SEARCH · Search NASA

Results for “Matrix Theory”

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 271 records · Page 15

All sources NASA NTRS DOE OSTI

NASA NTRS2000

High Temperature Tensile Properties of Unidirectional Hi-Nicalon/Celsian Composites In Air

High temperature tensile properties of unidirectional BN/SiC-coated Hi-Nicalon SiC fiber reinforced celsian matrix composites have been measured from room temperature to 1200 C (2190 F) in air. Young's modulus, the first matrix cracking stress, and the ultimate strength decreased from room temperature to 1200 C (2190 F). The applicability of various micromechanical models, in predicting room temperature values of various mechanical properties for this CMC, has also been investigated. The simple rule of mixtures produced an accurate estimate of the primary composite modulus. The first matrix cracking stress estimated from ACK theory was in good agreement with the experimental value. The modified fiber bundle failure theory of Evans gave a good estimate of the ultimate strength.

Gyekenyesi, John Z.↗

NASA NTRS2003

The Infrared Spectrum of Matrix Isolated Aminoacetonitrile: A Precursor to the Amino Acid Glycine

We present infrared (IR) spectral data from matrix isolation experiments and density functional theory calculations on the pre-biologically interesting molecule aminoacetonitrile, a precursor to glycine. We find that this nitrile has an unusually weak nitrile (C=N) stretch in the infrared, in contrast to expectations based on measurements and models of other nitriles under astrophysical conditions. The absence of an observable nitrile absorption feature in the infrared will make the IR search for this molecule considerably more difficult, and will raise estimates of upper limits on nitriles in interstellar and outer Solar System ices. This is also of relevance to assessing the formation routes of the amino acid glycine, since aminoacetonitrile is the putative precursor to glycine via the Strecker synthesis, the mechanism postulated to have produced the amino acids in meteorites.

Bernstein, Max P.↗

NASA NTRS1989

Ab initio determination of mode coupling in HSSH - The torsional splitting in the first excited S-S stretching state

A mechanism for the enhanced splitting detected in the millimeter-wave rotational spectra of the first excited S-S stretching state of HSSH (disulfane) has been studied. The mechanism, which involves a potential coupling between the first excited S-S stretching state and excited torsional states, has been investigated in part by the use of ab initio theory. Based on an ab initio potential surface, coupling matrix elements have been calculated, and the amount of splitting has then been estimated by second-order perturbation theory. The result, while not in quantitative agreement with the measured splitting, lends plausibility to the assumed mechanism.

Herbst, Eric↗

NASA NTRS1983

A refined finite element for vibration analysis of twisted blades based on beam theory

A finite element method of discretizing beam segments of pretwisted rotating blades is presented. Employing the matrix displacement method, stiffness and mass properties are developed from basic mechanics of a pretwisted beam theory. By introducing the proper displacement functions, the effect of rotor blade rotational motion on the stiffness matrix is obtained systematically from the kinetic energy expression. Comparing with other beam elements the derivation of this element is more fundamental. This allows one to apply the same approach to more complicated problems including nonlinear effects or complex dynamic motions. Illustrative examples are given comparing numerical results with available data and other numerical solutions from rotating and nonrotating force fields. These examples show that accurate prediction of vibration frequencies for pretwisted blades can be obtained by employing a quite modest number of degrees of freedom.

Sisto, F.↗

NASA NTRS1984

Line strengths of N2O in the 1120-1440/cm region

Line strengths of N2O and its isotopic derivatives in the 1120-1440/cm region were measured at low pressure and high resolution (0.0054/cm). The band strength, rotationless dipole moment matrix elements, and F factor coefficients were considered. First-order nondegenerate perturbation theory was employed to derive explicit expressions for the rotationless dipole moment matrix elements and F factor coefficients. This made it possible to obtain general expressions for the F factor. The derived expressions were also applicable to CO2 bands.

