Coding theory - The index of comma freedom in iterative codes
Propagation of comma-free properties of component codes of iterative codes - code matrices
DECODING↗
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Results for “matrix theories”
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.
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Theory of resonant tunneling in a variably spaced multiquantum well structure - An Airy function approach
A theoretical study of resonant tunneling in multilayered heterostructures is presented based on an exact solution of the Schroedinger equation under the application of a constant electric field. By use of the transfer matrix approach, the transmissivity of the structure is determined as a function of the incident electron energy. The approach presented herein is easily extended to many layer structures where it is more accurate than other existing transfer matrix or Wentzel-Kramers-Brillouin (WKB) models. The transmission resonances are compared to the bound-state energies calculated for a finite square well under bias using either an asymmetric square-well model or the exact solution of an infinite square well under the application of an electric field. The results show good agreement with other existing models as well as with the bound-state energies. The calculations were then applied to a new superlattice structure, the variably spaced superlattice energy filter, which is designed such that under bias the spatial quantization levels fully align. Based on these calculations, a new class of resonant tunneling superlattice devices can be designed.
Brennan, K. F.↗
Non-perturbative renormalization scheme for the C P -odd three-gluon operator
We define a regularization-independent momentum-subtraction scheme for the C P -odd three-gluon operator at dimension six. This operator appears in effective field theories for heavy physics beyond the Standard Model, describing the indirect effect of new sources of C P -violation at low energies. In a hadronic context, it induces permanent electric dipole moments. The hadronic matrix elements of the three-gluon operator are non-perturbative objects that should ideally be evaluated with lattice QCD. We define a non-perturbative renormalization scheme that can be implemented on the lattice and we compute the scheme transformation to \( \overline{\mathrm{MS}} \) at one loop. Our calculation can be used as an interface to future lattice-QCD calculations of the matrix elements of the three-gluon operator, in order to obtain theoretically robust constraints on physics beyond the Standard Model from measurements of the neutron electric dipole moment.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Dynamical signatures of symmetry protected topology following symmetry breaking
Not Available
1-dimensional spin chains↗
Mixed finite-difference scheme for analysis of simply supported thick plates.
A mixed finite-difference scheme is presented for the stress and free vibration analysis of simply supported nonhomogeneous and layered orthotropic thick plates. The analytical formulation is based on the linear, three-dimensional theory of orthotropic elasticity and a Fourier approach is used to reduce the governing equations to six first-order ordinary differential equations in the thickness coordinate. The governing equations possess a symmetric coefficient matrix and are free of derivatives of the elastic characteristics of the plate. In the finite difference discretization two interlacing grids are used for the different fundamental unknowns in such a way as to reduce both the local discretization error and the bandwidth of the resulting finite-difference field equations. Numerical studies are presented for the effects of reducing the interior and boundary discretization errors and of mesh refinement on the accuracy and convergence of solutions. It is shown that the proposed scheme, in addition to a number of other advantages, leads to highly accurate results, even when a small number of finite difference intervals is used.
Noor, A. K.↗
Sustained small oscillations in nonlinear control systems
Some results of bifurcation theory were used to study the existence of small-amplitude periodic behavior in launch vehicle dynamics, assuming that nonlinearity exists as a cubic term in the rudder response. The analysis follows closely Sattinger's (1973) approach to the theory of periodic bifurcations. The conditions under which a bifurcating branch of orbitally stable periodic solutions will exist are determined. It is shown that in more complicated cases, the conditions under which the system matrix has a pair of simple purely imaginary eigenvalues can be determined with the aid of linear stability techniques.
George, J. H.↗
Scattering from randomly oriented scatterers with strong permittivity fluctuations
Strong permittivity fluctuation theory is used to solve the problem of scattering from a medium composed of completely randomly oriented scatterers under a low frequency limit. Gaussian statistics are not assumed for the renormalized scattering sources. Numerical results on effective permittivity are illustrated for oblate and prolate spheroidal scatterers and compared with the results for spherical scatterers. The results are consistent with discrete scatterer theory. The effective permittivity of a random medium embedded with nonspherical scatterers shows a higher imaginary part than the spherical scatterer case with equal correlation volume. Under the distorted Born approximation, the polarimetric covariance matrix for the backscattered electric field is calculated for half-space randomly oriented scatterers. The nonspherical geometry of the scatterers shows significant effects on the cross-polarized backscattering returns, and the correlation coefficient between HH and VV returns. The polarimetric backscattering coefficients can provide useful information in distinguishing the geometry of scatterers.
