Numerically stable finite difference simulation for ultrasonic NDE in anisotropic composites

NASA Astrophysics Data System (ADS)

Leckey, Cara A. C.; Quintanilla, Francisco Hernando; Cole, Christina M.

2018-04-01

Simulation tools can enable optimized inspection of advanced materials and complex geometry structures. Recent work at NASA Langley is focused on the development of custom simulation tools for modeling ultrasonic wave behavior in composite materials. Prior work focused on the use of a standard staggered grid finite difference type of mathematical approach, by implementing a three-dimensional (3D) anisotropic Elastodynamic Finite Integration Technique (EFIT) code. However, observations showed that the anisotropic EFIT method displays numerically unstable behavior at the locations of stress-free boundaries for some cases of anisotropic materials. This paper gives examples of the numerical instabilities observed for EFIT and discusses the source of instability. As an alternative to EFIT, the 3D Lebedev Finite Difference (LFD) method has been implemented. The paper briefly describes the LFD approach and shows examples of stable behavior in the presence of stress-free boundaries for a monoclinic anisotropy case. The LFD results are also compared to experimental results and dispersion curves.

A diffuse-interface method for two-phase flows with soluble surfactants

PubMed Central

Teigen, Knut Erik; Song, Peng; Lowengrub, John; Voigt, Axel

2010-01-01

A method is presented to solve two-phase problems involving soluble surfactants. The incompressible Navier–Stokes equations are solved along with equations for the bulk and interfacial surfactant concentrations. A non-linear equation of state is used to relate the surface tension to the interfacial surfactant concentration. The method is based on the use of a diffuse interface, which allows a simple implementation using standard finite difference or finite element techniques. Here, finite difference methods on a block-structured adaptive grid are used, and the resulting equations are solved using a non-linear multigrid method. Results are presented for a drop in shear flow in both 2D and 3D, and the effect of solubility is discussed. PMID:21218125

An RBF-FD closest point method for solving PDEs on surfaces

NASA Astrophysics Data System (ADS)

Petras, A.; Ling, L.; Ruuth, S. J.

2018-10-01

Partial differential equations (PDEs) on surfaces appear in many applications throughout the natural and applied sciences. The classical closest point method (Ruuth and Merriman (2008) [17]) is an embedding method for solving PDEs on surfaces using standard finite difference schemes. In this paper, we formulate an explicit closest point method using finite difference schemes derived from radial basis functions (RBF-FD). Unlike the orthogonal gradients method (Piret (2012) [22]), our proposed method uses RBF centers on regular grid nodes. This formulation not only reduces the computational cost but also avoids the ill-conditioning from point clustering on the surface and is more natural to couple with a grid based manifold evolution algorithm (Leung and Zhao (2009) [26]). When compared to the standard finite difference discretization of the closest point method, the proposed method requires a smaller computational domain surrounding the surface, resulting in a decrease in the number of sampling points on the surface. In addition, higher-order schemes can easily be constructed by increasing the number of points in the RBF-FD stencil. Applications to a variety of examples are provided to illustrate the numerical convergence of the method.

Acceleration of FDTD mode solver by high-performance computing techniques.

PubMed

Han, Lin; Xi, Yanping; Huang, Wei-Ping

2010-06-21

A two-dimensional (2D) compact finite-difference time-domain (FDTD) mode solver is developed based on wave equation formalism in combination with the matrix pencil method (MPM). The method is validated for calculation of both real guided and complex leaky modes of typical optical waveguides against the bench-mark finite-difference (FD) eigen mode solver. By taking advantage of the inherent parallel nature of the FDTD algorithm, the mode solver is implemented on graphics processing units (GPUs) using the compute unified device architecture (CUDA). It is demonstrated that the high-performance computing technique leads to significant acceleration of the FDTD mode solver with more than 30 times improvement in computational efficiency in comparison with the conventional FDTD mode solver running on CPU of a standard desktop computer. The computational efficiency of the accelerated FDTD method is in the same order of magnitude of the standard finite-difference eigen mode solver and yet require much less memory (e.g., less than 10%). Therefore, the new method may serve as an efficient, accurate and robust tool for mode calculation of optical waveguides even when the conventional eigen value mode solvers are no longer applicable due to memory limitation.

A Parallel, Finite-Volume Algorithm for Large-Eddy Simulation of Turbulent Flows

NASA Technical Reports Server (NTRS)

Bui, Trong T.

