Predicting tidal currents in San Francisco Bay using a spectral model

USGS Publications Warehouse

Burau, Jon R.; Cheng, Ralph T.

1988-01-01

This paper describes the formulation of a spectral (or frequency based) model which solves the linearized shallow water equations. To account for highly variable basin bathymetry, spectral solutions are obtained using the finite element method which allows the strategic placement of the computation points in the specific areas of interest or in areas where the gradients of the dependent variables are expected to be large. Model results are compared with data using simple statistics to judge overall model performance in the San Francisco Bay estuary. Once the model is calibrated and verified, prediction of the tides and tidal currents in San Francisco Bay is accomplished by applying astronomical tides (harmonic constants deduced from field data) at the prediction time along the model boundaries.

A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gerritsma, Marc; Bochev, Pavel

Formulation of locally conservative least-squares finite element methods (LSFEMs) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require non-standard boundary conditions (Bochev and Gunzburger, 2009 [3]), while methods that admit the no-slip condition satisfy the incompressibility equation only approximately (Bochev and Gunzburger, 2009 [4, Chapter 7]). Here we address this problem by proving a new non-standard stability bound for the velocity–vorticity–pressure Stokes system augmented with a no-slip boundary condition. This bound gives rise to a norm-equivalent least-squares functional in which the velocity can be approximatedmore » by div-conforming finite element spaces, thereby enabling a locally-conservative approximations of this variable. Here, we also provide a practical realization of the new LSFEM using high-order spectral mimetic finite element spaces (Kreeft et al., 2011) and report several numerical tests, which confirm its mimetic properties.« less

A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition

DOE PAGES

Gerritsma, Marc; Bochev, Pavel

2016-03-22

Formulation of locally conservative least-squares finite element methods (LSFEMs) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require non-standard boundary conditions (Bochev and Gunzburger, 2009 [3]), while methods that admit the no-slip condition satisfy the incompressibility equation only approximately (Bochev and Gunzburger, 2009 [4, Chapter 7]). Here we address this problem by proving a new non-standard stability bound for the velocity–vorticity–pressure Stokes system augmented with a no-slip boundary condition. This bound gives rise to a norm-equivalent least-squares functional in which the velocity can be approximatedmore » by div-conforming finite element spaces, thereby enabling a locally-conservative approximations of this variable. Here, we also provide a practical realization of the new LSFEM using high-order spectral mimetic finite element spaces (Kreeft et al., 2011) and report several numerical tests, which confirm its mimetic properties.« less

A spectral hybridizable discontinuous Galerkin method for elastic-acoustic wave propagation

NASA Astrophysics Data System (ADS)

Terrana, S.; Vilotte, J. P.; Guillot, L.

2018-04-01

We introduce a time-domain, high-order in space, hybridizable discontinuous Galerkin (DG) spectral element method (HDG-SEM) for wave equations in coupled elastic-acoustic media. The method is based on a first-order hyperbolic velocity-strain formulation of the wave equations written in conservative form. This method follows the HDG approach by introducing a hybrid unknown, which is the approximation of the velocity on the elements boundaries, as the only globally (i.e. interelement) coupled degrees of freedom. In this paper, we first present a hybridized formulation of the exact Riemann solver at the element boundaries, taking into account elastic-elastic, acoustic-acoustic and elastic-acoustic interfaces. We then use this Riemann solver to derive an explicit construction of the HDG stabilization function τ for all the above-mentioned interfaces. We thus obtain an HDG scheme for coupled elastic-acoustic problems. This scheme is then discretized in space on quadrangular/hexahedral meshes using arbitrary high-order polynomial basis for both volumetric and hybrid fields, using an approach similar to the spectral element methods. This leads to a semi-discrete system of algebraic differential equations (ADEs), which thanks to the structure of the global conservativity condition can be reformulated easily as a classical system of first-order ordinary differential equations in time, allowing the use of classical explicit or implicit time integration schemes. When an explicit time scheme is used, the HDG method can be seen as a reformulation of a DG with upwind fluxes. The introduction of the velocity hybrid unknown leads to relatively simple computations at the element boundaries which, in turn, makes the HDG approach competitive with the DG-upwind methods. Extensive numerical results are provided to illustrate and assess the accuracy and convergence properties of this HDG-SEM. The approximate velocity is shown to converge with the optimal order of k + 1 in the L2-norm, when element polynomials of order k are used, and to exhibit the classical spectral convergence of SEM. Additional inexpensive local post-processing in both the elastic and the acoustic case allow to achieve higher convergence orders. The HDG scheme provides a natural framework for coupling classical, continuous Galerkin SEM with HDG-SEM in the same simulation, and it is shown numerically in this paper. As such, the proposed HDG-SEM can combine the efficiency of the continuous SEM with the flexibility of the HDG approaches. Finally, more complex numerical results, inspired from real geophysical applications, are presented to illustrate the capabilities of the method for wave propagation in heterogeneous elastic-acoustic media with complex geometries.

Equivalent Linearization Analysis of Geometrically Nonlinear Random Vibrations Using Commercial Finite Element Codes

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Muravyov, Alexander A.

2002-01-01

Two new equivalent linearization implementations for geometrically nonlinear random vibrations are presented. Both implementations are based upon a novel approach for evaluating the nonlinear stiffness within commercial finite element codes and are suitable for use with any finite element code having geometrically nonlinear static analysis capabilities. The formulation includes a traditional force-error minimization approach and a relatively new version of a potential energy-error minimization approach, which has been generalized for multiple degree-of-freedom systems. Results for a simply supported plate under random acoustic excitation are presented and comparisons of the displacement root-mean-square values and power spectral densities are made with results from a nonlinear time domain numerical simulation.

Tensor-product preconditioners for a space-time discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Diosady, Laslo T.; Murman, Scott M.

2014-10-01

A space-time discontinuous Galerkin spectral element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is presented. A diagonalized alternating direction implicit preconditioner is extended to a space-time formulation using entropy variables. The effectiveness of this technique is demonstrated for the direct numerical simulation of turbulent flow in a channel.

Spectrally formulated user-defined element in Abaqus for wave motion analysis and health monitoring of composite structures

NASA Astrophysics Data System (ADS)

Khalili, Ashkan

Wave propagation analysis in 1-D and 2-D composite structures is performed efficiently and accurately through the formulation of a User-Defined Element (UEL) based on the wavelet spectral finite element (WSFE) method. The WSFE method is based on the first order shear deformation theory which yields accurate results for wave motion at high frequencies. The wave equations are reduced to ordinary differential equations using Daubechies compactly supported, orthonormal, wavelet scaling functions for approximations in time and one spatial dimension. The 1-D and 2-D WSFE models are highly efficient computationally and provide a direct relationship between system input and output in the frequency domain. The UEL is formulated and implemented in Abaqus for wave propagation analysis in composite structures with complexities. Frequency domain formulation of WSFE leads to complex valued parameters, which are decoupled into real and imaginary parts and presented to Abaqus as real values. The final solution is obtained by forming a complex value using the real number solutions given by Abaqus. Several numerical examples are presented here for 1-D and 2-D composite waveguides. Wave motions predicted by the developed UEL correlate very well with Abaqus simulations using shear flexible elements. The results also show that the UEL largely retains computational efficiency of the WSFE method and extends its ability to model complex features. An enhanced cross-correlation method (ECCM) is developed in order to accurately predict damage location in plates. Three major modifications are proposed to the widely used cross-correlation method (CCM) to improve damage localization capabilities, namely actuator-sensor configuration, signal pre-processing method, and signal post-processing method. The ECCM is investigated numerically (FEM simulation) and experimentally. Experimental investigations for damage detection employ a PZT transducer as actuator and laser Doppler vibrometer as sensor. Both numerical and experimental results show that the developed method is capable of damage localization with high precision. Further, ECCM is used to detect and localize debonding in a composite material skin-stiffener joint. The UEL is used to represent the healthy case whereas the damaged case is simulated using Abaqus. It is shown that the ECCM successfully detects the location of the debond in the skin-stiffener joint.

Energy Finite Element Analysis Developments for Vibration Analysis of Composite Aircraft Structures

NASA Technical Reports Server (NTRS)

Vlahopoulos, Nickolas; Schiller, Noah H.

2011-01-01

The Energy Finite Element Analysis (EFEA) has been utilized successfully for modeling complex structural-acoustic systems with isotropic structural material properties. In this paper, a formulation for modeling structures made out of composite materials is presented. An approach based on spectral finite element analysis is utilized first for developing the equivalent material properties for the composite material. These equivalent properties are employed in the EFEA governing differential equations for representing the composite materials and deriving the element level matrices. The power transmission characteristics at connections between members made out of non-isotropic composite material are considered for deriving suitable power transmission coefficients at junctions of interconnected members. These coefficients are utilized for computing the joint matrix that is needed to assemble the global system of EFEA equations. The global system of EFEA equations is solved numerically and the vibration levels within the entire system can be computed. The new EFEA formulation for modeling composite laminate structures is validated through comparison to test data collected from a representative composite aircraft fuselage that is made out of a composite outer shell and composite frames and stiffeners. NASA Langley constructed the composite cylinder and conducted the test measurements utilized in this work.

Exact nonlinear model reduction for a von Kármán beam: Slow-fast decomposition and spectral submanifolds

NASA Astrophysics Data System (ADS)

Jain, Shobhit; Tiso, Paolo; Haller, George

2018-06-01

We apply two recently formulated mathematical techniques, Slow-Fast Decomposition (SFD) and Spectral Submanifold (SSM) reduction, to a von Kármán beam with geometric nonlinearities and viscoelastic damping. SFD identifies a global slow manifold in the full system which attracts solutions at rates faster than typical rates within the manifold. An SSM, the smoothest nonlinear continuation of a linear modal subspace, is then used to further reduce the beam equations within the slow manifold. This two-stage, mathematically exact procedure results in a drastic reduction of the finite-element beam model to a one-degree-of freedom nonlinear oscillator. We also introduce the technique of spectral quotient analysis, which gives the number of modes relevant for reduction as output rather than input to the reduction process.

Electromagnetic scattering analysis of a three-dimensional-cavity-backed aperture in an infinite ground plane using a combined finite element method/method of moments approach

NASA Technical Reports Server (NTRS)

Reddy, C. J.; Deshpande, Manohar D.; Cockrell, C. R.; Beck, F. B.

1995-01-01

A combined finite element method/method of moments (FEM/MoM) approach is used to analyze the electromagnetic scattering properties of a three-dimensional-cavity-backed aperture in an infinite ground plane. The FEM is used to formulate the fields inside the cavity, and the MoM (with subdomain bases) in both spectral and spatial domains is used to formulate the fields above the ground plane. Fields in the aperture and the cavity are solved using a system of equations resulting from the combination of the FEM and the MoM. By virtue of the FEM, this combined approach is applicable to all arbitrarily shaped cavities with inhomogeneous material fillings, and because of the subdomain bases used in the MoM, the apertures can be of any arbitrary shape. This approach leads to a partly sparse and partly full symmetric matrix, which is efficiently solved using a biconjugate gradient algorithm. Numerical results are presented to validate the analysis.

Spectral Elements Analysis for Viscoelastic Fluids at High Weissenberg Number Using Logarithmic conformation Tensor Model

NASA Astrophysics Data System (ADS)

Jafari, Azadeh; Deville, Michel O.; Fiétier, Nicolas

2008-09-01

This study discusses the capability of the constitutive laws for the matrix logarithm of the conformation tensor (LCT model) within the framework of the spectral elements method. The high Weissenberg number problems (HWNP) usually produce a lack of convergence of the numerical algorithms. Even though the question whether the HWNP is a purely numerical problem or rather a breakdown of the constitutive law of the model has remained somewhat of a mystery, it has been recognized that the selection of an appropriate constitutive equation constitutes a very crucial step although implementing a suitable numerical technique is still important for successful discrete modeling of non-Newtonian flows. The LCT model formulation of the viscoelastic equations originally suggested by Fattal and Kupferman is applied for 2-dimensional (2D) FENE-CR model. The Planar Poiseuille flow is considered as a benchmark problem to test this representation at high Weissenberg number. The numerical results are compared with numerical solution of the standard constitutive equation.

The Benard problem: A comparison of finite difference and spectral collocation eigen value solutions

NASA Technical Reports Server (NTRS)

Skarda, J. Raymond Lee; Mccaughan, Frances E.; Fitzmaurice, Nessan

1995-01-01

The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2nd order finite difference scheme. An exact solution to the Marangoni-Benard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.

Comparison of Fatigue Life Estimation Using Equivalent Linearization and Time Domain Simulation Methods

NASA Technical Reports Server (NTRS)

Mei, Chuh; Dhainaut, Jean-Michel

2000-01-01

The Monte Carlo simulation method in conjunction with the finite element large deflection modal formulation are used to estimate fatigue life of aircraft panels subjected to stationary Gaussian band-limited white-noise excitations. Ten loading cases varying from 106 dB to 160 dB OASPL with bandwidth 1024 Hz are considered. For each load case, response statistics are obtained from an ensemble of 10 response time histories. The finite element nonlinear modal procedure yields time histories, probability density functions (PDF), power spectral densities and higher statistical moments of the maximum deflection and stress/strain. The method of moments of PSD with Dirlik's approach is employed to estimate the panel fatigue life.

A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems

NASA Astrophysics Data System (ADS)

Liu, X.; Banerjee, J. R.

2017-03-01

A highly efficient and accurate analytical spectral dynamic stiffness (SDS) method for modal analysis of plane elastodynamic problems based on both plane stress and plane strain assumptions is presented in this paper. First, the general solution satisfying the governing differential equation exactly is derived by applying two types of one-dimensional modified Fourier series. Then the SDS matrix for an element is formulated symbolically using the general solution. The SDS matrices are assembled directly in a similar way to that of the finite element method, demonstrating the method's capability to model complex structures. Any arbitrary boundary conditions are represented accurately in the form of the modified Fourier series. The Wittrick-Williams algorithm is then used as the solution technique where the mode count problem (J0) of a fully-clamped element is resolved. The proposed method gives highly accurate solutions with remarkable computational efficiency, covering low, medium and high frequency ranges. The method is applied to both plane stress and plane strain problems with simple as well as complex geometries. All results from the theory in this paper are accurate up to the last figures quoted to serve as benchmarks.

Aircraft Engine Noise Scattering By Fuselage and Wings: A Computational Approach

NASA Technical Reports Server (NTRS)

Stanescu, D.; Hussaini, M. Y.; Farassat, F.

2003-01-01

The paper presents a time-domain method for computation of sound radiation from aircraft engine sources to the far-field. The effects of nonuniform flow around the aircraft and scattering of sound by fuselage and wings are accounted for in the formulation. The approach is based on the discretization of the inviscid flow equations through a collocation form of the Discontinuous Galerkin spectral element method. An isoparametric representation of the underlying geometry is used in order to take full advantage of the spectral accuracy of the method. Large-scale computations are made possible by a parallel implementation based on message passing. Results obtained for radiation from an axisymmetric nacelle alone are compared with those obtained when the same nacelle is installed in a generic configuration, with and without a wing.

Aircraft Engine Noise Scattering by Fuselage and Wings: A Computational Approach

NASA Technical Reports Server (NTRS)

Stanescu, D.; Hussaini, M. Y.; Farassat, F.

2003-01-01

The paper presents a time-domain method for computation of sound radiation from aircraft engine sources to the far-field. The effects of nonuniform flow around the aircraft and scattering of sound by fuselage and wings are accounted for in the formulation. The approach is based on the discretization of the inviscid flow equations through a collocation form of the Discontinuous Galerkin spectral element method. An isoparametric representation of the underlying geometry is used in order to take full advantage of the spectral accuracy of the method. Large-scale computations are made possible by a parallel implementation based on message passing. Results obtained for radiation from an axisymmetric nacelle alone are compared with those obtained when the same nacelle is installed in a generic configuration, with and without a wing.

Development of a low-cost, 11 µm spectral domain optical coherence tomography surface profilometry prototype

NASA Astrophysics Data System (ADS)

Suliali, Nyasha J.; Baricholo, Peter; Neethling, Pieter H.; Rohwer, Erich G.

2017-06-01

A spectral-domain Optical Coherence Tomography (OCT) surface profilometry prototype has been developed for the purpose of surface metrology of optical elements. The prototype consists of a light source, spectral interferometer, sample fixture and software currently running on Microsoft® Windows platforms. In this system, a broadband light emitting diode beam is focused into a Michelson interferometer with a plane mirror as its sample fixture. At the interferometer output, spectral interferograms of broadband sources were measured using a Czerny-Turner mount monochromator with a 2048-element complementary metal oxide semiconductor linear array as the detector. The software performs importation and interpolation of interferometer spectra to pre-condition the data for image computation. One dimensional axial OCT images were computed by Fourier transformation of the measured spectra. A first reflection surface profilometry (FRSP) algorithm was then formulated to perform imaging of step-function-surfaced samples. The algorithm re-constructs two dimensional colour-scaled slice images by concatenation of 21 and 13 axial scans to form a 10 mm and 3.0 mm slice respectively. Measured spectral interferograms, computed interference fringe signals and depth reflectivity profiles were comparable to simulations and correlated to displacements of a single reflector linearly translated about the arm null-mismatch point. Surface profile images of a double-step-function-surfaced sample, embedded with inclination and crack detail were plotted with an axial resolution of 11 μm. The surface shape, defects and misalignment relative to the incident beam were detected to the order of a micron, confirming high resolution of the developed system as compared to electro-mechanical surface profilometry techniques.

An analysis of spectral envelope-reduction via quadratic assignment problems

NASA Technical Reports Server (NTRS)

George, Alan; Pothen, Alex

1994-01-01

A new spectral algorithm for reordering a sparse symmetric matrix to reduce its envelope size was described. The ordering is computed by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. In this paper, we provide an analysis of the spectral envelope reduction algorithm. We described related 1- and 2-sum problems; the former is related to the envelope size, while the latter is related to an upper bound on the work involved in an envelope Cholesky factorization scheme. We formulate the latter two problems as quadratic assignment problems, and then study the 2-sum problem in more detail. We obtain lower bounds on the 2-sum by considering a projected quadratic assignment problem, and then show that finding a permutation matrix closest to an orthogonal matrix attaining one of the lower bounds justifies the spectral envelope reduction algorithm. The lower bound on the 2-sum is seen to be tight for reasonably 'uniform' finite element meshes. We also obtain asymptotically tight lower bounds for the envelope size for certain classes of meshes.

Entropy Stable Staggered Grid Spectral Collocation for the Burgers' and Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Parsani, Matteo; Fisher, Travis C.; Nielsen, Eric J.

2015-01-01

Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for Burgers' and the compressible Navier-Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [1, 2], extends the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to a combination of tensor product Legendre-Gauss (LG) and LGL points. The new semi-discrete operators discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality for both Burgers' and the compressible Navier-Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly to implement. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinearly stability proof for the compressible Navier-Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).

Theoretical and numerical studies of chaotic mixing

NASA Astrophysics Data System (ADS)

Kim, Ho Jun

Theoretical and numerical studies of chaotic mixing are performed to circumvent the difficulties of efficient mixing, which come from the lack of turbulence in microfluidic devices. In order to carry out efficient and accurate parametric studies and to identify a fully chaotic state, a spectral element algorithm for solution of the incompressible Navier-Stokes and species transport equations is developed. Using Taylor series expansions in time marching, the new algorithm employs an algebraic factorization scheme on multi-dimensional staggered spectral element grids, and extends classical conforming Galerkin formulations to nonconforming spectral elements. Lagrangian particle tracking methods are utilized to study particle dispersion in the mixing device using spectral element and fourth order Runge-Kutta discretizations in space and time, respectively. Comparative studies of five different techniques commonly employed to identify the chaotic strength and mixing efficiency in microfluidic systems are presented to demonstrate the competitive advantages and shortcomings of each method. These are the stirring index based on the box counting method, Poincare sections, finite time Lyapunov exponents, the probability density function of the stretching field, and mixing index inverse, based on the standard deviation of scalar species distribution. Series of numerical simulations are performed by varying the Peclet number (Pe) at fixed kinematic conditions. The mixing length (lm) is characterized as function of the Pe number, and lm ∝ ln(Pe) scaling is demonstrated for fully chaotic cases. Employing the aforementioned techniques, optimum kinematic conditions and the actuation frequency of the stirrer that result in the highest mixing/stirring efficiency are identified in a zeta potential patterned straight micro channel, where a continuous flow is generated by superposition of a steady pressure driven flow and time periodic electroosmotic flow induced by a stream-wise AC electric field. Finally, it is shown that the invariant manifold of hyperbolic periodic point determines the geometry of fast mixing zones in oscillatory flows in two-dimensional cavity.

An Operator-Integration-Factor Splitting (OIFS) method for Incompressible Flows in Moving Domains

DOE Office of Scientific and Technical Information (OSTI.GOV)

Patel, Saumil S.; Fischer, Paul F.; Min, Misun

In this paper, we present a characteristic-based numerical procedure for simulating incompressible flows in domains with moving boundaries. Our approach utilizes an operator-integration-factor splitting technique to help produce an effcient and stable numerical scheme. Using the spectral element method and an arbitrary Lagrangian-Eulerian formulation, we investigate flows where the convective acceleration effects are non-negligible. Several examples, ranging from laminar to turbulent flows, are considered. Comparisons with a standard, semi-implicit time-stepping procedure illustrate the improved performance of the scheme.

Stokes parameters of phase-locked partially coherent flat-topped array laser beams propagating through turbulent atmosphere

NASA Astrophysics Data System (ADS)

Golmohammady, Sh; Ghafary, B.

2016-06-01

In this study, generalized Stokes parameters of a phase-locked partially coherent flat-topped array beam based on the extended Huygens-Fresnel principle and the unified theory of coherence and polarization have been reported. Analytical formulas for 2  ×  2 cross-spectral density matrix elements, and consequently Stokes parameters of a phase-locked partially coherent flat-topped array beam propagating through the turbulent atmosphere have been formulated. Effects of many physical attributes such as wavelength, turbulence strength, flatness order and other source parameters on the Stokes parameters, and therefore spectral degree of polarization upon propagation have been studied thoroughly. The behaviour of the spectral degree of coherence of a delineated beam for different source conditions has been investigated. It can be shown that four generalized Stokes parameters increase by raising the flatness order at the same propagation distance. Increasing the number of beams leads to a decrease in the Stokes parameters to zero slowly. The results are of utmost importance for optical communications.

Green colorants based on energetic azole borates.

PubMed

Glück, Johann; Klapötke, Thomas M; Rusan, Magdalena; Stierstorfer, Jörg

2014-11-24

The investigation of green-burning boron-based compounds as colorants in pyrotechnic formulations as alternative for barium nitrate, which is a hazard to health and to the environment, is reported. Metal-free and nitrogen-rich dihydrobis(5-aminotetrazolyl)borate salts and dihydrobis(1,3,4-triazolyl)borate salts have been synthesized and characterized by NMR spectroscopy, elemental analysis, mass spectrometry, and vibrational spectroscopy. Their thermal and energetic properties have been determined as well. Several pyrotechnic compositions using selected azolyl borate salts as green colorants were investigated. Formulations with ammonium dinitramide and ammonium nitrate as oxidizers and boron and magnesium as fuels were tested. The burn time, dominant wavelength, spectral purity, luminous intensity, and luminous efficiency as well as the thermal and energetic properties of these compositions were measured. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Aircraft Engine Noise Scattering by Fuselage and Wings: A Computational Approach

NASA Technical Reports Server (NTRS)

Farassat, F.; Stanescu, D.; Hussaini, M. Y.

2003-01-01

The paper presents a time-domain method for computation of sound radiation from aircraft engine sources to the far field. The effects of non-uniform flow around the aircraft and scattering of sound by fuselage and wings are accounted for in the formulation. The approach is based on the discretization of the inviscid flow equations through a collocation form of the discontinuous Galerkin spectral element method. An isoparametric representation of the underlying geometry is used in order to take full advantage of the spectral accuracy of the method. Large-scale computations are made possible by a parallel implementation based on message passing. Results obtained for radiation from an axisymmetric nacelle alone are compared with those obtained when the same nacelle is installed in a generic configuration, with and without a wing. 0 2002 Elsevier Science Ltd. All rights reserved.

Numerical modeling of guided ultrasonic waves generated and received by piezoelectric wafer in a Delaminated composite beam

NASA Astrophysics Data System (ADS)

Xu, G. D.; Xu, B. Q.; Xu, C. G.; Luo, Y.

2017-05-01

A spectral finite element method (SFEM) is developed to analyze guided ultrasonic waves in a delaminated composite beam excited and received by a pair of surface-bonded piezoelectric wafers. The displacements of the composite beam and the piezoelectric wafer are represented by Timoshenko beam and Euler Bernoulli theory respectively. The linear piezoelectricity is used to model the electrical-mechanical coupling between the piezoelectric wafer and the beam. The coupled governing equations and the boundary conditions in time domain are obtained by using the Hamilton's principle, and then the SFEM are formulated by transforming the coupled governing equations into frequency domain via the discrete Fourier transform. The guided waves are analyzed while the interaction of waves with delamination is also discussed. The elements needed in SFEM is far fewer than those for finite element method (FEM), which result in a much faster solution speed in this study. The high accuracy of the present SFEM is verified by comparing with the finite element results.

A High Order, Locally-Adaptive Method for the Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Chan, Daniel

1998-11-01

I have extended the FOSLS method of Cai, Manteuffel and McCormick (1997) and implemented it within the framework of a spectral element formulation using the Legendre polynomial basis function. The FOSLS method solves the Navier-Stokes equations as a system of coupled first-order equations and provides the ellipticity that is needed for fast iterative matrix solvers like multigrid to operate efficiently. Each element is treated as an object and its properties are self-contained. Only C^0 continuity is imposed across element interfaces; this design allows local grid refinement and coarsening without the burden of having an elaborate data structure, since only information along element boundaries is needed. With the FORTRAN 90 programming environment, I can maintain a high computational efficiency by employing a hybrid parallel processing model. The OpenMP directives provides parallelism in the loop level which is executed in a shared-memory SMP and the MPI protocol allows the distribution of elements to a cluster of SMP's connected via a commodity network. This talk will provide timing results and a comparison with a second order finite difference method.

Pore-scale spectral induced polarization (SIP) signaturesassociated with FeS biomineral transformations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Slater, Lee; Ntarlagiannis, Dimitrios; Personna, Yves R.

2007-10-01

The authors measured Spectral Induced Polarization (SIP) signatures in sand columns during (1) FeS biomineralization produced by sulfate reducing bacteria (D. vulgaris) under anaerboci conditions, and (2) subsequent biomineral dissolution upon return to an aerobic state. The low-frequency (0.1-10 Hz peak) relaxations produced during biomineralization can be modeled with a Cole-Cole formulation, from which the evolution of the polarization magnitude and relaxation length scale can be estimated. They find that the modeled time constant is consistent with the polarizable elements being biomineral encrused pores. Evolution of the model parameters is consistent with FeS surface area increases and pore-size reduction duringmore » biomineral growth, and subsequent biomineral dissolution (FeS surface area decreases and pore expansion) upon return to the aerobic state. They conclude that SIP signatures are diagnostic of pore-scale geometrical changes associated with FeS biomineralization by sulfate reducing bacteria.« less

C deg continuity elements by Hybrid Stress method. M.S. Thesis, 1982 Final Report

NASA Technical Reports Server (NTRS)

Kang, David Sung-Soo

1991-01-01

An intensive study of the assumed variable distribution necessary for the Assumed Displacement Formulation, the Hellinger-Reissner Formulation, and the Hu-Washizu Formulation is made in a unified manner. With emphasis on physical explanation, a systematic method for the Hybrid Stress element construction is outlined. The numerical examples use four and eight node plane stress elements and eight and twenty node solid elements. Computation cost study indicates that the hybrid stress element derived using recently developed Uncoupled Stress Formulation is comparable in CPU time to the Assumed Displacement element. Overall, main emphasis is placed on providing a broader understanding of the Hybrid Stress Formulation.

A novel approach in formulation of special transition elements: Mesh interface elements

NASA Technical Reports Server (NTRS)

Sarigul, Nesrin

1991-01-01

The objective of this research program is in the development of more accurate and efficient methods for solution of singular problems encountered in various branches of mechanics. The research program can be categorized under three levels. The first two levels involve the formulation of a new class of elements called 'mesh interface elements' (MIE) to connect meshes of traditional elements either in three dimensions or in three and two dimensions. The finite element formulations are based on boolean sum and blending operators. MEI are being formulated and tested in this research to account for the steep gradients encountered in aircraft and space structure applications. At present, the heat transfer and structural analysis problems are being formulated from uncoupled theory point of view. The status report: (1) summarizes formulation for heat transfer and structural analysis; (2) explains formulation of MEI; (3) examines computational efficiency; and (4) shows verification examples.

Developments in variational methods for high performance plate and shell elements

NASA Technical Reports Server (NTRS)

Felippa, Carlos A.; Militello, Carmelo

1991-01-01

High performance elements are simple finite elements constructed to deliver engineering accuracy with coarse arbitrary grids. This is part of a series on the variational foundations of high-performance elements, with emphasis on plate and shell elements constructed with the free formulation (FF) and assumed natural strain (ANS) methods. Parameterized variational principles are studied that provide a common foundation for the FF and ANS methods, as well as for a combination of both. From this unified formulation a variant of the ANS formulation, called the assumed natural deviatoric strain (ANDES) formulation, emerges as an important special case. The first ANDES element, a high-performance 9 degrees of freedom triangular Kirchhoff plate bending element, is briefly described to illustrate the use of the new formulation.

3-D frequency-domain seismic wave modelling in heterogeneous, anisotropic media using a Gaussian quadrature grid approach

NASA Astrophysics Data System (ADS)

Zhou, Bing; Greenhalgh, S. A.

2011-01-01

We present an extension of the 3-D spectral element method (SEM), called the Gaussian quadrature grid (GQG) approach, to simulate in the frequency-domain seismic waves in 3-D heterogeneous anisotropic media involving a complex free-surface topography and/or sub-surface geometry. It differs from the conventional SEM in two ways. The first is the replacement of the hexahedral element mesh with 3-D Gaussian quadrature abscissae to directly sample the physical properties or model parameters. This gives a point-gridded model which more exactly and easily matches the free-surface topography and/or any sub-surface interfaces. It does not require that the topography be highly smooth, a condition required in the curved finite difference method and the spectral method. The second is the derivation of a complex-valued elastic tensor expression for the perfectly matched layer (PML) model parameters for a general anisotropic medium, whose imaginary parts are determined by the PML formulation rather than having to choose a specific class of viscoelastic material. Furthermore, the new formulation is much simpler than the time-domain-oriented PML implementation. The specified imaginary parts of the density and elastic moduli are valid for arbitrary anisotropic media. We give two numerical solutions in full-space homogeneous, isotropic and anisotropic media, respectively, and compare them with the analytical solutions, as well as show the excellent effectiveness of the PML model parameters. In addition, we perform numerical simulations for 3-D seismic waves in a heterogeneous, anisotropic model incorporating a free-surface ridge topography and validate the results against the 2.5-D modelling solution, and demonstrate the capability of the approach to handle realistic situations.

Application of the Spectral Element Method to Acoustic Radiation

NASA Technical Reports Server (NTRS)

Doyle, James F.; Rizzi, Stephen A. (Technical Monitor)

2000-01-01

This report summarizes research to develop a capability for analysis of interior noise in enclosed structures when acoustically excited by an external random source. Of particular interest was the application to the study of noise and vibration transmission in thin-walled structures as typified by aircraft fuselages. Three related topics are focused upon. The first concerns the development of a curved frame spectral element, the second shows how the spectral element method for wave propagation in folded plate structures is extended to problems involving curved segmented plates. These are of significance because by combining these curved spectral elements with previously presented flat spectral elements, the dynamic response of geometrically complex structures can be determined. The third topic shows how spectral elements, which incorporate the effect of fluid loading on the structure, are developed for analyzing acoustic radiation from dynamically loaded extended plates.

Application of p-Multigrid to Discontinuous Galerkin Formulations of the Poisson Equation

NASA Technical Reports Server (NTRS)

Helenbrook, B. T.; Atkins, H. L.

2006-01-01

We investigate p-multigrid as a solution method for several different discontinuous Galerkin (DG) formulations of the Poisson equation. Different combinations of relaxation schemes and basis sets have been combined with the DG formulations to find the best performing combination. The damping factors of the schemes have been determined using Fourier analysis for both one and two-dimensional problems. One important finding is that when using DG formulations, the standard approach of forming the coarse p matrices separately for each level of multigrid is often unstable. To ensure stability the coarse p matrices must be constructed from the fine grid matrices using algebraic multigrid techniques. Of the relaxation schemes, we find that the combination of Jacobi relaxation with the spectral element basis is fairly effective. The results using this combination are p sensitive in both one and two dimensions, but reasonable convergence rates can still be achieved for moderate values of p and isotropic meshes. A competitive alternative is a block Gauss-Seidel relaxation. This actually out performs a more expensive line relaxation when the mesh is isotropic. When the mesh becomes highly anisotropic, the implicit line method and the Gauss-Seidel implicit line method are the only effective schemes. Adding the Gauss-Seidel terms to the implicit line method gives a significant improvement over the line relaxation method.

Parallel Semi-Implicit Spectral Element Atmospheric Model

NASA Astrophysics Data System (ADS)

Fournier, A.; Thomas, S.; Loft, R.

2001-05-01

The shallow-water equations (SWE) have long been used to test atmospheric-modeling numerical methods. The SWE contain essential wave-propagation and nonlinear effects of more complete models. We present a semi-implicit (SI) improvement of the Spectral Element Atmospheric Model to solve the SWE (SEAM, Taylor et al. 1997, Fournier et al. 2000, Thomas & Loft 2000). SE methods are h-p finite element methods combining the geometric flexibility of size-h finite elements with the accuracy of degree-p spectral methods. Our work suggests that exceptional parallel-computation performance is achievable by a General-Circulation-Model (GCM) dynamical core, even at modest climate-simulation resolutions (>1o). The code derivation involves weak variational formulation of the SWE, Gauss(-Lobatto) quadrature over the collocation points, and Legendre cardinal interpolators. Appropriate weak variation yields a symmetric positive-definite Helmholtz operator. To meet the Ladyzhenskaya-Babuska-Brezzi inf-sup condition and avoid spurious modes, we use a staggered grid. The SI scheme combines leapfrog and Crank-Nicholson schemes for the nonlinear and linear terms respectively. The localization of operations to elements ideally fits the method to cache-based microprocessor computer architectures --derivatives are computed as collections of small (8x8), naturally cache-blocked matrix-vector products. SEAM also has desirable boundary-exchange communication, like finite-difference models. Timings on on the IBM SP and Compaq ES40 supercomputers indicate that the SI code (20-min timestep) requires 1/3 the CPU time of the explicit code (2-min timestep) for T42 resolutions. Both codes scale nearly linearly out to 400 processors. We achieved single-processor performance up to 30% of peak for both codes on the 375-MHz IBM Power-3 processors. Fast computation and linear scaling lead to a useful climate-simulation dycore only if enough model time is computed per unit wall-clock time. An efficient SI solver is essential to substantially increase this rate. Parallel preconditioning for an iterative conjugate-gradient elliptic solver is described. We are building a GCM dycore capable of 200 GF% lOPS sustained performance on clustered RISC/cache architectures using hybrid MPI/OpenMP programming.

Implementation of Free-Formulation-Based Flat Shell Elements into NASA Comet Code and Development of Nonlinear Shallow Shell Element

NASA Technical Reports Server (NTRS)

Barut, A.; Madenci, Erdogan; Tessler, A.

1997-01-01

This study presents a transient nonlinear finite element analysis within the realm of a multi-body dynamics formulation for determining the dynamic response of a moderately thick laminated shell undergoing a rapid and large rotational motion and nonlinear elastic deformations. Nonlinear strain measure and rotation, as well as 'the transverse shear deformation, are explicitly included in the formulation in order to capture the proper motion-induced stiffness of the laminate. The equations of motion are derived from the virtual work principle. The analysis utilizes a shear deformable shallow shell element along with the co-rotational form of the updated Lagrangian formulation. The shallow shell element formulation is based on the Reissner-Mindlin and Marguerre theory.

CAM-SE: A scalable spectral element dynamical core for the Community Atmosphere Model.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dennis, John; Edwards, Jim; Evans, Kate J

2012-01-01

The Community Atmosphere Model (CAM) version 5 includes a spectral element dynamical core option from NCAR's High-Order Method Modeling Environment. It is a continuous Galerkin spectral finite element method designed for fully unstructured quadrilateral meshes. The current configurations in CAM are based on the cubed-sphere grid. The main motivation for including a spectral element dynamical core is to improve the scalability of CAM by allowing quasi-uniform grids for the sphere that do not require polar filters. In addition, the approach provides other state-of-the-art capabilities such as improved conservation properties. Spectral elements are used for the horizontal discretization, while most othermore » aspects of the dynamical core are a hybrid of well tested techniques from CAM's finite volume and global spectral dynamical core options. Here we first give a overview of the spectral element dynamical core as used in CAM. We then give scalability and performance results from CAM running with three different dynamical core options within the Community Earth System Model, using a pre-industrial time-slice configuration. We focus on high resolution simulations of 1/4 degree, 1/8 degree, and T340 spectral truncation.« less

Finite element techniques for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation

NASA Technical Reports Server (NTRS)

Glaisner, F.; Tezduyar, T. E.

1987-01-01

Finite element procedures for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation have been implemented. For both formulations, streamline-upwind/Petrov-Galerkin techniques are used for the discretization of the transport equations. The main problem associated with the vorticity stream-function formulation is the lack of boundary conditions for vorticity at solid surfaces. Here an implicit treatment of the vorticity at no-slip boundaries is incorporated in a predictor-multicorrector time integration scheme. For the primitive variable formulation, mixed finite-element approximations are used. A nine-node element and a four-node + bubble element have been implemented. The latter is shown to exhibit a checkerboard pressure mode and a numerical treatment for this spurious pressure mode is proposed. The two methods are compared from the points of view of simulating internal and external flows and the possibilities of extensions to three dimensions.

RF Wave Simulation Using the MFEM Open Source FEM Package

NASA Astrophysics Data System (ADS)

Stillerman, J.; Shiraiwa, S.; Bonoli, P. T.; Wright, J. C.; Green, D. L.; Kolev, T.

2016-10-01

A new plasma wave simulation environment based on the finite element method is presented. MFEM, a scalable open-source FEM library, is used as the basis for this capability. MFEM allows for assembling an FEM matrix of arbitrarily high order in a parallel computing environment. A 3D frequency domain RF physics layer was implemented using a python wrapper for MFEM and a cold collisional plasma model was ported. This physics layer allows for defining the plasma RF wave simulation model without user knowledge of the FEM weak-form formulation. A graphical user interface is built on πScope, a python-based scientific workbench, such that a user can build a model definition file interactively. Benchmark cases have been ported to this new environment, with results being consistent with those obtained using COMSOL multiphysics, GENRAY, and TORIC/TORLH spectral solvers. This work is a first step in bringing to bear the sophisticated computational tool suite that MFEM provides (e.g., adaptive mesh refinement, solver suite, element types) to the linear plasma-wave interaction problem, and within more complicated integrated workflows, such as coupling with core spectral solver, or incorporating additional physics such as an RF sheath potential model or kinetic effects. USDoE Awards DE-FC02-99ER54512, DE-FC02-01ER54648.

Spectral-Element Simulations of Wave Propagation in Porous Media: Finite-Frequency Sensitivity Kernels Based Upon Adjoint Methods

NASA Astrophysics Data System (ADS)

Morency, C.; Tromp, J.

2008-12-01

The mathematical formulation of wave propagation in porous media developed by Biot is based upon the principle of virtual work, ignoring processes at the microscopic level, and does not explicitly incorporate gradients in porosity. Based on recent studies focusing on averaging techniques, we derive the macroscopic porous medium equations from the microscale, with a particular emphasis on the effects of gradients in porosity. In doing so, we are able to naturally determine two key terms in the momentum equations and constitutive relationships, directly translating the coupling between the solid and fluid phases, namely a drag force and an interfacial strain tensor. In both terms, gradients in porosity arise. One remarkable result is that when we rewrite this set of equations in terms of the well known Biot variables us, w), terms involving gradients in porosity are naturally accommodated by gradients involving w, the fluid motion relative to the solid, and Biot's formulation is recovered, i.e., it remains valid in the presence of porosity gradients We have developed a numerical implementation of the Biot equations for two-dimensional problems based upon the spectral-element method (SEM) in the time domain. The SEM is a high-order variational method, which has the advantage of accommodating complex geometries like a finite-element method, while keeping the exponential convergence rate of (pseudo)spectral methods. As in the elastic and acoustic cases, poroelastic wave propagation based upon the SEM involves a diagonal mass matrix, which leads to explicit time integration schemes that are well-suited to simulations on parallel computers. Effects associated with physical dispersion & attenuation and frequency-dependent viscous resistance are addressed by using a memory variable approach. Various benchmarks involving poroelastic wave propagation in the high- and low-frequency regimes, and acoustic-poroelastic and poroelastic-poroelastic discontinuities have been successfully performed. We present finite-frequency sensitivity kernels for wave propagation in porous media based upon adjoint methods. We first show that the adjoint equations in porous media are similar to the regular Biot equations upon defining an appropriate adjoint source. Then we present finite-frequency kernels for seismic phases in porous media (e.g., fast P, slow P, and S). These kernels illustrate the sensitivity of seismic observables to structural parameters and form the basis of tomographic inversions. Finally, we show an application of this imaging technique related to the detection of buried landmines and unexploded ordnance (UXO) in porous environments.

Seismic waves in heterogeneous material: subcell resolution of the discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Castro, Cristóbal E.; Käser, Martin; Brietzke, Gilbert B.

2010-07-01

We present an important extension of the arbitrary high-order discontinuous Galerkin (DG) finite-element method to model 2-D elastic wave propagation in highly heterogeneous material. In this new approach we include space-variable coefficients to describe smooth or discontinuous material variations inside each element using the same numerical approximation strategy as for the velocity-stress variables in the formulation of the elastic wave equation. The combination of the DG method with a time integration scheme based on the solution of arbitrary accuracy derivatives Riemann problems still provides an explicit, one-step scheme which achieves arbitrary high-order accuracy in space and time. Compared to previous formulations the new scheme contains two additional terms in the form of volume integrals. We show that the increasing computational cost per element can be overcompensated due to the improved material representation inside each element as coarser meshes can be used which reduces the total number of elements and therefore computational time to reach a desired error level. We confirm the accuracy of the proposed scheme performing convergence tests and several numerical experiments considering smooth and highly heterogeneous material. As the approximation of the velocity and stress variables in the wave equation and of the material properties in the model can be chosen independently, we investigate the influence of the polynomial material representation on the accuracy of the synthetic seismograms with respect to computational cost. Moreover, we study the behaviour of the new method on strong material discontinuities, in the case where the mesh is not aligned with such a material interface. In this case second-order linear material approximation seems to be the best choice, with higher-order intra-cell approximation leading to potential instable behaviour. For all test cases we validate our solution against the well-established standard fourth-order finite difference and spectral element method.

Assessment of seismic risk in Tashkent, Uzbekistan and Bishkek, Kyrgyz Republic

USGS Publications Warehouse

Erdik, M.; Rashidov, T.; Safak, E.; Turdukulov, A.

2005-01-01

The impact of earthquakes in urban centers prone to disastrous earthquakes necessitates the analysis of associated risk for rational formulation of contingency plans and mitigation strategies. In urban centers the seismic risk is best quantified and portrayed through the preparation of 'Earthquake damage and Loss Scenarios'. The components of such scenarios are the assessment of the hazard, inventories and the vulnerabilities of elements at risk. For the development of earthquake risk scenario in Tashkent-Uzbekistan and Bishkek-Kyrgyzstan an approach based on spectral displacements is utilized. This paper will present the important features of a comprehensive study, highlight the methodology, discuss the results and provide insights to the future developments. ?? 2005 Elsevier Ltd. All rights reserved.

A finite element formulation preserving symmetric and banded diffusion stiffness matrix characteristics for fractional differential equations

NASA Astrophysics Data System (ADS)

Lin, Zeng; Wang, Dongdong

2017-10-01

Due to the nonlocal property of the fractional derivative, the finite element analysis of fractional diffusion equation often leads to a dense and non-symmetric stiffness matrix, in contrast to the conventional finite element formulation with a particularly desirable symmetric and banded stiffness matrix structure for the typical diffusion equation. This work first proposes a finite element formulation that preserves the symmetry and banded stiffness matrix characteristics for the fractional diffusion equation. The key point of the proposed formulation is the symmetric weak form construction through introducing a fractional weight function. It turns out that the stiffness part of the present formulation is identical to its counterpart of the finite element method for the conventional diffusion equation and thus the stiffness matrix formulation becomes trivial. Meanwhile, the fractional derivative effect in the discrete formulation is completely transferred to the force vector, which is obviously much easier and efficient to compute than the dense fractional derivative stiffness matrix. Subsequently, it is further shown that for the general fractional advection-diffusion-reaction equation, the symmetric and banded structure can also be maintained for the diffusion stiffness matrix, although the total stiffness matrix is not symmetric in this case. More importantly, it is demonstrated that under certain conditions this symmetric diffusion stiffness matrix formulation is capable of producing very favorable numerical solutions in comparison with the conventional non-symmetric diffusion stiffness matrix finite element formulation. The effectiveness of the proposed methodology is illustrated through a series of numerical examples.

Advances and future directions of research on spectral methods

NASA Technical Reports Server (NTRS)

Patera, A. T.

1986-01-01

Recent advances in spectral methods are briefly reviewed and characterized with respect to their convergence and computational complexity. Classical finite element and spectral approaches are then compared, and spectral element (or p-type finite element) approximations are introduced. The method is applied to the full Navier-Stokes equations, and examples are given of the application of the technique to several transitional flows. Future directions of research in the field are outlined.

Direct formulation of a 4-node hybrid shell element with rotational degrees of freedom

NASA Technical Reports Server (NTRS)

Aminpour, Mohammad A.

1990-01-01

A simple 4-node assumed-stress hybrid quadrilateral shell element with rotational or drilling degrees of freedom is formulated. The element formulation is based directly on a 4-node element. This direct formulation requires fewer computations than a similar element that is derived from an internal 8-node isoparametric element in which the midside degrees of freedom are eliminated in favor of rotational degree of freedom at the corner nodes. The formulation is based on the principle of minimum complementary energy. The membrane part of the element has 12 degrees of freedom including rotational degrees of freedom. The bending part of the element also has 12 degrees of freedom. The bending part of the quadratic variations for both in-plane and out-of-plane displacement fields and linear variations for both in-plane and out-of-plane rotation fields are assumed along the edges of the element. The element Cartesian-coordinate system is chosen such as to make the stress field invariant with respect to node numbering. The membrane part of the stress field is based on a 9-parameter equilibrating stress field, while the bending part is based on a 13-parameter equilibrating stress field. The element passes the patch test, is nearly insensitive to mesh distortion, does not lock, possesses the desirable invariance properties, has no spurious modes, and produces accurate and reliable results.

A Spectral Algorithm for Solving the Relativistic Vlasov-Maxwell Equations

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2001-01-01

A spectral method algorithm is developed for the numerical solution of the full six-dimensional Vlasov-Maxwell system of equations. Here, the focus is on the electron distribution function, with positive ions providing a constant background. The algorithm consists of a Jacobi polynomial-spherical harmonic formulation in velocity space and a trigonometric formulation in position space. A transform procedure is used to evaluate nonlinear terms. The algorithm is suitable for performing moderate resolution simulations on currently available supercomputers for both scientific and engineering applications.

High-Order Methods for Computational Fluid Dynamics: A Brief Review of Compact Differential Formulations on Unstructured Grids

NASA Technical Reports Server (NTRS)

Huynh, H. T.; Wang, Z. J.; Vincent, P. E.

2013-01-01

Popular high-order schemes with compact stencils for Computational Fluid Dynamics (CFD) include Discontinuous Galerkin (DG), Spectral Difference (SD), and Spectral Volume (SV) methods. The recently proposed Flux Reconstruction (FR) approach or Correction Procedure using Reconstruction (CPR) is based on a differential formulation and provides a unifying framework for these high-order schemes. Here we present a brief review of recent developments for the FR/CPR schemes as well as some pacing items.

Three-dimensional flat shell-to-shell coupling: numerical challenges

NASA Astrophysics Data System (ADS)

Guo, Kuo; Haikal, Ghadir

2017-11-01

The node-to-surface formulation is widely used in contact simulations with finite elements because it is relatively easy to implement using different types of element discretizations. This approach, however, has a number of well-known drawbacks, including locking due to over-constraint when this formulation is used as a twopass method. Most studies on the node-to-surface contact formulation, however, have been conducted using solid elements and little has been done to investigate the effectiveness of this approach for beam or shell elements. In this paper we show that locking can also be observed with the node-to-surface contact formulation when applied to plate and flat shell elements even with a singlepass implementation with distinct master/slave designations, which is the standard solution to locking with solid elements. In our study, we use the quadrilateral four node flat shell element for thin (Kirchhoff-Love) plate and thick (Reissner-Mindlin) plate theory, both in their standard forms and with improved formulations such as the linked interpolation [1] and the Discrete Kirchhoff [2] elements for thick and thin plates, respectively. The Lagrange multiplier method is used to enforce the node-to-surface constraints for all elements. The results show clear locking when compared to those obtained using a conforming mesh configuration.

Local spectrum analysis of field propagation in an anisotropic medium. Part I. Time-harmonic fields.

PubMed

Tinkelman, Igor; Melamed, Timor

2005-06-01

The phase-space beam summation is a general analytical framework for local analysis and modeling of radiation from extended source distributions. In this formulation, the field is expressed as a superposition of beam propagators that emanate from all points in the source domain and in all directions. In this Part I of a two-part investigation, the theory is extended to include propagation in anisotropic medium characterized by a generic wave-number profile for time-harmonic fields; in a companion paper [J. Opt. Soc. Am. A 22, 1208 (2005)], the theory is extended to time-dependent fields. The propagation characteristics of the beam propagators in a homogeneous anisotropic medium are considered. With use of Gaussian windows for the local processing of either ordinary or extraordinary electromagnetic field distributions, the field is represented by a phase-space spectral distribution in which the propagating elements are Gaussian beams that are formulated by using Gaussian plane-wave spectral distributions over the extended source plane. By applying saddle-point asymptotics, we extract the Gaussian beam phenomenology in the anisotropic environment. The resulting field is parameterized in terms of the spatial evolution of the beam curvature, beam width, etc., which are mapped to local geometrical properties of the generic wave-number profile. The general results are applied to the special case of uniaxial crystal, and it is found that the asymptotics for the Gaussian beam propagators, as well as the physical phenomenology attached, perform remarkably well.

Membrane triangles with corner drilling freedoms. I - The EFF element

NASA Technical Reports Server (NTRS)

Alvin, Ken; De La Fuente, Horacio M.; Haugen, Bjorn; Felippa, Carlos A.

1992-01-01

The formulation of 3-node 9-DOF membrane elements with normal-to-element-plane rotations (drilling freedoms) is examined in the context of parametrized variational principles. In particular, attention is given to the application of the extended free formulation (EFF) to the construction of a triangular membrane element with drilling freedoms that initially has complete quadratic polynomial expansions in each displacement component. The main advantage of the EFF over the free formulation triangle is that an explicit form is obtained for the higher-order stiffness.

A Spectral Finite Element Approach to Modeling Soft Solids Excited with High-Frequency Harmonic Loads

PubMed Central

Brigham, John C.; Aquino, Wilkins; Aguilo, Miguel A.; Diamessis, Peter J.

2010-01-01

An approach for efficient and accurate finite element analysis of harmonically excited soft solids using high-order spectral finite elements is presented and evaluated. The Helmholtz-type equations used to model such systems suffer from additional numerical error known as pollution when excitation frequency becomes high relative to stiffness (i.e. high wave number), which is the case, for example, for soft tissues subject to ultrasound excitations. The use of high-order polynomial elements allows for a reduction in this pollution error, but requires additional consideration to counteract Runge's phenomenon and/or poor linear system conditioning, which has led to the use of spectral element approaches. This work examines in detail the computational benefits and practical applicability of high-order spectral elements for such problems. The spectral elements examined are tensor product elements (i.e. quad or brick elements) of high-order Lagrangian polynomials with non-uniformly distributed Gauss-Lobatto-Legendre nodal points. A shear plane wave example is presented to show the dependence of the accuracy and computational expense of high-order elements on wave number. Then, a convergence study for a viscoelastic acoustic-structure interaction finite element model of an actual ultrasound driven vibroacoustic experiment is shown. The number of degrees of freedom required for a given accuracy level was found to consistently decrease with increasing element order. However, the computationally optimal element order was found to strongly depend on the wave number. PMID:21461402

Vertical discretization with finite elements for a global hydrostatic model on the cubed sphere

NASA Astrophysics Data System (ADS)

Yi, Tae-Hyeong; Park, Ja-Rin

2017-06-01

A formulation of Galerkin finite element with basis-spline functions on a hybrid sigma-pressure coordinate is presented to discretize the vertical terms of global Eulerian hydrostatic equations employed in a numerical weather prediction system, which is horizontally discretized with high-order spectral elements on a cubed sphere grid. This replaces the vertical discretization of conventional central finite difference that is first-order accurate in non-uniform grids and causes numerical instability in advection-dominant flows. Therefore, a model remains in the framework of Galerkin finite elements for both the horizontal and vertical spatial terms. The basis-spline functions, obtained from the de-Boor algorithm, are employed to derive both the vertical derivative and integral operators, since Eulerian advection terms are involved. These operators are used to discretize the vertical terms of the prognostic and diagnostic equations. To verify the vertical discretization schemes and compare their performance, various two- and three-dimensional idealized cases and a hindcast case with full physics are performed in terms of accuracy and stability. It was shown that the vertical finite element with the cubic basis-spline function is more accurate and stable than that of the vertical finite difference, as indicated by faster residual convergence, fewer statistical errors, and reduction in computational mode. This leads to the general conclusion that the overall performance of a global hydrostatic model might be significantly improved with the vertical finite element.

Optimizing a spectral element for modeling PZT-induced Lamb wave propagation in thin plates

NASA Astrophysics Data System (ADS)

Ha, Sungwon; Chang, Fu-Kuo

2010-01-01

Use of surface-mounted piezoelectric actuators to generate acoustic ultrasound has been demonstrated to be a key component of built-in nondestructive detection evaluation (NDE) techniques, which can automatically inspect and interrogate damage in hard-to-access areas in real time without disassembly of the structural parts. However, piezoelectric actuators create complex waves, which propagate through the structure. Having the capability to model piezoelectric actuator-induced wave propagation and understanding its physics are essential to developing advanced algorithms for the built-in NDE techniques. Therefore, the objective of this investigation was to develop an efficient hybrid spectral element for modeling piezoelectric actuator-induced high-frequency wave propagation in thin plates. With the hybrid element we take advantage of both a high-order spectral element in the in-plane direction and a linear finite element in the thickness direction in order to efficiently analyze Lamb wave propagation in thin plates. The hybrid spectral element out-performs other elements in terms of leading to significantly faster computation and smaller memory requirements. Use of the hybrid spectral element is proven to be an efficient technique for modeling PZT-induced (PZT: lead zirconate titanate) wave propagation in thin plates. The element enables fundamental understanding of PZT-induced wave propagation.

Finite Rotation Analysis of Highly Thin and Flexible Structures

NASA Technical Reports Server (NTRS)

Clarke, Greg V.; Lee, Keejoo; Lee, Sung W.; Broduer, Stephen J. (Technical Monitor)

2001-01-01

Deployable space structures such as sunshields and solar sails are extremely thin and highly flexible with limited bending rigidity. For analytical investigation of their responses during deployment and operation in space, these structures can be modeled as thin shells. The present work examines the applicability of the solid shell element formulation to modeling of deployable space structures. The solid shell element formulation that models a shell as a three-dimensional solid is convenient in that no rotational parameters are needed for the description of kinematics of deformation. However, shell elements may suffer from element locking as the thickness becomes smaller unless special care is taken. It is shown that, when combined with the assumed strain formulation, the solid shell element formulation results in finite element models that are free of locking even for extremely thin structures. Accordingly, they can be used for analysis of highly flexible space structures undergoing geometrically nonlinear finite rotations.

Achieving the resolution of the spectrograph of the 6m large Azimuthal telescope

NASA Astrophysics Data System (ADS)

Sazonenko, Dmitrii; Kukushkin, Dmitrii; Bakholdin, Alexey; Valyavin, Gennady

2016-08-01

Special Astrophysical Observatory of Russian Academy of Sciences (SAO RAS) creates a spectrograph with high spectral resolution for the 6-meter telescope. The spectrograph consists of a mobile unit located at the focus of the telescope's main mirror, a stationary part located under the telescope and optical fibers which transmit light from the mobile part to the stationary one. The spectral resolution of the stationary part should be R=100000. To achieve such a value, the scheme has two spectral elements, with cross-dispersion. The main spectral element is an echelle grating. The second spectral element is a prism with a diffraction grating on one facet.

Significance of Strain in Formulation in Theory of Solid Mechanics

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Coroneos, Rula M.; Hopkins, Dale A.

2003-01-01

The basic theory of solid mechanics was deemed complete circa 1860 when St. Venant provided the strain formulation or the field compatibility condition. The strain formulation was incomplete. The missing portion has been formulated and identified as the boundary compatibility condition (BCC). The BCC, derived through a variational formulation, has been verified through integral theorem and solution of problems. The BCC, unlike the field counterpart, do not trivialize when expressed in displacements. Navier s method and the stiffness formulation have to account for the extra conditions especially at the inter-element boundaries in a finite element model. Completion of the strain formulation has led to the revival of the direct force calculation methods: the Integrated Force Method (IFM) and its dual (IFMD) for finite element analysis, and the completed Beltrami-Michell formulation (CBMF) in elasticity. The benefits from the new methods in elasticity, in finite element analysis, and in design optimization are discussed. Existing solutions and computer codes may have to be adjusted for the compliance of the new conditions. Complacency because the discipline is over a century old and computer codes have been developed for half a century can lead to stagnation of the discipline.

Broadband microwave photonic fully tunable filter using a single heterogeneously integrated III-V/SOI-microdisk-based phase shifter.

PubMed

Lloret, Juan; Morthier, Geert; Ramos, Francisco; Sales, Salvador; Van Thourhout, Dries; Spuesens, Thijs; Olivier, Nicolas; Fédéli, Jean-Marc; Capmany, José

2012-05-07

A broadband microwave photonic phase shifter based on a single III-V microdisk resonator heterogeneously integrated on and coupled to a nanophotonic silicon-on-insulator waveguide is reported. The phase shift tunability is accomplished by modifying the effective index through carrier injection. A comprehensive semi-analytical model aiming at predicting its behavior is formulated and confirmed by measurements. Quasi-linear and continuously tunable 2π phase shifts at radiofrequencies greater than 18 GHz are experimentally demonstrated. The phase shifter performance is also evaluated when used as a key element in tunable filtering schemes. Distortion-free and wideband filtering responses with a tuning range of ~100% over the free spectral range are obtained.

Efficient Basis Formulation for (1 +1 )-Dimensional SU(2) Lattice Gauge Theory: Spectral Calculations with Matrix Product States

NASA Astrophysics Data System (ADS)

Bañuls, Mari Carmen; Cichy, Krzysztof; Cirac, J. Ignacio; Jansen, Karl; Kühn, Stefan

2017-10-01

We propose an explicit formulation of the physical subspace for a (1 +1 )-dimensional SU(2) lattice gauge theory, where the gauge degrees of freedom are integrated out. Our formulation is completely general, and might be potentially suited for the design of future quantum simulators. Additionally, it allows for addressing the theory numerically with matrix product states. We apply this technique to explore the spectral properties of the model and the effect of truncating the gauge degrees of freedom to a small finite dimension. In particular, we determine the scaling exponents for the vector mass. Furthermore, we also compute the entanglement entropy in the ground state and study its scaling towards the continuum limit.

Library Optimization in EDXRF Spectral Deconvolution for Multi-element Analysis of Ambient Aerosols

EPA Science Inventory

In multi-element analysis of atmospheric aerosols, attempts are made to fit overlapping elemental spectral lines for many elements that may be undetectable in samples due to low concentrations. Fitting with many library reference spectra has the unwanted effect of raising the an...

