SEARCH · Engineering Papers

Results for “Density matrix method”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4

All sources NASA NTRS DOE OSTI

DOE OSTI2025

Polariton spectra under the collective coupling regime. I. Efficient simulation of linear spectra and quantum dynamics

We outline two general theoretical techniques to simulate polariton quantum dynamics and optical spectra under the collective coupling regimes described by a Holstein–Tavis–Cummings (HTC) model Hamiltonian. The first one takes advantage of sparsity of the HTC Hamiltonian, which allows one to reduce the cost of acting polariton Hamiltonian onto a state vector to the linear order of the number of states, instead of the quadratic order. The second one is applying the well-known Chebyshev series expansion approach for quantum dynamics propagation and to simulate the polariton dynamics in the HTC system; this approach allows us to use a much larger time step for propagation and only requires a few recursive operations of the polariton Hamiltonian acting on state vectors. These two theoretical approaches are general and can be applied to any trajectory-based non-adiabatic quantum dynamics methods. We apply these two techniques with our previously developed Lindblad-partially linearized density matrix approach to simulate the linear absorption spectra of the HTC model system, with both inhomogeneous site energy disorders and dipolar orientational disorders. Our numerical results agree well with the previous analytic and numerical work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Performance of wave function and Green's function methods for non-equilibrium many-body dynamics

Theoretical descriptions of the non-equilibrium dynamics of quantum many-body systems essentially employ either (i) explicit treatments, relying on the truncation of the expansion of the many-body wave function, (ii) compressed representations of the many-body wave function, or (iii) evolution of an effective (downfolded) representation through Green's functions. In this work, we select representative cases of each of the methods and address how these complementary approaches capture the dynamics driven by intense field perturbations to non-equilibrium states. Under strong driving, the systems are characterized by strong entanglement of the single-particle density matrix and natural populations approaching those of a strongly interacting equilibrium system. We generate a representative set of results that are numerically exact and form a basis for a critical comparison of the distinct families of methods. We demonstrate that the compressed formulation based on similarity-transformed Hamiltonians (coupled-cluster approach) is practically exact in weak fields and, hence, weakly or moderately correlated systems. Coupled cluster, however, struggles for strong driving fields, under which the system exhibits strongly correlated behavior, as measured by the von Neumann entropy of the single-particle density matrix. The dynamics predicted by Green's functions in the (widely popular) G W approximation are less accurate, but improve significantly upon the mean-field results in the strongly driven regime. Published by the American Physical Society 2025

Reeves, Cian C. (ORCID:0009000642581845)↗

NASA NTRS1983

Ultrasonic wave propagation in two-phase media: Spherical inclusions

The scattering theory, recently developed via the extended method of equivalent inclusion, is used to study the propagation of time-harmonic waves in two-phase media of elastic matrix with randomly distributed elastic spherical inclusion materials. The elastic moduli and mass density of the composite medium are determined as functions of frequencies when given properties and concentration of the spheres and the matrix. Velocity and attenuation of ultrasonic waves in two-phase media are determined for cases of distributed spheres and localized damage. An averaging theorem that requires the equivalence of the strain energy and the kinetic energy between the effective medium and the original matrix with spherical inhomogeneities is employed to derive the effective moduli and mass density. The functional dependency of these quantities upon frequencies and concentration provides a method of data analysis in ultrasonic evaluation of material properties. Numerical results or moduli, velocity and/or attenuation as functions of concentration of inclusion material, or porosity, are graphically displayed.

Fu, L. S.↗

NASA NTRS1984

Ultrasonic wave propagation in two-phase media - Spherical inclusions

Fu, L. S.↗

NASA NTRS1997

Low-density resin impregnated ceramic article and method for making the same

A low-density resin impregnated ceramic article advantageously employed as a structural ceramic ablator comprising a matrix of ceramic fibers. The fibers of the ceramic matrix are coated with an organic resin film. The organic resin can be a thermoplastic resin or a cured thermosetting resin. In one embodiment, the resin is uniformly distributed within the ceramic article. In a second embodiment, the resin is distributed so as to provide a density gradient along at least one direction of the ceramic article. The resin impregnated ceramic article is prepared by providing a matrix of ceramic fibers; immersing the matrix of ceramic fibers in a solution of a solvent and an organic resin infiltrant; and removing the solvent to form a resin film on the ceramic fibers.