1999-01-01

A parallel, finite-volume algorithm has been developed for large-eddy simulation (LES) of compressible turbulent flows. This algorithm includes piecewise linear least-square reconstruction, trilinear finite-element interpolation, Roe flux-difference splitting, and second-order MacCormack time marching. Parallel implementation is done using the message-passing programming model. In this paper, the numerical algorithm is described. To validate the numerical method for turbulence simulation, LES of fully developed turbulent flow in a square duct is performed for a Reynolds number of 320 based on the average friction velocity and the hydraulic diameter of the duct. Direct numerical simulation (DNS) results are available for this test case, and the accuracy of this algorithm for turbulence simulations can be ascertained by comparing the LES solutions with the DNS results. The effects of grid resolution, upwind numerical dissipation, and subgrid-scale dissipation on the accuracy of the LES are examined. Comparison with DNS results shows that the standard Roe flux-difference splitting dissipation adversely affects the accuracy of the turbulence simulation. For accurate turbulence simulations, only 3-5 percent of the standard Roe flux-difference splitting dissipation is needed.

A General Formulation for Robust and Efficient Integration of Finite Differences and Phase Unwrapping on Sparse Multidimensional Domains

NASA Astrophysics Data System (ADS)

Costantini, Mario; Malvarosa, Fabio; Minati, Federico

2010-03-01

Phase unwrapping and integration of finite differences are key problems in several technical fields. In SAR interferometry and differential and persistent scatterers interferometry digital elevation models and displacement measurements can be obtained after unambiguously determining the phase values and reconstructing the mean velocities and elevations of the observed targets, which can be performed by integrating differential estimates of these quantities (finite differences between neighboring points).In this paper we propose a general formulation for robust and efficient integration of finite differences and phase unwrapping, which includes standard techniques methods as sub-cases. The proposed approach allows obtaining more reliable and accurate solutions by exploiting redundant differential estimates (not only between nearest neighboring points) and multi-dimensional information (e.g. multi-temporal, multi-frequency, multi-baseline observations), or external data (e.g. GPS measurements). The proposed approach requires the solution of linear or quadratic programming problems, for which computationally efficient algorithms exist.The validation tests obtained on real SAR data confirm the validity of the method, which was integrated in our production chain and successfully used also in massive productions.

The aggregated unfitted finite element method for elliptic problems

NASA Astrophysics Data System (ADS)

Badia, Santiago; Verdugo, Francesc; Martín, Alberto F.

2018-07-01

Unfitted finite element techniques are valuable tools in different applications where the generation of body-fitted meshes is difficult. However, these techniques are prone to severe ill conditioning problems that obstruct the efficient use of iterative Krylov methods and, in consequence, hinders the practical usage of unfitted methods for realistic large scale applications. In this work, we present a technique that addresses such conditioning problems by constructing enhanced finite element spaces based on a cell aggregation technique. The presented method, called aggregated unfitted finite element method, is easy to implement, and can be used, in contrast to previous works, in Galerkin approximations of coercive problems with conforming Lagrangian finite element spaces. The mathematical analysis of the new method states that the condition number of the resulting linear system matrix scales as in standard finite elements for body-fitted meshes, without being affected by small cut cells, and that the method leads to the optimal finite element convergence order. These theoretical results are confirmed with 2D and 3D numerical experiments.

A finite difference scheme for the equilibrium equations of elastic bodies

NASA Technical Reports Server (NTRS)

Phillips, T. N.; Rose, M. E.

1984-01-01

A compact difference scheme is described for treating the first-order system of partial differential equations which describe the equilibrium equations of an elastic body. An algebraic simplification enables the solution to be obtained by standard direct or iterative techniques.

Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units.

PubMed

Qi, Ruxi; Botello-Smith, Wesley M; Luo, Ray

2017-07-11

Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes the standard Nvidia CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.

Emergent kink statistics at finite temperature

DOE PAGES

Lopez-Ruiz, Miguel Angel; Yepez-Martinez, Tochtli; Szczepaniak, Adam; ...

2017-07-25

In this paper we use 1D quantum mechanical systems with Higgs-like interaction potential to study the emergence of topological objects at finite temperature. Two different model systems are studied, the standard double-well potential model and a newly introduced discrete kink model. Using Monte-Carlo simulations as well as analytic methods, we demonstrate how kinks become abundant at low temperatures. These results may shed useful insights on how topological phenomena may occur in QCD.

Aspects of numerical and representational methods related to the finite-difference simulation of advective and dispersive transport of freshwater in a thin brackish aquifer

USGS Publications Warehouse

Merritt, M.L.

1993-01-01

The simulation of the transport of injected freshwater in a thin brackish aquifer, overlain and underlain by confining layers containing more saline water, is shown to be influenced by the choice of the finite-difference approximation method, the algorithm for representing vertical advective and dispersive fluxes, and the values assigned to parametric coefficients that specify the degree of vertical dispersion and molecular diffusion that occurs. Computed potable water recovery efficiencies will differ depending upon the choice of algorithm and approximation method, as will dispersion coefficients estimated based on the calibration of simulations to match measured data. A comparison of centered and backward finite-difference approximation methods shows that substantially different transition zones between injected and native waters are depicted by the different methods, and computed recovery efficiencies vary greatly. Standard and experimental algorithms and a variety of values for molecular diffusivity, transverse dispersivity, and vertical scaling factor were compared in simulations of freshwater storage in a thin brackish aquifer. Computed recovery efficiencies vary considerably, and appreciable differences are observed in the distribution of injected freshwater in the various cases tested. The results demonstrate both a qualitatively different description of transport using the experimental algorithms and the interrelated influences of molecular diffusion and transverse dispersion on simulated recovery efficiency. When simulating natural aquifer flow in cross-section, flushing of the aquifer occurred for all tested coefficient choices using both standard and experimental algorithms. ?? 1993.