Nonconforming mortar element methods: Application to spectral discretizations

NASA Technical Reports Server (NTRS)

Maday, Yvon; Mavriplis, Cathy; Patera, Anthony

1988-01-01

Spectral element methods are p-type weighted residual techniques for partial differential equations that combine the generality of finite element methods with the accuracy of spectral methods. Presented here is a new nonconforming discretization which greatly improves the flexibility of the spectral element approach as regards automatic mesh generation and non-propagating local mesh refinement. The method is based on the introduction of an auxiliary mortar trace space, and constitutes a new approach to discretization-driven domain decomposition characterized by a clean decoupling of the local, structure-preserving residual evaluations and the transmission of boundary and continuity conditions. The flexibility of the mortar method is illustrated by several nonconforming adaptive Navier-Stokes calculations in complex geometry.

The first ANDES elements: 9-DOF plate bending triangles

NASA Technical Reports Server (NTRS)

Militello, Carmelo; Felippa, Carlos A.

1991-01-01

New elements are derived to validate and assess the assumed natural deviatoric strain (ANDES) formulation. This is a brand new variant of the assumed natural strain (ANS) formulation of finite elements, which has recently attracted attention as an effective method for constructing high-performance elements for linear and nonlinear analysis. The ANDES formulation is based on an extended parametrized variational principle developed in recent publications. The key concept is that only the deviatoric part of the strains is assumed over the element whereas the mean strain part is discarded in favor of a constant stress assumption. Unlike conventional ANS elements, ANDES elements satisfy the individual element test (a stringent form of the patch test) a priori while retaining the favorable distortion-insensitivity properties of ANS elements. The first application of this formulation is the development of several Kirchhoff plate bending triangular elements with the standard nine degrees of freedom. Linear curvature variations are sampled along the three sides with the corners as gage reading points. These sample values are interpolated over the triangle using three schemes. Two schemes merge back to conventional ANS elements, one being identical to the Discrete Kirchhoff Triangle (DKT), whereas the third one produces two new ANDES elements. Numerical experiments indicate that one of the ANDES element is relatively insensitive to distortion compared to previously derived high-performance plate-bending elements, while retaining accuracy for nondistorted elements.

Wavelength Scanning with a Tilting Interference Filter for Glow-Discharge Elemental Imaging.

PubMed

Storey, Andrew P; Ray, Steven J; Hoffmann, Volker; Voronov, Maxim; Engelhard, Carsten; Buscher, Wolfgang; Hieftje, Gary M

2017-06-01

Glow discharges have long been used for depth profiling and bulk analysis of solid samples. In addition, over the past decade, several methods of obtaining lateral surface elemental distributions have been introduced, each with its own strengths and weaknesses. Challenges for each of these techniques are acceptable optical throughput and added instrumental complexity. Here, these problems are addressed with a tilting-filter instrument. A pulsed glow discharge is coupled to an optical system comprising an adjustable-angle tilting filter, collimating and imaging lenses, and a gated, intensified charge-coupled device (CCD) camera, which together provide surface elemental mapping of solid samples. The tilting-filter spectrometer is instrumentally simpler, produces less image distortion, and achieves higher optical throughput than a monochromator-based instrument, but has a much more limited tunable spectral range and poorer spectral resolution. As a result, the tilting-filter spectrometer is limited to single-element or two-element determinations, and only when the target spectral lines fall within an appropriate spectral range and can be spectrally discerned. Spectral interferences that result from heterogeneous impurities can be flagged and overcome by observing the spatially resolved signal response across the available tunable spectral range. The instrument has been characterized and evaluated for the spatially resolved analysis of glow-discharge emission from selected but representative samples.

Local spectrum analysis of field propagation in an anisotropic medium. Part II. Time-dependent fields.

PubMed

Tinkelman, Igor; Melamed, Timor

2005-06-01

In Part I of this two-part investigation [J. Opt. Soc. Am. A 22, 1200 (2005)], we presented a theory for phase-space propagation of time-harmonic electromagnetic fields in an anisotropic medium characterized by a generic wave-number profile. In this Part II, these investigations are extended to transient fields, setting a general analytical framework for local analysis and modeling of radiation from time-dependent extended-source distributions. In this formulation the field is expressed as a superposition of pulsed-beam propagators that emanate from all space-time points in the source domain and in all directions. Using time-dependent quadratic-Lorentzian windows, we represent the field by a phase-space spectral distribution in which the propagating elements are pulsed beams, which are formulated by a transient plane-wave spectrum over the extended-source plane. By applying saddle-point asymptotics, we extract the beam phenomenology in the anisotropic environment resulting from short-pulsed processing. Finally, the general results are applied to the special case of uniaxial crystal and compared with a reference solution.

Reduced-Density-Matrix Description of Decoherence and Relaxation Processes for Electron-Spin Systems

NASA Astrophysics Data System (ADS)

Jacobs, Verne

2017-04-01

Electron-spin systems are investigated using a reduced-density-matrix description. Applications of interest include trapped atomic systems in optical lattices, semiconductor quantum dots, and vacancy defect centers in solids. Complimentary time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are self-consistently developed. The general non-perturbative and non-Markovian formulations provide a fundamental framework for systematic evaluations of corrections to the standard Born (lowest-order-perturbation) and Markov (short-memory-time) approximations. Particular attention is given to decoherence and relaxation processes, as well as spectral-line broadening phenomena, that are induced by interactions with photons, phonons, nuclear spins, and external electric and magnetic fields. These processes are treated either as coherent interactions or as environmental interactions. The environmental interactions are incorporated by means of the general expressions derived for the time-domain and frequency-domain Liouville-space self-energy operators, for which the tetradic-matrix elements are explicitly evaluated in the diagonal-resolvent, lowest-order, and Markov (short-memory time) approximations. Work supported by the Office of Naval Research through the Basic Research Program at The Naval Research Laboratory.

Radiative interactions in multi-dimensional chemically reacting flows using Monte Carlo simulations

NASA Technical Reports Server (NTRS)

Liu, Jiwen; Tiwari, Surendra N.

1994-01-01

The Monte Carlo method (MCM) is applied to analyze radiative heat transfer in nongray gases. The nongray model employed is based on the statistical narrow band model with an exponential-tailed inverse intensity distribution. The amount and transfer of the emitted radiative energy in a finite volume element within a medium are considered in an exact manner. The spectral correlation between transmittances of two different segments of the same path in a medium makes the statistical relationship different from the conventional relationship, which only provides the non-correlated results for nongray methods is discussed. Validation of the Monte Carlo formulations is conducted by comparing results of this method of other solutions. In order to further establish the validity of the MCM, a relatively simple problem of radiative interactions in laminar parallel plate flows is considered. One-dimensional correlated Monte Carlo formulations are applied to investigate radiative heat transfer. The nongray Monte Carlo solutions are also obtained for the same problem and they also essentially match the available analytical solutions. the exact correlated and non-correlated Monte Carlo formulations are very complicated for multi-dimensional systems. However, by introducing the assumption of an infinitesimal volume element, the approximate correlated and non-correlated formulations are obtained which are much simpler than the exact formulations. Consideration of different problems and comparison of different solutions reveal that the approximate and exact correlated solutions agree very well, and so do the approximate and exact non-correlated solutions. However, the two non-correlated solutions have no physical meaning because they significantly differ from the correlated solutions. An accurate prediction of radiative heat transfer in any nongray and multi-dimensional system is possible by using the approximate correlated formulations. Radiative interactions are investigated in chemically reacting compressible flows of premixed hydrogen and air in an expanding nozzle. The governing equations are based on the fully elliptic Navier-Stokes equations. Chemical reaction mechanisms were described by a finite rate chemistry model. The correlated Monte Carlo method developed earlier was employed to simulate multi-dimensional radiative heat transfer. Results obtained demonstrate that radiative effects on the flowfield are minimal but radiative effects on the wall heat transfer are significant. Extensive parametric studies are conducted to investigate the effects of equivalence ratio, wall temperature, inlet flow temperature, and nozzle size on the radiative and conductive wall fluxes.

Constrained and Unconstrained Variational Finite Element Formulation of Solutions to a Stress Wave Problem - a Numerical Comparison.

DTIC Science & Technology

1982-10-01

Element Unconstrained Variational Formulations," Innovativ’e Numerical Analysis For the Applied Engineering Science, R. P. Shaw, et at, Fitor...Initial Boundary Value of Gun Dynamics Solved by Finite Element Unconstrained Variational Formulations," Innovative Numerical Analysis For the Applied ... Engineering Science, R. P. Shaw, et al, Editors, University Press of Virginia, Charlottesville, pp. 733-741, 1980. 2 J. J. Wu, "Solutions to Initial

Specialty functions singularity mechanics problems

NASA Technical Reports Server (NTRS)

Sarigul, Nesrin

1989-01-01

The focus is in the development of more accurate and efficient advanced methods for solution of singular problems encountered in mechanics. At present, finite element methods in conjunction with special functions, boolean sum and blending interpolations are being considered. In dealing with systems which contain a singularity, special finite elements are being formulated to be used in singular regions. Further, special transition elements are being formulated to couple the special element to the mesh that models the rest of the system, and to be used in conjunction with 1-D, 2-D and 3-D elements within the same mesh. Computational simulation with a least squares fit is being utilized to construct special elements, if there is an unknown singularity in the system. A novel approach is taken in formulation of the elements in that: (1) the material properties are modified to include time, temperature, coordinate and stress dependant behavior within the element; (2) material properties vary at nodal points of the elements; (3) a hidden-symbolic computation scheme is developed and utilized in formulating the elements; and (4) special functions and boolean sum are utilized in order to interpolate the field variables and their derivatives along the boundary of the elements. It may be noted that the proposed methods are also applicable to fluids and coupled problems.

A contact layer element for large deformations

NASA Astrophysics Data System (ADS)

Weißenfels, C.; Wriggers, P.

2015-05-01

In many contact situations the material behavior of one contact member strongly influences the force acting between the two bodies. Unfortunately standard friction models cannot reproduce all of these material effects at the contact layer and often continuum interface elements are used instead. These elements are intrinsically tied to the fixed grid and hence cannot be used in large sliding simulations. Due to the shortcomings of the standard contact formulations and of the interface elements a new type of a contact layer element is developed in this work. The advantages of this element are the direct implementation of continuum models into the contact formulation and the application to arbitrary large deformations. Showing a relation between continuum and contact kinematics based on the solid-shell concept the new contact element is at the end a natural extension of the standard contact formulations into 3D. Two examples show that the continuum behavior can be exactly reproduced at the contact surface even in large sliding situations using this contact layer element. For the discretization of the new contact element the Mortar method is chosen exemplary, but it can be combined with all kinds of contact formulations.

Information-efficient spectral imaging sensor

DOEpatents

Sweatt, William C.; Gentry, Stephen M.; Boye, Clinton A.; Grotbeck, Carter L.; Stallard, Brian R.; Descour, Michael R.

2003-01-01

A programmable optical filter for use in multispectral and hyperspectral imaging. The filter splits the light collected by an optical telescope into two channels for each of the pixels in a row in a scanned image, one channel to handle the positive elements of a spectral basis filter and one for the negative elements of the spectral basis filter. Each channel for each pixel disperses its light into n spectral bins, with the light in each bin being attenuated in accordance with the value of the associated positive or negative element of the spectral basis vector. The spectral basis vector is constructed so that its positive elements emphasize the presence of a target and its negative elements emphasize the presence of the constituents of the background of the imaged scene. The attenuated light in the channels is re-imaged onto separate detectors for each pixel and then the signals from the detectors are combined to give an indication of the presence or not of the target in each pixel of the scanned scene. This system provides for a very efficient optical determination of the presence of the target, as opposed to the very data intensive data manipulations that are required in conventional hyperspectral imaging systems.

Preconditioned Mixed Spectral Element Methods for Elasticity and Stokes Problems

NASA Technical Reports Server (NTRS)

Pavarino, Luca F.

1996-01-01

Preconditioned iterative methods for the indefinite systems obtained by discretizing the linear elasticity and Stokes problems with mixed spectral elements in three dimensions are introduced and analyzed. The resulting stiffness matrices have the structure of saddle point problems with a penalty term, which is associated with the Poisson ratio for elasticity problems or with stabilization techniques for Stokes problems. The main results of this paper show that the convergence rate of the resulting algorithms is independent of the penalty parameter, the number of spectral elements Nu and mildly dependent on the spectral degree eta via the inf-sup constant. The preconditioners proposed for the whole indefinite system are block-diagonal and block-triangular. Numerical experiments presented in the final section show that these algorithms are a practical and efficient strategy for the iterative solution of the indefinite problems arising from mixed spectral element discretizations of elliptic systems.

The determination of elements in herbal teas and medicinal plant formulations and their tisanes.

PubMed

Pohl, Pawel; Dzimitrowicz, Anna; Jedryczko, Dominika; Szymczycha-Madeja, Anna; Welna, Maja; Jamroz, Piotr

2016-10-25

Elemental analysis of herbal teas and their tisanes is aimed at assessing their quality and safety in reference to specific food safety regulations and evaluating their nutritional value. This survey is dedicated to atomic spectroscopy and mass spectrometry element detection methods and sample preparation procedures used in elemental analysis of herbal teas and medicinal plant formulations. Referring to original works from the last 15 years, particular attention has been paid to tisane preparation, sample matrix decomposition, calibration and quality assurance of results in elemental analysis of herbal teas by different atomic and mass spectrometry methods. In addition, possible sources of elements in herbal teas and medicinal plant formulations have been discussed. Copyright © 2016 Elsevier B.V. All rights reserved.

On Formulations of Discontinuous Galerkin and Related Methods for Conservation Laws

NASA Technical Reports Server (NTRS)

Huynh, H. T.

2014-01-01

A formulation for the discontinuous Galerkin (DG) method that leads to solutions using the differential form of the equation (as opposed to the standard integral form) is presented. The formulation includes (a) a derivative calculation that involves only data within each cell with no data interaction among cells, and (b) for each cell, corrections to this derivative that deal with the jumps in fluxes at the cell boundaries and allow data across cells to interact. The derivative with no interaction is obtained by a projection, but for nodal-type methods, evaluating this derivative by interpolation at the nodal points is more economical. The corrections are derived using the approximate (Dirac) delta functions. The formulation results in a family of schemes: different approximate delta functions give rise to different methods. It is shown that the current formulation is essentially equivalent to the flux reconstruction (FR) formulation. Due to the use of approximate delta functions, an energy stability proof simpler than that of Vincent, Castonguay, and Jameson (2011) for a family of schemes is derived. Accuracy and stability of resulting schemes are discussed via Fourier analyses. Similar to FR, the current formulation provides a unifying framework for high-order methods by recovering the DG, spectral difference (SD), and spectral volume (SV) schemes. It also yields stable, accurate, and economical methods.

Error estimation and adaptive mesh refinement for parallel analysis of shell structures

NASA Technical Reports Server (NTRS)

Keating, Scott C.; Felippa, Carlos A.; Park, K. C.

1994-01-01

The formulation and application of element-level, element-independent error indicators is investigated. This research culminates in the development of an error indicator formulation which is derived based on the projection of element deformation onto the intrinsic element displacement modes. The qualifier 'element-level' means that no information from adjacent elements is used for error estimation. This property is ideally suited for obtaining error values and driving adaptive mesh refinements on parallel computers where access to neighboring elements residing on different processors may incur significant overhead. In addition such estimators are insensitive to the presence of physical interfaces and junctures. An error indicator qualifies as 'element-independent' when only visible quantities such as element stiffness and nodal displacements are used to quantify error. Error evaluation at the element level and element independence for the error indicator are highly desired properties for computing error in production-level finite element codes. Four element-level error indicators have been constructed. Two of the indicators are based on variational formulation of the element stiffness and are element-dependent. Their derivations are retained for developmental purposes. The second two indicators mimic and exceed the first two in performance but require no special formulation of the element stiffness mesh refinement which we demonstrate for two dimensional plane stress problems. The parallelizing of substructures and adaptive mesh refinement is discussed and the final error indicator using two-dimensional plane-stress and three-dimensional shell problems is demonstrated.

Mathematical aspects of finite element methods for incompressible viscous flows

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.

1986-01-01

Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.

[Rapid determination of major and trace elements in the salt lake clay minerals by X-ray fluorescence spectrometry].

PubMed

Wang, Xiao-Huan; Meng, Qing-Fen; Dong, Ya-Ping; Chen, Mei-Da; Li, Wu

2010-03-01

A rapid multi-element analysis method for clay mineral samples was described. This method utilized a polarized wave-length dispersive X-ray fluorescence spectrometer--Axios PW4400, which had a maximum tube power of 4 000 watts. The method was developed for the determination of As, Mn, Co, Cu, Cr, Dy, Ga, Mo, P, Pb, Rb, S, Sr, Ni, ,Cs, Ta, Th, Ti, U, V, Y, Zn, Zr, MgO, K2O, Na2O, CaO, Fe2O3, Al2O3, SiO2 and so on. Thirty elements in clay mineral species were measured by X-ray fluorescence spectrometry with pressed powder pellets. Spectral interferences, in particular the indirect interferences of each element, were studied. A method to distinguish the interference between each other periodic elements in element periodic table was put forward. The measuring conditions and existence were mainly investigated, and the selected background position as well as corrected spectral overlap for the trace elements were also discussed. It was found that the indirect spectral overlap line was the same important as direct spectral overlap line. Due to inducing the effect of indirect spectral overlap, some elements jlike Bi, Sn, W which do not need analysis were also added to the elements channel. The relative standard deviation (RSD) was in the range of 0.01% to 5.45% except three elements Mo, Cs and Ta. The detection limits, precisions and accuracies for most elements using this method can meet the requirements of sample analysis in clay mineral species.

Application of the boundary element method to the micromechanical analysis of composite materials

NASA Technical Reports Server (NTRS)

Goldberg, R. K.; Hopkins, D. A.

1995-01-01

A new boundary element formulation for the micromechanical analysis of composite materials is presented in this study. A unique feature of the formulation is the use of circular shape functions to convert the two-dimensional integrations of the composite fibers to one-dimensional integrations. To demonstrate the applicability of the formulations, several example problems including elastic and thermal analysis of laminated composites and elastic analyses of woven composites are presented and the boundary element results compared to experimental observations and/or results obtained through alternate analytical procedures. While several issues remain to be addressed in order to make the methodology more robust, the formulations presented here show the potential in providing an alternative to traditional finite element methods, particularly for complex composite architectures.

Structural vibration and acoustic radiation of coupled propeller-shafting and submarine hull system due to propeller forces

NASA Astrophysics Data System (ADS)

Qu, Yegao; Su, Jinpeng; Hua, Hongxing; Meng, Guang

2017-08-01

This paper investigates the structural and acoustic responses of a coupled propeller-shafting and submarine pressure hull system under different propeller force excitations. The entire system, which consists of a rigid propeller, a main shaft, two bearings and an orthogonally stiffened pressure hull, is submerged in a heavy fluid. The shaft is elastically connected to the pressure hull by a radial bearing and a thrust bearing. The theoretical model of the structural system is formulated based on a modified variational method, in which the propeller, the main shaft and the bearings are treated as a lumped mass, an elastic beam and spatially distributed spring-damper systems, respectively. The rings and stringers in the pressure hull are modeled as discrete structural elements. The acoustic field generated by the hull is calculated using a spectral Kirchhoff-Helmholtz integral formulation. A strongly coupled structure-acoustic interaction analysis is employed to achieve reasonable solutions for the coupled system. The displacement of the pressure hull and the sound pressure of the fluid are expanded in the form of a double mixed series using Fourier series and Chebyshev orthogonal polynomials, providing a flexible way for the present method to account for the individual contributions of circumferential wave modes to the vibration and acoustic responses of the pressure hull in an analytical manner. The contributions of different circumferential wave modes of the pressure hull to the structural and acoustic responses of the coupled system under axial, transversal and vertical propeller forces are investigated. Computed results are compared with those solutions obtained from the coupled finite element/boundary element method. Effects of the ring and the bearing stiffness on the acoustic responses of the coupled system are discussed.

Joint Biological Standoff Detection System increment II: Field Demonstration - SINBAHD Performances

DTIC Science & Technology

2007-12-01

of a dispersive element and a range-gated ICCD that limits the spectral information within the selected volume. This technique has showed an...bioaerosols. This LIF signal is spectrally collected by the combination of a dispersive element and a range-gated ICCD that records spectral...2001 in order to underline the robustness of the spectral signature of a particular biomaterial but of different origin, preparation and dispersion

Spectral element multigrid. Part 2: Theoretical justification

NASA Technical Reports Server (NTRS)

Maday, Yvon; Munoz, Rafael

1988-01-01

A multigrid algorithm is analyzed which is used for solving iteratively the algebraic system resulting from tha approximation of a second order problem by spectral or spectral element methods. The analysis, performed here in the one dimensional case, justifies the good smoothing properties of the Jacobi preconditioner that was presented in Part 1 of this paper.

The Spectral Element Method for Geophysical Flows

NASA Astrophysics Data System (ADS)

Taylor, Mark

1998-11-01

We will describe SEAM, a Spectral Element Atmospheric Model. SEAM solves the 3D primitive equations used in climate modeling and medium range forecasting. SEAM uses a spectral element discretization for the surface of the globe and finite differences in the vertical direction. The model is spectrally accurate, as demonstrated by a variety of test cases. It is well suited for modern distributed-shared memory computers, sustaining over 24 GFLOPS on a 240 processor HP Exemplar. This performance has allowed us to run several interesting simulations in full spherical geometry at high resolution (over 22 million grid points).

Formulation procedure and spectral data for a coatings system optimally employing the high intrinsic reflectance of barium sulphate

NASA Technical Reports Server (NTRS)

Schutt, J. B.; Stromberg, E.; Shai, C. M.; Arens, J. F.

1972-01-01

The use of polyvinyl alcohol as a binder for barium sulphate does not allow the intrinsically high reflectance of this material in the near vacuum ultraviolet to be optimally employed. In an effort to better utilize this property, completely inorganic coatings systems are described, where from the intrinsically high reflectance of barium sulphate in this spectral region can be gotten. Potassium sulphate turns out to be the preferred binder. Compositions, formulating procedures, and application techniques are included. For completeness, absolute and relative reflectance data are included for intra- and intersystem comparisons.

A new mathematical formulation of the line-by-line method in case of weak line overlapping

NASA Technical Reports Server (NTRS)

Ishov, Alexander G.; Krymova, Natalie V.

1994-01-01

A rigorous mathematical proof is presented for multiline representation on the equivalent width of a molecular band which consists in the general case of n overlapping spectral lines. The multiline representation includes a principal term and terms of minor significance. The principal term is the equivalent width of the molecular band consisting of the same n nonoverlapping spectral lines. The terms of minor significance take into consideration the overlapping of two, three and more spectral lines. They are small in case of the weak overlapping of spectral lines in the molecular band. The multiline representation can be easily generalized for optically inhomogeneous gas media and holds true for combinations of molecular bands. If the band lines overlap weakly the standard formulation of line-by-line method becomes too labor-consuming. In this case the multiline representation permits line-by-line calculations to be performed more effectively. Other useful properties of the multiline representation are pointed out.

Multiscale Approach For Simulating Nonlinear Wave Propagation In Materials with Localized Microdamage

NASA Astrophysics Data System (ADS)

Vanaverbeke, Sigfried; Van Den Abeele, Koen

2006-05-01

A multiscale model for the simulation of two-dimensional nonlinear wave propagation in microcracked materials exhibiting hysteretic nonlinearity is presented. We use trigger-like elements with a two state nonlinear stress-strain relation to simulate microcracks at the microlevel. A generalized Preisach space approach, based on the eigenstress-eigenstrain formulation, upscales the microscopic state relation to the mesoscopic level. The macroscopic response of the sample to an arbitrary excitation signal is then predicted using a staggered grid Elastodynamic Finite Integration Technique (EFIT) formalism. We apply the model to investigate spectral changes of a pulsed signal traversing a localized microdamaged region with hysteretic nonlinearity in a plate, and to study the influence of a superficial region with hysteretic nonlinearity on the nonlinear Rayleigh wave propagation.

Tensor-product preconditioners for higher-order space-time discontinuous Galerkin methods

NASA Astrophysics Data System (ADS)

Diosady, Laslo T.; Murman, Scott M.

2017-02-01

A space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high-order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

Tensor-Product Preconditioners for Higher-Order Space-Time Discontinuous Galerkin Methods

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2016-01-01

space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equat ions. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

A Novel Four-Node Quadrilateral Smoothing Element for Stress Enhancement and Error Estimation

NASA Technical Reports Server (NTRS)

Tessler, A.; Riggs, H. R.; Dambach, M.

1998-01-01

A four-node, quadrilateral smoothing element is developed based upon a penalized-discrete-least-squares variational formulation. The smoothing methodology recovers C1-continuous stresses, thus enabling effective a posteriori error estimation and automatic adaptive mesh refinement. The element formulation is originated with a five-node macro-element configuration consisting of four triangular anisoparametric smoothing elements in a cross-diagonal pattern. This element pattern enables a convenient closed-form solution for the degrees of freedom of the interior node, resulting from enforcing explicitly a set of natural edge-wise penalty constraints. The degree-of-freedom reduction scheme leads to a very efficient formulation of a four-node quadrilateral smoothing element without any compromise in robustness and accuracy of the smoothing analysis. The application examples include stress recovery and error estimation in adaptive mesh refinement solutions for an elasticity problem and an aerospace structural component.

Mixed formulation for seismic analysis of composite steel-concrete frame structures

NASA Astrophysics Data System (ADS)

Ayoub, Ashraf Salah Eldin

This study presents a new finite element model for the nonlinear analysis of structures made up of steel and concrete under monotonic and cyclic loads. The new formulation is based on a two-field mixed formulation. In the formulation, both forces and deformations are simultaneously approximated within the element through independent interpolation functions. The main advantages of the model is the accuracy in global and local response with very few elements while maintaining rapid numerical convergence and robustness even under severe cyclic loading. Overall four elements were developed based on the new formulation: an element that describes the behavior of anchored reinforcing bars, an element that describes the behavior of composite steel-concrete beams with deformable shear connectors, an element that describes the behavior of reinforced concrete beam-columns with bond-slip, and an element that describes the behavior of pretensioned or posttensioned, bonded or unbonded prestressed concrete structures. The models use fiber discretization of beam sections to describe nonlinear material response. The transfer of forces between steel and concrete is described with bond elements. Bond elements are modeled with distributed spring elements. The non-linear behavior of the composite element derives entirely from the constitutive laws of the steel, concrete and bond elements. Two additional elements are used for the prestressed concrete models, a friction element that models the effect of friction between the tendon and the duct during the posttensioning operation, and an anchorage element that describes the behavior of the prestressing tendon anchorage in posttensioned structures. Two algorithms for the numerical implementation of the new proposed model are presented; an algorithm that enforces stress continuity at element boundaries, and an algorithm in which stress continuity is relaxed locally inside the element. Stability of both algorithms is discussed. Comparison with standard displacement based models and earlier flexibility based models is presented through numerical studies. The studies prove the superiority of the mixed model over both displacement and flexibility models. Correlation studies of the proposed model with experimental results of structural specimens are conducted. The studies show the accuracy of the model and its numerical robustness even under severe cyclic loading conditions.

Connes distance function on fuzzy sphere and the connection between geometry and statistics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Devi, Yendrembam Chaoba, E-mail: chaoba@bose.res.in; Chakraborty, Biswajit, E-mail: biswajit@bose.res.in; Prajapat, Shivraj, E-mail: shraprajapat@gmail.com

An algorithm to compute Connes spectral distance, adaptable to the Hilbert-Schmidt operatorial formulation of non-commutative quantum mechanics, was developed earlier by introducing the appropriate spectral triple and used to compute infinitesimal distances in the Moyal plane, revealing a deep connection between geometry and statistics. In this paper, using the same algorithm, the Connes spectral distance has been calculated in the Hilbert-Schmidt operatorial formulation for the fuzzy sphere whose spatial coordinates satisfy the su(2) algebra. This has been computed for both the discrete and the Perelemov’s SU(2) coherent state. Here also, we get a connection between geometry and statistics which ismore » shown by computing the infinitesimal distance between mixed states on the quantum Hilbert space of a particular fuzzy sphere, indexed by n ∈ ℤ/2.« less

Michael Sprague | NREL

Science.gov Websites

student, he developed a parallel spectral finite element method for treating the interaction of large mechanics of fluids, structures, and their interaction|Spectral finite-element methods for time-dependent

Green method by diffuse reflectance infrared spectroscopy and spectral region selection for the quantification of sulphamethoxazole and trimethoprim in pharmaceutical formulations.

PubMed

da Silva, Fabiana E B; Flores, Érico M M; Parisotto, Graciele; Müller, Edson I; Ferrão, Marco F

2016-03-01

An alternative method for the quantification of sulphametoxazole (SMZ) and trimethoprim (TMP) using diffuse reflectance infrared Fourier-transform spectroscopy (DRIFTS) and partial least square regression (PLS) was developed. Interval Partial Least Square (iPLS) and Synergy Partial Least Square (siPLS) were applied to select a spectral range that provided the lowest prediction error in comparison to the full-spectrum model. Fifteen commercial tablet formulations and forty-nine synthetic samples were used. The ranges of concentration considered were 400 to 900 mg g-1SMZ and 80 to 240 mg g-1 TMP. Spectral data were recorded between 600 and 4000 cm-1 with a 4 cm-1 resolution by Diffuse Reflectance Infrared Fourier Transform Spectroscopy (DRIFTS). The proposed procedure was compared to high performance liquid chromatography (HPLC). The results obtained from the root mean square error of prediction (RMSEP), during the validation of the models for samples of sulphamethoxazole (SMZ) and trimethoprim (TMP) using siPLS, demonstrate that this approach is a valid technique for use in quantitative analysis of pharmaceutical formulations. The selected interval algorithm allowed building regression models with minor errors when compared to the full spectrum PLS model. A RMSEP of 13.03 mg g-1for SMZ and 4.88 mg g-1 for TMP was obtained after the selection the best spectral regions by siPLS.

Modular Approach to Structural Simulation for Vehicle Crashworthiness Prediction

DOT National Transportation Integrated Search

1975-03-01

A modular formulation for simulation of the structural deformation and deceleration of a vehicle for crashworthiness and collision compatibility is presented. This formulation includes three dimensional beam elements, various spring elements, rigid b...

Method for Balancing Detector Output to a Desired Level of Balance at a Frequency

NASA Technical Reports Server (NTRS)

Sachse, Glenn W. (Inventor)

2003-01-01

A multi-gas sensor is provided which modulates a polarized light beam over a broadband of wavelengths between two alternating orthogonal polarization components. The two orthogonal polarization components of the polarization modulated beam are directed along two distinct optical paths. At least one optical path contains one or more spectral discrimination elements, with each spectral discrimination element having spectral absorption features of one or more gases of interest being measured. The two optical paths then intersect, and one orthogonal component of the intersected components is transmitted and the other orthogonal component is reflected. The combined polarization modulated beam is partitioned into one or more smaller spectral regions of interest where one or more gases of interest has an absorption band. The difference in intensity between the two orthogonal polarization components is then determined in each partitioned spectral region of interest as an indication of the spectral emission/absorption of the light beam by the gases of interest in the measurement path. The spectral emission/absorption is indicative of the concentration of the one or more gases of interest in the measurement path. More specifically, one embodiment of the present invention is a gas filter correlation radiometer which comprises a polarizer, a polarization modulator, a polarization beam splitter, a beam combiner, wavelength partitioning element, and detection element. The gases of interest are measured simultaneously and, further, can be measured independently or non-independently. Furthermore, optical or electronic element are provided to balance optical intensities between the two optical paths.

Multi-Gas Sensor

NASA Technical Reports Server (NTRS)

Sachse, Glenn W. (Inventor); Wang, Liang-Guo (Inventor); LeBel, Peter J. (Inventor); Steele, Tommy C. (Inventor); Rana, Mauro (Inventor)

1999-01-01

A multi-gas sensor is provided which modulates a polarized light beam over a broadband of wavelengths between two alternating orthogonal polarization components. The two orthogonal polarization components of the polarization modulated beam are directed along two distinct optical paths. At least one optical path contains one or more spectral discrimination element, with each spectral discrimination element having spectral absorption features of one or more gases of interest being measured. The two optical paths then intersect, and one orthogonal component of the intersected components is transmitted and the other orthogonal component is reflected. The combined polarization modulated beam is partitioned into one or more smaller spectral regions of interest where one or more gases of interest has an absorption band. The difference in intensity between the two orthogonal polarization components is then determined in each partitioned spectral region of interest as an indication of the spectral emission/absorption of the light beam by the gases of interest in the measurement path. The spectral emission/absorption is indicative of the concentration of the one or more gases of interest in the measurement path. More specifically, one embodiment of the present invention is a gas filter correlation radiometer which comprises a polarizer, a polarization modulator, a polarization beam splitter, a beam combiner, wavelength partitioning element, and detection element. The gases of interest are measured simultaneously and, further, can be measured independently or non-independently. Furthermore, optical or electronic element are provided to balance optical intensities between the two optical paths.

Variational formulation of high performance finite elements: Parametrized variational principles

NASA Technical Reports Server (NTRS)

Felippa, Carlos A.; Militello, Carmello

1991-01-01

High performance elements are simple finite elements constructed to deliver engineering accuracy with coarse arbitrary grids. This is part of a series on the variational basis of high-performance elements, with emphasis on those constructed with the free formulation (FF) and assumed natural strain (ANS) methods. Parametrized variational principles that provide a foundation for the FF and ANS methods, as well as for a combination of both are presented.

On spectral synthesis on element-wise compact Abelian groups

NASA Astrophysics Data System (ADS)

Platonov, S. S.

2015-08-01

Let G be an arbitrary locally compact Abelian group and let C(G) be the space of all continuous complex-valued functions on G. A closed linear subspace \\mathscr H\\subseteq C(G) is referred to as an invariant subspace if it is invariant with respect to the shifts τ_y\\colon f(x)\\mapsto f(xy), y\\in G. By definition, an invariant subspace \\mathscr H\\subseteq C(G) admits strict spectral synthesis if \\mathscr H coincides with the closure in C(G) of the linear span of all characters of G belonging to \\mathscr H. We say that strict spectral synthesis holds in the space C(G) on G if every invariant subspace \\mathscr H\\subseteq C(G) admits strict spectral synthesis. An element x of a topological group G is said to be compact if x is contained in some compact subgroup of G. A group G is said to be element-wise compact if all elements of G are compact. The main result of the paper is the proof of the fact that strict spectral synthesis holds in C(G) for a locally compact Abelian group G if and only if G is element-wise compact. Bibliography: 14 titles.

Extension to linear dynamics for hybrid stress finite element formulation based on additional displacements

NASA Astrophysics Data System (ADS)

Sumihara, K.

Based upon legitimate variational principles, one microscopic-macroscopic finite element formulation for linear dynamics is presented by Hybrid Stress Finite Element Method. The microscopic application of Geometric Perturbation introduced by Pian and the introduction of infinitesimal limit core element (Baby Element) have been consistently combined according to the flexible and inherent interpretation of the legitimate variational principles initially originated by Pian and Tong. The conceptual development based upon Hybrid Finite Element Method is extended to linear dynamics with the introduction of physically meaningful higher modes.

A generic interface element for COMET-AR

NASA Technical Reports Server (NTRS)

Mccleary, Susan L.; Aminpour, Mohammad A.

1995-01-01

The implementation of an interface element capability within the COMET-AR software system is described. The report is intended for use by both users of currently implemented interface elements and developers of new interface element formulations. Guidance on the use of COMET-AR is given. A glossary is provided as an Appendix to this report for readers unfamiliar with the jargon of COMET-AR. A summary of the currently implemented interface element formulation is presented in Section 7.3 of this report.

A Comparison of Spectral Element and Finite Difference Methods Using Statically Refined Nonconforming Grids for the MHD Island Coalescence Instability Problem

NASA Astrophysics Data System (ADS)

Ng, C. S.; Rosenberg, D.; Pouquet, A.; Germaschewski, K.; Bhattacharjee, A.

2009-04-01

A recently developed spectral-element adaptive refinement incompressible magnetohydrodynamic (MHD) code [Rosenberg, Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)] is applied to simulate the problem of MHD island coalescence instability (\\ci) in two dimensions. \\ci is a fundamental MHD process that can produce sharp current layers and subsequent reconnection and heating in a high-Lundquist number plasma such as the solar corona [Ng and Bhattacharjee, Phys. Plasmas, 5, 4028 (1998)]. Due to the formation of thin current layers, it is highly desirable to use adaptively or statically refined grids to resolve them, and to maintain accuracy at the same time. The output of the spectral-element static adaptive refinement simulations are compared with simulations using a finite difference method on the same refinement grids, and both methods are compared to pseudo-spectral simulations with uniform grids as baselines. It is shown that with the statically refined grids roughly scaling linearly with effective resolution, spectral element runs can maintain accuracy significantly higher than that of the finite difference runs, in some cases achieving close to full spectral accuracy.

A Parameter-Free Dynamic Alternative to Hyper-Viscosity for Coupled Transport Equations: Application to the Simulation of 3D Squall Lines Using Spectral Elements

DTIC Science & Technology

2015-06-04

that involve physics coupling with phase change in the simulation of 3D deep convection. We show that the VMS+DC approach is a robust technique that can...of 3D deep convection. We show that the VMS+DC approach is a robust technique that can damp the high order modes characterizing the spectral element...of Spectral Elements, Deep Convection, Kessler Microphysics Preprint J. Comput. Phys. 283 (2015) 360-373 June 4, 2015 1. Introduction In the field of

Three-Dimensional High-Order Spectral Volume Method for Solving Maxwell's Equations on Unstructured Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel; Wang, Z. J.

2004-01-01

A three-dimensional, high-order, conservative, and efficient discontinuous spectral volume (SV) method for the solutions of Maxwell's equations on unstructured grids is presented. The concept of discontinuous 2nd high-order loca1 representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) method, but instead of using a Galerkin finite-element formulation, the SV method is based on a finite-volume approach to attain a simpler formulation. Conventional unstructured finite-volume methods require data reconstruction based on the least-squares formulation using neighboring cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In the SV method, one starts with a relatively coarse grid of triangles or tetrahedra, called spectral volumes (SVs), and partition each SV into a number of structured subcells, called control volumes (CVs), that support a polynomial expansion of a desired degree of precision. The unknowns are cell averages over CVs. If all the SVs are partitioned in a geometrically similar manner, the reconstruction becomes universal as a weighted sum of unknowns, and only a few universal coefficients need to be stored for the surface integrals over CV faces. Since the solution is discontinuous across the SV boundaries, a Riemann solver is thus necessary to maintain conservation. In the paper, multi-parameter and symmetric SV partitions, up to quartic for triangle and cubic for tetrahedron, are first presented. The corresponding weight coefficients for CV face integrals in terms of CV cell averages for each partition are analytically determined. These discretization formulas are then applied to the integral form of the Maxwell equations. All numerical procedures for outer boundary, material interface, zonal interface, and interior SV face are unified with a single characteristic formulation. The load balancing in a massive parallel computing environment is therefore easier to achieve. A parameter is introduced in the Riemann solver to control the strength of the smoothing term. Important aspects of the data structure and its effects to communication and the optimum use of cache memory are discussed. Results will be presented for plane TE and TM waves incident on a perfectly conducting cylinder for up to fifth order of accuracy, and a plane wave incident on a perfectly conducting sphere for up to fourth order of accuracy. Comparisons are made with exact solutions for these cases.

Improved assumed-stress hybrid shell element with drilling degrees of freedom for linear stress, buckling, and free vibration analyses

NASA Technical Reports Server (NTRS)

Rengarajan, Govind; Aminpour, Mohammad A.; Knight, Norman F., Jr.

1992-01-01

An improved four-node quadrilateral assumed-stress hybrid shell element with drilling degrees of freedom is presented. The formulation is based on Hellinger-Reissner variational principle and the shape functions are formulated directly for the four-node element. The element has 12 membrane degrees of freedom and 12 bending degrees of freedom. It has nine independent stress parameters to describe the membrane stress resultant field and 13 independent stress parameters to describe the moment and transverse shear stress resultant field. The formulation encompasses linear stress, linear buckling, and linear free vibration problems. The element is validated with standard tests cases and is shown to be robust. Numerical results are presented for linear stress, buckling, and free vibration analyses.

Hierarchical and non-hierarchical {lambda} elements for one dimensional problems with unknown strength of singularity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wong, K.K.; Surana, K.S.

1996-10-01

This paper presents a new and general procedure for designing hierarchical and non-hierarchical special elements called {lambda} elements for one dimensional singular problems where the strength of the singularity is unknown. The {lambda} element formulations presented here permit correct numerical simulation of linear as well as non-linear singular problems without a priori knowledge of the strength of the singularity. A procedure is also presented for determining the exact strength of the singularity using the converged solution. It is shown that in special instances, the general formulation of {lambda} elements can also be made hierarchical. The {lambda} elements presented here aremore » of type C{sup 0} and provide C{sup 0} inter-element continuity with p-version elements. One dimensional steady state radial flow of an upper convected Maxwell fluid is considered as a sample problem. Since in this case {lambda}{sub i} are known, this problem provides a good example for investigating the performance of the formulation proposed here. Least squares approach (or Least Squares Finite Element Formulation: LSFEF) is used to construct the integral form (error functional I) from the differential equations. Numerical studies are presented for radially inward flow of an upper convected Maxwell fluid with inner radius r{sub i} = .1 and .01 etc. and Deborah number De = 2.« less

The Impact of Varying the Physics Grid Resolution Relative to the Dynamical Core Resolution in CAM-SE-CSLAM

NASA Astrophysics Data System (ADS)

Herrington, A. R.; Lauritzen, P. H.; Reed, K. A.

2017-12-01

The spectral element dynamical core of the Community Atmosphere Model (CAM) has recently been coupled to an approximately isotropic, finite-volume grid per implementation of the conservative semi-Lagrangian multi-tracer transport scheme (CAM-SE-CSLAM; Lauritzen et al. 2017). In this framework, the semi-Lagrangian transport of tracers are computed on the finite-volume grid, while the adiabatic dynamics are solved using the spectral element grid. The physical parameterizations are evaluated on the finite-volume grid, as opposed to the unevenly spaced Gauss-Lobatto-Legendre nodes of the spectral element grid. Computing the physics on the finite-volume grid reduces numerical artifacts such as grid imprinting, possibly because the forcing terms are no longer computed at element boundaries where the resolved dynamics are least smooth. The separation of the physics grid and the dynamics grid allows for a unique opportunity to understand the resolution sensitivity in CAM-SE-CSLAM. The observed large sensitivity of CAM to horizontal resolution is a poorly understood impediment to improved simulations of regional climate using global, variable resolution grids. Here, a series of idealized moist simulations are presented in which the finite-volume grid resolution is varied relative to the spectral element grid resolution in CAM-SE-CSLAM. The simulations are carried out at multiple spectral element grid resolutions, in part to provide a companion set of simulations, in which the spectral element grid resolution is varied relative to the finite-volume grid resolution, but more generally to understand if the sensitivity to the finite-volume grid resolution is consistent across a wider spectrum of resolved scales. Results are interpreted in the context of prior ideas regarding resolution sensitivity of global atmospheric models.

Thermoelastic Formulation of Stiffened, Unsymmetric Composite Panels for Finite Element Analysis of High Speed Aircraft

NASA Technical Reports Server (NTRS)

Collier, Craig S.

2004-01-01

An emerging technology need for capturing 3-D panel thermoelastic response with 2-D planar finite element models (FEMs) is aided with an equivalent plate stiffness and thermal coefficient formulation. The formulation is general and applies to all panel concepts. Included with the formulation is the ability to provide membrane-bending coupling of unsymmetric sections and calculation of all thermal expansion and bending responses from in-plane and through-the-thickness temperature gradients. Thermal residual strains for both the laminates and plies are included. The general formulation is defined and then applied to a hat-shaped, corrugated stiffened panel. Additional formulations are presented where required to include all of the hat's unique characteristics. Each formulation is validated independently with 3-D FEA.

Optimization of compressive 4D-spatio-spectral snapshot imaging

NASA Astrophysics Data System (ADS)

Zhao, Xia; Feng, Weiyi; Lin, Lihua; Su, Wu; Xu, Guoqing

2017-10-01

In this paper, a modified 3D computational reconstruction method in the compressive 4D-spectro-volumetric snapshot imaging system is proposed for better sensing spectral information of 3D objects. In the design of the imaging system, a microlens array (MLA) is used to obtain a set of multi-view elemental images (EIs) of the 3D scenes. Then, these elemental images with one dimensional spectral information and different perspectives are captured by the coded aperture snapshot spectral imager (CASSI) which can sense the spectral data cube onto a compressive 2D measurement image. Finally, the depth images of 3D objects at arbitrary depths, like a focal stack, are computed by inversely mapping the elemental images according to geometrical optics. With the spectral estimation algorithm, the spectral information of 3D objects is also reconstructed. Using a shifted translation matrix, the contrast of the reconstruction result is further enhanced. Numerical simulation results verify the performance of the proposed method. The system can obtain both 3D spatial information and spectral data on 3D objects using only one single snapshot, which is valuable in the agricultural harvesting robots and other 3D dynamic scenes.

Emission spectra of selected SSME elements and materials

NASA Technical Reports Server (NTRS)

Tejwani, Gopal D.; Vandyke, David B.; Bircher, Felix E.; Gardner, Donald G.; Chenevert, Donald J.

1992-01-01

Stennis Space Center (SSC) is pursuing the advancement of experimental techniques and theoretical developments in the field of plume spectroscopy for application to rocket development testing programs and engine health monitoring. Exhaust plume spectral data for the Space Shuttle Main Engine (SSME) are routinely acquired. The usefulness of this data depends upon qualitative and quantitative interpretation of spectral features and their correlation with the engine performance. A knowledge of the emission spectral characteristics of effluent materials in the exhaust plume is essential. A study of SSME critical components and their materials identified 30 elements and 53 materials whose engine exhaust plume spectral might be required. The most important were evaluated using SSC's Diagnostic Testbed Facility Thruster (DTFT), a 1200-lbf, liquid oxygen/gaseous hydrogen rocket engine which very nearly replicates the temperature and pressure conditions of the SSME exhaust plume in the first Mach diamond. This report presents the spectral data for the 10 most important elements and 27 most important materials which are strongly to moderately emitting in the DTFT exhaust plume. The covered spectral range is 300 to 426 nm and the spectral resolution is 0.25 nm. Spectral line identification information is provided and line interference effects are considered.

Triangular prismatic solid-shell element with generalised deformation description

NASA Astrophysics Data System (ADS)

Mataix, Vicente; Flores, Fernando G.; Rossi, Riccardo; Oñate, Eugenio

2018-01-01

The solid-shells are an attractive kind of element for the simulation of f orming processes, due to the fact that any kind of generic 3D constitutive law can be employed without any kind of additional modification, besides the thermomechanic problem is formulated without additional assumptions. Additionally, this type of element allows the three-dimensional description of the deformable body, thus contact on both sides of the element can be treated easily. The present work consists in the development of a triangular prism element as a solid-shell, for the analysis of thin/thick shell, undergoing large deformations. The element is formulated in total Lagrangian formulation, and employs the neighbour (adjacent) elements to perform a local patch to enrich the displacement field. In the original formulation by Flores, a modified right Cauchy-Green deformation tensor (?) is obtained; in the present work a modified deformation gradient (?) is obtained, which allows to generalise the methodology and allows to employ a wide range of constitutive laws. The element is based in three modifications: (a) a classical assumed strain approach for transverse shear strains (b) an assumed strain approach for the in-plane components using information from neighbour elements and (c) an averaging of the volumetric strain over the element. The objective is to use this type of elements for the simulation of shells avoiding transverse shear locking, improving the membrane behaviour of the in-plane triangle and to handle quasi-incompressible materials or materials with isochoric plastic flow. Some examples have been evaluated to show the good performance of the element and results.

On Pythagoras Theorem for Products of Spectral Triples

NASA Astrophysics Data System (ADS)

D'Andrea, Francesco; Martinetti, Pierre

2013-05-01

We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non-pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and we provide non-unital counter-examples inspired by K-homology.

Phase-space evolution of x-ray coherence in phase-sensitive imaging.

PubMed

Wu, Xizeng; Liu, Hong

2008-08-01

X-ray coherence evolution in the imaging process plays a key role for x-ray phase-sensitive imaging. In this work we present a phase-space formulation for the phase-sensitive imaging. The theory is reformulated in terms of the cross-spectral density and associated Wigner distribution. The phase-space formulation enables an explicit and quantitative account of partial coherence effects on phase-sensitive imaging. The presented formulas for x-ray spectral density at the detector can be used for performing accurate phase retrieval and optimizing the phase-contrast visibility. The concept of phase-space shearing length derived from this phase-space formulation clarifies the spatial coherence requirement for phase-sensitive imaging with incoherent sources. The theory has been applied to x-ray Talbot interferometric imaging as well. The peak coherence condition derived reveals new insights into three-grating-based Talbot-interferometric imaging and gratings-based x-ray dark-field imaging.

Post-exposed fiber Bragg gratings

NASA Astrophysics Data System (ADS)

Miller, Gary A.

This thesis explains the development and characterization of a novel technique to fabricate weak fiber Bragg gratings for highly specific multi-element sensor arrays. This method, termed the "rescan technique," involves re-exposing a local region of a grating to fringeless ultraviolet light to "trim" unwanted portions of the reflection spectrum. The spectral effects that result from a rescan can only be adequately described by inventing the concept of a three-dimensional index growth surface, where induced index is a function of both the writing intensity and the exposure time. Using this information, it is possible to predict the spectral response of a rescanned grating using a numerical model. For our model, we have modified the piecewise-uniform approach to include coefficients within the coupled-mode formulism that imitate the same scattering properties as the actual grating. By taking high accuracy measurements of the refractive index change in germanosilicate fiber, we have created the necessary 3D map of photoinduced index to accurately model gratings and their post-exposure spectra. We will also demonstrate that optical fiber exhibits what we call "exposure history"; the final index change in a region depends on the previous exposures conditions.

Finite element formulation with embedded weak discontinuities for strain localization under dynamic conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jin, Tao; Mourad, Hashem M.; Bronkhorst, Curt A.

Here, we present an explicit finite element formulation designed for the treatment of strain localization under highly dynamic conditions. We also used a material stability analysis to detect the onset of localization behavior. Finite elements with embedded weak discontinuities are employed with the aim of representing subsequent localized deformation accurately. The formulation and its algorithmic implementation are described in detail. Numerical results are presented to illustrate the usefulness of this computational framework in the treatment of strain localization under highly dynamic conditions, and to examine its performance characteristics in the context of two-dimensional plane-strain problems.

Finite element formulation with embedded weak discontinuities for strain localization under dynamic conditions

DOE PAGES

Jin, Tao; Mourad, Hashem M.; Bronkhorst, Curt A.; ...

2017-09-13

Here, we present an explicit finite element formulation designed for the treatment of strain localization under highly dynamic conditions. We also used a material stability analysis to detect the onset of localization behavior. Finite elements with embedded weak discontinuities are employed with the aim of representing subsequent localized deformation accurately. The formulation and its algorithmic implementation are described in detail. Numerical results are presented to illustrate the usefulness of this computational framework in the treatment of strain localization under highly dynamic conditions, and to examine its performance characteristics in the context of two-dimensional plane-strain problems.

Development of an integrated BEM approach for hot fluid structure interaction

NASA Technical Reports Server (NTRS)

Dargush, Gary F.; Banerjee, Prasanta K.; Honkala, Keith A.

1991-01-01

The development of a boundary element formulation for the study of hot fluid-structure interaction in earth-to-orbit engine hot section components is described. The initial primary thrust of the program to date was directed quite naturally toward the examination of fluid flow, since boundary element methods for fluids are at a much less developed state. This required the development of integral formulations for both the solid and fluid, and some preliminary infrastructural enhancements to a boundary element code to permit coupling of the fluid-structure problem. Boundary element formulations are implemented in two dimensions for both the solid and the fluid. The solid is modeled as an uncoupled thermoelastic medium under plane strain conditions, while several formulations are investigated for the fluid. For example, both vorticity and primitive variable approaches are implemented for viscous, incompressible flow, and a compressible version is developed. All of the above boundary element implementations are incorporated in a general purpose two-dimensional code. Thus, problems involving intricate geometry, multiple generic modeling regions, and arbitrary boundary conditions are all supported.

New Variational Formulations of Hybrid Stress Elements

NASA Technical Reports Server (NTRS)

Pian, T. H. H.; Sumihara, K.; Kang, D.

1984-01-01

In the variational formulations of finite elements by the Hu-Washizu and Hellinger-Reissner principles the stress equilibrium condition is maintained by the inclusion of internal displacements which function as the Lagrange multipliers for the constraints. These versions permit the use of natural coordinates and the relaxation of the equilibrium conditions and render considerable improvements in the assumed stress hybrid elements. These include the derivation of invariant hybrid elements which possess the ideal qualities such as minimum sensitivity to geometric distortions, minimum number of independent stress parameters, rank sufficient, and ability to represent constant strain states and bending moments. Another application is the formulation of semiLoof thin shell elements which can yield excellent results for many severe test cases because the rigid body nodes, the momentless membrane strains, and the inextensional bending modes are all represented.

On pseudo-spectral time discretizations in summation-by-parts form

NASA Astrophysics Data System (ADS)

Ruggiu, Andrea A.; Nordström, Jan

2018-05-01

Fully-implicit discrete formulations in summation-by-parts form for initial-boundary value problems must be invertible in order to provide well functioning procedures. We prove that, under mild assumptions, pseudo-spectral collocation methods for the time derivative lead to invertible discrete systems when energy-stable spatial discretizations are used.

A Loomis-Sikorski theorem and functional calculus for a generalized Hermitian algebra

NASA Astrophysics Data System (ADS)

Foulis, David J.; Jenčová, Anna; Pulmannová, Sylvia

2017-10-01

A generalized Hermitian (GH-) algebra is a generalization of the partially ordered Jordan algebra of all Hermitian operators on a Hilbert space. We introduce the notion of a gh-tribe, which is a commutative GH-algebra of functions on a nonempty set X with pointwise partial order and operations, and we prove that every commutative GH-algebra is the image of a gh-tribe under a surjective GH-morphism. Using this result, we prove that each element a of a GH-algebra A corresponds to a real observable ξa on the σ-orthomodular lattice of projections in A and that ξa determines the spectral resolution of a. Also, if f is a continuous function defined on the spectrum of a, we formulate a definition of f (a), thus obtaining a continuous functional calculus for A.

Spectroscopic studies on two mono nuclear iron (III) complexes derived from a schiff base and an azodye

NASA Astrophysics Data System (ADS)

Mini, S.; Sadasivan, V.; Meena, S. S.; Bhatt, Pramod

2014-10-01

Two new mono nuclear Fe(III) complexes of an azodye (ANSN) and a Schiff base (FAHP) are reported. The azodye is prepared by coupling diazotized 1-amino-2-naphthol-4-sulphonicacid with 2-naphthol and the Schiff base is prepared by condensing 2-amino-3-hydroxy pyridine with furfural. The complexes were synthesized by the reaction of FeCl3˙2H2O with respective ligands. They were characterized on the basis of elemental analysis and spectral studies like IR, NMR, Electronic and M.ssbauer. Magnetic susceptibility and Molar conductance of complexes at room temperature were studied. Based on the spectroscopic evidences and other analytical data the complexes are formulated as[Fe(ANSN)Cl(H2O)2] and [Fe(FAHP)Cl2(H2O)2].

A finite element boundary integral formulation for radiation and scattering by cavity antennas using tetrahedral elements

NASA Technical Reports Server (NTRS)

Gong, J.; Volakis, J. L.; Chatterjee, A.; Jin, J. M.

1992-01-01

A hybrid finite element boundary integral formulation is developed using tetrahedral and/or triangular elements for discretizing the cavity and/or aperture of microstrip antenna arrays. The tetrahedral elements with edge based linear expansion functions are chosen for modeling the volume region and triangular elements are used for discretizing the aperture. The edge based expansion functions are divergenceless thus removing the requirement to introduce a penalty term and the tetrahedral elements permit greater geometrical adaptability than the rectangular bricks. The underlying theory and resulting expressions are discussed in detail together with some numerical scattering examples for comparison and demonstration.

Parallel Ellipsoidal Perfectly Matched Layers for Acoustic Helmholtz Problems on Exterior Domains

DOE PAGES

Bunting, Gregory; Prakash, Arun; Walsh, Timothy; ...

2018-01-26

Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and howmore » this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this study, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. Finally, this provides an additional advantage of PML over the infinite element approach.« less

Parallel Ellipsoidal Perfectly Matched Layers for Acoustic Helmholtz Problems on Exterior Domains

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bunting, Gregory; Prakash, Arun; Walsh, Timothy

Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and howmore » this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this study, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. Finally, this provides an additional advantage of PML over the infinite element approach.« less

Synthesis, spectral and thermal studies of some transition metal mixed ligand complexes: Modeling of equilibrium composition and biological activity

NASA Astrophysics Data System (ADS)

Neelakantan, M. A.; Sundaram, M.; Nair, M. Sivasankaran

2011-09-01

Several mixed ligand Ni(II), Cu(II) and Zn(II) complexes of 2-amino-3-hydroxypyridine (AHP) and imidazoles viz., imidazole (him), benzimidazole (bim), histamine (hist) and L-histidine (his) have been synthesized and characterized by elemental and spectral (vibrational, electronic, 1H NMR and EPR) data as well as by magnetic moment values. On the basis of elemental analysis and molar conductance values, all the complexes can be formulated as [MAB]Cl except histidine complexes as MAB. Thermogravimetric studies reveal the presence of coordinated water molecules in most of the complexes. From the magnetic measurements and electronic spectral data, octahedral structure was proposed for Ni(II) and Cu(II)-AHP-his, tetrahedral for Cu(II)-AHP-him/bim/hist, but square planar for the Cu(II)-AHP complex. The g∥/ A∥ calculated supports tetrahedral environment around the Cu(II) in Cu(II)-AHP-him/bim/hist and distorted octahedral for Cu(II)-AHP-his complexes. The morphology of the reported metal complexes was investigated by scanning electron micrographs (SEM). The potentiometric study has been performed in aqueous solution at 37 °C and I = 0.15 mol dm -3 NaClO 4. MABH, MAB and MAB 2 species has been identified in the present systems. Proton dissociation constants of AHP and stability constants of metal complexes were determined using MINIQUAD-75. The most probable structure of the mixed ligand species is discussed based upon their stability constants. The in vitro biological activity of the complexes was tested against the Gram positive and Gram negative bacteria, fungus and yeast. The oxidative DNA cleavage studies of the complexes were performed using gel electrophoresis method. Cu(II) complexes have been found to promote DNA cleavage in presence of biological reductant such as ascorbate and oxidant like hydrogen peroxide.

A 4-node assumed-stress hybrid shell element with rotational degrees of freedom

NASA Technical Reports Server (NTRS)

Aminpour, Mohammad A.

1990-01-01

An assumed-stress hybrid/mixed 4-node quadrilateral shell element is introduced that alleviates most of the deficiencies associated with such elements. The formulation of the element is based on the assumed-stress hybrid/mixed method using the Hellinger-Reissner variational principle. The membrane part of the element has 12 degrees of freedom including rotational or drilling degrees of freedom at the nodes. The bending part of the element also has 12 degrees of freedom. The bending part of the element uses the Reissner-Mindlin plate theory which takes into account the transverse shear contributions. The element formulation is derived from an 8-node isoparametric element. This process is accomplished by assuming quadratic variations for both in-plane and out-of-plane displacement fields and linear variations for both in-plane and out-of-plane rotation fields along the edges of the element. In addition, the degrees of freedom at midside nodes are approximated in terms of the degrees of freedom at corner nodes. During this process the rotational degrees of freedom at the corner nodes enter into the formulation of the element. The stress field are expressed in the element natural-coordinate system such that the element remains invariant with respect to node numbering.