Tran, Huy K.↗

NASA NTRS1990

Ultrasonic and radiographic evaluation of advanced aerospace materials: Ceramic composites

Two conventional nondestructive evaluation techniques were used to evaluate advanced ceramic composite materials. It was shown that neither ultrasonic C-scan nor radiographic imaging can individually provide sufficient data for an accurate nondestructive evaluation. Both ultrasonic C-scan and conventional radiographic imaging are required for preliminary evaluation of these complex systems. The material variations that were identified by these two techniques are porosity, delaminations, bond quality between laminae, fiber alignment, fiber registration, fiber parallelism, and processing density flaws. The degree of bonding between fiber and matrix cannot be determined by either of these methods. An alternative ultrasonic technique, angular power spectrum scanning (APSS) is recommended for quantification of this interfacial bond.

Generazio, Edward R.↗

DOE OSTI2026

Bootstrap embedding for interacting electrons in phonon coherent-state mean field

Here, we develop a Fermi–Bose bootstrap embedding framework for the ground state of interacting electrons coupled to a phonon mean field. The method combines bootstrap embedding for correlated electrons with a self-consistent coherent-state mean-field treatment for phonons. This method models the interacting electron–phonon problem as a system of correlated electrons traveling in a self-consistently specified potential landscape, allowing for efficient treatment of large lattice systems. Convergence of the methods for fragment size and total system size is demonstrated for the one-dimensional Hubbard–Holstein model for up to 350 sites. Finite-size scaling is performed to extrapolate to the infinite system size. Benchmarking against the density matrix renormalization group for a small 8-site system at half- and quarter-filling shows an orders-of-magnitude runtime advantage. The comparison further reveals that the method performs best in regimes dominated by localization, such as the Mott insulating phase and the strong-coupling tiny polaron regime, where the local embedding ansatz is still valid. However, due to the mean-field treatment for phonons, we find limitations of our methods in the weakly coupled delocalized region and at the Peierls transition, where quantum phonon fluctuations and long-range kinetic correlations become substantial.

Islam, Shariful [North Carolina State University, ↗

DOE OSTI2026

Multireference Embedding and Fragmentation Methods for Classical and Quantum Computers: From Model Systems to Realistic Applications

One of the primary challenges in quantum chemistry is the accurate modeling of strong electron correlation. While multireference methods effectively capture such correlation, their steep scaling with system size prohibits their application to large molecules and extended materials. Quantum embedding offers a promising solution by partitioning complex systems into manageable subsystems. In this Review, we highlight recent advances in multireference density matrix embedding and localized active space self-consistent field approaches for complex molecules and extended materials. We discuss both classical implementations and the emerging potential of these methods on quantum computers. Here, by extending classical embedding concepts to the quantum landscape, these algorithms have the potential to expand the reach of multireference methods in quantum chemistry and materials.

Algorithms↗

DOE OSTI2024

Determining the N -Representability of a Reduced Density Matrix via Unitary Evolution and Stochastic Sampling

The N-representability problem consists in determining whether, for a given p-body matrix, there exists at least one N-body density matrix from which the p-body matrix can be obtained by contraction, that is, if the given matrix is a p-body reduced density matrix (p-RDM). The knowledge of all necessary and sufficient conditions for a p-body matrix to be N-representable allows the constrained minimization of a many-body Hamiltonian expectation value with respect to the p-body density matrix and, thus, the determination of its exact ground state. However, the number of constraints that complete the N-representability conditions grows exponentially with system size, and hence, the procedure quickly becomes intractable for practical applications. This work introduces a hybrid quantum-stochastic algorithm to effectively replace the N-representability conditions. The algorithm consists of applying to an initial N-body density matrix a sequence of unitary evolution operators constructed from a stochastic process that successively approaches the reduced state of the density matrix on a p-body subsystem, represented by a p-RDM, to a target p-body matrix, potentially a p-RDM. The generators of the evolution operators follow the well-known adaptive derivative-assembled pseudo-Trotter method (ADAPT), while the stochastic component is implemented by using a simulated annealing process. The resulting algorithm is independent of any underlying Hamiltonian, and it can be used to decide whether a given p-body matrix is N-representable, establishing a criterion to determine its quality and correcting it. We apply the proposed hybrid ADAPT algorithm to alleged reduced density matrices from a quantum chemistry electronic Hamiltonian, from the reduced Bardeen–Cooper–Schrieffer model with constant pairing, and from the Heisenberg XXZ spin model. In all cases, the proposed method behaves as expected for 1-RDMs and 2-RDMs, evolving the initial matrices toward different targets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Quantum entanglement correlations in double quark PDFs

Methods from Quantum Information Theory are used to scrutinize quantum correlations encoded in the two-quark density matrix over light-cone momentum fractions x 1 and x 2 . A nonperturbative three quark model light-cone wavefunction predicts significant nonclassical correlations associated with the “entanglement negativity” measure for asymmetric and small quark momentum fractions. We perform one step of QCD scale evolution of the entire density matrix, not just its diagonal (dPDF), by computing collinearly divergent corrections due to the emission of a gluon. Finally, we present first qualitative numerical results for single-step scale evolution of quantum entanglement correlations in double quark PDFs. At a higher Q 2 scale, the nonclassical correlations manifest in the dPDF for nearly symmetric momentum fractions.