Toth, R. A.↗

NASA NTRS1989

Power flow for spacecraft power systems

A method for constructing the generalized system-level admittance matrix for use with a Newton-Raphson power flow is presented. The network modeling technique presented does not use the standard pi-equivalent models, which assume a lossless return path, for the transmission line and transformer. If the return path cannot be assumed lossless, then the standard algorithms for constructing the system admittance matrix cannot be used. The method presented here uses concepts from linear graph theory to combine network modules to form the system-level admittance matrix. The modeling technique is presented, and the resulting matrix is used with a standard Newton-Raphson power flow to calculate all system voltages and current (power) flows.

Halpin, S. M.↗

DOE OSTI2025

Splitting regions and shrinking islands from higher point constraints

We study constraints from higher-point amplitudes on 2 → 2 scattering in the context of effective field theory (EFT) using the perturbative numerical S-matrix bootstrap. Specifically, we investigate the class of weakly coupled EFTs with amplitudes that obey the hidden zero and split conditions that are known to hold both for Tr(Φ 3 ) theory and for certain string tree amplitudes, including at 4-point the beta function. Requiring the splitting condition for the 5-point amplitude not only fixes nearly all its contact terms, but it also imposes non-linear constraints among the 4-point EFT Wilson coefficients. When included in the bootstrap, the resulting allowed region consistent with positivity is no longer convex but is restricted to a smaller non-convex region — which has a sharp corner near the string beta function! Assuming the absence of an infinite spin tower at the mass gap, the allowed region bifurcates into a trivial region (with states only above a chosen cutoff) and an island that continues to shrink around the string as more constraints are included in the bootstrap. The numerics indicate that in the absence of single-mass infinite spin towers the string beta function is the unique 4-point amplitude compatible with hidden zero and the 5-point splitting constraints. The analysis provides a prototype example for how features of higher-point amplitudes constrain the bootstrap of 4-point amplitudes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2008

Micromechanics-Based Progressive Failure Analysis of Composite Laminates Using Different Constituent Failure Theories

Predicting failure in a composite can be done with ply level mechanisms and/or micro level mechanisms. This paper uses the Generalized Method of Cells and High-Fidelity Generalized Method of Cells micromechanics theories, coupled with classical lamination theory, as implemented within NASA's Micromechanics Analysis Code with Generalized Method of Cells. The code is able to implement different failure theories on the level of both the fiber and the matrix constituents within a laminate. A comparison is made among maximum stress, maximum strain, Tsai-Hill, and Tsai-Wu failure theories. To verify the failure theories the Worldwide Failure Exercise (WWFE) experiments have been used. The WWFE is a comprehensive study that covers a wide range of polymer matrix composite laminates. The numerical results indicate good correlation with the experimental results for most of the composite layups, but also point to the need for more accurate resin damage progression models.

Moncada, Albert M.↗

DOE OSTI2026

Connecting ground-state properties of 6 Li to each other and to scattering data

We examine the relationship between the asymptotic normalization coefficient (ANC) of 6 Li and other low-energy observables in the α–deuteron system. Our analysis uses a set of calculations carried out within the ab initio no core shell model with continuum (NCSMC) using a variety of inter-nucleon interactions and basis sizes, and yielding 6 Li deuteron separation energies between 1.3 and 1.8 MeV (Hebborn et al 2022 Phys. Rev. Lett. 129 042503). These NCSMC calculations show that the square of the ANC is strongly correlated with the separation energy over this range. In this work, we investigate the origin of this correlation using the phenomenological R-matrix, a single-channel potential and a perturbative approach. We show that this correlation occurs because the depth of the α–deuteron central potential changes by only a small relative amount as the separation energy varies. We then investigate if the ANC can be accurately extracted from α–deuteron phase shifts in an ideal case in which low-energy data are available and there are no experimental errors. We find that both R-matrix and Coulomb-modified effective-range theory (CM-ERE) yield extracted ANCs close to, although not exactly equal to, the NCSMC value, provided the extrapolation is constrained by the known position of the bound-state pole and at least three terms are included in the fit function. The R-matrix approach converges faster than the CM-ERE as the number of parameters increases and is also more robust against the inclusion of low-energy and high-energy phase shift data. Finally, our study also shows that a naive quantification of uncertainties by comparing different truncations used in both theories is not accurate, and suggests the accuracy of ANCs extracted from phase shift data needs further investigation.