The Application of Deterministic Spectral Domain Method to the Analysis of Planar Circuit Discontinuities on Open Substrates

DTIC Science & Technology

1990-08-01

the spectral domain is extended to include the effects of two-dimensional, two-component current flow in planar transmission line discontinuities 6n...PROFESSOR: Tatsuo Itoh A deterministic formulation of the method of moments carried out in the spectral domain is extended to include the effects of...two-dimensional, two- component current flow in planar transmission line discontinuities on open substrates. The method includes the effects of space

Application of variational and Galerkin equations to linear and nonlinear finite element analysis

NASA Technical Reports Server (NTRS)

Yu, Y.-Y.

1974-01-01

The paper discusses the application of the variational equation to nonlinear finite element analysis. The problem of beam vibration with large deflection is considered. The variational equation is shown to be flexible in both the solution of a general problem and in the finite element formulation. Difficulties are shown to arise when Galerkin's equations are used in the consideration of the finite element formulation of two-dimensional linear elasticity and of the linear classical beam.

Spectroscopic and biological approach in the characterization of a novel 14-membered [N4] macrocyclic ligand and its Palladium(II), Platinum(II), Ruthenium(III) and Iridium(III) complexes

NASA Astrophysics Data System (ADS)

Rani, Soni; Kumar, Sumit; Chandra, Sulekh

2014-01-01

A novel, tetradentate nitrogen donor [N4] macrocyclic ligand, i.e. 3,5,14,16-tetramethyl-2,6,13,17-tetraazatricyclo[12,0,07-12] cosa-1(22),2,5,7,9,11,13,16,18,20-decaene(L), has been synthesized and characterized by elemental analyses, IR, Mass, and 1H NMR spectral studies. Complexes of Pd(II), Pt(II), Ru(III) and Ir(III) have been prepared and characterized by elemental analyses, molar conductance measurements, magnetic susceptibility measurements, IR, Mass, electronic spectral and thermal studies. On the basis of molar conductance the complexes may be formulated as [PdL]Cl2, [PtL]Cl2, [Ru(L)Cl2]Cl and [Ir(L)Cl2]Cl. The complexes are insoluble in most common solvents, including water, ethanol, carbon tetrachloride and acetonitrile, but soluble in DMF/DMSO. The value of magnetic moment indicates that all the complexes are diamagnetic except Ru(III) complex which shows magnetic moment corresponding to one unpaired electron. The magnetic moment of Ru(III) complex is 1.73 B.M. at room temperature. The antimicrobial activities of ligand and its complexes have been screened in vitro, as growth inhibiting agents. The antifungal and antibacterial screening were carried out using Food Poison and Disc Diffusion Method against plant pathogenic fungi and bacteria Alternaria porri, Fusarium oxysporum, Xanthomonas compestris and Pseudomonas aeruginosa respectively. The compounds were dissolved in DMSO to get the required solutions. The required medium used for these activities was PDA and nutrient agar.

A hybridized formulation for the weak Galerkin mixed finite element method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mu, Lin; Wang, Junping; Ye, Xiu

This paper presents a hybridized formulation for the weak Galerkin mixed finite element method (WG-MFEM) which was introduced and analyzed in Wang and Ye (2014) for second order elliptic equations. The WG-MFEM method was designed by using discontinuous piecewise polynomials on finite element partitions consisting of polygonal or polyhedral elements of arbitrary shape. The key to WG-MFEM is the use of a discrete weak divergence operator which is defined and computed by solving inexpensive problems locally on each element. The hybridized formulation of this paper leads to a significantly reduced system of linear equations involving only the unknowns arising frommore » the Lagrange multiplier in hybridization. Optimal-order error estimates are derived for the hybridized WG-MFEM approximations. In conclusion, some numerical results are reported to confirm the theory and a superconvergence for the Lagrange multiplier.« less

A hybridized formulation for the weak Galerkin mixed finite element method

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2016-01-14

This paper presents a hybridized formulation for the weak Galerkin mixed finite element method (WG-MFEM) which was introduced and analyzed in Wang and Ye (2014) for second order elliptic equations. The WG-MFEM method was designed by using discontinuous piecewise polynomials on finite element partitions consisting of polygonal or polyhedral elements of arbitrary shape. The key to WG-MFEM is the use of a discrete weak divergence operator which is defined and computed by solving inexpensive problems locally on each element. The hybridized formulation of this paper leads to a significantly reduced system of linear equations involving only the unknowns arising frommore » the Lagrange multiplier in hybridization. Optimal-order error estimates are derived for the hybridized WG-MFEM approximations. In conclusion, some numerical results are reported to confirm the theory and a superconvergence for the Lagrange multiplier.« less

Heat transfer model and finite element formulation for simulation of selective laser melting

NASA Astrophysics Data System (ADS)

Roy, Souvik; Juha, Mario; Shephard, Mark S.; Maniatty, Antoinette M.

2017-10-01

A novel approach and finite element formulation for modeling the melting, consolidation, and re-solidification process that occurs in selective laser melting additive manufacturing is presented. Two state variables are introduced to track the phase (melt/solid) and the degree of consolidation (powder/fully dense). The effect of the consolidation on the absorption of the laser energy into the material as it transforms from a porous powder to a dense melt is considered. A Lagrangian finite element formulation, which solves the governing equations on the unconsolidated reference configuration is derived, which naturally considers the effect of the changing geometry as the powder melts without needing to update the simulation domain. The finite element model is implemented into a general-purpose parallel finite element solver. Results are presented comparing to experimental results in the literature for a single laser track with good agreement. Predictions for a spiral laser pattern are also shown.

A finite element formulation for scattering from electrically large 2-dimensional structures

NASA Technical Reports Server (NTRS)

Ross, Daniel C.; Volakis, John L.

1992-01-01

A finite element formulation is given using the scattered field approach with a fictitious material absorber to truncate the mesh. The formulation includes the use of arbitrary approximation functions so that more accurate results can be achieved without any modification to the software. Additionally, non-polynomial approximation functions can be used, including complex approximation functions. The banded system that results is solved with an efficient sparse/banded iterative scheme and as a consequence, large structures can be analyzed. Results are given for simple cases to verify the formulation and also for large, complex geometries.

An arbitrary Lagrangian–Eulerian finite element formulation for a poroelasticity problem stemming from mixture theory

DOE PAGES

Costanzo, Francesco; Miller, Scott T.

2017-05-22

In this paper, a finite element formulation is developed for a poroelastic medium consisting of an incompressible hyperelastic skeleton saturated by an incompressible fluid. The governing equations stem from mixture theory and the application is motivated by the study of interstitial fluid flow in brain tissue. The formulation is based on the adoption of an arbitrary Lagrangian–Eulerian (ALE) perspective. We focus on a flow regime in which inertia forces are negligible. Finally, the stability and convergence of the formulation is discussed, and numerical results demonstrate agreement with the theory.

An arbitrary Lagrangian–Eulerian finite element formulation for a poroelasticity problem stemming from mixture theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Costanzo, Francesco; Miller, Scott T.

In this paper, a finite element formulation is developed for a poroelastic medium consisting of an incompressible hyperelastic skeleton saturated by an incompressible fluid. The governing equations stem from mixture theory and the application is motivated by the study of interstitial fluid flow in brain tissue. The formulation is based on the adoption of an arbitrary Lagrangian–Eulerian (ALE) perspective. We focus on a flow regime in which inertia forces are negligible. Finally, the stability and convergence of the formulation is discussed, and numerical results demonstrate agreement with the theory.

A Poisson equation formulation for pressure calculations in penalty finite element models for viscous incompressible flows

NASA Technical Reports Server (NTRS)

Sohn, J. L.; Heinrich, J. C.

1990-01-01

The calculation of pressures when the penalty-function approximation is used in finite-element solutions of laminar incompressible flows is addressed. A Poisson equation for the pressure is formulated that involves third derivatives of the velocity field. The second derivatives appearing in the weak formulation of the Poisson equation are calculated from the C0 velocity approximation using a least-squares method. The present scheme is shown to be efficient, free of spurious oscillations, and accurate. Examples of applications are given and compared with results obtained using mixed formulations.

Development of spectral analysis math models and software program and spectral analyzer, digital converter interface equipment design

NASA Technical Reports Server (NTRS)

Hayden, W. L.; Robinson, L. H.

1972-01-01

Spectral analyses of angle-modulated communication systems is studied by: (1) performing a literature survey of candidate power spectrum computational techniques, determining the computational requirements, and formulating a mathematical model satisfying these requirements; (2) implementing the model on UNIVAC 1230 digital computer as the Spectral Analysis Program (SAP); and (3) developing the hardware specifications for a data acquisition system which will acquire an input modulating signal for SAP. The SAP computational technique uses extended fast Fourier transform and represents a generalized approach for simple and complex modulating signals.

Membrane triangles with corner drilling freedoms. III - Implementation and performance evaluation

NASA Technical Reports Server (NTRS)

Felippa, Carlos A.; Alexander, Scott

1992-01-01

This paper completes a three-part series on the formulation of 3-node, 9-dof membrane triangles with corner drilling freedoms based on parametrized variational principles. The first four sections cover element implementation details including determination of optimal parameters and treatment of distributed loads. Then three elements of this type, labeled ALL, FF and EFF-ANDES, are tested on standard plane stress problems. ALL represents numerically integrated versions of Allman's 1988 triangle; FF is based on the free formulation triangle presented by Bergan and Felippa in 1985; and EFF-ANDES represent two different formulations of the optimal triangle derived in Parts I and II. The numerical studies indicate that the ALL, FF and EFF-ANDES elements are comparable in accuracy for elements of unitary aspect ratios. The ALL elements are found to stiffen rapidly in inplane bending for high aspect ratios, whereas the FF and EFF elements maintain accuracy. The EFF and ANDES implementations have a moderate edge in formation speed over the FF.

A proposed method for enhanced eigen-pair extraction using finite element methods: Theory and application

NASA Technical Reports Server (NTRS)

Jara-Almonte, J.; Mitchell, L. D.

1988-01-01

The paper covers two distinct parts: theory and application. The goal of this work was the reduction of model size with an increase in eigenvalue/vector accuracy. This method is ideal for the condensation of large truss- or beam-type structures. The theoretical approach involves the conversion of a continuum transfer matrix beam element into an 'Exact' dynamic stiffness element. This formulation is implemented in a finite element environment. This results in the need to solve a transcendental eigenvalue problem. Once the eigenvalue is determined the eigenvectors can be reconstructed with any desired spatial precision. No discretization limitations are imposed on the reconstruction. The results of such a combined finite element and transfer matrix formulation is a much smaller FEM eigenvalue problem. This formulation has the ability to extract higher eigenvalues as easily and as accurately as lower eigenvalues. Moreover, one can extract many more eigenvalues/vectors from the model than the number of degrees of freedom in the FEM formulation. Typically, the number of eigenvalues accurately extractable via the 'Exact' element method are at least 8 times the number of degrees of freedom. In contrast, the FEM usually extracts one accurate (within 5 percent) eigenvalue for each 3-4 degrees of freedom. The 'Exact' element results in a 20-30 improvement in the number of accurately extractable eigenvalues and eigenvectors.

Finite elements based on consistently assumed stresses and displacements

NASA Technical Reports Server (NTRS)

Pian, T. H. H.

1985-01-01

Finite element stiffness matrices are derived using an extended Hellinger-Reissner principle in which internal displacements are added to serve as Lagrange multipliers to introduce the equilibrium constraint in each element. In a consistent formulation the assumed stresses are initially unconstrained and complete polynomials and the total displacements are also complete such that the corresponding strains are complete in the same order as the stresses. Several examples indicate that resulting properties for elements constructed by this consistent formulation are ideal and are less sensitive to distortions of element geometries. The method has been used to find the optimal stress terms for plane elements, 3-D solids, axisymmetric solids, and plate bending elements.

Element free Galerkin formulation of composite beam with longitudinal slip

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahmad, Dzulkarnain; Mokhtaram, Mokhtazul Haizad; Badli, Mohd Iqbal

2015-05-15

Behaviour between two materials in composite beam is assumed partially interact when longitudinal slip at its interfacial surfaces is considered. Commonly analysed by the mesh-based formulation, this study used meshless formulation known as Element Free Galerkin (EFG) method in the beam partial interaction analysis, numerically. As meshless formulation implies that the problem domain is discretised only by nodes, the EFG method is based on Moving Least Square (MLS) approach for shape functions formulation with its weak form is developed using variational method. The essential boundary conditions are enforced by Langrange multipliers. The proposed EFG formulation gives comparable results, after beenmore » verified by analytical solution, thus signify its application in partial interaction problems. Based on numerical test results, the Cubic Spline and Quartic Spline weight functions yield better accuracy for the EFG formulation, compares to other proposed weight functions.« less

Hyper-spectral image segmentation using spectral clustering with covariance descriptors

NASA Astrophysics Data System (ADS)

Kursun, Olcay; Karabiber, Fethullah; Koc, Cemalettin; Bal, Abdullah

2009-02-01

Image segmentation is an important and difficult computer vision problem. Hyper-spectral images pose even more difficulty due to their high-dimensionality. Spectral clustering (SC) is a recently popular clustering/segmentation algorithm. In general, SC lifts the data to a high dimensional space, also known as the kernel trick, then derive eigenvectors in this new space, and finally using these new dimensions partition the data into clusters. We demonstrate that SC works efficiently when combined with covariance descriptors that can be used to assess pixelwise similarities rather than in the high-dimensional Euclidean space. We present the formulations and some preliminary results of the proposed hybrid image segmentation method for hyper-spectral images.

Rapid Elemental Analysis and Provenance Study of Blumea balsamifera DC Using Laser-Induced Breakdown Spectroscopy

PubMed Central

Liu, Xiaona; Zhang, Qiao; Wu, Zhisheng; Shi, Xinyuan; Zhao, Na; Qiao, Yanjiang

2015-01-01

Laser-induced breakdown spectroscopy (LIBS) was applied to perform a rapid elemental analysis and provenance study of Blumea balsamifera DC. Principal component analysis (PCA) and partial least squares discriminant analysis (PLS-DA) were implemented to exploit the multivariate nature of the LIBS data. Scores and loadings of computed principal components visually illustrated the differing spectral data. The PLS-DA algorithm showed good classification performance. The PLS-DA model using complete spectra as input variables had similar discrimination performance to using selected spectral lines as input variables. The down-selection of spectral lines was specifically focused on the major elements of B. balsamifera samples. Results indicated that LIBS could be used to rapidly analyze elements and to perform provenance study of B. balsamifera. PMID:25558999

Spectral diffraction efficiency characterization of broadband diffractive optical elements.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choi, Junoh; Cruz-Cabrera, Alvaro Augusto; Tanbakuchi, Anthony

Diffractive optical elements, with their thin profile and unique dispersion properties, have been studied and utilized in a number of optical systems, often yielding smaller and lighter systems. Despite the interest in and study of diffractive elements, the application has been limited to narrow spectral bands. This is due to the etch depths, which are optimized for optical path differences of only a single wavelength, consequently leading to rapid decline in efficiency as the working wavelength shifts away from the design wavelength. Various broadband diffractive design methodologies have recently been developed that improve spectral diffraction efficiency and expand the workingmore » bandwidth of diffractive elements. We have developed diffraction efficiency models and utilized the models to design, fabricate, and test two such extended bandwidth diffractive designs.« less

On the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach

NASA Astrophysics Data System (ADS)

Gerstmayr, Johannes; Irschik, Hans

2008-12-01

In finite element methods that are based on position and slope coordinates, a representation of axial and bending deformation by means of an elastic line approach has become popular. Such beam and plate formulations based on the so-called absolute nodal coordinate formulation have not yet been verified sufficiently enough with respect to analytical results or classical nonlinear rod theories. Examining the existing planar absolute nodal coordinate element, which uses a curvature proportional bending strain expression, it turns out that the deformation does not fully agree with the solution of the geometrically exact theory and, even more serious, the normal force is incorrect. A correction based on the classical ideas of the extensible elastica and geometrically exact theories is applied and a consistent strain energy and bending moment relations are derived. The strain energy of the solid finite element formulation of the absolute nodal coordinate beam is based on the St. Venant-Kirchhoff material: therefore, the strain energy is derived for the latter case and compared to classical nonlinear rod theories. The error in the original absolute nodal coordinate formulation is documented by numerical examples. The numerical example of a large deformation cantilever beam shows that the normal force is incorrect when using the previous approach, while a perfect agreement between the absolute nodal coordinate formulation and the extensible elastica can be gained when applying the proposed modifications. The numerical examples show a very good agreement of reference analytical and numerical solutions with the solutions of the proposed beam formulation for the case of large deformation pre-curved static and dynamic problems, including buckling and eigenvalue analysis. The resulting beam formulation does not employ rotational degrees of freedom and therefore has advantages compared to classical beam elements regarding energy-momentum conservation.

Analytic Simulation of the Elastic Waves Propagation in the Neighborhood of Fluid Filled Wells with Monopole Sources

NASA Astrophysics Data System (ADS)

Ávila-Carrera, R.; Sánchez-Sesma, F. J.; Spurlin, James H.; Valle-Molina, C.; Rodríguez-Castellanos, A.

2014-09-01

An analytic formulation to understand the scattering, diffraction and attenuation of elastic waves at the neighborhood of fluid filled wells is presented. An important, and not widely exploited, technique to carefully investigate the wave propagation in exploration wells is the logging of sonic waveforms. Fundamental decisions and production planning in petroleum reservoirs are made by interpretation of such recordings. Nowadays, geophysicists and engineers face problems related to the acquisition and interpretation under complex conditions associated with conducting open-hole measurements. A crucial problem that directly affects the response of sonic logs is the eccentricity of the measuring tool with respect to the center of the borehole. Even with the employment of centralizers, this simple variation, dramatically changes the physical conditions on the wave propagation around the well. Recent works in the numerical field reported advanced studies in modeling and simulation of acoustic wave propagation around wells, including complex heterogeneities and anisotropy. However, no analytical efforts have been made to formally understand the wireline sonic logging measurements acquired with borehole-eccentered tools. In this paper, the Graf's addition theorem was used to describe monopole sources in terms of solutions of the wave equation. The formulation was developed from the three-dimensional discrete wave-number method in the frequency domain. The cylindrical Bessel functions of the third kind and order zero were re-derived to obtain a simplified set of equations projected into a bi-dimensional plane-space for displacements and stresses. This new and condensed analytic formulation allows the straightforward calculation of all converted modes and their visualization in the time domain via Fourier synthesis. The main aim was to obtain spectral surfaces of transfer functions and synthetic seismograms that might be useful to understand the wave motion produced by the eccentricity of the source and explain in detail the new arising borehole propagation modes. Finally, time histories and amplitude spectra for relevant examples are presented and the validation of time traces using the spectral element method is reported.

Dispersion analysis of the Pn -Pn-1DG mixed finite element pair for atmospheric modelling

NASA Astrophysics Data System (ADS)

Melvin, Thomas

2018-02-01

Mixed finite element methods provide a generalisation of staggered grid finite difference methods with a framework to extend the method to high orders. The ability to generate a high order method is appealing for applications on the kind of quasi-uniform grids that are popular for atmospheric modelling, so that the method retains an acceptable level of accuracy even around special points in the grid. The dispersion properties of such schemes are important to study as they provide insight into the numerical adjustment to imbalance that is an important component in atmospheric modelling. This paper extends the recent analysis of the P2 - P1DG pair, that is a quadratic continuous and linear discontinuous finite element pair, to higher polynomial orders and also spectral element type pairs. In common with the previously studied element pair, and also with other schemes such as the spectral element and discontinuous Galerkin methods, increasing the polynomial order is found to provide a more accurate dispersion relation for the well resolved part of the spectrum but at the cost of a number of unphysical spectral gaps. The effects of these spectral gaps are investigated and shown to have a varying impact depending upon the width of the gap. Finally, the tensor product nature of the finite element spaces is exploited to extend the dispersion analysis into two-dimensions.

Application of self-organizing maps to the study of U-Zr-Ti-Nb distribution in sandstone-hosted uranium ores

NASA Astrophysics Data System (ADS)

Klus, Jakub; Pořízka, Pavel; Prochazka, David; Mikysek, Petr; Novotný, Jan; Novotný, Karel; Slobodník, Marek; Kaiser, Jozef

2017-05-01

This paper presents a novel approach for processing the spectral information obtained from high-resolution elemental mapping performed by means of Laser-Induced Breakdown Spectroscopy. The proposed methodology is aimed at the description of possible elemental associations within a heterogeneous sample. High-resolution elemental mapping provides a large number of measurements. Moreover, typical laser-induced plasma spectrum consists of several thousands of spectral variables. Analysis of heterogeneous samples, where valuable information is hidden in a limited fraction of sample mass, requires special treatment. The sample under study is a sandstone-hosted uranium ore that shows irregular distribution of ore elements such as zirconium, titanium, uranium and niobium. Presented processing methodology shows the way to reduce the dimensionality of data and retain the spectral information by utilizing self-organizing maps (SOM). The spectral information from SOM is processed further to detect either simultaneous or isolated presence of elements. Conclusions suggested by SOM are in good agreement with geological studies of mineralization phases performed at the deposit. Even deeper investigation of the SOM results enables discrimination of interesting measurements and reveals new possibilities in the visualization of chemical mapping information. Suggested approach improves the description of elemental associations in mineral phases, which is crucial for the mining industry.

Calibration-Free Laser-Induced Breakdown Spectroscopy (CF-LIBS) with Standard Reference Line for the Analysis of Stainless Steel.

PubMed

Fu, Hongbo; Dong, Fengzhong; Wang, Huadong; Jia, Junwei; Ni, Zhibo

2017-08-01

In this work, calibration-free laser-induced breakdown spectroscopy (CF-LIBS) is used to analyze a certified stainless steel sample. Due to self-absorption of the spectral lines from the major element Fe and the sparse lines of trace elements, it is usually not easy to construct the Boltzmann plots of all species. A standard reference line method is proposed here to solve this difficulty under the assumption of local thermodynamic equilibrium so that the same temperature value for all elements present into the plasma can be considered. Based on the concentration and rich spectral lines of Fe, the Stark broadening of Fe(I) 381.584 nm and Saha-Boltzmann plots of this element are used to calculate the electron density and the plasma temperature, respectively. In order to determine the plasma temperature accurately, which is seriously affected by self-absorption, a pre-selection procedure for eliminating those spectral lines with strong self-absorption is employed. Then, one spectral line of each element is selected to calculate its corresponding concentration. The results from the standard reference lines with and without self-absorption of Fe are compared. This method allows us to measure trace element content and effectively avoid the adverse effects due to self-absorption.

Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel

2004-01-01

A new, high-order, conservative, and efficient discontinuous spectral finite difference (SD) method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. Conventional unstructured finite-difference and finite-volume methods require data reconstruction based on the least-squares formulation using neighboring point or cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every point or cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In addition, the finite-difference method does not satisfy the integral conservation in general. By contrast, the DG and SV methods employ a local, universal reconstruction of a given order of accuracy in each cell in terms of internally defined conservative unknowns. Since the solution is discontinuous across cell boundaries, a Riemann solver is necessary to evaluate boundary flux terms and maintain conservation. In the DG method, a Galerkin finite-element method is employed to update the nodal unknowns within each cell. This requires the inversion of a mass matrix, and the use of quadratures of twice the order of accuracy of the reconstruction to evaluate the surface integrals and additional volume integrals for nonlinear flux functions. In the SV method, the integral conservation law is used to update volume averages over subcells defined by a geometrically similar partition of each grid cell. As the order of accuracy increases, the partitioning for 3D requires the introduction of a large number of parameters, whose optimization to achieve convergence becomes increasingly more difficult. Also, the number of interior facets required to subdivide non-planar faces, and the additional increase in the number of quadrature points for each facet, increases the computational cost greatly.

Rocket-Plume Spectroscopy Simulation for Hydrocarbon-Fueled Rocket Engines

NASA Technical Reports Server (NTRS)

Tejwani, Gopal D.

2010-01-01

The UV-Vis spectroscopic system for plume diagnostics monitors rocket engine health by using several analytical tools developed at Stennis Space Center (SSC), including the rocket plume spectroscopy simulation code (RPSSC), to identify and quantify the alloys from the metallic elements observed in engine plumes. Because the hydrocarbon-fueled rocket engine is likely to contain C2, CO, CH, CN, and NO in addition to OH and H2O, the relevant electronic bands of these molecules in the spectral range of 300 to 850 nm in the RPSSC have been included. SSC incorporated several enhancements and modifications to the original line-by-line spectral simulation computer program implemented for plume spectral data analysis and quantification in 1994. These changes made the program applicable to the Space Shuttle Main Engine (SSME) and the Diagnostic Testbed Facility Thruster (DTFT) exhaust plume spectral data. Modifications included updating the molecular and spectral parameters for OH, adding spectral parameter input files optimized for the 10 elements of interest in the spectral range from 320 to 430 nm and linking the output to graphing and analysis packages. Additionally, the ability to handle the non-uniform wavelength interval at which the spectral computations are made was added. This allowed a precise superposition of wavelengths at which the spectral measurements have been made with the wavelengths at which the spectral computations are done by using the line-by-line (LBL) code. To account for hydrocarbon combustion products in the plume, which might interfere with detection and quantification of metallic elements in the spectral region of 300 to 850 nm, the spectroscopic code has been enhanced to include the carbon-based combustion species of C2, CO, and CH. In addition, CN and NO have spectral bands in 300 to 850 nm and, while these molecules are not direct products of hydrocarbon-oxygen combustion systems, they can show up if nitrogen or a nitrogen compound is present as an impurity in the propellants and/or these can form in the boundary layer as a result of interaction of the hot plume with the atmosphere during the ground testing of engines. Ten additional electronic band systems of these five molecules have been included into the code. A comprehensive literature search was conducted to obtain the most accurate values for the molecular and the spectral parameters, including Franck-Cordon factors and electronic transition moments for all ten band systems. For each elemental transition in the RPSSC, six spectral parameters - Doppler broadened line width at half-height, pressure-broadened line width at half-height, electronic multiplicity of the upper state, electronic term energy of the upper state, Einstein transition probability coefficient, and the atomic line center - are required. Input files have been created for ten elements of Ni, Fe, Cr, Co, Cu, Ca, Mn, Al, Ag, and Pd, which retain only relatively moderate to strong transitions in 300 to 430 nm spectral range for each element. The number of transitions in the input files is 68 for Ni; 148 for Fe; 6 for Cr; 87 for Co; 1 for Ca; 3 for Mn; 2 each for Cu, Al, and Ag; and 11 for Pd.

A well-posed optimal spectral element approximation for the Stokes problem

NASA Technical Reports Server (NTRS)

Maday, Y.; Patera, A. T.; Ronquist, E. M.

1987-01-01

A method is proposed for the spectral element simulation of incompressible flow. This method constitutes in a well-posed optimal approximation of the steady Stokes problem with no spurious modes in the pressure. The resulting method is analyzed, and numerical results are presented for a model problem.

Energy-Based Design of Reconfigurable Micro Air Vehicle (MAV) Flight Structures

DTIC Science & Technology

2014-02-01

plate bending element derived herein. The purpose of the six degree-of-freedom model was to accommodate in-plane and out-of-plane aerodynamic loading...combinations. The FE model was validated and the MATLAB implementation was verified with classical beam and plate solutions. A compliance minimization...formulation was not found among the finite element literature. Therefore a formulation of such a bending element was derived using classic Kirchoff plate

Spectral element method for elastic and acoustic waves in frequency domain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shi, Linlin; Zhou, Yuanguo; Wang, Jia-Min

Numerical techniques in time domain are widespread in seismic and acoustic modeling. In some applications, however, frequency-domain techniques can be advantageous over the time-domain approach when narrow band results are desired, especially if multiple sources can be handled more conveniently in the frequency domain. Moreover, the medium attenuation effects can be more accurately and conveniently modeled in the frequency domain. In this paper, we present a spectral-element method (SEM) in frequency domain to simulate elastic and acoustic waves in anisotropic, heterogeneous, and lossy media. The SEM is based upon the finite-element framework and has exponential convergence because of the usemore » of GLL basis functions. The anisotropic perfectly matched layer is employed to truncate the boundary for unbounded problems. Compared with the conventional finite-element method, the number of unknowns in the SEM is significantly reduced, and higher order accuracy is obtained due to its spectral accuracy. To account for the acoustic-solid interaction, the domain decomposition method (DDM) based upon the discontinuous Galerkin spectral-element method is proposed. Numerical experiments show the proposed method can be an efficient alternative for accurate calculation of elastic and acoustic waves in frequency domain.« less

Numerical Modeling of 3D Seismic Wave Propagation around Yogyakarta, the Southern Part of Central Java, Indonesia, Using Spectral-Element Method on MPI-GPU Cluster

NASA Astrophysics Data System (ADS)

Sudarmaji; Rudianto, Indra; Eka Nurcahya, Budi

2018-04-01

A strong tectonic earthquake with a magnitude of 5.9 Richter scale has been occurred in Yogyakarta and Central Java on May 26, 2006. The earthquake has caused severe damage in Yogyakarta and the southern part of Central Java, Indonesia. The understanding of seismic response of earthquake among ground shaking and the level of building damage is important. We present numerical modeling of 3D seismic wave propagation around Yogyakarta and the southern part of Central Java using spectral-element method on MPI-GPU (Graphics Processing Unit) computer cluster to observe its seismic response due to the earthquake. The homogeneous 3D realistic model is generated with detailed topography surface. The influences of free surface topography and layer discontinuity of the 3D model among the seismic response are observed. The seismic wave field is discretized using spectral-element method. The spectral-element method is solved on a mesh of hexahedral elements that is adapted to the free surface topography and the internal discontinuity of the model. To increase the data processing capabilities, the simulation is performed on a GPU cluster with implementation of MPI (Message Passing Interface).

Numerical simulation using vorticity-vector potential formulation

NASA Technical Reports Server (NTRS)

Tokunaga, Hiroshi

1993-01-01

An accurate and efficient computational method is needed for three-dimensional incompressible viscous flows in engineering applications. On solving the turbulent shear flows directly or using the subgrid scale model, it is indispensable to resolve the small scale fluid motions as well as the large scale motions. From this point of view, the pseudo-spectral method is used so far as the computational method. However, the finite difference or the finite element methods are widely applied for computing the flow with practical importance since these methods are easily applied to the flows with complex geometric configurations. However, there exist several problems in applying the finite difference method to direct and large eddy simulations. Accuracy is one of most important problems. This point was already addressed by the present author on the direct simulations on the instability of the plane Poiseuille flow and also on the transition to turbulence. In order to obtain high efficiency, the multi-grid Poisson solver is combined with the higher-order, accurate finite difference method. The formulation method is also one of the most important problems in applying the finite difference method to the incompressible turbulent flows. The three-dimensional Navier-Stokes equations have been solved so far in the primitive variables formulation. One of the major difficulties of this method is the rigorous satisfaction of the equation of continuity. In general, the staggered grid is used for the satisfaction of the solenoidal condition for the velocity field at the wall boundary. However, the velocity field satisfies the equation of continuity automatically in the vorticity-vector potential formulation. From this point of view, the vorticity-vector potential method was extended to the generalized coordinate system. In the present article, we adopt the vorticity-vector potential formulation, the generalized coordinate system, and the 4th-order accurate difference method as the computational method. We present the computational method and apply the present method to computations of flows in a square cavity at large Reynolds number in order to investigate its effectiveness.

Fem Formulation for Heat and Mass Transfer in Porous Medium

NASA Astrophysics Data System (ADS)

Azeem; Soudagar, Manzoor Elahi M.; Salman Ahmed, N. J.; Anjum Badruddin, Irfan

2017-08-01

Heat and mass transfer in porous medium can be modelled using three partial differential equations namely, momentum equation, energy equation and mass diffusion. These three equations are coupled to each other by some common terms that turn the whole phenomenon into a complex problem with inter-dependable variables. The current article describes the finite element formulation of heat and mass transfer in porous medium with respect to Cartesian coordinates. The problem under study is formulated into algebraic form of equations by using Galerkin's method with the help of two-node linear triangular element having three nodes. The domain is meshed with smaller sized elements near the wall region and bigger size away from walls.

Compact Assumption Applied to the Monopole Term of Farassat's Formulations

NASA Technical Reports Server (NTRS)

Lopes, Leonard V.

2015-01-01

Farassat's formulations provide an acoustic prediction at an observer location provided a source surface, including motion and flow conditions. This paper presents compact forms for the monopole term of several of Farassat's formulations. When the physical surface is elongated, such as the case of a high aspect ratio rotorcraft blade, compact forms can be derived which are shown to be a function of the blade cross sectional area by reducing the computation from a surface integral to a line integral. The compact forms of all formulations are applied to two example cases: a short span wing with constant airfoil cross section moving at three forward flight Mach numbers and a rotor at two advance ratios. Acoustic pressure time histories and power spectral densities of monopole noise predicted from the compact forms of all the formulations at several observer positions are shown to compare very closely to the predictions from their non-compact counterparts. A study on the influence of rotorcraft blade shape on the high frequency portion of the power spectral density shows that there is a direct correlation between the aspect ratio of the airfoil and the error incurred by using the compact form. Finally, a prediction of pressure gradient from the non-compact and compact forms of the thickness term of Formulation G1A shows that using the compact forms results in a 99.6% improvement in computation time, which will be critical when noise is incorporated into a design environment.

A finite element-boundary integral method for cavities in a circular cylinder

NASA Technical Reports Server (NTRS)

Kempel, Leo C.; Volakis, John L.

1992-01-01

Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. However, due to a lack of rigorous mathematical models for conformal antenna arrays, antenna designers resort to measurement and planar antenna concepts for designing non-planar conformal antennas. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. We extend this formulation to conformal arrays on large metallic cylinders. In this report, we develop the mathematical formulation. In particular, we discuss the shape functions, the resulting finite elements and the boundary integral equations, and the solution of the conformal finite element-boundary integral system. Some validation results are presented and we further show how this formulation can be applied with minimal computational and memory resources.

Koopmans-Compliant Spectral Functionals for Extended Systems

NASA Astrophysics Data System (ADS)

Nguyen, Ngoc Linh; Colonna, Nicola; Ferretti, Andrea; Marzari, Nicola

2018-04-01

Koopmans-compliant functionals have been shown to provide accurate spectral properties for molecular systems; this accuracy is driven by the generalized linearization condition imposed on each charged excitation, i.e., on changing the occupation of any orbital in the system, while accounting for screening and relaxation from all other electrons. In this work, we discuss the theoretical formulation and the practical implementation of this formalism to the case of extended systems, where a third condition, the localization of Koopmans's orbitals, proves crucial to reach seamlessly the thermodynamic limit. We illustrate the formalism by first studying one-dimensional molecular systems of increasing length. Then, we consider the band gaps of 30 paradigmatic solid-state test cases, for which accurate experimental and computational results are available. The results are found to be comparable with the state of the art in many-body perturbation theory, notably using just a functional formulation for spectral properties and the generalized-gradient approximation for the exchange and correlation functional.

State-constrained booster trajectory solutions via finite elements and shooting

NASA Technical Reports Server (NTRS)

Bless, Robert R.; Hodges, Dewey H.; Seywald, Hans

1993-01-01

This paper presents an extension of a FEM formulation based on variational principles. A general formulation for handling internal boundary conditions and discontinuities in the state equations is presented, and the general formulation is modified for optimal control problems subject to state-variable inequality constraints. Solutions which only touch the state constraint and solutions which have a boundary arc of finite length are considered. Suitable shape and test functions are chosen for a FEM discretization. All element quadrature (equivalent to one-point Gaussian quadrature over each element) may be done in closed form. The final form of the algebraic equations is then derived. A simple state-constrained problem is solved. Then, for a practical application of the use of the FEM formulation, a launch vehicle subject to a dynamic pressure constraint (a first-order state inequality constraint) is solved. The results presented for the launch-vehicle trajectory have some interesting features, including a touch-point solution.

A finite element-boundary integral formulation for scattering by three-dimensional cavity-backed apertures

NASA Technical Reports Server (NTRS)

Jin, Jian-Ming; Volakis, John L.

1990-01-01

A numerical technique is proposed for the electromagnetic characterization of the scattering by a three-dimensional cavity-backed aperture in an infinite ground plane. The technique combines the finite element and boundary integral methods to formulate a system of equations for the solution of the aperture fields and those inside the cavity. Specifically, the finite element method is employed to formulate the fields in the cavity region and the boundary integral approach is used in conjunction with the equivalence principle to represent the fields above the ground plane. Unlike traditional approaches, the proposed technique does not require knowledge of the cavity's Green's function and is, therefore, applicable to arbitrary shape depressions and material fillings. Furthermore, the proposed formulation leads to a system having a partly full and partly sparse as well as symmetric and banded matrix which can be solved efficiently using special algorithms.

On the stability analysis of hyperelastic boundary value problems using three- and two-field mixed finite element formulations

NASA Astrophysics Data System (ADS)

Schröder, Jörg; Viebahn, Nils; Wriggers, Peter; Auricchio, Ferdinando; Steeger, Karl

2017-09-01

In this work we investigate different mixed finite element formulations for the detection of critical loads for the possible occurrence of bifurcation and limit points. In detail, three- and two-field formulations for incompressible and quasi-incompressible materials are analyzed. In order to apply various penalty functions for the volume dilatation in displacement/pressure mixed elements we propose a new consistent scheme capturing the non linearities of the penalty constraints. It is shown that for all mixed formulations, which can be reduced to a generalized displacement scheme, a straight forward stability analysis is possible. However, problems based on the classical saddle-point structure require a different analyses based on the change of the signature of the underlying matrix system. The basis of these investigations is the work from Auricchio et al. (Comput Methods Appl Mech Eng 194:1075-1092, 2005, Comput Mech 52:1153-1167, 2013).

Numerical Simulation of Delamination Growth in Composite Materials

NASA Technical Reports Server (NTRS)

Camanho, P. P.; Davila, C. G.; Ambur, D. R.

2001-01-01

The use of decohesion elements for the simulation of delamination in composite materials is reviewed. The test methods available to measure the interfacial fracture toughness used in the formulation of decohesion elements are described initially. After a brief presentation of the virtual crack closure technique, the technique most widely used to simulate delamination growth, the formulation of interfacial decohesion elements is described. Problems related with decohesion element constitutive equations, mixed-mode crack growth, element numerical integration and solution procedures are discussed. Based on these investigations, it is concluded that the use of interfacial decohesion elements is a promising technique that avoids the need for a pre-existing crack and pre-defined crack paths, and that these elements can be used to simulate both delamination onset and growth.

Theoretical study on electronic excitation spectra: A matrix form of numerical algorithm for spectral shift

NASA Astrophysics Data System (ADS)

Ming, Mei-Jun; Xu, Long-Kun; Wang, Fan; Bi, Ting-Jun; Li, Xiang-Yuan

2017-07-01

In this work, a matrix form of numerical algorithm for spectral shift is presented based on the novel nonequilibrium solvation model that is established by introducing the constrained equilibrium manipulation. This form is convenient for the development of codes for numerical solution. By means of the integral equation formulation polarizable continuum model (IEF-PCM), a subroutine has been implemented to compute spectral shift numerically. Here, the spectral shifts of absorption spectra for several popular chromophores, N,N-diethyl-p-nitroaniline (DEPNA), methylenecyclopropene (MCP), acrolein (ACL) and p-nitroaniline (PNA) were investigated in different solvents with various polarities. The computed spectral shifts can explain the available experimental findings reasonably. Discussions were made on the contributions of solute geometry distortion, electrostatic polarization and other non-electrostatic interactions to spectral shift.

Slitless Solar Spectroscopy

NASA Technical Reports Server (NTRS)

Davila, Joseph M.; Jones, Sahela

2011-01-01

Spectrographs have traditionally suffered from the inability to obtain line intensities, widths, and Doppler shifts over large spatial regions of the Sun quickly because of the narrow instantaneous field of view. This has limited the spectroscopic analysis of rapidly varying solar features like, flares, CME eruptions, coronal jets, and reconnection regions. Imagers have provided high time resolution images of the full Sun with limited spectral resolution. In this paper we present recent advances in deconvolving spectrally dispersed images obtained through broad slits. We use this new theoretical formulation to examine the effectiveness of various potential observing scenarios, spatial and spectral resolutions, signal to noise ratio, and other instrument characteristics. This information will lay the foundation for a new generation of spectral imagers optimized for slitless spectral operation, while retaining the ability to obtain spectral information in transient solar events.

Spectral K-edge subtraction imaging

NASA Astrophysics Data System (ADS)

Zhu, Y.; Samadi, N.; Martinson, M.; Bassey, B.; Wei, Z.; Belev, G.; Chapman, D.

2014-05-01

We describe a spectral x-ray transmission method to provide images of independent material components of an object using a synchrotron x-ray source. The imaging system and process is similar to K-edge subtraction (KES) imaging where two imaging energies are prepared above and below the K-absorption edge of a contrast element and a quantifiable image of the contrast element and a water equivalent image are obtained. The spectral method, termed ‘spectral-KES’ employs a continuous spectrum encompassing an absorption edge of an element within the object. The spectrum is prepared by a bent Laue monochromator with good focal and energy dispersive properties. The monochromator focuses the spectral beam at the object location, which then diverges onto an area detector such that one dimension in the detector is an energy axis. A least-squares method is used to interpret the transmitted spectral data with fits to either measured and/or calculated absorption of the contrast and matrix material-water. The spectral-KES system is very simple to implement and is comprised of a bent Laue monochromator, a stage for sample manipulation for projection and computed tomography imaging, and a pixelated area detector. The imaging system and examples of its applications to biological imaging are presented. The system is particularly well suited for a synchrotron bend magnet beamline with white beam access.

Molecular modelling, spectroscopic characterization and biological studies of tetraazamacrocyclic metal complexes

NASA Astrophysics Data System (ADS)

Rathi, Parveen; Sharma, Kavita; Singh, Dharam Pal

2014-09-01

Macrocyclic complexes of the type [MLX]X2; where L is (C30H28N4), a macrocyclic ligand, M = Cr(III) and Fe(III) and X = Cl-, CH3COO- or NO3-, have been synthesized by template condensation reaction of 1,8-diaminonaphthalene and acetylacetone in the presence of trivalent metal salts in a methanolic medium. The complexes have been formulated as [MLX]X2 due to 1:2 electrolytic nature of these complexes. The complexes have been characterized with the help of elemental analyses, molar conductance measurements, magnetic susceptibility measurements, electronic, infrared, far infrared, Mass spectral studies and molecular modelling. Molecular weight of these complexes indicates their monomeric nature. On the basis of all these studies, a five coordinated square pyramidal geometry has been proposed for all these complexes. These metal complexes have also been screened for their in vitro antimicrobial activities.

Visualization of Discontinuous Galerkin Based High-Order Methods

DTIC Science & Technology

2015-08-19

function and the reference- to physical- space mapping functions. This formulation can be used to measure the quality of a high-order element and also for...to physical- space mapping functions. This formulation can be used to measure the quality of a high-order element and also for AMR. We find that the

Design sensitivity analysis of boundary element substructures

NASA Technical Reports Server (NTRS)

Kane, James H.; Saigal, Sunil; Gallagher, Richard H.

1989-01-01

The ability to reduce or condense a three-dimensional model exactly, and then iterate on this reduced size model representing the parts of the design that are allowed to change in an optimization loop is discussed. The discussion presents the results obtained from an ongoing research effort to exploit the concept of substructuring within the structural shape optimization context using a Boundary Element Analysis (BEA) formulation. The first part contains a formulation for the exact condensation of portions of the overall boundary element model designated as substructures. The use of reduced boundary element models in shape optimization requires that structural sensitivity analysis can be performed. A reduced sensitivity analysis formulation is then presented that allows for the calculation of structural response sensitivities of both the substructured (reduced) and unsubstructured parts of the model. It is shown that this approach produces significant computational economy in the design sensitivity analysis and reanalysis process by facilitating the block triangular factorization and forward reduction and backward substitution of smaller matrices. The implementatior of this formulation is discussed and timings and accuracies of representative test cases presented.

Formulation of image quality prediction criteria for the Viking lander camera

NASA Technical Reports Server (NTRS)

Huck, F. O.; Jobson, D. J.; Taylor, E. J.; Wall, S. D.

1973-01-01

Image quality criteria are defined and mathematically formulated for the prediction computer program which is to be developed for the Viking lander imaging experiment. The general objective of broad-band (black and white) imagery to resolve small spatial details and slopes is formulated as the detectability of a right-circular cone with surface properties of the surrounding terrain. The general objective of narrow-band (color and near-infrared) imagery to observe spectral characteristics if formulated as the minimum detectable albedo variation. The general goal to encompass, but not exceed, the range of the scene radiance distribution within single, commandable, camera dynamic range setting is also considered.

Study of multi-dimensional radiative energy transfer in molecular gases

NASA Technical Reports Server (NTRS)

Liu, Jiwen; Tiwari, S. N.

1993-01-01

The Monte Carlo method (MCM) is applied to analyze radiative heat transfer in nongray gases. The nongray model employed is based on the statistical arrow band model with an exponential-tailed inverse intensity distribution. Consideration of spectral correlation results in some distinguishing features of the Monte Carlo formulations. Validation of the Monte Carlo formulations has been conducted by comparing results of this method with other solutions. Extension of a one-dimensional problem to a multi-dimensional problem requires some special treatments in the Monte Carlo analysis. Use of different assumptions results in different sets of Monte Carlo formulations. The nongray narrow band formulations provide the most accurate results.

Consistent linearization of the element-independent corotational formulation for the structural analysis of general shells

NASA Technical Reports Server (NTRS)

Rankin, C. C.

1988-01-01

A consistent linearization is provided for the element-dependent corotational formulation, providing the proper first and second variation of the strain energy. As a result, the warping problem that has plagued flat elements has been overcome, with beneficial effects carried over to linear solutions. True Newton quadratic convergence has been restored to the Structural Analysis of General Shells (STAGS) code for conservative loading using the full corotational implementation. Some implications for general finite element analysis are discussed, including what effect the automatic frame invariance provided by this work might have on the development of new, improved elements.

Visible and infrared linear detector arrays for the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)

NASA Technical Reports Server (NTRS)

Bailey, Gary C.

1987-01-01

The Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) instrument uses four separate focal plane assemblies consisting of line array detectors that are multiplexed to a common J-FET preamp using a FET switch multiplexing (MUX) technique. A 32-element silicon line array covers the spectral range from 0.41 to 0.70 microns. Three additional 64-element indium antimonide (InSb) line arrays cover the spectral range from 0.68 to 2.45 microns. The spectral sampling interval per detector element is nominally 9.8 nm, giving a total of 224 spectral channels. All focal planes operate at liquid nitrogen temperature and are housed in separate dewars. Electrical performance characteristics include a read noise of less than 1000 e(-) in all channels, response and dark nonuniformity of 5 percent peak to peak, and quantum efficiency of greater than 60 percent.

The spectral cell method in nonlinear earthquake modeling

NASA Astrophysics Data System (ADS)

Giraldo, Daniel; Restrepo, Doriam

2017-12-01

This study examines the applicability of the spectral cell method (SCM) to compute the nonlinear earthquake response of complex basins. SCM combines fictitious-domain concepts with the spectral-version of the finite element method to solve the wave equations in heterogeneous geophysical domains. Nonlinear behavior is considered by implementing the Mohr-Coulomb and Drucker-Prager yielding criteria. We illustrate the performance of SCM with numerical examples of nonlinear basins exhibiting physically and computationally challenging conditions. The numerical experiments are benchmarked with results from overkill solutions, and using MIDAS GTS NX, a finite element software for geotechnical applications. Our findings show good agreement between the two sets of results. Traditional spectral elements implementations allow points per wavelength as low as PPW = 4.5 for high-order polynomials. Our findings show that in the presence of nonlinearity, high-order polynomials (p ≥ 3) require mesh resolutions above of PPW ≥ 10 to ensure displacement errors below 10%.

Application of a boundary element method to the study of dynamical torsion of beams

NASA Technical Reports Server (NTRS)

Czekajski, C.; Laroze, S.; Gay, D.

1982-01-01

During dynamic torsion of beam elements, consideration of nonuniform warping effects involves a more general technical formulation then that of Saint-Venant. Nonclassical torsion constants appear in addition to the well known torsional rigidity. The adaptation of the boundary integral element method to the calculation of these constants for general section shapes is described. The suitability of the formulation is investigated with some examples of thick as well as thin walled cross sections.

Extension and Validation of a Hybrid Particle-Finite Element Method for Hypervelocity Impact Simulation. Chapter 2

NASA Technical Reports Server (NTRS)

Fahrenthold, Eric P.; Shivarama, Ravishankar

2004-01-01

The hybrid particle-finite element method of Fahrenthold and Horban, developed for the simulation of hypervelocity impact problems, has been extended to include new formulations of the particle-element kinematics, additional constitutive models, and an improved numerical implementation. The extended formulation has been validated in three dimensional simulations of published impact experiments. The test cases demonstrate good agreement with experiment, good parallel speedup, and numerical convergence of the simulation results.

A Spectral Element Ocean Model on the Cray T3D: the interannual variability of the Mediterranean Sea general circulation

NASA Astrophysics Data System (ADS)

Molcard, A. J.; Pinardi, N.; Ansaloni, R.

A new numerical model, SEOM (Spectral Element Ocean Model, (Iskandarani et al, 1994)), has been implemented in the Mediterranean Sea. Spectral element methods combine the geometric flexibility of finite element techniques with the rapid convergence rate of spectral schemes. The current version solves the shallow water equations with a fifth (or sixth) order accuracy spectral scheme and about 50.000 nodes. The domain decomposition philosophy makes it possible to exploit the power of parallel machines. The original MIMD master/slave version of SEOM, written in F90 and PVM, has been ported to the Cray T3D. When critical for performance, Cray specific high-performance one-sided communication routines (SHMEM) have been adopted to fully exploit the Cray T3D interprocessor network. Tests performed with highly unstructured and irregular grid, on up to 128 processors, show an almost linear scalability even with unoptimized domain decomposition techniques. Results from various case studies on the Mediterranean Sea are shown, involving realistic coastline geometry, and monthly mean 1000mb winds from the ECMWF's atmospheric model operational analysis from the period January 1987 to December 1994. The simulation results show that variability in the wind forcing considerably affect the circulation dynamics of the Mediterranean Sea.

Rigid body formulation in a finite element context with contact interaction

NASA Astrophysics Data System (ADS)

Refachinho de Campos, Paulo R.; Gay Neto, Alfredo

2018-03-01

The present work proposes a formulation to employ rigid bodies together with flexible bodies in the context of a nonlinear finite element solver, with contact interactions. Inertial contributions due to distribution of mass of a rigid body are fully developed, considering a general pole position associated with a single node, representing a rigid body element. Additionally, a mechanical constraint is proposed to connect a rigid region composed by several nodes, which is useful for linking rigid/flexible bodies in a finite element environment. Rodrigues rotation parameters are used to describe finite rotations, by an updated Lagrangian description. In addition, the contact formulation entitled master-surface to master-surface is employed in conjunction with the rigid body element and flexible bodies, aiming to consider their interaction in a rigid-flexible multibody environment. New surface parameterizations are presented to establish contact pairs, permitting pointwise interaction in a frictional scenario. Numerical examples are provided to show robustness and applicability of the methods.

The MHOST finite element program: 3-D inelastic analysis methods for hot section components. Volume 1: Theoretical manual

NASA Technical Reports Server (NTRS)

Nakazawa, Shohei

1991-01-01

Formulations and algorithms implemented in the MHOST finite element program are discussed. The code uses a novel concept of the mixed iterative solution technique for the efficient 3-D computations of turbine engine hot section components. The general framework of variational formulation and solution algorithms are discussed which were derived from the mixed three field Hu-Washizu principle. This formulation enables the use of nodal interpolation for coordinates, displacements, strains, and stresses. Algorithmic description of the mixed iterative method includes variations for the quasi static, transient dynamic and buckling analyses. The global-local analysis procedure referred to as the subelement refinement is developed in the framework of the mixed iterative solution, of which the detail is presented. The numerically integrated isoparametric elements implemented in the framework is discussed. Methods to filter certain parts of strain and project the element discontinuous quantities to the nodes are developed for a family of linear elements. Integration algorithms are described for linear and nonlinear equations included in MHOST program.

Primal-mixed formulations for reaction-diffusion systems on deforming domains

NASA Astrophysics Data System (ADS)

Ruiz-Baier, Ricardo

2015-10-01

We propose a finite element formulation for a coupled elasticity-reaction-diffusion system written in a fully Lagrangian form and governing the spatio-temporal interaction of species inside an elastic, or hyper-elastic body. A primal weak formulation is the baseline model for the reaction-diffusion system written in the deformed domain, and a finite element method with piecewise linear approximations is employed for its spatial discretization. On the other hand, the strain is introduced as mixed variable in the equations of elastodynamics, which in turn acts as coupling field needed to update the diffusion tensor of the modified reaction-diffusion system written in a deformed domain. The discrete mechanical problem yields a mixed finite element scheme based on row-wise Raviart-Thomas elements for stresses, Brezzi-Douglas-Marini elements for displacements, and piecewise constant pressure approximations. The application of the present framework in the study of several coupled biological systems on deforming geometries in two and three spatial dimensions is discussed, and some illustrative examples are provided and extensively analyzed.

Non-conforming finite-element formulation for cardiac electrophysiology: an effective approach to reduce the computation time of heart simulations without compromising accuracy

NASA Astrophysics Data System (ADS)

Hurtado, Daniel E.; Rojas, Guillermo

2018-04-01

Computer simulations constitute a powerful tool for studying the electrical activity of the human heart, but computational effort remains prohibitively high. In order to recover accurate conduction velocities and wavefront shapes, the mesh size in linear element (Q1) formulations cannot exceed 0.1 mm. Here we propose a novel non-conforming finite-element formulation for the non-linear cardiac electrophysiology problem that results in accurate wavefront shapes and lower mesh-dependance in the conduction velocity, while retaining the same number of global degrees of freedom as Q1 formulations. As a result, coarser discretizations of cardiac domains can be employed in simulations without significant loss of accuracy, thus reducing the overall computational effort. We demonstrate the applicability of our formulation in biventricular simulations using a coarse mesh size of ˜ 1 mm, and show that the activation wave pattern closely follows that obtained in fine-mesh simulations at a fraction of the computation time, thus improving the accuracy-efficiency trade-off of cardiac simulations.

Finite Element Analysis of Active and Sensory Thermopiezoelectric Composite Materials. Degree awarded by Northwestern Univ., Dec. 2000

NASA Technical Reports Server (NTRS)

Lee, Ho-Jun

2001-01-01

Analytical formulations are developed to account for the coupled mechanical, electrical, and thermal response of piezoelectric composite materials. The coupled response is captured at the material level through the thermopiezoelectric constitutive equations and leads to the inherent capability to model both the sensory and active responses of piezoelectric materials. A layerwise laminate theory is incorporated to provide more accurate analysis of the displacements, strains, stresses, electric fields, and thermal fields through-the-thickness. Thermal effects which arise from coefficient of thermal expansion mismatch, pyroelectric effects, and temperature dependent material properties are explicitly accounted for in the formulation. Corresponding finite element formulations are developed for piezoelectric beam, plate, and shell elements to provide a more generalized capability for the analysis of arbitrary piezoelectric composite structures. The accuracy of the current formulation is verified with comparisons from published experimental data and other analytical models. Additional numerical studies are also conducted to demonstrate additional capabilities of the formulation to represent the sensory and active behaviors. A future plan of experimental studies is provided to characterize the high temperature dynamic response of piezoelectric composite materials.

Dispersion characteristics of plasmonic waveguides for THz waves

NASA Astrophysics Data System (ADS)

Markides, Christos; Viphavakit, Charusluk; Themistos, Christos; Komodromos, Michael; Kalli, Kyriacos; Quadir, Anita; Rahman, Azizur

2013-05-01

Today there is an increasing surge in Surface Plasmon based research and recent studies have shown that a wide range of plasmon-based optical elements and techniques have led to the development of a variety of active switches, passive waveguides, biosensors, lithography masks, to name just a few. The Terahertz (THz) frequency region of the electromagnetic spectrum is located between the traditional microwave spectrum and the optical frequencies, and offers a significant scientific and technological potential in many fields, such as in sensing, in imaging and in spectroscopy. Waveguiding in this intermediate spectral region is a major challenge. Amongst the various THz waveguides suggested, the metal-clad waveguides supporting surface plasmon modes waves and specifically hollow core structures, coated with insulating material are showing the greatest promise as low-loss waveguides for their use in active components and as well as passive waveguides. The H-field finite element method (FEM) based full-vector formulation is used to study the vectorial modal field properties and the complex propagation characteristics of Surface Plasmon modes of a hollow-core dielectric coated rectangular waveguide structure. Additionally, the finite difference time domain (FDTD) method is used to estimate the dispersion parameters and the propagation loss of the rectangular waveguide.

High-precision solution to the moving load problem using an improved spectral element method

NASA Astrophysics Data System (ADS)

Wen, Shu-Rui; Wu, Zhi-Jing; Lu, Nian-Li

2018-02-01

In this paper, the spectral element method (SEM) is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means that the element number and the degree of freedom can be reduced significantly. Based on the variational method and the Laplace transform theory, the spectral stiffness matrix and the equivalent nodal force of the beam-column element are established. The static Green function is employed to deduce the improved function. The proposed method is applied to two typical engineering practices—the one-span bridge and the horizontal jib of the tower crane. The results have revealed the following. First, the new method can yield extremely high-precision results of the dynamic deflection, the bending moment and the shear force in the moving load problem. In most cases, the relative errors are smaller than 1%. Second, by comparing with the finite element method, one can obtain the highly accurate results using the improved SEM with smaller element numbers. Moreover, the method can be widely used for statically determinate as well as statically indeterminate structures. Third, the dynamic deflection of the twin-lift jib decreases with the increase in the moving load speed, whereas the curvature of the deflection increases. Finally, the dynamic deflection, the bending moment and the shear force of the jib will all increase as the magnitude of the moving load increases.

Mixed mimetic spectral element method for Stokes flow: A pointwise divergence-free solution

NASA Astrophysics Data System (ADS)

Kreeft, Jasper; Gerritsma, Marc

2013-05-01

In this paper we apply the recently developed mimetic discretization method to the mixed formulation of the Stokes problem in terms of vorticity, velocity and pressure. The mimetic discretization presented in this paper and in Kreeft et al. [51] is a higher-order method for curvilinear quadrilaterals and hexahedrals. Fundamental is the underlying structure of oriented geometric objects, the relation between these objects through the boundary operator and how this defines the exterior derivative, representing the grad, curl and div, through the generalized Stokes theorem. The mimetic method presented here uses the language of differential k-forms with k-cochains as their discrete counterpart, and the relations between them in terms of the mimetic operators: reduction, reconstruction and projection. The reconstruction consists of the recently developed mimetic spectral interpolation functions. The most important result of the mimetic framework is the commutation between differentiation at the continuous level with that on the finite dimensional and discrete level. As a result operators like gradient, curl and divergence are discretized exactly. For Stokes flow, this implies a pointwise divergence-free solution. This is confirmed using a set of test cases on both Cartesian and curvilinear meshes. It will be shown that the method converges optimally for all admissible boundary conditions.

A geometric nonlinear degenerated shell element using a mixed formulation with independently assumed strain fields. Final Report; Ph.D. Thesis, 1989

NASA Technical Reports Server (NTRS)

Graf, Wiley E.

1991-01-01

A mixed formulation is chosen to overcome deficiencies of the standard displacement-based shell model. Element development is traced from the incremental variational principle on through to the final set of equilibrium equations. Particular attention is paid to developing specific guidelines for selecting the optimal set of strain parameters. A discussion of constraint index concepts and their predictive capability related to locking is included. Performance characteristics of the elements are assessed in a wide variety of linear and nonlinear plate/shell problems. Despite limiting the study to geometric nonlinear analysis, a substantial amount of additional insight concerning the finite element modeling of thin plate/shell structures is provided. For example, in nonlinear analysis, given the same mesh and load step size, mixed elements converge in fewer iterations than equivalent displacement-based models. It is also demonstrated that, in mixed formulations, lower order elements are preferred. Additionally, meshes used to obtain accurate linear solutions do not necessarily converge to the correct nonlinear solution. Finally, a new form of locking was identified associated with employing elements designed for biaxial bending in uniaxial bending applications.

On 3D inelastic analysis methods for hot section components

NASA Technical Reports Server (NTRS)

Mcknight, R. L.; Chen, P. C.; Dame, L. T.; Holt, R. V.; Huang, H.; Hartle, M.; Gellin, S.; Allen, D. H.; Haisler, W. E.

