Grassmannian.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Complementarity and the unitarity of the black hole S -matrix

Recently, Akers et al. proposed a non-isometric holographic map from the interior of a black hole to its exterior. Within this model, we study properties of the black hole S-matrix, which are in principle accessible to observers who stay outside the black hole. Specifically, we investigate a scenario in which an infalling agent interacts with radiation both outside and inside the black hole. Because the holographic map involves postselection, the unitarity of the S-matrix is not guaranteed in this scenario, but we find that unitarity is satisfied to very high precision if suitable conditions are met. If the internal black hole dynamics is described by a pseudorandom unitary transformation, and if the operations performed by the infaller have computational complexity scaling polynomially with the black hole entropy, then the S-matrix is unitary up to corrections that are superpolynomially small in the black hole entropy. Furthermore, while in principle quantum computation assisted by postselection can be very powerful, we find under similar assumptions that the S-matrix of an evaporating black hole has polynomial computational complexity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Trigonometric continuous-variable gates and hybrid quantum simulations of the sine-Gordon model

Hybrid qubit-qumode quantum computing platforms provide a natural setting for simulating interacting bosonic quantum field theories. However, existing continuous-variable gate constructions rely predominantly on polynomial functions of canonical quadratures. In this work, we introduce a complementary universality paradigm based on trigonometric continuous-variable gates, which enable a Fourier-like representation of bosonic operators and are particularly well suited for periodic and non-perturbative interactions. We present an ancilla-based framework for implementing trigonometric gates with arguments given by arbitrary Hermitian functions of qumode quadratures. The protocol yields unitary gates deterministically, and non-unitary gates through probabilistic post-selection. As a concrete application, we develop a hybrid qubit-qumode quantum simulation of the lattice sine-Gordon model. Using these gates, we prepare ground states via quantum imaginary-time evolution, simulate real-time dynamics, compute time-dependent vertex two-point correlation functions, and extract quantum kink profiles under topological boundary conditions. Our results demonstrate that trigonometric continuous-variable gates provide a physically natural framework for simulating interacting field theories on near-term hybrid quantum hardware, while establishing a parallel route to universality beyond polynomial gate constructions. We expect that the trigonometric gates introduced here to find broader applications, including quantum simulations of condensed matter systems, quantum chemistry, and biological models.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

The ghost in the radiation: robust encodings of the black hole interior

We reconsider the black hole firewall puzzle, emphasizing that quantum error-correction, computational complexity, and pseudorandomness are crucial concepts for understanding the black hole interior. We assume that the Hawking radiation emitted by an old black hole is pseudorandom, meaning that it cannot be distinguished from a perfectly thermal state by any efficient quantum computation acting on the radiation alone. We then infer the existence of a subspace of the radiation system which we interpret as an encoding of the black hole interior. This encoded interior is entangled with the late outgoing Hawking quanta emitted by the old black hole, and is inaccessible to computationally bounded observers who are outside the black hole. Specifically, efficient operations acting on the radiation, those with quantum computational complexity polynomial in the entropy of the remaining black hole, commute with a complete set of logical operators acting on the encoded interior, up to corrections which are exponentially small in the entropy. Thus, under our pseudorandomness assumption, the black hole interior is well protected from exterior observers as long as the remaining black hole is macroscopic. On the other hand, if the radiation is not pseudorandom, an exterior observer may be able to create a firewall by applying a polynomial-time quantum computation to the radiation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Spectral fluctuations in the Sachdev-Ye-Kitaev model

