Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Random 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.

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

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

A statistical approach to multifield inflation: many-field perturbations beyond slow roll

We study multifield contributions to the scalar power spectrum in an ensemble of six-field inflationary models obtained in string theory. We identify examples in which inflation occurs by chance, near an approximate inflection point, and we compute the primordial perturbations numerically, both exactly and using an array of truncated models. The scalar mass spectrum and the number of fluctuating fields are accurately described by a simple random matrix model. During the approach to the inflection point, bending trajectories and violations of slow roll are commonplace, and 'many-field' effects, in which three or more fields influence the perturbations, are often important. However, in a large fraction of models consistent with constraints on the tilt the signatures of multifield evolution occur on unobservably large scales. Our scenario is a concrete microphysical realization of quasi-single-field inflation, with scalar masses of order H, but the cubic and quartic couplings are typically too small to produce detectable non-Gaussianity. We argue that our results are characteristic of a broader class of models arising from multifield potentials that are natural in the Wilsonian sense.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Regenesis and quantum traversable wormholes

Recent gravity discussions of a traversable wormhole indicate that in holographic systems signals generated by a source could reappear long after they have dissipated, with the need of only performing some simple operations. In this paper we argue the phenomenon, to which we refer as “regenesis”, is universal in general quantum chaotic many-body systems, and elucidate its underlying physics. The essential elements behind the phenomenon are: (i) scrambling which in a chaotic system makes out-of-time-ordered correlation functions (OTOCs) vanish at large times, (ii) the entanglement structure of the state of the system. The latter aspect also implies that the regenesis phenomenon requires fine tuning of the initial state. Compared to other manifestations of quantum chaos such as the initial growth of OTOCs which deals with early times, and a random matrix-type energy spectrum which reflects very large time behavior, regenesis concerns with intermediate times, of order the scrambling time of a system. We also study the phenomenon in detail in general two-dimensional conformal field theories in the large central charge limit, and highlight some interesting features including a resonant enhancement of regenesis signals near the scrambling time and their oscillations in coupling. Finally, we discuss gravity implications of the phenomenon for systems with a gravity dual, arguing that there exist regimes for which traversability of a wormhole is quantum in nature, i.e. cannot be associated with a semi-classical spacetime causal structure.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1992

Radiative transfer theory for polarimetric remote sensing of pine forest

The radiative transfer theory is applied to interpret polarimetric radar backscatter from pine forest with clustered vegetation structures. To take into account the clustered structures with the radiative transfer theory, the scattering function of each cluster is calculated by incorporating the phase interference of scattered fields from each component. Subsequently, the resulting phase matrix is used in the radiative transfer equations to evaluate the polarimetric backscattering coefficients from random medium layers embedded with vegetation clusters. Upon including the multi-scale structures, namely, trunks, primary and secondary branches, as well as needles, we interpret and simulate the polarimetric radar responses from pine forest for different frequencies and looking angles. The preliminary results are shown to be in good agreement with the measured backscattering coefficients at the Landes maritime pine forest during the MAESTRO-1 experiment.

Hsu, C. C.↗
NASA NTRS1986

Radar scene generation for tactical decision aids

The Mueller matrix and polarization covariance matrix for polarimetric radar systems was studied. The clutter was modeled by a layer of random permittivity, described by a three-dimensional correlation function, with variance, and horizontal and vertical correlation lengths. This model was applied, using the wave theory with Born approximations carried to the second order, to find the backscattering elements of the polarimetric matrices. Theoretical predictions are matched with experimental data for vegetation fields. The strong fluctuation theory was used to derive the backscattering cross sections. A two-layer anisotropic random medium model was developed for the active and passive microwave remote sensing of ice fields. A three-layer random medium model was adopted to study the volume scattering effects for the active and passive microwave remote sensing of snow-covered ice fields.