1986-01-01

Accomplishments are described for the 2-year program, to develop advanced 3-D inelastic structural stress analysis methods and solution strategies for more accurate and cost effective analysis of combustors, turbine blades and vanes. The approach was to develop a matrix of formulation elements and constitutive models. Three constitutive models were developed in conjunction with optimized iterating techniques, accelerators, and convergence criteria within a framework of dynamic time incrementing. Three formulations models were developed; an eight-noded mid-surface shell element, a nine-noded mid-surface shell element and a twenty-noded isoparametric solid element. A separate computer program was developed for each combination of constitutive model-formulation model. Each program provides a functional stand alone capability for performing cyclic nonlinear structural analysis. In addition, the analysis capabilities incorporated into each program can be abstracted in subroutine form for incorporation into other codes or to form new combinations.

The 3D inelastic analysis methods for hot section components

NASA Technical Reports Server (NTRS)

Mcknight, R. L.; Maffeo, R. J.; Tipton, M. T.; Weber, G.

1992-01-01

A two-year program to develop advanced 3D inelastic structural stress analysis methods and solution strategies for more accurate and cost effective analysis of combustors, turbine blades, and vanes is described. The approach was to develop a matrix of formulation elements and constitutive models. Three constitutive models were developed in conjunction with optimized iterating techniques, accelerators, and convergence criteria within a framework of dynamic time incrementing. Three formulation models were developed: an eight-noded midsurface shell element; a nine-noded midsurface shell element; and a twenty-noded isoparametric solid element. A separate computer program has been developed for each combination of constitutive model-formulation model. Each program provides a functional stand alone capability for performing cyclic nonlinear structural analysis. In addition, the analysis capabilities incorporated into each program can be abstracted in subroutine form for incorporation into other codes or to form new combinations.

Probabilistic finite elements for transient analysis in nonlinear continua

NASA Technical Reports Server (NTRS)

Liu, W. K.; Belytschko, T.; Mani, A.

1985-01-01

The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.

A boundary integral method for numerical computation of radar cross section of 3D targets using hybrid BEM/FEM with edge elements

NASA Astrophysics Data System (ADS)

Dodig, H.

2017-11-01

This contribution presents the boundary integral formulation for numerical computation of time-harmonic radar cross section for 3D targets. Method relies on hybrid edge element BEM/FEM to compute near field edge element coefficients that are associated with near electric and magnetic fields at the boundary of the computational domain. Special boundary integral formulation is presented that computes radar cross section directly from these edge element coefficients. Consequently, there is no need for near-to-far field transformation (NTFFT) which is common step in RCS computations. By the end of the paper it is demonstrated that the formulation yields accurate results for canonical models such as spheres, cubes, cones and pyramids. Method has demonstrated accuracy even in the case of dielectrically coated PEC sphere at interior resonance frequency which is common problem for computational electromagnetic codes.

A finite element-boundary integral method for conformal antenna arrays on a circular cylinder

NASA Technical Reports Server (NTRS)

Kempel, Leo C.; Volakis, John L.; Woo, Alex C.; Yu, C. Long

1992-01-01

Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. In the past, antenna designers have had to resort to expensive measurements in order to develop a conformal array design. This is due to the lack of rigorous mathematical models for conformal antenna arrays, and as a result the design of conformal arrays is primarily based on planar antenna design concepts. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. Herewith we shall extend this formulation for conformal arrays on large metallic cylinders. In this we develop the mathematical formulation. In particular we discuss the finite element equations, the shape elements, and the boundary integral evaluation, and it is shown how this formulation can be applied with minimal computation and memory requirements. The implementation shall be discussed in a later report.

A finite element-boundary integral method for conformal antenna arrays on a circular cylinder

NASA Technical Reports Server (NTRS)

Kempel, Leo C.; Volakis, John L.

1992-01-01

Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. In the past, antenna designers have had to resort to expensive measurements in order to develop a conformal array design. This was due to the lack of rigorous mathematical models for conformal antenna arrays. As a result, the design of conformal arrays was primarily based on planar antenna design concepts. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. We are extending this formulation to conformal arrays on large metallic cylinders. In doing so, we will develop a mathematical formulation. In particular, we discuss the finite element equations, the shape elements, and the boundary integral evaluation. It is shown how this formulation can be applied with minimal computation and memory requirements.

A reconstruction theorem for Connes-Landi deformations of commutative spectral triples

NASA Astrophysics Data System (ADS)

Ćaćić, Branimir

2015-12-01

We formulate and prove an extension of Connes's reconstruction theorem for commutative spectral triples to so-called Connes-Landi or isospectral deformations of commutative spectral triples along the action of a compact Abelian Lie group G, also known as toric noncommutative manifolds. In particular, we propose an abstract definition for such spectral triples, where noncommutativity is entirely governed by a deformation parameter sitting in the second group cohomology of the Pontryagin dual of G, and then show that such spectral triples are well-behaved under further Connes-Landi deformation, thereby allowing for both quantisation from and dequantisation to G-equivariant abstract commutative spectral triples. We then use a refinement of the Connes-Dubois-Violette splitting homomorphism to conclude that suitable Connes-Landi deformations of commutative spectral triples by a rational deformation parameter are almost-commutative in the general, topologically non-trivial sense.

Comparison of SP-LIBS and DP-LIBS on metal and non-metal testing based on LIBS

NASA Astrophysics Data System (ADS)

Lin, Xiaomei; Sun, Haoran; Lin, Jingjun

2017-10-01

Laser-induced breakdown spectroscopy (LIBS) technology for metal and nonmetallic detection accuracy is the key technology to be solved in LIBS measurement, Due to metal elements and non-metallic elements in the lively, atomic structure and the degree of excitation of the laser are totally different, so the laser induced plasma evolution and spectral intensity are absolutely different. Among the many factors that affect measurement accuracy, the single and double pulse of the laser has a great influence on the measurement accuracy of metal and non-metal, they both have their own advantages, but also have their own shortcomings. In order to compare the effect of SP-LIBS and DP-LIBS on the measurement results of different elements, in this experiment, we put the metal element aluminum and non-metallic element carbon as the sample, the laser energy as a variable, using the high-speed camera shooting SP- LIBS and DP- LIBS plasma images. Using the spectral analyzer to record the spectral intensity of the elements, by calculating the relative RSD of the signal intensity and comparing the spectral intensity and the signal stability for different elements, develop an optimized experimental program. The experimental results show that under the same energy condition, the metal aluminum ion image under the DP- LIBS and the non-metallic carbon ion image under the SP- LIBS are the most suitable images. By considering the stability of the line intensity and the signal stability, we find that the sensitivity and stability of the signal strength of the metal elements under the double pulse are better than that of the single pulse, and for the non-metallic element, the single pulse laser is better than the double pulse.

Study of propellant dynamics in a shuttle type launch vehicle

NASA Technical Reports Server (NTRS)

Jones, C. E.; Feng, G. C.

1972-01-01

A method and an associated digital computer program for evaluating the vibrational characteristics of large liquid-filled rigid wall tanks of general shape are presented. A solution procedure was developed in which slosh modes and frequencies are computed for systems mathematically modeled as assemblages of liquid finite elements. To retain sparsity in the assembled system mass and stiffness matrices, a compressible liquid element formulation was incorporated in the program. The approach taken in the liquid finite element formulation is compatible with triangular and quadrilateral structural finite elements so that the analysis of liquid motion can be coupled with flexible tank wall motion at some future time. The liquid element repertoire developed during the course of this study consists of a two-dimensional triangular element and a three-dimensional tetrahedral element.

SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.

1999-03-01

This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples ofmore » the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.« less

RAMI4PILPS: An intercomparison of formulations for the partitioning of solar radiation in land surface models

NASA Astrophysics Data System (ADS)

Widlowski, J.-L.; Pinty, B.; Clerici, M.; Dai, Y.; de Kauwe, M.; De Ridder, K.; Kallel, A.; Kobayashi, H.; Lavergne, T.; Ni-Meister, W.; Olchev, A.; Quaife, T.; Wang, S.; Yang, W.; Yang, Y.; Yuan, H.

2011-06-01

Remotely sensed, multiannual data sets of shortwave radiative surface fluxes are now available for assimilation into land surface schemes (LSSs) of climate and/or numerical weather prediction models. The RAMI4PILPS suite of virtual experiments assesses the accuracy and consistency of the radiative transfer formulations that provide the magnitudes of absorbed, reflected, and transmitted shortwave radiative fluxes in LSSs. RAMI4PILPS evaluates models under perfectly controlled experimental conditions in order to eliminate uncertainties arising from an incomplete or erroneous knowledge of the structural, spectral and illumination related canopy characteristics typical for model comparison with in situ observations. More specifically, the shortwave radiation is separated into a visible and near-infrared spectral region, and the quality of the simulated radiative fluxes is evaluated by direct comparison with a 3-D Monte Carlo reference model identified during the third phase of the Radiation transfer Model Intercomparison (RAMI) exercise. The RAMI4PILPS setup thus allows to focus in particular on the numerical accuracy of shortwave radiative transfer formulations and to pinpoint to areas where future model improvements should concentrate. The impact of increasing degrees of structural and spectral subgrid variability on the simulated fluxes is documented and the relevance of any thus emerging biases with respect to gross primary production estimates and shortwave radiative forcings due to snow and fire events are investigated.

Rational approach for assumed stress finite elements

NASA Technical Reports Server (NTRS)

Pian, T. H. H.; Sumihara, K.

1984-01-01

A new method for the formulation of hybrid elements by the Hellinger-Reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element. The equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co-ordinates. The resulting element possesses all the ideal qualities, i.e. it is invariant, it is less sensitive to geometric distortion, it contains a minimum number of stress parameters and it provides accurate stress calculations. For the formulation of a 4-node plane stress element, a small perturbation method is used to determine the equilibrium constraint equations. The element has been proved to be always rank sufficient.

Application of the control volume mixed finite element method to a triangular discretization

USGS Publications Warehouse

Naff, R.L.

2012-01-01

A two-dimensional control volume mixed finite element method is applied to the elliptic equation. Discretization of the computational domain is based in triangular elements. Shape functions and test functions are formulated on the basis of an equilateral reference triangle with unit edges. A pressure support based on the linear interpolation of elemental edge pressures is used in this formulation. Comparisons are made between results from the standard mixed finite element method and this control volume mixed finite element method. Published 2011. This article is a US Government work and is in the public domain in the USA. ?? 2012 John Wiley & Sons, Ltd. This article is a US Government work and is in the public domain in the USA.

Parallel Finite Element Domain Decomposition for Structural/Acoustic Analysis

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.; Tungkahotara, Siroj; Watson, Willie R.; Rajan, Subramaniam D.

2005-01-01

A domain decomposition (DD) formulation for solving sparse linear systems of equations resulting from finite element analysis is presented. The formulation incorporates mixed direct and iterative equation solving strategics and other novel algorithmic ideas that are optimized to take advantage of sparsity and exploit modern computer architecture, such as memory and parallel computing. The most time consuming part of the formulation is identified and the critical roles of direct sparse and iterative solvers within the framework of the formulation are discussed. Experiments on several computer platforms using several complex test matrices are conducted using software based on the formulation. Small-scale structural examples are used to validate thc steps in the formulation and large-scale (l,000,000+ unknowns) duct acoustic examples are used to evaluate the ORIGIN 2000 processors, and a duster of 6 PCs (running under the Windows environment). Statistics show that the formulation is efficient in both sequential and parallel computing environmental and that the formulation is significantly faster and consumes less memory than that based on one of the best available commercialized parallel sparse solvers.

High-Order Moving Overlapping Grid Methodology in a Spectral Element Method

NASA Astrophysics Data System (ADS)

Merrill, Brandon E.

A moving overlapping mesh methodology that achieves spectral accuracy in space and up to second-order accuracy in time is developed for solution of unsteady incompressible flow equations in three-dimensional domains. The targeted applications are in aerospace and mechanical engineering domains and involve problems in turbomachinery, rotary aircrafts, wind turbines and others. The methodology is built within the dual-session communication framework initially developed for stationary overlapping meshes. The methodology employs semi-implicit spectral element discretization of equations in each subdomain and explicit treatment of subdomain interfaces with spectrally-accurate spatial interpolation and high-order accurate temporal extrapolation, and requires few, if any, iterations, yet maintains the global accuracy and stability of the underlying flow solver. Mesh movement is enabled through the Arbitrary Lagrangian-Eulerian formulation of the governing equations, which allows for prescription of arbitrary velocity values at discrete mesh points. The stationary and moving overlapping mesh methodologies are thoroughly validated using two- and three-dimensional benchmark problems in laminar and turbulent flows. The spatial and temporal global convergence, for both methods, is documented and is in agreement with the nominal order of accuracy of the underlying solver. Stationary overlapping mesh methodology was validated to assess the influence of long integration times and inflow-outflow global boundary conditions on the performance. In a turbulent benchmark of fully-developed turbulent pipe flow, the turbulent statistics are validated against the available data. Moving overlapping mesh simulations are validated on the problems of two-dimensional oscillating cylinder and a three-dimensional rotating sphere. The aerodynamic forces acting on these moving rigid bodies are determined, and all results are compared with published data. Scaling tests, with both methodologies, show near linear strong scaling, even for moderately large processor counts. The moving overlapping mesh methodology is utilized to investigate the effect of an upstream turbulent wake on a three-dimensional oscillating NACA0012 extruded airfoil. A direct numerical simulation (DNS) at Reynolds Number 44,000 is performed for steady inflow incident upon the airfoil oscillating between angle of attack 5.6° and 25° with reduced frequency k=0.16. Results are contrasted with subsequent DNS of the same oscillating airfoil in a turbulent wake generated by a stationary upstream cylinder.

Analysis of Site Effect in the Izmit Basin of Turkey by Wave Propagation Simulation Using the Spectral Element Method: Preliminary Results

NASA Astrophysics Data System (ADS)

Firtana Elcomert, K.; Kocaoglu, A. H.

2013-12-01

Sedimentary basins generally cause significant ground motion amplification during an earthquake. Along with the resonance controlled by the impedance contrast between the sedimentary cover and bedrock, surface waves generated within the basin make the waveforms more complex and longer in duration. When a dense network of weak and/or strong motion sensors is available, site effect or more specifically sedimentary basin amplification can be directly estimated experimentally provided that significant earthquakes occur during the period of study. Alternatively, site effect can be investigated through simulation of ground motion. The objective of this study is to investigate the 2-D and/or 3-D site effect in the Izmit Basin located in the eastern Marmara region of Turkey, using the currently available bedrock topography and shear-wave velocity data. The Izmit Basin was formed in Plio-Quaternary period and is known to be controlled by the northern branch of the North Anatolian Fault Zone. A thorough analysis of seismic hazard is important since the city of Izmit and its metropolitan area is located in this region. This work presents some of the preliminary results obtained from 2-D and 3-D seismic wave propagation simulations using the spectral element method, which is based on high order polynomial approximation of the weak formulation of the wave equation. In this study, the numerical simulations were carried out with SPECFEM2D/3D program. Comparison of seismograms recorded on the top of sedimentary layer with those recorded on the bedrock show more complex waveforms with higher amplitudes on seismograms recorded at the free surface. Furthermore, modeling clearly reveals that observed seismograms include surface waves whose excitation is clearly related with the basin geometry.

Studying the surface of Mercury with BepiColombo

NASA Astrophysics Data System (ADS)

Helbert, J.; Benkhoff, J.

2015-12-01

The payload of the ESA-JAXA mission BepiColombo had been proposed long before the NASA MESSENGER mission provided us with new insights into the innermost of the terrestrial planets. The discoveries of the MESSENGER fundamentally changed our view of Mercury. It revealed a surface that has been reshaped by volcanism over large parts of geological history. Volatile elements like sulfur have been detected with unexpectedly high abundances of up to 4%. MESSENGER imagined structures that are most likely formed by pyroclastic eruptions in recent geologic history. Among the most exciting discoveries of MESSENGER are hollows - bright irregularly shaped depressions that show sign of ongoing loss of material. BepiColombo will be building on what has been learned from the MESSENGER mission and extend the knowledge. Due to its more circular orbit BepiColombo will provide good spatial resolution for both hemispheres of Mercury. The mission will give us the first good look at the southern hemisphere of the planet. All spectral instruments are imaging and cover a wider spectral range than the instruments on MESSENGER. Some instruments will provide us datasets that have not been obtained by MESSENGER in any form. MERTIS will for example provide the first temperature map of Mercury and will map the surface composition of the planet for the first time in the thermal infrared. The telescopic imaging channel of the XRS instrument will provide elemental composition at an unprecedented spatial resolution. The MESSENGER results will be key to formulate the observation plan for the surface instruments on BepiColombo. They also have motivated a wide range of laboratory experiments that will help to better understand the results returned by the suite of instruments.

FTIR, magnetic, 1H NMR spectral and thermal studies of some chelates of caproic acid: inhibitory effect on different kinds of bacteria.

PubMed

Refat, Moamen S; El-Korashy, Sabry A; Kumar, Deo Nandan; Ahmed, Ahmed S

2008-06-01

A convenient method for the preparation of complexes of the Cr3+, Mn2+, Fe3+, Co2+, Ni2+, Zn2+, ZrO2+, UO2(2+), Zr4+ and Th4+ ions with caproic acid (Hcap) is reported and this has enabled 10 complexes of caproate anion to be formulated: [Cr(cap)3].5H2O, [Mn(cap)2(H2O)2], [Fe(cap)3].12H2O, [Co(cap)2(H2O)2].4H2O, [Ni(cap)2(H2O)2].3H2O, [Zn(cap)2], [ZrO(cap)2].3H2O, [UO2(cap)(NO3)], [Zr(cap)2(Cl)2] and [Th(cap)4]. These new complexes were synthesized and characterized by elemental analysis, molar conductivity, magnetic measurements, spectral methods (mid infrared, 1H NMR and UV-vis spectra) and simultaneous thermal analysis (TG and DTG) techniques. It has been found from the elemental analysis as well as thermal studies that the caproate ligand behaves as bidentate ligand and forming chelates with 1:1 (metal:ligand) stoichiometry for UO2(2+), 1:2 for (Mn2+, Co2+, Ni2+, Zn2+, ZrO2+ and Zr4+), 1:3 stoichiometry for (Cr3+ and Fe3+) and 1:4 for Th4+ caproate complexes, respectively, as bidentate chelating. The molar conductance measurements proved that the caproate complexes are non-electrolytes. The kinetic thermodynamic parameters such as: E*, DeltaH*, DeltaS* and DeltaG* are estimated from the DTG curves. The antibacterial activity of the caproic acid and their complexes was evaluated against some gram positive/negative bacteria.

Spectroscopic and biological approach in the characterization of a novel 14-membered [N4] macrocyclic ligand and its palladium(II), platinum(II), ruthenium(III) and iridium(III) complexes.

PubMed

Rani, Soni; Kumar, Sumit; Chandra, Sulekh

2014-01-24

A novel, tetradentate nitrogen donor [N4] macrocyclic ligand, i.e. 3,5,14,16-tetramethyl-2,6,13,17-tetraazatricyclo[12,0,0(7-12)] cosa-1(22),2,5,7,9,11,13,16,18,20-decaene(L), has been synthesized and characterized by elemental analyses, IR, Mass, and (1)H NMR spectral studies. Complexes of Pd(II), Pt(II), Ru(III) and Ir(III) have been prepared and characterized by elemental analyses, molar conductance measurements, magnetic susceptibility measurements, IR, Mass, electronic spectral and thermal studies. On the basis of molar conductance the complexes may be formulated as [PdL]Cl2, [PtL]Cl2, [Ru(L)Cl2]Cl and [Ir(L)Cl2]Cl. The complexes are insoluble in most common solvents, including water, ethanol, carbon tetrachloride and acetonitrile, but soluble in DMF/DMSO. The value of magnetic moment indicates that all the complexes are diamagnetic except Ru(III) complex which shows magnetic moment corresponding to one unpaired electron. The magnetic moment of Ru(III) complex is 1.73 B.M. at room temperature. The antimicrobial activities of ligand and its complexes have been screened in vitro, as growth inhibiting agents. The antifungal and antibacterial screening were carried out using Food Poison and Disc Diffusion Method against plant pathogenic fungi and bacteria Alternaria porri, Fusarium oxysporum, Xanthomonas compestris and Pseudomonas aeruginosa respectively. The compounds were dissolved in DMSO to get the required solutions. The required medium used for these activities was PDA and nutrient agar. Copyright © 2013 Elsevier B.V. All rights reserved.

Advanced solid elements for sheet metal forming simulation

NASA Astrophysics Data System (ADS)

Mataix, Vicente; Rossi, Riccardo; Oñate, Eugenio; Flores, Fernando G.

2016-08-01

The solid-shells are an attractive kind of element for the simulation of forming processes, due to the fact that any kind of generic 3D constitutive law can be employed without any additional hypothesis. The present work consists in the improvement of a triangular prism solid-shell originally developed by Flores[2, 3]. The solid-shell can be used in the analysis of thin/thick shell, undergoing large deformations. The element is formulated in total Lagrangian formulation, and employs the neighbour (adjacent) elements to perform a local patch to enrich the displacement field. In the original formulation a modified right Cauchy-Green deformation tensor (C) is obtained; in the present work a modified deformation gradient (F) is obtained, which allows to generalise the methodology and allows to employ the Pull-Back and Push-Forwards operations. The element is based in three modifications: (a) a classical assumed strain approach for transverse shear strains (b) an assumed strain approach for the in-plane components using information from neighbour elements and (c) an averaging of the volumetric strain over the element. The objective is to use this type of elements for the simulation of shells avoiding transverse shear locking, improving the membrane behaviour of the in-plane triangle and to handle quasi-incompressible materials or materials with isochoric plastic flow.

Factorizing the factorization - a spectral-element solver for elliptic equations with linear operation count

NASA Astrophysics Data System (ADS)

Huismann, Immo; Stiller, Jörg; Fröhlich, Jochen

2017-10-01

The paper proposes a novel factorization technique for static condensation of a spectral-element discretization matrix that yields a linear operation count of just 13N multiplications for the residual evaluation, where N is the total number of unknowns. In comparison to previous work it saves a factor larger than 3 and outpaces unfactored variants for all polynomial degrees. Using the new technique as a building block for a preconditioned conjugate gradient method yields linear scaling of the runtime with N which is demonstrated for polynomial degrees from 2 to 32. This makes the spectral-element method cost effective even for low polynomial degrees. Moreover, the dependence of the iterative solution on the element aspect ratio is addressed, showing only a slight increase in the number of iterations for aspect ratios up to 128. Hence, the solver is very robust for practical applications.

Coupling finite element and spectral methods: First results

NASA Technical Reports Server (NTRS)

Bernardi, Christine; Debit, Naima; Maday, Yvon

1987-01-01

A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares, a finite element approximation is used on the first square and a spectral discretization is used on the second one. Two kinds of matching conditions on the interface are presented and compared. In both cases, error estimates are proved.

Application of the Spectral Element Method to Interior Noise Problems

NASA Technical Reports Server (NTRS)

Doyle, James F.

1998-01-01

The primary effort of this research project was focused the development of analytical methods for the accurate prediction of structural acoustic noise and response. Of particular interest was the development of curved frame and shell spectral elements for the efficient computational of structural response and of schemes to match this to the surrounding fluid.

The ISPM experiment for spectral, composition and anistropy measurements of charged particles at low energie

NASA Technical Reports Server (NTRS)

Lanzerotti, L. J.; Gold, R. E.; Anderson, K. A.; Armstrong, T. P.; Lin, R. P.; Krimigis, S. M.; Pick, M.; Roelof, E. C.; Sarris, E. T.; Simnett, G. M.

1983-01-01

The Heliosphere Instrument for Spectral, Composition, and Anisotropy at Low Energies (HI-SCALE) designed to measure interplanetary ions and electrons is described. Ions and electrons are detected by five separate solid-state detector telescopes oriented to give complete pitch angle coverage from the spinning spacecraft. Ion elemental abundances are determined by a telescope using a thin front detector element in a three-element telescope. Experiment operation is controlled by a microprocessor-based data system. Inflight calibration is provided by radioactive sources mounted on closable telescope covers. Ion and electron spectral information is determined using broad-energy-range rate channels, and a pulse-height analyzer for more detailed spectra. The instrument weighs 5.775 kg and uses 4.0 W power.

Optical filters for the Multispectral Instrument (MSI) on Sentinel-2

NASA Astrophysics Data System (ADS)

Merschdorf, M.; Camus, F.; Kirschner, V.

2017-11-01

Multi-spectral optical filters are essential parts of spaceborne optical imagers such as the Multispectral Instrument (MSI) for the Sentinel-2 satellite in the framework of ESA's GMES programme for earth observation. In this development, Jena-Optronik is responsible for the design, manufacturing and test of the spectral filter assemblies. They are the key elements that define the spectral quality of the instrument. Besides the challenging spectral requirements straylight aspects are of crucial importance due to the close neighbourhood of the filter elements to the detector. Results will be presented of the extensive analyses and measurements that have been performed on component and assembly level to ensure the optical performance.

Determination of rare-earth elements in Luna 16 regolith sample by chemical spectral method

NASA Technical Reports Server (NTRS)

Stroganova, N. S.; Ryabukhin, V. A.; Laktinova, N. V.; Ageyeva, L. V.; Galkina, I. P.; Gatinskaya, N. G.; Yermakov, A. N.; Karyakin, A. V.

1974-01-01

An analysis was made of regolith from layer A of the Luna 16 sample for rare earth elements, by a chemical spectral method. Chemical and ion exchange concentrations were used to determine the content of 12 elements and Y at the level 0.001 to 0.0001 percent with 10 to 15 percent reproducibility of the emission determination. Results within the limits of reproducibility agree with data obtained by mass spectra, activation, and X-ray fluorescent methods.

Advanced development of BEM for elastic and inelastic dynamic analysis of solids

NASA Technical Reports Server (NTRS)

Banerjee, P. K.; Ahmad, S.; Wang, H. C.

1989-01-01

Direct Boundary Element formulations and their numerical implementation for periodic and transient elastic as well as inelastic transient dynamic analyses of two-dimensional, axisymmetric and three-dimensional solids are presented. The inelastic formulation is based on an initial stress approach and is the first of its kind in the field of Boundary Element Methods. This formulation employs the Navier-Cauchy equation of motion, Graffi's dynamic reciprocal theorem, Stokes' fundamental solution, and the divergence theorem, together with kinematical and constitutive equations to obtain the pertinent integral equations of the problem in the time domain within the context of the small displacement theory of elastoplasticity. The dynamic (periodic, transient as well as nonlinear transient) formulations have been applied to a range of problems. The numerical formulations presented here are included in the BEST3D and GPBEST systems.

An iterative approach for compound detection in an unknown pharmaceutical drug product: Application on Raman microscopy.

PubMed

Boiret, Mathieu; Gorretta, Nathalie; Ginot, Yves-Michel; Roger, Jean-Michel

2016-02-20

Raman chemical imaging provides both spectral and spatial information on a pharmaceutical drug product. Even if the main objective of chemical imaging is to obtain distribution maps of each formulation compound, identification of pure signals in a mixture dataset remains of huge interest. In this work, an iterative approach is proposed to identify the compounds in a pharmaceutical drug product, assuming that the chemical composition of the product is not known by the analyst and that a low dose compound can be present in the studied medicine. The proposed approach uses a spectral library, spectral distances and orthogonal projections to iteratively detect pure compounds of a tablet. Since the proposed method is not based on variance decomposition, it should be well adapted for a drug product which contains a low dose product, interpreted as a compound located in few pixels and with low spectral contributions. The method is tested on a tablet specifically manufactured for this study with one active pharmaceutical ingredient and five excipients. A spectral library, constituted of 24 pure pharmaceutical compounds, is used as a reference spectral database. Pure spectra of active and excipients, including a modification of the crystalline form and a low dose compound, are iteratively detected. Once the pure spectra are identified, multivariate curve resolution-alternating least squares process is performed on the data to provide distribution maps of each compound in the studied sample. Distributions of the two crystalline forms of active and the five excipients were in accordance with the theoretical formulation. Copyright © 2015 Elsevier B.V. All rights reserved.

Spectral wave dissipation by submerged aquatic vegetation in a back-barrier estuary

USGS Publications Warehouse

Nowacki, Daniel J.; Beudin, Alexis; Ganju, Neil K.

2017-01-01

Submerged aquatic vegetation is generally thought to attenuate waves, but this interaction remains poorly characterized in shallow-water field settings with locally generated wind waves. Better quantification of wave–vegetation interaction can provide insight to morphodynamic changes in a variety of environments and also is relevant to the planning of nature-based coastal protection measures. Toward that end, an instrumented transect was deployed across a Zostera marina (common eelgrass) meadow in Chincoteague Bay, Maryland/Virginia, U.S.A., to characterize wind-wave transformation within the vegetated region. Field observations revealed wave-height reduction, wave-period transformation, and wave-energy dissipation with distance into the meadow, and the data informed and calibrated a spectral wave model of the study area. The field observations and model results agreed well when local wind forcing and vegetation-induced drag were included in the model, either explicitly as rigid vegetation elements or implicitly as large bed-roughness values. Mean modeled parameters were similar for both the explicit and implicit approaches, but the spectral performance of the explicit approach was poor compared to the implicit approach. The explicit approach over-predicted low-frequency energy within the meadow because the vegetation scheme determines dissipation using mean wavenumber and frequency, in contrast to the bed-friction formulations, which dissipate energy in a variable fashion across frequency bands. Regardless of the vegetation scheme used, vegetation was the most important component of wave dissipation within much of the study area. These results help to quantify the influence of submerged aquatic vegetation on wave dynamics in future model parameterizations, field efforts, and coastal-protection measures.

Least-Squares Regression and Spectral Residual Augmented Classical Least-Squares Chemometric Models for Stability-Indicating Analysis of Agomelatine and Its Degradation Products: A Comparative Study.

PubMed

Naguib, Ibrahim A; Abdelrahman, Maha M; El Ghobashy, Mohamed R; Ali, Nesma A

2016-01-01

Two accurate, sensitive, and selective stability-indicating methods are developed and validated for simultaneous quantitative determination of agomelatine (AGM) and its forced degradation products (Deg I and Deg II), whether in pure forms or in pharmaceutical formulations. Partial least-squares regression (PLSR) and spectral residual augmented classical least-squares (SRACLS) are two chemometric models that are being subjected to a comparative study through handling UV spectral data in range (215-350 nm). For proper analysis, a three-factor, four-level experimental design was established, resulting in a training set consisting of 16 mixtures containing different ratios of interfering species. An independent test set consisting of eight mixtures was used to validate the prediction ability of the suggested models. The results presented indicate the ability of mentioned multivariate calibration models to analyze AGM, Deg I, and Deg II with high selectivity and accuracy. The analysis results of the pharmaceutical formulations were statistically compared to the reference HPLC method, with no significant differences observed regarding accuracy and precision. The SRACLS model gives comparable results to the PLSR model; however, it keeps the qualitative spectral information of the classical least-squares algorithm for analyzed components.

Nouvelles techniques pratiques pour la modelisation du comportement dynamique des systèmes eau-structure

NASA Astrophysics Data System (ADS)

Miquel, Benjamin

The dynamic or seismic behavior of hydraulic structures is, as for conventional structures, essential to assure protection of human lives. These types of analyses also aim at limiting structural damage caused by an earthquake to prevent rupture or collapse of the structure. The particularity of these hydraulic structures is that not only the internal displacements are caused by the earthquake, but also by the hydrodynamic loads resulting from fluid-structure interaction. This thesis reviews the existing complex and simplified methods to perform such dynamic analysis for hydraulic structures. For the complex existing methods, attention is placed on the difficulties arising from their use. Particularly, interest is given in this work on the use of transmitting boundary conditions to simulate the semi infinity of reservoirs. A procedure has been developed to estimate the error that these boundary conditions can introduce in finite element dynamic analysis. Depending on their formulation and location, we showed that they can considerably affect the response of such fluid-structure systems. For practical engineering applications, simplified procedures are still needed to evaluate the dynamic behavior of structures in contact with water. A review of the existing simplified procedures showed that these methods are based on numerous simplifications that can affect the prediction of the dynamic behavior of such systems. One of the main objectives of this thesis has been to develop new simplified methods that are more accurate than those existing. First, a new spectral analysis method has been proposed. Expressions for the fundamental frequency of fluid-structure systems, key parameter of spectral analysis, have been developed. We show that this new technique can easily be implemented in a spreadsheet or program, and that its calculation time is near instantaneous. When compared to more complex analytical or numerical method, this new procedure yields excellent prediction of the dynamic behavior of fluid-structure systems. Spectral analyses ignore the transient and oscillatory nature of vibrations. When such dynamic analyses show that some areas of the studied structure undergo excessive stresses, time history analyses allow a better estimate of the extent of these zones as well as a time notion of these excessive stresses. Furthermore, the existing spectral analyses methods for fluid-structure systems account only for the static effect of higher modes. Thought this can generally be sufficient for dams, for flexible structures the dynamic effect of these modes should be accounted for. New methods have been developed for fluid-structure systems to account for these observations as well as the flexibility of foundations. A first method was developed to study structures in contact with one or two finite or infinite water domains. This new technique includes flexibility of structures and foundations as well as the dynamic effect of higher vibration modes and variations of the levels of the water domains. Extension of this method was performed to study beam structures in contact with fluids. These new developments have also allowed extending existing analytical formulations of the dynamic properties of a dry beam to a new formulation that includes effect of fluid-structure interaction. The method yields a very good estimate of the dynamic behavior of beam-fluid systems or beam like structures in contact with fluid. Finally, a Modified Accelerogram Method (MAM) has been developed to modify the design earthquake into a new accelerogram that directly accounts for the effect of fluid-structure interaction. This new accelerogram can therefore be applied directly to the dry structure (i.e. without water) in order to calculate the dynamic response of the fluid-structure system. This original technique can include numerous parameters that influence the dynamic response of such systems and allows to treat analytically the fluid-structure interaction while keeping the advantages of finite element modeling.

Probabilistic Structures Analysis Methods (PSAM) for select space propulsion system components

NASA Technical Reports Server (NTRS)

1991-01-01

The basic formulation for probabilistic finite element analysis is described and demonstrated on a few sample problems. This formulation is based on iterative perturbation that uses the factorized stiffness on the unperturbed system as the iteration preconditioner for obtaining the solution to the perturbed problem. This approach eliminates the need to compute, store and manipulate explicit partial derivatives of the element matrices and force vector, which not only reduces memory usage considerably, but also greatly simplifies the coding and validation tasks. All aspects for the proposed formulation were combined in a demonstration problem using a simplified model of a curved turbine blade discretized with 48 shell elements, and having random pressure and temperature fields with partial correlation, random uniform thickness, and random stiffness at the root.

On the utilization of novel spectral laser scanning for three-dimensional classification of vegetation elements.

PubMed

Li, Zhan; Schaefer, Michael; Strahler, Alan; Schaaf, Crystal; Jupp, David

2018-04-06

The Dual-Wavelength Echidna Lidar (DWEL), a full waveform terrestrial laser scanner (TLS), has been used to scan a variety of forested and agricultural environments. From these scanning campaigns, we summarize the benefits and challenges given by DWEL's novel coaxial dual-wavelength scanning technology, particularly for the three-dimensional (3D) classification of vegetation elements. Simultaneous scanning at both 1064 nm and 1548 nm by DWEL instruments provides a new spectral dimension to TLS data that joins the 3D spatial dimension of lidar as an information source. Our point cloud classification algorithm explores the utilization of both spectral and spatial attributes of individual points from DWEL scans and highlights the strengths and weaknesses of each attribute domain. The spectral and spatial attributes for vegetation element classification each perform better in different parts of vegetation (canopy interior, fine branches, coarse trunks, etc.) and under different vegetation conditions (dead or live, leaf-on or leaf-off, water content, etc.). These environmental characteristics of vegetation, convolved with the lidar instrument specifications and lidar data quality, result in the actual capabilities of spectral and spatial attributes to classify vegetation elements in 3D space. The spectral and spatial information domains thus complement each other in the classification process. The joint use of both not only enhances the classification accuracy but also reduces its variance across the multiple vegetation types we have examined, highlighting the value of the DWEL as a new source of 3D spectral information. Wider deployment of the DWEL instruments is in practice currently held back by challenges in instrument development and the demands of data processing required by coaxial dual- or multi-wavelength scanning. But the simultaneous 3D acquisition of both spectral and spatial features, offered by new multispectral scanning instruments such as the DWEL, opens doors to study biophysical and biochemical properties of forested and agricultural ecosystems at more detailed scales.

A new family of stable elements for the Stokes problem based on a mixed Galerkin/least-squares finite element formulation

NASA Technical Reports Server (NTRS)

Franca, Leopoldo P.; Loula, Abimael F. D.; Hughes, Thomas J. R.; Miranda, Isidoro

1989-01-01

Adding to the classical Hellinger-Reissner formulation, a residual form of the equilibrium equation, a new Galerkin/least-squares finite element method is derived. It fits within the framework of a mixed finite element method and is stable for rather general combinations of stress and velocity interpolations, including equal-order discontinuous stress and continuous velocity interpolations which are unstable within the Galerkin approach. Error estimates are presented based on a generalization of the Babuska-Brezzi theory. Numerical results (not presented herein) have confirmed these estimates as well as the good accuracy and stability of the method.

A three-dimensional nonlinear Timoshenko beam based on the core-congruential formulation

NASA Technical Reports Server (NTRS)

Crivelli, Luis A.; Felippa, Carlos A.

1992-01-01

A three-dimensional, geometrically nonlinear two-node Timoshenkoo beam element based on the total Larangrian description is derived. The element behavior is assumed to be linear elastic, but no restrictions are placed on magnitude of finite rotations. The resulting element has twelve degrees of freedom: six translational components and six rotational-vector components. The formulation uses the Green-Lagrange strains and second Piola-Kirchhoff stresses as energy-conjugate variables and accounts for the bending-stretching and bending-torsional coupling effects without special provisions. The core-congruential formulation (CCF) is used to derived the discrete equations in a staged manner. Core equations involving the internal force vector and tangent stiffness matrix are developed at the particle level. A sequence of matrix transformations carries these equations to beam cross-sections and finally to the element nodal degrees of freedom. The choice of finite rotation measure is made in the next-to-last transformation stage, and the choice of over-the-element interpolation in the last one. The tangent stiffness matrix is found to retain symmetry if the rotational vector is chosen to measure finite rotations. An extensive set of numerical examples is presented to test and validate the present element.

Phase field modeling of brittle fracture for enhanced assumed strain shells at large deformations: formulation and finite element implementation

NASA Astrophysics Data System (ADS)

Reinoso, J.; Paggi, M.; Linder, C.

2017-06-01

Fracture of technological thin-walled components can notably limit the performance of their corresponding engineering systems. With the aim of achieving reliable fracture predictions of thin structures, this work presents a new phase field model of brittle fracture for large deformation analysis of shells relying on a mixed enhanced assumed strain (EAS) formulation. The kinematic description of the shell body is constructed according to the solid shell concept. This enables the use of fully three-dimensional constitutive models for the material. The proposed phase field formulation integrates the use of the (EAS) method to alleviate locking pathologies, especially Poisson thickness and volumetric locking. This technique is further combined with the assumed natural strain method to efficiently derive a locking-free solid shell element. On the computational side, a fully coupled monolithic framework is consistently formulated. Specific details regarding the corresponding finite element formulation and the main aspects associated with its implementation in the general purpose packages FEAP and ABAQUS are addressed. Finally, the applicability of the current strategy is demonstrated through several numerical examples involving different loading conditions, and including linear and nonlinear hyperelastic constitutive models.

Quantitative spatial distribution of sirolimus and polymers in drug-eluting stents using confocal Raman microscopy.

PubMed

Balss, K M; Llanos, G; Papandreou, G; Maryanoff, C A

2008-04-01

Raman spectroscopy was used to differentiate each component found in the CYPHER Sirolimus-eluting Coronary Stent. The unique spectral features identified for each component were then used to develop three separate calibration curves to describe the solid phase distribution found on drug-polymer coated stents. The calibration curves were obtained by analyzing confocal Raman spectral depth profiles from a set of 16 unique formulations of drug-polymer coatings sprayed onto stents and planar substrates. The sirolimus model was linear from 0 to 100 wt % of drug. The individual polymer calibration curves for poly(ethylene-co-vinyl acetate) [PEVA] and poly(n-butyl methacrylate) [PBMA] were also linear from 0 to 100 wt %. The calibration curves were tested on three independent drug-polymer coated stents. The sirolimus calibration predicted the drug content within 1 wt % of the laboratory assay value. The polymer calibrations predicted the content within 7 wt % of the formulation solution content. Attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectra from five formulations confirmed a linear response to changes in sirolimus and polymer content. Copyright 2007 Wiley Periodicals, Inc.

Gaussian-windowed frame based method of moments formulation of surface-integral-equation for extended apertures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shlivinski, A., E-mail: amirshli@ee.bgu.ac.il; Lomakin, V., E-mail: vlomakin@eng.ucsd.edu

2016-03-01

Scattering or coupling of electromagnetic beam-field at a surface discontinuity separating two homogeneous or inhomogeneous media with different propagation characteristics is formulated using surface integral equation, which are solved by the Method of Moments with the aid of the Gabor-based Gaussian window frame set of basis and testing functions. The application of the Gaussian window frame provides (i) a mathematically exact and robust tool for spatial-spectral phase-space formulation and analysis of the problem; (ii) a system of linear equations in a transmission-line like form relating mode-like wave objects of one medium with mode-like wave objects of the second medium; (iii)more » furthermore, an appropriate setting of the frame parameters yields mode-like wave objects that blend plane wave properties (as if solving in the spectral domain) with Green's function properties (as if solving in the spatial domain); and (iv) a representation of the scattered field with Gaussian-beam propagators that may be used in many large (in terms of wavelengths) systems.« less

Network representations of angular regions for electromagnetic scattering

PubMed Central

2017-01-01

Network modeling in electromagnetics is an effective technique in treating scattering problems by canonical and complex structures. Geometries constituted of angular regions (wedges) together with planar layers can now be approached with the Generalized Wiener-Hopf Technique supported by network representation in spectral domain. Even if the network representations in spectral planes are of great importance by themselves, the aim of this paper is to present a theoretical base and a general procedure for the formulation of complex scattering problems using network representation for the Generalized Wiener Hopf Technique starting basically from the wave equation. In particular while the spectral network representations are relatively well known for planar layers, the network modelling for an angular region requires a new theory that will be developed in this paper. With this theory we complete the formulation of a network methodology whose effectiveness is demonstrated by the application to a complex scattering problem with practical solutions given in terms of GTD/UTD diffraction coefficients and total far fields for engineering applications. The methodology can be applied to other physics fields. PMID:28817573

Alternative formulations of the Laplace transform boundary element (LTBE) numerical method for the solution of diffusion-type equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moridis, G.

1992-03-01

The Laplace Transform Boundary Element (LTBE) method is a recently introduced numerical method, and has been used for the solution of diffusion-type PDEs. It completely eliminates the time dependency of the problem and the need for time discretization, yielding solutions numerical in space and semi-analytical in time. In LTBE solutions are obtained in the Laplace spare, and are then inverted numerically to yield the solution in time. The Stehfest and the DeHoog formulations of LTBE, based on two different inversion algorithms, are investigated. Both formulations produce comparable, extremely accurate solutions.

Supercomputer implementation of finite element algorithms for high speed compressible flows

NASA Technical Reports Server (NTRS)

Thornton, E. A.; Ramakrishnan, R.

1986-01-01

Prediction of compressible flow phenomena using the finite element method is of recent origin and considerable interest. Two shock capturing finite element formulations for high speed compressible flows are described. A Taylor-Galerkin formulation uses a Taylor series expansion in time coupled with a Galerkin weighted residual statement. The Taylor-Galerkin algorithms use explicit artificial dissipation, and the performance of three dissipation models are compared. A Petrov-Galerkin algorithm has as its basis the concepts of streamline upwinding. Vectorization strategies are developed to implement the finite element formulations on the NASA Langley VPS-32. The vectorization scheme results in finite element programs that use vectors of length of the order of the number of nodes or elements. The use of the vectorization procedure speeds up processing rates by over two orders of magnitude. The Taylor-Galerkin and Petrov-Galerkin algorithms are evaluated for 2D inviscid flows on criteria such as solution accuracy, shock resolution, computational speed and storage requirements. The convergence rates for both algorithms are enhanced by local time-stepping schemes. Extension of the vectorization procedure for predicting 2D viscous and 3D inviscid flows are demonstrated. Conclusions are drawn regarding the applicability of the finite element procedures for realistic problems that require hundreds of thousands of nodes.

An Ellipsoidal Particle-Finite Element Method for Hypervelocity Impact Simulation. Chapter 1

NASA Technical Reports Server (NTRS)

Shivarama, Ravishankar; Fahrenthold, Eric P.

2004-01-01

A number of coupled particle-element and hybrid particle-element methods have been developed for the simulation of hypervelocity impact problems, to avoid certain disadvantages associated with the use of pure continuum based or pure particle based methods. To date these methods have employed spherical particles. In recent work a hybrid formulation has been extended to the ellipsoidal particle case. A model formulation approach based on Lagrange's equations, with particles entropies serving as generalized coordinates, avoids the angular momentum conservation problems which have been reported with ellipsoidal smooth particle hydrodynamics models.

Finite element analysis of steady and transiently moving/rolling nonlinear viscoelastic structure. III - Impact/contact simulations

NASA Technical Reports Server (NTRS)

Nakajima, Yukio; Padovan, Joe

1987-01-01

In a three-part series of papers, a generalized finite element methodology is formulated to handle traveling load problems involving large deformation fields in structure composed of viscoelastic media. The main thrust of this paper is to develop an overall finite element methodology and associated solution algorithms to handle the transient aspects of moving problems involving contact impact type loading fields. Based on the methodology and algorithms formulated, several numerical experiments are considered. These include the rolling/sliding impact of tires with road obstructions.

Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel; Wang, Z. J.

2004-01-01

A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. A discussion on the Discontinuous Spectral Difference (SD) Method, locations of the unknowns and flux points and numerical results are also presented.

Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix

DOE PAGES

Smallwood, D. O.

1996-01-01

It is shown that the usual method for estimating the coherence functions (ordinary, partial, and multiple) for a general multiple-input! multiple-output problem can be expressed as a modified form of Cholesky decomposition of the cross-spectral density matrix of the input and output records. The results can be equivalently obtained using singular value decomposition (SVD) of the cross-spectral density matrix. Using SVD suggests a new form of fractional coherence. The formulation as a SVD problem also suggests a way to order the inputs when a natural physical order of the inputs is absent.

A finite element analysis of viscoelastically damped sandwich plates

NASA Astrophysics Data System (ADS)

Ma, B.-A.; He, J.-F.

1992-01-01

A finite element analysis associated with an asymptotic solution method for the harmonic flexural vibration of viscoelastically damped unsymmetrical sandwich plates is given. The element formulation is based on generalization of the discrete Kirchhoff theory (DKT) element formulation. The results obtained with the first order approximation of the asymptotic solution presented here are the same as those obtained by means of the modal strain energy (MSE) method. By taking more terms of the asymptotic solution, with successive calculations and use of the Padé approximants method, accuracy can be improved. The finite element computation has been verified by comparison with an analytical exact solution for rectangular plates with simply supported edges. Results for the same plates with clamped edges are also presented.

A two-field modified Lagrangian formulation for robust simulations of extrinsic cohesive zone models

NASA Astrophysics Data System (ADS)

Cazes, F.; Coret, M.; Combescure, A.

2013-06-01

This paper presents the robust implementation of a cohesive zone model based on extrinsic cohesive laws (i.e. laws involving an infinite initial stiffness). To this end, a two-field Lagrangian weak formulation in which cohesive tractions are chosen as the field variables along the crack's path is presented. Unfortunately, this formulation cannot model the infinite compliance of the broken elements accurately, and no simple criterion can be defined to determine the loading-unloading change of state at the integration points of the cohesive elements. Therefore, a modified Lagrangian formulation using a fictitious cohesive traction instead of the classical cohesive traction as the field variable is proposed. Thanks to this change of variable, the cohesive law becomes an increasing function of the equivalent displacement jump, which eliminates the problems mentioned previously. The ability of the proposed formulations to simulate fracture accurately and without field oscillations is investigated through three numerical test examples.

Resolution-enhanced Mapping Spectrometer

NASA Technical Reports Server (NTRS)

Kumer, J. B.; Aubrun, J. N.; Rosenberg, W. J.; Roche, A. E.

1993-01-01

A familiar mapping spectrometer implementation utilizes two dimensional detector arrays with spectral dispersion along one direction and spatial along the other. Spectral images are formed by spatially scanning across the scene (i.e., push-broom scanning). For imaging grating and prism spectrometers, the slit is perpendicular to the spatial scan direction. For spectrometers utilizing linearly variable focal-plane-mounted filters the spatial scan direction is perpendicular to the direction of spectral variation. These spectrometers share the common limitation that the number of spectral resolution elements is given by the number of pixels along the spectral (or dispersive) direction. Resolution enhancement by first passing the light input to the spectrometer through a scanned etalon or Michelson is discussed. Thus, while a detector element is scanned through a spatial resolution element of the scene, it is also temporally sampled. The analysis for all the pixels in the dispersive direction is addressed. Several specific examples are discussed. The alternate use of a Michelson for the same enhancement purpose is also discussed. Suitable for weight constrained deep space missions, hardware systems were developed including actuators, sensor, and electronics such that low-resolution etalons with performance required for implementation would weigh less than one pound.

Spectral Interferences Manganese (Mn) - Europium (Eu) Lines in X-Ray Fluorescence Spectrometry Spectrum

NASA Astrophysics Data System (ADS)

Tanc, Beril; Kaya, Mustafa; Gumus, Lokman; Kumral, Mustafa

2016-04-01

X-ray fluorescence (XRF) spectrometry is widely used for quantitative and semi quantitative analysis of many major, minor and trace elements in geological samples. Some advantages of the XRF method are; non-destructive sample preparation, applicability for powder, solid, paste and liquid samples and simple spectrum that are independent from chemical state. On the other hand, there are some disadvantages of the XRF methods such as poor sensitivity for low atomic number elements, matrix effect (physical matrix effects, such as fine versus course grain materials, may impact XRF performance) and interference effect (the spectral lines of elements may overlap distorting results for one or more elements). Especially, spectral interferences are very significant factors for accurate results. In this study, semi-quantitative analyzed manganese (II) oxide (MnO, 99.99%) was examined. Samples were pelleted and analyzed with XRF spectrometry (Bruker S8 Tiger). Unexpected peaks were obtained at the side of the major Mn peaks. Although sample does not contain Eu element, in results 0,3% Eu2O3 was observed. These result can occur high concentration of MnO and proximity of Mn and Eu lines. It can be eliminated by using correction equation or Mn concentration can confirm with other methods (such as Atomic absorption spectroscopy). Keywords: Spectral Interferences; Manganese (Mn); Europium (Eu); X-Ray Fluorescence Spectrometry Spectrum.

Nonlinear Legendre Spectral Finite Elements for Wind Turbine Blade Dynamics: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Q.; Sprague, M. A.; Jonkman, J.

2014-01-01

This paper presents a numerical implementation and examination of new wind turbine blade finite element model based on Geometrically Exact Beam Theory (GEBT) and a high-order spectral finite element method. The displacement-based GEBT is presented, which includes the coupling effects that exist in composite structures and geometric nonlinearity. Legendre spectral finite elements (LSFEs) are high-order finite elements with nodes located at the Gauss-Legendre-Lobatto points. LSFEs can be an order of magnitude more efficient that low-order finite elements for a given accuracy level. Interpolation of the three-dimensional rotation, a major technical barrier in large-deformation simulation, is discussed in the context ofmore » LSFEs. It is shown, by numerical example, that the high-order LSFEs, where weak forms are evaluated with nodal quadrature, do not suffer from a drawback that exists in low-order finite elements where the tangent-stiffness matrix is calculated at the Gauss points. Finally, the new LSFE code is implemented in the new FAST Modularization Framework for dynamic simulation of highly flexible composite-material wind turbine blades. The framework allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples showing validation and LSFE performance will be provided in the final paper.« less

Nonlinear finite element formulation for the large displacement analysis in multibody system dynamics

NASA Technical Reports Server (NTRS)

Rismantab-Sany, J.; Chang, B.; Shabana, A. A.

1989-01-01

A total Lagrangian finite element formulation for the deformable bodies in multibody mechanical systems that undergo finite relative rotations is developed. The deformable bodies are discretized using finite element methods. The shape functions that are used to describe the displacement field are required to include the rigid body modes that describe only large translational displacements. This does not impose any limitations on the technique because most commonly used shape functions satisfy this requirement. The configuration of an element is defined using four sets of coordinate systems: Body, Element, Intermediate element, Global. The body coordinate system serves as a unique standard for the assembly of the elements forming the deformable body. The element coordinate system is rigidly attached to the element and therefore it translates and rotates with the element. The intermediate element coordinate system, whose axes are initially parallel to the element axes, has an origin which is rigidly attached to the origin of the body coordinate system and is used to conveniently describe the configuration of the element in undeformed state with respect to the body coordinate system.

A Mixed Multi-Field Finite Element Formulation for Thermopiezoelectric Composite Shells

NASA Technical Reports Server (NTRS)

Lee, Ho-Jun; Saravanos, Dimitris A.

1999-01-01

Analytical formulations are presented which account for the coupled mechanical, electrical, and thermal response of piezoelectric composite shell structures. A new mixed multi-field laminate theory is developed which combines "single layer" assumptions for the displacements along with layerwise fields for the electric potential and temperature. This laminate theory is formulated using curvilinear coordinates and is based on the principles of linear thermopiezoelectricity. The mechanics have the inherent capability to explicitly model both the active and sensory responses of piezoelectric composite shells in thermal environment. Finite element equations are derived and implemented for an eight-noded shell element. Numerical studies are conducted to investigate both the sensory and active responses of piezoelectric composite shell structures subjected to thermal loads. Results for a cantilevered plate with an attached piezoelectric layer are com- pared with corresponding results from a commercial finite element code and a previously developed program. Additional studies are conducted on a cylindrical shell with an attached piezoelectric layer to demonstrate capabilities to achieve thermal shape control on curved piezoelectric structures.

Potentiating the antibacterial effect of silver nanospheres by surface-capping with chlorhexidine gluconate

NASA Astrophysics Data System (ADS)

Priyadarshini, Balasankar Meera; Fawzy, Amr S.

2017-04-01

In this work, the commercial polyvinylpyrrolidone (PVP)-capped silver nanospheres (Ag-NSP) were surface decorated with chlorhexidine gluconate (CHXg) for potentiating the antibacterial properties of Ag-NSP. Different formulations of CHXg-loaded Ag-NSP (Ag-NSP/CHXg) were prepared by varying the incubation times (0.5, 1.5, and 3 h). A thorough characterization of Ag-NSP/CHXg nanospheres has been carried out by dynamic light scattering (DLS), transmission electron microscopy (TEM), energy-dispersive surface elemental composition spectral analysis (SEM/EDX), Fourier transform infrared spectroscopy (FTIR), percentage (%) CHXg loading efficiency (LE), in vitro CHXg and Ag+ ion release, antibacterial/biofilm inhibition assay, and human mesenchymal stem cells (hMSCs) cytotoxicity evaluation. DLS measured nanospheres to be <160 nm and indicated that CHXg treatment drastically shifted the surface charge from negative to high positive values, with homogenous distribution. TEM revealed spherical Ag-NSP/CHXg nanospheres with a clearly visible surface coating of CHXg. FTIR confirmed association of CHXg with Ag-NSP nanospheres, whereas SEM/EDX data verified presence of spectral peaks specific to silver (Ag), CHXg, and PVP. The %LE gradually increased with increasing incubation times. In vitro CHXg release exhibited a bi-phasic fashion showing maximum release of 74.83 ± 20.67% from Ag-NSP/CHXg-3h at 14 days. A slow release of Ag+ ions was detected; however, the surface decoration of Ag-NSP substantially hampered/restricted the liberation of ions. Agar well diffusion, MTS (3-(4,5-dimethylthiazol-2-yl)-5-(3-carboxymethoxyphenyl)-2-(4-sulfophenyl)-2H-tetrazolium), and crystal violet assay suggested good antibacterial/antibiofilm activity of Ag-NSP/CHXg that correlated with the increasing %LE of nanospheres. hMSCs cytotoxicity study showed low toxicity properties of all nanosphere formulations, except for Ag-NSP/CHXg-3h, affecting the cell viability at all proposed concentrations and exposure time points. CHXg accentuated the antibacterial properties of Ag-NSP.

Finite element analysis of large transient elastic-plastic deformations of simple structures, with application to the engine rotor fragment containment/deflection problem

NASA Technical Reports Server (NTRS)

Wu, R. W.; Witmer, E. A.

1972-01-01

Assumed-displacement versions of the finite-element method are developed to predict large-deformation elastic-plastic transient deformations of structures. Both the conventional and a new improved finite-element variational formulation are derived. These formulations are then developed in detail for straight-beam and curved-beam elements undergoing (1) Bernoulli-Euler-Kirchhoff or (2) Timoshenko deformation behavior, in one plane. For each of these categories, several types of assumed-displacement finite elements are developed, and transient response predictions are compared with available exact solutions for small-deflection, linear-elastic transient responses. The present finite-element predictions for large-deflection elastic-plastic transient responses are evaluated via several beam and ring examples for which experimental measurements of transient strains and large transient deformations and independent finite-difference predictions are available.

A survey of the core-congruential formulation for geometrically nonlinear TL finite elements

NASA Technical Reports Server (NTRS)

Felippa, Carlos A.; Crivelli, Luis A.; Haugen, Bjorn

1994-01-01

This article presents a survey of the core-congruential formulation (CCF) for geometrically nonlinear mechanical finite elements based on the total Lagrangian (TL) kinematic description. Although the key ideas behind the CCF can be traced back to Rajasekaran and Murray in 1973, it has not subsequently received serious attention. The CCF is distinguished by a two-phase development of the finite element stiffness equations. The initial phase developed equations for individual particles. These equations are expressed in terms of displacement gradients as degrees of freedom. The second phase involves congruential-type transformations that eventually binds the element particles of an individual element in terms of its node-displacement degrees of freedom. Two versions of the CCF, labeled direct and generalized, are distinguished. The direct CCF (DCCF) is first described in general form and then applied to the derivation of geometrically nonlinear bar, and plane stress elements using the Green-Lagrange strain measure. The more complex generalized CCF (GCCF) is described and applied to the derivation of 2D and 3D Timoshenko beam elements. Several advantages of the CCF, notably the physically clean separation of material and geometric stiffnesses, and its independence with respect to the ultimate choice of shape functions and element degrees of freedom, are noted. Application examples involving very large motions solved with the 3D beam element display the range of applicability of this formulation, which transcends the kinematic limitations commonly attributed to the TL description.

Spectral likelihood expansions for Bayesian inference

NASA Astrophysics Data System (ADS)

Nagel, Joseph B.; Sudret, Bruno

2016-03-01

A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this spectral likelihood expansion all statistical quantities of interest can be calculated semi-analytically. The posterior is formally represented as the product of a reference density and a linear combination of polynomial basis functions. Both the model evidence and the posterior moments are related to the expansion coefficients. This formulation avoids Markov chain Monte Carlo simulation and allows one to make use of linear least squares instead. The pros and cons of spectral Bayesian inference are discussed and demonstrated on the basis of simple applications from classical statistics and inverse modeling.

Linear and nonlinear dynamic analysis by boundary element method. Ph.D. Thesis, 1986 Final Report

NASA Technical Reports Server (NTRS)

Ahmad, Shahid

1991-01-01

An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons with available analytical and numerical results, the stability and high accuracy of these dynamic analysis techniques are established.