Yueh, S. H.↗
Experimental verification of a progressive damage model for composite laminates based on continuum damage mechanics
Progressive failure is a crucial concern when using laminated composites in structural design. Therefore the ability to model damage and predict the life of laminated composites is vital. The purpose of this research was to experimentally verify the application of the continuum damage model, a progressive failure theory utilizing continuum damage mechanics, to a toughened material system. Damage due to tension-tension fatigue was documented for the IM7/5260 composite laminates. Crack density and delamination surface area were used to calculate matrix cracking and delamination internal state variables, respectively, to predict stiffness loss. A damage dependent finite element code qualitatively predicted trends in transverse matrix cracking, axial splits and local stress-strain distributions for notched quasi-isotropic laminates. The predictions were similar to the experimental data and it was concluded that the continuum damage model provided a good prediction of stiffness loss while qualitatively predicting damage growth in notched laminates.
Coats, Timothy William↗
Modeling of Electromagnetic Scattering by Discrete and Discretely Heterogeneous Random Media by Using Numerically Exact Solutions of the Maxwell Equations
In this paper, we discuss some aspects of numerical modeling of electromagnetic scattering by discrete random medium by using numerically exact solutions of the macroscopic Maxwell equations. Typical examples of such media are clouds of interstellar dust, clouds of interplanetary dust in the Solar system, dusty atmospheres of comets, particulate planetary rings, clouds in planetary atmospheres, aerosol particles with numerous inclusions and so on. Our study is based on the results of extensive computations of different characteristics of electromagnetic scattering obtained by using the superposition T-matrix method which represents a direct computer solver of the macroscopic Maxwell equations for an arbitrary multisphere configuration. As a result, in particular, we clarify the range of applicability of the low-density theories of radiative transfer and coherent backscattering as well as of widely used effective-medium approximations.
Dlugach, Janna M.↗
Theoretical Prediction of Thermal Expansion Anisotropy for Y 2 Si 2 O 7 Environmental Barrier Coatings Using a Deep Neural Network Potential and Comparison to Experiment
Environmental barrier coatings (EBCs) are an enabling technology for silicon carbide (SiC)-based ceramic matrix composites (CMCs) in extreme environments such as gas turbine engines. However, development of new coating systems is hindered by the large design space and difficulty in predicting properties for these materials. Density Functional Theory (DFT) has successfully been used to model and predict some thermodynamic and thermo-mechanical properties of high-temperature ceramics for EBCs, although these calculations are challenging due to their high computational costs. In this work, we use machine learning to train a deep neural network potential (DNP) for Y 2 Si 2 O 7 , which is then applied to calculate thermodynamic and thermo-mechanical properties at near-DFT accuracy much faster and using less computational resources than DFT. We use this DNP to predict phonon-based thermodynamic properties of Y 2 Si 2 O 7 with good agreement to DFT and experiments. We also utilize the DNP to calculate the anisotropic, lattice direction-dependent coefficients of thermal expansion (CTEs) for Y 2 Si 2 O 7 . Molecular dynamics trajectories using the DNP correctly demonstrate accurate prediction of the anisotropy of the CTE in good agreement with diffraction experiments. In the future, this DNP could be applied to accelerate additional property calculations for Y 2 Si 2 O 7 compared to DFT or experiments.
