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NASA NTRS1991

Combined thermal and bending fatigue of high-temperature metal-matrix composites: Computational simulation

The nonlinear behavior of a high-temperature metal-matrix composite (HT-MMC) was simulated by using the metal matrix composite analyzer (METCAN) computer code. The simulation started with the fabrication process, proceeded to thermomechanical cyclic loading, and ended with the application of a monotonic load. Classical laminate theory and composite micromechanics and macromechanics are used in METCAN, along with a multifactor interaction model for the constituents behavior. The simulation of the stress-strain behavior from the macromechanical and the micromechanical points of view, as well as the initiation and final failure of the constituents and the plies in the composite, were examined in detail. It was shown that, when the fibers and the matrix were perfectly bonded, the fracture started in the matrix and then propagated with increasing load to the fibers. After the fibers fractured, the composite lost its capacity to carry additional load and fractured.

Gotsis, Pascal K.↗

NASA NTRS1992

Combined bending and thermal fatigue of high-temperature metal-matrix composites - Computational simulation

Gotsis, Pascal K.↗

DOE OSTI2024

Kernel polynomial method for linear spin wave theory

Calculating dynamical spin correlations is essential for matching model magnetic exchange Hamiltonians to momentum-resolved spectroscopic measurements. A major numerical bottleneck is the diagonalization of the dynamical matrix, especially in systems with large magnetic unit cells, such as those with incommensurate magnetic structures or quenched disorder. In this paper, we demonstrate an efficient scheme based on the kernel polynomial method for calculating dynamical correlations of relevance to inelastic neutron scattering experiments. This method reduces the scaling of numerical cost from cubic to linear in the magnetic unit cell size.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Towards precise and accurate calculations of neutrinoless double-beta decay

We present the results of a National Science Foundation Project Scoping Workshop, the purpose of which was to assess the current status of calculations for the nuclear matrix elements governing neutrinoless double-beta decay and determine if more work on them is required. After reviewing important recent progress in the application of effective field theory, lattice quantum chromodynamics, and ab initio nuclear-structure theory to double-beta decay, we discuss the state of the art in nuclear-physics uncertainty quantification and then construct a roadmap for work in all these areas to fully complement the increasingly sensitive experiments in operation and under development. The roadmap includes specific projects in theoretical and computational physics as well as the use of Bayesian methods to quantify both intra- and inter-model uncertainties. Here, the goal of this ambitious program is a set of accurate and precise matrix elements, in all nuclei of interest to experimentalists, delivered together with carefully assessed uncertainties. Such calculations will allow crisp conclusions from the observation or non-observation of neutrinoless double-beta decay, no matter what new physics is at play.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Gauge invariance and color charge fluctuations

The nature of confinement is connected with color charge. Unfortunately, the color charge densities in QCD, the Noether charge densities associated with the global color invariance, are not invariant under local color rotations. This implies that the expectation values of the net color charge in any region of any physical state in QCD—states that satisfy the color Gauss law—are automatically zero for all components of color. In this Letter, it is shown that the expectation value of the square of the net color charge in a region—a measure of the color charge fluctuations—is necessarily nonzero when evaluated in physical states and the result, while depending on the scheme and scale by which the theory is regulated, is gauge invariant. This holds despite the formal lack of gauge invariance of the operator. Moreover, there is a particular combination of the color charge fluctuations for the vacuum and for a system describable by a nontrivial density matrix that is independent that has a well-defined continuum limit.

color confinement↗

NASA NTRS1991

Closed-form solutions for linear regulator design of mechanical systems including optimal weighting matrix selection

Vibration in modern structural and mechanical systems can be reduced in amplitude by increasing stiffness, redistributing stiffness and mass, and/or adding damping if design techniques are available to do so. Linear Quadratic Regulator (LQR) theory in modern multivariable control design, attacks the general dissipative elastic system design problem in a global formulation. The optimal design, however, allows electronic connections and phase relations which are not physically practical or possible in passive structural-mechanical devices. The restriction of LQR solutions (to the Algebraic Riccati Equation) to design spaces which can be implemented as passive structural members and/or dampers is addressed. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical system. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist.