Entanglement in field theory↗

DOE OSTI2025

Ab Initio Design of High-Entropy Thermal/ Environmental Barrier Coatings

Next generation thermal/environmental barrier coatings (TEBC) require carefully balancing various properties including phase stability, thermal conductivity, coefficient of thermal expansion (CTE), mechanical properties, and resistance against hot corrosion and water vapor recession. This work mainly focuses on rapid design of cost-effective high entropy rare-earth disilicates and aluminum garnets to protect SiC-based ceramic matrix composites and nickel-based superalloys in the hot section of gas turbine engines using density functional theory methods. Our calculations identify several low-cost high entropy TEBC exhibiting ultralow thermal conductivity at 1500 K and desirable CTE while maintaining good mechanical properties, including Er1/2Y3/4Yb3/4Si2O7, Gd1/4Er1/4Y3/4Yb3/4Si2O7, Eu1/4Er1/4Y3/4Yb3/4Si2O7, and (Y1/4Gd1/4Er1/4Yb1/4)3Al5O12. This work also aims to gain fundamental understanding of oxygen diffusion in model disilicates. Minimizing oxidizer (such as water vapor and oxygen) permeability through the EBC layer can significantly decrease the growth rate of thermally grown oxide and extend the service life of the coating system. Oxygen diffusion mechanisms including formation energy of defects under varying oxygen conditions and defect migration energy barriers will be presented.

coefficient of thermal expansion↗

NASA NTRS1998

MoSi2-Base Hybrid Composite Passed Engine Test

The intermetallics compound molybdenum disilicide (MoSi2) is an attractive high-temperature structural material for advanced engine applications. It has excellent oxidation resistance, a high melting point, relatively low density, and high thermal conductivity, and it is easily machined. Past research'at the NASA Lewis Research Center has resulted in the development of a hybrid composite consisting of a MoSi2 matrix reinforced with silicon nitride (Si3N4) Particulate and silicon carbide (SiC) fibers. This composite has demonstrated attractive strength, toughness, thermal fatigue, and oxidation resistance, including resistance to "pest" oxidation. These properties attracted the interest of the Office of Naval Research and Pratt & Whitney, and a joint NASA/Navy/Pratt & Whitney effort was developed to continue to mature the MoSi2 Composite technology. A turbine blade outer air seal, which was part of the Integrated High Performance Turbine Engine Technology (IHPTET) program, was chosen as a first component on which to focus. The first tasks of the materials development effort were to develop improved processing methods to reduce costs and to use fine-diameter fibers that enable the manufacturing of complex shapes. Tape-casting methods were developed to fully infiltrate the fine SiC fibers with matrix powders. The resulting composites were hot pressed to 100-percent density. Composites with cross-plied fiber architectures with 30 vol. % hi-nicalon SiC fibers and 30 vol. % nitride particles are now made routinely and demonstrate a good balance of properties. The next task entailed the measurement of a wide variety of mechanical properties to confirm the suitability of this composite in engines. In particular, participants in this effort demonstrated that composites made with Hi-Nicalon fibers had strength and toughness properties equal to or better than those of the composites made with the large-diameter fibers that had been used previously. Another critically important property measured was impact resistance. Aircraft engine components require sufficient toughness to resist manufacturing defects, assembly damage, stress concentrations at notches, and foreign object damage. Engine company designers indicated that impact resistance would have to be measured before they would seriously consider these types of composites. The Charpy V-notch test was chosen to assess impact resistance, and both monolithic and composite versions Of MOSi2 were tested from -300 to 1400 C. The results (see the following graphs) show that nitride-particulate-reinforced MoSi2 exhibited impact resistance higher than that of many monolithic ceramics and intermetallics, and that the fiber-reinforced composites had even higher values, approaching that of cast superalloys.

