Search NASA⌕ Search

SEARCH · Search NASA

Results for “Random Matrix”

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 235 records · Page 13

Estimation of full modal damping matrices from complex test modes

This paper describes the refinements of a previously published method for estimating a full modal damping matrix from complex test modes. It also documents application of the refined method to a structure where complex test modes were derived by the ERA method from multi-input random vibration test data. A numerical example based on simulated test data is presented to demonstrate the validity of the method. The application using real data was not successful, presumably because of noise in the small phase angles of the measured complex modes. Alternative test and data reduction procedures are suggested as possible remedies to the problem. A careful analysis of measurement and data processing errors should be made to examine basic feasibility before implementing the alternative procedures. The ability to estimate a full modal damping matrix is considered important for the preflight estimation of on-orbit damping, and for the synthesis of structural damping from substructure tests.

Hasselman, T. K.↗

Living on the edge: a non-perturbative resolution to the negativity of bulk entropies

Lin, Maldacena, Rozenberg, and Shan (LMRS) presented a new information paradox in black hole physics by noticing that the entanglement and Rényi entropies in a two-sided black hole can become negative when the geometry contains a very large number of matter excitations behind the black hole horizon. While originally this puzzle was presented in the context of BPS two-sided black holes in two-dimensional supergravity, the negativity in fact persists for more general two-sided black holes in the presence of a large number of matter excitations. Since the entanglement and Rényi entropies in ordinary quantum systems cannot be negative, resolving this puzzle is a necessary step towards understanding the quantum mechanical description of black holes. In this paper, we explain how to address the entanglement negativity puzzle, both in the original setting discussed by LMRS and in more general non-supersymmetric settings, by summing over all non-perturbative contributions to the gravitational path integral. We then interpret this result from the point of view of a dual matrix integral, which we use to extend our analysis beyond the regime of validity of the genus re-summation performed in the gravitational path integral. In this regime, positivity is rescued by new saddles of the matrix integral, a one-eigenvalue instanton and a two-eigenvalue instanton. Finally, we formulate a similar puzzle and its resolution using random tensor network techniques.

FOS: Physical sciences↗

Multifrequency imaging radar polarimetry: Depolarisation of radar echoes at three wavelengths

It is shown that high resolution imaging radar polarimeters can describe depolarization effects in great detail by measuring the complete Stokes matrix for small regions on the Earth's surface, permitting to distinguish between coherent polarization transformation by the surface and diffuse interactions that randomize the polarization state of the received wave. Multiwavelength polarimeter observations of a variety of types of terrain, including images of the coherent and diffuse parts of the received signal are presented. The diffuse image, in particular, is highly indicative of small-scale surface roughness, an effect illustrated by analyzing a set of polarimeter images acquired over lava fields of varying roughness.

Zebker, H. A.↗

A Multivariate Randomization Text of Association Applied to Cognitive Test Results

Randomization tests provide a conceptually simple, distribution-free way to implement significance testing. We have applied this method to the problem of evaluating the significance of the association among a number (k) of variables. The randomization method was the random re-ordering of k-1 of the variables. The criterion variable was the value of the largest eigenvalue of the correlation matrix.

Ahumada, Albert↗

Tool for Generation of MAC/GMC Representative Unit Cell for CMC/PMC Analysis

This document describes a recently developed analysis tool that enhances the resident capabilities of the Micromechanics Analysis Code with the Generalized Method of Cells (MAC/GMC) 4.0. This tool is especially useful in analyzing ceramic matrix composites (CMCs), where higher fidelity with improved accuracy of local response is needed. The tool, however, can be used for analyzing polymer matrix composites (PMCs) as well. MAC/GMC 4.0 is a composite material and laminate analysis software developed at NASA Glenn Research Center. The software package has been built around the concept of the generalized method of cells (GMC). The computer code is developed with a user friendly framework, along with a library of local inelastic, damage, and failure models. Further, application of simulated thermomechanical loading, generation of output results, and selection of architectures to represent the composite material have been automated to increase the user friendliness, as well as to make it more robust in terms of input preparation and code execution. Finally, classical lamination theory has been implemented within the software, wherein GMC is used to model the composite material response of each ply. Thus, the full range of GMC composite material capabilities is available for analysis of arbitrary laminate configurations as well. The primary focus of the current effort is to provide a graphical user interface (GUI) capability that generates a number of different user-defined repeating unit cells (RUCs). In addition, the code has provisions for generation of a MAC/GMC-compatible input text file that can be merged with any MAC/GMC input file tailored to analyze composite materials. Although the primary intention was to address the three different constituents and phases that are usually present in CMCs-namely, fibers, matrix, and interphase-it can be easily modified to address two-phase polymer matrix composite (PMC) materials where an interphase is absent. Currently, the tool capability includes generation of RUCs for square packing, hexagonal packing, and random fiber packing as well as RUCs based on actual composite micrographs. All these options have the fibers modeled as having a circular cross-sectional area. In addition, a simplified version of RUC is provided where the fibers are treated as having a square cross section and are distributed randomly. This RUC facilitates a speedy analysis using the higher fidelity version of GMC known as HFGMC. The first four mentioned options above support uniform subcell discretization. The last one has variable subcell sizes due to the primary intention of keeping the RUC size to a minimum to gain the speed ups using the higher fidelity version of MAC. The code is implemented within the MATLAB (The Mathworks, Inc., Natick, MA) developmental framework; however, a standalone application that does not need a priori MATLAB installation is also created with the aid of the MATLAB compiler.

