Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “matrix approximation”

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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A deep learning upscaling framework: Reactive transport and mineral precipitation in fracture-matrix systems

Pore-scale modeling has limited applicability at large scales due to its high computational cost. One common approach to upscale pore-scale models is the use of effective medium theories, which homogenize small-scale features in a porous structure and characterize the medium by macroscale properties (e.g., permeability) and equations (e.g., Darcy’s law). However, there are classes of physical processes for which effective medium approximations may become inaccurate, e.g., mineral precipitation and clogging during reactive transport. We have developed a deep learning upscaling framework, in which pore-scale modeling is directly employed in macroscale systems, without relying on effective medium approximations. The upscaling framework is first developed for general multiscale systems and then applied to modeling reactive transport with mineral precipitation in the altered layer in fracture-matrix structures. Solute transport from the fractures to the matrix is modeled as a wall boundary condition for the fractures, which, in turn, is predicted by recurrent neural networks using the concentration histories at the fracture-matrix boundary. Specifically, we consider a meter-scale fracture network embedded in sandstones, where the smallest feature is at the micron scale. Here the proposed framework allows us to span five orders of magnitude in length scales by capturing mineral precipitation in the altered layer of the rock matrix at the pore scale across the entire meter-scale fracture network.

42 ENGINEERING↗
DOE OSTI2021

A Feynman-Kac based numerical method for the exit time probability of a class of transport problems

The exit time probability, which gives the likelihood that an initial condition leaves a prescribed region of the phase space of a dynamical system at, or before, a given time, is arguably one of the most natural and important transport problems. In this work, we present an accurate and efficient numerical method for computing this probability for systems described by non-autonomous (time-dependent) stochastic differential equations (SDEs) or their equivalent Fokker-Planck partial differential equations. The method is based on the direct approximation of the Feynman-Kac formula that establishes a link between the adjoint Fokker-Planck equation and the forward SDE. The Feynman-Kac formula is approximated using the Gauss-Hermite quadrature rules and piecewise cubic Hermite interpolating polynomials, and a GPU accelerated matrix representation is used to compute the entire time evolution of the exit time probability using a single pass of the algorithm. The method is unconditionally stable, exhibits second order convergence in space, first order convergence in time, and it is straightforward to parallelize. Applications are presented to the advection diffusion of a passive tracer in a fluid flow exhibiting chaotic advection, and to the runaway acceleration of electrons in a plasma in the presence of an electric field, collisions, and radiation damping. Benchmarks against analytical solutions as well as comparisons with explicit and implicit finite difference standard methods for the adjoint Fokker-Planck equation are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Variance reduction in lattice QCD observables via normalizing flows

Normalizing flows can be used to construct unbiased, reduced-variance estimators for lattice field theory observables that are defined by a derivative with respect to action parameters. This work implements the approach for observables involving gluonic operator insertions in the SU(3) Yang-Mills theory and two-flavor QCD in four space-time dimensions. Variance reduction by factors of 10–60 is achieved in glueball correlation functions and in gluonic matrix elements related to hadron structure, with demonstrated computational advantages. The observed variance reduction is found to be approximately independent of the lattice volume, so volume transfer can be utilized to minimize training costs.

Abbott, Ryan [Columbia U.; MIT, Cambridge, CTP; IA↗
DOE OSTI2023

Operator Relaxation and the Optimal Depth of Classical Shadows

Classical shadows are a powerful method for learning many properties of quantum states in a sample-efficient manner, by making use of randomized measurements. Here we study the sample complexity of learning the expectation value of Pauli operators via “shallow shadows,” a recently proposed version of classical shadows in which the randomization step is effected by a local unitary circuit of variable depth t. Here we show that the shadow norm (the quantity controlling the sample complexity) is expressed in terms of properties of the Heisenberg time evolution of operators under the randomizing (“twirling”) circuit—namely the evolution of the weight distribution characterizing the number of sites on which an operator acts nontrivially. For spatially contiguous Pauli operators of weight k, this entails a competition between two processes: operator spreading (whereby the support of an operator grows over time, increasing its weight) and operator relaxation (whereby the bulk of the operator develops an equilibrium density of identity operators, decreasing its weight). From this simple picture we derive (i) an upper bound on the shadow norm which, for depth t~log⁡(k), guarantees an exponential gain in sample complexity over the t=0 protocol in any spatial dimension, and (ii) quantitative results in one dimension within a mean-field approximation, including a universal subleading correction to the optimal depth, found to be in excellent agreement with infinite matrix product state numerical simulations. Our Letter connects fundamental ideas in quantum many-body dynamics to applications in quantum information science, and paves the way to highly optimized protocols for learning different properties of quantum states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

