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At least 289 records · Page 16

Hierarchical Poly Tree Configurations for the Solution of Dynamically Refined Finte Element Models

This paper demonstrates how a multilevel substructuring technique, called the Hierarchical Poly Tree (HPT), can be used to integrate a localized mesh refinement into the original finite element model more efficiently. The optimal HPT configurations for solving isoparametrically square h-, p-, and hp-extensions on single and multiprocessor computers is derived. In addition, the reduced number of stiffness matrix elements that must be stored when employing this type of solution strategy is quantified. Moreover, the HPT inherently provides localize 'error-trapping' and a logical, efficient means with which to isolate physically anomalous and analytically singular behavior.

Gute, G. D.↗

3D Higher Order Modeling in the BEM/FEM Hybrid Formulation

Higher order divergence- and curl-conforming bases have been shown to provide significant benefits, in both convergence rate and accuracy, in the 2D hybrid finite element/boundary element formulation (P. Fink and D. Wilton, National Radio Science Meeting, Boulder, CO, Jan. 2000). A critical issue in achieving the potential for accuracy of the approach is the accurate evaluation of all matrix elements. These involve products of high order polynomials and, in some instances, singular Green's functions. In the 2D formulation, the use of a generalized Gaussian quadrature method was found to greatly facilitate the computation and to improve the accuracy of the boundary integral equation self-terms. In this paper, a 3D, hybrid electric field formulation employing higher order bases and higher order elements is presented. The improvements in convergence rate and accuracy, compared to those resulting from lower order modeling, are established. Techniques developed to facilitate the computation of the boundary integral self-terms are also shown to improve the accuracy of these terms. Finally, simple preconditioning techniques are used in conjunction with iterative solution procedures to solve the resulting linear system efficiently. In order to handle the boundary integral singularities in the 3D formulation, the parent element- either a triangle or rectangle-is subdivided into a set of sub-triangles with a common vertex at the singularity. The contribution to the integral from each of the sub-triangles is computed using the Duffy transformation to remove the singularity. This method is shown to greatly facilitate t'pe self-term computation when the bases are of higher order. In addition, the sub-triangles can be further divided to achieve near arbitrary accuracy in the self-term computation. An efficient method for subdividing the parent element is presented. The accuracy obtained using higher order bases is compared to that obtained using lower order bases when the number of unknowns is approximately equal. Also, convergence rates obtained using higher order bases are compared to those obtained with lower order bases for selected sample

Fink, P. W.↗

Coherent state constructions of bases for some physically relevant group chains

Rotor coherent state constructions are given for the Wigner supermultiplet SU(4) contains SU(2)xSU(2) and for the special irreducible representations (N0) of the SO(5) contains SO(3) contains SO(2) group chain in exact parallel with the rotor coherent state construction for the SU(3) contains SO(3) contains SO(2) case given by Rowe, LeBlanc,, and Repka. Matrix elements of the coherent state realizations of the group generators are given in all cases by very simple expressions in terms of angular momentum Wigner coefficients involving intrinsic projection labels K. The K-matrix technique of vector coherent state theory is used to effectively elevate these K labels to the status of good quantum numbers. Analytic expressions are given for the (K K*)-matrices for many of the more important irreducible representations.

Hecht, Karl T.↗

Remote sensing of earth terrain

A systematic approach for the identification of terrain media such as vegetation canopy, forest, and snow covered fields is developed using the optimum polarimetric classifier. The covariance matrices for the various terrain cover are computed from theoretical models of random medium by evaluating the full polarimetric scattering matrix elements. The optimal classification scheme makes use of a quadratic distance measure and is applied to classify a vegetation canopy consisting of both trees and grass. Experimentally measured data are used to validate the classification scheme. Theoretical probability of classification error using the full polarimetric matrix are compared with classification based on single features including the phase difference between the VV and HH polarization returns. It is shown that the full polarimetric results are optimal and provide better classification performance than single feature measurements.

Kong, J. A.↗

Remote sensing of earth terrain

A systematic approach for the identification of terrain media such as vegetation canopy, forest, and snow covered fields is developed using the optimum polarimetric classifier. The covariance matrices for the various terrain covers are computed from the theoretical models of random medium by evaluating the full polarimetric scattering matrix elements. The optimal classification scheme makes use of a quadratic distance measure and is applied to classify a vegetation canopy consisting of both trees and grass. Experimentally measured data are used to validate the classification scheme. Theoretical probability of classification error using the full polarimetric matrix are compared with classification based on single features including the phase difference between the VV and HH polarization returns. It is shown that the full polarimetric results are optimal and provide better classification performance than single feature measurements. A systematic approach is presented for obtaining the optimal polarimetric matched filter which produces maximum contrast between two scattering classes, each represented by its respective covariance matrix.

