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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 73 records · Page 4

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NASA NTRS1990

Matrix elements in the coupled-cluster approach - With application to low-lying states in Li

A procedure is suggested for evaluating matrix elements of an operator between wavefunctions in the coupled-cluster form. The use of the exponential ansatz leads to compact exponential expressions also for matrix elements. Algorithms are developed for summing all effects of one-particle clusters and certain chains of two-particle clusters (containing the well-known random-phase approximation as a subset). The treatment of one-particle perturbations in single valence states is investigated in detail. As examples the oscillator strength for the 2s-2p transition in Li as well as the hyperfine structure for the two states are studied and compared to earlier work.

Martensson-Pendrill, Ann-Marie↗

DOE OSTI2021

Calculating elements of matrix functions using divided differences

In this work, we introduce a method for calculating individual elements of matrix functions. Our technique makes use of a novel series expansion for the action of matrix functions on basis vectors that is memory efficient even for very large matrices. We showcase our approach by calculating the matrix elements of the exponential of a transverse-field Ising model and evaluating quantum transition amplitudes for large many-body Hamiltonians of sizes up to 2 64 x 2 64 on a single workstation. We also discuss the application of the method to matrix inverses. We relate and compare our method to the state-of-the-art and demonstrate its advantages. We also discuss practical applications of our method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

H ∞ Control for Energy Dispatch in Autonomous Nanogrid With Communication Delays

This paper proposes an optimal controller and estimator for energy dispatch to balance the power supply and demand considering communication delays. The proposed algorithm involves modeling an autonomous nanogrid (ANG) consisting of distributed energy resources, energy storage systems, loads, an $H$ ∞ controller with a reference power modulation technique, and a state estimator. The ANG was developed to express the dynamic supply-demand energy balance of a nanogird system. Reference power modulation was designed to generate the desired ESS power based on the imbalanced energy. Random communication delays were modeled using a stochastic variable satisfying the Bernoulli random binary distribution. The optimal $H$ ∞ controller and estimator were developed using a linear matrix inequality approach to exponentially stabilize the closed-loop system. Simulations were performed using real daily demand forecasts obtained from the Korea Meteorological Administration to demonstrate the effectiveness of the proposed real-time optimization algorithm.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Multirate Exponential Rosenbrock Methods

In this paper we propose a novel class of methods for high-order accurate integration of multirate systems of ordinary differential equation initial-value problems. The proposed methods construct multirate schemes by approximating the action of matrix φ functions within explicit exponential Rosenbrock (ExpRB) methods, thereby called multirate ExpRB (MERB) methods. They consist of the solution to a sequence of modified “fast” initial-value problems, which may themselves be approximated through subcycling any desired initial-value problem solver. In addition to proving how to construct MERB methods from certain classes of ExpRB methods, we provide rigorous convergence analysis of these methods and derive efficient MERB schemes of orders 2 through 6 (the highest-order infinitesimal multirate methods to date). Lastly, we then present numerical simulations to confirm these theoretical convergence rates and to compare the efficiency of MERB methods against other recently introduced high-order multirate methods.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2015

Theoretical Studies of Spectroscopic Line Mixing in Remote Sensing Applications

The phenomenon of collisional transfer of intensity due to line mixing has an increasing importance for atmospheric monitoring. From a theoretical point of view, all relevant information about the collisional processes is contained in the relaxation matrix where the diagonal elements give half-widths and shifts, and the off-diagonal elements correspond to line interferences. For simple systems such as those consisting of diatom-atom or diatom-diatom, accurate fully quantum calculations based on interaction potentials are feasible. However, fully quantum calculations become unrealistic for more complex systems. On the other hand, the semi-classical Robert-Bonamy (RB) formalism, which has been widely used to calculate half-widths and shifts for decades, fails in calculating the off-diagonal matrix elements. As a result, in order to simulate atmospheric spectra where the effects from line mixing are important, semi-empirical fitting or scaling laws such as the ECS (Energy-Corrected Sudden) and IOS (Infinite-Order Sudden) models are commonly used. Recently, while scrutinizing the development of the RB formalism, we have found that these authors applied the isolated line approximation in their evaluating matrix elements of the Liouville scattering operator given in exponential form. Since the criterion of this assumption is so stringent, it is not valid for many systems of interest in atmospheric applications. Furthermore, it is this assumption that blocks the possibility to calculate the whole relaxation matrix at all. By eliminating this unjustified application, and accurately evaluating matrix elements of the exponential operators, we have developed a more capable formalism. With this new formalism, we are now able not only to reduce uncertainties for calculated half-widths and shifts, but also to remove a once insurmountable obstacle to calculate the whole relaxation matrix. This implies that we can address the line mixing with the semi-classical theory based on interaction potentials between molecular absorber and molecular perturber. We have applied this formalism to address the line mixing for Raman and infrared spectra of molecules such as N2, C2H2, CO2, NH3, and H2O. By carrying out rigorous calculations, our calculated relaxation matrices are in good agreement with both experimental data and results derived from the ECS model.