Algorithmic vs. finite difference Jacobians for infrared atmospheric radiative transfer

NASA Astrophysics Data System (ADS)

Schreier, Franz; Gimeno García, Sebastián; Vasquez, Mayte; Xu, Jian

2015-10-01

Jacobians, i.e. partial derivatives of the radiance and transmission spectrum with respect to the atmospheric state parameters to be retrieved from remote sensing observations, are important for the iterative solution of the nonlinear inverse problem. Finite difference Jacobians are easy to implement, but computationally expensive and possibly of dubious quality; on the other hand, analytical Jacobians are accurate and efficient, but the implementation can be quite demanding. GARLIC, our "Generic Atmospheric Radiation Line-by-line Infrared Code", utilizes algorithmic differentiation (AD) techniques to implement derivatives w.r.t. atmospheric temperature and molecular concentrations. In this paper, we describe our approach for differentiation of the high resolution infrared and microwave spectra and provide an in-depth assessment of finite difference approximations using "exact" AD Jacobians as a reference. The results indicate that the "standard" two-point finite differences with 1 K and 1% perturbation for temperature and volume mixing ratio, respectively, can exhibit substantial errors, and central differences are significantly better. However, these deviations do not transfer into the truncated singular value decomposition solution of a least squares problem. Nevertheless, AD Jacobians are clearly recommended because of the superior speed and accuracy.

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.

Existence of standard models of conic fibrations over non-algebraically-closed fields

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

Avilov, A A

2014-12-31

We prove an analogue of Sarkisov's theorem on the existence of a standard model of a conic fibration over an algebraically closed field of characteristic different from two for three-dimensional conic fibrations over an arbitrary field of characteristic zero with an action of a finite group. Bibliography: 16 titles.

Implementing the Standards. Teaching Discrete Mathematics in Grades 7-12.

ERIC Educational Resources Information Center

Hart, Eric W.; And Others

1990-01-01

Discrete mathematics are defined briefly. A course in discrete mathematics for high school students and teaching discrete mathematics in grades 7 and 8 including finite differences, recursion, and graph theory are discussed. (CW)

A symplectic integration method for elastic filaments

NASA Astrophysics Data System (ADS)

Ladd, Tony; Misra, Gaurav

2009-03-01

Elastic rods are a ubiquitous coarse-grained model of semi-flexible biopolymers such as DNA, actin, and microtubules. The Worm-Like Chain (WLC) is the standard numerical model for semi-flexible polymers, but it is only a linearized approximation to the dynamics of an elastic rod, valid for small deflections; typically the torsional motion is neglected as well. In the standard finite-difference and finite-element formulations of an elastic rod, the continuum equations of motion are discretized in space and time, but it is then difficult to ensure that the Hamiltonian structure of the exact equations is preserved. Here we discretize the Hamiltonian itself, expressed as a line integral over the contour of the filament. This discrete representation of the continuum filament can then be integrated by one of the explicit symplectic integrators frequently used in molecular dynamics. The model systematically approximates the continuum partial differential equations, but has the same level of computational complexity as molecular dynamics and is constraint free. Numerical tests show that the algorithm is much more stable than a finite-difference formulation and can be used for high aspect ratio filaments, such as actin. We present numerical results for the deterministic and stochastic motion of single filaments.

An Artificial Neural Networks Method for Solving Partial Differential Equations

NASA Astrophysics Data System (ADS)

Alharbi, Abir

2010-09-01

While there already exists many analytical and numerical techniques for solving PDEs, this paper introduces an approach using artificial neural networks. The approach consists of a technique developed by combining the standard numerical method, finite-difference, with the Hopfield neural network. The method is denoted Hopfield-finite-difference (HFD). The architecture of the nets, energy function, updating equations, and algorithms are developed for the method. The HFD method has been used successfully to approximate the solution of classical PDEs, such as the Wave, Heat, Poisson and the Diffusion equations, and on a system of PDEs. The software Matlab is used to obtain the results in both tabular and graphical form. The results are similar in terms of accuracy to those obtained by standard numerical methods. In terms of speed, the parallel nature of the Hopfield nets methods makes them easier to implement on fast parallel computers while some numerical methods need extra effort for parallelization.

Plane wave diffraction by a finite plate with impedance boundary conditions.