Hanks, Brantley R.↗

DOE OSTI2022

Matrix-Model Simulations Using Quantum Computing, Deep Learning, and Lattice Monte Carlo

Matrix quantum mechanics plays various important roles in theoretical physics, such as a holographic description of quantum black holes, and it underpins the only practical numerical approach to the study of complex high-dimensional supergravity theories. Understanding quantum black holes and the role of entanglement in a holographic setup is of paramount importance for the realization of a quantum theory of gravity. Moreover, a complete numerical understanding of the holographic duality and the emergence of geometric space-time features from microscopic degrees of freedom could pave the way for new discoveries in quantum information science. Euclidean lattice Monte Carlo simulations are the de facto numerical tool for understanding the spectrum of large matrix models and have been used to test the holographic duality. However, they are not tailored to extract dynamical properties or even the quantum wave function of the ground state of matrix models. Quantum computing and deep learning provide potentially useful approaches to study the dynamics of matrix quantum mechanics. If successful in the context of matrix models, these rapidly improving numerical techniques could become the new Swiss army knife of quantum gravity practitioners. In this paper, we perform the first systematic survey for quantum computing and deep-learning approaches to matrix quantum mechanics, comparing them to lattice Monte Carlo simulations. These provide baseline benchmarks before addressing more complicated problems. In particular, we test the performance of each method by calculating the low-energy spectrum.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Scalar Breit interaction for molecular calculations

Variational treatment of the Dirac–Coulomb–Gaunt or Dirac–Coulomb–Breit two-electron interaction at the Dirac–Hartree–Fock level is the starting point of high-accuracy four-component calculations of atomic and molecular systems. In this work, we introduce, for the first time, the scalar Hamiltonians derived from the Dirac–Coulomb–Gaunt and Dirac–Coulomb–Breit operators based on spin separation in the Pauli quaternion basis. While the widely used spin-free Dirac–Coulomb Hamiltonian includes only the direct Coulomb and exchange terms that resemble nonrelativistic two-electron interactions, the scalar Gaunt operator adds a scalar spin–spin term. The spin separation of the gauge operator gives rise to an additional scalar orbit-orbit interaction in the scalar Breit Hamiltonian. Benchmark calculations of Au n (n = 2–8) show that the scalar Dirac–Coulomb–Breit Hamiltonian can capture 99.99% of the total energy with only 10% of the computational cost when real-valued arithmetic is used, compared to the full Dirac–Coulomb–Breit Hamiltonian. In conclusion, the scalar relativistic formulation developed in this work lays the theoretical foundation for the development of high-accuracy, low-cost correlated variational relativistic many-body theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Phase diagram of the anisotropic triangular lattice Hubbard model

In a recent study [Phys. Rev. X 10, 021042 (2020)], we showed using large-scale density matrix renormalization group (DMRG) simulations on infinite cylinders that the triangular lattice Hubbard model has a chiral spin liquid phase. In this work, we introduce hopping anisotropy in the model, making one of the three distinct bonds on the lattice stronger or weaker compared with the other two. We implement the anisotropy in two inequivalent ways, one which respects the mirror symmetry of the cylinder and one which breaks this symmetry. In the full range of anisotropy, from the square lattice to weakly coupled one-dimensional chains, we find a variety of phases. Near the isotropic limit we find the three phases identified in our previous work: metal, chiral spin liquid, and 120$^\circ$ spiral order; we note that a recent paper suggests the apparently metallic phase may actually be a Luther-Emery liquid, which would also be in agreement with our results. Furthermore, when one bond is weakened by a relatively small amount, the ground state quickly becomes the square lattice N\'{e}el order. When one bond is strengthened, the story is much less clear, with the phases that we find depending on the orientation of the anisotropy and on the cylinder circumference. While our work is to our knowledge the first DMRG study of the anisotropic triangular lattice Hubbard model, the overall phase diagram we find is broadly consistent with that found previously using other methods, such as variational Monte Carlo and dynamical mean field theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Modern quantum chemistry with [Open]Molcas

MOLCAS/OpenMolcas is an ab initio electronic structure program providing a large set of computational methods from Hartree–Fock and density functional theory to various implementations of multiconfigurational theory. This article provides a comprehensive overview of the main features of the code, specifically reviewing the use of the code in previously reported chemical applications as well as more recent applications including the calculation of magnetic properties from optimized density matrix renormalization group wave functions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Factorization at subleading power and endpoint divergences in h → γγ decay. Part II. Renormalization and scale evolution

Building on the recent derivation of a bare factorization theorem for the b-quark induced contribution to the h → γγ decay amplitude based on soft-collinear effective theory, we derive the first renormalized factorization theorem for a process described at subleading power in scale ratios, where λ = m b /M h « 1 in our case. We prove two refactorization conditions for a matching coefficient and an operator matrix element in the endpoint region, where they exhibit singularities giving rise to divergent convolution integrals. The refactorization conditions ensure that the dependence of the decay amplitude on the rapidity regulator, which regularizes the endpoint singularities, cancels out to all orders of perturbation theory. We establish the renormalized form of the factorization formula, proving that extra contributions arising from the fact that “endpoint regularization” does not commute with renormalization can be absorbed, to all orders, by a redefinition of one of the matching coefficients. We derive the renormalization-group evolution equation satisfied by all quantities in the factorization formula and use them to predict the large logarithms of order $αα^2_sL^k$ in the three-loop decay amplitude, where $L=ln(-M^2_h/m^2_b)$ and k = 6, 5, 4, 3. We find perfect agreement with existing numerical results for the amplitude and analytical results for the three-loop contributions involving a massless quark loop. On the other hand, we disagree with the results of previous attempts to predict the series of subleading logarithms $~αα^n_sL^{2n+1}$