rare earth silicates↗
Effects of Thermal Cycling on Thermal Expansion and Mechanical Properties of Sic Fiber-reinforced Reaction-bonded Si3n4 Composites
Thermal expansion curves for SiC fiber-reinforced reaction-bonded Si3N4 matrix composites (SiC/RBSN) and unreinforced RBSN were measured from 25 to 1400 C in nitrogen and in oxygen. The effects of fiber/matrix bonding and cycling on the thermal expansion curves and room-temperature tensile properties of unidirectional composites were determined. The measured thermal expansion curves were compared with those predicted from composite theory. Predicted thermal expansion curves parallel to the fiber direction for both bonding cases were similar to that of the weakly bonded composites, but those normal to the fiber direction for both bonding cases resulted in no net dimensional changes at room temperature, and no loss in tensile properties from the as-fabricated condition. In contrast, thermal cycling in oxygen for both composites caused volume expansion primarily due to internal oxidation of RBSN. Cyclic oxidation affected the mechanical properties of the weakly bonded SiC/RBSN composites the most, resulting in loss of strain capability beyond matrix fracture and catastrophic, brittle fracture. Increased bonding between the SiC fiber and RBSN matrix due to oxidation of the carbon-rich fiber surface coating and an altered residual stress pattern in the composite due to internal oxidation of the matrix are the main reasons for the poor mechanical performance of these composites.
Bhatt, R. T.↗
Department of Energy Project DE-SC0012198: Probing Electron-Molecule Scattering with HHG: Theory and Experiment (Final Report)
The study of the motion of atoms in molecules is important to understanding many areas of physical and life sciences. Such motion occurs on many different times scales, with electronic motion occurring on a sub-femtosecond time scale, and simple vibrational motion in tens to hundreds of femtoseconds. One way to follow such processes in real time is by the use of shortpulsed lasers, and in particular by studying time-resolved photoionization and the related process of high-harmonic generation (HHG). Thus there has been much effort to develop the tools necessary to probe molecular systems using short pulse lasers and understanding the sensitivity of the different possible probes to the time dependent geometric structure as well as the electronic structure of molecules. Our research has particularly focused on the connection between high-field processes and the more traditional weak field photoionization processes. Strong field and weak field processes can be connected through models that involve the same matrix elements. We have demonstrated in our study of HHG from SF 6 that the spectrum is sensitive to the interplay between the angular dependence of the ionization step and recombination step. In our study of rescattering spectroscopy, we have shown that with a combination of experiment and theory, we can use this high-field spectroscopy to determine molecular structure in molecules such as C 2 H 4 . We have also developed new computational tools based on overset grids to enable studies on larger molecular systems which use much more robust numerical approaches so that the resulting code can be a tool that non-specialists can use to study related systems.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Spectral Equivalence of Low-Order Discretizations for High-Order H(curl) and H(div) Spaces
In this paper, we present spectral equivalence results for high-order tensor product edge- and face-based finite elements for the H(curl) and H(div) function spaces. Specifically, we show for certain choices of shape functions that the mass and stiffness matrices of the high-order elements are spectrally equivalent to those for an assembly of low-order elements on the associated Gauss--Lobatto--Legendre mesh. Based on this equivalence, efficient preconditioners can be designed with favorable computational complexity. Numerical results are presented which confirm the theory and demonstrate the benefits of the equivalence results for overlapping Schwarz preconditioners.
97 MATHEMATICS AND COMPUTING↗
The operator theory of the pseudo-inverse. i - bounded operators.
Operator theory of pseudo-inverse generalized to encompass linear bounded operators on Hilbert spaces
HILBERT SPACE↗
Mesh refinement in finite element analysis by minimization of the stiffness matrix trace
Most finite element packages provide means to generate meshes automatically. However, the user is usually confronted with the problem of not knowing whether the mesh generated is appropriate for the problem at hand. Since the accuracy of the finite element results is mesh dependent, mesh selection forms a very important step in the analysis. Indeed, in accurate analyses, meshes need to be refined or rezoned until the solution converges to a value so that the error is below a predetermined tolerance. A-posteriori methods use error indicators, developed by using the theory of interpolation and approximation theory, for mesh refinements. Some use other criterions, such as strain energy density variation and stress contours for example, to obtain near optimal meshes. Although these methods are adaptive, they are expensive. Alternatively, a priori methods, until now available, use geometrical parameters, for example, element aspect ratio. Therefore, they are not adaptive by nature. An adaptive a-priori method is developed. The criterion is that the minimization of the trace of the stiffness matrix with respect to the nodal coordinates, leads to a minimization of the potential energy, and as a consequence provide a good starting mesh. In a few examples the method is shown to provide the optimal mesh. The method is also shown to be relatively simple and amenable to development of computer algorithms. When the procedure is used in conjunction with a-posteriori methods of grid refinement, it is shown that fewer refinement iterations and fewer degrees of freedom are required for convergence as opposed to when the procedure is not used. The mesh obtained is shown to have uniform distribution of stiffness among the nodes and elements which, as a consequence, leads to uniform error distribution. Thus the mesh obtained meets the optimality criterion of uniform error distribution.