Materials Engineering↗

Structured interactions drive abrupt transitions in the spatial organization of microbial communities

Bacteria possess diverse mechanisms to regulate their motility in response to environmental and physiological signals, enabling them to navigate complex habitats and adapt their behavior. Some of these mechanisms are species specific and enable cells to modulate their movement based on the ecological identity of neighboring species. Here, we introduce a model in which bacteria interact via local signals that either enhance or suppress the motility of neighboring cells depending on species type. Through large-scale simulations and a coarse-grained stochastic model, we demonstrate the emergence of a sharp transition driven by nucleation processes: increasing the density of motility-suppressing interactions drives the system from a fully mixed, motile phase to a state characterized by large, stationary bacterial clusters. Remarkably, in systems with a large number of interacting species, this transition can be triggered solely by altering the structure of the motility-regulation interaction matrix while maintaining species and interaction densities constant. In particular, we find that heterogeneous and modular interactions promote the transition more readily than homogeneous random ones. These findings add a dimension to the theory of motility-induced phase separation and contribute to the ongoing effort to understand microbial interactions, suggesting that structured, nonrandom ones may be key to reproducing commonly observed spatial patterns in microbial communities.

bacterial communities↗

A transfer matrix approach to vibration localization in mistuned blade assemblies

A study of mode localization in mistuned bladed disks is performed using transfer matrices. The transfer matrix approach yields the free response of a general, mono-coupled, perfectly cyclic assembly in closed form. A mistuned structure is represented by random transfer matrices, and the expansion of these matrices in terms of the small mistuning parameter leads to the definition of a measure of sensitivity to mistuning. An approximation of the localization factor, the spatially averaged rate of exponential attenuation per blade-disk sector, is obtained through perturbation techniques in the limits of high and low sensitivity. The methodology is applied to a common model of a bladed disk and the results verified by Monte Carlo simulations. The easily calculated sensitivity measure may prove to be a valuable design tool due to its system-independent quantification of mistuning effects such as mode localization.

Ottarson, Gisli↗

Meteorite Material Model for Structural Properties

To assess the threat posed by an asteroid entering Earth's atmosphere, one must predict if, when, and how it fragments during entry. A comprehensive understanding of the asteroid material properties is needed to achieve this objective. At present, the meteorite material found on earth are the only objects from an entering asteroid that can be used as representative material and be tested inside a laboratory setting. Due to complex petrology, it is technically challenging and expensive to obtain reliable material properties by means of laboratory test for a family of meteorites. In order to circumvent this challenge, meteorite unit models are developed to determine the effective material properties including Youngs modulus, compressive and tensile strengths and Poissons ratio, that in turn would help deduce the properties of asteroids. The meteorite unit is a representative volume that accounts for diverse minerals, porosity, cracks and matrix composition. The Youngs Modulus and Poissons Ratio in the meteorite units are calculated by performing several hundreds of Monte-Carlo simulations by randomly distributing the various phases inside these units. Once these values are obtained, cracks are introduced in these meteorite units. The size, orientation and distribution of cracks are derived by extensive CT-scans and visual scans of various meteorites from the same family. Subsequently, simulations are performed to attain stress-strain relations, strength and effective modulus values in the presence of these cracks. The meteorite unit models are presented for H, L and LL ordinary chondrites, as well as for terrestrial basalt. In the case of the latter, data from the simulations is compared with experimental data to validate the methodology. These material models will be subsequently used in fragmentation modeling of full scale asteroids.