Kong, J. A.↗
DOE OSTI2022

Global calculation of two-neutrino double- β decay within the finite amplitude method in nuclear density functional theory

Two-neutrino double-beta (2νββ) decay has been used to constrain the neutron-proton part of effective interactions, which in turn is used to compute the nuclear matrix elements for neutrinoless double-beta decay, the observation of which would have important consequences for fundamental physics. We carefully examine 2νββ matrix elements within the proton-neutron quasiparticle random-phase approximation with nuclear energy density functionals. Here we work with functionals that are fit globally to single-beta-decay half-lives and charge-exchange giant-resonance energies, but not to 2νββ half-lives themselves, to evaluate the 2νββ nuclear matrix elements for all important nuclei, including those whose half-lives have not yet been measured. Such a comprehensive evaluation in large model spaces without configuration truncation requires an efficient computational scheme; we employ a double contour integration within the finite amplitude method. The results generally reproduce the nuclear matrix element extracted from half-lives well, without the use of any of those half-lives in the fitting procedure. We present predictions of the matrix elements in a total of 27 nuclei with half-lives that are still unmeasured.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2013

Kerov's interlacing sequences and random matrices

To a N × N real symmetric matrix Kerov assigns a piecewise linear function whose local minima are the eigenvalues of this matrix and whose local maxima are the eigenvalues of its (N − 1) × (N − 1) submatrix. We study the scaling limit of Kerov's piecewise linear functions for Wigner and Wishart matrices. For Wigner matrices the scaling limit is given by the Verhik-Kerov-Logan-Shepp curve which is known from asymptotic representation theory. For Wishart matrices the scaling limit is also explicitly found, and we explain its relation to the Marchenko-Pastur limit spectral law.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1991

Polarimetric signatures of a layer of random nonspherical discrete scatterers overlying a homogeneous half-space based on first- and second-order vector radiative transfer theory

Complete polarimetric signatures of a layer of random, nonspherical discrete scatterers overlying a homogeneous half space are studied with the first- and second-order solutions of the vector radiative transfer theory. Some of the salient features of the numerical results are as follows: (1) the inclusion of the nondiagonal extinction matrix in the vector radiative transfer theory accounts for an appreciable phase difference between vv and hh polarizations, particularly for aligned scatterers; (2) the ensemble-averaged scattered Stokes vector is generally partially polarized, with the degree of polarization less than unity; (3) there generally exists a pedestal in the copolarization return when plotted as a function of ellipticity and orientation angles, which may be due to heterogeneity of scattering objects and/or multiple scattering effects; and (4) multiple scattering effects generally enhance the pedestal in copolarization return, decrease the degree of polarization, affect phase difference, and also enhance the depolarization return.

Tsang, Leung↗
NASA NTRS1995

Nonsphericity of dust-like tropospheric aerosols: Implications for aerosol remote sensing and climate modeling

T-matrix computations of light scattering by polydispersions of randomly oriented nonspherical aerosols and Mie computations for equivalent spheres are compared. Findings show that even moderate nonsphericity results in suubstantial errors in the retrieved aerosol optical thickness if satellite reflectance measurements are analyzed using Mie theory. On the other hand, the use of Mie theory for nonspherical aerosols produces negligible errors in the computation of albedo and flux related quantities, provided that the aerosol size distribution and optical thickness are known beforehand. The first result can be explained by large nonspherical-spherical differences in scattering phase function, while the second result follows from small nonspherical-spherical differences in single-scattering albedo and asymmetry parameter. No cancellation of errors occurs if one consistently uses Mie theory in the retrieval algorithm and then in computing the albedo for the retrieved aerosol optical thickness.

Mishchenko, M. I.↗
DOE OSTI2016

Disordered quivers and cold horizons

We analyze the low temperature structure of a supersymmetric quiver quantum mechanics with randomized superpotential coefficients, treating them as quenched disorder. These theories describe features of the low energy dynamics of wrapped branes, which in large number backreact into extremal black holes. We show that the low temperature theory, in the limit of a large number of bifundamentals, exhibits a time reparametrization symmetry as well as a specific heat linear in the temperature. Both these features resemble the behavior of black hole horizons in the zero temperature limit. We demonstrate similarities between the low temperature physics of the random quiver model and a theory of large N free fermions with random masses.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Random Phase Approximation Correlation Energy Using Real-Space Density Functional Perturbation Theory