Kong, J. A.↗

Towards excitations and dynamical quantities in correlated lattices with density matrix embedding theory

Density matrix embedding theory (DMET) provides a framework to describe ground-state expectation values in strongly correlated systems, but its extension to dynamical quantities is still an open problem. We show one route to obtaining excitations and dynamical spectral functions by using the techniques of DMET to approximate the matrix elements that arise in a single-mode inspired excitation ansatz. We demonstrate this approach in the one-dimensional Hubbard model, comparing the neutral excitations, single-particle density of states, charge, and spin dynamical structure factors to benchmarks from the Bethe ansatz and density matrix renormalization group. Finally, our work highlights the potential of these ideas in building computationally efficient approaches for dynamical quantities.

1-dimensional systems↗

Elimination on sparse symmetric systems of a special structure.

Consideration of the problem of finding a permutation of rows and columns and an algorithm for solving ordered systems of linear algebraic equations with sparse matrices having a certain regular structure. Two approaches to the solution of this problem, in which the sparsity is used to some extent, are outlined. One of them is a very general approach where optimal (or nearly optimal) ordering is sought and the algorithm for solving the ordered system treats the matrix element by element to perform only necessary operations. The other approach involves the use of band matrices. After comparing these two approaches, a third approach is then suggested which involves the use of pipe matrices, and a means of ordering the rows and columns to obtain this type of matrix is presented. Examples of matrices reordered by the proposed procedure are cited.

Segethova, J.↗

On the S-matrix of Ising field theory in two dimensions

We explore the analytic structure of the non-perturbative S-matrix in arguably the simplest family of massive non-integrable quantum field theories: the Ising field theory (IFT) in two dimensions, which may be viewed as the Ising CFT deformed by its two relevant operators, or equivalently, the scaling limit of the Ising model in a magnetic field. Our strategy is that of collider physics: we employ Hamiltonian truncation method (TFFSA) to extract the scattering phase of the lightest particles in the elastic regime, and combine it with S-matrix bootstrap methods based on unitarity and analyticity assumptions to determine the analytic continuation of the 2 → 2 S-matrix element to the complex s-plane. Focusing primarily on the “high temperature” regime in which the IFT interpolates between that of a weakly coupled massive fermion and the E 8 affine Toda theory, we will numerically determine 3-particle amplitudes, follow the evolution of poles and certain resonances of the S-matrix, and exclude the possibility of unknown wide resonances up to reasonably high energies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Bulk electronic structure of lanthanum hexaboride (LaB 6 ) by hard x-ray angle-resolved photoelectron spectroscopy

In the last decade rare-earth hexaborides have been investigated for their fundamental importance in condensed matter, and for their applications in advanced technological fields. Among these compounds, LaB 6 has a special place, being a traditional d-band metal without additional f- bands. In order to understand the bulk electronic structure of the more complex rare-earth hexaborides, in this paper we investigate the bulk electronic structure of LaB 6 using tender/hard x-ray photoemission spectroscopy, measuring both core-level and angle-resolved valence-band spectra. Furthermore, we compare the La 3d core level spectrum to cluster model calculations in order to understand the bulk-like core-hole screening effects. The results show that the La 3d well-screened peak is at a lower binding energy compared to the main poorly-screened peak; the relative intensity between these peaks depends on how strong the hybridization is between La and B atoms. Here, we show that the recoil effect, negligible in the soft x-ray regime, becomes prominent at higher kinetic energies for lighter elements, such as boron, but is still negligible for heavy elements, such as lanthanum. In addition, we report the bulk-like band structure of LaB6 determined by tender/hard x-ray angle-resolved photoemission spectroscopy (HARPES). We compare HARPES experimental results to the free-electron final-state calculations and to the more precise one-step photoemission theory including matrix element and phonon excitation effects. The agreement between the features present in the experimental ARPES data and the theoretical calculations is very good. In addition, we consider the nature and the magnitude of phonon excitations in order to interpret HARPES experimental data measured at different temperatures and excitation energies. We demonstrate that one step theory of photoemission and HARPES experiments provide, at present, the only approach capable of probing, both experimentally and theoretically, true “bulk-like” electronic band structure of rare-earth hexaborides and strongly correlated materials.

