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At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Emergence of many-body quantum chaos via spontaneous breaking of unitarity

It is suggested that many-body quantum chaos appears as the spontaneous symmetry breaking of unitarity in interacting quantum many-body systems. It has been shown that many-body level statistics, probed by the spectral form factor (SFF) defined as K(η,t)=$\langle$|Tr exp(-ηH+itH)| 2 $\rangle$, is dominated by a diffuson-type mode in a field theory analysis. The key finding of this Letter is that the “unitary” η = 0 case is different from the η → 0 ± limit, with the latter leading to a finite mass of these modes due to interactions. This mass suppresses a rapid exponential ramp in the SFF, which is responsible for the fast emergence of Poisson statistics in the noninteracting case, and gives rise to a nontrivial random matrix structure of many-body levels. The interaction-induced mass in the SFF shares similarities with the dephasing rate in the theory of weak localization and the Lyapunov exponent of the out-of-time-ordered correlators.

36 MATERIALS SCIENCE↗
NASA NTRS1987

Controller design for the improvement of feedback properties: A method for tuning the weight in the evaluation function of the LQG theory

In the controller design of a linear time-invariant system, it is important to improve the feedback properties such as robust stability and sensitivity. In the multi-input multi-output case, these properties can be estimated by using the singular values of return difference matrix. The design method to obtain better singular-value-points is desired. How to tune the weight matrix of performance index and/or covariance matrix of noise in the Linear Quadratic Gaussian (LQC) theory to get a desired singular-value-plot was studied. First, the property of singular-value plots of return difference matrix of a system designed by LQG theory is examined from the viewpoint of tuning weight. Second, a distance between real singular-value-plots and a desired plot is defined, and the weight of performance index is numerically determined by quasi-Newton method so that the distance is minimized.

Saeki, Masami↗
NASA NTRS2012

Computational Implementation of a Thermodynamically Based Work Potential Model For Progressive Microdamage and Transverse Cracking in Fiber-Reinforced Laminates

A continuum-level, dual internal state variable, thermodynamically based, work potential model, Schapery Theory, is used capture the effects of two matrix damage mechanisms in a fiber-reinforced laminated composite: microdamage and transverse cracking. Matrix microdamage accrues primarily in the form of shear microcracks between the fibers of the composite. Whereas, larger transverse matrix cracks typically span the thickness of a lamina and run parallel to the fibers. Schapery Theory uses the energy potential required to advance structural changes, associated with the damage mechanisms, to govern damage growth through a set of internal state variables. These state variables are used to quantify the stiffness degradation resulting from damage growth. The transverse and shear stiffness of the lamina are related to the internal state variables through a set of measurable damage functions. Additionally, the damage variables for a given strain state can be calculated from a set of evolution equations. These evolution equations and damage functions are implemented into the finite element method and used to govern the constitutive response of the material points in the model. Additionally, an axial failure criterion is included in the model. The response of a center-notched, buffer strip-stiffened panel subjected to uniaxial tension is investigated and results are compared to experiment.

Pineda, Evan J.↗
NASA NTRS1989

Non-steady state cracking in ceramic matrix composites

A micromechanics analytical model based on the consistent shear lag theory is developed for predicting the failure modes in a fiber-reinforced unidirectional ceramic matrix composite. The model accounts for the relatively large matrix stiffness. The fiber and matrix stresses are established as functions of the applied stress, crack geometry, and most importantly, the microstructural properties of the constituents. From the predicted stress, the mode of failure is established based on the point stress criterion. The role of the microstructural properties on the failure mode and ultimate strength is assessed.