We present a real-space method for computing the random phase approximation (RPA) correlation energy within Kohn–Sham density functional theory, leveraging the low-rank nature of the frequency-dependent density response operator. In particular, we employ a cubic-scaling formalism based on density functional perturbation theory that circumvents the calculation of the response function matrix, instead relying on the ability to compute its product with a vector through the solution of the associated Sternheimer linear systems. We develop a large-scale parallel implementation of this formalism using the subspace iteration method in conjunction with the spectral quadrature method while employing the Kronecker product-based method for the application of the Coulomb operator and the conjugate orthogonal conjugate gradient method for the solution of the linear systems. We demonstrate convergence with respect to key parameters and verify the method’s accuracy by comparing with plane-wave results. We show that the framework achieves good strong scaling to many thousands of processors, reducing the time to solution for a lithium hydride system with 128 electrons to around 150 s on 4608 processors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1989

The normal modes of a resonant cavity containing discrete inhomogeneities - The influence of fibril magnetic fields on the solar acoustic oscillations

Motivated by considerations of the interaction between fibril magnetic fields and solar p-modes, the acoustic spectrum of a cylindrical cavity filled with ideal gas in which a number of magnetic flux tubes are embedded is studied. A formalism, based on the T-matrix approach to acoustic scattering, is developed which can be used to determine the eigenfrequencies and eigenfunctions for any arbitrary distribution of flux tubes. For weak scatterers, the frequency shifts and velocity eigenfunctions are calculated using perturbation theory for the cases of a single flux tube and a random distribution of up to 100 flux tubes. The results of this 'exact' approach are used to give a critical appraisal of the predictions of theories based on some form of averaging, such as the one discussed recently by Bogdan and Zweibel (1987).

Bogdan, Thomas J.↗
DOE OSTI2023

Symmetries and spectral statistics in chaotic conformal field theories

We discuss spectral correlations in coarse-grained chaotic two-dimensional CFTs with large central charge. We study a partition function describing the dense part of the spectrum of primary states in a way that disentangles the chaotic properties of the spectrum from those which are a consequence of Virasoro symmetry and modular invariance. We argue that random matrix universality in the near-extremal limit is an independent feature of each spin sector separately; this is a non-trivial statement because the exact spectrum is fully determined by only the spectrum of spin zero primaries and those of a single non-zero spin (“spectral determinacy”). We then describe an argument analogous to the one leading to Cardy’s formula for the averaged density of states, but in our case applying it to spectral correlations: assuming statistical universalities in the near-extremal spectrum in all spin sectors, we find similar random matrix universality in a large spin regime far from extremality.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Classical and quantum simulations of 1+1-dimensional ${\mathbb{Z}}_{2}$ gauge theory at finite temperature and density

Simulating strongly coupled gauge theories at finite temperature and density is a longstanding challenge in nuclear and high-energy physics with fundamental implications for condensed matter physics. Here, we simulate such systems using minimally entangled typical thermal state (METTS) approaches, which combine classical random sampling with imaginary-time evolution, implementable on either classical or quantum computers, to estimate thermal averages of observables. We study 1+1-dimensional ${\mathbb{Z}}_{2}$ gauge theory coupled to spinless fermionic matter, which maps onto a local quantum spin chain. We benchmark both a classical matrix-product-state implementation of METTS and a recently proposed adaptive variational approach for near-term quantum devices, focusing on the equation of state and measures of fermion confinement. Of particular importance is the choice of basis for METTS sampling, which impacts both the sampling overhead and quantum circuit complexity. Our work sets the stage for future studies of strongly coupled gauge theories using classical and quantum hardware.

Chen, I-Chi [Iowa State Univ., Ames, IA (United St↗
NASA NTRS1993

Stochastic damage evolution in textile laminates

A probabilistic model utilizing random material characteristics to predict damage evolution in textile laminates is presented. Model is based on a division of each ply into two sublaminas consisting of cells. The probability of cell failure is calculated using stochastic function theory and maximal strain failure criterion. Three modes of failure, i.e. fiber breakage, matrix failure in transverse direction, as well as matrix or interface shear cracking, are taken into account. Computed failure probabilities are utilized in reducing cell stiffness based on the mesovolume concept. A numerical algorithm is developed predicting the damage evolution and deformation history of textile laminates. Effect of scatter of fiber orientation on cell properties is discussed. Weave influence on damage accumulation is illustrated with the help of an example of a Kevlar/epoxy laminate.