Meteorite↗

Electromagnetic Scattering by Discrete Random Media Illuminated by a Gaussian Beam II: Solution of the Radiative Transfer Equation

In this paper, we present numerical methods for solving the phenomenological scalar radiative transfer equation for a discrete random medium illuminated by a Gaussian beam. These rely on the Fourier transform method for the horizontal variables and the discrete ordinate method with matrix exponential for solving the underlying one-dimensional radiative transfer equation in the wavenumber domain. The problem of a Gaussian beam at oblique and normal incidence, as well as, the searchlight problem are treated. A complete description of the methods and the numerical algorithms is provided.

Gaussian beam↗

Angiotensin-converting enzyme and matrix metalloproteinase inhibition with developing heart failure: comparative effects on left ventricular function and geometry

The progression of congestive heart failure (CHF) is left ventricular (LV) myocardial remodeling. The matrix metalloproteinases (MMPs) contribute to tissue remodeling and therefore MMP inhibition may serve as a useful therapeutic target in CHF. Angiotensin converting enzyme (ACE) inhibition favorably affects LV myocardial remodeling in CHF. This study examined the effects of specific MMP inhibition, ACE inhibition, and combined treatment on LV systolic and diastolic function in a model of CHF. Pigs were randomly assigned to five groups: 1) rapid atrial pacing (240 beats/min) for 3 weeks (n = 8); 2) ACE inhibition (fosinopril, 2.5 mg/kg b.i.d. orally) and rapid pacing (n = 8); 3) MMP inhibition (PD166793 2 mg/kg/day p.o.) and rapid pacing (n = 8); 4) combined ACE and MMP inhibition (2.5 mg/kg b.i.d. and 2 mg/kg/day, respectively) and rapid pacing (n = 8); and 5) controls (n = 9). LV peak wall stress increased by 2-fold with rapid pacing and was reduced in all treatment groups. LV fractional shortening fell by nearly 2-fold with rapid pacing and increased in all treatment groups. The circumferential fiber shortening-systolic stress relation was reduced with rapid pacing and increased in the ACE inhibition and combination groups. LV myocardial stiffness constant was unchanged in the rapid pacing group, increased nearly 2-fold in the MMP inhibition group, and was normalized in the ACE inhibition and combination treatment groups. Increased MMP activation contributes to the LV dilation and increased wall stress with pacing CHF and a contributory downstream mechanism of ACE inhibition is an effect on MMP activity.

Non-NASA Center↗

Modeling and observation of the radar polarization signature of forested areas

To understand radar measurements of forested areas, the authors have developed a model of L-band (25-cm) microwave scattering from a forest. The forest floor is modeled as a rough dielectric surface above which is a layer of nearly vertical dielectric cylinders representing tree trunks. Above this layer is a second layer consisting of randomly oriented cylinders which represent branches. The authors identify several scattering mechanisms and calculate the corresponding Stokes matrices, which combine to give the total Stokes matrix and resulting polarization signature. It is found that this simple model permits accurate prediction of the polarization of the scattered waves and that additional mechanisms, including the effects of leaves and twigs, are not required for the 25-cm observation of the forests studied. The authors present measurements of the polarization signature acquired over a forested area and show comparisons with model calculations.

Durden, Stephen L.↗

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.↗

Electromagnetic Scattering by Discrete Random Media. III: The Vector Radiative Transfer Equation

A vector radiative transfer equation with an additional source term typical of dense media is obtained. The analysis includes (i) the derivation of an integral equation for the correlation matrix of the exciting field coefficients accounting for the correlation between the particles, (ii) the derivation of an integral representation for the specific coherency dyadicin terms of this matrix, and (iii) the simplification of the integral equation for the correlation matrix and of the integral representation for the specific coherency dyadic by employing a series of approximations which are characteristic of sparse media.