PubMed

Nawaz, Rab; Ayub, Muhammad; Javaid, Akmal

2014-01-01

In this study we have examined a plane wave diffraction problem by a finite plate having different impedance boundaries. The Fourier transforms were used to reduce the governing problem into simultaneous Wiener-Hopf equations which are then solved using the standard Wiener-Hopf procedure. Afterwards the separated and interacted fields were developed asymptotically by using inverse Fourier transform and the modified stationary phase method. Detailed graphical analysis was also made for various physical parameters we were interested in.

Finite element modeling of frictionally restrained composite interfaces

NASA Technical Reports Server (NTRS)

Ballarini, Roberto; Ahmed, Shamim

1989-01-01

The use of special interface finite elements to model frictional restraint in composite interfaces is described. These elements simulate Coulomb friction at the interface, and are incorporated into a standard finite element analysis of a two-dimensional isolated fiber pullout test. Various interfacial characteristics, such as the distribution of stresses at the interface, the extent of slip and delamination, load diffusion from fiber to matrix, and the amount of fiber extraction or depression are studied for different friction coefficients. The results are compared to those obtained analytically using a singular integral equation approach, and those obtained by assuming a constant interface shear strength. The usefulness of these elements in micromechanical modeling of fiber-reinforced composite materials is highlighted.

Finite element simulation of cracks formation in parabolic flume above fixed service live

NASA Astrophysics Data System (ADS)

Bandurin, M. A.; Volosukhin, V. A.; Mikheev, A. V.; Volosukhin, Y. V.; Bandurina, I. P.

2018-03-01

In the article, digital simulation data on influence of defect different characteristics on cracks formation in a parabolic flume are presented. The finite element method is based on general hypotheses of the theory of elasticity. The studies showed that the values of absolute movements satisfy the standards of design. The results of the digital simulation of stresses and strains for cracks formation in concrete parabolic flumes after long-term service above the fixed service life are described. Stressed and strained state of reinforced concrete bearing elements under different load combinations is considered. Intensive threshold of danger to form longitudinal cracks in reinforced concrete elements is determined.

Finite-size scaling and integer-spin Heisenberg chains

NASA Astrophysics Data System (ADS)

Bonner, Jill C.; Müller, Gerhard

1984-03-01

Finite-size scaling (phenomenological renormalization) techniques are trusted and widely applied in low-dimensional magnetism and, particularly, in lattice gauge field theory. Recently, investigations have begun which subject the theoretical basis to systematic and intensive scrutiny to determine the validity of finite-size scaling in a variety of situations. The 2D ANNNI model is an example of a situation where finite-size scaling methods encounter difficulty, related to the occurrence of a disorder line (one-dimensional line). A second example concerns the behavior of the spin-1/2 antiferromagnetic XXZ model where the T=0 critical behavior is exactly known and features an essential singularity at the isotropic Heisenberg point. Standard finite-size scaling techniques do not convincingly reproduce the exact phase behavior and this is attributable to the essential singularity. The point is relevant in connection with a finite-size scaling analysis of a spin-one antiferromagnetic XXZ model, which claims to support a conjecture by Haldane that the T=0 phase behavior of integer-spin Heisenberg chains is significantly different from that of half-integer-spin Heisenberg chains.

Calculating the Malliavin derivative of some stochastic mechanics problems

PubMed Central

Hauseux, Paul; Hale, Jack S.

2017-01-01

The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to calculate the Malliavin derivative, the derivative of the expectation of a quantity of interest of a model with respect to its underlying stochastic parameters, for four problems found in mechanics. The non-intrusive approach uses the Malliavin Weight Sampling (MWS) method in conjunction with a standard Monte Carlo method. The models are expressed as ODEs or PDEs and discretised using the finite difference or finite element methods. Specifically, we consider stochastic extensions of; a 1D Kelvin-Voigt viscoelastic model discretised with finite differences, a 1D linear elastic bar, a hyperelastic bar undergoing buckling, and incompressible Navier-Stokes flow around a cylinder, all discretised with finite elements. A further contribution of this paper is an extension of the MWS method to the more difficult case of non-Gaussian random variables and the calculation of second-order derivatives. We provide open-source code for the numerical examples in this paper. PMID:29261776

High-order asynchrony-tolerant finite difference schemes for partial differential equations

NASA Astrophysics Data System (ADS)

Aditya, Konduri; Donzis, Diego A.

2017-12-01

Synchronizations of processing elements (PEs) in massively parallel simulations, which arise due to communication or load imbalances between PEs, significantly affect the scalability of scientific applications. We have recently proposed a method based on finite-difference schemes to solve partial differential equations in an asynchronous fashion - synchronization between PEs is relaxed at a mathematical level. While standard schemes can maintain their stability in the presence of asynchrony, their accuracy is drastically affected. In this work, we present a general methodology to derive asynchrony-tolerant (AT) finite difference schemes of arbitrary order of accuracy, which can maintain their accuracy when synchronizations are relaxed. We show that there are several choices available in selecting a stencil to derive these schemes and discuss their effect on numerical and computational performance. We provide a simple classification of schemes based on the stencil and derive schemes that are representative of different classes. Their numerical error is rigorously analyzed within a statistical framework to obtain the overall accuracy of the solution. Results from numerical experiments are used to validate the performance of the schemes.