Dharani, L. R.↗
NASA NTRS1990

A creep model for metallic composites based on matrix testing: Application to Kanthal composites

An anisotropic creep model is formulated for metallic composites with strong fibers and low to moderate fiber volume percent (less than 40 percent). The idealization admits no creep in the local fiber direction and assumes equal creep strength in longitudinal and transverse shear. Identification of the matrix behavior with that of the isotropic limit of the theory permits characterization of the composite through uniaxial creep tests on the matrix material. Constant and step-wise creep tests are required as a data base. The model provides an upper bound on the transverse creep strength of a composite having strong fibers embedded in a particular matrix material. Comparison of the measured transverse strength with the upper bound gives an assessment of the integrity of the composite. Application is made to a Kanthal composite, a model high-temperature composite system. Predictions are made of the creep response of fiber reinforced Kanthal tubes under interior pressure.

Binienda, W. K.↗
NASA NTRS1993

High temperature composite analyzer (HITCAN) user's manual, version 1.0

This manual describes 'how-to-use' the computer code, HITCAN (HIgh Temperature Composite ANalyzer). HITCAN is a general purpose computer program for predicting nonlinear global structural and local stress-strain response of arbitrarily oriented, multilayered high temperature metal matrix composite structures. This code combines composite mechanics and laminate theory with an internal data base for material properties of the constituents (matrix, fiber and interphase). The thermo-mechanical properties of the constituents are considered to be nonlinearly dependent on several parameters including temperature, stress and stress rate. The computation procedure for the analysis of the composite structures uses the finite element method. HITCAN is written in FORTRAN 77 computer language and at present has been configured and executed on the NASA Lewis Research Center CRAY XMP and YMP computers. This manual describes HlTCAN's capabilities and limitations followed by input/execution/output descriptions and example problems. The input is described in detail including (1) geometry modeling, (2) types of finite elements, (3) types of analysis, (4) material data, (5) types of loading, (6) boundary conditions, (7) output control, (8) program options, and (9) data bank.

Lackney, J. J.↗
NASA NTRS1989

Elastic crack bridging in ceramic and intermetallic matrix composites

A micromechanics analytical model based on the consistent shear lag theory is developed for predicting the failure modes in a fiber reinforced unidirectional ceramic and intermetallic matrix composite. The model accounts for the relatively large matrix stiffness. The fiber and matrix stresses are established as functions of the applied stress, crack geometry, and most importantly, the microstructural properties of the constituents. From the predicted stress, the mode of failure is established based on the point stress criterion.

Dharani, L. R.↗
DOE OSTI2023

A fast, dense Chebyshev solver for electronic structure on GPUs

Matrix diagonalization is almost always involved in computing the density matrix needed in quantum chemistry calculations. In the case of modest matrix sizes (≲4000), performance of traditional dense diagonalization algorithms on modern GPUs is underwhelming compared to the peak performance of these devices. This motivates the exploration of alternative algorithms better suited to these types of architectures. We newly derive, and present in detail, an existing Chebyshev expansion algorithm whose number of required matrix multiplications scales with the square root of the number of terms in the expansion. Focusing on dense matrices of modest size, our implementation on GPUs results in large speed ups when compared to diagonalization. Additionally, we improve upon this existing method by capitalizing on the inherent task parallelism and concurrency in the algorithm. Furthermore, this improvement is implemented on GPUs by using CUDA and HIP streams via the MAGMA library and leads to a significant speed up over the serial-only approach for smaller (≲1000) matrix sizes. Finally, we apply our technique to a model system with a high density of states around the Fermi level, which typically presents significant challenges.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Analytical continuation of matrix-valued functions: Carathéodory formalism

Finite-temperature quantum field theories are formulated in terms of Green's functions and self-energies on the Matsubara axis. In multiorbital systems, these quantities are related to positive semidefinite matrix-valued functions of the Carathéodory and Schur class. Analysis, interpretation, and evaluation of derived quantities such as real-frequency response functions requires analytic continuation of the off-diagonal elements to the real axis. Here we derive the criteria under which such functions exist for given Matsubara data and present an interpolation algorithm that intrinsically respects their mathematical properties. For small systems with precise Matsubara data, we find that the continuation exactly recovers all off-diagonal and diagonal elements. In real-materials systems, we show that the precision of the continuation is sufficient for the analytic continuation to commute with the Dyson equation, and we show that the truncation of the off-diagonal self-energy elements leads to considerable approximation artifacts.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Sub-leading structures in superconformal indices: subdominant saddles and logarithmic contributions

