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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Quantum simulation of quantum phase transitions using the convex geometry of reduced density matrices

Transitions of many-particle quantum systems between distinct phases at absolute-zero temperature, known as quantum phase transitions, require an exacting treatment of particle correlations. Here in this work, we present a general quantum-computing approach to quantum phase transitions that exploits the geometric structure of reduced density matrices. While typical approaches to quantum phase transitions examine discontinuities in the order parameters, the origin of phase transitions—their order parameters and symmetry breaking—can be understood geometrically in terms of the set of two-particle reduced density matrices (2-RDMs). The convex set of 2-RDMs provides a comprehensive map of the quantum system including its distinct phases as well as the transitions connecting these phases. Because 2-RDMs can potentially be computed on quantum computers at nonexponential cost, even when the quantum system is strongly correlated, they are ideally suited for a quantum-computing approach to quantum phase transitions. We compute the convex set of 2-RDMs for a Lipkin-Meshkov-Glick spin model on IBM superconducting-qubit quantum processors. Even though computations are limited to few-particle models due to device noise, comparisons with a classically solvable 1000-particle model reveal that the finite-particle quantum solutions capture the key features of the phase transitions including the strong correlation and the symmetry breaking.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Generalized Analytical Estimation of Sensitivity Matrices in Unbalanced Distribution Networks

Fast and accurate estimation of sensitivity matrices is significant for the enhancement of distribution system modeling and automation. Analytical estimations have mainly focused on voltage magnitude sensitivity to active/reactive power injections for unbalanced networks with Wye-connected loads and neglecting DERs' smart inverter functionality. Hence, this paper enhances the scope of analytical estimation of sensitivity matrices for unbalanced networks with 1- Φ, 2- Φ, and 3- Φ Delta/Wye-connected loads, DERs with smart inverter functionality, and substation/line step-voltage regulators (SVR). A composite bus model comprising of DER, Delta- and Wye-connected load is proposed to represent a generic distribution bus, which can be simplified to load, PV, or voltage-controlled bus as required. Furthermore, the proposed matrix-based analytical method consolidates voltage magnitude and angle sensitivity to active/reactive power injection and tap-position of all SVRs into a single algorithm. Extensive case studies on IEEE and EPRI networks show the accuracy and wide scope of the proposed algorithm compared to the existing benchmark method.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

A customized MOF-polymer composite for rapid gold extraction from water matrices

With the fast-growing accumulation of electronic waste and rising demand for rare metals, it is compelling to develop technologies that can promotionally recover targeted metals, like gold, from waste, a process referred to as urban mining. Thus, there is increasing interest in the design of materials to achieve rapid, selective gold capture while maintaining high adsorption capacity, especially in complex aqueous-based matrices. Here, a highly porous metal-organic framework (MOF)–polymer composite, BUT-33–poly(para-phenylenediamine) (PpPD), is assessed for gold extraction from several matrices including river water, seawater, and leaching solutions from CPUs. BUT-33–PpPD exhibits a record-breaking extraction rate, with high Au3+ removal efficiency (>99%) within seconds (less than 45 s), a competitive capacity (1600 mg/g), high selectivity, long-term stability, and recycling ability. Furthermore, the high porosity and redox adsorption mechanism were shown to be underlying reasons for the material’s excellent performance. Given the accumulation of recovered metallic gold nanoparticles inside, the material was also efficiently applied as a catalyst.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Explicit Quantum Circuits for Block Encodings of Certain Sparse Matrices

Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding embeds a properly scaled matrix of interest A in a larger unitary transformation U that can be decomposed into a product of simpler unitaries and implemented efficiently on a quantum computer. Although quantum algorithms can potentially achieve exponential speedup in solving linear algebra problems compared to the best classical algorithm, such a gain in efficiency ultimately hinges on our ability to construct an efficient quantum circuit for the block encoding of A, which is difficult in general, and not trivial even for well structured sparse matrices. Here, in this paper, we give a few examples on how efficient quantum circuits can be explicitly constructed for some well structured sparse matrices and discuss a few strategies used in these constructions. We also provide implementations of these quantum circuits in MATLAB.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Fast and Scalable FFT-Based GPU-Accelerated Algorithms for Block-Triangular Toeplitz Matrices with Application to Linear Inverse Problems Governed by Autonomous Dynamical Systems