Dzenis, Yuris A.↗
DOE OSTI2020

Giant Wilson loops and AdS 2 /dCFT 1

The 1/2-BPS Wilson loop in N = 4 supersymmetric Yang-Mills theory is an important and well-studied example of conformal defect. In particular, much work has been done for the correlation functions of operator insertions on the Wilson loop in the fundamental representation. In this paper, we extend such analyses to Wilson loops in the large-rank symmetric and antisymmetric representations, which correspond to probe D3 and D5 branes with AdS 2 × S 2 and AdS 2 × S 4 worldvolume geometries, ending at the AdS 5 boundary along a one-dimensional contour. We first compute the correlation functions of protected scalar insertions from supersymmetric localization, and obtain a representation in terms of multiple integrals that are similar to the eigenvalue integrals of the random matrix, but with important differences. Using ideas from the Fermi Gas formalism and the Clustering method, we evaluate their large N limit exactly as a function of the ’t Hooft coupling. The results are given by simple integrals of polynomials that resemble the Q-functions of the Quantum Spectral Curve, with integration measures depending on the number of insertions. Next, we study the correlation functions of fluctuations on the probe D3 and D5 branes in AdS. We compute a selection of three- and four-point functions from perturbation theory on the D-branes, and show that they agree with the results of localization when restricted to supersymmetric kinematics. We also explain how the difference of the internal geometries of the D3 and D5 branes manifests itself in the localization computation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1992

Radiative transfer theory for polarimetric remote sensing of pine forest

The radiative transfer theory is applied to interpret polarimetric radar backscatter from pine forest with clustered vegetation structures. The scattering function of each cluster is calculated by incorporating the phase interference of scattered fields from each component. The resulting phase matrix is used in the radiative transfer equations to evaluate the polarimetric backscattering coefficients from random medium layers embedded with vegetation clusters. Upon including multiscale structures (trunks, primary and secondary branches, and needles), polarimetric radar responses from pine forest for different frequencies and looking angles are interpreted and simulated. Preliminary results are shown to be in good agreement with the measured backscattering coefficients at the Landes maritime pine forest during the MAESTRO-1 experiment.

Hsu, C. C.↗
DOE OSTI2024

Modeling graphene sheet growth and dynamical matrix calculations using molecular dynamics

Molecular dynamics (MD) has been an incredibly useful tool to model physical processes that were synthesized experimentally but not fully understood. MD, through the use of semi-empirical inter-atomic potentials, has allowed understanding of different physical processes in materials science. Yet as well as providing useful insights into materials science, molecular dynamics has a wider range of usability. In this report, I will be detailing how MD can be used to study graphene formation from a carbon liquid which requires high temperatures and pressures. Beyond this, I will describe the usefulness of MD for understanding the physics for phonon transport quantum sensors. To do this, MD was employed to determine the dynamical matrix by treating atoms as coupled oscillators. An accurate understanding of the dynamical matrix of a system is required to calculate the non-equilibrium Green’s function used to describe the phonon transport within phonon wave-guides. I found that, across multiple pressures and temperatures, randomly placed carbon atoms will show evidence of pent-first formation with semi-empirical models. Density functional theory (DFT), on the other hand, was too computationally expensive to use for full scale MD simulations, but we have the possibility of training a machine learned interatomic potential to approximate DFT for carbon in the environments being studied for pent-first graphene sheet formation.

36 MATERIALS SCIENCE↗
NASA NTRS1988

Polarimetric clutter modeling: Theory and application

The two-layer anisotropic random medium model is used to investigate fully polarimetric scattering properties of earth terrain media. The polarization covariance matrices for the untilted and tilted uniaxial random medium are evaluated using the strong fluctuation theory and distorted Born approximation. In order to account for the azimuthal randomness in the growth direction of leaves in tree and grass fields, an averaging scheme over the azimuthal direction is also applied. It is found that characteristics of terrain clutter can be identified through the analysis of each element of the covariance matrix. Theoretical results are illustrated by the comparison with experimental data provided by MIT Lincoln Laboratory for tree and grass fields.

Kong, J. A.↗