Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “matrix product state”

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 127 records · Page 7

Adaptive Filtering for Large Space Structures: A Closed-Form Solution

In a previous paper Schaechter proposes using an extended Kalman filter to estimate adaptively the (slowly varying) frequencies and damping ratios of a large space structure. The time varying gains for estimating the frequencies and damping ratios can be determined in closed form so it is not necessary to integrate the matrix Riccati equations. After certain approximations, the time varying adaptive gain can be written as the product of a constant matrix times a matrix derived from the components of the estimated state vector. This is an important savings of computer resources and allows the adaptive filter to be implemented with approximately the same effort as the nonadaptive filter. The success of this new approach for adaptive filtering was demonstrated using synthetic data from a two mode system.

Rauch, H. E.↗

Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth

Matrix chain multiplication -- computing $\mathcal{W} = M^{(0)}\cdots M^{(K-1)}$ where $M^{(k)} \in \mathbb{R}^{P_k \times P_{k+1}}$-- arises in scientific computing, machine learning, and graph analysis. Despite the importance of this problem, for chains of distinct matrices, the classical number of operations grows linearly with the chain length $K$ and polynomially in the matrix dimensions. We present \emph{Two-Tower Matrix Multiplication}, a quantum subroutine that encodes the product $\mathcal{W}$ of the $K$ matrices into a quantum state in circuit depth $\mathcal{O}(\max_{k} \mathrm{polylog} (P_k P_{k+1}))$, which is independent of~$K$ within the QRAM-based state-preparation model, whereas the qubit count is $\mathcal{O}\bigl(\sum_{k} \log P_k \bigr)$; the total gate count remains linear in $K$, so the gain is in the circuit depth. The construction interleaves state-preparation operators across two layers; within each layer, all operators act on disjoint registers and execute in parallel. This subroutine can be specialized for the chain-vector case, which computes the product of $K-1$ matrices applied to a vector. We prove the correctness of the subroutine for all $K$ and provide two implementations using the Qiskit and QCLAB frameworks. The subroutine is applicable to any downstream quantum algorithm that operates on a matrix encoded in the statevector, including norm estimation, graph-matrix powers, linear system solving, and quantum machine learning kernels.

Antonioli, Giacomo [Pisa U.] (ORCID:00090000668703↗

A Challenge for Discrimination of Color-Singlet versus Color-Octet Quarkonium Production

The precise mechanism for production of quarkonium at hadron colliders is still an open question. Within non-relativistic quantum chromodynamics, quarkonium production cross sections can be factorized into short-distance, perturbative contributions and universal, non-perturbative, long-distance matrix elements, and then summed over quantum numbers of the heavy quark pair. In principle, at short-distances, the heavy quark pair can be either in a color-singlet or color-octet state, and it is desirable to establish the relative contributions to compare with data and to make predictions in different experimental environments. From the explicit form of the lowest-order perturbative matrix elements for color-singlet and color-octet production, we show that the structure of the optimal observable for discrimination on phase space, the likelihood ratio, has strong dependence on the angular momentum state of the heavy quark pair. This presents an obstruction for construction of a single, robust discrimination observable that can be applied to production of an arbitrary quarkonium state.

Larkoski, Andrew↗

The capacity of the Hopfield associative memory

Techniques from coding theory are applied to study rigorously the capacity of the Hopfield associative memory. Such a memory stores n-tuple of + or - 1s. The components change depending on a hard-limited version of linear functions of all other components. With symmetric connections between components, a stable state is ultimately reached. By building up the connection matrix as a sum-of-outer products of m fundamental memories, it may be possible to recover a certain one of the m memories by using an initial n-tuple probe vector less than a Hamming distance n/2 away from the fundamental memory. If m fundamental memories are chosen at random, the maximum asymptotic value of m in order that most of the m original memories are exactly recoverable is n/(2 log n). With the added restriction that every one of the m fundamental memories be recoverable exactly, m can be no more than n/(4 log n) asymptotically as n approaches infinity. Extensions are also considered, in particular to capacity under quantization of the outer-product connection matrix. This quantized memory-capacity problem is closely related to the capacity of the quantized Gaussian channel.