In this work, we present an efficient and scalable algorithm for performing matrix-vector multiplications (matvecs) for block Toeplitz matrices. Such matrices, which are shift-invariant with respect to their blocks, arise in the context of solving inverse problems governed by autonomous systems, and time-invariant systems in particular. In this article, we consider inverse problems that infer unknown parameters from observational data of a linear time-invariant dynamical system given in the form of partial differential equations (PDEs). Matrix-free Newton-conjugate-gradient methods are often the gold standard for solving these inverse problems, but they require numerous actions of the Hessian on a vector. Matrix-free adjoint-based Hessian matvecs require solution of a pair of linearized forward/adjoint PDE solves per Hessian action, which may be prohibitive for large-scale inverse problems. Time invariance of the forward PDE problem leads to a block Toeplitz structure of the discretized parameter-to-observable (p2o) map defining the mapping from inputs (parameters) to outputs (observables) of the PDEs. This block Toeplitz structure enables us to exploit two key properties: (1) compact storage of the p2o map and its adjoint, and (2) efficient fast Fourier transform–based Hessian matvecs. The proposed algorithm is mapped onto large multi-GPU clusters and achieves more than 80% of peak bandwidth on NVIDIA A100 GPUs. Excellent weak scaling is shown for up to 48 A100 GPUs. For the targeted problems, the implementation executes Hessian matvecs within fractions of a second, which is orders of magnitude faster than can be achieved by conventional matrix-free Hessian matvecs via forward/adjoint PDE solves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Factorization of Binary Matrices: Rank Relations, Uniqueness and Model Selection of Boolean Decomposition

The application of binary matrices are numerous. Representing a matrix as a mixture of a small collection of latent vectors via low-rank decomposition is often seen as an advantageous method to interpret and analyze data. In this work, we examine the factorizations of binary matrices using standard arithmetic (real and nonnegative) and logical operations (Boolean and $\mathbb{Z}$ 2 ). We examine the relationships between the different ranks, and discuss when factorization is unique. In particular, we characterize when a Boolean factorization X = W$\land$H has a unique W, a unique H (for a fixed W), and when both W and H are unique, given a rank constraint. We introduce a method for robust Boolean model selection, called BMFk, and show on numerical examples that BMFk not only accurately determines the correct number of Boolean latent features but reconstruct the pre-determined factors accurately.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Brief Announcement: Communication Optimal Sparse LU Factorization for Planar Matrices

We introduce a new parallel algorithm for solving sparse LU factorization of planar matrices, which commonly arise in the finite element method for 2D PDEs. Existing scalable methods, such as the multifrontal approach with subtree-to-subcube mapping by Gupta et al. [1] and right-looking with 3D mapping by Sao et al. [2] fail to achieve optimal communication costs for these matrices. Our new algorithm combines 3D mapping and subtree-to-subcube mapping to minimize communication costs while allowing trade-offs between extra memory and reduced communication. We demonstrate that our proposed algorithm attains the communication lower bound up to a factor of O(log log n) in the memory-optimal case and up to a factor of O(log P) in the memory-independent case for an n-dimensional planar sparse matrix on P processors.

Sao, Piyush↗
DOE OSTI2024

Rare Earth Elements (REEs) Measurement in Coal and Rock Mineral Matrices

Although critical minerals including rare earth elements (REEs) can be analyzed in laboratory by some established and reliable laboratory based analytical techniques, their in-situ measurements in the field have always been challenging. For identification of REE-rich sites and REEs distribution measurement, portable field applicable technologies are paramount. As Laser-induced breakdown spectroscopy (LIBS) has enormous potential for field measurement, it has been explored for REEs measurements by many research groups. However, most of the studies are still dealing with simulated samples with traditional bench top experiments. In real world, REEs are available in various types of natural complex matrices in low content depending on the geographical locations. Considering this, LIBS has been evaluated for REE measurement in two different complex coal and rock mineral matrices representing some natural REE-rich sites. In addition, multiple samples collected from some natural sites in Wyoming, USA were experimented by using NETL’s bench top as well as miniaturized prototype setups for REE measurements.

Bhatt, Chet R.↗
DOE OSTI2025

Rare Earth Element Detection and Quantification in Coal and Rock Mineral Matrices

As global demand for rare earth elements (REEs) increases, maintaining the production and supply chain is critical. Technologies capable of being used in the field and in situ in the subsurface for rapid REE detection and quantification facilitates the efficient mining of known resources and exploration of new and unconventional resources. Laser-induced breakdown spectroscopy (LIBS) is a promising technique for rapid elemental analysis both in the laboratory and in the field. Multiple articles have been published evaluating LIBS for detection and quantification of REEs; however, REEs in their natural deposits have not been adequately studied. In this work, detection and quantification of two REEs, La and Nd, have been studied in both synthetic and natural mineral matrices at concentrations relevant to REE extraction. Measurements were performed on REE-containing rock and coal samples (natural and synthetic) utilizing different LIBS instruments and techniques, specifically a commercial benchtop instrument, a custom benchtop instrument (single- and double-pulse modes), and a custom LIBS probe currently being developed for in situ, subsurface, borehole wall detection and quantification of REEs. Plasma expansion, emission intensity, detection limits, and double-pulse signal enhancement were studied. The limits of detection (LOD) were found to be 10/14 ppm for La and 15/25 ppm for Nd in simulated coal/rock matrices in single-pulse mode. Signal enhancement of 3.5 to 6-fold was obtained with double-pulse mode as compared to single-pulse operation.