We systematically study various sub-leading structures in the superconformal index of N = 4 supersymmetric Yang-Mills theory with SU(N) gauge group. We concentrate in the superconformal index description as a matrix model of elliptic gamma functions and in the Bethe-Ansatz presentation. Our saddle-point approximation goes beyond the Cardy-like limit and we uncover various saddles governed by a matrix model corresponding to SU(N) Chern-Simons theory. The dominant saddle, however, leads to perfect agreement with the Bethe-Ansatz approach. We also determine the logarithmic correction to the superconformal index to be log N, finding precise agreement between the saddle-point and Bethe-Ansatz approaches in their respective approximations. We generalize the two approaches to cover a large class of 4d N = 1 superconformal theories. We find that also in this case both approximations agree all the way down to a universal contribution of the form log N. The universality of this last result constitutes a robust signature of this ultraviolet description of asymptotically AdS 5 black holes and could be tested by low-energy IIB supergravity.

1/N expansion↗
DOE OSTI2020

Density-Matrix Based Extended Lagrangian Born–Oppenheimer Molecular Dynamics

Extended Lagrangian Born–Oppenheimer molecular dynamics [ Phys. Rev. Lett. 2008, 100, 123004] is presented for Hartree–Fock theory, where the extended electronic degrees of freedom are represented by a density matrix, including fractional occupation numbers at elevated electronic temperatures. In contrast to regular direct Born–Oppenheimer molecular dynamics simulations, no iterative self-consistent field optimization is required prior to the force evaluations. To sample regions of the potential energy landscape where the gap is small or vanishing, which leads to particular convergence problems in regular direct Born–Oppenheimer molecular dynamics simulations, an adaptive integration scheme for the extended electronic degrees of freedom is presented. The integration scheme is based on a tunable, low-rank approximation of a fourth-order kernel, K, that determines the metric tensor, T ≡ K T K, used in the extended harmonic oscillator of the Lagrangian that generates the dynamics of the electronic degrees of freedom. Here, the formulation and algorithms provide a general guide to implement extended Lagrangian Born–Oppenheimer molecular dynamics for quantum chemistry, density functional theory, and semiempirical methods using a density matrix formalism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Wormholes, branes and finite matrices in sine dilaton gravity

We compute the double trumpet in sine dilaton gravity via WdW quantization. The wormhole size is discretized. The wormhole amplitude matches the spectral correlation of a finite-cut matrix integral, where matrices have large but finite dimensions. This strongly suggests an identification of the sine dilaton gravity theory with the q-deformed JT gravity matrix integral. At the very least, it captures all universal content of that matrix model. The disk decomposes into the physical (gauge invariant) solutions of the WdW equation, which are trumpets with discrete sizes. This decomposition modifies the usual no-boundary wavefunction to a normalizable one in sine dilaton gravity.

2D Gravity↗
NASA NTRS1977

An Analytical State Transition Matrix for Orbits Perturbed by an Oblate Spheroid

An analytical state transition matrix and its inverse, which include the short period and secular effects of the second zonal harmonic, were developed from the nonsingular PS satellite theory. The fact that the independent variable in the PS theory is not time is in no respect disadvantageous, since any explicit analytical solution must be expressed in the true or eccentric anomaly. This is shown to be the case for the simple conic matrix. The PS theory allows for a concise, accurate, and algorithmically simple state transition matrix. The improvement over the conic matrix ranges from 2 to 4 digits accuracy.

Mueller, A. C.↗
NASA NTRS1978

A high order accurate finite element algorithm for high Reynolds number flow prediction

A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.