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory

Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn–Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin–orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in the nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Topics in String Theory, Quantum Field Theory And Quantum Gravity

This is the final technical report for DOE Award No. DE-SC0021528 - Topics in string theory, quantum field theory and quantum gravity. The goals of the research program were in three areas - understanding quantum gravity and the internal description of quantum systems using the gauge/gravity correspondence, aspects of entanglement in eld theory, gravity and string theory, and the characterization of the behavior of strongly interacting quantum eld theories. The primary results were on the microscopic understanding of the ER=EPR correspondence as a string duality, and on a matrix model description of the addition of end of the world branes and propagating matter to two dimensional Jackiw-Teitelboim gravity. The former led to the completion of the work shortly after the end of the reporting period and continuing work investigating the properties of the associated stringy black hole microstates. The latter led to the work, which also appeared shortly after the end of the reporting period, and a continuing project to nd a matrix model formulation of the eigenstate thermalization hypothesis and JT gravity with propagating matter.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1967

Long-range first-order interaction energy between two excited hydrogen atoms in either 2s or 2p states.

Long range first order interaction between two excited hydrogen atoms yielding perturbation energy matrix, discussing diagonalization process

HYDROGEN ATOM↗

NASA NTRS1980

The Split Coefficient Matrix method for hyperbolic systems of gasdynamic equations

The Split Coefficient Matrix (SCM) finite difference method for solving hyperbolic systems of equations is presented. This new method is based on the mathematical theory of characteristics. The development of the method from characteristic theory is presented. Boundary point calculation procedures consistent with the SCM method used at interior points are explained. The split coefficient matrices that define the method for steady supersonic and unsteady inviscid flows are given for several examples. The SCM method is used to compute several flow fields to demonstrate its accuracy and versatility. The similarities and differences between the SCM method and the lambda-scheme are discussed.

Chakravarthy, S. R.↗

NASA NTRS1986

Finite state model and compatibility theory - New analysis tools for permutation networks

A simple model to describe the fundamental operation theory of shuffle-exchange-type permutation networks, the finite permutation machine (FPM), is described, and theorems which transform the control matrix result to a continuous compatible vector result are developed. It is found that only 2n-1 shuffle exchange passes are necessary, and that 3n-3 passes are sufficient, to realize all permutations, reducing the sufficient number of passes by two from previous results. The flexibility of the approach is demonstrated by the description of a stack permutation machine (SPM) which can realize all permutations, and by showing that the FPM corresponding to the Benes (1965) network belongs to the SPM. The FPM corresponding to the network with two cascaded reverse-exchange networks is found to realize all permutations, and a simple mechanism to verify several equivalence relationships of various permutation networks is discussed.

Huang, S.-T.↗

NASA NTRS1987

Imaging radar polarization signatures - Theory and observation

Radar polarimetry theory is reviewed, and comparison between theory and experimental results obtained with an imaging radar polarimeter employing two orthogonally polarized antennas is made. Knowledge of the scattering matrix permits calculation of the scattering cross section of a scatterer for any transmit and receive polarization combination, and a new way of displaying the resulting scattering cross section as a function of polarization is introduced. Examples of polarization signatures are presented for several theoretical models of surface scattering, and these signatures are compared with experimentally measured polarization signatures. The coefficient of variation, derived from the polarization signature, may provide information regarding the amount of variation in scattering properties for a given area.

Van Zyl, Jakob J.↗

NASA NTRS1991

Micro-mechanical analysis of damage growth and fracture in discontinuous fiber reinforced metal matrix composites

An experimental verification is presented for a new two parameter fracture model based on the equivalent remote biaxial stresses (ERBS). A detailed comparison is made between the new theory and the constant K(sub IC) approach of linear elastic fracture mechanics (LEFM). Fracture is predicted through a failure curve representing the change in a variable fracture toughness K(sub IC) with the ERBS ratio B(sub E). The nonsingular term (T) in the series expansion of the near crack-tip transverse stress is included in the model. Experimental results for polymethyl methacrylate (PPMA) show that the theory can account for the effects of geometry on fracture toughness as well as indicate the initiation of crack branching. It is shown that the new criterion predicts failure for PMMA with a 95 percent confidence zone which is nearly three times smaller than that of the LEFM K(sub IC) approach.

Goree, James G.↗