La detection↗
DOE OSTI2024

Entropy Analysis of FPGA Interconnect and Switch Matrices for Physical Unclonable Functions

Random variations in microelectronic circuit structures represent the source of entropy for physical unclonable functions (PUFs). In this paper, we investigate delay variations that occur through the routing network and switch matrices of a field-programmable gate array (FPGA). The delay variations are isolated from other components of the programmable logic, e.g., look-up tables (LUTs), flip-flops (FFs), etc., using a feature of Xilinx FPGAs called dynamic partial reconfiguration (DPR). A set of partial designs is created to fix the placement of a time-to-digital converter (TDC) and supporting infrastructure to enable the path delays through the target interconnect and switch matrices to be extracted by subtracting out common-mode delay components. Delay variations are analyzed in the different levels of routing resources available within FPGAs, i.e., local routing and across-chip routing. Data are collected from a set of Xilinx Zynq 7010 devices, and a statistical analysis of within-die variations in delay through a set of the randomly-generated and hand-crafted interconnects is presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Square Root Statistics of Density Matrices and Their Applications

To estimate the degree of quantum entanglement of random pure states, it is crucial to understand the statistical behavior of entanglement indicators such as the von Neumann entropy, quantum purity, and entanglement capacity. These entanglement metrics are functions of the spectrum of density matrices, and their statistical behavior over different generic state ensembles have been intensively studied in the literature. As an alternative metric, in this work, we study the sum of the square root spectrum of density matrices, which is relevant to negativity and fidelity in quantum information processing. In particular, we derive the finite-size mean and variance formulas of the sum of the square root spectrum over the Bures–Hall ensemble, extending known results obtained recently over the Hilbert–Schmidt ensemble.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Biomass for Carbon Removal and Storage (BiCRS) Variables Matrices

The Biomass for Carbon Removal and Storage (BiCRS) Variables Matrices provide insights related to measured, monitored, reported and verified (MMRV) components (variables) across a BiCRS value chain. Suggested variable values and components to be measured with literature references and context obtained from industry and scientists are provided for several biomass sources, conversion routes and storage scenarios. The Variables Matrices are meant to support life cycle assessment and MMRV efforts for BiCRS projects. These variables and insights may need to be updated in the future as additional information, scientific advancements, and data become available (Version 1 issued in 2025).

09 BIOMASS FUELS↗
NASA NTRS1971

Synthesis of stiffness and mass matrices from experimental vibration modes.

With highly complex structures, it is sometimes desirable to derive a dynamic model of the system from experimental vibration data. This paper presents algorithms for synthesizing the mass and stiffness matrices from experimentally derived modal data in a way which preserves the physical significance of the individual mass and stiffness elements. The synthesizing procedures allow for the incorporation of other mass and stiffness data, whether empirical or based on the analyst's insight. The mass and stiffness matrices are derived for a cantilever beam example and are compared with those obtained using earlier techniques.

Ross, R. G., Jr.↗
NASA NTRS1972

Derivation of mass and stiffness matrices from dynamic test data.

A technique is described by which orthonormal modal vectors, computed from dynamic test response data, are used to derive mass, stiffness, and damping matrices for a discrete model of the distributed elastic system. Matrices thus computed from subsystems tests may be readily incorporated into larger system models. The method has been applied to a test of the Saturn V S-II stage LOX tank-engine support system. The dynamic responses of the discrete model are shown to correlate well with test data throughout the frequency range tested.

Thoren, A. R.↗
NASA NTRS1972

An Algorithm for Synthesizing Mass and Stiffness Matrices from Experimental Vibration Modes

An algorithm is described for synthesizing the mass and stiffness matrices from experimentally derived modal data in a way that preserves the physical significance of the individual mass and stiffness elements. The mass and stiffness matrices are derived for a rollup solar array example, and are then used to define the modal response of a modified array.

Ross, R. G., Jr.↗
NASA NTRS1972

Study of modeling of substructure damping matrices.

Several methods are presented for developing proportional substructure damping matrices from modal test data. Examples demonstrate the significance of the nonuniqueness of the resulting proportional damping matrices. Several alternate modal synthesis procedures are presented for the systematic calculation of system modal damping from substructure damping information. The relative merits of these procedures are discussed, and one procedure is recommended.

Hart, G. C.↗