Keith, Theo G., Jr.↗

DOE OSTI2026

Machine Learning–Based Condition Monitoring of a Circulating Water System of a Canadian Nuclear Plant

With the need to maintain long-term reliable energy using nuclear power plants, there is an underlying demand to ensure that the maintenance of plant components and systems is also done in an efficient and cost-effective manner. One way to achieve this is by moving from time-based maintenance to condition-based maintenance. The research presented in this paper focuses on applying statistical and machine-learning-based methods to capture anomalies within data for fault detection to further develop into condition monitoring. This paper focuses on system data for a circulating water system (CWS) of a pressurized heavy-water reactor for detecting anomalies. The different methodologies used for detecting and capturing anomalies in the CWS data are matrix profile, density-based spatial clustering of applications with noise (DBSCAN), and support vector machines (SVMs). Matrix profile and DBSCAN are used to distinguish between normal data and anomalous data. This paper presents a hybrid method using DBSCAN and SVM when a portion of the data is used for DBSCAN to generate clusters. This portion of data is then used to train the SVM along with the clusters generated by DBSCAN as output. SVM is then tested on unseen data as a predictive tool, which can work in real time to categorize data points as either normal or anomalous. This paper presents results that show the high accuracies of DBSCAN and SVM in capturing anomalies within the data for a CWS for fault detection. Thus, the maintenance plan would be focused on component condition rather than a time-based schedule by switching to an automated system to identify and predict faults within a CWS.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

NASA NTRS2004

CMC Property Variability and Life Prediction Methods for Turbine Engine Component Application

The ever increasing need for lower density and higher temperature-capable materials for aircraft engines has led to the development of Ceramic Matrix Composites (CMCs). Today's aircraft engines operate with >3000"F gas temperatures at the entrance to the turbine section, but unless heavily cooled, metallic components cannot operate above approx.2000 F. CMCs attempt to push component capability to nearly 2700 F with much less cooling, which can help improve engine efficiency and performance in terms of better fuel efficiency, higher thrust, and reduced emissions. The NASA Glenn Research Center has been researching the benefits of the SiC/SiC CMC for engine applications. A CMC is made up of a matrix material, fibers, and an interphase, which is a protective coating over the fibers. There are several methods or architectures in which the orientation of the fibers can be manipulated to achieve a particular material property objective as well as a particular component geometric shape and size. The required shape manipulation can be a limiting factor in the design and performance of the component if there is a lack of bending capability of the fiber as making the fiber more flexible typically sacrifices strength and other fiber properties. Various analysis codes are available (pcGINA, CEMCAN) that can predict the effective Young's Moduli, thermal conductivities, coefficients of thermal expansion (CTE), and various other properties of a CMC. There are also various analysis codes (NASAlife) that can be used to predict the life of CMCs under expected engine service conditions. The objective of this summer study is to utilize and optimize these codes for examining the tradeoffs between CMC properties and the complex fiber architectures that will be needed for several different component designs. For example, for the pcGINA code, there are six variations of architecture available. Depending on which architecture is analyzed, the user is able to specify the fiber tow size, tow spacing, weave parameter, and angle of orientation of fibers. By holding the volume fraction of the fibers constant, variations in tow spacing can be explored for different architectures. The CMC material properties are usually calculated assuming the component is manufactured perfectly. However, this is typically not the case so that a quantification of the material property variability is needed to account for processing and/or manufacturing imperfections. The overall inputs and outputs are presented using a regression software to rapidly investigate the tradeoffs associated with fiber architecture, material properties, and ultimately cost. This information is then propagated through lifing models and Larson-Miller data to assess timehemperature-dependent CMC strength. In addition, a first order cost estimation will be quantified from a current qualitative perspective. This cost estimation includes the manufacturing challenges, such as tooling, as well as the component cost for a particular application. Ultimately, a cost to performance ratio should be established that compares the effectiveness of CMCs to their current rival, nickel superalloys.

Cheplak, Matthew L.↗

DOE OSTI2025

All-optical control of charge-trapping defects in rare-earth doped oxides

Abstract Charge-trapping defects in crystalline solids play important roles in applications ranging from microelectronics, optical storage, sensing and quantum technologies. On one hand, depleting trapped charges in the host matrix reduces charge noise and enhances coherence of solid-state quantum emitters. On the other hand, stable charge traps can enable high-density optical storage systems. Here we report all-optical control of charge-trapping defects via optical charge trapping (OCT) spectroscopy of a rare-earth ion doped oxide (Y 2 O 3 ). Charge trapping is realized by low intensity optical excitation in the 200–375 nm range. Charge detrapping or depletion is carried out by optically stimulated luminescence (OSL) under 532 nm stimulation. Using a Pr-doped Y 2 O 3 polycrystalline ceramic host matrix, we observe charging pathways via the inter-band optical absorption of Y 2 O 3 and via the 4f-5d transitions of Pr 3+ . We demonstrate effective control of the density of trapped charges within the Y 2 O 3 matrix at ambient environment. These results point to a viable method for controlling the local charge environment in rare-earth doped crystals via all-optical means, and pave the way for further development of efficient optical storage technologies with ultrahigh storage capacity, as well as for the localized control of quantum coherence in rare-earth doped solids.