Mceliece, Robert J.↗

Development of an image converter of radical design

A long term investigation of thin film sensors, monolithic photo-field effect transistors, and epitaxially diffused phototransistors and photodiodes to meet requirements to produce acceptable all solid state, electronically scanned imaging system, led to the production of an advanced engineering model camera which employs a 200,000 element phototransistor array (organized in a matrix of 400 rows by 500 columns) to secure resolution comparable to commercial television. The full investigation is described for the period July 1962 through July 1972, and covers the following broad topics in detail: (1) sensor monoliths; (2) fabrication technology; (3) functional theory; (4) system methodology; and (5) deployment profile. A summary of the work and conclusions are given, along with extensive schematic diagrams of the final solid state imaging system product.

Irwin, E. L.↗

Variational Discrete Action Theory

In this work, we propose the variational discrete action theory (VDAT) to study the ground state properties of quantum many-body Hamiltonians. VDAT is a variational theory based on the sequential product density matrix (SPD) ansatz, characterized by an integer $\mathscr{N}$, which monotonically approaches the exact solution with increasing $\mathscr{N}$. To evaluate the SPD, we introduce a discrete action and a corresponding integer time Green’s function. We use VDAT to exactly evaluate the SPD in two canonical models of interacting electrons: the Anderson impurity model and the d = ∞ Hubbard model. For the latter, we evaluate $\mathscr{N}$ = 2 – 4, where $\mathscr{N}$ = 2 recovers the Gutzwiller approximation (GA), and we show that $\mathscr{N}$ = 3, which exactly evaluates the Gutzwiller-Baeriswyl wave function, provides a truly minimal yet precise description of Mott physics with a cost similar to that of the GA. VDAT is a flexible theory for studying quantum Hamiltonians, competing both with state-of-the-art methods and simple, efficient approaches all within a single framework.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

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↗

Direct interpolative construction of the discrete Fourier transform as a matrix product operator

The quantum Fourier transform (QFT), which can be viewed as a reindexing of the discrete Fourier transform (DFT), has been shown to be compressible as a low-rank matrix product operator (MPO) or quantized tensor train (QTT) operator. However, the original proof of this fact does not furnish a construction of the MPO with a guaranteed error bound. Meanwhile, the existing practical construction of this MPO, based on the compression of a quantum circuit, is not as efficient as possible. We present a simple closed-form construction of the QFT MPO using the interpolative decomposition, with guaranteed near-optimal compression error for a given rank. This construction can speed up the application of the QFT and the DFT, respectively, in quantum circuit simulations and QTT applications. We also connect our interpolative construction to the approximate quantum Fourier transform (AQFT) by demonstrating that the AQFT can be viewed as an MPO constructed using a different interpolation scheme.

97 MATHEMATICS AND COMPUTING↗

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↗

Derivation of the chemical-equilibrium rate coefficient using scattering theory

Scattering theory is applied to derive the equilibrium rate coefficient for a general homogeneous chemical reaction involving ideal gases. The reaction rate is expressed in terms of the product of a number of normalized momentum distribution functions, the product of the number of molecules with a given internal energy state, and the spin-averaged T-matrix elements. An expression for momentum distribution at equilibrium for an arbitrary molecule is presented, and the number of molecules with a given internal-energy state is represented by an expression which includes the partition function.

Mickens, R. E.↗

An intrinsically n-dimensional generalized flux vector splitting implicit finite element Euler algorithm

A generalized flux-vector splitting implicit Galerkin finite-element algorithm for the Euler equations in curvilinear coordinates for ideal and reacting gases is derived. For an arbitrary equation of state, the curvilinear-coordinate flux vector is split in kinematic and kinetic components, and the associated jacobian matrix eigenvalues explicitly depend on the metric data. After directional semidiscretization, the terminal ordinary differential-equation system is solved via a nonlinearly stable implicit Runge-Kutta scheme in concert with an accurate tensor matrix product factorization. The results for selected two-dimensional supersonic and axisymmetric hypersonic flows validate the algorithm and verify its robustness for curvilinear-coordinate computations. The evolution towards a steady state is achieved for large Courant numbers without indication of numerical instabilities.

Iannelli, G. S.↗

Extracting the Pion Distribution Amplitude from Lattice QCD through Pseudo-Distributions

The Light-Cone Distribution Amplitude (LCDA) encodes the non-perturbative information of the leading Fock component of the hadron wave function, therefore required for processes including exclusive hadron production. As the Pseudo-Nambu-Goldstone boson of QCD, the nonperturbative structure of the pion is of particular interest. Progress on the Lattice QCD calculation of the pion LCDA on O(a) -improved Wilson fermion ensembles at several lattice spacings is presented. Excited-state systematics are taken into account within a Bayesian Model Averaging framework. A Renormalization-Group-Invariant (RGI) ratio of matrix elements is formed for further extraction of the pion LCDA.