Digital Equivalent Data System for XRF Labeling of Objects

NASA Technical Reports Server (NTRS)

Schramm, Harry F.; Kaiser, Bruce

2005-01-01

A digital equivalent data system (DEDS) is a system for identifying objects by means of the x-ray fluorescence (XRF) spectra of labeling elements that are encased in or deposited on the objects. As such, a DEDS is a revolutionary new major subsystem of an XRF system. A DEDS embodies the means for converting the spectral data output of an XRF scanner to an ASCII alphanumeric or barcode label that can be used to identify (or verify the assumed or apparent identity of) an XRF-scanned object. A typical XRF spectrum of interest contains peaks at photon energies associated with specific elements on the Periodic Table (see figure). The height of each spectral peak above the local background spectral intensity is proportional to the relative abundance of the corresponding element. Alphanumeric values are assigned to the relative abundances of the elements. Hence, if an object contained labeling elements in suitably chosen proportions, an alphanumeric representation of the object could be extracted from its XRF spectrum. The mixture of labeling elements and for reading the XRF spectrum would be compatible with one of the labeling conventions now used for bar codes and binary matrix patterns (essentially, two-dimensional bar codes that resemble checkerboards). A further benefit of such compatibility is that it would enable the conversion of the XRF spectral output to a bar or matrix-coded label, if needed. In short, a process previously used only for material composition analysis has been reapplied to the world of identification. This new level of verification is now being used for "authentication."

Fluid-structure finite-element vibrational analysis

NASA Technical Reports Server (NTRS)

Feng, G. C.; Kiefling, L.

1974-01-01

A fluid finite element has been developed for a quasi-compressible fluid. Both kinetic and potential energy are expressed as functions of nodal displacements. Thus, the formulation is similar to that used for structural elements, with the only differences being that the fluid can possess gravitational potential, and the constitutive equations for fluid contain no shear coefficients. Using this approach, structural and fluid elements can be used interchangeably in existing efficient sparse-matrix structural computer programs such as SPAR. The theoretical development of the element formulations and the relationships of the local and global coordinates are shown. Solutions of fluid slosh, liquid compressibility, and coupled fluid-shell oscillation problems which were completed using a temporary digital computer program are shown. The frequency correlation of the solutions with classical theory is excellent.

A new hybrid transfinite element computational methodology for applicability to conduction/convection/radiation heat transfer

NASA Technical Reports Server (NTRS)

Tamma, Kumar K.; Railkar, Sudhir B.

1988-01-01

This paper describes new and recent advances in the development of a hybrid transfinite element computational methodology for applicability to conduction/convection/radiation heat transfer problems. The transfinite element methodology, while retaining the modeling versatility of contemporary finite element formulations, is based on application of transform techniques in conjunction with classical Galerkin schemes and is a hybrid approach. The purpose of this paper is to provide a viable hybrid computational methodology for applicability to general transient thermal analysis. Highlights and features of the methodology are described and developed via generalized formulations and applications to several test problems. The proposed transfinite element methodology successfully provides a viable computational approach and numerical test problems validate the proposed developments for conduction/convection/radiation thermal analysis.

Modelling of structural flexiblity in multibody railroad vehicle systems

NASA Astrophysics Data System (ADS)

Escalona, José L.; Sugiyama, Hiroyuki; Shabana, Ahmed A.

2013-07-01

This paper presents a review of recent research investigations on the computer modelling of flexible bodies in railroad vehicle systems. The paper will also discuss the influence of the structural flexibility of various components, including the wheelset, the truck frames, tracks, pantograph/catenary systems, and car bodies, on the dynamics of railroad vehicles. While several formulations and computer techniques for modelling structural flexibility are discussed in this paper, a special attention is paid to the floating frame of reference formulation which is widely used and leads to reduced-order finite-element models for flexible bodies by employing component modes synthesis techniques. Other formulations and numerical methods such as semi-analytical approaches, absolute nodal coordinate formulation, finite-segment method, boundary elements method, and discrete elements method are also discussed. This investigation is motivated by the fact that the structural flexibility can have a significant effect on the overall dynamics of railroad vehicles, ride comfort, vibration suppression and noise level reduction, lateral stability, track response to vehicle forces, stress analysis, wheel-rail contact forces, wear and crashworthiness.

Flux-Based Finite Volume representations for general thermal problems

NASA Technical Reports Server (NTRS)

Mohan, Ram V.; Tamma, Kumar K.

1993-01-01

Flux-Based Finite Volume (FV) element representations for general thermal problems are given in conjunction with a generalized trapezoidal gamma-T family of algorithms, formulated following the spirit of what we term as the Lax-Wendroff based FV formulations. The new flux-based representations introduced offer an improved physical interpretation of the problem along with computationally convenient and attractive features. The space and time discretization emanate from a conservation form of the governing equation for thermal problems, and in conjunction with the flux-based element representations give rise to a physically improved and locally conservative numerical formulations. The present representations seek to involve improved locally conservative properties, improved physical representations and computational features; these are based on a 2D, bilinear FV element and can be extended for other cases. Time discretization based on a gamma-T family of algorithms in the spirit of a Lax-Wendroff based FV formulations are employed. Numerical examples involving linear/nonlinear steady and transient situations are shown to demonstrate the applicability of the present representations for thermal analysis situations.

An assumed-stress hybrid 4-node shell element with drilling degrees of freedom

NASA Technical Reports Server (NTRS)

Aminpour, M. A.

1992-01-01

An assumed-stress hybrid/mixed 4-node quadrilateral shell element is introduced that alleviates most of the deficiencies associated with such elements. The formulation of the element is based on the assumed-stress hybrid/mixed method using the Hellinger-Reissner variational principle. The membrane part of the element has 12 degrees of freedom including rotational or 'drilling' degrees of freedom at the nodes. The bending part of the element also has 12 degrees of freedom. The bending part of the element uses the Reissner-Mindlin plate theory which takes into account the transverse shear contributions. The element formulation is derived from an 8-node isoparametric element by expressing the midside displacement degrees of freedom in terms of displacement and rotational degrees of freedom at corner nodes. The element passes the patch test, is nearly insensitive to mesh distortion, does not 'lock', possesses the desirable invariance properties, has no hidden spurious modes, and for the majority of test cases used in this paper produces more accurate results than the other elements employed herein for comparison.

On Raviart-Thomas and VMS formulations for flow in heterogeneous materials.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Turner, Daniel Zack

It is well known that the continuous Galerkin method (in its standard form) is not locally conservative, yet many stabilized methods are constructed by augmenting the standard Galerkin weak form. In particular, the Variational Multiscale (VMS) method has achieved popularity for combating numerical instabilities that arise for mixed formulations that do not otherwise satisfy the LBB condition. Among alternative methods that satisfy local and global conservation, many employ Raviart-Thomas function spaces. The lowest order Raviart-Thomas finite element formulation (RT0) consists of evaluating fluxes over the midpoint of element edges and constant pressures within the element. Although the RT0 element posesmore » many advantages, it has only been shown viable for triangular or tetrahedral elements (quadrilateral variants of this method do not pass the patch test). In the context of heterogenous materials, both of these methods have been used to model the mixed form of the Darcy equation. This work aims, in a comparative fashion, to evaluate the strengths and weaknesses of either approach for modeling Darcy flow for problems with highly varying material permeabilities and predominantly open flow boundary conditions. Such problems include carbon sequestration and enhanced oil recovery simulations for which the far-field boundary is typically described with some type of pressure boundary condition. We intend to show the degree to which the VMS formulation violates local mass conservation for these types of problems and compare the performance of the VMS and RT0 methods at boundaries between disparate permeabilities.« less

A survey on the measure of combat readiness

NASA Astrophysics Data System (ADS)

Wen, Kwong Fook; Nor, Norazman Mohamad; Soon, Lee Lai

2014-09-01

Measuring the combat readiness in military forces involves the measures of tangible and intangible elements of combat power. Though these measures are applicable, the mathematical models and formulae used focus mainly on either the tangible or the intangible elements. In this paper, a review is done to highlight the research gap in the formulation of a mathematical model that incorporates tangible elements with intangible elements to measure the combat readiness of a military force. It highlights the missing link between the tangible and intangible elements of combat power. To bridge the gap and missing link, a mathematical model could be formulated that measures both the tangible and intangible aspects of combat readiness by establishing the relationship between the causal (tangible and intangible) elements and its effects on the measure of combat readiness. The model uses multiple regression analysis as well as mathematical modeling and simulation which digest the capability component reflecting its assets and resources, the morale component reflecting human needs, and the quality of life component reflecting soldiers' state of satisfaction in life. The results of the review provide a mean to bridge the research gap through the formulation of a mathematical model that shows the total measure of a military force's combat readiness. The results also significantly identify parameters for each of the variables and factors in the model.

A case for poroelasticity in skeletal muscle finite element analysis: experiment and modeling.

PubMed

Wheatley, Benjamin B; Odegard, Gregory M; Kaufman, Kenton R; Haut Donahue, Tammy L

2017-05-01

Finite element models of skeletal muscle typically ignore the biphasic nature of the tissue, associating any time dependence with a viscoelastic formulation. In this study, direct experimental measurement of permeability was conducted as a function of specimen orientation and strain. A finite element model was developed to identify how various permeability formulations affect compressive response of the tissue. Experimental and modeling results suggest the assumption of a constant, isotropic permeability is appropriate. A viscoelastic only model differed considerably from a visco-poroelastic model, suggesting the latter is more appropriate for compressive studies.

A spectral reflectance estimation technique using multispectral data from the Viking lander camera

NASA Technical Reports Server (NTRS)

Park, S. K.; Huck, F. O.

1976-01-01

A technique is formulated for constructing spectral reflectance curve estimates from multispectral data obtained with the Viking lander camera. The multispectral data are limited to six spectral channels in the wavelength range from 0.4 to 1.1 micrometers and most of these channels exhibit appreciable out-of-band response. The output of each channel is expressed as a linear (integral) function of the (known) solar irradiance, atmospheric transmittance, and camera spectral responsivity and the (unknown) spectral responsivity and the (unknown) spectral reflectance. This produces six equations which are used to determine the coefficients in a representation of the spectral reflectance as a linear combination of known basis functions. Natural cubic spline reflectance estimates are produced for a variety of materials that can be reasonably expected to occur on Mars. In each case the dominant reflectance features are accurately reproduced, but small period features are lost due to the limited number of channels. This technique may be a valuable aid in selecting the number of spectral channels and their responsivity shapes when designing a multispectral imaging system.

Spectral methods for CFD

NASA Technical Reports Server (NTRS)

Zang, Thomas A.; Streett, Craig L.; Hussaini, M. Yousuff

1989-01-01

One of the objectives of these notes is to provide a basic introduction to spectral methods with a particular emphasis on applications to computational fluid dynamics. Another objective is to summarize some of the most important developments in spectral methods in the last two years. The fundamentals of spectral methods for simple problems will be covered in depth, and the essential elements of several fluid dynamical applications will be sketched.

Parallelized modelling and solution scheme for hierarchically scaled simulations

NASA Technical Reports Server (NTRS)

Padovan, Joe

1995-01-01

This two-part paper presents the results of a benchmarked analytical-numerical investigation into the operational characteristics of a unified parallel processing strategy for implicit fluid mechanics formulations. This hierarchical poly tree (HPT) strategy is based on multilevel substructural decomposition. The Tree morphology is chosen to minimize memory, communications and computational effort. The methodology is general enough to apply to existing finite difference (FD), finite element (FEM), finite volume (FV) or spectral element (SE) based computer programs without an extensive rewrite of code. In addition to finding large reductions in memory, communications, and computational effort associated with a parallel computing environment, substantial reductions are generated in the sequential mode of application. Such improvements grow with increasing problem size. Along with a theoretical development of general 2-D and 3-D HPT, several techniques for expanding the problem size that the current generation of computers are capable of solving, are presented and discussed. Among these techniques are several interpolative reduction methods. It was found that by combining several of these techniques that a relatively small interpolative reduction resulted in substantial performance gains. Several other unique features/benefits are discussed in this paper. Along with Part 1's theoretical development, Part 2 presents a numerical approach to the HPT along with four prototype CFD applications. These demonstrate the potential of the HPT strategy.

An Investigation of Energy Transmission Due to Flexural Wave Propagation in Lightweight, Built-Up Structures. Thesis

NASA Technical Reports Server (NTRS)

Mickol, John Douglas; Bernhard, R. J.

1986-01-01

A technique to measure flexural structure-borne noise intensity is investigated. Two accelerometers serve as transducers in this cross-spectral technique. The structure-borne sound power is obtained by two different techniques and compared. In the first method, a contour integral of intensity is performed from the values provided by the two-accelerometer intensity technique. In the second method, input power is calculated directly from the output of force and acceleration transducers. A plate and two beams were the subjects of the sound power comparisons. Excitation for the structures was either band-limited white noise or a deterministic signal similar to a swept sine. The two-accelerometer method was found to be sharply limited by near field and transducer spacing limitations. In addition, for the lightweight structures investigated, it was found that the probe inertia can have a significant influence on the power input to the structure. In addition to the experimental investigation of structure-borne sound energy, an extensive study of the point harmonically forced, point-damped beam boundary value problem was performed to gain insight into measurements of this nature. The intensity formulations were also incorporated into the finite element method. Intensity mappings were obtained analytically via finite element modeling of simple structures.

Linear stochastic evaluation of tyre vibration due to tyre/road excitation

NASA Astrophysics Data System (ADS)

Rustighi, E.; Elliott, S. J.; Finnveden, S.; Gulyás, K.; Mócsai, T.; Danti, M.

2008-03-01

Tyre/road interaction is recognised as the main source of interior and exterior noise for velocities over the 40 km/h. In this paper, a three-dimensional (3D) elemental approach has been adopted to predict the stochastic tyre vibration and hence the interior and exterior noise due to this kind of excitation. The road excitation has been modelled from the spectral density of a common road profile, supposing the road to be an isotropic surface. A linear Winkler bedding connects the 3D model of the tyre with the ground. The exterior noise has been evaluated by an elemental calculation of the radiation matrix of the tyre deformed by the static load on a concrete road. The noise inside the vehicle has also been calculated, using the transfer functions from the force transmitted to the hub and the noise inside the vehicle, which have been computed by a FEM model of a common car body. The simple formulation allows much quicker calculation than traditional nonlinear approaches, and appears to give results consistent with available measurements, although the effects of tyre rotation and of the nonlinearities in the contact model are yet to be quantified, and the method requires further experimental validation before practical application.

Polarizing beam splitter based on the anisotropic spectral reflectivity characteristic of form-birefringent multilayer gratings.

PubMed

Tyan, R C; Sun, P C; Scherer, A; Fainman, Y

1996-05-15

We introduce a novel polarizing beam splitter that uses the anisotropic spectral reflectivity (ASR) characteristic of a high-spatial-frequency multilayer binary grating. Such ASR effects allow us to design an optical element that is transparent for TM polarization and reflective for TE polarization. For normally incident light our element acts as a polarization-selective mirror. The properties of this polarizing beam splitter are investigated with rigorous coupled-wave analysis. The design results show that an ASR polarizing beam splitter can provide a high polarization extinction ratio for optical waves from a wide range of incident angles and a broad optical spectral bandwidth.

Exact solutions to the fermion propagator Schwinger-Dyson equation in Minkowski space with on-shell renormalization for quenched QED

DOE PAGES

Jia, Shaoyang; Pennington, M. R.

2017-08-01

With the introduction of a spectral representation, the Schwinger-Dyson equation (SDE) for the fermion propagator is formulated in Minkowski space in QED. After imposing the on-shell renormalization conditions, analytic solutions for the fermion propagator spectral functions are obtained in four dimensions with a renormalizable version of the Gauge Technique anzatz for the fermion-photon vertex in the quenched approximation in the Landau gauge. Despite the limitations of this model, having an explicit solution provides a guiding example of the fermion propagator with the correct analytic structure. The Padé approximation for the spectral functions is also investigated.

Exact solutions to the fermion propagator Schwinger-Dyson equation in Minkowski space with on-shell renormalization for quenched QED

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jia, Shaoyang; Pennington, M. R.

With the introduction of a spectral representation, the Schwinger-Dyson equation (SDE) for the fermion propagator is formulated in Minkowski space in QED. After imposing the on-shell renormalization conditions, analytic solutions for the fermion propagator spectral functions are obtained in four dimensions with a renormalizable version of the Gauge Technique anzatz for the fermion-photon vertex in the quenched approximation in the Landau gauge. Despite the limitations of this model, having an explicit solution provides a guiding example of the fermion propagator with the correct analytic structure. The Padé approximation for the spectral functions is also investigated.

Le Châtelier reciprocal relations and the mechanical analog

NASA Astrophysics Data System (ADS)

Gilmore, Robert

1983-08-01

Le Châtelier's principle is discussed carefully in terms of two sets of simple thermodynamic examples. The principle is then formulated quantitatively for general thermodynamic systems. The formulation is in terms of a perturbation-response matrix, the Le Châtelier matrix [L]. Le Châtelier's principle is contained in the diagonal elements of this matrix, all of which exceed one. These matrix elements describe the response of a system to a perturbation of either its extensive or intensive variables. These response ratios are inverses of each other. The Le Châtelier matrix is symmetric, so that a new set of thermodynamic reciprocal relations is derived. This quantitative formulation is illustrated by a single simple example which includes the original examples and shows the reciprocities among them. The assumptions underlying this new quantitative formulation of Le Châtelier's principle are general and applicable to a wide variety of nonthermodynamic systems. Le Châtelier's principle is formulated quantitatively for mechanical systems in static equilibrium, and mechanical examples of this formulation are given.

Selective Optimization

DTIC Science & Technology

2015-07-06

NUMBER 5b. GRANT NUMBER AFOSR FA9550-12-1-0154 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Shabbir Ahmed and Santanu S. Dey 5d. PROJECT NUMBER 5e. TASK...standard mixed-integer programming (MIP) formulations of selective optimization problems. While such formulations can be attacked by commercial...F33615-86-C-5169. 5b. GRANT NUMBER. Enter all grant numbers as they appear in the report, e.g. AFOSR-82-1234. 5c. PROGRAM ELEMENT NUMBER. Enter

Application of a handheld NIR spectrometer in prediction of drug content in inkjet printed orodispersible formulations containing prednisolone and levothyroxine.

PubMed

Vakili, Hossein; Wickström, Henrika; Desai, Diti; Preis, Maren; Sandler, Niklas

2017-05-30

Quality control tools to assess the quality of printable orodispersible formulations are yet to be defined. Four different orodispersible dosage forms containing two poorly soluble drugs, levothyroxine and prednisolone, were produced on two different edible substrates by piezoelectric inkjet printing. Square shaped units of 4cm 2 were printed in different resolutions to achieve an escalating drug dose by highly accurate and uniform displacement of droplets in picoliter range from the printhead onto the substrates. In addition, the stability of drug inks in a course of 24h as well as the mechanical properties and disintegration behavior of the printed units were examined. A compact handheld near-infrared (NIR) spectral device in the range of 1550-1950nm was used for quantitative estimation of the drug amount in printed formulations. The spectral data was treated with mean centering, Savitzky-Golay filtering and a third derivative approach. Principal component analysis (PCA) and orthogonal partial least squares (OPLS) regression were applied to build predictive models for quality control of the printed dosage forms. The accurate tuning of the dose in each formulation was confirmed by UV spectrophotometry for prednisolone (0.43-1.95mg with R 2 =0.999) and high performance liquid chromatography for levothyroxine (0.15-0.86mg with R 2 =0.997). It was verified that the models were capable of clustering and predicting the drug dose in the formulations with both Q 2 and R 2 Y values between 0.94-0.99. Copyright © 2017 Elsevier B.V. All rights reserved.

Efficient Trajectory Propagation for Orbit Determination Problems

NASA Technical Reports Server (NTRS)

Roa, Javier; Pelaez, Jesus

2015-01-01

Regularized formulations of orbital motion apply a series of techniques to improve the numerical integration of the orbit. Despite their advantages and potential applications little attention has been paid to the propagation of the partial derivatives of the corresponding set of elements or coordinates, required in many orbit-determination scenarios and optimization problems. This paper fills this gap by presenting the general procedure for integrating the state-transition matrix of the system together with the nominal trajectory using regularized formulations and different sets of elements. The main difficulty comes from introducing an independent variable different from time, because the solution needs to be synchronized. The correction of the time delay is treated from a generic perspective not focused on any particular formulation. The synchronization using time-elements is also discussed. Numerical examples include strongly-perturbed orbits in the Pluto system, motivated by the recent flyby of the New Horizons spacecraft, together with a geocentric flyby of the NEAR spacecraft.

Parallel Domain Decomposition Formulation and Software for Large-Scale Sparse Symmetrical/Unsymmetrical Aeroacoustic Applications

NASA Technical Reports Server (NTRS)

Nguyen, D. T.; Watson, Willie R. (Technical Monitor)

2005-01-01

The overall objectives of this research work are to formulate and validate efficient parallel algorithms, and to efficiently design/implement computer software for solving large-scale acoustic problems, arised from the unified frameworks of the finite element procedures. The adopted parallel Finite Element (FE) Domain Decomposition (DD) procedures should fully take advantages of multiple processing capabilities offered by most modern high performance computing platforms for efficient parallel computation. To achieve this objective. the formulation needs to integrate efficient sparse (and dense) assembly techniques, hybrid (or mixed) direct and iterative equation solvers, proper pre-conditioned strategies, unrolling strategies, and effective processors' communicating schemes. Finally, the numerical performance of the developed parallel finite element procedures will be evaluated by solving series of structural, and acoustic (symmetrical and un-symmetrical) problems (in different computing platforms). Comparisons with existing "commercialized" and/or "public domain" software are also included, whenever possible.

Determination of hazardous ingredients in personal care products using laser-induced breakdown spectroscopy

NASA Astrophysics Data System (ADS)

Abrar, M.; Iqbal, T.; Fahad, M.; Andleeb, M.; Farooq, Z.; Afsheen, S.

2018-05-01

In the present work, the laser-induced breakdown spectroscopy technique is applied to explore the concentration of toxic elements present in cosmetic materials. The elemental analysis of chromium (Cr), magnesium (Mg), cadmium (Cd) and lead (Pb) are selected as major elements and manganese (Mn), sodium (Na), potassium (P), sulfur (S), silicon (Si) and titanium (Ti) as minor elements in cosmetic products. In this technique, a plasma plume is generated by using an Nd:YAG Laser of 532 nm wavelength and spectral lines for the respective samples are observed. Four different samples of cosmetic products are selected, i.e. two samples for lipstick and two for eyeshadow. The observed spectral lines of all major and minor elements are used to calculate their concentration in all samples through the intensity ratio method. Among selected lipstick and eyeshadow samples, one sample is branded, and one is collected from the local market. It is observed that chromium, magnesium and lead have strong spectral lines and consequently show high concentration. The calculated concentrations are then compared to permissible limits set by the Food and Drug Administration with regard to the cosmetics industry. The concentration of these toxic elements in selected local cosmetic samples exceeds the safe permissible limit for human use and could lead to serious health problems.

Miniature infrared hyperspectral imaging sensor for airborne applications

NASA Astrophysics Data System (ADS)

Hinnrichs, Michele; Hinnrichs, Bradford; McCutchen, Earl

2017-05-01

Pacific Advanced Technology (PAT) has developed an infrared hyperspectral camera, both MWIR and LWIR, small enough to serve as a payload on a miniature unmanned aerial vehicles. The optical system has been integrated into the cold-shield of the sensor enabling the small size and weight of the sensor. This new and innovative approach to infrared hyperspectral imaging spectrometer uses micro-optics and will be explained in this paper. The micro-optics are made up of an area array of diffractive optical elements where each element is tuned to image a different spectral region on a common focal plane array. The lenslet array is embedded in the cold-shield of the sensor and actuated with a miniature piezo-electric motor. This approach enables rapid infrared spectral imaging with multiple spectral images collected and processed simultaneously each frame of the camera. This paper will present our optical mechanical design approach which results in an infrared hyper-spectral imaging system that is small enough for a payload on a mini-UAV or commercial quadcopter. The diffractive optical elements used in the lenslet array are blazed gratings where each lenslet is tuned for a different spectral bandpass. The lenslets are configured in an area array placed a few millimeters above the focal plane and embedded in the cold-shield to reduce the background signal normally associated with the optics. We have developed various systems using a different number of lenslets in the area array. Depending on the size of the focal plane and the diameter of the lenslet array will determine the spatial resolution. A 2 x 2 lenslet array will image four different spectral images of the scene each frame and when coupled with a 512 x 512 focal plane array will give spatial resolution of 256 x 256 pixel each spectral image. Another system that we developed uses a 4 x 4 lenslet array on a 1024 x 1024 pixel element focal plane array which gives 16 spectral images of 256 x 256 pixel resolution each frame.

Infrared hyperspectral imaging miniaturized for UAV applications

NASA Astrophysics Data System (ADS)

Hinnrichs, Michele; Hinnrichs, Bradford; McCutchen, Earl

2017-02-01

Pacific Advanced Technology (PAT) has developed an infrared hyperspectral camera, both MWIR and LWIR, small enough to serve as a payload on a miniature unmanned aerial vehicles. The optical system has been integrated into the cold-shield of the sensor enabling the small size and weight of the sensor. This new and innovative approach to infrared hyperspectral imaging spectrometer uses micro-optics and will be explained in this paper. The micro-optics are made up of an area array of diffractive optical elements where each element is tuned to image a different spectral region on a common focal plane array. The lenslet array is embedded in the cold-shield of the sensor and actuated with a miniature piezo-electric motor. This approach enables rapid infrared spectral imaging with multiple spectral images collected and processed simultaneously each frame of the camera. This paper will present our optical mechanical design approach which results in an infrared hyper-spectral imaging system that is small enough for a payload on a mini-UAV or commercial quadcopter. Also, an example of how this technology can easily be used to quantify a hydrocarbon gas leak's volume and mass flowrates. The diffractive optical elements used in the lenslet array are blazed gratings where each lenslet is tuned for a different spectral bandpass. The lenslets are configured in an area array placed a few millimeters above the focal plane and embedded in the cold-shield to reduce the background signal normally associated with the optics. We have developed various systems using a different number of lenslets in the area array. Depending on the size of the focal plane and the diameter of the lenslet array will determine the spatial resolution. A 2 x 2 lenslet array will image four different spectral images of the scene each frame and when coupled with a 512 x 512 focal plane array will give spatial resolution of 256 x 256 pixel each spectral image. Another system that we developed uses a 4 x 4 lenslet array on a 1024 x 1024 pixel element focal plane array which gives 16 spectral images of 256 x 256 pixel resolution each frame.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wintermeyer, Niklas; Winters, Andrew R., E-mail: awinters@math.uni-koeln.de; Gassner, Gregor J.

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving schememore » we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.« less

Adjoint Sensitivity Analysis for Scale-Resolving Turbulent Flow Solvers

NASA Astrophysics Data System (ADS)

Blonigan, Patrick; Garai, Anirban; Diosady, Laslo; Murman, Scott

2017-11-01

Adjoint-based sensitivity analysis methods are powerful design tools for engineers who use computational fluid dynamics. In recent years, these engineers have started to use scale-resolving simulations like large-eddy simulations (LES) and direct numerical simulations (DNS), which resolve more scales in complex flows with unsteady separation and jets than the widely-used Reynolds-averaged Navier-Stokes (RANS) methods. However, the conventional adjoint method computes large, unusable sensitivities for scale-resolving simulations, which unlike RANS simulations exhibit the chaotic dynamics inherent in turbulent flows. Sensitivity analysis based on least-squares shadowing (LSS) avoids the issues encountered by conventional adjoint methods, but has a high computational cost even for relatively small simulations. The following talk discusses a more computationally efficient formulation of LSS, ``non-intrusive'' LSS, and its application to turbulent flows simulated with a discontinuous-Galkerin spectral-element-method LES/DNS solver. Results are presented for the minimal flow unit, a turbulent channel flow with a limited streamwise and spanwise domain.

A space-fractional Monodomain model for cardiac electrophysiology combining anisotropy and heterogeneity on realistic geometries

NASA Astrophysics Data System (ADS)

Cusimano, N.; Gerardo-Giorda, L.

2018-06-01

Classical models of electrophysiology do not typically account for the effects of high structural heterogeneity in the spatio-temporal description of excitation waves propagation. We consider a modification of the Monodomain model obtained by replacing the diffusive term of the classical formulation with a fractional power of the operator, defined in the spectral sense. The resulting nonlocal model describes different levels of tissue heterogeneity as the fractional exponent is varied. The numerical method for the solution of the fractional Monodomain relies on an integral representation of the nonlocal operator combined with a finite element discretisation in space, allowing to handle in a natural way bounded domains in more than one spatial dimension. Numerical tests in two spatial dimensions illustrate the features of the model. Activation times, action potential duration and its dispersion throughout the domain are studied as a function of the fractional parameter: the expected peculiar behaviour driven by tissue heterogeneities is recovered.

Generalised summation-by-parts operators and variable coefficients

NASA Astrophysics Data System (ADS)

Ranocha, Hendrik

2018-06-01

High-order methods for conservation laws can be highly efficient if their stability is ensured. A suitable means mimicking estimates of the continuous level is provided by summation-by-parts (SBP) operators and the weak enforcement of boundary conditions. Recently, there has been an increasing interest in generalised SBP operators both in the finite difference and the discontinuous Galerkin spectral element framework. However, if generalised SBP operators are used, the treatment of the boundaries becomes more difficult since some properties of the continuous level are no longer mimicked discretely - interpolating the product of two functions will in general result in a value different from the product of the interpolations. Thus, desired properties such as conservation and stability are more difficult to obtain. Here, new formulations are proposed, allowing the creation of discretisations using general SBP operators that are both conservative and stable. Thus, several shortcomings that might be attributed to generalised SBP operators are overcome (cf. Nordström and Ruggiu (2017) [38] and Manzanero et al. (2017) [39]).

Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method

DOE PAGES

Kalchev, Delyan Z.; Lee, C. S.; Villa, U.; ...

2016-09-22

Here, we propose two multilevel spectral techniques for constructing coarse discretization spaces for saddle-point problems corresponding to PDEs involving a divergence constraint, with a focus on mixed finite element discretizations of scalar self-adjoint second order elliptic equations on general unstructured grids. We use element agglomeration algebraic multigrid (AMGe), which employs coarse elements that can have nonstandard shape since they are agglomerates of fine-grid elements. The coarse basis associated with each agglomerated coarse element is constructed by solving local eigenvalue problems and local mixed finite element problems. This construction leads to stable upscaled coarse spaces and guarantees the inf-sup compatibility ofmore » the upscaled discretization. Also, the approximation properties of these upscaled spaces improve by adding more local eigenfunctions to the coarse spaces. The higher accuracy comes at the cost of additional computational effort, as the sparsity of the resulting upscaled coarse discretization (referred to as operator complexity) deteriorates when we introduce additional functions in the coarse space. We also provide an efficient solver for the coarse (upscaled) saddle-point system by employing hybridization, which leads to a symmetric positive definite (s.p.d.) reduced system for the Lagrange multipliers, and to solve the latter s.p.d. system, we use our previously developed spectral AMGe solver. Numerical experiments, in both two and three dimensions, are provided to illustrate the efficiency of the proposed upscaling technique.« less

Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kalchev, Delyan Z.; Lee, C. S.; Villa, U.

Here, we propose two multilevel spectral techniques for constructing coarse discretization spaces for saddle-point problems corresponding to PDEs involving a divergence constraint, with a focus on mixed finite element discretizations of scalar self-adjoint second order elliptic equations on general unstructured grids. We use element agglomeration algebraic multigrid (AMGe), which employs coarse elements that can have nonstandard shape since they are agglomerates of fine-grid elements. The coarse basis associated with each agglomerated coarse element is constructed by solving local eigenvalue problems and local mixed finite element problems. This construction leads to stable upscaled coarse spaces and guarantees the inf-sup compatibility ofmore » the upscaled discretization. Also, the approximation properties of these upscaled spaces improve by adding more local eigenfunctions to the coarse spaces. The higher accuracy comes at the cost of additional computational effort, as the sparsity of the resulting upscaled coarse discretization (referred to as operator complexity) deteriorates when we introduce additional functions in the coarse space. We also provide an efficient solver for the coarse (upscaled) saddle-point system by employing hybridization, which leads to a symmetric positive definite (s.p.d.) reduced system for the Lagrange multipliers, and to solve the latter s.p.d. system, we use our previously developed spectral AMGe solver. Numerical experiments, in both two and three dimensions, are provided to illustrate the efficiency of the proposed upscaling technique.« less

High-order polygonal discontinuous Petrov-Galerkin (PolyDPG) methods using ultraweak formulations

NASA Astrophysics Data System (ADS)

Vaziri Astaneh, Ali; Fuentes, Federico; Mora, Jaime; Demkowicz, Leszek

2018-04-01

This work represents the first endeavor in using ultraweak formulations to implement high-order polygonal finite element methods via the discontinuous Petrov-Galerkin (DPG) methodology. Ultraweak variational formulations are nonstandard in that all the weight of the derivatives lies in the test space, while most of the trial space can be chosen as copies of $L^2$-discretizations that have no need to be continuous across adjacent elements. Additionally, the test spaces are broken along the mesh interfaces. This allows one to construct conforming polygonal finite element methods, termed here as PolyDPG methods, by defining most spaces by restriction of a bounding triangle or box to the polygonal element. The only variables that require nontrivial compatibility across elements are the so-called interface or skeleton variables, which can be defined directly on the element boundaries. Unlike other high-order polygonal methods, PolyDPG methods do not require ad hoc stabilization terms thanks to the crafted stability of the DPG methodology. A proof of convergence of the form $h^p$ is provided and corroborated through several illustrative numerical examples. These include polygonal meshes with $n$-sided convex elements and with highly distorted concave elements, as well as the modeling of discontinuous material properties along an arbitrary interface that cuts a uniform grid. Since PolyDPG methods have a natural a posteriori error estimator a polygonal adaptive strategy is developed and compared to standard adaptivity schemes based on constrained hanging nodes. This work is also accompanied by an open-source $\\texttt{PolyDPG}$ software supporting polygonal and conventional elements.

Diffractive Optical Elements for Spectral Imaging

NASA Technical Reports Server (NTRS)

Wilson, D.; Maker, P.; Muller, R.; Mourolis, P.; Descour, M.; Volin, C.; Dereniak, E.

2000-01-01

Diffractive optical elements fabricated on flat and non-flat substrates frequently act as dispersive elements in imaging spectrometers. We describe the design and electron-beam fabrication of blazed and computer-generated-hologram gratings for slit and tomographic imaging spectrometer.

Diffractive Optical Elements for Spectral Imaging

NASA Technical Reports Server (NTRS)

Wilson, D.; Maker, P.; Muller, R.; Maker, P.; Mouroulis, P.; Descour, M.; Volin, C.; Dereniak, E.

2000-01-01

Diffractive optical elements fabricated on flat and non-flat substrates frequently act as dispersive elements in imaging spectrometers. We describe the design and electron-beam fabrication of blazed and computer-generated-hologram gratings for slit and tomographic imaging spectrometers.

Apparatus and method using a holographic optical element for converting a spectral distribution to image points

NASA Technical Reports Server (NTRS)

McGill, Matthew J. (Inventor); Scott, Vibart S. (Inventor); Marzouk, Marzouk (Inventor)

2001-01-01

A holographic optical element transforms a spectral distribution of light to image points. The element comprises areas, each of which acts as a separate lens to image the light incident in its area to an image point. Each area contains the recorded hologram of a point source object. The image points can be made to lie in a line in the same focal plane so as to align with a linear array detector. A version of the element has been developed that has concentric equal areas to match the circular fringe pattern of a Fabry-Perot interferometer. The element has high transmission efficiency, and when coupled with high quantum efficiency solid state detectors, provides an efficient photon-collecting detection system. The element may be used as part of the detection system in a direct detection Doppler lidar system or multiple field of view lidar system.

Investigating the effect of characteristic x-rays in cadmium zinc telluride detectors under breast computerized tomography operating conditions

PubMed Central

Glick, Stephen J.; Didier, Clay

2013-01-01

A number of research groups have been investigating the use of dedicated breast computerized tomography (CT). Preliminary results have been encouraging, suggesting an improved visualization of masses on breast CT as compared to conventional mammography. Nonetheless, there are many challenges to overcome before breast CT can become a routine clinical reality. One potential improvement over current breast CT prototypes would be the use of photon counting detectors with cadmium zinc telluride (CZT) (or CdTe) semiconductor material. These detectors can operate at room temperature and provide high detection efficiency and the capability of multi-energy imaging; however, one factor in particular that limits image quality is the emission of characteristic x-rays. In this study, the degradative effects of characteristic x-rays are examined when using a CZT detector under breast CT operating conditions. Monte Carlo simulation software was used to evaluate the effect of characteristic x-rays and the detector element size on spatial and spectral resolution for a CZT detector used under breast CT operating conditions. In particular, lower kVp spectra and thinner CZT thicknesses were studied than that typically used with CZT based conventional CT detectors. In addition, the effect of characteristic x-rays on the accuracy of material decomposition in spectral CT imaging was explored. It was observed that when imaging with 50-60 kVp spectra, the x-ray transmission through CZT was very low for all detector thicknesses studied (0.5–3.0 mm), thus retaining dose efficiency. As expected, characteristic x-ray escape from the detector element of x-ray interaction increased with decreasing detector element size, approaching a 50% escape fraction for a 100 μm size detector element. The detector point spread function was observed to have only minor degradation with detector element size greater than 200 μm and lower kV settings. Characteristic x-rays produced increasing distortion in the spectral response with decreasing detector element size. If not corrected for, this caused a large bias in estimating tissue density parameters for material decomposition. It was also observed that degradation of the spectral response due to characteristic x-rays caused worsening precision in the estimation of tissue density parameters. It was observed that characteristic x-rays do cause some degradation in the spatial and spectral resolution of thin CZT detectors operating under breast CT conditions. These degradations should be manageable with careful selection of the detector element size. Even with the observed spectral distortion from characteristic x-rays, it is still possible to correctly estimate tissue parameters for material decomposition using spectral CT if accurate modeling is used. PMID:24187383

Finite element method for optimal guidance of an advanced launch vehicle

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Bless, Robert R.; Calise, Anthony J.; Leung, Martin

1992-01-01

A temporal finite element based on a mixed form of Hamilton's weak principle is summarized for optimal control problems. The resulting weak Hamiltonian finite element method is extended to allow for discontinuities in the states and/or discontinuities in the system equations. An extension of the formulation to allow for control inequality constraints is also presented. The formulation does not require element quadrature, and it produces a sparse system of nonlinear algebraic equations. To evaluate its feasibility for real-time guidance applications, this approach is applied to the trajectory optimization of a four-state, two-stage model with inequality constraints for an advanced launch vehicle. Numerical results for this model are presented and compared to results from a multiple-shooting code. The results show the accuracy and computational efficiency of the finite element method.

A Spectral Element Discretisation on Unstructured Triangle / Tetrahedral Meshes for Elastodynamics

NASA Astrophysics Data System (ADS)

May, Dave A.; Gabriel, Alice-A.

2017-04-01

The spectral element method (SEM) defined over quadrilateral and hexahedral element geometries has proven to be a fast, accurate and scalable approach to study wave propagation phenomena. In the context of regional scale seismology and or simulations incorporating finite earthquake sources, the geometric restrictions associated with hexahedral elements can limit the applicability of the classical quad./hex. SEM. Here we describe a continuous Galerkin spectral element discretisation defined over unstructured meshes composed of triangles (2D), or tetrahedra (3D). The method uses a stable, nodal basis constructed from PKD polynomials and thus retains the spectral accuracy and low dispersive properties of the classical SEM, in addition to the geometric versatility provided by unstructured simplex meshes. For the particular basis and quadrature rule we have adopted, the discretisation results in a mass matrix which is not diagonal, thereby mandating linear solvers be utilised. To that end, we have developed efficient solvers and preconditioners which are robust with respect to the polynomial order (p), and possess high arithmetic intensity. Furthermore, we also consider using implicit time integrators, together with a p-multigrid preconditioner to circumvent the CFL condition. Implicit time integrators become particularly relevant when considering solving problems on poor quality meshes, or meshes containing elements with a widely varying range of length scales - both of which frequently arise when meshing non-trivial geometries. We demonstrate the applicability of the new method by examining a number of two- and three-dimensional wave propagation scenarios. These scenarios serve to characterise the accuracy and cost of the new method. Lastly, we will assess the potential benefits of using implicit time integrators for regional scale wave propagation simulations.

Effect of joint spacing and joint dip on the stress distribution around tunnels using different numerical methods

NASA Astrophysics Data System (ADS)

Nikadat, Nooraddin; Fatehi Marji, Mohammad; Rahmannejad, Reza; Yarahmadi Bafghi, Alireza

2016-11-01

Different conditions may affect the stability of tunnels by the geometry (spacing and orientation) of joints in the surrounded rock mass. In this study, by comparing the results obtained by the three novel numerical methods i.e. finite element method (Phase2), discrete element method (UDEC) and indirect boundary element method (TFSDDM), the effects of joint spacing and joint dips on the stress distribution around rock tunnels are numerically studied. These comparisons indicate the validity of the stress analyses around circular rock tunnels. These analyses also reveal that for a semi-continuous environment, boundary element method gives more accurate results compared to the results of finite element and distinct element methods. In the indirect boundary element method, the displacements due to joints of different spacing and dips are estimated by using displacement discontinuity (DD) formulations and the total stress distribution around the tunnel are obtained by using fictitious stress (FS) formulations.

Laminated Composite Shell Element Using Absolute Nodal Coordinate Formulation and Its Application to ANCF Tire Model

DTIC Science & Technology

2015-04-24

Paramsothy Jayakumar US Army TARDEC 6501 E. 11 Mile Road Warren, MI 48397-5000 Hiroyuki Sugiyama Department of Mechanical and Industrial...Part 2: Development of a Physical Tyre Model", Vehicle System Dynamics, vol. 50, pp. 339-356. [4] Sugiyama, H., Yamashita, H. and Jayakumar , P., 2014... Jayakumar , P. and Sugiyama, H., "Continuum Mechanics Based Bi-Linear Shear Deformable Shell Element using Absolute Nodal Coordinate Formulation", ASME

Reissner-Mindlin Legendre Spectral Finite Elements with Mixed Reduced Quadrature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brito, K. D.; Sprague, M. A.

2012-10-01

Legendre spectral finite elements (LSFEs) are examined through numerical experiments for static and dynamic Reissner-Mindlin plate bending and a mixed-quadrature scheme is proposed. LSFEs are high-order Lagrangian-interpolant finite elements with nodes located at the Gauss-Lobatto-Legendre quadrature points. Solutions on unstructured meshes are examined in terms of accuracy as a function of the number of model nodes and total operations. While nodal-quadrature LSFEs have been shown elsewhere to be free of shear locking on structured grids, locking is demonstrated here on unstructured grids. LSFEs with mixed quadrature are, however, locking free and are significantly more accurate than low-order finite-elements for amore » given model size or total computation time.« less

Frequency domain modeling and dynamic characteristics evaluation of existing wind turbine systems

NASA Astrophysics Data System (ADS)

Chiang, Chih-Hung; Yu, Chih-Peng

2016-04-01

It is quite well accepted that frequency domain procedures are suitable for the design and dynamic analysis of wind turbine structures, especially for floating offshore wind turbines, since random wind loads and wave induced motions are most likely simulated in the frequency domain. This paper presents specific applications of an effective frequency domain scheme to the linear analysis of wind turbine structures in which a 1-D spectral element was developed based on the axially-loaded member. The solution schemes are summarized for the spectral analyses of the tower, the blades, and the combined system with selected frequency-dependent coupling effect from foundation-structure interactions. Numerical examples demonstrate that the modal frequencies obtained using spectral-element models are in good agreement with those found in the literature. A 5-element mono-pile model results in less than 0.3% deviation from an existing 160-element model. It is preliminarily concluded that the proposed scheme is relatively efficient in performing quick verification for test data obtained from the on-site vibration measurement using the microwave interferometer.

A New High-Order Spectral Difference Method for Simulating Viscous Flows on Unstructured Grids with Mixed Elements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Mao; Qiu, Zihua; Liang, Chunlei

In the present study, a new spectral difference (SD) method is developed for viscous flows on meshes with a mixture of triangular and quadrilateral elements. The standard SD method for triangular elements, which employs Lagrangian interpolating functions for fluxes, is not stable when the designed accuracy of spatial discretization is third-order or higher. Unlike the standard SD method, the method examined here uses vector interpolating functions in the Raviart-Thomas (RT) spaces to construct continuous flux functions on reference elements. Studies have been performed for 2D wave equation and Euler equa- tions. Our present results demonstrated that the SDRT method ismore » stable and high-order accurate for a number of test problems by using triangular-, quadrilateral-, and mixed- element meshes.« less

A boundary element method for steady incompressible thermoviscous flow

NASA Technical Reports Server (NTRS)

Dargush, G. F.; Banerjee, P. K.

1991-01-01

A boundary element formulation is presented for moderate Reynolds number, steady, incompressible, thermoviscous flows. The governing integral equations are written exclusively in terms of velocities and temperatures, thus eliminating the need for the computation of any gradients. Furthermore, with the introduction of reference velocities and temperatures, volume modeling can often be confined to only a small portion of the problem domain, typically near obstacles or walls. The numerical implementation includes higher order elements, adaptive integration and multiregion capability. Both the integral formulation and implementation are discussed in detail. Several examples illustrate the high level of accuracy that is obtainable with the current method.

Layerwise Finite Elements for Smart Piezoceramic Composite Plates in Thermal Environments

NASA Technical Reports Server (NTRS)

Saravanos, Dimitris A.; Lee, Ho-Jun

1996-01-01

Analytical formulations are presented which account for the coupled mechanical, electrical, and thermal response of piezoelectric composite laminates and plate structures. A layerwise theory is formulated with the inherent capability to explicitly model the active and sensory response of piezoelectric composite plates having arbitrary laminate configurations in thermal environments. Finite element equations are derived and implemented for a bilinear 4-noded plate element. Application cases demonstrate the capability to manage thermally induced bending and twisting deformations in symmetric and antisymmetric composite plates with piezoelectric actuators, and show the corresponding electrical response of distributed piezoelectric sensors. Finally, the resultant stresses in the thermal piezoelectric composite laminates are investigated.

FINITE-ELEMENT ANALYSIS OF MULTIPHASE IMMISCIBLE FLOW THROUGH SOILS

EPA Science Inventory

A finite-element model is developed for multiphase flow through soil involving three immiscible fluids: namely, air, water, and a nonaqueous phase liquid (NAPL). A variational method is employed for the finite-element formulation corresponding to the coupled differential equation...

Finite element method formulation in polar coordinates for transient heat conduction problems

NASA Astrophysics Data System (ADS)

Duda, Piotr

2016-04-01

The aim of this paper is the formulation of the finite element method in polar coordinates to solve transient heat conduction problems. It is hard to find in the literature a formulation of the finite element method (FEM) in polar or cylindrical coordinates for the solution of heat transfer problems. This document shows how to apply the most often used boundary conditions. The global equation system is solved by the Crank-Nicolson method. The proposed algorithm is verified in three numerical tests. In the first example, the obtained transient temperature distribution is compared with the temperature obtained from the presented analytical solution. In the second numerical example, the variable boundary condition is assumed. In the last numerical example the component with the shape different than cylindrical is used. All examples show that the introduction of the polar coordinate system gives better results than in the Cartesian coordinate system. The finite element method formulation in polar coordinates is valuable since it provides a higher accuracy of the calculations without compacting the mesh in cylindrical or similar to tubular components. The proposed method can be applied for circular elements such as boiler drums, outlet headers, flux tubes. This algorithm can be useful during the solution of inverse problems, which do not allow for high density grid. This method can calculate the temperature distribution in the bodies of different properties in the circumferential and the radial direction. The presented algorithm can be developed for other coordinate systems. The examples demonstrate a good accuracy and stability of the proposed method.

High brightness diode lasers controlled by volume Bragg gratings

NASA Astrophysics Data System (ADS)

Glebov, Leonid

2017-02-01

Volume Bragg gratings (VBGs) recorded in photo-thermo-refractive (PTR) glass are holographic optical elements that are effective spectral and angular filters withstanding high power laser radiation. Reflecting VBGs are narrow-band spectral filters while transmitting VBGs are narrow-band angular filters. The use of these optical elements in external resonators of semiconductor lasers enables extremely resonant feedback that provides dramatic spectral and angular narrowing of laser diodes radiation without significant power and efficiency penalty. Spectral narrowing of laser diodes by reflecting VBGs demonstrated in wide spectral region from near UV to 3 μm. Commercially available VBGs have spectral width ranged from few nanometers to few tens of picometers. Efficient spectral locking was demonstrated for edge emitters (single diodes, bars, modules, and stacks), vertical cavity surface emitting lasers (VCSELs), grating coupled surface emitting lasers (GCSELs), and interband cascade lasers (ICLs). The use of multiplexed VBGs provides multiwavelength emission from a single emitter. Spectrally locked semiconductor lasers demonstrated CW power from milliwatts to a kilowatt. Angular narrowing by transmitting VBGs enables single transverse mode emission from wide aperture diode lasers having resonators with great Fresnel numbers. This feature provides close to diffraction limit divergence along a slow axis of wide stripe edge emitters. Radiation exchange between lasers by means of spatially profiled or multiplexed VBGs enables coherent combining of diode lasers. Sequence of VBGs or multiplexed VBGs enable spectral combining of spectrally narrowed diode lasers or laser modules. Thus the use of VBGs for diode lasers beam control provides dramatic increase of brightness.

Physics-based Stabilization of Spectral Elements for the 3D Euler Equations of Moist Atmospheric Convection

DTIC Science & Technology

2014-06-01

6000 s. 7 Table 1: Case 3. Comparative results of front location at 900s. LES (SEM), VMS (FE), WRF -ARW V2.2 (FD), f-wave (FV), filtered Spectral Elements...NO 14629 VMS [15] (75 m) NO 14487 VMS [15] (100 m) NO 14355 WRF -ARW 50 m YES 14470 SE [6] 50m YES 14767 DG [6] 50m YES 14767 f-wave (FV) [1] 50 m YES

Symplectic discretization for spectral element solution of Maxwell's equations

NASA Astrophysics Data System (ADS)

Zhao, Yanmin; Dai, Guidong; Tang, Yifa; Liu, Qinghuo

2009-08-01

Applying the spectral element method (SEM) based on the Gauss-Lobatto-Legendre (GLL) polynomial to discretize Maxwell's equations, we obtain a Poisson system or a Poisson system with at most a perturbation. For the system, we prove that any symplectic partitioned Runge-Kutta (PRK) method preserves the Poisson structure and its implied symplectic structure. Numerical examples show the high accuracy of SEM and the benefit of conserving energy due to the use of symplectic methods.

Terascale spectral element algorithms and implementations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fischer, P. F.; Tufo, H. M.

1999-08-17

We describe the development and implementation of an efficient spectral element code for multimillion gridpoint simulations of incompressible flows in general two- and three-dimensional domains. We review basic and recently developed algorithmic underpinnings that have resulted in good parallel and vector performance on a broad range of architectures, including the terascale computing systems now coming online at the DOE labs. Sustained performance of 219 GFLOPS has been recently achieved on 2048 nodes of the Intel ASCI-Red machine at Sandia.

Verification of a non-hydrostatic dynamical core using horizontally spectral element vertically finite difference method: 2-D aspects

NASA Astrophysics Data System (ADS)

Choi, S.-J.; Giraldo, F. X.; Kim, J.; Shin, S.

2014-06-01

The non-hydrostatic (NH) compressible Euler equations of dry atmosphere are solved in a simplified two dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal discretization and a finite difference method (FDM) for the vertical discretization. The SEM uses high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto-Legendre (GLL) quadrature points. The FDM employs a third-order upwind biased scheme for the vertical flux terms and a centered finite difference scheme for the vertical derivative terms and quadrature. The Euler equations used here are in a flux form based on the hydrostatic pressure vertical coordinate, which are the same as those used in the Weather Research and Forecasting (WRF) model, but a hybrid sigma-pressure vertical coordinate is implemented in this model. We verified the model by conducting widely used standard benchmark tests: the inertia-gravity wave, rising thermal bubble, density current wave, and linear hydrostatic mountain wave. The results from those tests demonstrate that the horizontally spectral element vertically finite difference model is accurate and robust. By using the 2-D slice model, we effectively show that the combined spatial discretization method of the spectral element and finite difference method in the horizontal and vertical directions, respectively, offers a viable method for the development of a NH dynamical core.

A fully-coupled discontinuous Galerkin spectral element method for two-phase flow in petroleum reservoirs

NASA Astrophysics Data System (ADS)

Taneja, Ankur; Higdon, Jonathan

2018-01-01

A high-order spectral element discontinuous Galerkin method is presented for simulating immiscible two-phase flow in petroleum reservoirs. The governing equations involve a coupled system of strongly nonlinear partial differential equations for the pressure and fluid saturation in the reservoir. A fully implicit method is used with a high-order accurate time integration using an implicit Rosenbrock method. Numerical tests give the first demonstration of high order hp spatial convergence results for multiphase flow in petroleum reservoirs with industry standard relative permeability models. High order convergence is shown formally for spectral elements with up to 8th order polynomials for both homogeneous and heterogeneous permeability fields. Numerical results are presented for multiphase fluid flow in heterogeneous reservoirs with complex geometric or geologic features using up to 11th order polynomials. Robust, stable simulations are presented for heterogeneous geologic features, including globally heterogeneous permeability fields, anisotropic permeability tensors, broad regions of low-permeability, high-permeability channels, thin shale barriers and thin high-permeability fractures. A major result of this paper is the demonstration that the resolution of the high order spectral element method may be exploited to achieve accurate results utilizing a simple cartesian mesh for non-conforming geological features. Eliminating the need to mesh to the boundaries of geological features greatly simplifies the workflow for petroleum engineers testing multiple scenarios in the face of uncertainty in the subsurface geology.

Finite element computation of compressible flows with the SUPG formulation

NASA Technical Reports Server (NTRS)

Le Beau, G. J.; Tezduyar, T. E.

1991-01-01

Finite element computation of compressible Euler equations is presented in the context of the streamline-upwind/Petrov-Galerkin (SUPG) formulation. The SUPG formulation, which is based on adding stabilizing terms to the Galerkin formulation, is further supplemented with a shock capturing operator which addresses the difficulty in maintaining a satisfactory solution near discontinuities in the solution field. The shock capturing operator, which has been derived from work done in entropy variables for a similar operator, is shown to lead to an appropriate level of additional stabilization near shocks, without resulting in excessive numerical diffusion. An implicit treatment of the impermeable wall boundary condition is also presented. This treatment of the no-penetration condition offers increased stability for large Courant numbers, and accelerated convergence of the computations for both implicit and explicit applications. Several examples are presented to demonstrate the ability of this method to solve the equations governing compressible fluid flow.

Imaging spectroscopy using embedded diffractive optical arrays

NASA Astrophysics Data System (ADS)

Hinnrichs, Michele; Hinnrichs, Bradford

2017-09-01

Pacific Advanced Technology (PAT) has developed an infrared hyperspectral camera based on diffractive optic arrays. This approach to hyperspectral imaging has been demonstrated in all three infrared bands SWIR, MWIR and LWIR. The hyperspectral optical system has been integrated into the cold-shield of the sensor enabling the small size and weight of this infrared hyperspectral sensor. This new and innovative approach to an infrared hyperspectral imaging spectrometer uses micro-optics that are made up of an area array of diffractive optical elements where each element is tuned to image a different spectral region on a common focal plane array. The lenslet array is embedded in the cold-shield of the sensor and actuated with a miniature piezo-electric motor. This approach enables rapid infrared spectral imaging with multiple spectral images collected and processed simultaneously each frame of the camera. This paper will present our optical mechanical design approach which results in an infrared hyper-spectral imaging system that is small enough for a payload on a small satellite, mini-UAV, commercial quadcopter or man portable. Also, an application of how this spectral imaging technology can easily be used to quantify the mass and volume flow rates of hydrocarbon gases. The diffractive optical elements used in the lenslet array are blazed gratings where each lenslet is tuned for a different spectral bandpass. The lenslets are configured in an area array placed a few millimeters above the focal plane and embedded in the cold-shield to reduce the background signal normally associated with the optics. The detector array is divided into sub-images covered by each lenslet. We have developed various systems using a different number of lenslets in the area array. Depending on the size of the focal plane and the diameter of the lenslet array will determine the number of simultaneous different spectral images collected each frame of the camera. A 2 x 2 lenslet array will image four different spectral images of the scene each frame and when coupled with a 512 x 512 focal plane array will give spatial resolution of 256 x 256 pixel each spectral image. Another system that we developed uses a 4 x 4 lenslet array on a 1024 x 1024 pixel element focal plane array which gives 16 spectral images of 256 x 256 pixel resolution each frame. This system spans the SWIR and MWIR bands with a single optical array and focal plane array.

A thermodynamically consistent discontinuous Galerkin formulation for interface separation

DOE PAGES

Versino, Daniele; Mourad, Hashem M.; Dávila, Carlos G.; ...

2015-07-31

Our paper describes the formulation of an interface damage model, based on the discontinuous Galerkin (DG) method, for the simulation of failure and crack propagation in laminated structures. The DG formulation avoids common difficulties associated with cohesive elements. Specifically, it does not introduce any artificial interfacial compliance and, in explicit dynamic analysis, it leads to a stable time increment size which is unaffected by the presence of stiff massless interfaces. This proposed method is implemented in a finite element setting. Convergence and accuracy are demonstrated in Mode I and mixed-mode delamination in both static and dynamic analyses. Significantly, numerical resultsmore » obtained using the proposed interface model are found to be independent of the value of the penalty factor that characterizes the DG formulation. By contrast, numerical results obtained using a classical cohesive method are found to be dependent on the cohesive penalty stiffnesses. The proposed approach is shown to yield more accurate predictions pertaining to crack propagation under mixed-mode fracture because of the advantage. Furthermore, in explicit dynamic analysis, the stable time increment size calculated with the proposed method is found to be an order of magnitude larger than the maximum allowable value for classical cohesive elements.« less

Solving transient acoustic boundary value problems with equivalent sources using a lumped parameter approach.

PubMed

Fahnline, John B

2016-12-01

An equivalent source method is developed for solving transient acoustic boundary value problems. The method assumes the boundary surface is discretized in terms of triangular or quadrilateral elements and that the solution is represented using the acoustic fields of discrete sources placed at the element centers. Also, the boundary condition is assumed to be specified for the normal component of the surface velocity as a function of time, and the source amplitudes are determined to match the known elemental volume velocity vector at a series of discrete time steps. Equations are given for marching-on-in-time schemes to solve for the source amplitudes at each time step for simple, dipole, and tripole source formulations. Several example problems are solved to illustrate the results and to validate the formulations, including problems with closed boundary surfaces where long-time numerical instabilities typically occur. A simple relationship between the simple and dipole source amplitudes in the tripole source formulation is derived so that the source radiates primarily in the direction of the outward surface normal. The tripole source formulation is shown to eliminate interior acoustic resonances and long-time numerical instabilities.

A locally conservative non-negative finite element formulation for anisotropic advective-diffusive-reactive systems

NASA Astrophysics Data System (ADS)

Mudunuru, M. K.; Shabouei, M.; Nakshatrala, K.

2015-12-01

Advection-diffusion-reaction (ADR) equations appear in various areas of life sciences, hydrogeological systems, and contaminant transport. Obtaining stable and accurate numerical solutions can be challenging as the underlying equations are coupled, nonlinear, and non-self-adjoint. Currently, there is neither a robust computational framework available nor a reliable commercial package known that can handle various complex situations. Herein, the objective of this poster presentation is to present a novel locally conservative non-negative finite element formulation that preserves the underlying physical and mathematical properties of a general linear transient anisotropic ADR equation. In continuous setting, governing equations for ADR systems possess various important properties. In general, all these properties are not inherited during finite difference, finite volume, and finite element discretizations. The objective of this poster presentation is two fold: First, we analyze whether the existing numerical formulations (such as SUPG and GLS) and commercial packages provide physically meaningful values for the concentration of the chemical species for various realistic benchmark problems. Furthermore, we also quantify the errors incurred in satisfying the local and global species balance for two popular chemical kinetics schemes: CDIMA (chlorine dioxide-iodine-malonic acid) and BZ (Belousov--Zhabotinsky). Based on these numerical simulations, we show that SUPG and GLS produce unphysical values for concentration of chemical species due to the violation of the non-negative constraint, contain spurious node-to-node oscillations, and have large errors in local and global species balance. Second, we proposed a novel finite element formulation to overcome the above difficulties. The proposed locally conservative non-negative computational framework based on low-order least-squares finite elements is able to preserve these underlying physical and mathematical properties. Several representative numerical examples are discussed to illustrate the importance of the proposed numerical formulations to accurately describe various aspects of mixing process in chaotic flows and to simulate transport in highly heterogeneous anisotropic media.