R-matrix↗

DOE OSTI2024

Field Theory of the Fermi Function

The Fermi function F ( Z , E ) accounts for QED corrections to beta decays that are enhanced at either small electron velocity β or large nuclear charge Z . For precision applications, the Fermi function must be combined with other radiative corrections and with scale- and scheme-dependent hadronic matrix elements. We formulate the Fermi function as a field theory object and present a new factorization formula for QED radiative corrections to beta decays. We provide new results for the anomalous dimension of the corresponding effective operator complete through three loops, and resum perturbative logarithms and π enhancements with renormalization-group methods. Our results are important for tests of fundamental physics with precision beta decay and related processes. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1987

The matrix exponential in transient structural analysis

The primary usefulness of the presented theory is in the ability to represent the effects of high frequency linear response with accuracy, without requiring very small time steps in the analysis of dynamic response. The matrix exponential contains a series approximation to the dynamic model. However, unlike the usual analysis procedure which truncates the high frequency response, the approximation in the exponential matrix solution is in the time domain. By truncating the series solution to the matrix exponential short, the solution is made inaccurate after a certain time. Yet, up to that time the solution is extremely accurate, including all high frequency effects. By taking finite time increments, the exponential matrix solution can compute the response very accurately. Use of the exponential matrix in structural dynamics is demonstrated by simulating the free vibration response of multi degree of freedom models of cantilever beams.

Minnetyan, Levon↗

NASA NTRS1990

A simplified orthotropic viscoplasticity theory based on overstress

The viscoplasticity theory based on overstress, a simplified version of Sutcu (1985) theory, is presented for the case of orthotropy. The theory permits asymptotic solutions for checking numerical experiments and for identification of material properties. It is applicable to materials with rate(time) dependence, hysteresis, and a permanent set, such as cubic crystals, directionally solidified alloys, and metal matrix composites. Though it is a unified type theory, with effects of creep and plasticity not separated, it allows to identify viscous and plastic contributions to the stress in the asymptotic state.

Sutcu, M.↗

DOE OSTI2026

Extended JT supergravity and random matrix models: The power of the string equation

A number of supersymmetric Jackiw-Teitelboim (JT) gravity theories are known to be described (in the Euclidean path integral formulation) by double-scaled random matrix models. Such matrix models can be characterized using a certain “string equation”. It was shown recently that in extended supergravity, when the number of BPS states scales as e$^{S_0}$, where $S_0$ is the extremal entropy, a special ansatz for the leading order solution of the string equation yields the supergravity spectrum. Somewhat miraculously, the construction showed that the functional form of the non-BPS (continuum) sector predicts the precise form of the BPS sector, showing the robustness of the supergravity/matrix-model correspondence. In this paper, we refine the analysis and show that the string equation, combined with some simple requirements on solutions, are powerful tools for constraining the spectrum of extended JT supergravity theories. We re-explore the cases of $\mathcal{N} = 2$ and (small) $\mathcal{N} = 4$ JT supergravity, and then explore the new cases of spectra from $\mathcal{N} = 3$ and $\mathcal{N} = 4$ large JT supergravity (recently derived by Heydeman, Shi, and Turiaci) showing that our approach also works naturally for (nearly) all the models. Based on this success, we conjecture that these new supergravity models also have matrix model descriptions.

Extended Supersymmetry↗

NASA NTRS1988

Prediction of high temperature metal matrix composite ply properties

The application of the finite element method (superelement technique) in conjunction with basic concepts from mechanics of materials theory is demonstrated to predict the thermomechanical behavior of high temperature metal matrix composites (HTMMC). The simulated behavior is used as a basis to establish characteristic properties of a unidirectional composite idealized an as equivalent homogeneous material. The ply properties predicted include: thermal properties (thermal conductivities and thermal expansion coefficients) and mechanical properties (moduli and Poisson's ratio). These properties are compared with those predicted by a simplified, analytical composite micromechanics model. The predictive capabilities of the finite element method and the simplified model are illustrated through the simulation of the thermomechanical behavior of a P100-graphite/copper unidirectional composite at room temperature and near matrix melting temperature. The advantage of the finite element analysis approach is its ability to more precisely represent the composite local geometry and hence capture the subtle effects that are dependent on this. The closed form micromechanics model does a good job at representing the average behavior of the constituents to predict composite behavior.