Formalism↗

NASA NTRS2003

Quantum Search in Hilbert Space

A proposed quantum-computing algorithm would perform a search for an item of information in a database stored in a Hilbert-space memory structure. The algorithm is intended to make it possible to search relatively quickly through a large database under conditions in which available computing resources would otherwise be considered inadequate to perform such a task. The algorithm would apply, more specifically, to a relational database in which information would be stored in a set of N complex orthonormal vectors, each of N dimensions (where N can be exponentially large). Each vector would constitute one row of a unitary matrix, from which one would derive the Hamiltonian operator (and hence the evolutionary operator) of a quantum system. In other words, all the stored information would be mapped onto a unitary operator acting on a quantum state that would represent the item of information to be retrieved. Then one could exploit quantum parallelism: one could pose all search queries simultaneously by performing a quantum measurement on the system. In so doing, one would effectively solve the search problem in one computational step. One could exploit the direct- and inner-product decomposability of the unitary matrix to make the dimensionality of the memory space exponentially large by use of only linear resources. However, inasmuch as the necessary preprocessing (the mapping of the stored information into a Hilbert space) could be exponentially expensive, the proposed algorithm would likely be most beneficial in applications in which the resources available for preprocessing were much greater than those available for searching.

Zak, Michail↗

NASA NTRS1983

Closed-form solutions for a class of optimal quadratic tracking problems

Closed-form solutions are derived for a class of tracking problems including a linear optimal regulator and a prefilter for a time-invariant plant. The solutions for the prefilter equation and state trajectory coupled by the Riccati equation are exponentially related to the stability matrix of the plant. A computational procedure is presented in recursive form when the desired output state dynamics is assumed linear and time-invariant. Several examples are given for illustration.

Turner, J. D.↗

NASA NTRS1985

Space Mathematics: A Resource for Secondary School Teachers

A collection of mathematical problems related to NASA space science projects is presented. In developing the examples and problems, attention was given to preserving the authenticity and significance of the original setting while keeping the level of mathematics within the secondary school curriculum. Computation and measurement, algebra, geometry, probability and statistics, exponential and logarithmic functions, trigonometry, matrix algebra, conic sections, and calculus are among the areas addressed.

Kastner, Bernice↗

DOE OSTI2023

Molecular-Dynamics Analysis of the Mechanical Behavior of Plasma-Facing Tungsten

We report a systematic computational analysis of the mechanical behavior of plasma-facing component (PFC) tungsten focusing on the impact of void and helium (He) bubble defects on the mechanical response beyond the elastic regime. Specifically, we explore the effects of porosity and He atomic fraction on the mechanical properties and structural response of PFC tungsten, at varying temperature and bubble size. We find that the Young modulus of defective tungsten undergoes substantial softening that follows an exponential scaling relation as a function of matrix porosity and He atomic content. Beyond the elastic regime, our high strain rate simulations reveal that the presence of nanoscale spherical defects (empty voids and He bubbles) reduces the yield strength of tungsten in a monotonically decreasing fashion, obeying an exponential scaling relation as a function of tungsten matrix porosity and He concentration. Our detailed analysis of the structural response of PFC tungsten near the yield point reveals that yielding is initiated by emission of dislocation loops from bubble/matrix interfaces, mainly 1/2<111> shear loops, followed by gliding and growth of these loops and reactions to form <100> dislocations. Furthermore, dislocation gliding on the <111>{211} twin systems nucleates 1/6<111> twin regions in the tungsten matrix. These dynamical processes reduce the stress in the matrix substantially. Subsequent dislocation interactions and depletion of the twin phases via nucleation and propagation of detwinning partials lead the tungsten matrix to a next deformation stage characterized by stress increase during applied straining. Furthermore, our structural analysis reveals that the depletion of twin boundaries (areal defects) is strongly impacted by the density of He bubbles at higher porosities. After the initial stress relief upon yielding, increase in the dislocation density in conjunction with decrease in the areal defect density facilitates the initiation of dislocation-driven deformation mechanisms in the PFC crystal.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Theory of the effect of external stress on the activated dynamics and transport of dilute penetrants in supercooled liquids and glasses