Three-Dimensional Finite Element Analysis of Sheet-Pile Cellular Cofferdams

DTIC Science & Technology

1992-04-01

requirements were in selecting the shell element for this study: * Nodes only at the midsurface of the element. * Higher-order shape functions to...on orthogonal curvilinear coordinate (shell coordinates) system with the ref- erence surface of the element midsurface (Figure 4.13). The formulation...element was selected which allows for: * Nodes at the midsurface of the element only. 150 CHAPTER 4. ADDITIONS TO THE ELEMENT LIBRARY " Higher-order

Spectrum Analyzers Incorporating Tunable WGM Resonators

NASA Technical Reports Server (NTRS)

Savchenkov, Anatoliy; Matsko, Andrey; Strekalov, Dmitry; Maleki, Lute

2009-01-01

A photonic instrument is proposed to boost the resolution for ultraviolet/ optical/infrared spectral analysis and spectral imaging allowing the detection of narrow (0.00007-to-0.07-picometer wavelength resolution range) optical spectral signatures of chemical elements in space and planetary atmospheres. The idea underlying the proposal is to exploit the advantageous spectral characteristics of whispering-gallery-mode (WGM) resonators to obtain spectral resolutions at least three orders of magnitude greater than those of optical spectrum analyzers now in use. Such high resolutions would enable measurement of spectral features that could not be resolved by prior instruments.

Improved documentation of spectral lines for inductively coupled plasma emission spectrometry

NASA Astrophysics Data System (ADS)

Doidge, Peter S.

2018-05-01

An approach to improving the documentation of weak spectral lines falling near the prominent analytical lines used in inductively coupled plasma optical emission spectrometry (ICP-OES) is described. Measurements of ICP emission spectra in the regions around several hundred prominent lines, using concentrated solutions (up to 1% w/v) of some 70 elements, and comparison of the observed spectra with both recent published work and with the output of a computer program that allows calculation of transitions between the known energy levels, show that major improvements can be made in the coverage of spectral atlases for ICP-OES, with respect to "classical" line tables. It is argued that the atomic spectral data (wavelengths, energy levels) required for the reliable identification and documentation of a large majority of the weak interfering lines of the elements detectable by ICP-OES now exist, except for most of the observed lines of the lanthanide elements. In support of this argument, examples are provided from a detailed analysis of a spectral window centered on the prominent Pb II 220.353 nm line, and from a selected line-rich spectrum (W). Shortcomings in existing analyses are illustrated with reference to selected spectral interferences due to Zr. This approach has been used to expand the spectral-line library used in commercial ICP-ES instruments (Agilent 700-ES/5100-ES). The precision of wavelength measurements is evaluated in terms of the shot-noise limit, while the absolute accuracy of wavelength measurement is characterised through comparison with a small set of precise Ritz wavelengths for Sb I, and illustrated through the identification of Zr III lines; it is further shown that fractional-pixel absolute wavelength accuracies can be achieved. Finally, problems with the wavelengths and classifications of certain Au I lines are discussed.

Co-simulation coupling spectral/finite elements for 3D soil/structure interaction problems

NASA Astrophysics Data System (ADS)

Zuchowski, Loïc; Brun, Michael; De Martin, Florent

2018-05-01

The coupling between an implicit finite elements (FE) code and an explicit spectral elements (SE) code has been explored for solving the elastic wave propagation in the case of soil/structure interaction problem. The coupling approach is based on domain decomposition methods in transient dynamics. The spatial coupling at the interface is managed by a standard coupling mortar approach, whereas the time integration is dealt with an hybrid asynchronous time integrator. An external coupling software, handling the interface problem, has been set up in order to couple the FE software Code_Aster with the SE software EFISPEC3D.

Wave propagation modeling in composites reinforced by randomly oriented fibers

NASA Astrophysics Data System (ADS)

Kudela, Pawel; Radzienski, Maciej; Ostachowicz, Wieslaw

2018-02-01

A new method for prediction of elastic constants in randomly oriented fiber composites is proposed. It is based on mechanics of composites, the rule of mixtures and total mass balance tailored to the spectral element mesh composed of 3D brick elements. Selected elastic properties predicted by the proposed method are compared with values obtained by another theoretical method. The proposed method is applied for simulation of Lamb waves in glass-epoxy composite plate reinforced by randomly oriented fibers. Full wavefield measurements conducted by the scanning laser Doppler vibrometer are in good agreement with simulations performed by using the time domain spectral element method.

A Living Periodic Table.

ERIC Educational Resources Information Center

Marshall, James L.

2000-01-01

Introduces a portable and permanent set of the elemental collection including 87 samples of elements which are, minimum, one gram or more. Demonstrates radioactivity, magnetism, fluorescence, melting solids, spectral analysis, and conduction of heat. Includes a display of minerals associated with the elements. (YDS)

The application of contraction theory to an iterative formulation of electromagnetic scattering

NASA Technical Reports Server (NTRS)

Brand, J. C.; Kauffman, J. F.

1985-01-01

Contraction theory is applied to an iterative formulation of electromagnetic scattering from periodic structures and a computational method for insuring convergence is developed. A short history of spectral (or k-space) formulation is presented with an emphasis on application to periodic surfaces. To insure a convergent solution of the iterative equation, a process called the contraction corrector method is developed. Convergence properties of previously presented iterative solutions to one-dimensional problems are examined utilizing contraction theory and the general conditions for achieving a convergent solution are explored. The contraction corrector method is then applied to several scattering problems including an infinite grating of thin wires with the solution data compared to previous works.

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

NASA Technical Reports Server (NTRS)

Fink, P. W.; Wilton, D. R.

2000-01-01

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

Optimal Orbit Maneuvers with Electrodynamic Tethers

DTIC Science & Technology

2006-06-01

orbital elements , which completely describe a unique orbit ; equinoctial elements are not employed but left for future iterations of the formulation...periods in the maneuver. Follow on work, uch as the transformation of this state vector from classical orbital elements to the quinoctial set of...

Shape and Stress Sensing of Multilayered Composite and Sandwich Structures Using an Inverse Finite Element Method

NASA Technical Reports Server (NTRS)

Cerracchio, Priscilla; Gherlone, Marco; Di Sciuva, Marco; Tessler, Alexander

2013-01-01

The marked increase in the use of composite and sandwich material systems in aerospace, civil, and marine structures leads to the need for integrated Structural Health Management systems. A key capability to enable such systems is the real-time reconstruction of structural deformations, stresses, and failure criteria that are inferred from in-situ, discrete-location strain measurements. This technology is commonly referred to as shape- and stress-sensing. Presented herein is a computationally efficient shape- and stress-sensing methodology that is ideally suited for applications to laminated composite and sandwich structures. The new approach employs the inverse Finite Element Method (iFEM) as a general framework and the Refined Zigzag Theory (RZT) as the underlying plate theory. A three-node inverse plate finite element is formulated. The element formulation enables robust and efficient modeling of plate structures instrumented with strain sensors that have arbitrary positions. The methodology leads to a set of linear algebraic equations that are solved efficiently for the unknown nodal displacements. These displacements are then used at the finite element level to compute full-field strains, stresses, and failure criteria that are in turn used to assess structural integrity. Numerical results for multilayered, highly heterogeneous laminates demonstrate the unique capability of this new formulation for shape- and stress-sensing.

A Three-Dimensional Finite-Element Model for Simulating Water Flow in Variably Saturated Porous Media

NASA Astrophysics Data System (ADS)

Huyakorn, Peter S.; Springer, Everett P.; Guvanasen, Varut; Wadsworth, Terry D.

1986-12-01

A three-dimensional finite-element model for simulating water flow in variably saturated porous media is presented. The model formulation is general and capable of accommodating complex boundary conditions associated with seepage faces and infiltration or evaporation on the soil surface. Included in this formulation is an improved Picard algorithm designed to cope with severely nonlinear soil moisture relations. The algorithm is formulated for both rectangular and triangular prism elements. The element matrices are evaluated using an "influence coefficient" technique that avoids costly numerical integration. Spatial discretization of a three-dimensional region is performed using a vertical slicing approach designed to accommodate complex geometry with irregular boundaries, layering, and/or lateral discontinuities. Matrix solution is achieved using a slice successive overrelaxation scheme that permits a fairly large number of nodal unknowns (on the order of several thousand) to be handled efficiently on small minicomputers. Six examples are presented to verify and demonstrate the utility of the proposed finite-element model. The first four examples concern one- and two-dimensional flow problems used as sample problems to benchmark the code. The remaining examples concern three-dimensional problems. These problems are used to illustrate the performance of the proposed algorithm in three-dimensional situations involving seepage faces and anisotropic soil media.

Quantum spectral curve of the N=6 supersymmetric Chern-Simons theory.

PubMed

Cavaglià, Andrea; Fioravanti, Davide; Gromov, Nikolay; Tateo, Roberto

2014-07-11

Recently, it was shown that the spectrum of anomalous dimensions and other important observables in planar N=4 supersymmetric Yang-Mills theory are encoded into a simple nonlinear Riemann-Hilbert problem: the Pμ system or quantum spectral curve. In this Letter, we extend this formulation to the N=6 supersymmetric Chern-Simons theory introduced by Aharony, Bergman, Jafferis, and Maldacena. This may be an important step towards the exact determination of the interpolating function h(λ) characterizing the integrability of this model. We also discuss a surprising relation between the quantum spectral curves for the N=4 supersymmetric Yang-Mills theory and the N=6 supersymmetric Chern-Simons theory considered here.

Deep Learning Based Binaural Speech Separation in Reverberant Environments.

PubMed

Zhang, Xueliang; Wang, DeLiang

2017-05-01

Speech signal is usually degraded by room reverberation and additive noises in real environments. This paper focuses on separating target speech signal in reverberant conditions from binaural inputs. Binaural separation is formulated as a supervised learning problem, and we employ deep learning to map from both spatial and spectral features to a training target. With binaural inputs, we first apply a fixed beamformer and then extract several spectral features. A new spatial feature is proposed and extracted to complement the spectral features. The training target is the recently suggested ideal ratio mask. Systematic evaluations and comparisons show that the proposed system achieves very good separation performance and substantially outperforms related algorithms under challenging multi-source and reverberant environments.

Nonlinear thermo-mechanical analysis of stiffened composite laminates by a new finite element

NASA Astrophysics Data System (ADS)

Barut, Atila

A new stiffened shell element combining shallow beam and shallow shell elements is developed for geometrically nonlinear analysis of stiffened composite laminates under thermal and/or mechanical loading. The formulation of this element is based on the principal of virtual displacements in conjunction with the co-rotational form of the total Lagrangian description of motion. In the finite element formulation, both the shell and the beam (stiffener) elements account for transverse shear deformations and material anisotropy. The cross-section of the stiffener (beam) can be arbitrary in geometry and lamination. In order to combine the stiffener with the shell element, constraint conditions are applied to the displacement and rotation fields of the stiffener. These constraint conditions ensure that the cross-section of the stiffener remains co-planar with the shell section after deformation. The resulting expressions for the displacement and rotation fields of the stiffener involve only the nodal unknowns of the shell element, thus reducing the total number of degrees of freedom. Also, the discretization of the entire stiffened shell structure becomes more flexible.

A p-version finite element method for steady incompressible fluid flow and convective heat transfer

NASA Technical Reports Server (NTRS)

Winterscheidt, Daniel L.

1993-01-01

A new p-version finite element formulation for steady, incompressible fluid flow and convective heat transfer problems is presented. The steady-state residual equations are obtained by considering a limiting case of the least-squares formulation for the transient problem. The method circumvents the Babuska-Brezzi condition, permitting the use of equal-order interpolation for velocity and pressure, without requiring the use of arbitrary parameters. Numerical results are presented to demonstrate the accuracy and generality of the method.

Finite-element simulation of ceramic drying processes

NASA Astrophysics Data System (ADS)

Keum, Y. T.; Jeong, J. H.; Auh, K. H.

2000-07-01

A finite-element simulation for the drying process of ceramics is performed. The heat and moisture movements in green ceramics caused by the temperature gradient, moisture gradient, conduction, convection and evaporation are considered. The finite-element formulation for solving the temperature and moisture distributions, which not only change the volume but also induce the hygro-thermal stress, is carried out. Employing the internally discontinuous interface elements, the numerical divergence problem arising from sudden changes in heat capacity in the phase zone is solved. In order to verify the reliability of the formulation, the drying process of a coal and the wetting process of a graphite epoxy are simulated and the results are compared with the analytical solution and another investigator's result. Finally, the drying process of a ceramic electric insulator is simulated.

Drekar v.2.0

DOE Office of Scientific and Technical Information (OSTI.GOV)

Seefeldt, Ben; Sondak, David; Hensinger, David M.

Drekar is an application code that solves partial differential equations for fluids that can be optionally coupled to electromagnetics. Drekar solves low-mach compressible and incompressible computational fluid dynamics (CFD), compressible and incompressible resistive magnetohydrodynamics (MHD), and multiple species plasmas interacting with electromagnetic fields. Drekar discretization technology includes continuous and discontinuous finite element formulations, stabilized finite element formulations, mixed integration finite element bases (nodal, edge, face, volume) and an initial arbitrary Lagrangian Eulerian (ALE) capability. Drekar contains the implementation of the discretized physics and leverages the open source Trilinos project for both parallel solver capabilities and general finite element discretization tools.more » The code will be released open source under a BSD license. The code is used for fundamental research for simulation of fluids and plasmas on high performance computing environments.« less

Simulation of Hypervelocity Impact on Aluminum-Nextel-Kevlar Orbital Debris Shields

NASA Technical Reports Server (NTRS)

Fahrenthold, Eric P.

2000-01-01

An improved hybrid particle-finite element method has been developed for hypervelocity impact simulation. The method combines the general contact-impact capabilities of particle codes with the true Lagrangian kinematics of large strain finite element formulations. Unlike some alternative schemes which couple Lagrangian finite element models with smooth particle hydrodynamics, the present formulation makes no use of slidelines or penalty forces. The method has been implemented in a parallel, three dimensional computer code. Simulations of three dimensional orbital debris impact problems using this parallel hybrid particle-finite element code, show good agreement with experiment and good speedup in parallel computation. The simulations included single and multi-plate shields as well as aluminum and composite shielding materials. at an impact velocity of eleven kilometers per second.

Simulation of laminate composites degradation using mesoscopic non-local damage model and non-local layered shell element

NASA Astrophysics Data System (ADS)

Germain, Norbert; Besson, Jacques; Feyel, Frédéric

2007-07-01

Simulating damage and failure of laminate composites structures often fails when using the standard finite element procedure. The difficulties arise from an uncontrolled mesh dependence caused by damage localization and an increase in computational costs. One of the solutions to the first problem, widely used to predict the failure of metallic materials, consists of using non-local damage constitutive equations. The second difficulty can then be solved using specific finite element formulations, such as shell element, which decrease the number of degrees of freedom. The main contribution of this paper consists of extending these techniques to layered materials such as polymer matrix composites. An extension of the non-local implicit gradient formulation, accounting for anisotropy and stratification, and an original layered shell element, based on a new partition of the unity, are proposed. Finally the efficiency of the resulting numerical scheme is studied by comparing simulation with experimental results.

A combined finite element-boundary element formulation for solution of axially symmetric bodies

NASA Technical Reports Server (NTRS)

Collins, Jeffrey D.; Volakis, John L.

1991-01-01

A new method is presented for the computation of electromagnetic scattering from axially symmetric bodies. To allow the simulation of inhomogeneous cross sections, the method combines the finite element and boundary element techniques. Interior to a fictitious surface enclosing the scattering body, the finite element method is used which results in a sparce submatrix, whereas along the enclosure the Stratton-Chu integral equation is enforced. By choosing the fictitious enclosure to be a right circular cylinder, most of the resulting boundary integrals are convolutional and may therefore be evaluated via the FFT with which the system is iteratively solved. In view of the sparce matrix associated with the interior fields, this reduces the storage requirement of the entire system to O(N) making the method attractive for large scale computations. The details of the corresponding formulation and its numerical implementation are described.

Comparison of inversion accuracy of soil copper content from vegetation indices under different spectral resolution

NASA Astrophysics Data System (ADS)

Sun, Zhongqing; Shang, Kun; Jia, Lingjun

2018-03-01

Remote sensing inversion of heavy metal in vegetation leaves is generally based on the physiological characteristics of vegetation spectrum under heavy metal stress, and empirical models with vegetation indices are established to inverse the heavy metal content of vegetation leaves. However, the research of inversion of heavy metal content in vegetation-covered soil is still rare. In this study, Pulang is chosen as study area. The regression model of a typical heavy metal element, copper (Cu), is established with vegetation indices. We mainly investigate the inversion accuracies of Cu element in vegetation-covered soil by different vegetation indices according to specific spectral resolutions of ASD (Analytical Spectral Device) and Hyperion data. The inversion results of soil copper content in the vegetation-covered area shows a good accuracy, and the vegetation indices under ASD spectral resolution correspond to better results.

A comparison of FE beam and continuum elements for typical nitinol stent geometries

NASA Astrophysics Data System (ADS)

Ballew, Wesley; Seelecke, Stefan

2009-03-01

With interest in improved efficiency and a more complete description of the SMA material, this paper compares finite element (FE) simulations of typical stent geometries using two different constitutive models and two different element types. Typically, continuum elements are used for the simulation of stents, for example the commercial FE software ANSYS offers a continuum element based on Auricchio's SMA model. Almost every stent geometry, however, is made up of long and slender components and can be modeled more efficiently, in the computational sense, with beam elements. Using the ANSYS user programmable material feature, we implement the free energy based SMA model developed by Mueller and Seelecke into the ANSYS beam element 188. Convergence behavior for both, beam and continuum formulations, is studied in terms of element and layer number, respectively. This is systematically illustrated first for the case of a straight cantilever beam under end loading, and subsequently for a section of a z-bend wire, a typical stent sub-geometry. It is shown that the computation times for the beam element are reduced to only one third of those of the continuum element, while both formulations display a comparable force/displacement response.

Spectral densities for Frenkel exciton dynamics in molecular crystals: A TD-DFTB approach

NASA Astrophysics Data System (ADS)

Plötz, Per-Arno; Megow, Jörg; Niehaus, Thomas; Kühn, Oliver

2017-02-01

Effects of thermal fluctuations on the electronic excitation energies and intermonomeric Coulomb couplings are investigated for a perylene-tetracarboxylic-diimide crystal. To this end, time dependent density functional theory based tight binding (TD-DFTB) in the linear response formulation is used in combination with electronic ground state classical molecular dynamics. As a result, a parametrized Frenkel exciton Hamiltonian is obtained, with the effect of exciton-vibrational coupling being described by spectral densities. Employing dynamically defined normal modes, these spectral densities are analyzed in great detail, thus providing insight into the effect of specific intramolecular motions on excitation energies and Coulomb couplings. This distinguishes the present method from approaches using fixed transition densities. The efficiency by which intramolecular contributions to the spectral density can be calculated is a clear advantage of this method as compared with standard TD-DFT.

The spectral element method (SEM) on variable-resolution grids: evaluating grid sensitivity and resolution-aware numerical viscosity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guba, O.; Taylor, M. A.; Ullrich, P. A.

2014-11-27

We evaluate the performance of the Community Atmosphere Model's (CAM) spectral element method on variable-resolution grids using the shallow-water equations in spherical geometry. We configure the method as it is used in CAM, with dissipation of grid scale variance, implemented using hyperviscosity. Hyperviscosity is highly scale selective and grid independent, but does require a resolution-dependent coefficient. For the spectral element method with variable-resolution grids and highly distorted elements, we obtain the best results if we introduce a tensor-based hyperviscosity with tensor coefficients tied to the eigenvalues of the local element metric tensor. The tensor hyperviscosity is constructed so that, formore » regions of uniform resolution, it matches the traditional constant-coefficient hyperviscosity. With the tensor hyperviscosity, the large-scale solution is almost completely unaffected by the presence of grid refinement. This later point is important for climate applications in which long term climatological averages can be imprinted by stationary inhomogeneities in the truncation error. We also evaluate the robustness of the approach with respect to grid quality by considering unstructured conforming quadrilateral grids generated with a well-known grid-generating toolkit and grids generated by SQuadGen, a new open source alternative which produces lower valence nodes.« less

The spectral element method on variable resolution grids: evaluating grid sensitivity and resolution-aware numerical viscosity

DOE PAGES

Guba, O.; Taylor, M. A.; Ullrich, P. A.; ...

2014-06-25

We evaluate the performance of the Community Atmosphere Model's (CAM) spectral element method on variable resolution grids using the shallow water equations in spherical geometry. We configure the method as it is used in CAM, with dissipation of grid scale variance implemented using hyperviscosity. Hyperviscosity is highly scale selective and grid independent, but does require a resolution dependent coefficient. For the spectral element method with variable resolution grids and highly distorted elements, we obtain the best results if we introduce a tensor-based hyperviscosity with tensor coefficients tied to the eigenvalues of the local element metric tensor. The tensor hyperviscosity ismore » constructed so that for regions of uniform resolution it matches the traditional constant coefficient hyperviscsosity. With the tensor hyperviscosity the large scale solution is almost completely unaffected by the presence of grid refinement. This later point is important for climate applications where long term climatological averages can be imprinted by stationary inhomogeneities in the truncation error. We also evaluate the robustness of the approach with respect to grid quality by considering unstructured conforming quadrilateral grids generated with a well-known grid-generating toolkit and grids generated by SQuadGen, a new open source alternative which produces lower valence nodes.« less

Accurate quantitative CF-LIBS analysis of both major and minor elements in alloys via iterative correction of plasma temperature and spectral intensity

NASA Astrophysics Data System (ADS)

Shuxia, ZHAO; Lei, ZHANG; Jiajia, HOU; Yang, ZHAO; Wangbao, YIN; Weiguang, MA; Lei, DONG; Liantuan, XIAO; Suotang, JIA

2018-03-01

The chemical composition of alloys directly determines their mechanical behaviors and application fields. Accurate and rapid analysis of both major and minor elements in alloys plays a key role in metallurgy quality control and material classification processes. A quantitative calibration-free laser-induced breakdown spectroscopy (CF-LIBS) analysis method, which carries out combined correction of plasma temperature and spectral intensity by using a second-order iterative algorithm and two boundary standard samples, is proposed to realize accurate composition measurements. Experimental results show that, compared to conventional CF-LIBS analysis, the relative errors for major elements Cu and Zn and minor element Pb in the copper-lead alloys has been reduced from 12%, 26% and 32% to 1.8%, 2.7% and 13.4%, respectively. The measurement accuracy for all elements has been improved substantially.

Updated Lagrangian finite element formulations of various biological soft tissue non-linear material models: a comprehensive procedure and review.

PubMed

Townsend, Molly T; Sarigul-Klijn, Nesrin

2016-01-01

Simplified material models are commonly used in computational simulation of biological soft tissue as an approximation of the complicated material response and to minimize computational resources. However, the simulation of complex loadings, such as long-duration tissue swelling, necessitates complex models that are not easy to formulate. This paper strives to offer the updated Lagrangian formulation comprehensive procedure of various non-linear material models for the application of finite element analysis of biological soft tissues including a definition of the Cauchy stress and the spatial tangential stiffness. The relationships between water content, osmotic pressure, ionic concentration and the pore pressure stress of the tissue are discussed with the merits of these models and their applications.

Membrane triangles with corner drilling freedoms. II - The ANDES element

NASA Technical Reports Server (NTRS)

Felippa, Carlos A.; Militello, Carmelo

1992-01-01

This is the second article in a three-part series on the construction of 3-node, 9-dof membrane elements with normal-to-its-plane rotational freedoms (the so-called drilling freedoms) using parametrized variational principles. In this part, one such element is derived within the context of the assumed natural deviatoric strain (ANDES) formulation. The higher-order strains are obtained by constructing three parallel-to-sides pure-bending modes from which natural strains are obtained at the corner points and interpolated over the element. To attain rank sufficiency, an additional higher-order 'torsional' mode, corresponding to equal hierarchical rotations at each corner with all other motions precluded, is incorporated. The resulting formulation has five free parameters. When these parameters are optimized against pure bending by energy balance methods, the resulting element is found to coalesce with the optimal EFF element derived in Part I. Numerical integration as a strain filtering device is found to play a key role in this achievement.

Film-forming formulations containing porous silica for the sustained delivery of actives to the skin.

PubMed

Heck, Rouven; Hermann, Sabrina; Lunter, Dominique J; Daniels, Rolf

2016-11-01

The purpose of this study was to develop film-forming formulations facilitating long-term treatment of chronic pruritus with capsaicinoids. To this end, an oily solution of nonivamide was loaded into porous silica particles which were then suspended in the dispersion of a sustained release polymer. Such formulations form a film when applied to the skin and encapsulate the drug loaded silica particles in a dry polymeric matrix. Dermal delivery and permeation of the antipruritic drug nonivamide (NVA) are controlled by the matrix. The film-forming formulations were examined regarding homogeneity, storage stability, substantivity and ex vivo skin permeation. Confocal Raman spectral imaging proved the stability of silica-based film-forming formulations over a period of 6 months. Substantivity was found to be enhanced substantially compared to a conventional semisolid formulation. Permeation rates of nonivamide from film-forming formulations through the skin are much lower compared to those achieved with a conventional immediate release formulation with the same drug amount. Due to the drug reservoir in the polymer matrix, a sustained permeation is enabled. Film-forming formulations may therefore improve the treatment of chronic pruritus with capsaicinoids by enhancing patient compliance through a sustained release regime. Copyright © 2016 Elsevier B.V. All rights reserved.

Dipole excitation of surface plasmon on a conducting sheet: Finite element approximation and validation

NASA Astrophysics Data System (ADS)

Maier, Matthias; Margetis, Dionisios; Luskin, Mitchell

2017-06-01

We formulate and validate a finite element approach to the propagation of a slowly decaying electromagnetic wave, called surface plasmon-polariton, excited along a conducting sheet, e.g., a single-layer graphene sheet, by an electric Hertzian dipole. By using a suitably rescaled form of time-harmonic Maxwell's equations, we derive a variational formulation that enables a direct numerical treatment of the associated class of boundary value problems by appropriate curl-conforming finite elements. The conducting sheet is modeled as an idealized hypersurface with an effective electric conductivity. The requisite weak discontinuity for the tangential magnetic field across the hypersurface can be incorporated naturally into the variational formulation. We carry out numerical simulations for an infinite sheet with constant isotropic conductivity embedded in two spatial dimensions; and validate our numerics against the closed-form exact solution obtained by the Fourier transform in the tangential coordinate. Numerical aspects of our treatment such as an absorbing perfectly matched layer, as well as local refinement and a posteriori error control are discussed.

Development and applications of a flat triangular element for thin laminated shells

NASA Astrophysics Data System (ADS)

Mohan, P.

Finite element analysis of thin laminated shells using a three-noded flat triangular shell element is presented. The flat shell element is obtained by combining the Discrete Kirchhoff Theory (DKT) plate bending element and a membrane element similar to the Allman element, but derived from the Linear Strain Triangular (LST) element. The major drawback of the DKT plate bending element is that the transverse displacement is not explicitly defined within the interior of the element. In the present research, free vibration analysis is performed both by using a lumped mass matrix and a so called consistent mass matrix, obtained by borrowing shape functions from an existing element, in order to compare the performance of the two methods. Several numerical examples are solved to demonstrate the accuracy of the formulation for both small and large rotation analysis of laminated plates and shells. The results are compared with those available in the existing literature and those obtained using the commercial finite element package ABAQUS and are found to be in good agreement. The element is employed for two main applications involving large flexible structures. The first application is the control of thermal deformations of a spherical mirror segment, which is a segment of a multi-segmented primary mirror used in a space telescope. The feasibility of controlling the surface distortions of the mirror segment due to arbitrary thermal fields, using discrete and distributed actuators, is studied. The second application is the analysis of an inflatable structure, being considered by the US Army for housing vehicles and personnel. The updated Lagrangian formulation of the flat shell element has been developed primarily for the nonlinear analysis of the tent structure, since such a structure is expected to undergo large deformations and rotations under the action of environmental loads like the wind and snow loads. The follower effects of the pressure load have been included in the updated Lagrangian formulation of the flat shell element and have been validated using standard examples in the literature involving deformation-dependent pressure loads. The element can be used to obtain the nonlinear response of the tent structure under wind and snow loads. (Abstract shortened by UMI.)

Rigorous joining of advanced reduced-dimensional beam models to three-dimensional finite element models

NASA Astrophysics Data System (ADS)

Song, Huimin

In the aerospace and automotive industries, many finite element analyses use lower-dimensional finite elements such as beams, plates and shells, to simplify the modeling. These simplified models can greatly reduce the computation time and cost; however, reduced-dimensional models may introduce inaccuracies, particularly near boundaries and near portions of the structure where reduced-dimensional models may not apply. Another factor in creation of such models is that beam-like structures frequently have complex geometry, boundaries and loading conditions, which may make them unsuitable for modeling with single type of element. The goal of this dissertation is to develop a method that can accurately and efficiently capture the response of a structure by rigorous combination of a reduced-dimensional beam finite element model with a model based on full two-dimensional (2D) or three-dimensional (3D) finite elements. The first chapter of the thesis gives the background of the present work and some related previous work. The second chapter is focused on formulating a system of equations that govern the joining of a 2D model with a beam model for planar deformation. The essential aspect of this formulation is to find the transformation matrices to achieve deflection and load continuity on the interface. Three approaches are provided to obtain the transformation matrices. An example based on joining a beam to a 2D finite element model is examined, and the accuracy of the analysis is studied by comparing joint results with the full 2D analysis. The third chapter is focused on formulating the system of equations for joining a beam to a 3D finite element model for static and free-vibration problems. The transition between the 3D elements and beam elements is achieved by use of the stress recovery technique of the variational-asymptotic method as implemented in VABS (the Variational Asymptotic Beam Section analysis). The formulations for an interface transformation matrix and the generalized Timoshenko beam are discussed in this chapter. VABS is also used to obtain the beam constitutive properties and warping functions for stress recovery. Several 3D-beam joint examples are presented to show the convergence and accuracy of the analysis. Accuracy is accessed by comparing the joint results with the full 3D analysis. The fourth chapter provides conclusions from present studies and recommendations for future work.

Mixed finite-element formulations in piezoelectricity and flexoelectricity

PubMed Central

2016-01-01

Flexoelectricity, the linear coupling of strain gradient and electric polarization, is inherently a size-dependent phenomenon. The energy storage function for a flexoelectric material depends not only on polarization and strain, but also strain-gradient. Thus, conventional finite-element methods formulated solely on displacement are inadequate to treat flexoelectric solids since gradients raise the order of the governing differential equations. Here, we introduce a computational framework based on a mixed formulation developed previously by one of the present authors and a colleague. This formulation uses displacement and displacement-gradient as separate variables which are constrained in a ‘weighted integral sense’ to enforce their known relation. We derive a variational formulation for boundary-value problems for piezo- and/or flexoelectric solids. We validate this computational framework against available exact solutions. Our new computational method is applied to more complex problems, including a plate with an elliptical hole, stationary cracks, as well as tension and shear of solids with a repeating unit cell. Our results address several issues of theoretical interest, generate predictions of experimental merit and reveal interesting flexoelectric phenomena with potential for application. PMID:27436967

Mixed finite-element formulations in piezoelectricity and flexoelectricity.

PubMed

Mao, Sheng; Purohit, Prashant K; Aravas, Nikolaos

2016-06-01

Flexoelectricity, the linear coupling of strain gradient and electric polarization, is inherently a size-dependent phenomenon. The energy storage function for a flexoelectric material depends not only on polarization and strain, but also strain-gradient. Thus, conventional finite-element methods formulated solely on displacement are inadequate to treat flexoelectric solids since gradients raise the order of the governing differential equations. Here, we introduce a computational framework based on a mixed formulation developed previously by one of the present authors and a colleague. This formulation uses displacement and displacement-gradient as separate variables which are constrained in a 'weighted integral sense' to enforce their known relation. We derive a variational formulation for boundary-value problems for piezo- and/or flexoelectric solids. We validate this computational framework against available exact solutions. Our new computational method is applied to more complex problems, including a plate with an elliptical hole, stationary cracks, as well as tension and shear of solids with a repeating unit cell. Our results address several issues of theoretical interest, generate predictions of experimental merit and reveal interesting flexoelectric phenomena with potential for application.

A feasibility study of a 3-D finite element solution scheme for aeroengine duct acoustics

NASA Technical Reports Server (NTRS)

Abrahamson, A. L.

1980-01-01

The advantage from development of a 3-D model of aeroengine duct acoustics is the ability to analyze axial and circumferential liner segmentation simultaneously. The feasibility of a 3-D duct acoustics model was investigated using Galerkin or least squares element formulations combined with Gaussian elimination, successive over-relaxation, or conjugate gradient solution algorithms on conventional scalar computers and on a vector machine. A least squares element formulation combined with a conjugate gradient solver on a CDC Star vector computer initially appeared to have great promise, but severe difficulties were encountered with matrix ill-conditioning. These difficulties in conditioning rendered this technique impractical for realistic problems.

An accurate and efficient acoustic eigensolver based on a fast multipole BEM and a contour integral method

NASA Astrophysics Data System (ADS)

Zheng, Chang-Jun; Gao, Hai-Feng; Du, Lei; Chen, Hai-Bo; Zhang, Chuanzeng

2016-01-01

An accurate numerical solver is developed in this paper for eigenproblems governed by the Helmholtz equation and formulated through the boundary element method. A contour integral method is used to convert the nonlinear eigenproblem into an ordinary eigenproblem, so that eigenvalues can be extracted accurately by solving a set of standard boundary element systems of equations. In order to accelerate the solution procedure, the parameters affecting the accuracy and efficiency of the method are studied and two contour paths are compared. Moreover, a wideband fast multipole method is implemented with a block IDR (s) solver to reduce the overall solution cost of the boundary element systems of equations with multiple right-hand sides. The Burton-Miller formulation is employed to identify the fictitious eigenfrequencies of the interior acoustic problems with multiply connected domains. The actual effect of the Burton-Miller formulation on tackling the fictitious eigenfrequency problem is investigated and the optimal choice of the coupling parameter as α = i / k is confirmed through exterior sphere examples. Furthermore, the numerical eigenvalues obtained by the developed method are compared with the results obtained by the finite element method to show the accuracy and efficiency of the developed method.

A momentum-space formulation without partial wave decomposition for scattering of two spin-half particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fachruddin, Imam, E-mail: imam.fachruddin@sci.ui.ac.id; Salam, Agus

2016-03-11

A new momentum-space formulation for scattering of two spin-half particles, both either identical or unidentical, is formulated. As basis states the free linear-momentum states are not expanded into the angular-momentum states, the system’s spin states are described by the product of the spin states of the two particles, and the system’s isospin states by the total isospin states of the two particles. We evaluate the Lippmann-Schwinger equations for the T-matrix elements in these basis states. The azimuthal behavior of the potential and of the T-matrix elements leads to a set of coupled integral equations for the T-matrix elements in twomore » variables only, which are the magnitude of the relative momentum and the scattering angle. Some symmetry relations for the potential and the T-matrix elements reduce the number of the integral equations to be solved. A set of six spin operators to express any interaction of two spin-half particles is introduced. We show the spin-averaged differential cross section as being calculated in terms of the solution of the set of the integral equations.« less

Simulation of time-dispersion spectral device with sample spectra accumulation

NASA Astrophysics Data System (ADS)

Zhdanov, Arseny; Khansuvarov, Ruslan; Korol, Georgy

2014-09-01

This research is conducted in order to design a spectral device for light sources power spectrum analysis. The spectral device should process radiation from sources, direct contact with radiation of which is either impossible or undesirable. Such sources include jet blast of an aircraft, optical radiation in metallurgy and textile industry. In proposed spectral device optical radiation is guided out of unfavorable environment via a piece of optical fiber with high dispersion. It is necessary for analysis to make samples of analyzed radiation as short pulses. Dispersion properties of such optical fiber cause spectral decomposition of input optical pulses. The faster time of group delay vary the stronger the spectral decomposition effect. This effect allows using optical fiber with high dispersion as a major element of proposed spectral device. Duration of sample must be much shorter than group delay time difference of a dispersive system. In the given frequency range this characteristic has to be linear. The frequency range is 400 … 500 THz for typical optical fiber. Using photonic-crystal fiber (PCF) gives much wider spectral range for analysis. In this paper we propose simulation of single pulse transmission through dispersive system with linear dispersion characteristic and quadratic-detected output responses accumulation. During simulation we propose studying influence of optical fiber dispersion characteristic angle on spectral measurement results. We also consider pulse duration and group delay time difference impact on output pulse shape and duration. Results show the most suitable dispersion characteristic that allow choosing the structure of PCF - major element of time-dispersion spectral analysis method and required number of samples for reliable assessment of measured spectrum.

Spectral Element Method for the Simulation of Unsteady Compressible Flows

NASA Technical Reports Server (NTRS)

Diosady, Laslo Tibor; Murman, Scott M.

2013-01-01

This work uses a discontinuous-Galerkin spectral-element method (DGSEM) to solve the compressible Navier-Stokes equations [1{3]. The inviscid ux is computed using the approximate Riemann solver of Roe [4]. The viscous fluxes are computed using the second form of Bassi and Rebay (BR2) [5] in a manner consistent with the spectral-element approximation. The method of lines with the classical 4th-order explicit Runge-Kutta scheme is used for time integration. Results for polynomial orders up to p = 15 (16th order) are presented. The code is parallelized using the Message Passing Interface (MPI). The computations presented in this work are performed using the Sandy Bridge nodes of the NASA Pleiades supercomputer at NASA Ames Research Center. Each Sandy Bridge node consists of 2 eight-core Intel Xeon E5-2670 processors with a clock speed of 2.6Ghz and 2GB per core memory. On a Sandy Bridge node the Tau Benchmark [6] runs in a time of 7.6s.

High-Order Entropy Stable Formulations for Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Fisher, Travis C.

2013-01-01

A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.

An enriched finite element method to fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Luan, Shengzhi; Lian, Yanping; Ying, Yuping; Tang, Shaoqiang; Wagner, Gregory J.; Liu, Wing Kam

2017-08-01

In this paper, an enriched finite element method with fractional basis [ 1,x^{α }] for spatial fractional partial differential equations is proposed to obtain more stable and accurate numerical solutions. For pure fractional diffusion equation without advection, the enriched Galerkin finite element method formulation is demonstrated to simulate the exact solution successfully without any numerical oscillation, which is advantageous compared to the traditional Galerkin finite element method with integer basis [ 1,x] . For fractional advection-diffusion equation, the oscillatory behavior becomes complex due to the introduction of the advection term which can be characterized by a fractional element Peclet number. For the purpose of addressing the more complex numerical oscillation, an enriched Petrov-Galerkin finite element method is developed by using a dimensionless fractional stabilization parameter, which is formulated through a minimization of the residual of the nodal solution. The effectiveness and accuracy of the enriched finite element method are demonstrated by a series of numerical examples of fractional diffusion equation and fractional advection-diffusion equation, including both one-dimensional and two-dimensional, steady-state and time-dependent cases.

Static, free vibration and thermal analysis of composite plates and shells using a flat triangular shell element

NASA Astrophysics Data System (ADS)

Kapania, R. K.; Mohan, P.

1996-09-01

Finite element static, free vibration and thermal analysis of thin laminated plates and shells using a three noded triangular flat shell element is presented. The flat shell element is a combination of the Discrete Kirchhoff Theory (DKT) plate bending element and a membrane element derived from the Linear Strain Triangular (LST) element with a total of 18 degrees of freedom (3 translations and 3 rotations per node). Explicit formulations are used for the membrane, bending and membrane-bending coupling stiffness matrices and the thermal load vector. Due to a strong analogy between the induced strain caused by the thermal field and the strain induced in a structure due to an electric field the present formulation is readily applicable for the analysis of structures excited by surface bonded or embedded piezoelectric actuators. The results are presented for (i) static analysis of (a) simply supported square plates under doubly sinusoidal load and uniformly distributed load (b) simply supported spherical shells under a uniformly distributed load, (ii) free vibration analysis of (a) square cantilever plates, (b) skew cantilever plates and (c) simply supported spherical shells; (iii) Thermal deformation analysis of (a) simply supported square plates, (b) simply supported-clamped square plate and (c) simply supported spherical shells. A numerical example is also presented demonstrating the application of the present formulation to analyse a symmetrically laminated graphite/epoxy laminate excited by a layer of piezoelectric polyvinylidene flouride (PVDF). The results presented are in good agreement with those available in the literature.

Analysis of X-ray Spectra of High-Z Elements obtained on Nike with high spectral and spatial resolution

NASA Astrophysics Data System (ADS)

Aglitskiy, Yefim; Weaver, J. L.; Karasik, M.; Serlin, V.; Obenschain, S. P.; Ralchenko, Yu.

2014-10-01

The spectra of multi-charged ions of Hf, Ta, W, Pt, Au and Bi have been studied on Nike krypton-fluoride laser facility with the help of two kinds of X-ray spectrometers. First, survey instrument covering a spectral range from 0.5 to 19.5 angstroms which allows simultaneous observation of both M- and N- spectra of above mentioned elements with high spectral resolution. Second, an imaging spectrometer with interchangeable spherically bent Quartz crystals that added higher efficiency, higher spectral resolution and high spatial resolution to the qualities of the former one. Multiple spectral lines with X-ray energies as high as 4 keV that belong to the isoelectronic sequences of Fe, Co, Ni, Cu and Zn were identified with the help of NOMAD package developed by Dr. Yu. Ralchenko and colleagues. In our continuous effort to support DOE-NNSA's inertial fusion program, this campaign covered a wide range of plasma conditions that result in production of relatively energetic X-rays. Work supported by the US DOE/NNSA.

[Analysis of software for identifying spectral line of laser-induced breakdown spectroscopy based on LabVIEW].

PubMed

Hu, Zhi-yu; Zhang, Lei; Ma, Wei-guang; Yan, Xiao-juan; Li, Zhi-xin; Zhang, Yong-zhi; Wang, Le; Dong, Lei; Yin, Wang-bao; Jia, Suo-tang

2012-03-01

Self-designed identifying software for LIBS spectral line was introduced. Being integrated with LabVIEW, the soft ware can smooth spectral lines and pick peaks. The second difference and threshold methods were employed. Characteristic spectrum of several elements matches the NIST database, and realizes automatic spectral line identification and qualitative analysis of the basic composition of sample. This software can analyze spectrum handily and rapidly. It will be a useful tool for LIBS.

From UV Protection to Protection in the Whole Spectral Range of the Solar Radiation: New Aspects of Sunscreen Development.

PubMed

Zastrow, Leonhard; Meinke, Martina C; Albrecht, Stephanie; Patzelt, Alexa; Lademann, Juergen

2017-01-01

Sunscreens have been constantly improving in the past few years. Today, they provide an efficient protection not only in the UVB but also in the UVA spectral region of the solar radiation. Recently it could be demonstrated that 50% of all free radicals induced in the skin due to solar radiation are formed in the visible and infrared spectral region. The good protective efficacy of sunscreens in the UV region prompts people to stay much longer in the sun than if they had left their skin unprotected. However, as no protection in the visible and infrared spectral region is provided, high amounts of free radicals are induced here that could easily exceed the critical radical concentration. This chapter describes how the effect of sunscreens can be extended to cover also the visible and infrared spectral region of the solar radiation by adding pigments and antioxidants with high radical protection factors to the sunscreen formulations.

Group theoretical approach to the Dirac operator on S 2

NASA Astrophysics Data System (ADS)

Gutiérrez, Sergio; Huet, Idrish

2018-04-01

In this revision we outline the group theoretical approach to formulate and solve the eigenvalue problem of the Dirac operator on the round 2-sphere conceived as the right coset S 2 = SU(2)/U(1). Starting from general symmetry considerations we illustrate the formulation of the Dirac operator through left action or right action differential operators, whose properties on a right coset are quite different. The construction of the spinor space and the solution of the spectral problem using group theoretical methods is also presented.

Optimal network modification for spectral radius dependent phase transitions

NASA Astrophysics Data System (ADS)

Rosen, Yonatan; Kirsch, Lior; Louzoun, Yoram

2016-09-01

The dynamics of contact processes on networks is often determined by the spectral radius of the networks adjacency matrices. A decrease of the spectral radius can prevent the outbreak of an epidemic, or impact the synchronization among systems of coupled oscillators. The spectral radius is thus tightly linked to network dynamics and function. As such, finding the minimal change in network structure necessary to reach the intended spectral radius is important theoretically and practically. Given contemporary big data resources such as large scale communication or social networks, this problem should be solved with a low runtime complexity. We introduce a novel method for the minimal decrease in weights of edges required to reach a given spectral radius. The problem is formulated as a convex optimization problem, where a global optimum is guaranteed. The method can be easily adjusted to an efficient discrete removal of edges. We introduce a variant of the method which finds optimal decrease with a focus on weights of vertices. The proposed algorithm is exceptionally scalable, solving the problem for real networks of tens of millions of edges in a short time.

A high-order 3-D spectral-element method for the forward modelling and inversion of gravimetric data—Application to the western Pyrenees

NASA Astrophysics Data System (ADS)

Martin, Roland; Chevrot, Sébastien; Komatitsch, Dimitri; Seoane, Lucia; Spangenberg, Hannah; Wang, Yi; Dufréchou, Grégory; Bonvalot, Sylvain; Bruinsma, Sean

2017-04-01

We image the internal density structure of the Pyrenees by inverting gravity data using an a priori density model derived by scaling a Vp model obtained by full waveform inversion of teleseismic P-waves. Gravity anomalies are computed via a 3-D high-order finite-element integration in the same high-order spectral-element grid as the one used to solve the wave equation and thus to obtain the velocity model. The curvature of the Earth and surface topography are taken into account in order to obtain a density model as accurate as possible. The method is validated through comparisons with exact semi-analytical solutions. We show that the spectral-element method drastically accelerates the computations when compared to other more classical methods. Different scaling relations between compressional velocity and density are tested, and the Nafe-Drake relation is the one that leads to the best agreement between computed and observed gravity anomalies. Gravity data inversion is then performed and the results allow us to put more constraints on the density structure of the shallow crust and on the deep architecture of the mountain range.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ting Yuan-Sen; Conroy, Charlie; Cargile, Phillip

Understanding the evolution of the Milky Way calls for the precise abundance determination of many elements in many stars. A common perception is that deriving more than a few elemental abundances ([Fe/H], [ α /Fe], perhaps [C/H], [N/H]) requires medium-to-high spectral resolution, R ≳ 10,000, mostly to overcome the effects of line blending. In a recent work, we presented an efficient and practical way to model the full stellar spectrum, even when fitting a large number of stellar labels simultaneously. In this paper, we quantify to what precision the abundances of many different elements can be recovered, as a functionmore » of spectroscopic resolution and wavelength range. In the limit of perfect spectral models and spectral normalization, we show that the precision of elemental abundances is nearly independent of resolution, for a fixed exposure time and number of detector pixels; low-resolution spectra simply afford much higher S/N per pixel and generally larger wavelength range in a single setting. We also show that estimates of most stellar labels are not strongly correlated with one another once R ≳ 1000. Modest errors in the line-spread function, as well as small radial velocity errors, do not affect these conclusions, and data-driven models indicate that spectral (continuum) normalization can be achieved well enough in practice. These results, to be confirmed with an analysis of observed low-resolution data, open up new possibilities for the design of large spectroscopic stellar surveys and for the reanalysis of archival low-resolution data sets.« less

Self Diagnostic Adhesive for Bonded Joints in Aircraft Structures

DTIC Science & Technology

2016-10-04

validated under the fatigue/dynamic loading condition. 3) Both SEM (Spectral Element Modeling) and FEM ( Finite Element Modeling) simulation of the...Sensors ..................................................................... 22 Parametric Study of Sensor Performance via Finite Element Simulation...The frequency range that we are interested is around 800 kHz. Conventional linear finite element method (FEM) requires a very fine spatial

Distortion Representation of Forecast Errors for Model Skill Assessment and Objective Analysis

NASA Technical Reports Server (NTRS)

Hoffman, Ross N.

2001-01-01

We completed the formulation of the smoothness penalty functional this past quarter. We used a simplified procedure for estimating the statistics of the FCA solution spectral coefficients from the results of the unconstrained, low-truncation FCA (stopping criterion) solutions. During the current reporting period we have completed the calculation of GEOS-2 model-equivalent brightness temperatures for the 6.7 micron and 11 micron window channels used in the GOES imagery for all 10 cases from August 1999. These were simulated using the AER-developed Optimal Spectral Sampling (OSS) model.

Performance of mixed formulations for the particle finite element method in soil mechanics problems

NASA Astrophysics Data System (ADS)

Monforte, Lluís; Carbonell, Josep Maria; Arroyo, Marcos; Gens, Antonio

2017-07-01

This paper presents a computational framework for the numerical analysis of fluid-saturated porous media at large strains. The proposal relies, on one hand, on the particle finite element method (PFEM), known for its capability to tackle large deformations and rapid changing boundaries, and, on the other hand, on constitutive descriptions well established in current geotechnical analyses (Darcy's law; Modified Cam Clay; Houlsby hyperelasticity). An important feature of this kind of problem is that incompressibility may arise either from undrained conditions or as a consequence of material behaviour; incompressibility may lead to volumetric locking of the low-order elements that are typically used in PFEM. In this work, two different three-field mixed formulations for the coupled hydromechanical problem are presented, in which either the effective pressure or the Jacobian are considered as nodal variables, in addition to the solid skeleton displacement and water pressure. Additionally, several mixed formulations are described for the simplified single-phase problem due to its formal similitude to the poromechanical case and its relevance in geotechnics, since it may approximate the saturated soil behaviour under undrained conditions. In order to use equal-order interpolants in displacements and scalar fields, stabilization techniques are used in the mass conservation equation of the biphasic medium and in the rest of scalar equations. Finally, all mixed formulations are assessed in some benchmark problems and their performances are compared. It is found that mixed formulations that have the Jacobian as a nodal variable perform better.

Algebraic theory of molecules

NASA Technical Reports Server (NTRS)

Iachello, Franco

1995-01-01

An algebraic formulation of quantum mechanics is presented. In this formulation, operators of interest are expanded onto elements of an algebra, G. For bound state problems in nu dimensions the algebra G is taken to be U(nu + 1). Applications to the structure of molecules are presented.

The Schwinger Model on S 1: Hamiltonian Formulation, Vacuum and Anomaly

NASA Astrophysics Data System (ADS)

Stuart, David

2014-12-01

We present a Hamiltonian formulation of the Schwinger model with spatial domain taken to be the circle. It is shown that, in Coulomb gauge, the Hamiltonian is a semi-bounded, self-adjoint operator which is invariant under the group of large gauge transformations. There is a nontrivial action of on fermionic Fock space and its vacuum. This action plays a role analogous to that played by the spectral flow in the infinite Dirac sea formalism. The formulation allows (1) a description of the anomaly and its relation to the group action, and (2) an explicit identification of the vacuum. The anomaly in the chiral conservation law appears as a consequence of insisting upon semi-boundedness and gauge invariance of the quantized Hamiltonian.

On the convergence of an iterative formulation of the electromagnetic scattering from an infinite grating of thin wires

NASA Technical Reports Server (NTRS)

Brand, J. C.

1985-01-01

Contraction theory is applied to an iterative formulation of electromagnetic scattering from periodic structures and a computational method for insuring convergence is developed. A short history of spectral (or k-space) formulation is presented with an emphasis on application to periodic surfaces. The mathematical background for formulating an iterative equation is covered using straightforward single variable examples including an extension to vector spaces. To insure a convergent solution of the iterative equation, a process called the contraction corrector method is developed. Convergence properties of previously presented iterative solutions to one-dimensional problems are examined utilizing contraction theory and the general conditions for achieving a convergent solution are explored. The contraction corrector method is then applied to several scattering problems including an infinite grating of thin wires with the solution data compared to previous works.

Spectral analysis of pharmaceutical formulations prepared according to ancient recipes in comparison with old museum remains.

PubMed

Gamberini, M Cristina; Baraldi, C; Freguglia, G; Baraldi, P

2011-10-01

A study of the composition of the remains of ancient ointments from museums was undertaken to enable understanding of the preparation techniques. Comparison of ancient recipes from different historical periods and spectroscopic characteristics of inorganic and/or organic remains recovered in museum vessels enabled preparation of ancient pharmaceutical-cosmetic formulations. Farmacopea Augustana by Occo was one the most important books studied for the 14 formulations prepared in the laboratory. Three formulations are discussed in detail and raw materials and new preparations were proposed for ozone ageing. The most important micro Raman results are discussed. The spectra of the raw materials lipids, beeswax, and resins are discussed; beeswax and pig suet (axŭngia) Raman spectra were found to be similar, but different from those of the aged oils. SERS was applied to ancient ointments and galbanum and the Raman spectra are reported and discussed for the first time.

Development of a controlled release formulation by continuous twin screw granulation: Influence of process and formulation parameters.

PubMed

Vanhoorne, V; Vanbillemont, B; Vercruysse, J; De Leersnyder, F; Gomes, P; Beer, T De; Remon, J P; Vervaet, C

2016-05-30

The aim of this study was to evaluate the potential of twin screw granulation for the continuous production of controlled release formulations with hydroxypropylmethylcellulose as hydrophilic matrix former. Metoprolol tartrate was included in the formulation as very water soluble model drug. A premix of metoprolol tartrate, hydroxypropylmethylcellulose and filler (ratio 20/20/60, w/w) was granulated with demineralized water via twin screw granulation. After oven drying and milling, tablets were produced on a rotary Modul™ P tablet press. A D-optimal design (29 experiments) was used to assess the influence of process (screw speed, throughput, barrel temperature and screw design) and formulation parameters (starch content of the filler) on the process (torque), granule (size distribution, shape, friability, density) and tablet (hardness, friability and dissolution) critical quality attributes. The torque was dominated by the number of kneading elements and throughput, whereas screw speed and filling degree only showed a minor influence on torque. Addition of screw mixing elements after a block of kneading elements improved the yield of the process before milling as it resulted in less oversized granules and also after milling as less fines were present. Temperature was also an important parameter to optimize as a higher temperature yielded less fines and positively influenced the aspect ratio. The shape of hydroxypropylmethylcellulose granules was comparable to that of immediate release formulations. Tensile strength and friability of tablets were not dependent on the process parameters. The use of starch as filler was not beneficial with regard to granule and tablet properties. Complete drug release was obtained after 16-20h and was independent of the design's parameters. Copyright © 2016 Elsevier B.V. All rights reserved.

Evolution of CMB spectral distortion anisotropies and tests of primordial non-Gaussianity

NASA Astrophysics Data System (ADS)

Chluba, Jens; Dimastrogiovanni, Emanuela; Amin, Mustafa A.; Kamionkowski, Marc

2017-04-01

Anisotropies in distortions to the frequency spectrum of the cosmic microwave background (CMB) can be created through spatially varying heating processes in the early Universe. For instance, the dissipation of small-scale acoustic modes does create distortion anisotropies, in particular for non-Gaussian primordial perturbations. In this work, we derive approximations that allow describing the associated distortion field. We provide a systematic formulation of the problem using Fourier-space window functions, clarifying and generalizing previous approximations. Our expressions highlight the fact that the amplitudes of the spectral-distortion fluctuations induced by non-Gaussianity depend also on the homogeneous value of those distortions. Absolute measurements are thus required to obtain model-independent distortion constraints on primordial non-Gaussianity. We also include a simple description for the evolution of distortions through photon diffusion, showing that these corrections can usually be neglected. Our formulation provides a systematic framework for computing higher order correlation functions of distortions with CMB temperature anisotropies and can be extended to describe correlations with polarization anisotropies.

Simulation of multivariate stationary stochastic processes using dimension-reduction representation methods

NASA Astrophysics Data System (ADS)

Liu, Zhangjun; Liu, Zenghui; Peng, Yongbo

2018-03-01

In view of the Fourier-Stieltjes integral formula of multivariate stationary stochastic processes, a unified formulation accommodating spectral representation method (SRM) and proper orthogonal decomposition (POD) is deduced. By introducing random functions as constraints correlating the orthogonal random variables involved in the unified formulation, the dimension-reduction spectral representation method (DR-SRM) and the dimension-reduction proper orthogonal decomposition (DR-POD) are addressed. The proposed schemes are capable of representing the multivariate stationary stochastic process with a few elementary random variables, bypassing the challenges of high-dimensional random variables inherent in the conventional Monte Carlo methods. In order to accelerate the numerical simulation, the technique of Fast Fourier Transform (FFT) is integrated with the proposed schemes. For illustrative purposes, the simulation of horizontal wind velocity field along the deck of a large-span bridge is proceeded using the proposed methods containing 2 and 3 elementary random variables. Numerical simulation reveals the usefulness of the dimension-reduction representation methods.

Spectral properties of common intraocular lens (IOL) types

NASA Astrophysics Data System (ADS)

Milne, Peter J.; Chapon, Pascal F.; Hamaoui, Marie; Parel, Jean-Marie A.; Clayman, H.; Rol, Pascal O.

1999-06-01

Currently over 50 kinds of intraocular lenses (IOLs) are approved for patient use in the treatment of cataracts and ametropia. These lenses are manufactured from at least 2 kinds of silicones as well as several kinds of acrylic polymers including polyHEMA, Poly HOXEMA, a range of polymethacrylate and polyacrylate formulations. We sought to measure spectral transmission curves of a range of IOLS in the UV-visible and near IR spectral regions in order to better characterize their optical properties and to provide a baseline from which to assess their alteration following implantation over time. Consideration of how this may best be achieved are discussed. The variable ability of both explained IOLs and some samples from a range of manufacturers to block UV wavelengths is commented upon.

A probabilistic Hu-Washizu variational principle

NASA Technical Reports Server (NTRS)

Liu, W. K.; Belytschko, T.; Besterfield, G. H.

1987-01-01

A Probabilistic Hu-Washizu Variational Principle (PHWVP) for the Probabilistic Finite Element Method (PFEM) is presented. This formulation is developed for both linear and nonlinear elasticity. The PHWVP allows incorporation of the probabilistic distributions for the constitutive law, compatibility condition, equilibrium, domain and boundary conditions into the PFEM. Thus, a complete probabilistic analysis can be performed where all aspects of the problem are treated as random variables and/or fields. The Hu-Washizu variational formulation is available in many conventional finite element codes thereby enabling the straightforward inclusion of the probabilistic features into present codes.

Explicit formulation of an anisotropic Allman/DKT 3-node thin triangular flat shell elements

NASA Astrophysics Data System (ADS)

Ertas, A.; Krafcik, J. T.; Ekwaro-Osire, S.

A simple, explicit formulation of the stiffness matrix for an anisotropic, 3-node, thin triangular, flat shell element in global coordinates is presented. An Allman triangle is used for membrane stiffness. The membrane stiffness matrix is explicitly derived by applying an Allman transformation to a Felippa 6-node linear strain triangle (LST). Bending stiffness is incorporated by the use of a discrete Kirchhoff triangle (DKT) bending triangle. Stiffness terms resulting from anisotropic membrane-bending coupling are included by integrating, in area coordinates, membrane and bending strain-displacement matrices.

Modeling Electromagnetic Scattering From Complex Inhomogeneous Objects

NASA Technical Reports Server (NTRS)

Deshpande, Manohar; Reddy, C. J.

2011-01-01

This software innovation is designed to develop a mathematical formulation to estimate the electromagnetic scattering characteristics of complex, inhomogeneous objects using the finite-element-method (FEM) and method-of-moments (MoM) concepts, as well as to develop a FORTRAN code called FEMOM3DS (Finite Element Method and Method of Moments for 3-Dimensional Scattering), which will implement the steps that are described in the mathematical formulation. Very complex objects can be easily modeled, and the operator of the code is not required to know the details of electromagnetic theory to study electromagnetic scattering.

Least-squares finite element solution of 3D incompressible Navier-Stokes problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, Tsung-Liang; Povinelli, Louis A.