França, Leonardo V. S. [Pritzker School of Molecul↗

NASA NTRS2006

Nonlinear Spring Finite Elements for Predicting Mode I-Dominated Delamination Growth in Laminated Structure with Through-Thickness reinforcement

One particular concern of polymer matrix composite laminates is the relatively low resistance to delamination cracking, in particular when the dominant type of failure is mode I opening. One method proposed for alleviating this problem involves the insertion pultruded carbon pins through the laminate thickness. The pins, known as z-pins, are inserted into the prepreg laminate using an ultrasonic hammer prior to the curing process, resulting in a field of pins embedded normal to the laminate plane as illustrated in Figure. 1. Pin diameters range between 0.28-mm to 0.5-mm and standard areal densities range from 0.5% to 4%. The z-pins are provided by the manufacturer, Aztex(Registered TradeMark) , in a low-density foam preform, which acts to stabilize orientation of the pins during the insertion process [1-3]. Typical pin materials include boron and carbon fibers embedded in a polymer matrix. A number of methods have been developed for predicting delamination growth in laminates reinforced with z-pins. During a study on the effect of z-pin reinforcement on mode I delamination resistance, finite element analyses of z-pin reinforced double cantilever beam (DCB) specimens were performed by Cartie and Partridge [4]. The z-pin bridging stresses were modeled by applying equivalent forces at the pin locations. Single z-pin pull-out tests were performed to characterize the traction law of the pins under mode I loading conditions. Analytical solutions for delamination growth in z-pin reinforced DCB specimens were independently derived by Robinson and Das [5] and Ratcliffe and O'Brien [6]. In the former case, pin bridging stresses were modeled using a distributed load and in the latter example the bridging stresses were discretely modeled by way of grounded springs. Additionally, Robinson and Das developed a data reduction strategy for calculating mode I fracture toughness, G(sub Ic), from a z-pin reinforced DCB specimen test [5]. In both cases a traction law similar to that adopted by Cartie and Partridge was used to represent z-pin failure under mode I loading conditions. In the current work spring elements available in most commercial finite element codes were used to model z-pins. The traction law used in previous analyses [4-6] was employed to represent z-pin damage. This method is intended for and is limited to simulating z-pins in composite laminate structure containing mode I-dominated delamination cracking. The current technique differs from previous analyses in that spring finite elements (available in commercial codes) are employed for simulating zpins, reducing the complexity of the analysis construction process. Furthermore, the analysis method can be applied to general structure that experiences mode I-dominated delamination cracking, in contrast to existing analytical solutions that are only applicable to coupon DCB specimens.

Ratcliffe, James G.↗

NASA NTRS1976

The use of the Winograd matrix multiplication algorithm in digital multispectral processing

The Winograd procedure for matrix multiplication provides a method whereby general matrix products may be computed more efficiently than the normal method. The algorithm and the time savings that can be effected are described. A FORTRAN program is provided which performs a general matrix multiply according to this algorithm. A variation of this procedure that may be used to calculate Gaussian probability density functions is also described. It is shown how a time savings can be effected in this calculation. The extension of this method to other similar calculations should yield similar savings.

Vanrooy, D. L.↗

NASA NTRS1992

Prediction of thermal cycling induced matrix cracking

Thermal fatigue has been observed to cause matrix cracking in laminated composite materials. A method is presented to predict transverse matrix cracks in composite laminates subjected to cyclic thermal load. Shear lag stress approximations and a simple energy-based fracture criteria are used to predict crack densities as a function of temperature. Prediction of crack densities as a function of thermal cycling is accomplished by assuming that fatigue degrades the material's inherent resistance to cracking. The method is implemented as a computer program. A simple experiment provides data on progressive cracking of a laminate with decreasing temperature. Existing data on thermal fatigue is also used. Correlations of the analytical predictions to the data are very good. A parametric study using the analytical method is presented which provides insight into material behavior under cyclical thermal loads.

Mcmanus, Hugh L.↗