We generalize the self-consistent cooperative hopping theory for a dilute spherical penetrant or tracer activated dynamics in dense metastable hard sphere fluids and glasses to address the effect of external stress, the consequences of which are systematically established as a function of matrix packing fraction and penetrant-to-matrix size ratio. All relaxation processes speed up under stress, but the difference between the penetrant and matrix hopping (alpha relaxation) times decreases significantly with stress corresponding to less time scale decoupling. A dynamic crossover occurs at a critical “slaving onset” stress beyond which the matrix activated hopping relaxation time controls the penetrant hopping time. This characteristic stress increases (decreases) exponentially with packing fraction (size ratio) and can be well below the absolute yield stress of the matrix. Below the slaving onset, the penetrant hopping time is predicted to vary exponentially with stress, differing from the power law dependence of the pure matrix alpha time due to system-specificity of the stress-induced changes in the penetrant local cage and elastic barriers. An exponential growth of the penetrant alpha relaxation time with size ratio under stress is predicted, and at a fixed matrix packing fraction, the exponential relation between penetrant hopping time and stress for different size ratios can be collapsed onto a master curve. Direct connections between the short- and long-time activated penetrant dynamics and between the penetrant (or matrix) alpha relaxation time and matrix thermodynamic dimensionless compressibility are also predicted. The presented results should be testable in future experiments and simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1973

Quantum theory of an optical maser. VI - Transient behavior.

The transient behavior of a laser is discussed using the quantum theory as did Scully and Lamb. The formal solution of the density-matrix equation is expressed in terms of exponentially decaying eigenmodes. Some of the lower decay constants are obtained numerically. The equations for the moments of the density matrix are then derived and solved by a truncation method. The equations of motion are integrated numerically for the case where the average number of photons in a laser cavity has the realistically large value 1.3 x 100,000. An alternative Fokker-Planck-equation approach is discussed.

Wang, Y. K.↗

DOE OSTI2023

Perturbative readout-error mitigation for near-term quantum computers

Readout errors on near-term quantum computers can introduce significant error to the empirical probability distribution sampled from the output of a quantum circuit. These errors can be mitigated by classical postprocessing given the access of an experimental response matrix that describes the error associated with the measurement of each computational basis state. However, the resources required to characterize a complete response matrix and to compute the corrected probability distribution scale exponentially with the number of qubits, n . In this work, we modify standard matrix inversion techniques using perturbative approximations with significantly reduced complexity and bounded error when the likelihood of high-order bit-flip events is strongly suppressed. Given a characteristic error rate q , we discuss a method to recover the probability of the all-zeros bit string p 0 by sampling only a small subspace of the response matrix before inverting readout error, resulting in a relative speedup of poly [ 2 n / ( n w ) ] , which we motivate using a simplified error model for which the approximation incurs only O ( q w ) error for some integer w . We then provide a generalized technique to efficiently recover full output distributions with O ( q w ) error in the perturbative limit. These approximate techniques for readout-error correction may greatly accelerate near-term quantum computing applications.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1987

Doubly differential cross sections for galactic heavy-ion fragmentation

An abrasion-ablation T-matrix formulation is applied to the calculation of double differential-cross sections in projectile fragmentation of 2.1 GeV/nucleon O-16 on Be-9 and 86 MeV/nucleon C-12 on C-12 and Ag-108. An exponential parameterization of the ablation T-matrix is used and the total width of the intermediate states is taken as a parameter. Fitted values of the total width to experimental results are used to predict the lifetime of the ablation stage and indicate a decay time on the order of 10 to the -19th power sec.

Cucinotta, Francis A.↗

DOE OSTI2025

A quantum eigenvalue solver based on tensor networks

Electronic ground states are of central importance in chemical simulations, but have remained beyond the reach of efficient classical algorithms except in cases of weak electron correlation or one-dimensional spatial geometry. We introduce a hybrid quantum-classical eigenvalue solver that constructs a wavefunction ansatz from a linear combination of matrix product states in rotated orbital bases, enabling the characterization of strongly correlated ground states with arbitrary spatial geometry. The energy is converged via a gradient-free generalized sweep algorithm based on quantum subspace diagonalization, with a potentially exponential speedup in the off-diagonal matrix element contractions upon translation into compact quantum circuits of linear depth in the number of qubits. Chemical accuracy is attained in numerical experiments for both a stretched water molecule and an octahedral arrangement of hydrogen atoms, achieving substantially better correlation energies compared to a unitary coupled-cluster benchmark, with orders of magnitude reductions in quantum resource estimates and a surprisingly high tolerance to shot noise. This proof-of-concept study suggests a promising new avenue for scaling up simulations of strongly correlated chemical systems on near-term quantum hardware.