1992-01-01

Although significant progress has been made in the finite element solution of incompressible viscous flow problems. Development of more efficient methods is still needed before large-scale computation of 3D problems becomes feasible. This paper presents such a development. The most popular finite element method for the solution of incompressible Navier-Stokes equations is the classic Galerkin mixed method based on the velocity-pressure formulation. The mixed method requires the use of different elements to interpolate the velocity and the pressure in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for the existence of the solution. On the other hand, due to the lack of symmetry and positive definiteness of the linear equations arising from the mixed method, iterative methods for the solution of linear systems have been hard to come by. Therefore, direct Gaussian elimination has been considered the only viable method for solving the systems. But, for three-dimensional problems, the computer resources required by a direct method become prohibitively large. In order to overcome these difficulties, a least-squares finite element method (LSFEM) has been developed. This method is based on the first-order velocity-pressure-vorticity formulation. In this paper the LSFEM is extended for the solution of three-dimensional incompressible Navier-Stokes equations written in the following first-order quasi-linear velocity-pressure-vorticity formulation.

Achromatic registration of quadrature components of the optical spectrum in spectral domain optical coherence tomography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shilyagin, P A; Gelikonov, G V; Gelikonov, V M

2014-07-31

We have thoroughly investigated the method of simultaneous reception of spectral components with the achromatised quadrature phase shift between two portions of a reference wave, designed for the effective suppression of the 'mirror' artefact in the resulting image obtained by means of spectral domain optical coherence tomography (SD OCT). We have developed and experimentally tested a phase-shifting element consisting of a beam divider, which splits the reference optical beam into the two beams, and of delay lines being individual for each beam, which create a mutual phase difference of π/2 in the double pass of the reference beam. The phasemore » shift achromatism over a wide spectral range is achieved by using in the delay lines the individual elements with different dispersion characteristics. The ranges of admissible adjustment parameters of the achromatised delay line are estimated for exact and inexact conformity of the geometric characteristics of its components to those calculated. A possibility of simultaneous recording of the close-to-quadrature spectral components with a single linear photodetector element is experimentally confirmed. The suppression of the artefact mirror peak in the OCT-signal by an additional 9 dB relative to the level of its suppression is experimentally achieved when the air delay line is used. Two-dimensional images of the surface positioned at an angle to the axis of the probe beam are obtained with the correction of the 'mirror' artefact while maintaining the dynamic range of the image. (laser biophotonics)« less

A probabilistic model of a porous heat exchanger

NASA Technical Reports Server (NTRS)

Agrawal, O. P.; Lin, X. A.

1995-01-01

This paper presents a probabilistic one-dimensional finite element model for heat transfer processes in porous heat exchangers. The Galerkin approach is used to develop the finite element matrices. Some of the submatrices are asymmetric due to the presence of the flow term. The Neumann expansion is used to write the temperature distribution as a series of random variables, and the expectation operator is applied to obtain the mean and deviation statistics. To demonstrate the feasibility of the formulation, a one-dimensional model of heat transfer phenomenon in superfluid flow through a porous media is considered. Results of this formulation agree well with the Monte-Carlo simulations and the analytical solutions. Although the numerical experiments are confined to parametric random variables, a formulation is presented to account for the random spatial variations.

Calculation of precision satellite orbits with nonsingular elements /VOP formulation/

NASA Technical Reports Server (NTRS)

Velez, C. E.; Cefola, P. J.; Long, A. C.; Nimitz, K. S.

1974-01-01

Review of some results obtained in an effort to develop efficient, high-precision trajectory computation processes for artificial satellites by optimum selection of the form of the equations of motion of the satellite and the numerical integration method. In particular, the matching of a Gaussian variation-of-parameter (VOP) formulation is considered which is expressed in terms of equinoctial orbital elements and partially decouples the motion of the orbital frame from motion within the orbital frame. The performance of the resulting orbit generators is then compared with the popular classical Cowell/Gauss-Jackson formulation/integrator pair for two distinctly different orbit types - namely, the orbit of the ATS satellite at near-geosynchronous conditions and the near-circular orbit of the GEOS-C satellite at 1000 km.

Numerical computation of transonic flows by finite-element and finite-difference methods

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Wellford, L. C.; Merkle, C. L.; Murman, E. M.

1978-01-01

Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.

Slave finite elements: The temporal element approach to nonlinear analysis

NASA Technical Reports Server (NTRS)

Gellin, S.

1984-01-01

A formulation method for finite elements in space and time incorporating nonlinear geometric and material behavior is presented. The method uses interpolation polynomials for approximating the behavior of various quantities over the element domain, and only explicit integration over space and time. While applications are general, the plate and shell elements that are currently being programmed are appropriate to model turbine blades, vanes, and combustor liners.

Penalty-Based Interface Technology for Prediction of Delamination Growth in Laminated Structures

NASA Technical Reports Server (NTRS)

Averill, Ronald C.

2004-01-01

An effective interface element technology has been developed for connecting and simulating crack growth between independently modeled finite element subdomains (e.g., composite plies). This method has been developed using penalty constraints and allows coupling of finite element models whose nodes do not necessarily coincide along their common interface. Additionally, the present formulation leads to a computational approach that is very efficient and completely compatible with existing commercial software. The present interface element has been implemented in the commercial finite element code ABAQUS as a User Element Subroutine (UEL), making it easy to test the approach for a wide range of problems. The interface element technology has been formulated to simulate delamination growth in composite laminates. Thanks to its special features, the interface element approach makes it possible to release portions of the interface surface whose length is smaller than that of the finite elements. In addition, the penalty parameter can vary within the interface element, allowing the damage model to be applied to a desired fraction of the interface between the two meshes. Results for double cantilever beam DCB, end-loaded split (ELS) and fixed-ratio mixed mode (FRMM) specimens are presented. These results are compared to measured data to assess the ability of the present damage model to simulate crack growth.

WARP3D-Release 10.8: Dynamic Nonlinear Analysis of Solids using a Preconditioned Conjugate Gradient Software Architecture

NASA Technical Reports Server (NTRS)

Koppenhoefer, Kyle C.; Gullerud, Arne S.; Ruggieri, Claudio; Dodds, Robert H., Jr.; Healy, Brian E.

1998-01-01

This report describes theoretical background material and commands necessary to use the WARP3D finite element code. WARP3D is under continuing development as a research code for the solution of very large-scale, 3-D solid models subjected to static and dynamic loads. Specific features in the code oriented toward the investigation of ductile fracture in metals include a robust finite strain formulation, a general J-integral computation facility (with inertia, face loading), an element extinction facility to model crack growth, nonlinear material models including viscoplastic effects, and the Gurson-Tver-gaard dilatant plasticity model for void growth. The nonlinear, dynamic equilibrium equations are solved using an incremental-iterative, implicit formulation with full Newton iterations to eliminate residual nodal forces. The history integration of the nonlinear equations of motion is accomplished with Newmarks Beta method. A central feature of WARP3D involves the use of a linear-preconditioned conjugate gradient (LPCG) solver implemented in an element-by-element format to replace a conventional direct linear equation solver. This software architecture dramatically reduces both the memory requirements and CPU time for very large, nonlinear solid models since formation of the assembled (dynamic) stiffness matrix is avoided. Analyses thus exhibit the numerical stability for large time (load) steps provided by the implicit formulation coupled with the low memory requirements characteristic of an explicit code. In addition to the much lower memory requirements of the LPCG solver, the CPU time required for solution of the linear equations during each Newton iteration is generally one-half or less of the CPU time required for a traditional direct solver. All other computational aspects of the code (element stiffnesses, element strains, stress updating, element internal forces) are implemented in the element-by- element, blocked architecture. This greatly improves vectorization of the code on uni-processor hardware and enables straightforward parallel-vector processing of element blocks on multi-processor hardware.

Modeling of fatigue crack induced nonlinear ultrasonics using a highly parallelized explicit local interaction simulation approach

NASA Astrophysics Data System (ADS)

Shen, Yanfeng; Cesnik, Carlos E. S.

2016-04-01

This paper presents a parallelized modeling technique for the efficient simulation of nonlinear ultrasonics introduced by the wave interaction with fatigue cracks. The elastodynamic wave equations with contact effects are formulated using an explicit Local Interaction Simulation Approach (LISA). The LISA formulation is extended to capture the contact-impact phenomena during the wave damage interaction based on the penalty method. A Coulomb friction model is integrated into the computation procedure to capture the stick-slip contact shear motion. The LISA procedure is coded using the Compute Unified Device Architecture (CUDA), which enables the highly parallelized supercomputing on powerful graphic cards. Both the explicit contact formulation and the parallel feature facilitates LISA's superb computational efficiency over the conventional finite element method (FEM). The theoretical formulations based on the penalty method is introduced and a guideline for the proper choice of the contact stiffness is given. The convergence behavior of the solution under various contact stiffness values is examined. A numerical benchmark problem is used to investigate the new LISA formulation and results are compared with a conventional contact finite element solution. Various nonlinear ultrasonic phenomena are successfully captured using this contact LISA formulation, including the generation of nonlinear higher harmonic responses. Nonlinear mode conversion of guided waves at fatigue cracks is also studied.

The nonconforming virtual element method for eigenvalue problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gardini, Francesca; Manzini, Gianmarco; Vacca, Giuseppe

We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible formulations of the discrete problem, derived respectively by the nonstabilized and stabilized approximation of the L 2-inner product, and we study the convergence properties of the corresponding discrete eigenvalue problems. The proposed schemes provide a correct approximation of the spectrum and we prove optimal-order error estimates for the eigenfunctions and the usual double order of convergence of the eigenvalues. Finally we show a large set of numericalmore » tests supporting the theoretical results, including a comparison with the conforming Virtual Element choice.« less

Development of an integrated BEM approach for hot fluid structure interaction

NASA Technical Reports Server (NTRS)

Dargush, Gary F.; Banerjee, Prasanta K.; Honkala, Keith A.

1988-01-01

In the present work, the boundary element method (BEM) is chosen as the basic analysis tool, principally because the definition of temperature, flux, displacement and traction are very precise on a boundary-based discretization scheme. One fundamental difficulty is, of course, that a BEM formulation requires a considerable amount of analytical work, which is not needed in the other numerical methods. Progress made toward the development of a boundary element formulation for the study of hot fluid-structure interaction in Earth-to-Orbit engine hot section components is reported. The primary thrust of the program to date has been directed quite naturally toward the examination of fluid flow, since boundary element methods for fluids are at a much less developed state.

Multiple-element semiquantitative analysis of one-milligram geochemical samples by D.C. arc emission spectrography

USGS Publications Warehouse

Rait, N.

1981-01-01

A modified method is described for a 1-mg sample multi-element semiquantitative spectrographic analysis. This method uses a direct-current arc source, carbon instead of graphite electrodes, and an 80% argon-20% oxygen atmosphere instead of air. Although this is a destructive method, an analysis can be made for 68 elements in all mineral and geochemical samples. Carbon electrodes have been an aid in improving the detection limits of many elements. The carbon has a greater resistance to heat conductance and develops a better tip, facilitating sample volatilization and counter balancing the cooling effect of a flow of the argon-oxygen mixture around the anode. Where such an argon-oxygen atmosphere is used instead of air, the cyanogen band lines are greatly diminished in intensity, and thus more spectral lines of analysis elements are available for use; the spectral background is also lower. The main advantage of using the carbon electrode and the 80% argon-20% oxygen atmosphere is the improved detection limits of 36 out of 68 elements. The detection limits remain the same for 23 elements, and are not as good for only nine elements. ?? 1981.

A new axi-symmetric element for thin walled structures

NASA Astrophysics Data System (ADS)

Cardoso, Rui P. R.; Yoon, Jeong Whan; Dick, Robert E.

2010-03-01

A new axi-symmetric finite element for thin walled structures is presented in this work. It uses the solid-shell element’s concept with only a single element and multiple integration points along the thickness direction. The cross-section of the element is composed of four nodes with two degrees of freedom each. The proposed formulation overcomes many locking pathologies including transverse shear locking, Poisson’s locking and volumetric locking. For transverse shear locking, the formulation uses the selective reduced integration technique, for Poisson’s locking it uses the enhanced assumed strain (EAS) method with only one enhancing variable. The B-bar approach is used to eliminate the isochoric deformations in the hourglass field while the EAS method is used to alleviate the volumetric locking in the constant part of the deformation tensor. Several examples are shown to demonstrate the performance and accuracy of the proposed element with special focus on the numerical simulations for the beverage can industry.

A numerical spectral approach to solve the dislocation density transport equation

NASA Astrophysics Data System (ADS)

Djaka, K. S.; Taupin, V.; Berbenni, S.; Fressengeas, C.

2015-09-01

A numerical spectral approach is developed to solve in a fast, stable and accurate fashion, the quasi-linear hyperbolic transport equation governing the spatio-temporal evolution of the dislocation density tensor in the mechanics of dislocation fields. The approach relies on using the Fast Fourier Transform algorithm. Low-pass spectral filters are employed to control both the high frequency Gibbs oscillations inherent to the Fourier method and the fast-growing numerical instabilities resulting from the hyperbolic nature of the transport equation. The numerical scheme is validated by comparison with an exact solution in the 1D case corresponding to dislocation dipole annihilation. The expansion and annihilation of dislocation loops in 2D and 3D settings are also produced and compared with finite element approximations. The spectral solutions are shown to be stable, more accurate for low Courant numbers and much less computation time-consuming than the finite element technique based on an explicit Galerkin-least squares scheme.

Multilayer photosensitive structures based on porous silicon and rare-earth-element compounds: Study of spectral characteristics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kirsanov, N. Yu.; Latukhina, N. V., E-mail: natalat@yandex.ru; Lizunkova, D. A.

2017-03-15

The spectral characteristics of the specular reflectance, photosensitivity, and photoluminescence (PL) of multilayer structures based on porous silicon with rare-earth-element (REE) ions are investigated. It is shown that the photosensitivity of these structures in the wavelength range of 0.4–1.0 μm is higher than in structures free of REEs. The structures with Er{sup 3+} ions exhibit a luminescence response at room temperature in the spectral range from 1.1 to 1.7 μm. The PL spectrum of the erbium impurity is characterized by a fine line structure, which is determined by the splitting of the {sup 4}I{sub 15/2} multiplet of the Er{sup 3+}more » ion. It is shown that the structures with a porous layer on the working surface have a much lower reflectance in the entire spectral range under study (0.2–1.0 μm).« less

A survey of mixed finite element methods

NASA Technical Reports Server (NTRS)

Brezzi, F.

1987-01-01

This paper is an introduction to and an overview of mixed finite element methods. It discusses the mixed formulation of certain basic problems in elasticity and hydrodynamics. It also discusses special techniques for solving the discrete problem.

Compositional studies of Mare Moscoviense: New perspectives from Chandrayaan-1 VIS-NIR data

NASA Astrophysics Data System (ADS)

Bhatt, Megha; Wöhler, Christian; Dhingra, Deepak; Thangjam, Guneshwar; Rommel, Daniela; Mall, Urs; Bhardwaj, Anil; Grumpe, Arne

2018-03-01

Moscoviense is one of the prominent mare-filled basin on the lunar far side holding key insights about volcanic activity on the far side. Here, we present spectral and elemental maps of mare Moscoviense, using the Moon Mineralogy Mapper (M3) and Infrared Spectrometer-2 (SIR-2) data-sets. The different mare units are mapped based on their spectral properties analyzing both quantitatively (band center, band depth) and qualitatively (Integrated Band Depth composite images), and also using their elemental compositions. We find a total of five distinct spectral units from the basin floor based on the spectral properties. Our analysis suggests that the northern part which was mapped as Iltm unit (Imbrian low Ti, low Fe) by earlier researchers is actually a distinct unit, which is different in composition and age, named as Ivltm unit (Imbrian very low Ti and very low Fe). We obtain the absolute model age of 3.2 Ga with uncertainties of +0.2/ -0.5 Ga for the unit Ivltm. The newly identified basalt unit Ivltm is compositionally intermediate to the units Im and Iltm in FeO and TiO2 abundances. We find a total of five distinct spectral units from the basin floor based on the spectral properties. The units Im (Imbrian very low Ti) from southern and northern regions of the basin floor are spectrally distinct in terms of band center position and corresponding band depths but considered a single unit based on the elemental abundance analysis. The units Ivltm and Im are consistent with a high-Al basalt composition. Our detailed analysis of the entire Moscoviense basin indicates that the concentrations of orthopyroxene, olivine, and Mg-rich spinel, named as OOS rock family are widespread and dominant at the western and southern side of the middle ring of the basin with one isolated area found on the northern side of the peak ring.

Photon counting spectral breast CT: effect of adaptive filtration on CT numbers, noise, and contrast to noise ratio.

PubMed

Silkwood, Justin D; Matthews, Kenneth L; Shikhaliev, Polad M

2013-05-01

Photon counting spectral (PCS) computed tomography (CT) shows promise for breast imaging. An issue with current photon-counting detectors is low count rate capabilities, artifacts resulting from nonuniform count rate across the field of view, and suboptimal spectral information. These issues are addressed in part by using tissue-equivalent adaptive filtration of the x-ray beam. The purpose of the study was to investigate the effect of adaptive filtration on different aspects of PCS breast CT. The theoretical formulation for the filter shape was derived for different filter materials and evaluated by simulation and an experimental prototype of the filter was fabricated from a tissue-like material (acrylic). The PCS CT images of a glandular breast phantom with adipose and iodine contrast elements were simulated at 40, 60, 90, and 120 kVp tube voltages, with and without adaptive filter. The CT numbers, CT noise, and contrast-to-noise ratio (CNR) were compared for spectral CT images acquired with and without adaptive filters. Similar comparison was made for material-decomposed PCS CT images. The adaptive filter improved the uniformity of CT numbers, CT noise, and CNR in both ordinary and material decomposed PCS CT images. At the same tube output the average CT noise with adaptive filter, although uniform, was higher than the average noise without adaptive filter due to x-ray absorption by the filter. Increasing tube output, so that average skin exposure with the adaptive filter was same as without filter, made the noise with adaptive filter comparable to or lower than that without adaptive filter. Similar effects were observed when energy weighting was applied, and when material decompositions were performed using energy selective CT data. An adaptive filter decreases count rate requirements to the photon counting detectors which enables PCS breast CT based on commercially available detector technologies. Adaptive filter also improves image quality in PCS breast CT by decreasing beam hardening artifacts and by eliminating spatial nonuniformities of CT numbers, noise, and CNR.

A miniaturized capacitively coupled plasma microtorch optical emission spectrometer and a Rh coiled-filament as small-sized electrothermal vaporization device for simultaneous determination of volatile elements from liquid microsamples: spectral and analytical characterization.

PubMed

Frentiu, Tiberiu; Darvasi, Eugen; Butaciu, Sinziana; Ponta, Michaela; Petreus, Dorin; Mihaltan, Alin I; Frentiu, Maria

2014-11-01

A low power and low argon consumption (13.56 MHz, 15 W, 150 ml min(-1)) capacitively coupled plasma microtorch interfaced with a low-resolution microspectrometer and a small-sized electrothermal vaporization Rh coiled-filament as liquid microsample introduction device into the plasma was investigated for the simultaneous determination of several volatile elements of interest for environment. Constructive details, spectral and analytical characteristics, and optimum operating conditions of the laboratory equipment for the simultaneous determination of Ag, Cd, Cu, Pb and Zn requiring low vaporization power are provided. The method involves drying of 10 μl sample at 100°C, vaporization at 1500°C and emission measurement by capture of 20 successive spectral episodes each at an integration time of 500 ms. Experiments showed that emission of elements and plasma background were disturbed by the presence of complex matrix and hot Ar flow transporting the microsample into plasma. The emission spectrum of elements is simple, dominated by the resonance lines. The analytical system provided detection limits in the ng ml(-1) range: 0.5(Ag); 1.5(Cd); 5.6(Cu); 20(Pb) and 3(Zn) and absolute detection limits of the order of pg: 5(Ag); 15(Cd); 56(Cu); 200(Pb) and 30(Zn). It was demonstrated the utility and capability of the miniaturized analytical system in the simultaneous determination of elements in soil and water sediment using the standard addition method to compensate for the non-spectral effects of alkali and earth alkaline elements. The analysis of eight certified reference materials exhibited reliable results with recovery in the range of 95-108% and precision of 0.5-9.0% for the five examined elements. The proposed miniaturized analytical system is attractive due to the simple construction of the electrothermal vaporization device and microtorch, low costs associated to plasma generation, high analytical sensitivity and easy-to-run for simultaneous multielemental analysis of liquid microsamples. Copyright © 2014. Published by Elsevier B.V.

Mechanical circulator for elastic waves by using the nonreciprocity of flexible rotating rings

NASA Astrophysics Data System (ADS)

Beli, Danilo; Silva, Priscilla Brandão; Arruda, José Roberto de França

2018-01-01

Circulators have a wide range of applications in wave manipulation. They provide a nonreciprocal response by breaking the time-reversal symmetry. In the mechanical field, nonlinear isolators and ferromagnetic circulators can be used for this objective. However, they require high power and high volumes. Herein, a flexible rotating ring is used to break the time-reversal symmetry as a result of the combined effect of Coriolis acceleration and material damping. Complete asymmetry of oscillating and evanescent components of wavenumbers is achieved. The elastic ring produces a nonreciprocal response that is used to design a three port mechanical circulator. The rotational speed for maximum transmission in one port and isolation in the other one is determined using analytical equations. A spectral element formulation is used to compute the complex dispersion diagrams and the forced response. Waveguides that support longitudinal and flexural waves are investigated. In this case, the ring nonreciprocity is modulated by the waveguide reciprocal response and the transmission coefficients can be affected. The proposed device is compact, nonferromagnetic, and may open new directions for elastic wave manipulation.

An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry

NASA Astrophysics Data System (ADS)

Wintermeyer, Niklas; Winters, Andrew R.; Gassner, Gregor J.; Kopriva, David A.

2017-07-01

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.

The Iron Project

NASA Technical Reports Server (NTRS)

Pradhan, Anil K.

2000-01-01

Recent advances in theoretical atomic physics have enabled large-scale calculation of atomic parameters for a variety of atomic processes with high degree of precision. The development and application of these methods is the aim of the Iron Project. At present the primary focus is on collisional processes for all ions of iron, Fe I - FeXXVI, and other iron-peak elements; new work on radiative processes has also been initiated. Varied applications of the Iron Project work to X-ray astronomy are discussed, and more general applications to other spectral ranges are pointed out. The IP work forms the basis for more specialized projects such as the RmaX Project, and the work on photoionization/recombination, and aims to provide a comprehensive and self-consistent set of accurate collisional and radiative cross sections, and transition probabilities, within the framework of relativistic close coupling formulation using the Breit-Pauli R-Matrix method. An illustrative example is presented of how the IP data may be utilized in the formation of X-ray spectra of the K alpha complex at 6.7 keV from He-like Fe XXV.

Maximum entropy formalism for the analytic continuation of matrix-valued Green's functions

NASA Astrophysics Data System (ADS)

Kraberger, Gernot J.; Triebl, Robert; Zingl, Manuel; Aichhorn, Markus

2017-10-01

We present a generalization of the maximum entropy method to the analytic continuation of matrix-valued Green's functions. To treat off-diagonal elements correctly based on Bayesian probability theory, the entropy term has to be extended for spectral functions that are possibly negative in some frequency ranges. In that way, all matrix elements of the Green's function matrix can be analytically continued; we introduce a computationally cheap element-wise method for this purpose. However, this method cannot ensure important constraints on the mathematical properties of the resulting spectral functions, namely positive semidefiniteness and Hermiticity. To improve on this, we present a full matrix formalism, where all matrix elements are treated simultaneously. We show the capabilities of these methods using insulating and metallic dynamical mean-field theory (DMFT) Green's functions as test cases. Finally, we apply the methods to realistic material calculations for LaTiO3, where off-diagonal matrix elements in the Green's function appear due to the distorted crystal structure.

Formulation of Efficient Finite Element Prediction Models.

DTIC Science & Technology

1980-01-01

vorticity-divergence FEM formulation. This paper will compare these FEM formulations by considering the Vgeostrophic adjustment process with the linearized...by Fourier transforming the terms that are independent of t in (2.12)-(2.14) or (2.19)-(2.21). However, in this paper the final state will be...filtering in a baroclinic primitive equation model. 17 L . , 5. Conclusions The objective of this paper is to determine the response of various finite

Crashworthiness of light aircraft fuselage structures: A numerical and experimental investigation

NASA Technical Reports Server (NTRS)

Nanyaro, A. P.; Tennyson, R. C.; Hansen, J. S.

1984-01-01

The dynamic behavior of aircraft fuselage structures subject to various impact conditions was investigated. An analytical model was developed based on a self-consistent finite element (CFE) formulation utilizing shell, curved beam, and stringer type elements. Equations of motion were formulated and linearized (i.e., for small displacements), although material nonlinearity was retained to treat local plastic deformation. The equations were solved using the implicit Newmark-Beta method with a frontal solver routine. Stiffened aluminum fuselage models were also tested in free flight using the UTIAS pendulum crash test facility. Data were obtained on dynamic strains, g-loads, and transient deformations (using high speed photography in the latter case) during the impact process. Correlations between tests and predicted results are presented, together with computer graphics, based on the CFE model. These results include level and oblique angle impacts as well as the free-flight crash test. Comparisons with a hybrid, lumped mass finite element computer model demonstrate that the CFE formulation provides the test overall agreement with impact test data for comparable computing costs.

Dual boundary element formulation for elastoplastic fracture mechanics

NASA Astrophysics Data System (ADS)

Leitao, V.; Aliabadi, M. H.; Rooke, D. P.

1995-01-01

In this paper the extension of the dual boundary element method (DBEM) to the analysis of elastoplastic fracture mechanics (EPFM) problems is presented. The dual equations of the method are the displacement and the traction boundary integral equations. When the displacement equation is applied on one of the crack surfaces and the traction equation on the other, general mixed-mode crack problems can be solved with a single-region formulation. In order to avoid collocation at crack tips, crack kinks and crack-edge corners, both crack surfaces are discretized with discontinuous quadratic boundary elements. The elasto-plastic behavior is modelled through the use of an approximation for the plastic component of the strain tensor on the region expected to yield. This region is discretized with internal quadratic, quadrilateral and/or triangular cells. This formulation was implemented for two-dimensional domains only, although there is no theoretical or numerical limitation to its application to three-dimensional ones. A center-cracked plate and a slant edge-cracked plate subjected to tensile load are analysed and the results are compared with others available in the literature. J-type integrals are calculated.

Arbitrary order 2D virtual elements for polygonal meshes: part II, inelastic problem

NASA Astrophysics Data System (ADS)

Artioli, E.; Beirão da Veiga, L.; Lovadina, C.; Sacco, E.

2017-10-01

The present paper is the second part of a twofold work, whose first part is reported in Artioli et al. (Comput Mech, 2017. doi: 10.1007/s00466-017-1404-5), concerning a newly developed Virtual element method (VEM) for 2D continuum problems. The first part of the work proposed a study for linear elastic problem. The aim of this part is to explore the features of the VEM formulation when material nonlinearity is considered, showing that the accuracy and easiness of implementation discovered in the analysis inherent to the first part of the work are still retained. Three different nonlinear constitutive laws are considered in the VEM formulation. In particular, the generalized viscoelastic model, the classical Mises plasticity with isotropic/kinematic hardening and a shape memory alloy constitutive law are implemented. The versatility with respect to all the considered nonlinear material constitutive laws is demonstrated through several numerical examples, also remarking that the proposed 2D VEM formulation can be straightforwardly implemented as in a standard nonlinear structural finite element method framework.

Finite element formulation of viscoelastic sandwich beams using fractional derivative operators

NASA Astrophysics Data System (ADS)

Galucio, A. C.; Deü, J.-F.; Ohayon, R.

This paper presents a finite element formulation for transient dynamic analysis of sandwich beams with embedded viscoelastic material using fractional derivative constitutive equations. The sandwich configuration is composed of a viscoelastic core (based on Timoshenko theory) sandwiched between elastic faces (based on Euler-Bernoulli assumptions). The viscoelastic model used to describe the behavior of the core is a four-parameter fractional derivative model. Concerning the parameter identification, a strategy to estimate the fractional order of the time derivative and the relaxation time is outlined. Curve-fitting aspects are focused, showing a good agreement with experimental data. In order to implement the viscoelastic model into the finite element formulation, the Grünwald definition of the fractional operator is employed. To solve the equation of motion, a direct time integration method based on the implicit Newmark scheme is used. One of the particularities of the proposed algorithm lies in the storage of displacement history only, reducing considerably the numerical efforts related to the non-locality of fractional operators. After validations, numerical applications are presented in order to analyze truncation effects (fading memory phenomena) and solution convergence aspects.

Finite element model for MOI applications using A-V formulation

NASA Astrophysics Data System (ADS)

Xuan, L.; Shanker, B.; Udpa, L.; Shih, W.; Fitzpatrick, G.

2001-04-01

Magneto-optic imaging (MOI) is a relatively new sensor application of an extension of bubble memory technology to NDT and produce easy-to-interpret, real time analog images. MOI systems use a magneto-optic (MO) sensor to produce analog images of magnetic flux leakage from surface and subsurface defects. The instrument's capability in detecting the relatively weak magnetic fields associated with subsurface defects depends on the sensitivity of the magneto-optic sensor. The availability of a theoretical model that can simulate the MOI system performance is extremely important for optimization of the MOI sensor and hardware system. A nodal finite element model based on magnetic vector potential formulation has been developed for simulating MOI phenomenon. This model has been used for predicting the magnetic fields in simple test geometry with corrosion dome defects. In the case of test samples with multiple discontinuities, a more robust model using the magnetic vector potential Ā and electrical scalar potential V is required. In this paper, a finite element model based on A-V formulation is developed to model complex circumferential crack under aluminum rivets in dimpled countersink.

New triangular and quadrilateral plate-bending finite elements

NASA Technical Reports Server (NTRS)

Narayanaswami, R.

1974-01-01

A nonconforming plate-bending finite element of triangular shape and associated quadrilateral elements are developed. The transverse displacement is approximated within the element by a quintic polynomial. The formulation takes into account the effects of transverse shear deformation. Results of the static and dynamic analysis of a square plate, with edges simply supported or clamped, are compared with exact solutions. Good accuracy is obtained in all calculations.

On the numerical modeling of sliding beams: A comparison of different approaches

NASA Astrophysics Data System (ADS)

Steinbrecher, Ivo; Humer, Alexander; Vu-Quoc, Loc

2017-11-01

The transient analysis of sliding beams represents a challenging problem of structural mechanics. Typically, the sliding motion superimposed by large flexible deformation requires numerical methods as, e.g., finite elements, to obtain approximate solutions. By means of the classical sliding spaghetti problem, the present paper provides a guideline to the numerical modeling with conventional finite element codes. For this purpose, two approaches, one using solid elements and one using beam elements, respectively, are employed in the analysis, and the characteristics of each approach are addressed. The contact formulation realizing the interaction of the beam with its support demands particular attention in the context of sliding structures. Additionally, the paper employs the sliding-beam formulation as a third approach, which avoids the numerical difficulties caused by the large sliding motion through a suitable coordinate transformation. The present paper briefly outlines the theoretical fundamentals of the respective approaches for the modeling of sliding structures and gives a detailed comparison by means of the sliding spaghetti serving as a representative example. The specific advantages and limitations of the different approaches with regard to accuracy and computational efficiency are discussed in detail. Through the comparison, the sliding-beam formulation, which proves as an effective approach for the modeling, can be validated for the general problem of a sliding structure subjected to large deformation.

Optimization of the sources in local hyperthermia using a combined finite element-genetic algorithm method.

PubMed

Siauve, N; Nicolas, L; Vollaire, C; Marchal, C

2004-12-01

This article describes an optimization process specially designed for local and regional hyperthermia in order to achieve the desired specific absorption rate in the patient. It is based on a genetic algorithm coupled to a finite element formulation. The optimization method is applied to real human organs meshes assembled from computerized tomography scans. A 3D finite element formulation is used to calculate the electromagnetic field in the patient, achieved by radiofrequency or microwave sources. Space discretization is performed using incomplete first order edge elements. The sparse complex symmetric matrix equation is solved using a conjugate gradient solver with potential projection pre-conditionning. The formulation is validated by comparison of calculated specific absorption rate distributions in a phantom to temperature measurements. A genetic algorithm is used to optimize the specific absorption rate distribution to predict the phases and amplitudes of the sources leading to the best focalization. The objective function is defined as the specific absorption rate ratio in the tumour and healthy tissues. Several constraints, regarding the specific absorption rate in tumour and the total power in the patient, may be prescribed. Results obtained with two types of applicators (waveguides and annular phased array) are presented and show the faculties of the developed optimization process.

A general-purpose approach to computer-aided dynamic analysis of a flexible helicopter

NASA Technical Reports Server (NTRS)

Agrawal, Om P.

1988-01-01

A general purpose mathematical formulation is described for dynamic analysis of a helicopter consisting of flexible and/or rigid bodies that undergo large translations and rotations. Rigid body and elastic sets of generalized coordinates are used. The rigid body coordinates define the location and the orientation of a body coordinate frame (global frame) with respect to an inertial frame. The elastic coordinates are introduced using a finite element approach in order to model flexible components. The compatibility conditions between two adjacent elements in a flexible body are imposed using a Boolean matrix, whereas the compatibility conditions between two adjacent bodies are imposed using the Lagrange multiplier approach. Since the form of the constraint equations depends upon the type of kinematic joint and involves only the generalized coordinates of the two participating elements, then a library of constraint elements can be developed to impose the kinematic constraint in an automated fashion. For the body constraints, the Lagrange multipliers yield the reaction forces and torques of the bodies at the joints. The virtual work approach is used to derive the equations of motion, which are a system of differential and algebraic equations that are highly nonlinear. The formulation presented is general and is compared with hard-wired formulations commonly used in helicopter analysis.

Simplified Discontinuous Galerkin Methods for Systems of Conservation Laws with Convex Extension

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

1999-01-01

Simplified forms of the space-time discontinuous Galerkin (DG) and discontinuous Galerkin least-squares (DGLS) finite element method are developed and analyzed. The new formulations exploit simplifying properties of entropy endowed conservation law systems while retaining the favorable energy properties associated with symmetric variable formulations.

Fourier Transforms for Chemists Part III. Fourier Transforms in Data Treatment.

ERIC Educational Resources Information Center

Glasser, L.

1987-01-01

Discusses the factors affecting the behavior of a spectral function. Lists some important properties of Fourier transform (FT) pairs that are helpful when using the FT. Notes that these properties of the mathematical formulation have identical counterparts in the physical behavior of FT systems. (TW)

Mixed formulation for frictionless contact problems

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Kim, Kyun O.

1989-01-01

Simple mixed finite element models and a computational precedure are presented for the solution of frictionless contact problems. The analytical formulation is based on a form of Reissner's large rotation theory of the structure with the effects of transverse shear deformation included. The contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the internal forces (stress resultants), the generalized displacements, and the Lagrange multipliers associated with the contact conditions. The element characteristic array are obtained by using a modified form of the two-field Hellinger-Reissner mixed variational principle. The internal forces and the Lagrange multipliers are allowed to be discontinuous at interelement boundaries. The Newton-Raphson iterative scheme is used for the solution of the nonlinear algebraic equations, and the determination of the contact area and the contact pressures.

An Interface Damage Model for the Simulation of Delamination Under Variable-Mode Ratio in Composite Materials

NASA Technical Reports Server (NTRS)

Turon, Albert; Camanho, Pedro P.; Costa, Josep; Davila, Carlos G.

2004-01-01

A thermodynamically consistent damage model for the simulation of progressive delamination under variable mode ratio is presented. The model is formulated in the context of the Damage Mechanics (DM). The constitutive equations that result from the variation of the free energy with damage are used to model the initiation and propagation of delamination. A new delamination initiation criterion is developed to assure that the formulation can account for changes in the loading mode in a thermodynamically consistent way. Interfacial penetration of two adjacent layers after complete decohesion is prevented by the formulation of the free energy. The model is implemented into the commercial finite element code ABAQUS by means of a user-written decohesion element. Finally, the numerical predictions given by the model are compared with experimental results.

Review of an initial experience with an experimental spectral photon-counting computed tomography system

NASA Astrophysics Data System (ADS)

Si-Mohamed, Salim; Bar-Ness, Daniel; Sigovan, Monica; Cormode, David P.; Coulon, Philippe; Coche, Emmanuel; Vlassenbroek, Alain; Normand, Gabrielle; Boussel, Loic; Douek, Philippe

2017-11-01

Spectral photon-counting CT (SPCCT) is an emerging X-ray imaging technology that extends the scope of available diagnostic imaging tools. The main advantage of photon-counting CT technology is better sampling of the spectral information from the transmitted spectrum in order to benefit from additional physical information being produced during matter interaction, including photo-electric and Compton effects, and the K-edge effect. The K-edge, which is specific for a given element, is the increase in X-ray absorption of the element above the binding energy between its inner electronic shell and the nucleus. Hence, the spectral information contributes to better characterization of tissues and materials of interest, explaining the excitement surrounding this area of X-ray imaging. Other improvements of SPCCT compared with conventional CT, such as higher spatial resolution, lower radiation exposure and lower noise are also expected to provide benefits for diagnostic imaging. In this review, we describe multi-energy CT imaging, from dual energy to photon counting technology, and our initial experience results using a clinical-scale spectral photon counting CT (SPCCT) prototype system in vitro and in vivo. In addition, possible clinical applications are introduced.

Discrete conservation properties for shallow water flows using mixed mimetic spectral elements

NASA Astrophysics Data System (ADS)

Lee, D.; Palha, A.; Gerritsma, M.

2018-03-01

A mixed mimetic spectral element method is applied to solve the rotating shallow water equations. The mixed method uses the recently developed spectral element histopolation functions, which exactly satisfy the fundamental theorem of calculus with respect to the standard Lagrange basis functions in one dimension. These are used to construct tensor product solution spaces which satisfy the generalized Stokes theorem, as well as the annihilation of the gradient operator by the curl and the curl by the divergence. This allows for the exact conservation of first order moments (mass, vorticity), as well as higher moments (energy, potential enstrophy), subject to the truncation error of the time stepping scheme. The continuity equation is solved in the strong form, such that mass conservation holds point wise, while the momentum equation is solved in the weak form such that vorticity is globally conserved. While mass, vorticity and energy conservation hold for any quadrature rule, potential enstrophy conservation is dependent on exact spatial integration. The method possesses a weak form statement of geostrophic balance due to the compatible nature of the solution spaces and arbitrarily high order spatial error convergence.

EIT Imaging Regularization Based on Spectral Graph Wavelets.

PubMed

Gong, Bo; Schullcke, Benjamin; Krueger-Ziolek, Sabine; Vauhkonen, Marko; Wolf, Gerhard; Mueller-Lisse, Ullrich; Moeller, Knut

2017-09-01

The objective of electrical impedance tomographic reconstruction is to identify the distribution of tissue conductivity from electrical boundary conditions. This is an ill-posed inverse problem usually solved under the finite-element method framework. In previous studies, standard sparse regularization was used for difference electrical impedance tomography to achieve a sparse solution. However, regarding elementwise sparsity, standard sparse regularization interferes with the smoothness of conductivity distribution between neighboring elements and is sensitive to noise. As an effect, the reconstructed images are spiky and depict a lack of smoothness. Such unexpected artifacts are not realistic and may lead to misinterpretation in clinical applications. To eliminate such artifacts, we present a novel sparse regularization method that uses spectral graph wavelet transforms. Single-scale or multiscale graph wavelet transforms are employed to introduce local smoothness on different scales into the reconstructed images. The proposed approach relies on viewing finite-element meshes as undirected graphs and applying wavelet transforms derived from spectral graph theory. Reconstruction results from simulations, a phantom experiment, and patient data suggest that our algorithm is more robust to noise and produces more reliable images.

Non-stationary pre-envelope covariances of non-classically damped systems

NASA Astrophysics Data System (ADS)

Muscolino, G.

1991-08-01

A new formulation is given to evaluate the stationary and non-stationary response of linear non-classically damped systems subjected to multi-correlated non-separable Gaussian input processes. This formulation is based on a new and more suitable definition of the impulse response function matrix for such systems. It is shown that, when using this definition, the stochastic response of non-classically damped systems involves the evaluation of quantities similar to those of classically damped ones. Furthermore, considerations about non-stationary cross-covariances, spectral moments and pre-envelope cross-covariances are presented for a monocorrelated input process.

Efficiency trade-offs of steady-state methods using FEM and FDM. [iterative solutions for nonlinear flow equations

NASA Technical Reports Server (NTRS)

Gartling, D. K.; Roache, P. J.

1978-01-01

The efficiency characteristics of finite element and finite difference approximations for the steady-state solution of the Navier-Stokes equations are examined. The finite element method discussed is a standard Galerkin formulation of the incompressible, steady-state Navier-Stokes equations. The finite difference formulation uses simple centered differences that are O(delta x-squared). Operation counts indicate that a rapidly converging Newton-Raphson-Kantorovitch iteration scheme is generally preferable over a Picard method. A split NOS Picard iterative algorithm for the finite difference method was most efficient.

On integrable boundaries in the 2 dimensional O(N) σ-models

NASA Astrophysics Data System (ADS)

Aniceto, Inês; Bajnok, Zoltán; Gombor, Tamás; Kim, Minkyoo; Palla, László

2017-09-01

We make an attempt to map the integrable boundary conditions for 2 dimensional non-linear O(N) σ-models. We do it at various levels: classically, by demanding the existence of infinitely many conserved local charges and also by constructing the double row transfer matrix from the Lax connection, which leads to the spectral curve formulation of the problem; at the quantum level, we describe the solutions of the boundary Yang-Baxter equation and derive the Bethe-Yang equations. We then show how to connect the thermodynamic limit of the boundary Bethe-Yang equations to the spectral curve.

Spectral response of fiber-coupled Fabry-Perot etalons.

PubMed

Ionov, Pavel

2014-03-01

In many remote sensing applications one or multiple Fabry-Perot etalons are used as high-spectral-resolution filter elements. These etalons are often coupled to a receiving telescope with a multimode fiber, leading to subtle effects of the fiber mode order on the overall spectral response of the system. A theoretical model is developed to treat the spectral response of the combined system: fiber, collimator, and etalon. The method is based on a closed-form expression of the diffracted mode in terms of a Hankel transform. In this representation, it is shown how the spectral effect of the fiber and collimator can be separated from the details of the etalon and can be viewed as a mode-dependent spectral broadening and shift.

3D tensor-based blind multispectral image decomposition for tumor demarcation

NASA Astrophysics Data System (ADS)

Kopriva, Ivica; Peršin, Antun

2010-03-01

Blind decomposition of multi-spectral fluorescent image for tumor demarcation is formulated exploiting tensorial structure of the image. First contribution of the paper is identification of the matrix of spectral responses and 3D tensor of spatial distributions of the materials present in the image from Tucker3 or PARAFAC models of 3D image tensor. Second contribution of the paper is clustering based estimation of the number of the materials present in the image as well as matrix of their spectral profiles. 3D tensor of the spatial distributions of the materials is recovered through 3-mode multiplication of the multi-spectral image tensor and inverse of the matrix of spectral profiles. Tensor representation of the multi-spectral image preserves its local spatial structure that is lost, due to vectorization process, when matrix factorization-based decomposition methods (such as non-negative matrix factorization and independent component analysis) are used. Superior performance of the tensor-based image decomposition over matrix factorization-based decompositions is demonstrated on experimental red-green-blue (RGB) image with known ground truth as well as on RGB fluorescent images of the skin tumor (basal cell carcinoma).

Assessment of the Spectral Stability of Libya 4, Libya 1, and Mauritania 2 Sites Using Earth Observing One Hyperion

NASA Technical Reports Server (NTRS)

Choi, Taeyoung; Xiong, Xiaoxiong; Angal, Amit; Chander, Gyanesh; Qu, John J.

2014-01-01

The objective of this paper is to formulate a methodology to assess the spectral stability of the Libya 4, Libya 1, and Mauritania 2 pseudo-invariant calibration sites (PICS) using Earth Observing One (EO-1) Hyperion sensor. All the available Hyperion collections, downloaded from the Earth Explorer website, were utilized for the three PICS. In each site, a reference spectrum is selected at a specific day in the vicinity of the region of interest (ROI) defined by Committee on Earth Observation Satellites (CEOS). A series of ROIs are predefined in the along-track direction with 196 spectral top-of-atmosphere reflectance values in each ROI. Based on the reference ROI spectrum, the spectral stability of these ROIs is evaluated by average deviations (ADs) and spectral angle mapper (SAM) methods in the specific ranges of time and geo-spatial locations. Time and ROI location-dependent SAM and AD results are very stable within +/- 2 deg and +/-1.7% of 1sigma standard deviations. Consequently, the Libya 4, Mauritania 2, and Libya 1 CEOS selected PICS are spectrally stable targets within the time and spatial swath ranges of the Hyperion collections.

Simulation of surface hardening in the deep rolling process by means of an axial symmetric nodal averaged finite element

NASA Astrophysics Data System (ADS)

Morrev, P. G.; Gordon, V. A.

2018-03-01

Surface hardening by deep rolling can be considered as the axial symmetric problem in some special events (namely, when large R and small r radii of the deforming roller meet the requirement R>> r). An axisymmetric nodal averaged stabilized finite element is formulated. The formulation is based on a variational principle with a penalty (stabilizing) item in order to involve large elastic-plastic strain and near to incompressible materials. The deep rolling process for a steel rod is analyzed. Axial residual stress, yield stress, and Odkvist’s parameter are calculated. The residual stress is compared with the data obtained by other authors using a three-dimensional statement of the problem. The results obtained demonstrate essential advantages of the newly developed finite element.

Constitutive Behavior and Finite Element Analysis of FRP Composite and Concrete Members.

PubMed

Ann, Ki Yong; Cho, Chang-Geun

2013-09-10

The present study concerns compressive and flexural constitutive models incorporated into an isoparametric beam finite element scheme for fiber reinforced polymer (FRP) and concrete composites, using their multi-axial constitutive behavior. The constitutive behavior of concrete was treated in triaxial stress states as an orthotropic hypoelasticity-based formulation to determine the confinement effect of concrete from a three-dimensional failure surface in triaxial stress states. The constitutive behavior of the FRP composite was formulated from the two-dimensional classical lamination theory. To predict the flexural behavior of circular cross-section with FRP sheet and concrete composite, a layered discretization of cross-sections was incorporated into nonlinear isoparametric beam finite elements. The predicted constitutive behavior was validated by a comparison to available experimental results in the compressive and flexural beam loading test.

Weak Galerkin method for the Biot’s consolidation model

DOE PAGES

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

2017-08-23

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Weak Galerkin method for the Biot’s consolidation model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

A Poisson nonnegative matrix factorization method with parameter subspace clustering constraint for endmember extraction in hyperspectral imagery

NASA Astrophysics Data System (ADS)

Sun, Weiwei; Ma, Jun; Yang, Gang; Du, Bo; Zhang, Liangpei

2017-06-01

A new Bayesian method named Poisson Nonnegative Matrix Factorization with Parameter Subspace Clustering Constraint (PNMF-PSCC) has been presented to extract endmembers from Hyperspectral Imagery (HSI). First, the method integrates the liner spectral mixture model with the Bayesian framework and it formulates endmember extraction into a Bayesian inference problem. Second, the Parameter Subspace Clustering Constraint (PSCC) is incorporated into the statistical program to consider the clustering of all pixels in the parameter subspace. The PSCC could enlarge differences among ground objects and helps finding endmembers with smaller spectrum divergences. Meanwhile, the PNMF-PSCC method utilizes the Poisson distribution as the prior knowledge of spectral signals to better explain the quantum nature of light in imaging spectrometer. Third, the optimization problem of PNMF-PSCC is formulated into maximizing the joint density via the Maximum A Posterior (MAP) estimator. The program is finally solved by iteratively optimizing two sub-problems via the Alternating Direction Method of Multipliers (ADMM) framework and the FURTHESTSUM initialization scheme. Five state-of-the art methods are implemented to make comparisons with the performance of PNMF-PSCC on both the synthetic and real HSI datasets. Experimental results show that the PNMF-PSCC outperforms all the five methods in Spectral Angle Distance (SAD) and Root-Mean-Square-Error (RMSE), and especially it could identify good endmembers for ground objects with smaller spectrum divergences.

An Integrated Approach for the Large-Scale Simulation of Sedimentary Basins to Study Seismic Wave Amplification

NASA Astrophysics Data System (ADS)

Poursartip, B.

2015-12-01

Seismic hazard assessment to predict the behavior of infrastructures subjected to earthquake relies on ground motion numerical simulation because the analytical solution of seismic waves is limited to only a few simple geometries. Recent advances in numerical methods and computer architectures make it ever more practical to reliably and quickly obtain the near-surface response to seismic events. The key motivation stems from the need to access the performance of sensitive components of the civil infrastructure (nuclear power plants, bridges, lifelines, etc), when subjected to realistic scenarios of seismic events. We discuss an integrated approach that deploys best-practice tools for simulating seismic events in arbitrarily heterogeneous formations, while also accounting for topography. Specifically, we describe an explicit forward wave solver based on a hybrid formulation that couples a single-field formulation for the computational domain with an unsplit mixed-field formulation for Perfectly-Matched-Layers (PMLs and/or M-PMLs) used to limit the computational domain. Due to the material heterogeneity and the contrasting discretization needs it imposes, an adaptive time solver is adopted. We use a Runge-Kutta-Fehlberg time-marching scheme that adjusts optimally the time step such that the local truncation error rests below a predefined tolerance. We use spectral elements for spatial discretization, and the Domain Reduction Method in accordance with double couple method to allow for the efficient prescription of the input seismic motion. Of particular interest to this development is the study of the effects idealized topographic features have on the surface motion when compared against motion results that are based on a flat-surface assumption. We discuss the components of the integrated approach we followed, and report the results of parametric studies in two and three dimensions, for various idealized topographic features, which show motion amplification that depends, as expected, on the relation between the topographic feature's characteristics and the dominant wavelength. Lastly, we report results involving three-dimensional simulations.

Novel residual-based large eddy simulation turbulence models for incompressible magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Sondak, David

The goal of this work was to develop, introduce, and test a promising computational paradigm for the development of turbulence models for incompressible magnetohydrodynamics (MHD). MHD governs the behavior of an electrically conducting fluid in the presence of an external electromagnetic (EM) field. The incompressible MHD model is used in many engineering and scientific disciplines from the development of nuclear fusion as a sustainable energy source to the study of space weather and solar physics. Many interesting MHD systems exhibit the phenomenon of turbulence which remains an elusive problem from all scientific perspectives. This work focuses on the computational perspective and proposes techniques that enable the study of systems involving MHD turbulence. Direct numerical simulation (DNS) is not a feasible approach for studying MHD turbulence. In this work, turbulence models for incompressible MHD were developed from the variational multiscale (VMS) formulation wherein the solution fields were decomposed into resolved and unresolved components. The unresolved components were modeled with a term that is proportional to the residual of the resolved scales. Two additional MHD models were developed based off of the VMS formulation: a residual-based eddy viscosity (RBEV) model and a mixed model that partners the VMS formulation with the RBEV model. These models are endowed with several special numerical and physics features. Included in the numerical features is the internal numerical consistency of each of the models. Physically, the new models are able to capture desirable MHD physics such as the inverse cascade of magnetic energy and the subgrid dynamo effect. The models were tested with a Fourier-spectral numerical method and the finite element method (FEM). The primary test problem was the Taylor-Green vortex. Results comparing the performance of the new models to DNS were obtained. The performance of the new models was compared to classic and cutting-edge dynamic Smagorinsky eddy viscosity (DSEV) models. The new models typically outperform the classical models.

Chemical stability study of vitamins thiamine, riboflavin, pyridoxine and ascorbic acid in parenteral nutrition for neonatal use

PubMed Central

2011-01-01

Background The objective of this work was to study the vitamins B1, B2, B6 and C stability in a pediatric formulation containing high amounts of calcium in the presence of organic phosphate, amino acids, glucose, sodium chloride, magnesium sulfate, pediatric vitamins and trace elements under different conditions using developed and validated analytical methods. Methods The study was carried out during 72 h with formulations packaged in recommended storage temperature (4°C) and 25°C, with and without photoprotection. Results The results showed that the methodologies used for assessing the chemical stability of vitamins B1, B2, B6 and C in the formulation were selective, linear, precise and accurate. The vitamins could be considered stable in the formulation during the three days of study if stored at 4°C. When stored at 25°C vitamin C presented instability after 48 h. Conclusion The pediatric formulation containing high amount of calcium in the presence of organic phosphate, amino acids, glucose, sodium chloride, magnesium sulphate, pediatric vitamins and trace elements packaged in bag-type trilaminate presented a shelf life of the 72 h, when maintained under refrigeration, between 2°C and 8°C. This shelf life was measured considering the vitamins studied. Further studies are needed including all the vitamins present in this formulation. PMID:21569609

Biobased extreme pressure additives: Structure-property considerations

USDA-ARS?s Scientific Manuscript database

Extreme pressure additives are widely used in lubricant formulations for engine oils, hydraulic fluids, gear oils, metalworking fluids, and many others. Extreme pressure additives contain selected elements such as sulfur, phosphorus, and halogens in their structures. These elements, under extreme tr...

Production development of organic nonflammable spacecraft potting encapsulating and conformal coating compounds. Volume 2: Tables

NASA Technical Reports Server (NTRS)

Lieberman, S. L.

1974-01-01

Tables are presented which include: material properties; elemental analysis; silicone RTV formulations; polyester systems and processing; epoxy preblends and processing; urethane materials and processing; epoxy-urethanes elemental analysis; flammability test results, and vacuum effects.

A comparative study of finite element and finite difference methods for Cauchy-Riemann type equations

NASA Technical Reports Server (NTRS)

Fix, G. J.; Rose, M. E.

1983-01-01

A least squares formulation of the system divu = rho, curlu = zeta is surveyed from the viewpoint of both finite element and finite difference methods. Closely related arguments are shown to establish convergence estimates.

Reliability of Next Generation Power Electronics Packaging Under Concurrent Vibration, Thermal and High Power Loads

DTIC Science & Technology

2008-02-01

combined thermal g effect and initial current field. The model is implemented using Abaqus user element subroutine and verified against the experimental...Finite Element Formulation The proposed model is implemented with ABAQUS general purpose finite element program using thermal -displacement analysis...option. ABAQUS and other commercially available finite element codes do not have the capability to solve general electromigration problem directly. Thermal

Raman spectral, elemental, crystallinity, and oxygen-isotope variations in conodont apatite during diagenesis

NASA Astrophysics Data System (ADS)

Zhang, Lei; Cao, Ling; Zhao, Laishi; Algeo, Thomas J.; Chen, Zhong-Qiang; Li, Zhihong; Lv, Zhengyi; Wang, Xiangdong

2017-08-01

Conodont apatite has long been used in paleoenvironmental studies, often with minimal evaluation of the influence of diagenesis on measured elemental and isotopic signals. In this study, we evaluate diagenetic influences on conodonts using an integrated set of analytical techniques. A total of 92 points in 19 coniform conodonts from Ordovician marine units of South China were analyzed by micro-laser Raman spectroscopy (M-LRS), laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS), high-resolution X-ray microdiffraction (HXRD), and secondary ion mass spectrometry (SIMS). Each conodont element was analyzed along its full length, including the albid crown, hyaline crown, and basal body, in either a whole specimen (i.e., reflecting the composition of its outer layer) or a split specimen (i.e., reflecting the composition of its interior). In the conodonts of this study, the outer surfaces consist of hydroxyfluorapatite and the interiors of strontian hydroxyfluorapatite. Ionic substitutions resulted in characteristic Raman spectral shifts in the position (SS1) and width (SS2) of the ν1-PO43- stretching band. Although multiple elements were enriched (Sr2+, Mg2+) and depleted (Fe3+, Mn2+, Ca2+) during diagenesis, geochemical modeling constraints and known Raman spectral patterns suggest that Sr uptake was the dominant influence on diagenetic redshifts of SS1. All study specimens show lower SS2 values than modern bioapatite and synthetic apatite, suggesting that band width decreases with time in ancient bioapatite, possibly through an annealing process that produces larger, more uniform crystal domains. Most specimens consist mainly of amorphous or poorly crystalline apatite, which is inferred to represent the original microstructure of conodonts. In a subset of specimens, some tissues (especially albid crown) exhibit an increased degree of crystallinity developed through aggrading neomorphism. However, no systematic relationship was observed between crystallinity and Raman spectral or elemental parameters. Oxygen isotopes show substantial variation within the conodont study specimens. Albid crown is on average 0.28-0.32‰ more depleted in 18O (equivalent to 1.2-1.4 °C higher temperatures) than hyaline crown and basal body, and the interiors of conodont elements are 1.08 ± 0.37‰ more depleted in 18O (equivalent to 3.0-6.4 °C higher temperatures) relative to their outer layers. Although albid crown is widely regarded as better preserved than other conodont tissue types, its 18O-depleted composition and greater development of secondary crystallinity suggest that, in fact, it may be the most strongly altered tissue type. We conclude that Raman spectral, LA elemental, and HXRD microstructural data can provide useful information about the extent of diagenetic alteration of conodont elements, and that such information should be taken into consideration in using conodont elemental and oxygen-isotope data in paleoenvironmental studies.

Generalized Fourier analyses of the advection-diffusion equation - Part I: one-dimensional domains

NASA Astrophysics Data System (ADS)

Christon, Mark A.; Martinez, Mario J.; Voth, Thomas E.

2004-07-01

This paper presents a detailed multi-methods comparison of the spatial errors associated with finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. The errors are reported in terms of non-dimensional phase and group speed, discrete diffusivity, artificial diffusivity, and grid-induced anisotropy. It is demonstrated that Fourier analysis provides an automatic process for separating the discrete advective operator into its symmetric and skew-symmetric components and characterizing the spectral behaviour of each operator. For each of the numerical methods considered, asymptotic truncation error and resolution estimates are presented for the limiting cases of pure advection and pure diffusion. It is demonstrated that streamline upwind Petrov-Galerkin and its control-volume finite element analogue, the streamline upwind control-volume method, produce both an artificial diffusivity and a concomitant phase speed adjustment in addition to the usual semi-discrete artifacts observed in the phase speed, group speed and diffusivity. The Galerkin finite element method and its streamline upwind derivatives are shown to exhibit super-convergent behaviour in terms of phase and group speed when a consistent mass matrix is used in the formulation. In contrast, the CVFEM method and its streamline upwind derivatives yield strictly second-order behaviour. In Part II of this paper, we consider two-dimensional semi-discretizations of the advection-diffusion equation and also assess the affects of grid-induced anisotropy observed in the non-dimensional phase speed, and the discrete and artificial diffusivities. Although this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common analysis framework. Published in 2004 by John Wiley & Sons, Ltd.

An assessment of exposure to rare earth elements among patients receiving long-term parenteral nutrition.

PubMed

Galusha, Aubrey L; Kruger, Pamela C; Howard, Lyn J; Parsons, Patrick J

2018-05-01

Patients receiving long-term parenteral nutrition (PN) are exposed to potentially toxic elements, which may accumulate in bone. Bone samples collected from seven PN patients (average = 14 years) and eighteen hip/knee samples were analyzed for Al as part of a previous investigation. Yttrium was serendipitously detected in the PN bone samples, leading to the present investigation of rare earth elements (REEs). A method for quantitating fifteen REEs in digested bone was developed based on tandem ICP-MS (ICP-MS/MS) to resolve spectral interferences. The method was validated against nine biological reference materials (RMs) for which assigned values were available for most REEs. Values found in two NIST bone SRMs (1400 Bone Ash and 1486 Bone Meal) compared favorably to those reported elsewhere. Method detection limits ranged from 0.9 ng g -1 (Tm) to 5.8 ng g -1 (Y). Median REE values in the PN patient group were at least fifteen times higher than the "control" group, and exceeded all previously reported data for eleven REEs in human bones. REE content in PN bones normalized to the Earth's upper crust revealed anomalies for Gd in two patients, likely from exposure to Gd-containing contrast agents used in MRI studies. A retrospective review of the medical record for one patient revealed an almost certain case of nephrogenic systemic fibrosis, associated with Gd exposure. Analysis of two current PN formulations showed traces of REEs with relative abundances similar to those found in the PN bones, providing convincing evidence that PN solutions were the primary source of REEs in this population. Copyright © 2018 Elsevier GmbH. All rights reserved.