Investigation of the Statistics of Pure Tone Sound Power Injection from Low Frequency, Finite Sized Sources in a Reverberant Room

NASA Technical Reports Server (NTRS)

Smith, Wayne Farrior

1973-01-01

The effect of finite source size on the power statistics in a reverberant room for pure tone excitation was investigated. Theoretical results indicate that the standard deviation of low frequency, pure tone finite sources is always less than that predicted by point source theory and considerably less when the source dimension approaches one-half an acoustic wavelength or greater. A supporting experimental study was conducted utilizing an eight inch loudspeaker and a 30 inch loudspeaker at eleven source positions. The resulting standard deviation of sound power output of the smaller speaker is in excellent agreement with both the derived finite source theory and existing point source theory, if the theoretical data is adjusted to account for experimental incomplete spatial averaging. However, the standard deviation of sound power output of the larger speaker is measurably lower than point source theory indicates, but is in good agreement with the finite source theory.

Design space exploration of high throughput finite field multipliers for channel coding on Xilinx FPGAs

NASA Astrophysics Data System (ADS)

de Schryver, C.; Weithoffer, S.; Wasenmüller, U.; Wehn, N.

2012-09-01

Channel coding is a standard technique in all wireless communication systems. In addition to the typically employed methods like convolutional coding, turbo coding or low density parity check (LDPC) coding, algebraic codes are used in many cases. For example, outer BCH coding is applied in the DVB-S2 standard for satellite TV broadcasting. A key operation for BCH and the related Reed-Solomon codes are multiplications in finite fields (Galois Fields), where extension fields of prime fields are used. A lot of architectures for multiplications in finite fields have been published over the last decades. This paper examines four different multiplier architectures in detail that offer the potential for very high throughputs. We investigate the implementation performance of these multipliers on FPGA technology in the context of channel coding. We study the efficiency of the multipliers with respect to area, frequency and throughput, as well as configurability and scalability. The implementation data of the fully verified circuits are provided for a Xilinx Virtex-4 device after place and route.

High-efficiency power transfer for silicon-based photonic devices

NASA Astrophysics Data System (ADS)

Son, Gyeongho; Yu, Kyoungsik

2018-02-01

We demonstrate an efficient coupling of guided light of 1550 nm from a standard single-mode optical fiber to a silicon waveguide using the finite-difference time-domain method and propose a fabrication method of tapered optical fibers for efficient power transfer to silicon-based photonic integrated circuits. Adiabatically-varying fiber core diameters with a small tapering angle can be obtained using the tube etching method with hydrofluoric acid and standard single-mode fibers covered by plastic jackets. The optical power transmission of the fundamental HE11 and TE-like modes between the fiber tapers and the inversely-tapered silicon waveguides was calculated with the finite-difference time-domain method to be more than 99% at a wavelength of 1550 nm. The proposed method for adiabatic fiber tapering can be applied in quantum optics, silicon-based photonic integrated circuits, and nanophotonics. Furthermore, efficient coupling within the telecommunication C-band is a promising approach for quantum networks in the future.

Practical wavelength calibration considerations for UV-visible Fourier-transform spectroscopy.

PubMed

Salit, M L; Travis, J C; Winchester, M R

1996-06-01

The intrinsic wavelength scale in a modern reference laser-controlled Michelson interferometer-sometimes referred to as the Connes advantage-offers excellent wavelength accuracy with relative ease. Truly superb wavelength accuracy, with total relative uncertainty in line position of the order of several parts in 10(8), should be within reach with single-point, multiplicative calibration. The need for correction of the wavelength scale arises from two practical effects: the use of a finite aperture, from which off-axis rays propagate through the interferometer, and imperfect geometric alignment of the sample beam with the reference beam and the optical axis of the moving mirror. Although an analytical correction can be made for the finite-aperture effect, calibration with a trusted wavelength standard is typically used to accomplish both corrections. Practical aspects of accurate calibration of an interferometer in the UV-visible region are discussed. Critical issues regarding accurate use of a standard external to the sample source and the evaluation and selection of an appropriate standard are addressed. Anomalous results for two different potential wavelength standards measured by Fabry-Perot interferometry (Ar II and (198)Hg I) are observed.

Data Combination and Instrumental Variables in Linear Models

ERIC Educational Resources Information Center

Khawand, Christopher

2012-01-01

Instrumental variables (IV) methods allow for consistent estimation of causal effects, but suffer from poor finite-sample properties and data availability constraints. IV estimates also tend to have relatively large standard errors, often inhibiting the interpretability of differences between IV and non-IV point estimates. Lastly, instrumental…

Wear in ceramic on ceramic type lumbar total disc replacement: effect of radial clearance.