chemistry↗

DOE OSTI2020

Elastic Properties of Plasma-Exposed Tungsten Predicted by Molecular-Dynamics Simulations

We report results of systematic molecular-dynamics computations of the elastic properties of single-crystalline tungsten containing structural defects, voids and overpressurized He nanobubbles, related to plasma exposure of tungsten serving as a plasma- facing component (PFC) in nuclear fusion devices. Our computations reveal that the empty voids are centers of dilatation resulting in development of tensile stress in the tungsten matrix, whereas He-filled voids (nanobubbles) introduce compressive stress in the plasma-exposed tungsten. We find that the dependence of the elastic moduli of plasma-exposed tungsten, namely, the bulk, Young, and shear modulus, on its void fraction follows a universal exponential scaling relation. We also find that the elastic moduli of plasma-exposed tungsten soften substantially as a function of He content in the tungsten matrix, following an exponential scaling relation; this He-induced exponential softening is in addition to the softening caused in the matrix with increasing temperature. A systematic characterization of the dependence of the elastic moduli on the He bubble size reveals that He bubble growth affects significantly both the bulk modulus and the Poisson ratio of plasma-exposed tungsten, while its effect on the Young and shear moduli of the plasma-exposed material is weak. Our findings contribute directly to the development of a structure-properties database that is required for the predictive modeling of the dynamical response of PFCs in nuclear fusion devices.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Beyond-classical computation in quantum simulation

Quantum computers hold the promise of solving certain problems that lie beyond the reach of conventional computers. However, establishing this capability, especially for impactful and meaningful problems, remains a central challenge. Here, we show that superconducting quantum annealing processors can rapidly generate samples in close agreement with solutions of the Schrödinger equation. We demonstrate area-law scaling of entanglement in the model quench dynamics of two-, three-, and infinite-dimensional spin glasses, supporting the observed stretched-exponential scaling of effort for matrix-product-state approaches. We show that several leading approximate methods based on tensor networks and neural networks cannot achieve the same accuracy as the quantum annealer within a reasonable time frame. Thus, quantum annealers can answer questions of practical importance that may remain out of reach for classical computation.

King, Andrew D. [D-Wave Quantum Inc., Burnaby, BC ↗

DOE OSTI2024

Explicit Form for the Most General Lorentz Transformation Revisited

Explicit formulae for the 4×4 Lorentz transformation matrices corresponding to a pure boost and a pure three-dimensional rotation are very well known. Significantly less well known is the explicit formula for a general Lorentz transformation with arbitrary non-zero boost and rotation parameters. We revisit this more general formula by presenting two different derivations. The first derivation (which is somewhat simpler than previous ones appearing in the literature) evaluates the exponential of a 4×4 real matrix A, where A is a product of the diagonal matrix diag(+1,−1,−1,−1) and an arbitrary 4×4 real antisymmetric matrix. The formula for expA depends only on the eigenvalues of A and makes use of the Lagrange interpolating polynomial. The second derivation exploits the observation that the spinor product η†σ¯μχ transforms as a Lorentz four-vector, where χ and η are two-component spinors. The advantage of the latter derivation is that the corresponding formula for a general Lorentz transformation Λ reduces to the computation of the trace of a product of 2×2 matrices. Both computations are shown to yield equivalent expressions for Λ.

Science & Technology - Other Topics↗

NASA NTRS1985

Multiprocessor sparse L/U decomposition with controlled fill-in

Generation of the maximal compatibles of pivot elements for a class of small sparse matrices is studied. The algorithm involves a binary tree search and has a complexity exponential in the order of the matrix. Different strategies for selection of a set of compatible pivots based on the Markowitz criterion are investigated. The competing issues of parallelism and fill-in generation are studied and results are provided. A technque for obtaining an ordered compatible set directly from the ordered incompatible table is given. This technique generates a set of compatible pivots with the property of generating few fills. A new hueristic algorithm is then proposed that combines the idea of an ordered compatible set with a limited binary tree search to generate several sets of compatible pivots in linear time. Finally, an elimination set to reduce the matrix is selected. Parameters are suggested to obtain a balance between parallelism and fill-ins. Results of applying the proposed algorithms on several large application matrices are presented and analyzed.

Alaghband, G.↗