36 MATERIALS SCIENCE↗

A T Matrix Method Based upon Scalar Basis Functions

A surface integral formulation is developed for the T matrix of a homogenous and isotropic particle of arbitrary shape, which employs scalar basis functions represented by the translation matrix elements of the vector spherical wave functions. The formulation begins with the volume integral equation for scattering by the particle, which is transformed so that the vector and dyadic components in the equation are replaced with associated dipole and multipole level scalar harmonic wave functions. The approach leads to a volume integral formulation for the T matrix, which can be extended, by use of Green's identities, to the surface integral formulation. The result is shown to be equivalent to the traditional surface integral formulas based on the VSWF basis.

wave functions↗

Target space entanglement in Matrix Models

We study target space entanglement in gauged multi-matrix models as models of entanglement between groups of D-branes separated by a planar entangling surface, paying close attention to the implementation of gauge invariance. We open with a review of target space entanglement between identical particles, which shares some important features (specifically a gauged permutation symmetry) with our main problem. For our matrix models, we implement a gauge fixing well-adapted to the entangling surface. In this gauge, we map the matrix model problem to that of entanglement of a U(1) gauge theory on a complete or all-to-all lattice. Matrix elements corresponding to open strings stretching across the entangling surface in the target space lead to interesting contributions to the entanglement entropy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

ORNL_AISD-Ex: Quantum chemical prediction of UV/Vis absorption spectra for over 10 million organic molecules