PubMed

Shankar, S; Kesavan, D

2015-01-01

The wear of the bearing surfaces of total disc replacement (TDR) is a key problem leads to reduction in the lifetime of the prosthesis and it mainly occurs due to the range of clearances of the articulating surface between the superior plate and core. The objective of this paper is to estimate the wear using finite element concepts considering the different radial clearances between the articulating surfaces of ceramic on ceramic type Lumbar Total Disc Replacement (LTDR). The finite element (FE) model was subjected to wear testing protocols according to loading profile of International Standards Organization (ISO) 18192 standards through 10 million cycles. The radial clearance value of 0.05 mm showed less volumetric wear when compared with other radial clearance values. Hence, low radial clearance values are suitable for LTDR to minimize the wear.

Comparison of bursting pressure results of LPG tank using experimental and finite element method.

PubMed

Aksoley, M Egemen; Ozcelik, Babur; Bican, Ismail

2008-03-01

In this study, the resistance of liquefied-petroleum gas (LPG) tanks produced from carbon steel sheet metal of different thicknesses has been investigated by bursting pressure experiments and non-linear Finite Element Method (FEM) method by increasing internal pressure values. The designs of LPG tanks produced from sheet metal to be used at the study have been realized by analytical calculations made taking into consideration of related standards. Bursting pressure tests have been performed that were inclined to decreasing the sheet thickness of LPG tanks used in industry. It has been shown that the LPG tanks can be produced in compliance with the standards when the sheet thickness is lowered from 3 to 2.8mm. The FEM results have displayed close values with the bursting results obtained from the experiments.

Generalization of von Neumann analysis for a model of two discrete half-spaces: The acoustic case

USGS Publications Warehouse

Haney, M.M.

2007-01-01

Evaluating the performance of finite-difference algorithms typically uses a technique known as von Neumann analysis. For a given algorithm, application of the technique yields both a dispersion relation valid for the discrete time-space grid and a mathematical condition for stability. In practice, a major shortcoming of conventional von Neumann analysis is that it can be applied only to an idealized numerical model - that of an infinite, homogeneous whole space. Experience has shown that numerical instabilities often arise in finite-difference simulations of wave propagation at interfaces with strong material contrasts. These interface instabilities occur even though the conventional von Neumann stability criterion may be satisfied at each point of the numerical model. To address this issue, I generalize von Neumann analysis for a model of two half-spaces. I perform the analysis for the case of acoustic wave propagation using a standard staggered-grid finite-difference numerical scheme. By deriving expressions for the discrete reflection and transmission coefficients, I study under what conditions the discrete reflection and transmission coefficients become unbounded. I find that instabilities encountered in numerical modeling near interfaces with strong material contrasts are linked to these cases and develop a modified stability criterion that takes into account the resulting instabilities. I test and verify the stability criterion by executing a finite-difference algorithm under conditions predicted to be stable and unstable. ?? 2007 Society of Exploration Geophysicists.

A particle finite element method for machining simulations

NASA Astrophysics Data System (ADS)

Sabel, Matthias; Sator, Christian; Müller, Ralf

2014-07-01

The particle finite element method (PFEM) appears to be a convenient technique for machining simulations, since the geometry and topology of the problem can undergo severe changes. In this work, a short outline of the PFEM-algorithm is given, which is followed by a detailed description of the involved operations. The -shape method, which is used to track the topology, is explained and tested by a simple example. Also the kinematics and a suitable finite element formulation are introduced. To validate the method simple settings without topological changes are considered and compared to the standard finite element method for large deformations. To examine the performance of the method, when dealing with separating material, a tensile loading is applied to a notched plate. This investigation includes a numerical analysis of the different meshing parameters, and the numerical convergence is studied. With regard to the cutting simulation it is found that only a sufficiently large number of particles (and thus a rather fine finite element discretisation) leads to converged results of process parameters, such as the cutting force.

Finite element based model predictive control for active vibration suppression of a one-link flexible manipulator.

PubMed

Dubay, Rickey; Hassan, Marwan; Li, Chunying; Charest, Meaghan

2014-09-01

This paper presents a unique approach for active vibration control of a one-link flexible manipulator. The method combines a finite element model of the manipulator and an advanced model predictive controller to suppress vibration at its tip. This hybrid methodology improves significantly over the standard application of a predictive controller for vibration control. The finite element model used in place of standard modelling in the control algorithm provides a more accurate prediction of dynamic behavior, resulting in enhanced control. Closed loop control experiments were performed using the flexible manipulator, instrumented with strain gauges and piezoelectric actuators. In all instances, experimental and simulation results demonstrate that the finite element based predictive controller provides improved active vibration suppression in comparison with using a standard predictive control strategy. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

User-Defined Material Model for Progressive Failure Analysis

NASA Technical Reports Server (NTRS)

Knight, Norman F. Jr.; Reeder, James R. (Technical Monitor)