CELFE: Coupled Eulerian-Lagrangian Finite Element program for high velocity impact. Part 1: Theory and formulation. [hydroelasto-viscoplastic model

NASA Technical Reports Server (NTRS)

Lee, C. H.

1978-01-01

A 3-D finite element program capable of simulating the dynamic behavior in the vicinity of the impact point, together with predicting the dynamic response in the remaining part of the structural component subjected to high velocity impact is discussed. The finite algorithm is formulated in a general moving coordinate system. In the vicinity of the impact point contained by a moving failure front, the relative velocity of the coordinate system will approach the material particle velocity. The dynamic behavior inside the region is described by Eulerian formulation based on a hydroelasto-viscoplastic model. The failure front which can be regarded as the boundary of the impact zone is described by a transition layer. The layer changes the representation from the Eulerian mode to the Lagrangian mode outside the failure front by varying the relative velocity of the coordinate system to zero. The dynamic response in the remaining part of the structure described by the Lagrangian formulation is treated using advanced structural analysis. An interfacing algorithm for coupling CELFE with NASTRAN is constructed to provide computational capabilities for large structures.

Analytical instrumentation infrastructure for combinatorial and high-throughput development of formulated discrete and gradient polymeric sensor materials arrays

NASA Astrophysics Data System (ADS)

Potyrailo, Radislav A.; Hassib, Lamyaa

2005-06-01

Multicomponent polymer-based formulations of optical sensor materials are difficult and time consuming to optimize using conventional approaches. To address these challenges, our long-term goal is to determine relationships between sensor formulation and sensor response parameters using new scientific methodologies. As the first step, we have designed and implemented an automated analytical instrumentation infrastructure for combinatorial and high-throughput development of polymeric sensor materials for optical sensors. Our approach is based on the fabrication and performance screening of discrete and gradient sensor arrays. Simultaneous formation of multiple sensor coatings into discrete 4×6, 6×8, and 8×12 element arrays (3-15μL volume per element) and their screening provides not only a well-recognized acceleration in the screening rate, but also considerably reduces or even eliminates sources of variability, which are randomly affecting sensors response during a conventional one-at-a-time sensor coating evaluation. The application of gradient sensor arrays provides additional capabilities for rapid finding of the optimal formulation parameters.

Adaptive implicit-explicit and parallel element-by-element iteration schemes

NASA Technical Reports Server (NTRS)

Tezduyar, T. E.; Liou, J.; Nguyen, T.; Poole, S.

1989-01-01

Adaptive implicit-explicit (AIE) and grouped element-by-element (GEBE) iteration schemes are presented for the finite element solution of large-scale problems in computational mechanics and physics. The AIE approach is based on the dynamic arrangement of the elements into differently treated groups. The GEBE procedure, which is a way of rewriting the EBE formulation to make its parallel processing potential and implementation more clear, is based on the static arrangement of the elements into groups with no inter-element coupling within each group. Various numerical tests performed demonstrate the savings in the CPU time and memory.

Spectral resolution of SU(3)-invariant solutions of the Yang-Baxter equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alishauskas, S.I.; Kulish, P.P.

1986-11-20

The spectral resolution of invariant R-matrices is computed on the basis of solution of the defining equation. Multiple representations in the Clebsch-Gordon series are considered by means of the classifying operator A: a linear combination of known operators of third and fourth degrees in the group generators. The matrix elements of A in a nonorthonormal basis are found. Explicit expressions are presented for the spectral resolutions for a number of representations.

Spectral resolution of SU(3)-invariant solutions of the Yang-Baxter equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alishavskas, S.I.; Kulish, P.P.

1986-11-01

The spectral resolution of invariant R-matrices is computed on the basis of solution of the defining equation. Multiple representations in the Clebsch-Gordon series are considered by means of the classifying operator A: a linear combination of known operators of third and fourth degrees in the group generators. The matrix elements of A in a nonorthonormal basis are found. Explicit expressions are presented for the spectral resolutions for a number of representations.

A Fiber-Optic System Generating Pulses of High Spectral Density

NASA Astrophysics Data System (ADS)

Abramov, A. S.; Zolotovskii, I. O.; Korobko, D. A.; Fotiadi, A. A.

2018-03-01

A cascade fiber-optic system that generates pulses of high spectral density by using the effect of nonlinear spectral compression is proposed. It is demonstrated that the shape of the pulse envelope substantially influences the degree of compression of its spectrum. In so doing, maximum compression is achieved for parabolic pulses. The cascade system includes an optical fiber exhibiting normal dispersion that decreases along the fiber length, thereby ensuring that the pulse envelope evolves toward a parabolic shape, along with diffraction gratings and a fiber spectral compressor. Based on computer simulation, we determined parameters of cascade elements leading to maximum spectral density of radiation originating from a subpicosecond laser pulse of medium energy.

A Streamline-Upwind Petrov-Galerkin Finite Element Scheme for Non-Ionized Hypersonic Flows in Thermochemical Nonequilibrium

NASA Technical Reports Server (NTRS)

Kirk, Benjamin S.; Bova, Stephen W.; Bond, Ryan B.

2011-01-01

Presentation topics include background and motivation; physical modeling including governing equations and thermochemistry; finite element formulation; results of inviscid thermal nonequilibrium chemically reacting flow and viscous thermal equilibrium chemical reacting flow; and near-term effort.

Modeling of resistive sheets in finite element solutions

NASA Technical Reports Server (NTRS)

Jin, J. M.; Volakis, John L.; Yu, C. L.; Woo, A. C.

1992-01-01

A formulation is presented for modeling a resistive card in the context of the finite element method. The appropriate variational function is derived and for validation purposes, results are presented for the scattering by a metal-backed cavity loaded with a resistive card.

Modeling of resistive sheets in finite element solutions

NASA Technical Reports Server (NTRS)

Jin, J. M.; Volakis, John L.; Yu, C. L.; Woo, Alex C.

1992-01-01

A formulation is presented for modeling a resistive card in the context of the finite element method. The appropriate variational function is derived and for variational purposes results are presented for the scattering by a metal-backed cavity loaded with a resistive card.

Battery-operated, argon-hydrogen microplasma on hybrid, postage stamp-sized plastic-quartz chips for elemental analysis of liquid microsamples using a portable optical emission spectrometer.

PubMed

Weagant, Scott; Chen, Vivian; Karanassios, Vassili

2011-11-01

A battery-operated, atmospheric pressure, self-igniting, planar geometry Ar-H(2) microplasma for elemental analysis of liquid microsamples is described. The inexpensive microplasma device (MPD) fabricated for this work was a hybrid plastic-quartz structure that was formed on chips with an area (roughly) equal to that of a small-sized postage stamp (MPD footprint, 12.5-mm width by 38-mm length). Plastic substrates were chosen due to their low cost, for rapid prototyping purposes, and for a speedy microplasma device evaluation. To enhance portability, the microplasma was operated from an 18-V rechargeable battery. To facilitate portability even further, it was demonstrated that the battery can be recharged by a portable solar panel. The battery-supplied dc voltage was converted to a high-voltage ac. The ~750-μm (diameter) and 12-mm (long) Ar-H(2) (3% H(2)) microplasma was formed by applying the high-voltage ac between two needle electrodes. Spectral interference from the electrode materials or from the plastic substrate was not observed. Operating conditions were found to be key to igniting and sustaining a microplasma that was simply "warm" to the touch (thus alleviating the need for cooling or other thermal management) and that had a stable background emission. A small-sized (900 μL internal volume) electrothermal vaporization system (40-W max power) was used for microsample introduction. Microplasma background emission in the spectral region between 200 and 850 nm obtained using a portable fiber-optic spectrometer is reported and the effect of the operating conditions is described. Analyte emission from microliter volumes of dilute single-element standard solutions of Cd, Cu, K, Li, Mg, Mn, Na, Pb, and Zn is documented. The majority of spectral lines observed for the elements tested were from neutral atoms. The relative lack of emission from ion lines simplified the spectra, thus facilitating the use of a portable spectrometer. Despite the relative spectral simplicity, some spectral interference effects were noted when running a multi-element solution. An example of how interference in the spectral domain can be resolved in the time domain using selective thermal vaporization is provided. Analytical utility and performance characteristics are reported; for example, K concentrations in diluted (~30 times) bottled water were determined to be 4.1 ± 1.0 μg/mL (4 μg/mL was the stated concentration), precision was about 25%, and the estimated detection limits were in the picogram range (or in nanograms per milliliter in relative units).

Mining the HST "Advanced Spectral Library (ASTRAL) - Hot Stars": The High Definition UV Spectrum of the Ap Star HR 465

NASA Astrophysics Data System (ADS)

Carpenter, Kenneth G.; Ayres, T. R.; Nielsen, K. E.; Kober, G. V.; Wahlgren, G. M.; Adelman, S. J.; Cowley, C. R.

2014-01-01

The "Advanced Spectral Library (ASTRAL) Project: Hot Stars" is a Hubble Space Telescope (HST) Cycle 21 Treasury Program (GO-13346: Ayres PI). It is designed to collect a definitive set of representative, high-resolution ( 30,000-100,000), high signal/noise (S/N>100), and full UV coverage 1200 - 3000 A) spectra of 21 early-type stars, utilizing the high-performance Space Telescope Imaging Spectrograph (STIS). The targets span the range of spectral types between early-O and early-A, including both main sequence and evolved stars, fast and slow rotators, as well as chemically peculiar (CP) and magnetic objects. These extremely high-quality STIS UV echelle spectra will be available from the HST archive and, in post-processed and merged form, at http://casa.colorado.edu ayres/ASTRAL/. The UV "atlases" produced by this program will enable investigations of a broad range of problems -- stellar, interstellar, and beyond -- for many years to come. We offer a first look at one of the earliest datasets to come out of this observing program, a "high definition" UV spectrum of the Ap star HR 465, which was chosen as a prototypical example of an A-type magnetic CP star. HR 465 has a global magnetic field of ~2200 Gauss. Earlier analyses of IUE spectra show strong iron-peak element lines, along with heavy elements such as Ga and Pt, while being deficient in the abundance of some ions of low atomic number, such as carbon. We demonstrate the high quality of the ASTRAL data and present the identification of spectral lines for a number of elements. By comparison of the observed spectra with calculated spectra, we also provide estimates of element abundances, emphasizing heavy elements, and place these measurements in the context of earlier results for this and other Ap stars.

Influence of water vapour and permanent gases on the atmospheric optical depths and transmittance

NASA Astrophysics Data System (ADS)

Badescu, V.

1991-05-01

The influence of the atmospheric state on the extinction of direct solar radiation has been studied by using a four layer atmospheric model. Simple analytical formulae are established for the spectral optical depths of permanent gases and water vapour. These formulae use the ground level values of air pressure, temperature and relative huniidity. An additional parameter, related to the vertical distribution of the hunmidity content, is used for a better estimation of the water vapour optical depth. Good agreement between theory and measurements is found. The paper shows the dependence of the atmospheric spectral transmittance on the above mentioned parameters. L'influence de l'état atmosphérique sur l'extinction de la radiation solaire directe a été étudiée à l'aide d'un modèle atmosphérique développé antérieurement par l'auteur. Des formules simples ont été établies pour l'épaisseur optique spectrale des gaz et de la vapeur d'eau. Ces formules utilisent les valeurs de la pression atmosphérique, de la température et de l'humidité relative, mesurées au niveau du sol. Un paramètre supplémentaire, lié à la distribution verticale du contenu d'humidité, est utilisé pour calculer l'épaisseur optique due à la vapeur d'eau. La théorie est en bon accord avec les résultats des mesures. Le travail montre la dépendance de la transmittance atmosphérique spectrale en fonction des paramètres spécifiés ci-dessus.

Finite element modeling of electromagnetic fields and waves using NASTRAN

NASA Technical Reports Server (NTRS)

Moyer, E. Thomas, Jr.; Schroeder, Erwin

1989-01-01

The various formulations of Maxwell's equations are reviewed with emphasis on those formulations which most readily form analogies with Navier's equations. Analogies involving scalar and vector potentials and electric and magnetic field components are presented. Formulations allowing for media with dielectric and conducting properties are emphasized. It is demonstrated that many problems in electromagnetism can be solved using the NASTRAN finite element code. Several fundamental problems involving time harmonic solutions of Maxwell's equations with known analytic solutions are solved using NASTRAN to demonstrate convergence and mesh requirements. Mesh requirements are studied as a function of frequency, conductivity, and dielectric properties. Applications in both low frequency and high frequency are highlighted. The low frequency problems demonstrate the ability to solve problems involving media inhomogeneity and unbounded domains. The high frequency applications demonstrate the ability to handle problems with large boundary to wavelength ratios.

A rigorous approach to the formulation of extended Born-Oppenheimer equation for a three-state system

NASA Astrophysics Data System (ADS)

Sarkar, Biplab; Adhikari, Satrajit

If a coupled three-state electronic manifold forms a sub-Hilbert space, it is possible to express the non-adiabatic coupling (NAC) elements in terms of adiabatic-diabatic transformation (ADT) angles. Consequently, we demonstrate: (a) Those explicit forms of the NAC terms satisfy the Curl conditions with non-zero Divergences; (b) The formulation of extended Born-Oppenheimer (EBO) equation for any three-state BO system is possible only when there exists coordinate independent ratio of the gradients for each pair of ADT angles leading to zero Curls at and around the conical intersection(s). With these analytic advancements, we formulate a rigorous EBO equation and explore its validity as well as necessity with respect to the approximate one (Sarkar and Adhikari, J Chem Phys 2006, 124, 074101) by performing numerical calculations on two different models constructed with different chosen forms of the NAC elements.

Development of an orthotropic hole element

NASA Technical Reports Server (NTRS)

Smith, C. V.; Markham, J. W.; Kelley, J. W.; Kathiresan, K.

1981-01-01

A finite element was developed which adequately represents the state of stress in the region around a circular hole in orthotropic material experiencing reasonably general loading. This was achieved with a complementary virtual work formulation of the stiffness and stress matrices for a square element with center circular hole. The assumed stress state provides zero shearing stress on the hole boundary, so the element is suitable for problems involving load transfer without friction. The element has been implemented in the NASTRAN computer program, and sample problem results are presented.

Novel approaches to estimating the turbulent kinetic energy dissipation rate from low- and moderate-resolution velocity fluctuation time series

NASA Astrophysics Data System (ADS)

Wacławczyk, Marta; Ma, Yong-Feng; Kopeć, Jacek M.; Malinowski, Szymon P.

2017-11-01

In this paper we propose two approaches to estimating the turbulent kinetic energy (TKE) dissipation rate, based on the zero-crossing method by Sreenivasan et al. (1983). The original formulation requires a fine resolution of the measured signal, down to the smallest dissipative scales. However, due to finite sampling frequency, as well as measurement errors, velocity time series obtained from airborne experiments are characterized by the presence of effective spectral cutoffs. In contrast to the original formulation the new approaches are suitable for use with signals originating from airborne experiments. The suitability of the new approaches is tested using measurement data obtained during the Physics of Stratocumulus Top (POST) airborne research campaign as well as synthetic turbulence data. They appear useful and complementary to existing methods. We show the number-of-crossings-based approaches respond differently to errors due to finite sampling and finite averaging than the classical power spectral method. Hence, their application for the case of short signals and small sampling frequencies is particularly interesting, as it can increase the robustness of turbulent kinetic energy dissipation rate retrieval.

Spatial and spectral interpolation of ground-motion intensity measure observations

USGS Publications Warehouse

Worden, Charles; Thompson, Eric M.; Baker, Jack W.; Bradley, Brendon A.; Luco, Nicolas; Wilson, David

2018-01-01

Following a significant earthquake, ground‐motion observations are available for a limited set of locations and intensity measures (IMs). Typically, however, it is desirable to know the ground motions for additional IMs and at locations where observations are unavailable. Various interpolation methods are available, but because IMs or their logarithms are normally distributed, spatially correlated, and correlated with each other at a given location, it is possible to apply the conditional multivariate normal (MVN) distribution to the problem of estimating unobserved IMs. In this article, we review the MVN and its application to general estimation problems, and then apply the MVN to the specific problem of ground‐motion IM interpolation. In particular, we present (1) a formulation of the MVN for the simultaneous interpolation of IMs across space and IM type (most commonly, spectral response at different oscillator periods) and (2) the inclusion of uncertain observation data in the MVN formulation. These techniques, in combination with modern empirical ground‐motion models and correlation functions, provide a flexible framework for estimating a variety of IMs at arbitrary locations.

Matrix basis for plane and modal waves in a Timoshenko beam.

PubMed

Claeyssen, Julio Cesar Ruiz; Tolfo, Daniela de Rosso; Tonetto, Leticia

2016-11-01

Plane waves and modal waves of the Timoshenko beam model are characterized in closed form by introducing robust matrix basis that behave according to the nature of frequency and wave or modal numbers. These new characterizations are given in terms of a finite number of coupling matrices and closed form generating scalar functions. Through Liouville's technique, these latter are well behaved at critical or static situations. Eigenanalysis is formulated for exponential and modal waves. Modal waves are superposition of four plane waves, but there are plane waves that cannot be modal waves. Reflected and transmitted waves at an interface point are formulated in matrix terms, regardless of having a conservative or a dissipative situation. The matrix representation of modal waves is used in a crack problem for determining the reflected and transmitted matrices. Their euclidean norms are seen to be dominated by certain components at low and high frequencies. The matrix basis technique is also used with a non-local Timoshenko model and with the wave interaction with a boundary. The matrix basis allows to characterize reflected and transmitted waves in spectral and non-spectral form.

Comparison and Tensorial Formulation of Inelastic Constitutive Models of Salt Rock Behaviour and Efficient Numerical Implementatio

NASA Astrophysics Data System (ADS)

Nagel, T.; Böttcher, N.; Görke, U. J.; Kolditz, O.

2014-12-01

The design process of geotechnical installations includes the application of numerical simulation tools for safety assessment, dimensioning and long term effectiveness estimations. Underground salt caverns can be used for the storage of natural gas, hydrogen, oil, waste or compressed air. For their design one has to take into account fluctuating internal pressures due to different levels of filling, the stresses imposed by the surrounding rock mass, irregular geometries and possibly heterogeneous material properties [3] in order to estimate long term cavern convergence as well as locally critical wall stresses. Constitutive models applied to rock salt are usually viscoplastic in nature and most often based on a Burgers-type rheological model extended by non-linear viscosity functions and/or plastic friction elements. Besides plastic dilatation, healing and damage are sometimes accounted for as well [2]. The scales of the geotechnical system to be simulated and the laboratory tests from which material parameters are determined are vastly different. The most common material testing modalities to determine material parameters in geoengineering are the uniaxial and the triaxial compression tests. Some constitutive formulations in widespread use are formulated based on equivalent rather than tensorial quantities valid under these specific test conditions and are subsequently applied to heterogeneous underground systems and complex 3D load cases. We show here that this procedure is inappropriate and can lead to erroneous results. We further propose alternative formulations of the constitutive models in question that restore their validity under arbitrary loading conditions. For an efficient numerical simulation, the discussed constitutive models are integrated locally with a Newton-Raphson algorithm that directly provides the algorithmically consistent tangent matrix for the global Newton iteration of the displacement based finite element formulation. Finally, the finite element implementations of the proposed constitutive formulations are employed to simulate an underground salt cavern used for compressed air energy storage with OpenGeoSys [1]. Transient convergence and stress fields are evaluated for typical fluctuating operation pressure regimes.

A Hybrid Numerical Analysis Method for Structural Health Monitoring

NASA Technical Reports Server (NTRS)

Forth, Scott C.; Staroselsky, Alexander

2001-01-01

A new hybrid surface-integral-finite-element numerical scheme has been developed to model a three-dimensional crack propagating through a thin, multi-layered coating. The finite element method was used to model the physical state of the coating (far field), and the surface integral method was used to model the fatigue crack growth. The two formulations are coupled through the need to satisfy boundary conditions on the crack surface and the external boundary. The coupling is sufficiently weak that the surface integral mesh of the crack surface and the finite element mesh of the uncracked volume can be set up independently. Thus when modeling crack growth, the finite element mesh can remain fixed for the duration of the simulation as the crack mesh is advanced. This method was implemented to evaluate the feasibility of fabricating a structural health monitoring system for real-time detection of surface cracks propagating in engine components. In this work, the authors formulate the hybrid surface-integral-finite-element method and discuss the mechanical issues of implementing a structural health monitoring system in an aircraft engine environment.

Coupled Structural, Thermal, Phase-change and Electromagnetic Analysis for Superconductors, Volume 2

NASA Technical Reports Server (NTRS)

Felippa, C. A.; Farhat, C.; Park, K. C.; Militello, C.; Schuler, J. J.

1996-01-01

Described are the theoretical development and computer implementation of reliable and efficient methods for the analysis of coupled mechanical problems that involve the interaction of mechanical, thermal, phase-change and electromag subproblems. The focus application has been the modeling of superconductivity and associated quantum-state phase change phenomena. In support of this objective the work has addressed the following issues: (1) development of variational principles for finite elements, (2) finite element modeling of the electromagnetic problem, (3) coupling of thermel and mechanical effects, and (4) computer implementation and solution of the superconductivity transition problem. The main accomplishments have been: (1) the development of the theory of parametrized and gauged variational principles, (2) the application of those principled to the construction of electromagnetic, thermal and mechanical finite elements, and (3) the coupling of electromagnetic finite elements with thermal and superconducting effects, and (4) the first detailed finite element simulations of bulk superconductors, in particular the Meissner effect and the nature of the normal conducting boundary layer. The theoretical development is described in two volumes. Volume 1 describes mostly formulation specific problems. Volume 2 describes generalization of those formulations.

Approximate Solution Methods for Spectral Radiative Transfer in High Refractive Index Layers

NASA Technical Reports Server (NTRS)

Siegel, R.; Spuckler, C. M.

1994-01-01

Some ceramic materials for high temperature applications are partially transparent for radiative transfer. The refractive indices of these materials can be substantially greater than one which influences internal radiative emission and reflections. Heat transfer behavior of single and laminated layers has been obtained in the literature by numerical solutions of the radiative transfer equations coupled with heat conduction and heating at the boundaries by convection and radiation. Two-flux and diffusion methods are investigated here to obtain approximate solutions using a simpler formulation than required for exact numerical solutions. Isotropic scattering is included. The two-flux method for a single layer yields excellent results for gray and two band spectral calculations. The diffusion method yields a good approximation for spectral behavior in laminated multiple layers if the overall optical thickness is larger than about ten. A hybrid spectral model is developed using the two-flux method in the optically thin bands, and radiative diffusion in bands that are optically thick.

An efficient implementation of a high-order filter for a cubed-sphere spectral element model

NASA Astrophysics Data System (ADS)

Kang, Hyun-Gyu; Cheong, Hyeong-Bin

2017-03-01

A parallel-scalable, isotropic, scale-selective spatial filter was developed for the cubed-sphere spectral element model on the sphere. The filter equation is a high-order elliptic (Helmholtz) equation based on the spherical Laplacian operator, which is transformed into cubed-sphere local coordinates. The Laplacian operator is discretized on the computational domain, i.e., on each cell, by the spectral element method with Gauss-Lobatto Lagrange interpolating polynomials (GLLIPs) as the orthogonal basis functions. On the global domain, the discrete filter equation yielded a linear system represented by a highly sparse matrix. The density of this matrix increases quadratically (linearly) with the order of GLLIP (order of the filter), and the linear system is solved in only O (Ng) operations, where Ng is the total number of grid points. The solution, obtained by a row reduction method, demonstrated the typical accuracy and convergence rate of the cubed-sphere spectral element method. To achieve computational efficiency on parallel computers, the linear system was treated by an inverse matrix method (a sparse matrix-vector multiplication). The density of the inverse matrix was lowered to only a few times of the original sparse matrix without degrading the accuracy of the solution. For better computational efficiency, a local-domain high-order filter was introduced: The filter equation is applied to multiple cells, and then the central cell was only used to reconstruct the filtered field. The parallel efficiency of applying the inverse matrix method to the global- and local-domain filter was evaluated by the scalability on a distributed-memory parallel computer. The scale-selective performance of the filter was demonstrated on Earth topography. The usefulness of the filter as a hyper-viscosity for the vorticity equation was also demonstrated.

Numerical Analysis of Solids at Failure

DTIC Science & Technology

2011-08-20

failure analyses include the formulation of invariant finite elements for thin Kirchhoff rods, and preliminary initial studies of growth in...analysis of the failure of other structural/mechanical systems, including the finite element modeling of thin Kirchhoff rods and the constitutive...algorithm based on the connectivity graph of the underlying finite element mesh. In this setting, the discontinuities are defined by fronts propagating

Correlation Functions Aid Analyses Of Spectra

NASA Technical Reports Server (NTRS)

Beer, Reinhard; Norton, Robert H., Jr.

1989-01-01

New uses found for correlation functions in analyses of spectra. In approach combining elements of both pattern-recognition and traditional spectral-analysis techniques, spectral lines identified in data appear useless at first glance because they are dominated by noise. New approach particularly useful in measurement of concentrations of rare species of molecules in atmosphere.

Compatibility Condition in Theory of Solid Mechanics (Elasticity, Structures, and Design Optimization)

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Pai, Shantaram S.; Hopkins, Dale A.

2007-01-01

The strain formulation in elasticity and the compatibility condition in structural mechanics have neither been understood nor have they been utilized. This shortcoming prevented the formulation of a direct method to calculate stress. We have researched and understood the compatibility condition for linear problems in elasticity and in finite element analysis. This has lead to the completion of the method of force with stress (or stress resultant) as the primary unknown. The method in elasticity is referred to as the completed Beltrami-Michell formulation (CBMF), and it is the integrated force method (IFM) in structures. The dual integrated force method (IFMD) with displacement as the primary unknown has been formulated. IFM and IFMD produce identical responses. The variational derivation of the CBMF yielded the new boundary compatibility conditions. The CBMF can be used to solve stress, displacement, and mixed boundary value problems. The IFM in structures produced high-fidelity response even with a modest finite element model. The IFM has influenced structural design considerably. A fully utilized design method for strength and stiffness limitation has been developed. The singularity condition in optimization has been identified. The CBMF and IFM tensorial approaches are robust formulations because of simultaneous emphasis on the equilibrium equation and the compatibility condition.

Adaptive mesh refinement for time-domain electromagnetics using vector finite elements :a feasibility study.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Turner, C. David; Kotulski, Joseph Daniel; Pasik, Michael Francis

This report investigates the feasibility of applying Adaptive Mesh Refinement (AMR) techniques to a vector finite element formulation for the wave equation in three dimensions. Possible error estimators are considered first. Next, approaches for refining tetrahedral elements are reviewed. AMR capabilities within the Nevada framework are then evaluated. We summarize our conclusions on the feasibility of AMR for time-domain vector finite elements and identify a path forward.

Contribution of LANDSAT-4 thematic mapper data to geologic exploration

NASA Technical Reports Server (NTRS)

Everett, J. R.; Dykstra, J. D.; Sheffield, C. A.

1983-01-01

The increased number of carefully selected narrow spectral bands and the increased spatial resolution of thematic mapper data over previously available satellite data contribute greatly to geologic exploration, both by providing spectral information that permits lithologic differentiation and recognition of alteration and spatial information that reveals structure. As vegetation and soil cover increase, the value of spectral components of TM data decreases relative to the value of the spatial component of the data. However, even in vegetated areas, the greater spectral breadth and discrimination of TM data permits improved recognition and mapping of spatial elements of the terrain. As our understanding of the spectral manifestations of the responses of soils and vegetation to unusual chemical environments increases, the value of spectral components of TM data to exploration will greatly improve in covered areas.

A Galleria Boundary Element Method for two-dimensional nonlinear magnetostatics

NASA Astrophysics Data System (ADS)

Brovont, Aaron D.

The Boundary Element Method (BEM) is a numerical technique for solving partial differential equations that is used broadly among the engineering disciplines. The main advantage of this method is that one needs only to mesh the boundary of a solution domain. A key drawback is the myriad of integrals that must be evaluated to populate the full system matrix. To this day these integrals have been evaluated using numerical quadrature. In this research, a Galerkin formulation of the BEM is derived and implemented to solve two-dimensional magnetostatic problems with a focus on accurate, rapid computation. To this end, exact, closed-form solutions have been derived for all the integrals comprising the system matrix as well as those required to compute fields in post-processing; the need for numerical integration has been eliminated. It is shown that calculation of the system matrix elements using analytical solutions is 15-20 times faster than with numerical integration of similar accuracy. Furthermore, through the example analysis of a c-core inductor, it is demonstrated that the present BEM formulation is a competitive alternative to the Finite Element Method (FEM) for linear magnetostatic analysis. Finally, the BEM formulation is extended to analyze nonlinear magnetostatic problems via the Dual Reciprocity Method (DRBEM). It is shown that a coarse, meshless analysis using the DRBEM is able to achieve RMS error of 3-6% compared to a commercial FEM package in lightly saturated conditions.

Major and trace element concentrations in samples from 72275 and 72255. [chemical composition of lunar rocks

NASA Technical Reports Server (NTRS)

Haskin, L. A.; Blanchard, D. P.; Korotev, R.; Jacobs, J. W.; Brannon, J. A.; Herrmann, A. G.

1974-01-01

Analytical data have been obtained for Co, Sc, Hf, Zn, Cr, Ga, Rb, Cs, Ni, major elements, and rare earth elements in eight samples from boulder 1. The data for trace elements were obtained by radiochemical neutron activation analysis. Major elements, except Na and Mn, were obtained by atomic absorption spectral photometry. Values for Na and Mn were obtained by neutron activation analysis of the same powder that was later dissolved to provide the atomic absorption analyses.

Anti-Hermitian photodetector facilitating efficient subwavelength photon sorting.

PubMed

Kim, Soo Jin; Kang, Ju-Hyung; Mutlu, Mehmet; Park, Joonsuk; Park, Woosung; Goodson, Kenneth E; Sinclair, Robert; Fan, Shanhui; Kik, Pieter G; Brongersma, Mark L

2018-01-22

The ability to split an incident light beam into separate wavelength bands is central to a diverse set of optical applications, including imaging, biosensing, communication, photocatalysis, and photovoltaics. Entirely new opportunities are currently emerging with the recently demonstrated possibility to spectrally split light at a subwavelength scale with optical antennas. Unfortunately, such small structures offer limited spectral control and are hard to exploit in optoelectronic devices. Here, we overcome both challenges and demonstrate how within a single-layer metafilm one can laterally sort photons of different wavelengths below the free-space diffraction limit and extract a useful photocurrent. This chipscale demonstration of anti-Hermitian coupling between resonant photodetector elements also facilitates near-unity photon-sorting efficiencies, near-unity absorption, and a narrow spectral response (∼ 30 nm) for the different wavelength channels. This work opens up entirely new design paradigms for image sensors and energy harvesting systems in which the active elements both sort and detect photons.

Information-Efficient Spectral Imaging Sensor With Tdi

DOEpatents

Rienstra, Jeffrey L.; Gentry, Stephen M.; Sweatt, William C.

2004-01-13

A programmable optical filter for use in multispectral and hyperspectral imaging employing variable gain time delay and integrate arrays. A telescope focuses an image of a scene onto at least one TDI array that is covered by a multispectral filter that passes separate bandwidths of light onto the rows in the TDI array. The variable gain feature of the TDI array allows individual rows of pixels to be attenuated individually. The attenuations are functions of the magnitudes of the positive and negative components of a spectral basis vector. The spectral basis vector is constructed so that its positive elements emphasize the presence of a target and its negative elements emphasize the presence of the constituents of the background of the imaged scene. This system provides for a very efficient determination of the presence of the target, as opposed to the very data intensive data manipulations that are required in conventional hyperspectral imaging systems.

[Study on physical deviation factors on laser induced breakdown spectroscopy measurement].

PubMed

Wan, Xiong; Wang, Peng; Wang, Qi; Zhang, Qing; Zhang, Zhi-Min; Zhang, Hua-Ming

2013-10-01

In order to eliminate the deviation between the measured LIBS spectral line and the standard LIBS spectral line, and improve the accuracy of elements measurement, a research of physical deviation factors in laser induced breakdown spectroscopy technology was proposed. Under the same experimental conditions, the relationship of ablated hole effect and spectral wavelength was tested, the Stark broadening data of Mg plasma laser induced breakdown spectroscopy with sampling time-delay from 1.00 to 3.00 micros was also studied, thus the physical deviation influences such as ablated hole effect and Stark broadening could be obtained while collecting the spectrum. The results and the method of the research and analysis can also be applied to other laser induced breakdown spectroscopy experiment system, which is of great significance to improve the accuracy of LIBS elements measuring and is also important to the research on the optimum sampling time-delay of LIBS.

[Spectral characteristics of decomposition of incorporated straw in compound polluted arid loess].

PubMed

Fan, Chun-Hui; Zhang, Ying-Chao; Xu, Ji-Ting; Wang, Jia-Hong

2014-04-01

The original loess from western China was used as soil sample, the spectral methods of scanning electron microscope-energy dispersive X-ray spectroscopy (SEM-EDS), elemental analysis, Fourier transform infrared spectroscopy (FT-IR) and 13C nuclear magnetic resonance (13C NMR) were used to investigate the characteristics of decomposed straw and formed humic acids in compound polluted arid loess. The SEM micrographs show the variation from dense to decomposed surface, and finally to damaged structure, and the EDS data reveal the phenomenon of element transfer. The newly-formed humic acids are of low aromaticity, helpful for increasing the activity of organic matters in loess. The FTIR spectra in the whole process are similar, indicating the complexity of transformation dynamics of humic acids. The molecular structure of humic acids becomes simpler, shown from 13C NMR spectra. The spectral methods are useful for humic acids identification in loess region in straw incorporation process.

CURVILINEAR FINITE ELEMENT MODEL FOR SIMULATING TWO-WELL TRACER TESTS AND TRANSPORT IN STRATIFIED AQUIFERS

EPA Science Inventory

The problem of solute transport in steady nonuniform flow created by a recharging and discharging well pair is investigated. Numerical difficulties encountered with the standard Galerkin formulations in Cartesian coordinates are illustrated. An improved finite element solution st...

Development of an integrated BEM approach for hot fluid structure interaction

NASA Technical Reports Server (NTRS)

Dargush, Gary F.; Banerjee, Prasanta K.; Dunn, Michael G.

1988-01-01

Significant progress was made toward the goal of developing a general purpose boundary element method for hot fluid-structure interaction. For the solid phase, a boundary-only formulation was developed and implemented for uncoupled transient thermoelasticity in two dimensions. The elimination of volume discretization not only drastically reduces required modeling effort, but also permits unconstrained variation of the through-the-thickness temperature distribution. Meanwhile, for the fluids, fundamental solutions were derived for transient incompressible and compressible flow in the absence of the convective terms. Boundary element formulations were developed and described. For the incompressible case, the necessary kernal functions, under transient and steady-state conditions, were derived and fully implemented into a general purpose, multi-region boundary element code. Several examples were examined to study the suitability and convergence characteristics of the various algorithms.

Constitutive Behavior and Finite Element Analysis of FRP Composite and Concrete Members

PubMed Central

Ann, Ki Yong; Cho, Chang-Geun

2013-01-01

The present study concerns compressive and flexural constitutive models incorporated into an isoparametric beam finite element scheme for fiber reinforced polymer (FRP) and concrete composites, using their multi-axial constitutive behavior. The constitutive behavior of concrete was treated in triaxial stress states as an orthotropic hypoelasticity-based formulation to determine the confinement effect of concrete from a three-dimensional failure surface in triaxial stress states. The constitutive behavior of the FRP composite was formulated from the two-dimensional classical lamination theory. To predict the flexural behavior of circular cross-section with FRP sheet and concrete composite, a layered discretization of cross-sections was incorporated into nonlinear isoparametric beam finite elements. The predicted constitutive behavior was validated by a comparison to available experimental results in the compressive and flexural beam loading test. PMID:28788312

Analysis of wave motion in one-dimensional structures through fast-Fourier-transform-based wavelet finite element method

NASA Astrophysics Data System (ADS)

Shen, Wei; Li, Dongsheng; Zhang, Shuaifang; Ou, Jinping

2017-07-01

This paper presents a hybrid method that combines the B-spline wavelet on the interval (BSWI) finite element method and spectral analysis based on fast Fourier transform (FFT) to study wave propagation in One-Dimensional (1D) structures. BSWI scaling functions are utilized to approximate the theoretical wave solution in the spatial domain and construct a high-accuracy dynamic stiffness matrix. Dynamic reduction on element level is applied to eliminate the interior degrees of freedom of BSWI elements and substantially reduce the size of the system matrix. The dynamic equations of the system are then transformed and solved in the frequency domain through FFT-based spectral analysis which is especially suitable for parallel computation. A comparative analysis of four different finite element methods is conducted to demonstrate the validity and efficiency of the proposed method when utilized in high-frequency wave problems. Other numerical examples are utilized to simulate the influence of crack and delamination on wave propagation in 1D rods and beams. Finally, the errors caused by FFT and their corresponding solutions are presented.

Optimization of custom cementless stem using finite element analysis and elastic modulus distribution for reducing stress-shielding effect.

PubMed

Saravana Kumar, Gurunathan; George, Subin Philip

2017-02-01

This work proposes a methodology involving stiffness optimization for subject-specific cementless hip implant design based on finite element analysis for reducing stress-shielding effect. To assess the change in the stress-strain state of the femur and the resulting stress-shielding effect due to insertion of the implant, a finite element analysis of the resected femur with implant assembly is carried out for a clinically relevant loading condition. Selecting the von Mises stress as the criterion for discriminating regions for elastic modulus difference, a stiffness minimization method was employed by varying the elastic modulus distribution in custom implant stem. The stiffness minimization problem is formulated as material distribution problem without explicitly penalizing partial volume elements. This formulation enables designs that could be fabricated using additive manufacturing to make porous implant with varying levels of porosity. Stress-shielding effect, measured as difference between the von Mises stress in the intact and implanted femur, decreased as the elastic modulus distribution is optimized.

An atomic finite element model for biodegradable polymers. Part 1. Formulation of the finite elements.

PubMed

Gleadall, Andrew; Pan, Jingzhe; Ding, Lifeng; Kruft, Marc-Anton; Curcó, David

2015-11-01

Molecular dynamics (MD) simulations are widely used to analyse materials at the atomic scale. However, MD has high computational demands, which may inhibit its use for simulations of structures involving large numbers of atoms such as amorphous polymer structures. An atomic-scale finite element method (AFEM) is presented in this study with significantly lower computational demands than MD. Due to the reduced computational demands, AFEM is suitable for the analysis of Young's modulus of amorphous polymer structures. This is of particular interest when studying the degradation of bioresorbable polymers, which is the topic of an accompanying paper. AFEM is derived from the inter-atomic potential energy functions of an MD force field. The nonlinear MD functions were adapted to enable static linear analysis. Finite element formulations were derived to represent interatomic potential energy functions between two, three and four atoms. Validation of the AFEM was conducted through its application to atomic structures for crystalline and amorphous poly(lactide). Copyright © 2015 Elsevier Ltd. All rights reserved.

Bending response of cross-ply laminated composite plates with diagonally perturbed localized interfacial degeneration.

PubMed

Kam, Chee Zhou; Kueh, Ahmad Beng Hong

2013-01-01

A laminated composite plate element with an interface description is developed using the finite element approach to investigate the bending performance of two-layer cross-ply laminated composite plates in presence of a diagonally perturbed localized interfacial degeneration between laminae. The stiffness of the laminate is expressed through the assembly of the stiffnesses of lamina sub-elements and interface element, the latter of which is formulated adopting the well-defined virtually zero-thickness concept. To account for the extent of both shear and axial weak bonding, a degeneration ratio is introduced in the interface formulation. The model has the advantage of simulating a localized weak bonding at arbitrary locations, with various degeneration areas and intensities, under the influence of numerous boundary conditions since the interfacial description is expressed discretely. Numerical results show that the bending behavior of laminate is significantly affected by the aforementioned parameters, the greatest effect of which is experienced by those with a localized total interface degeneration, representing the case of local delamination.

Beampattern control of a microphone array to minimize secondary source contamination.

PubMed

Jordan, Peter; Fitzpatrick, John A; Meskell, Craig

2003-10-01

A null-steering technique is adapted and applied to a linear delay-and-sum beamformer in order to measure the noise generated by one of the propellers of a 1/8 scale twin propeller aircraft model. The technique involves shading the linear array using a set of weights, which are calculated according to the locations onto which the nulls need to be steered (in this case onto the second propeller). The technique is based on an established microwave antenna theory, and uses a plane-wave, or far field formulation in order to represent the response of the array by an nth-order polynomial, where n is the number of array elements. The roots of this polynomial correspond to the minima of the array response, and so by an appropriate choice of roots, a polynomial can be generated, the coefficients of which are the weights needed to achieve the prespecified set of null positions. It is shown that, for the technique to work with actual data, the cross-spectral matrix must be conditioned before array shading is implemented. This ensures that the shading function is not distorted by the intrinsic element weighting which can occur as a result of the directional nature of aeroacoustic systems. A difference of 6 dB between measurements before and after null steering shows the technique to have been effective in eliminating the contribution from one of the propellers, thus providing a quantitative measure of the acoustic energy from the other.

Estimation of spectral kurtosis

NASA Astrophysics Data System (ADS)

Sutawanir

2017-03-01

Rolling bearings are the most important elements in rotating machinery. Bearing frequently fall out of service for various reasons: heavy loads, unsuitable lubrications, ineffective sealing. Bearing faults may cause a decrease in performance. Analysis of bearing vibration signals has attracted attention in the field of monitoring and fault diagnosis. Bearing vibration signals give rich information for early detection of bearing failures. Spectral kurtosis, SK, is a parameter in frequency domain indicating how the impulsiveness of a signal varies with frequency. Faults in rolling bearings give rise to a series of short impulse responses as the rolling elements strike faults, SK potentially useful for determining frequency bands dominated by bearing fault signals. SK can provide a measure of the distance of the analyzed bearings from a healthy one. SK provides additional information given by the power spectral density (psd). This paper aims to explore the estimation of spectral kurtosis using short time Fourier transform known as spectrogram. The estimation of SK is similar to the estimation of psd. The estimation falls in model-free estimation and plug-in estimator. Some numerical studies using simulations are discussed to support the methodology. Spectral kurtosis of some stationary signals are analytically obtained and used in simulation study. Kurtosis of time domain has been a popular tool for detecting non-normality. Spectral kurtosis is an extension of kurtosis in frequency domain. The relationship between time domain and frequency domain analysis is establish through power spectrum-autocovariance Fourier transform. Fourier transform is the main tool for estimation in frequency domain. The power spectral density is estimated through periodogram. In this paper, the short time Fourier transform of the spectral kurtosis is reviewed, a bearing fault (inner ring and outer ring) is simulated. The bearing response, power spectrum, and spectral kurtosis are plotted to visualize the pattern of each fault. Keywords: frequency domain Fourier transform, spectral kurtosis, bearing fault

A Kernel-Free Particle-Finite Element Method for Hypervelocity Impact Simulation. Chapter 4

NASA Technical Reports Server (NTRS)

Park, Young-Keun; Fahrenthold, Eric P.

2004-01-01

An improved hybrid particle-finite element method has been developed for the simulation of hypervelocity impact problems. Unlike alternative methods, the revised formulation computes the density without reference to any kernel or interpolation functions, for either the density or the rate of dilatation. This simplifies the state space model and leads to a significant reduction in computational cost. The improved method introduces internal energy variables as generalized coordinates in a new formulation of the thermomechanical Lagrange equations. Example problems show good agreement with exact solutions in one dimension and good agreement with experimental data in a three dimensional simulation.

Cross-Shear Implementation in Sliding-Distance-Coupled Finite Element Analysis of Wear in Metal-on-Polyethylene Total Joint Arthroplasty: Intervertebral Total Disc Replacement as an Illustrative Application

PubMed Central

Goreham-Voss, Curtis M.; Hyde, Philip J.; Hall, Richard M.; Fisher, John; Brown, Thomas D.

2010-01-01

Computational simulations of wear of orthopaedic total joint replacement implants have proven to valuably complement laboratory physical simulators, for pre-clinical estimation of abrasive/adhesive wear propensity. This class of numerical formulations has primarily involved implementation of the Archard/Lancaster relationship, with local wear computed as the product of (finite element) contact stress, sliding speed, and a bearing-couple-dependent wear factor. The present study introduces an augmentation, whereby the influence of interface cross-shearing motion transverse to the prevailing molecular orientation of the polyethylene articular surface is taken into account in assigning the instantaneous local wear factor. The formulation augment is implemented within a widely-utilized commercial finite element software environment (ABAQUS). Using a contemporary metal-on-polyethylene total disc replacement (ProDisc-L) as an illustrative implant, physically validated computational results are presented to document the role of cross-shearing effects in alternative laboratory consensus testing protocols. Going forward, this formulation permits systematically accounting for cross-shear effects in parametric computational wear studies of metal-on-polyethylene joint replacements, heretofore a substantial limitation of such analyses. PMID:20399432

Kinetic and spectral descriptions of autoionization phenomena associated with atomic processes in plasmas

NASA Astrophysics Data System (ADS)

Jacobs, Verne L.

2017-06-01

This investigation has been devoted to the theoretical description and computer modeling of atomic processes giving rise to radiative emission in energetic electron and ion beam interactions and in laboratory plasmas. We are also interested in the effects of directed electron and ion collisions and of anisotropic electric and magnetic fields. In the kinetic-theory description, we treat excitation, de-excitation, ionization, and recombination in electron and ion encounters with partially ionized atomic systems, including the indirect contributions from processes involving autoionizing resonances. These fundamental collisional and electromagnetic interactions also provide particle and photon transport mechanisms. From the spectral perspective, the analysis of atomic radiative emission can reveal detailed information on the physical properties in the plasma environment, such as non-equilibrium electron and charge-state distributions as well as electric and magnetic field distributions. In this investigation, a reduced-density-matrix formulation is developed for the microscopic description of atomic electromagnetic interactions in the presence of environmental (collisional and radiative) relaxation and decoherence processes. Our central objective is a fundamental microscopic description of atomic electromagnetic processes, in which both bound-state and autoionization-resonance phenomena can be treated in a unified and self-consistent manner. The time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations of the reduced-density-matrix approach are developed in a unified and self-consistent manner. This is necessary for our ultimate goal of a systematic and self-consistent treatment of non-equilibrium (possibly coherent) atomic-state kinetics and high-resolution (possibly overlapping) spectral-line shapes. We thereby propose the introduction of a generalized collisional-radiative atomic-state kinetics model based on a reduced-density-matrix formulation. It will become apparent that the full atomic data needs for the precise modeling of extreme non-equilibrium plasma environments extend beyond the conventional radiative-transition-probability and collisional-cross-section data sets.

Characterisation methods for the hyperspectral sensor HySpex at DLR's calibration home base

NASA Astrophysics Data System (ADS)

Baumgartner, Andreas; Gege, Peter; Köhler, Claas; Lenhard, Karim; Schwarzmaier, Thomas

2012-09-01

The German Aerospace Center's (DLR) Remote Sensing Technology Institute (IMF) operates a laboratory for the characterisation of imaging spectrometers. Originally designed as Calibration Home Base (CHB) for the imaging spectrometer APEX, the laboratory can be used to characterise nearly every airborne hyperspectral system. Characterisation methods will be demonstrated exemplarily with HySpex, an airborne imaging spectrometer system from Norsk Elektro Optikks A/S (NEO). Consisting of two separate devices (VNIR-1600 and SWIR-320me) the setup covers the spectral range from 400 nm to 2500 nm. Both airborne sensors have been characterised at NEO. This includes measurement of spectral and spatial resolution and misregistration, polarisation sensitivity, signal to noise ratios and the radiometric response. The same parameters have been examined at the CHB and were used to validate the NEO measurements. Additionally, the line spread functions (LSF) in across and along track direction and the spectral response functions (SRF) for certain detector pixels were measured. The high degree of lab automation allows the determination of the SRFs and LSFs for a large amount of sampling points. Despite this, the measurement of these functions for every detector element would be too time-consuming as typical detectors have 105 elements. But with enough sampling points it is possible to interpolate the attributes of the remaining pixels. The knowledge of these properties for every detector element allows the quantification of spectral and spatial misregistration (smile and keystone) and a better calibration of airborne data. Further laboratory measurements are used to validate the models for the spectral and spatial properties of the imaging spectrometers. Compared to the future German spaceborne hyperspectral Imager EnMAP, the HySpex sensors have the same or higher spectral and spatial resolution. Therefore, airborne data will be used to prepare for and validate the spaceborne system's data.

Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix

PubMed Central

Andreoli, Daria; Volpe, Giorgio; Popoff, Sébastien; Katz, Ori; Grésillon, Samuel; Gigan, Sylvain

2015-01-01

We present a method to measure the spectrally-resolved transmission matrix of a multiply scattering medium, thus allowing for the deterministic spatiospectral control of a broadband light source by means of wavefront shaping. As a demonstration, we show how the medium can be used to selectively focus one or many spectral components of a femtosecond pulse, and how it can be turned into a controllable dispersive optical element to spatially separate different spectral components to arbitrary positions. PMID:25965944

A System for Compressive Spectral and Polarization Imaging at Short Wave Infrared (SWIR) Wavelengths

DTIC Science & Technology

2017-10-18

2016). H. Rueda, H. Arguello and G. R. Arce, “DMD-based implementation of patterned optical filter arrays for compressive spectral imaging”, Journal...3)  a  set  of   optical   filters  which   allow   to   discriminate   spectrally   the   coded   and   sheared...system   that   includes   objective   lens,   spatial   light   modulator,   dispersive   element,   optical   filters

Flammability of Epoxy Resins Containing Phosphorus

NASA Technical Reports Server (NTRS)

Hergenrother, P. M.; Thompson, C. M.; Smith, J. G.; Connell, J. W.; Hinkley, J. A.

2005-01-01

As part of a program to develop fire-resistant exterior composite structures for future subsonic commercial and general aviation aircraft, flame-retardant epoxy resins are under investigation. Epoxies and their curing agents (aromatic diamines) containing phosphorus were synthesized and used to prepare epoxy formulations. Phosphorus was incorporated within the backbone of the epoxy resin and not used as an additive. The resulting cured neat epoxy formulations were characterized by thermogravimetric analysis, propane torch test, elemental analysis, microscale combustion calorimetry, and fire calorimetry. Several formulations showed excellent flame retardation with phosphorous contents as low as 1.5% by weight. The fracture toughness and compressive strength of several cured formulations showed no detrimental effect due to phosphorus content. The chemistry and properties of these new epoxy formulations are discussed.

The General Formulation and Practical Calculation of the Diffusion Coefficient in a Lattice Containing Cavities; FORMULATION GENERALE ET CALCUL PRATIQUE DU COEFFICIENT DE DIFFUSION DANS UN RESEAU COMPORTANT DES CAVITES (in French)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Benoist, P.

The calculation of diffusion coefficients in a lattice necessitates the knowledge of a correct method of weighting the free paths of the different constituents. An unambiguous definition of this weighting method is given here, based on the calculation of leakages from a zone of a reactor. The formulation obtained, which is both simple and general, reduces the calculation of diffusion coefficients to that of collision probabilities in the different media; it reveals in the expression for the radial coefficient the series of the terms of angular correlation (cross terms) recently shown by several authors. This formulation is then used tomore » calculate the practical case of a classical type of lattice composed of a moderator and a fuel element surrounded by an empty space. Analytical and numerical comparison of the expressions obtained with those inferred from the theory of BEHRENS shows up the importance of several new terms some of which are linked with the transparency of the fuel element. Cross terms up to the second order are evaluated. A practical formulary is given at the end of the paper. (author) [French] Le calcul des coefficients de diffusion dans un reseau suppose la connaissance d'un mode de ponderation correct des libres parcours des differents constituants. On definit ici sans ambiguite ce mode de ponderation a partir du calcul des fuites hors d'une zone de reacteur. La formulation obtenue, simple et generale, ramene le calcul des coefficients de diffusion a celui des probabilites de collision dans les differents milieux; elle fait apparaitre dans l'expression du coefficient radial la serie des termes de correlation angulaire (termes rectangles), mis en evidence recemment par plusieurs auteurs. Cette formulation est ensuite appliquee au calcul pratique d'un reseau classique, compose d'un moderateur et d'un element combustible entoure d'une cavite; la comparaison analytique et numerique des expressions obtenues avec celles deduites de la theorie de BEHRENS fait apparaitre l'importance de plusieurs termes nouveaux, dont certains sont lies a la transparence de l'element combustible; les termes rectangles sont calcules jusqu'a l'ordre 2. Un formulaire pratique est donne a la fin de cette etude. (auteur)« less

Spectral element simulation of precession driven flows in the outer cores of spheroidal planets

NASA Astrophysics Data System (ADS)

Vormann, Jan; Hansen, Ulrich

2015-04-01

A common feature of the planets in the solar system is the precession of the rotation axes, driven by the gravitational influence of another body (e.g. the Earth's moon). In a precessing body, the rotation axis itself is rotating around another axis, describing a cone during one precession period. Similar to the coriolis and centrifugal force appearing from the transformation to a rotating system, the addition of precession adds another term to the Navier-Stokes equation, the so called Poincaré force. The main geophysical motivation in studying precession driven flows comes from their ability to act as magnetohydrodynamic dynamos in planets and moons. Precession may either act as the only driving force or operate together with other forces such as thermochemical convection. One of the challenges in direct numerical simulations of such flows lies in the spheroidal shape of the fluid volume, which should not be neglected since it contributes an additional forcing trough pressure torques. Codes developed for the simulation of flows in spheres mostly use efficient global spectral algorithms that converge fast, but lack geometric flexibility, while local methods are usable in more complex shapes, but often lack high accuracy. We therefore adapted the spectral element code Nek5000, developed at Argonne National Laboratory, to the problem. The spectral element method is capable of solving for the flow in arbitrary geometries while still offering spectral convergence. We present first results for the simulation of a purely hydrodynamic, precession-driven flow in a spheroid with no-slip boundaries and an inner core. The driving by the Poincaré force is in a range where theoretical work predicts multiple solutions for a laminar flow. Our simulations indicate a transition to turbulent flows for Ekman numbers of 10-6 and lower.

Finite and spectral cell method for wave propagation in heterogeneous materials

NASA Astrophysics Data System (ADS)

Joulaian, Meysam; Duczek, Sascha; Gabbert, Ulrich; Düster, Alexander

2014-09-01

In the current paper we present a fast, reliable technique for simulating wave propagation in complex structures made of heterogeneous materials. The proposed approach, the spectral cell method, is a combination of the finite cell method and the spectral element method that significantly lowers preprocessing and computational expenditure. The spectral cell method takes advantage of explicit time-integration schemes coupled with a diagonal mass matrix to reduce the time spent on solving the equation system. By employing a fictitious domain approach, this method also helps to eliminate some of the difficulties associated with mesh generation. Besides introducing a proper, specific mass lumping technique, we also study the performance of the low-order and high-order versions of this approach based on several numerical examples. Our results show that the high-order version of the spectral cell method together requires less memory storage and less CPU time than other possible versions, when combined simultaneously with explicit time-integration algorithms. Moreover, as the implementation of the proposed method in available finite element programs is straightforward, these properties turn the method into a viable tool for practical applications such as structural health monitoring [1-3], quantitative ultrasound applications [4], or the active control of vibrations and noise [5, 6].

Broadband ground motion simulation using a paralleled hybrid approach of Frequency Wavenumber and Finite Difference method

NASA Astrophysics Data System (ADS)

Chen, M.; Wei, S.

2016-12-01

The serious damage of Mexico City caused by the 1985 Michoacan earthquake 400 km away indicates that urban areas may be affected by remote earthquakes. To asses earthquake risk of urban areas imposed by distant earthquakes, we developed a hybrid Frequency Wavenumber (FK) and Finite Difference (FD) code implemented with MPI, since the computation of seismic wave propagation from a distant earthquake using a single numerical method (e.g. Finite Difference, Finite Element or Spectral Element) is very expensive. In our approach, we compute the incident wave field (ud) at the boundaries of the excitation box, which surrounding the local structure, using a paralleled FK method (Zhu and Rivera, 2002), and compute the total wave field (u) within the excitation box using a parallelled 2D FD method. We apply perfectly matched layer (PML) absorbing condition to the diffracted wave field (u-ud). Compared to previous Generalized Ray Theory and Finite Difference (Wen and Helmberger, 1998), Frequency Wavenumber and Spectral Element (Tong et al., 2014), and Direct Solution Method and Spectral Element hybrid method (Monteiller et al., 2013), our absorbing boundary condition dramatically suppress the numerical noise. The MPI implementation of our method can greatly speed up the calculation. Besides, our hybrid method also has a potential use in high resolution array imaging similar to Tong et al. (2014).

Imaging the density distributions at the regional scale using full waveform and gravity data inversion - Application to the Pyrenees

NASA Astrophysics Data System (ADS)

Martin, Roland; Chevrot, Sébastien; Wang, Yi; Spangenberg, Hannah; Goubet, Marie; Monteiller, Vadim; Komatitsch, Dimitri; Seoane, Lucia; Dufréchou, Grégory

2017-04-01

We present a hybrid inversion method that allows us to image density distributions at the regional scale using both seismic and gravity data. One main goal is to obtain densities and seismic wave velocities (P and S) in the lithosphere with a fine resolution to get important constraints on the mineralogic composition and thermal state of the lithosphere. In the context of the Pyrenees (located between Spain and France), accurate Vp and Vs seismic velocity models are computed first on a 3D spectral element grid at the scale of the Pyrenees by inverting teleseismic full waveforms. In a second step, Vp velocities are mapped to densities using empirical relations to build an a priori density model. BGI and BRGM Bouguer gravity anomaly data sets are then inverted on the same 3D spectral element grid as the Vp model at a resolution of 1-2 km by using high-order numerical integration formulae. Solutions are compared to those obtained using classical semi-analytical techniques. This procedure opens the possibility to invert both teleseismic and gravity data on the same finite-element grid. It can handle topography of the free surface in the same spectral-element distorted mesh that is used to solve the wave equation, without performing extra interpolations between different grids and models. WGS84 curvature, SRTM or ETOPO1 topographies are used.

Book Review: Book review

NASA Astrophysics Data System (ADS)

Wald, Robert M.

There is no question that the formulation of general relativity was one of the most remarkable episodes in the history of science. As a physicist and researcher in general relativity, the story of the formulation of general relativity that I have heard (and repeated) many times goes basically as follows: In 1907, Einstein obtained his fundamental insight-the "equivalence principle"-that gravitation and inertia are intimately connected; a freely falling observer does not "feel" gravitational force. It then took the genius of Einstein many years of "struggle"-during which he mastered the elements of differential geometry-to formulate a theory that properly incorporated this idea. In November, 1915, he finally succeeded in formulating general relativity.

Carrying capacity as "informed judgment": The values of science and the science of values

Treesearch

Robert E. Manning

2001-01-01

Contemporary carrying capacity frameworks, such as Limits of Acceptable Change and Visitor Experience and Resource Protection, rely on formulation of standards of quality, which are defined as minimum acceptable resource and social conditions in parks and wilderness. Formulation of standards of quality involves elements of both science and values, and both of these...

Analysis of Aerospike Plume Induced Base-Heating Environment

NASA Technical Reports Server (NTRS)

Wang, Ten-See

1998-01-01

Computational analysis is conducted to study the effect of an aerospike engine plume on X-33 base-heating environment during ascent flight. To properly account for the effect of forebody and aftbody flowfield such as shocks and to allow for potential plume-induced flow-separation, thermo-flowfield of trajectory points is computed. The computational methodology is based on a three-dimensional finite-difference, viscous flow, chemically reacting, pressure-base computational fluid dynamics formulation, and a three-dimensional, finite-volume, spectral-line based weighted-sum-of-gray-gases radiation absorption model computational heat transfer formulation. The predicted convective and radiative base-heat fluxes are presented.

Wide-Angle, Flat-Field Telescope

NASA Technical Reports Server (NTRS)

Hallam, K. L.; Howell, B. J.; Wilson, M. E.

1987-01-01

All-reflective system unvignetted. Wide-angle telescope uses unobstructed reflecting elements to produce flat image. No refracting elements, no chromatic aberration, and telescope operates over spectral range from infrared to far ultraviolet. Telescope used with such image detectors as photographic firm, vidicons, and solid-state image arrays.