Kovner, Daniel↗

Effect of fiber orientation on the fracture toughness of brittle matrix composites

The effective fracture toughness of brittle matrix materials can be increased through the addition of short, poorly bonded fibers which bridge the growing crack. The orientation distribution of the fibers is likely to be biased, and not in an ideal random or aligned state. A micromechanical model is formulated for the postcracking behavior using the force-displacement relation for an arbitrary fiber bridging a crack, the fiber orientation density function, and the fiber location density function. This model is then used to determine an effective traction law for the bridging fibers, as well as the steady state bridging toughness increment. In most cases, the results may be placed in the form of a product of the aligned fiber results times a modifying integrated orientation factor. The frictional shear stress on fiber pull-out is allowed to vary during pull-out, modeling the effects of matrix breakdown, fiber surface smoothing or wear debris accumulation. Results are presented for a variety of representative planar and three-dimensional fiber orientation states.

Jain, L. K.↗

Measurement of single top-quark production in the s-channel in proton–proton collisions at $\sqrt{s}$ = 13 TeV with the ATLAS detector

A measurement of single top-quark production in the s-channel is performed in proton–proton collisions at a centre-of-mass energy of 13 TeV with the ATLAS detector at the CERN Large Hadron Collider. The dataset corresponds to an integrated luminosity of 139 fb –1 . The analysis is performed on events with an electron or muon, missing transverse momentum and exactly two $b$-tagged jets in the final state. A discriminant based on matrix element calculations is used to separate single-top-quark s-channel events from the main background contributions, which are top-quark pair production and $W$-boson production in association with jets. The observed (expected) signal significance over the background-only hypothesis is 3.3 (3.9) standard deviations, and the measured cross-section is $σ$ = ${8.2}_{-2.9}^{+3.5}$ pb, consistent with the Standard Model prediction of $σ^{SM}$ = ${10.32}_{–0.36}^{+0.40}$ pb.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Conformal collider physics meets LHC data

The remarkably high energies of the Large Hadron Collider (LHC) have allowed for the first measurements of the shapes and scalings of multipoint correlators of energy flow operators, ⟨ Ψ | E ( n → 1 ) E ( n → 2 ) ⋯ E ( n → k ) | Ψ ⟩ , providing new insights into the Lorentzian dynamics of quantum chromodynamics (QCD). In this letter, we use recent advances in effective field theory to derive a rigorous factorization theorem for the light-ray density matrix, ρ = | Ψ ⟩ ⟨ Ψ | , inside high transverse momentum jets at the LHC. Using the light-ray operator product expansion, the scaling behavior of multipoint correlators can be computed from the expectation value of the twist-2 spin- J light-ray operators, O [ J ] , in this state, Tr [ ρ O [ J ] ] . We compute the light-ray density matrix at next-to-leading order, and combine this with results for the next-to-leading logarithmic scaling behavior of the correlators up to six-points, comparing with CMS open data. This theoretical accuracy allows us to resolve the quantum scaling dimensions of QCD light-ray operators inside jets at the LHC. Our factorization theorem for the light-ray density matrix at the LHC completes the link between recent developments in the study of energy correlators and LHC phenomenology, opening the door to a wide variety of precision jet substructure studies. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Hydrothermal Alteration on Basaltic Mauna Kea Volcano as a Template for Identification of Hydrothermal Alteration on Basaltic Mars

Certain samples of palagonitic tephra from Mauna Kea Volcano (Hawaii) are spectral analogues for bright martian surface materials at visible and near-IR wavelengths because both are characterized by a ferric absorption edge extending from about 400 to 750 nm and relatively constant reflectivity extending from about 750 nm to beyond 2000 nm. Palagonite is a yellow or orange isotropic mineraloid formed by hydration and devitrification of basaltic glass. For Mars-analogue palagonite, the pigment is nanometersized ferric oxide particles (np-Ox) dispersed throughout an allophane-like hydrated basaltic glass matrix. Crystalline phyllosilicates are not generally detected, and the hydration state of the is not known. The poorly crystalline nature of glass alteration products implies relatively low temperature formation pathways. We report here x-ray diffraction, major element, Mossbauer, and VNIR data for 9 basaltic tephras. Thermal emission spectra are reported in a separate abstract. Our multidisciplinary approach both tightly constrains mineralogical interpretations and maximizes overlap with datasets available for the martian surface available now and in the future.