The second-generation Shifted Boundary Method and its numerical analysis

Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we present enhanced variational SBM formulations for the Poisson and Stokes problems with improved flexibility and robustness. These simplified variational forms allow to relax some of the assumptions required by the mathematical proofs of stability and convergence of earlier implementations. First, we show that these new SBM implementations can be proved asymptotically stable and convergent even without the rather restrictive assumption that the inner product between the normals to the true and surrogate boundaries is positive. Second, we show that it is not necessary to introduce a stabilization term involving the tangential derivatives of the solution at Dirichlet boundaries, therefore avoiding the calibration of an additional stabilization parameter. Finally, we prove enhanced L 2 -estimates without the cumbersome assumption – of earlier proofs – that the surrogate domain is convex. Instead we rely on a conventional assumption that the boundary of the true domain is smooth, which can also be replaced by requiring convexity of the true domain. The aforementioned improvements open the way to a more general and efficient implementation of the Shifted Boundary Method, particularly in complex three-dimensional geometries. We complement these theoretical developments with numerical experiments in two and three dimensions.

42 ENGINEERING↗
DOE OSTI2025

Destructive PIE and Safety Testing of Six AGR-5/6/7 Capsule 2 Compacts

This study evaluates fission product retention and particle failure mechanisms in AGR-5/6/7 Capsule 2 uranium carbide and uranium oxide (UCO) tristructural isotropic (TRISO) fuel under high-temperature gas reactor accident-relevant conditions using high-temperature safety tests and destructive postirradiation examination. Three Capsule 2 compacts were held isothermally at 1600°C for approximately 300 hours and one compact at 1800°C for approximately 300 hours; two additional compacts were examined in the as-irradiated state. Post-test deconsolidation–leach–burn–leach (DLBL) quantified nuclide inventories in matrix and particles. Individual particles were surveyed for radioisotope inventories, and microanalytical approaches resolved microstructural evolution and fission product distributions within the coating layers. At 1600°C, no krypton was detected above the minimum detectable limit, and cesium releases were far below a single particle equivalent, indicating the absence of full TRISO failure or SiC failures. Silver releases were limited and primarily reflected depleted postirradiation inventories, consistent with prior compact-level exams indicating substantial in-pile 110mAg loss. At 1800°C, cumulative 134Cs release of approximately 2.5 particle equivalents and delayed 85Kr totaling approximately 0.53 particle equivalents were consistent with one full TRISO failure and two SiC failures. Europium and strontium releases were roughly one order of magnitude higher than at 1600°C and comparable to AGR-1/AGR-2 high-temperature tests, with sustained late-hold rates indicating diffusion through intact coatings coupled with matrix depletion. Overall, AGR-5/6/7 Capsule 2 UCO fuel demonstrated fission product retention during safety testing consistent with prior AGR campaigns, while distinctive in-pile 110mAg depletion and measurable 1600°C europium loss motivate targeted follow-on studies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Destructive PIE and Safety Testing of Six AGR-5/6/7 Capsule 2 Compacts

This study evaluates fission product retention and particle failure mechanisms in AGR-5/6/7 Capsule 2 uranium carbide and uranium oxide (UCO) tristructural isotropic (TRISO) fuel under high-temperature gas reactor accident-relevant conditions using high-temperature safety tests and destructive post-irradiation examination. Three Capsule 2 compacts were held isothermally at 1600°C for approximately 300 hours and one compact at 1800°C for approximately 300 hours; two additional compacts were examined in the as-irradiated state. Post-test deconsolidation–leach–burn–leach (DLBL) quantified nuclide inventories in matrix and particles. Individual particles were surveyed for radioisotope inventories, and microanalytical approaches resolved microstructural evolution and fission product distributions within the coating layers. At 1600°C, no krypton was detected above the minimum detectable limit, and cesium releases were far below a single particle equivalent, indicating the absence of full TRISO failure or SiC failures. Silver releases were limited and primarily reflected depleted post-irradiation inventories, consistent with prior compact-level exams indicating substantial in-pile 110m Ag loss. At 1800°C, cumulative 134 Cs release of approximately 2.5 particle equivalents and delayed 85 Kr totaling approximately 0.53 particle equivalents were consistent with one full TRISO failure and two SiC failures. Europium and strontium releases were roughly one order of magnitude higher than at 1600°C and comparable to AGR-1/AGR-2 high-temperature tests, with sustained late-hold rates indicating diffusion through intact coatings coupled with matrix depletion. Overall, AGR-5/6/7 Capsule 2 UCO fuel demonstrated fission product retention during safety testing consistent with prior AGR campaigns, while distinctive in-pile 110m Ag depletion and measurable 1600°C europium loss motivate targeted follow-on studies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