We present a detailed quantitative analysis of spectral correlations in the Sachdev-Ye-Kitaev (SYK) model. We find that the deviations from universal Random Matrix Theory (RMT) behavior are due to a small number of long-wavelength fluctuations (of the order of the number of Majorana fermions N ) from one realization of the ensemble to the next one. These modes can be parameterized effectively in terms of Q-Hermite orthogonal polynomials, the main contribution being due to scale fluctuations for which we give a simple analytical estimate. Our numerical results for N = 32 show that only the lowest eight polynomials are needed to eliminate the nonuniversal part of the spectral fluctuations. The covariance matrix of the coefficients of this expansion can be obtained analytically from low-order double-trace moments. We evaluate the covariance matrix of the first six moments and find that it agrees with the numerics. We also analyze the spectral correlations in terms of a nonlinear σ-model, which is derived through a Fierz transformation, and evaluate the one and two-point spectral correlation functions to two-loop order. The wide correlator is given by the sum of the universal RMT result and corrections whose lowest-order term corresponds to scale fluctuations. However, the loop expansion of the σ-model results in an ill-behaved expansion of the resolvent, and it gives universal RMT fluctuations not only for q= 4 or higher even q-body interactions, but also for the q= 2 SYK model albeit with a much smaller Thouless energy while the correct result in this case should have been Poisson statistics. In our numerical studies we analyze the number variance and spectral form factor for N = 32 and q = 4. We show that the quadratic deviation of the number variance for large energies appears as a peak for small times in the spectral form factor. After eliminating the long-wavelength fluctuations, we find quantitative agreement with RMT up to an exponentially large number of level spacings for the number variance or exponentially short times in the case of the spectral form factor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

On the Trotter Error in Many-body Quantum Dynamics with Coulomb Potentials

Efficient simulation of many-body quantum systems is central to advances in physics, chemistry, and quantum computing, with a key question being whether the simulation cost scales polynomially with the system size. Here, in this work, we analyze many-body quantum systems with Coulomb interactions, which are fundamental to electronic and molecular systems. We prove that Trotterization for such unbounded Hamiltonians achieves a 1/4-order convergence rate, with explicit polynomial dependence on the number of particles. The result holds for all initial wavefunctions in the domain of the Hamiltonian, and the 1/4-order convergence rate is optimal, as previous work has numerically demonstrated that it can be saturated by a specific initial ground state. The main challenges arise from the many-body structure and the singular nature of the Coulomb potential. Our proof strategy differs from prior state-of-the-art Trotter analyses, addressing both difficulties in a unified framework. Our analysis treats the Coulomb potential as an unbounded operator without modification or regularization, and does not rely on spatial discretization, making it compatible with both first- and second-quantized circuit constructions.

Fang, Di [Duke Univ., Durham, NC (United States)]↗
DOE OSTI2019

Sparse low rank approximation of potential energy surfaces with applications in estimation of anharmonic zero point energies and frequencies

We introduce a method that exploits sparse representation of potential energy surfaces (PES) on a polynomial basis set selected by compressed sensing . The method is useful for studies involving large numbers of PES evaluations, such as the search for local minima, transition states, or integration. We apply this method for estimating zero point energies and frequencies of molecules using a three step approach. In the first step, we interpret the PES as a sparse tensor on polynomial basis and determine its entries by a compressed sensing based algorithm using only a few PES evaluations. Then, we establish a rank reduction strategy to compress this tensor in a suitable low-rank canonical tensor format using standard tensor compression tools. This allows representing a high dimensional PES as a small sum of products of one dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate the product of sparse canonical low-rank representation of PES and Green’s function in the second-order diagrammatic vibrational many-body Green’s function theory (XVH2) for estimation of zero-point energies and frequencies. Numerical tests on molecules considered in this work indicate a more efficient scaling of computational cost with molecular size as compared to other methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Positivity Limiters for Filtered Spectral Approximations of Linear Kinetic Transport Equations

We analyze the properties and compare the performance of several positivity limiters for spectral approximations with respect to the angular variable of linear transport equations. It is well-known that spectral methods suffer from the occurrence of (unphysical) negative spatial particle concentrations due to the fact that the underlying polynomial approximations are not always positive at the kinetic level. Positivity limiters address this defect by enforcing positivity of the polynomial approximation on a finite set of preselected points. With a proper PDE solver, they ensure positivity of the particle concentration at each step in a time integration scheme. We review several known positivity limiters proposed in other contexts and also introduce a modification for one of them. We give error estimates for the consistency of the positive approximations produced by these limiters and compare the theoretical estimates to numerical results. We then solve two benchmark problems with these limiters, make qualitative and quantitative observations about the solutions, and then compare the efficiency of the different limiters.

97 MATHEMATICS AND COMPUTING↗