Morris, R. V.↗

Inclusive prompt photon-jet correlations as a probe of gluon saturation in electron-nucleus scattering at small x

We compute the differential cross-section for inclusive prompt photon+quark production in deeply inelastic scattering of electrons off nuclei at small x (e + A DIS) in the framework of the Color Glass Condensate effective field theory. The result is expressed as a convolution of the leading order (in the strong coupling α s ) impact factor for the process and universal dipole matrix elements, in the limit of hard photon transverse momentum relative to the nuclear saturation scale Q s,A (x). We perform a numerical study of this process for the kinematics of the Electron-Ion Collider (EIC), exploring in particular the azimuthal angle correlations between the final state photon and quark. We observe a systematic suppression and broadening pattern of the back-to-back peak in the relative azimuthal angle distribution, as the saturation scale is increased by replacing proton targets with gold nuclei. Our results suggest that photon+jet final states in inclusive e + A DIS at high energies are in general a promising channel for exploring gluon saturation that is complementary to inclusive and diffractive dijet production. They also provide a sensitive empirical test of the universality of dipole matrix elements when compared to identical measurements in proton-nucleus collisions. However because photon+jet correlations at small x in EIC kinematics require jet reconstruction at small k ⊥ , it will be important to study their feasibility relative to photon-hadron correlations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Dynamic Mode Decomposition of Unsteady Pressure-Sensitive Paint Measurements for the NASA Unitary Plan Wind Tunnel Tests

This paper describes the Dynamic Mode Decomposition (DMD) of the pressures on the scale model of the Space Launch System (SLS) Block 1 cargo vehicle with the Unsteady Pressure-Sensitive Paint (uPSP) measurements, which were collected in the Ascent Transient Aerodynamics Tests with the Unitary Plan Wind Tunnel 11-by-11-foot Transonic Wind Tunnel in September 2019 at NASA Ames Research Center. The work described in this paper is a part of NASA’s development of a new state-of-the-art uPSP capability in production wind tunnels. The conventional DMD algorithm is based on the Singular Value Decomposition (SVD) of the data matrix. For the matrix of the uPSP measurements of the SLS ATAT, the number of rows is equal to the number of nodes in the grid of the scale model, and the number of columns is equal to the number of frames in the videos taken with 4 Phantom high-speed cameras. In this paper, it is verified that, for the time series with zero mean value, the DMD is equivalent to the decomposition with the Discrete Fourier Transform (DFT). Considering the uPSP is mainly used in the assessment of the unsteady, aerodynamic phenomena, the DMD of the uPSP measurements can be implemented in two steps: (1) subtract the mean value from the uPSP measurement on each of the grid nodes; (2) apply the Fast Fourier Transform (FFT) on the resulting zero-mean time series. The DMD of the uPSP measurements with FFT has two advantages: (1) the computational complexity of FFT is O(N*logN), where N is the length of the time series; (2) compared to the SVD-based DMD algorithm, the DMD with FFT can be easily implemented in parallel processing. A sample matrix of uPSP measurements, at the size of 341 grid nodes and 128 frames, is generated. Figures 1 and 2 show the eigenvalues and the ratios of the eigenvectors, respectively, of the sample matrix, without and with the mean value removed on each of the grid nodes, computed with the SVD-based DMD and the FFT. The figures demonstrate the equivalence of the SVD-based DMD and the decomposition with DFT/FFT for the time series with zero mean value. The results of DMD of the uPSP measurements of the SLS ATAT in September 2019 are presented in the paper. The DMD modes at different frequencies are shown, the aerodynamic phenomena (e.g. shockwave and vortex shedding) are demonstrated and the correlation of the DMD modes with the test configuration parameter (e.g., the Mach Number) is discussed. Figure 3 shows a software tool to visualize the DMD modes. The code to implement the algorithm described in this paper was written in C, with libraries of FFTW for FFT and MPI/OpenMP for parallel processing, and executed on the NASA Pleiades supercomputer. Funding for this research was provided by the NASA Aerosciences Evaluation and Test Capabilities Project.

Pressure-Sensitive Paint↗