2006-01-01

An overview of different types of composite material system architectures and a brief review of progressive failure material modeling methods used for structural analysis including failure initiation and material degradation are presented. Different failure initiation criteria and material degradation models are described that define progressive failure formulations. These progressive failure formulations are implemented in a user-defined material model (or UMAT) for use with the ABAQUS/Standard1 nonlinear finite element analysis tool. The failure initiation criteria include the maximum stress criteria, maximum strain criteria, the Tsai-Wu failure polynomial, and the Hashin criteria. The material degradation model is based on the ply-discounting approach where the local material constitutive coefficients are degraded. Applications and extensions of the progressive failure analysis material model address two-dimensional plate and shell finite elements and three-dimensional solid finite elements. Implementation details and use of the UMAT subroutine are described in the present paper. Parametric studies for composite structures are discussed to illustrate the features of the progressive failure modeling methods that have been implemented.

Data Modeling Using Finite Differences

ERIC Educational Resources Information Center

Rhoads, Kathryn; Mendoza Epperson, James A.

2017-01-01

The Common Core State Standards for Mathematics (CCSSM) states that high school students should be able to recognize patterns of growth in linear, quadratic, and exponential functions and construct such functions from tables of data (CCSSI 2010). In their work with practicing secondary teachers, the authors found that teachers may make some tacit…

Accurate finite difference methods for time-harmonic wave propagation

NASA Technical Reports Server (NTRS)

Harari, Isaac; Turkel, Eli

1994-01-01

Finite difference methods for solving problems of time-harmonic acoustics are developed and analyzed. Multidimensional inhomogeneous problems with variable, possibly discontinuous, coefficients are considered, accounting for the effects of employing nonuniform grids. A weighted-average representation is less sensitive to transition in wave resolution (due to variable wave numbers or nonuniform grids) than the standard pointwise representation. Further enhancement in method performance is obtained by basing the stencils on generalizations of Pade approximation, or generalized definitions of the derivative, reducing spurious dispersion, anisotropy and reflection, and by improving the representation of source terms. The resulting schemes have fourth-order accurate local truncation error on uniform grids and third order in the nonuniform case. Guidelines for discretization pertaining to grid orientation and resolution are presented.

The Relation of Finite Element and Finite Difference Methods

NASA Technical Reports Server (NTRS)

Vinokur, M.

1976-01-01

Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.

High performance computation of radiative transfer equation using the finite element method

NASA Astrophysics Data System (ADS)

Badri, M. A.; Jolivet, P.; Rousseau, B.; Favennec, Y.

2018-05-01

This article deals with an efficient strategy for numerically simulating radiative transfer phenomena using distributed computing. The finite element method alongside the discrete ordinate method is used for spatio-angular discretization of the monochromatic steady-state radiative transfer equation in an anisotropically scattering media. Two very different methods of parallelization, angular and spatial decomposition methods, are presented. To do so, the finite element method is used in a vectorial way. A detailed comparison of scalability, performance, and efficiency on thousands of processors is established for two- and three-dimensional heterogeneous test cases. Timings show that both algorithms scale well when using proper preconditioners. It is also observed that our angular decomposition scheme outperforms our domain decomposition method. Overall, we perform numerical simulations at scales that were previously unattainable by standard radiative transfer equation solvers.

Finite element predictions of active buckling control of stiffened panels

NASA Astrophysics Data System (ADS)

Thompson, Danniella M.; Griffin, O. H., Jr.

1993-04-01

Materials systems and structures that can respond 'intelligently' to their environment are currently being proposed and investigated. A series of finite element analyses was performed to investigate the potential for active buckling control of two different stiffened panels by embedded shape memory alloy (SMA) rods. Changes in the predicted buckling load increased with the magnitude of the actuation level for a given structural concept. Increasing the number of actuators for a given concept yielded greater predicted increases in buckling load. Considerable control authority was generated with a small number of actuators, with greater authority demonstrated for those structural concepts where the activated SMA rods could develop greater forces and moments on the structure. Relatively simple and inexpensive analyses were performed with standard finite elements to determine such information, indicating the viability of these types of models for design purposes.

Quantum field-theoretical description of neutrino and neutral kaon oscillations

NASA Astrophysics Data System (ADS)

Volobuev, Igor P.

2018-05-01

It is shown that the neutrino and neutral kaon oscillation processes can be consistently described in quantum field theory using only plane waves of the mass eigenstates of neutrinos and neutral kaons. To this end, the standard perturbative S-matrix formalism is modified so that it can be used for calculating the amplitudes of the processes passing at finite distances and finite time intervals. The distance-dependent and time-dependent parts of the amplitudes of the neutrino and neutral kaon oscillation processes are calculated and the results turn out to be in accordance with those of the standard quantum mechanical description of these processes based on the notion of neutrino flavor states and neutral kaon states with definite strangeness. However, the physical picture of the phenomena changes radically: now, there are no oscillations of flavor or definite strangeness states, but, instead of it, there is interference of amplitudes due to different virtual mass eigenstates.