Enhancing photoionization rate calculations in low-temperature plasmas using spectral methods

Photoionization plays a central role in the development of streamer discharges and other non-equilibrium plasma phenomena. It creates seed electrons, which are essential for positive streamer propagation, allowing the ionization front to move forward. Because of this, accurate modeling of photoionization is very important for predicting streamer behavior and plasma evolution. The photoionization process in air (N 2 – O 2 mixture) is often described by the Zheleznyak model (1982). This model is usually solved through Helmholtz-type equations that approximate the Zheleznyak photoionization model (Zheleznyak et al. 1982) as Partial Differential Equations (PDEs). Conventional numerical methods, such as the Finite Difference Method (FDM) or Finite Volume Method (FVM), are widely used to solve these equations. Although they are prevalent, the computational cost of these methods due to their need for matrix operations and iterative solver is demanding. To address this challenge, this work develops a spectral solver based on the Fast Fourier Transform (FFT) combined with Discrete Cosine Transform (DCT) and Discrete Sine Transform (DST) to calculate the photoionization rate efficiently in an axisymmetric cylindrical domain. This method naturally satisfies the boundary conditions used in the model and converts the PDE into algebraic ones in spectral space. Thus, avoids the need for iterative matrix solvers. When compared with FDM results, it is demonstrated that the new solver not only maintains accuracy, but also reduces the computational cost, showing a performance increase of approximately 100 compared to FDM over a wide range of problem sizes. The method is parallelized using Message Passing Interface (MPI) and has been integrated into a fluid plasma model for streamer simulation. Here, this FFT-based approach provides a fast and reliable alternative for calculating photoionization in fluid models, helping large-scale plasma simulations run faster and efficiently, and allows higher-resolution simulation without extra computational cost.

Axisymmetric system↗
DOE OSTI2023

Enabling attractive-repulsive potentials in binary-collision-approximation monte-carlo codes for ion-surface interactions

Abstract Binary Collision Approximation (BCA) codes for ion-material interactions, such as SRIM, Tridyn, F-TRIDYN, and SDtrimSP, have historically been limited to screened Coulomb potentials even at low energies due to the difficulty in numerically solving the Distance of Closest Approach (DOCA) problem for attractive-repulsive potentials. Techniques such as direct n-body simulation or modifications to Newton’s method are either prohibitively costly or not guaranteed to work for all potentials. Advanced rootfinding techniques, such as companion matrix solvers, offer a solution. For many attractive-repulsive potentials, however, a companion matrix cannot be used directly, because there is no way to put the associated functions into a monomial basis form. A complementary technique is proxy rootfinding—by finding the best-fit polynomial approximant of a function, the zeros of the approximant can be guaranteed to be close to the zeros of the function. Using the Chebyshev basis and grid offers additional guarantees with regards to the quality of the approximation, the speed of convergence, and the avoidance of Runge’s phenomenon. By finding Chebyshev interpolants and using the Chebyshev-Frobenius companion matrix, the zeros of any real function on a bounded domain can be found. Here we show that using an Adaptive Chebyshev Proxy Rootfinder with Automatic Subdivision (ACPRAS) with appropriate scaling functions, numerical issues presented by attractive-repulsive potentials, including those of scale, can be handled. Using these techniques, we show that it is possible to include any physically reasonable interatomic potential in a BCA code, and to guarantee correctness of the resulting scattering angle calculations.

Materials Science↗
DOE OSTI2023

Multimodal photon and neutron imaging devices with fast event-by-event multisampling readout and optimized particle type discrimination

A particle imaging method for distinguishing between types of incident particles, such as neutrons, photons, and alphas, and improving the position resolution of particle imaging devices with matrix readout. The method includes high frequency multisampling readout electronics that provides the sequences of multiple measurements for each detected event, resulting in recorded detailed waveform information describing the signals. Such detailed information is used to approximate each signal waveform with a parameterized function in which the extracted parameter sets determine the type of the incident particle in an optimized fashion. The detailed event-by-event multisampling information for each signal readout channel in the matrix readout of the radiation imaging devices improves and optimizes the position resolution for variable shapes of the signals. Such devices can be used in mixed radiation fields, creating a new class of multimodal photon and neutron imagers.