We performed calculations of electronic excitation energies and associated oscillator strengths based on the time-dependent density-functional tight-binding (TD-DFTB) method [1]. The SMILES (Simplified molecular-input line-entry system) strings of the molecules from the AISD HOMO-LUMO database [2] were converted to a 3D atomistic structure and stored in a PDB file after preliminary geometry optimization using the Merck Molecular Force Field (MMFF94) in RDKit [3,4]. The primary information stored in the PDB file archive consists of Cartesian coordinates for each atom of the molecule in their 3D location in space, along with summary information about the structure, sequence, and experiment. We then performed molecular geometry optimization using the density-functional tight-binding (DFTB) method [5] in the electronic ground state, followed by single-point excited states calculations, as described below. We note that, since RDKit employs a random choice for the generation of molecular conformers, the molecular geometries obtained in this dataset could be different from the ones that were generated when the AISD HOMO-LUMO dataset was generated. The computed excitation energies and associated oscillator strengths can be converted to predict UV/Vis absorption spectra, where excitation energies correspond to absorption peak positions, and oscillator strengths are a good measure of the probability of absorption of visible or UV light in transitions between electronic ground and excited states. The conversion of SMILES strings to 3D Cartesian coordinates of fully DFTB-optimized molecules was successful for 10,502,904 out of 10,502,917 molecules. For these molecules, both geometry optimizations and excited states calculations were successful. The DFTB calculations did not complete for 13 molecules of the original AISD HOMO-LUMO dataset. We still provide information about the geometry of these molecules. The molecules are diverse for chemical compositions (which span 5 non-hydrogen elements: oxygen, carbon, nitrogen, fluorine, sulfur) and molecular size (the smallest molecule contains 5 non-hydrogen atoms, and the largest molecule contains 71 non-hydrogen atoms). The DFTB method [5] is an approximation to density functional theory (DFT), utilizing a minimal basis set in conjunction with a two-center approximation to the electronic Hamiltonian and overlap matrix elements. The DFTB total energy is the sum of an electronic and a repulsive energy contribution, and their calculation requires optimized electronic parameters and diatomic repulsive potential energy functions. All DFTB calculations were performed using the DFTB+ code [6] (version 21.2) and the wrapper for DFTB+ in the Atomic Simulation Environment (ASE) (version 3.22.1) [7], which performed an internal conversion of Cartesian coordinates from PDB to the .gen file format. For the geometry optimizations on the electronic ground state potential energy surface of the molecules, we have chosen the third-order DFTB (DFTB3) method [5c] and employed the matching 3ob set of electronic parameters and repulsive potentials [8]. The empirical γ-damping for hydrogen bond correction, and Grimme's D3 empirical dispersion correction with Becke-Johnson damping (D3(BJ)) [9] dispersion correction was included to improve the description of non-covalent interactions. For excited states single-point energy calculations, we employed the TD-DFTB method in conjunction with the DFTB2 method [5b] and the matching mio [5b,10] and halorg [11] parameter sets. We opted to request the simultaneous calculation of 50 excited states for singlet transition to investigate sufficient number of excited states, based on linear response theory using the Casida equation [Ref: T. A. Niehaus, S. Suhai, F. Della Sala, P Lugli, M. Elstner, G. Seifert, and Th. Frauenheim. Tight-binding approach to time-dependent density-functional response theory. Phys. Rev. B, 63:085108, 2001] and the ARPACK diagonalizer [R. B. Lehoucq, D. C. Sorensen, and C. Yang. Arpack users guide: Solution of large-scale eigenvalue problems by implicitly restarted arnoldi methods, 1997. 46, 51]. The dataset contains 1001 tar.gz files. Tar files are named as “ornl_aisd_ex_1.tar.gz†through “ornl_aisd_ex_1000.tar.gzâ€. Additionally, the 13 failed molecules are in “ornl_aisd_ex_unprocessed.tar.gzâ€. Except for the tar files listed below, each tar file contains 10,500 molecules. Tar files numbered 34, 121, 128, 352, 360, 429, 495, 509, 518, 627, 676, 668, and 862 contain 10,499 molecules each. The last tar file numbered 1000 contains 13,417 molecules. The total size of the uncompressed dataset is over 283 Gigabytes. The code for calculating the electronic excitation energies and statistical analysis of the dataset is provided at the following GitLab repository: https://github.com/ORNL/Analysis-of-Large-Scale-Molecular-Datasets-with-Python Calculating the UV spectrum of a molecule requires performing 3 main operations: 1. Converting the smiles string representation of a molecule into a geometric structure where each atom is assigned XYZ coordinates. The geometric structure is written to the file smiles.pdb. 2. Using smiles.pdb to compute the relaxed geometry of the molecule, which corresponds with the position of the atoms at the position of equilibrium at the ground state. This generates the files band.out, detailed.out, and geo_end.gen. 3. Using geo_end.gen to calculate the UV spectrum of the molecule which is written into the file EXC.DAT. Every molecule in the dataset has its own directory. The files contained in each molecule directory are as follows: 1. geo_end.gen 2. detailed.out 3. band.out 4. EXC.DAT 5. smiles.pdb REFERENCES [1] Niehaus, T. A.; Suhai, S.; Della Salla, F.; Lugli, P.; Elstner, M.; Seifert, G.; Frauenheim, Th. Tight-binding approach to time-dependent density-functional response theory. Phys. Rev. B, 2001, 63, 085108/1-9. [2] Blanchard, A.; Gounley, J.; Metha, K.; Yoo, P.; Irle, S. AISD HOMO-LUMO. DOI: 10.13139/ORNLNCCS/1869409 [3] RDKit: Cheminformatics and Machine Learning Software. 2013, [http://www.rdkit.org] [4] Tosco, P.; Stiefl, N. and Landrum, G. Bringing the MMFF force field to the RDKit: implementation and validation. J Cheminform. 2014, 6, 1–4. [5] a) Porezag, D.; Frauenheim, T.; Kohler, T.; Seifert, G.; Kaschner, Construction of tight-binding-like potentials on the basis of density-functional theory: Application to carbon, R. Phys. Rev. B 1995, 51, 12947-12957; b) Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, Th.; Suhai, S.; Seifert, G.; Phys. Rev. B 1998, 58, 7260-7268; c) Gaus, M.; Cui, Q.; Elstner, M. DFTB3: Extension of the Self-Consistent-Charge Density-Functional Tight-Binding Method (SCC-DFTB), J. Chem. Theory Comput. 2011, 7, 931-948; d) Cui, Q.; Elstner, M. Density functional tight binding: values of semi-empirical methods in an ab initio era, Phys. Chem. Chem. Phys. 2014, 16, 14368-14377. [6] Hourahine, B. et al. DFTB+, a software package for efficient approximate density functional theory based atomistic simulations, J. Chem. Phys. 2020, 152, 124101/1-19. [7] Larsen, A. H. et al. The atomic simulation environment—a Python library for working with atoms. J. Phys.: Cond. Matter 2017, 29, 273002. [8] Kubillus, M.; Kubar, T.; Gaus, M.; Rezac, J.; Elstner, M. Parameterization of the DFTB3 Method for Br, Ca, Cl, F, I, K, and Na in Organic and Biological Systems, J. Chem. Theory Comput. 2015, 11, 332-342. [9] Brandenburg, J. G.; Grimme, S. Accurate Modeling of Organic Molecular Crystals by Dispersion-Corrected Density Functional Tight Binding (DFTB), J. Phys. Chem. Lett. 2014, 5, 1785−1789. [10] a) Niehaus, T. A.; Elstner, M.; Frauenheim, Th.; Suhai, S. Application of an approximate density-functional method to sulfur containing compounds. J. Mol. Struct.: THEOCHEM 2001, 541, 185-94; b) Elstner, M.; Hobza, P.; Frauenheim, Th.; Suhai, S.; Kaxiras, E. Hydrogen bonding and stacking interactions of nucleic acid base pairs: A density-functional-theory based treatment. J. Chem. Phys. 2001, 114, 5149-55. [11] Kubar, T.; Bodrog, Z.; Gaus, M.; Köhler, C.; Aradi, B.; Frauenheim, Th.; Elstner, M. Parametrization of the SCC-DFTB Method for Halogens. J. Chem. Theory Comput. 2013, 9, 2939-49.