Caruso, J. J.↗

DOE OSTI2025

Thermal bootstrap of matrix quantum mechanics

We implement a bootstrap method that combines stationary state conditions, thermal inequalities, and semidefinite relaxations of matrix logarithm in the ungauged one-matrix quantum mechanics, at finite rank N as well as in the large N limit, and determine finite temperature observables that interpolate between available analytic results in the low and high temperature limits respectively. We also obtain bootstrap bounds on thermal phase transition as well as preliminary results in the ungauged two-matrix quantum mechanics.

1/N Expansion↗

NASA NTRS1985

A complex T-matrix derivation of a resonance amplitude

Time-dependent perturbation-theory techniques are used to derive a compact expression, valid to arbitrary order and displaying time dependence explicitly, for a quantum-mechanical transition amplitude applicable to the description of resonances. A solution representing a complex-energy generalization of the usual real-energy (nonresonant) amplitude is obtained and generalized to all orders by introducing a complex-energy T matrix. Applications to physical problems such as the extension of the Fermi golden rules to resonances (Norbury and Deutchman, 1984); pion production in relativistic nucleus-nucleus collisions (Norbury et al., 1985); and the determination of resonant cross sections for nuclear, atomic, or molecular processes involving the formation and decay of intermediate discrete or continuum states are indicated.

Norbury, J. W.↗

NASA NTRS1979

Space Shuttle communications RF switch matrix

The Shuttle Orbiter communications equipment includes phase modulation (PM) and frequency modulation (FM) channels. The PM section has the capability of routing high levels of energy (175 W) from any one of four transmitters to any one of four antennas, mutually exclusive. The FM channel uses a maximum of 15-W power routed from either of two transmitters to one of two antennas, mutually exclusive. The paper describes the design and the theory of a logic-controlled RF switch matrix devised for the purposes cited. Both PM and FM channels are computer-controlled with manual overrides. The logic interface is realized with CMOS logic for low power consumption and high noise immunity. The interior of the switch matrix is maintained at a pressure of 15 psi (90% nitrogen, 10% helium) by an electron beam-welded encapsulation. The computational results confirm the viability of the RF switch matrix concept.

Winch, R.↗

NASA NTRS1993

Deriving the intermediate spectra and photocycle kinetics from time-resolved difference spectra of bacteriorhodopsin. The simpler case of the recombinant D96N protein

The bacteriorhodopsin photocycle contains more than five spectrally distinct intermediates, and the complexity of their interconversions has precluded a rigorous solution of the kinetics. A representation of the photocycle of mutated D96N bacteriorhodopsin near neutral pH was given earlier (Varo, G., and J. K. Lanyi. 1991. Biochemistry. 30:5008-5015) as BRhv-->K<==>L<==>M1-->M2--> BR. Here we have reduced a set of time-resolved difference spectra for this simpler system to three base spectra, each assumed to consist of an unknown mixture of the pure K, L, and M difference spectra represented by a 3 x 3 matrix of concentration values between 0 and 1. After generating all allowed sets of spectra for K, L, and M (i.e., M1 + M2) at a 1:50 resolution of the matrix elements, invalid solutions were eliminated progressively in a search based on what is expected, empirically and from the theory of polyene excited states, for rhodopsin spectra. Significantly, the average matrix values changed little after the first and simplest of the search criteria that disallowed negative absorptions and more than one maximum for the M intermediate. We conclude from the statistics that during the search the solutions strongly converged into a narrow region of the multidimensional space of the concentration matrix. The data at three temperatures between 5 and 25 degrees C yielded a single set of spectra for K, L, and M; their fits are consistent with the earlier derived photocycle model for the D96N protein.

NASA Program Exobiology↗