Baker, A. J.↗
NASA NTRS1991

Expert system training and control based on the fuzzy relation matrix

Fuzzy knowledge, that for which the terms of reference are not crisp but overlapped, seems to characterize human expertise. This can be shown from the fact that an experienced human operator can control some complex plants better than a computer can. Proposed here is fuzzy theory to build a fuzzy expert relation matrix (FERM) from given rules or/and examples, either in linguistic terms or in numerical values to mimic human processes of perception and decision making. The knowledge base is codified in terms of many implicit fuzzy rules. Fuzzy knowledge thus codified may also be compared with explicit rules specified by a human expert. It can also provide a basis for modeling the human operator and allow comparison of what a human operator says to what he does in practice. Two experiments were performed. In the first, control of liquid in a tank, demonstrates how the FERM knowledge base is elicited and trained. The other shows how to use a FERM, build up from linguistic rules, and to control an inverted pendulum without a dynamic model.

Ren, Jie↗
DOE OSTI2024

Gauge Theory Bootstrap

We propose the gauge theory bootstrap, a method to compute the pion S matrix that describes the low-energy physics of the strong interaction and other similar gauge theories. The phase shifts of the S 0 , P 1 , and S 2 waves obtained are in good agreement with experimental results. The only numerical inputs are the quark mass m q , the QCD scale Λ QCD , the pion mass m π , and the pion decay constant f π without any other experimental data. We make use of the form-factor bootstrap recently proposed by Karateev, Kuhn, and Penedones together with a finite energy version of the Shifman-Veinshtein-Zakharov sum rules. Published by the American Physical Society 2024

He, Yifei (ORCID:0000000213666157)↗
DOE OSTI2024

Hybrid programming-model strategies for GPU offloading of electronic structure calculation kernels

To address the challenge of performance portability and facilitate the implementation of electronic structure solvers, we developed the basic matrix library (BML) and Parallel, Rapid O(N), and Graph-based Recursive Electronic Structure Solver (PROGRESS) library. The BML implements linear algebra operations necessary for electronic structure kernels using a unified user interface for various matrix formats (dense and sparse) and architectures (CPUs and GPUs). Focusing on density functional theory and tight-binding models, PROGRESS implements several solvers for computing the single-particle density matrix and relies on BML. In this paper, we describe the general strategies used for these implementations on various computer architectures, using OpenMP target functionalities on GPUs, in conjunction with third-party libraries to handle performance critical numerical kernels. In this study, we demonstrate the portability of this approach and its performance in benchmark problems.

36 MATERIALS SCIENCE↗
NASA NTRS2020

An Improved Plastically Dilatant Unified Viscoplastic Constitutive Formulation for Multiscale Analysis of Polymer Matrix Composites Under High Strain Rate Loading

Polymer matrix composites are commonly used to fabricate energy-absorbing structures expected to experience impact loading. As such, a detailed understanding of the dynamic response of the constituent materials is necessary. Since the rate, temperature, and pressure dependence of carbon fiber reinforced polymer matrix composites are primarily manifestations of the rate, temperature, and pressure dependence of the polymer matrix, it is crucial that the constitutive behavior of the matrix be accurately characterized. In this work, an existing unified viscoplastic constitutive formulation is extended to ensure thermodynamic consistency and to more accurately account for the tension-compression asymmetry observed in the response of polymeric materials. A new plastic potential function is proposed, and elementary loading conditions are utilized to determine relations between model constants to ensure nonnegative plastic dissipation, a necessary thermodynamic requirement. Expressions for plastic Poisson’s ratios are derived and are bounded by enforcing nonnegative plastic dissipation. The model is calibrated against available experimental data from tests conducted over a range of strain rates, temperatures, and loading cases on a representative thermoset epoxy; good correlation between simulations and experimental data is obtained. Temperature rises due to the conversion of plastic work to heat are computed via the adiabatic heat energy equation. The viscoplastic polymer model is then used as a constitutive model in the generalized method of cells micromechanics theory to investigate the effects of matrix adiabatic heating on the high strain rate response of a unidirectional composite. The thermodynamic consistency of the model ensures plastic dissipation can only cause an increase in temperature. Simulation results indicate that significant thermal softening due to the conversion of plastic work to heat is observed in the composite for matrix dominated deformation modes.

Impact loading↗