Degtiarenko, Pavel V.↗
DOE OSTI2025

Design of Silicide-Strengthened Nb–Si–Cr–(Mo) alloys for additive manufacturing

Three high–intermetallic volume Nb–Si–Cr–(Mo) alloys were designed using CALPHAD modeling with the goal of identifying high–specific strength, oxidation-resistant alloys that can be additively manufactured using powder bed fusion. The silicides Nb 5 Si 3 and Nb 9 Si 2 Cr3 were targeted as the primary strengthening phases, and the addition of Cr promoted the NbCr 2 phase. These alloys were cast and surface-processed with electron beam welding at different speeds to simulate additive manufacturing, and the phases and microstructures of both cast and welded regions were characterized. The weld processing was found to produce fine-grained microstructures in each alloy with fine-scale intermetallics uniformly distributed among a body-centered cubic Nb matrix. Microstructural refinement and hardness were found to increase with weld velocity; one alloy reached its highest hardness of approximately 16 GPa before the brittleness at higher velocities became detrimental. One alloy was found to be qualitatively the least brittle while also attaining a hardness of 13 GPa and was therefore identified as a good candidate for additive manufacturing.

36 MATERIALS SCIENCE↗
DOE OSTI2025

The polarized-signal density matrix: A practical way to recover molecular frame information from isotropic samples

We present a novel approach to model ultrafast time-dependent nonlinear optical polarization sensitive signals emitted from randomly oriented molecules. By projecting the laboratory-frame analyzer polarization axis into the molecular-frame and linking that axis with the density matrix through a tensor product, we demonstrate an approach to find a specific molecular orientation that yields a good approximation to simulated four-wave mixing signals produced by the same model but with averaging over molecular orientation.

Thurston, Richard L↗
DOE OSTI2025

An Application of Molecular Recognition for the Efficient Removal of Cesium from Hanford Nuclear Waste by Modular Solvent Extraction

In this work, experimental results leading to flowsheet design are presented showing how a calixarene-crown ether based solvent-extraction process can meet the challenge of cesium removal from nuclear tank wastes stored at the US Department of Energy Hanford site. Cleanup of legacy Cold War nuclear waste stored in underground tanks represents one of the greatest environmental challenges facing the US Department of Energy in terms of risk, cost, and effectiveness of applicable science and technology. Planning for the cleanup at the Hanford Site calls for the removal of the radioactive fission product 137Cs from its alkaline salt waste, including the use of modular processes that can be deployed near the tank farms. To meet the resulting need for extremely high selectivity, the Next-Generation Caustic-Side Solvent Extraction (NG-CSSX) process employing a calix[4]arene-crown ether in modified kerosene has been adapted to remove sub-millimolar cesium in competition with molar sodium and potassium in a high-nitrate alkaline matrix. Potassium loading in the solvent was determined in extraction, scrubbing, and stripping, leading to an empirical model closely approximating cesium distribution ratios for a variety of Hanford waste types. Process chemistry has been developed based on this molecular-recognition approach, focusing on the competitive effect of potassium loading and the mitigating process modifications needed, including extending the scrub section. The result is a modular flowsheet design that can achieve cesium decontamination factors well in excess of 15,000 even for the worst-case Hanford waste.

Williams, Neil [ORNL] (ORCID:000000023159226X)↗
DOE OSTI2023

A Polarization Tensor for Neutron Optics

A rank 2 dimension 3 tensor formulation for polarized neutron transport in a magnetic field is derived. Using this formulation, the rotating magnetic field problem is revisited to produce a single 3 × 3 vector-transformation matrix that describes the polarization transport. That result is then used to fashion a new strategy for a numerical approximation of polarization transport in an arbitrary magnetic field using time-dependent perturbation theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Thin film design of amorphous hafnium oxide nanocomposites enabling strong interfacial resistive switching uniformity