36 MATERIALS SCIENCE↗

Determination of the Raman polarizability tensor in the optically anisotropic crystal potassium dihydrogen phosphate and its deuterated analog

Abstract The Raman tensor of the dominant A 1 modes of the nonlinear optical crystalline material potassium dihydrogen phosphate and its 70% deuterated analog have been ascertained. Challenges in determining the A 1 mode tensor element values based on previous reports have been resolved using a specially designed experimental setup that makes use of spherical crystal samples. This novel experimental design enabled the determination of measurement artifacts, including polarization rotation of the pump and/or scattered light propagating through the sample and the contribution of additional overlapping phonon modes, which have hindered previous efforts. Results confirmed that the polarization tensor is diagonal, and matrix elements were determined with high accuracy.

36 MATERIALS SCIENCE↗

New method for calculating electromagnetic effects in semileptonic beta-decays of mesons

We construct several classes of hadronic matrix elements and relate them to the low-energy constants in Chiral Perturbation Theory that describe the electromagnetic effects in the semileptonic beta decay of the pion and the kaon. We propose to calculate them using lattice QCD, and argue that such a calculation will make an immediate impact to a number of interesting topics at the precision frontier, including the outstanding anomalies in |V us | and the top-row Cabibbo-Kobayashi-Maskawa matrix unitarity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Entanglement in the Quantum Hall Matrix Model

Characterizing the entanglement of matrix degrees of freedom is essential for understanding the holographic emergence of spacetime. The Quantum Hall Matrix Model is a gauged U(N) matrix quantum mechanics with two matrices whose ground state is known exactly and describes an emergent spatial disk with incompressible bulk dynamics. We define and compute an entanglement entropy in the ground state associated to a cut through the disk. There are two contributions. A collective field describing the eigenvalues of one of the matrices gives a gauge-invariant chiral boundary mode leading to an expected logarithmic entanglement entropy. Further, the cut through the bulk splits certain ‘off-diagonal’ matrix elements that must be duplicated and associated to both sides of the cut. Sewing these duplicated modes together in a gauge-invariant way leads to a bulk ‘area law’ contribution to the entanglement entropy. All of these entropies are regularized by finite N.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A windowed mean trajectory approximation for condensed phase dynamics

We propose a trajectory-based quasi-classical method for approximating dynamics in condensed phase systems. Building upon the previously developed optimized mean trajectory approximation that has been used to compute linear and nonlinear spectra, we borrow some ideas from filtering trajectory methods to obtain a novel semiclassical method for the dynamical propagation of density matrices. This new approximation is tested rigorously against standard multistate electronic models, spin-boson models, and models of the Fenna–Matthews–Olson complex. For dissipative systems, the current method is significantly better or as good as many other semiclassical methods available, especially at low temperatures and for off-diagonal density matrix elements, whereas for scattering models, the current method bears similar limitations as mean-field propagation schemes. All results are tested against the numerically exact hierarchical equations of motion method. In conclusion, the new method shows excellent agreement across various parameter regimes with numerically exact results, highlighting the robustness and accuracy of our approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