Kittur, Madan G.↗
A method for characterization of multiple dynamic constitutive parameters of FRCs
We propose a method to measure multiple dynamic material constitutive parameters of unidirectional fiber reinforced composites (FRCs) in a single experiment. Dynamic short-beam shear (DSBS) experiments were performed on a modified Kolsky compression bar, with integration of high-speed imaging and digital image correlation (DIC). The unidirectional FRCs investigated were S-2 glass fiber reinforced matrix of TGDDM-Jeffamine® D230 with monoamine functionalized partially reacted substructures (mPRS) and commercially available SC-15. Analytical solutions of normal and shear strains of a composite beam were derived based on Timoshenko beam theory, assuming material to be transversely isotropic and have different moduli in tension and compression in each principle material orientation. Tensile and compressive moduli were inversely computed through monitoring normal strain slope when specimen was constantly loaded at a speed of ~7.3 m/s within a small deflection. Non-linear shear stress-strain behavior of the composite was described via Ramberg–Osgood equation. Finite element (FE) analysis was conducted in ABAQUS, simultaneously defining via user subroutine UMAT the transverse isotropy of material, bi-modulus constitutive model, and non-linear shear stress-strain relation. The method proposed in this work was validated by comparing strain distributions computed by FE model and DIC measurements. Comparing with traditional dynamic tensile, compressive, and shear experiments on FRCs, this method significantly simplifies the specimen preparation and design of complicated gripping fixtures for multiple experiments. Here, systematic errors resulting from variations of specimen geometry and dimension, loading direction, and instrumentation are reduced, thereby providing compatible data for numerical studies on impact behavior of composites.
36 MATERIALS SCIENCE↗
Theory of strong-field sequential double ionization of polyatomic molecules
Understanding of strong-field sequential double ionization (SDI) of molecules by a highly intense infrared laser pulse could be the key to observing electron motion in molecules in the attosecond to femtosecond timescale. Based on a novel density matrix approach for SDI (DM-SDI), a recent theoretical study has shown that SDI can be used as a probe to monitor the changes in vibronic coherence in homonuclear diatomic molecules. In this article, we extend the DM-SDI model to general molecules that could possess permanent dipole moments and arbitrary symmetry. We apply the model to SDI of a water molecule and identify the formation pathway of individual dication states. We further deduce that kinetic energy release spectra from two- and three-body fragments could carry the signature of vibronic coherence between the lowest two states of the water cation. Furthermore, our results suggest that observables from the SDI probe can be interpreted intuitively with only the knowledge of electronic structures of populated ionic states, making the SDI probe to be a highly desirable probing scheme for vibronic coherence in generic molecules.
74 ATOMIC AND MOLECULAR PHYSICS↗
Uncertainty quantification of an empirical shell-model interaction using principal component analysis
Recent investigations have emphasized the importance of uncertainty quantification (UQ) in nuclear theory. Here, we carry out UQ for configuration-interaction shell-model calculations in the 1$\textit{s}$–0$\textit{d}$ valence space, investigating the sensitivity of observables to perturbations in the 66 parameters (matrix elements) of a high-quality empirical interaction. The large parameter space makes computing the corresponding Hessian numerically costly, so we compare a cost-effective approximation, using the Feynman-Hellmann theorem, to the full Hessian and find it works well. Diagonalizing the Hessian yields the principal components of the interaction: linear combinations of parameters ordered by sensitivity. This approximately decoupled distribution of parameters facilitates theoretical uncertainty propagation onto structure observables: electromagnetic transitions, Gamow-Teller decays, and dark matter-nucleus scattering matrix elements.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