A design concept of phase-separated amorphous nanocomposite thin films is presented that realizes interfacial resistive switching (RS) in hafnium-oxide-based devices. The films are formed by incorporating an average of 7% Ba into hafnium oxide during pulsed laser deposition at temperatures ≤400°C. The added Ba prevents the films from crystallizing and leads to ~20-nm-thin films consisting of an amorphous HfO x host matrix interspersed with ~2-nm-wide, ~5-to-10-nm-pitch Ba-rich amorphous nanocolumns penetrating approximately two-thirds through the films. This restricts the RS to an interfacial Schottky-like energy barrier whose magnitude is tuned by ionic migration under an applied electric field. Resulting devices achieve stable cycle-to-cycle, device-to-device, and sample-to-sample reproducibility with a measured switching endurance of ≥10 4 cycles for a memory window ≥10 at switching voltages of ±2 V. Each device can be set to multiple intermediate resistance states, which enables synaptic spike-timing–dependent plasticity. The presented concept unlocks additional design variables for RS devices.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Time-dependent-bases with local CUR decomposition method for accelerating turbulent combustion simulations

Here, this study presents a novel reduced-order modeling framework, Time-Dependent Bases with Local CUR decomposition (TDB-L-CUR), designed to efficiently and accurately approximate the species transport equations in reacting flow simulations. The method extends the existing TDB-CUR approach for chemically reacting flows (Jung et al. Comput. Methods Appl. Mech. Engrg. 437 (2025) 117758), which leverages matrix decomposition techniques to form a global-in-space, time-dependent low-dimensional manifold. While TDB-CUR performs well in homogeneous systems, it may be less well-suited to spatially heterogeneous systems such as turbulent flames, where higher-rank approximations are typically required. The proposed TDB-L-CUR framework introduces two methodological extensions to the baseline approach. First, it applies unsupervised clustering to partition the physical domain into distinct regions, enabling spatially localized manifold construction, thereby reducing the rank required for the reduced-order representation. Second, it incorporates a computational singular perturbation (CSP)-based scheme for identifying and penalizing fast species, allowing for spatio-temporally adaptive mitigation of chemical stiffness. The proposed framework is validated on a hierarchy of test cases, including a one-dimensional premixed flame, a two-dimensional nonpremixed ignition case with vortex interaction, and a three-dimensional turbulent premixed flame. TDB-L-CUR significantly improves accuracy over TDB-CUR while further reducing computational cost. The fully on-the-fly formulation of TDB-L-CUR (i.e., requiring no offline training or prior knowledge) makes it a robust and scalable tool for reduced-order modeling of reactive flows.

Local manifold↗
DOE OSTI2021

Quantum simulation of molecules without fermionic encoding of the wave function

Abstract Molecular simulations generally require fermionic encoding in which fermion statistics are encoded into the qubit representation of the wave function. Recent calculations suggest that fermionic encoding of the wave function can be bypassed, leading to more efficient quantum computations. Here we show that the two-electron reduced density matrix (2-RDM) can be expressed as a unique functional of the unencoded N -qubit-particle wave function without approximation, and hence, the energy can be expressed as a functional of the 2-RDM without fermionic encoding of the wave function. In contrast to current hardware-efficient methods, the derived functional has a unique, one-to-one (and onto) mapping between the qubit-particle wave functions and 2-RDMs, which avoids the over-parametrization that can lead to optimization difficulties such as barren plateaus. An application to computing the ground-state energy and 2-RDM of H 4 is presented.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Quantum state reduction: Generalized bipartitions from algebras of observables

Reduced density matrices are a powerful tool in the analysis of entanglement structure, approximate or coarse-grained dynamics, decoherence, and the emergence of classicality. It is straightforward to produce a reduced density matrix with the partial-trace map by tracing out part of the quantum state, but in many natural situations this reduction may not be achievable. We investigate the general problem of identifying how the quantum state is reduced given a restriction on the observables. For example, in an experimental setting, the set of observables that can actually be measured is usually modest (compared to the set of all possible observables) and their resolution is limited. In such situations, the appropriate state-reduction map can be defined via a generalized bipartition, which is associated with the structure of irreducible representations of the algebra generated by the restricted set of observables. One of our main technical results is a general, not inherently numeric, algorithm for finding irreducible representations of matrix algebras. In our work, we demonstrate the viability of this approach with two examples of limited-resolution observables. The definition of quantum state reductions can also be extended beyond algebras of observables. To accomplish this task we introduce a more flexible notion of bipartition, the partial bipartition, which describes coarse grainings preserving information about a limited set (not necessarily algebra) of observables. We describe a variational method to choose the coarse grainings most compatible with a specified Hamiltonian, which exhibit emergent classicality in the reduced state space. We apply this construction to the concrete example of the one-dimensional Ising model. Our results have relevance for quantum information, bulk reconstruction in holography, and quantum gravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