Adrian Doicu↗

Coherence-Induced Deep Thermalization Transition in Random Permutation Quantum Dynamics

We report a phase transition in the projected ensemble—the collection of postmeasurement wave functions of a local subsystem obtained by measuring its complement. The transition emerges in systems undergoing random permutation dynamics, a type of quantum time evolution wherein computational basis states are shuffled without creating superpositions. It separates a phase exhibiting deep thermalization, where the projected ensemble is distributed over Hilbert space in a maximally entropic fashion (Haar random), from a phase where it is minimally entropic (“classical bit-string ensemble”). Crucially, this deep thermalization transition is invisible to the subsystem’s density matrix, which always exhibits thermalization to infinite temperature across the phase diagram. Through a combination of analytical arguments and numerical simulations, we show that the transition is tuned by the total amount of injected by the input state and the measurement basis, and is exhibited robustly across different microscopic models. Our findings represent a novel form of ergodicity-breaking universality in quantum many-body dynamics, characterized not by a failure of regular thermalization, but rather by a failure of deep thermalization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Power-Law Entanglement and Hilbert Space Fragmentation in Nonreciprocal Quantum Circuits

Quantum circuits utilizing measurement to evolve a quantum wave function offer a new and rich playground to engineer unconventional entanglement dynamics. Here, in this work, we introduce a hybrid, nonreciprocal setup featuring a quantum circuit, whose updates are conditioned on the state of a classical dynamical agent. In our example the circuit is represented by a Majorana quantum chain controlled by a classical N-state Potts chain undergoing pair flips. The local orientation of the classical spins controls whether randomly drawn local measurements on the quantum chain are allowed or not. This imposes a dynamical kinetic constraint on the entanglement growth, described by the transfer matrix of an N-colored loop model. It yields an equivalent description of the circuit by an SU(N)-symmetric Temperley-Lieb Hamiltonian or by a kinetically constrained surface growth model for an N-component height field. For N = 2, we find a diffusive growth of the half-chain entanglement toward a stationary profile S(L) ~ L 1/2 for L sites. For N ≥ 3, the kinetic constraints impose Hilbert space fragmentation, yielding subdiffusive growth toward S(L) ~ L 0.57 . This showcases how the control by a classical dynamical agent can enrich the entanglement dynamics in quantum circuits, paving a route toward novel entanglement dynamics in nonreciprocal hybrid circuit architectures.

1-dimensional spin chains↗

Quasiprobabilistic Readout Correction of Midcircuit Measurements for Adaptive Feedback via Measurement Randomized Compiling

Quantum measurements are a fundamental component of quantum computing. However, on present-day quantum computers, measurements can be more error prone than quantum gates and are susceptible to nonunital errors as well as nonlocal correlations due to measurement crosstalk. While readout errors can be mitigated in postprocessing, this is inefficient in the number of qubits due to a combinatorially large number of possible states that need to be characterized. In this work, we show that measurement errors can be tailored into a simple stochastic error model using randomized compiling, enabling the efficient mitigation of readout errors via quasiprobability distributions reconstructed from the measurement of a single preparation state in an exponentially large confusion matrix. We demonstrate the scalability and power of this approach by correcting readout errors without matrix inversion on a large number of different preparation states applied to a register of eight superconducting transmon qubits. Moreover, we show that this method can be extended to midcircuit measurements used for active feedback via quasiprobabilistic error cancellation, and we demonstrate the correction of measurement errors on an ancilla qubit used to detect and actively correct bit-flip errors on an entangled memory qubit. Our approach enables the correction of readout errors on large numbers of qubits and offers a strategy for correcting readout errors in adaptive circuits in which the results of midcircuit measurements are used to perform conditional operations on nonlocal qubits in real time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A finite element technique for non-deterministic thermal deformation analyses including temperature dependent material properties

A technique utilizing the finite element displacement method is developed for the static analysis of structures subjected to non-deterministic thermal loading in which the material properties, assumed isotropic, are temperature dependent. Matrix equations are developed for the first two statistical moments of the displacements using a third order series expansion for the displacements in terms of the random temperatures. Sample problems are included to demonstrate the range of applicability of the third order series solutions. These solutions are compared with results from Monte Carlo analyses and also, for some problems, with solutions obtained by numerically integrating equations for the statistical properties of the displacements. In general, it is shown that the effect of temperature dependent material properties can have a significant effect on the covariances of the displacements.

Case, W. R., Jr.↗

Response of stiffened panels for applications to acoustic fatigue

The surface protection systems of aerospace and aircraft structures are often constructed from discretely stiffened panels. This paper presents an analytical study on dynamic stress response of these structures to random surface flow and acoustic loads. To account for aerodynamic heating of high speed flow, thermal effects are included in the structural model. A generalized transfer matrix procedure is developed to obtain the required dynamic response solutions. Numerical results include spectral densities of stress, response root mean square values and fatigue damage for a variety of loading and thermal conditions.

Vaicaitis, R.↗