Finite difference computation of Casimir forces

NASA Astrophysics Data System (ADS)

Pinto, Fabrizio

2016-09-01

In this Invited paper, we begin by a historical introduction to provide a motivation for the classical problems of interatomic force computation and associated challenges. This analysis will lead us from early theoretical and experimental accomplishments to the integration of these fascinating interactions into the operation of realistic, next-generation micro- and nanodevices both for the advanced metrology of fundamental physical processes and in breakthrough industrial applications. Among several powerful strategies enabling vastly enhanced performance and entirely novel technological capabilities, we shall specifically consider Casimir force time-modulation and the adoption of non-trivial geometries. As to the former, the ability to alter the magnitude and sign of the Casimir force will be recognized as a crucial principle to implement thermodynamical nano-engines. As to the latter, we shall first briefly review various reported computational approaches. We shall then discuss the game-changing discovery, in the last decade, that standard methods of numerical classical electromagnetism can be retooled to formulate the problem of Casimir force computation in arbitrary geometries. This remarkable development will be practically illustrated by showing that such an apparently elementary method as standard finite-differencing can be successfully employed to numerically recover results known from the Lifshitz theory of dispersion forces in the case of interacting parallel-plane slabs. Other geometries will be also be explored and consideration given to the potential of non-standard finite-difference methods. Finally, we shall introduce problems at the computational frontier, such as those including membranes deformed by Casimir forces and the effects of anisotropic materials. Conclusions will highlight the dramatic transition from the enduring perception of this field as an exotic application of quantum electrodynamics to the recent demonstration of a human climbing vertically on smooth glass.

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.

Computational strategy for the solution of large strain nonlinear problems using the Wilkins explicit finite-difference approach

NASA Technical Reports Server (NTRS)

Hofmann, R.

1980-01-01

The STEALTH code system, which solves large strain, nonlinear continuum mechanics problems, was rigorously structured in both overall design and programming standards. The design is based on the theoretical elements of analysis while the programming standards attempt to establish a parallelism between physical theory, programming structure, and documentation. These features have made it easy to maintain, modify, and transport the codes. It has also guaranteed users a high level of quality control and quality assurance.

Curvilinear grids for WENO methods in astrophysical simulations

NASA Astrophysics Data System (ADS)

Grimm-Strele, H.; Kupka, F.; Muthsam, H. J.

2014-03-01

We investigate the applicability of curvilinear grids in the context of astrophysical simulations and WENO schemes. With the non-smooth mapping functions from Calhoun et al. (2008), we can tackle many astrophysical problems which were out of scope with the standard grids in numerical astrophysics. We describe the difficulties occurring when implementing curvilinear coordinates into our WENO code, and how we overcome them. We illustrate the theoretical results with numerical data. The WENO finite difference scheme works only for high Mach number flows and smooth mapping functions, whereas the finite volume scheme gives accurate results even for low Mach number flows and on non-smooth grids.

The Finite-Surface Method for incompressible flow: a step beyond staggered grid

NASA Astrophysics Data System (ADS)

Hokpunna, Arpiruk; Misaka, Takashi; Obayashi, Shigeru

2017-11-01

We present a newly developed higher-order finite surface method for the incompressible Navier-Stokes equations (NSE). This method defines the velocities as a surface-averaged value on the surfaces of the pressure cells. Consequently, the mass conservation on the pressure cells becomes an exact equation. The only things left to approximate is the momentum equation and the pressure at the new time step. At certain conditions, the exact mass conservation enables the explicit n-th order accurate NSE solver to be used with the pressure treatment that is two or four order less accurate without loosing the apparent convergence rate. This feature was not possible with finite volume of finite difference methods. We use Fourier analysis with a model spectrum to determine the condition and found that the range covers standard boundary layer flows. The formal convergence and the performance of the proposed scheme is compared with a sixth-order finite volume method. Finally, the accuracy and performance of the method is evaluated in turbulent channel flows. This work is partially funded by a research colloaboration from IFS, Tohoku university and ASEAN+3 funding scheme from CMUIC, Chiang Mai University.

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for the Convective Wave Equation

NASA Technical Reports Server (NTRS)

Baumeister, K. J.; Kreider, K. L.

1996-01-01

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in ducts. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Experimental and numerical investigation of strain rate effect on low cycle fatigue behaviour of AA 5754 alloy

NASA Astrophysics Data System (ADS)

Kumar, P.; Singh, A.

2018-04-01

The present study deals with evaluation of low cycle fatigue (LCF) behavior of aluminum alloy 5754 (AA 5754) at different strain rates. This alloy has magnesium (Mg) as main alloying element (Al-Mg alloy) which makes this alloy suitable for Marines and Cryogenics applications. The testing procedure and specimen preparation are guided by ASTM E606 standard. The tests are performed at 0.5% strain amplitude with three different strain rates i.e. 0.5×10-3 sec-1, 1×10-3 sec-1 and 2×10-3 sec-1 thus the frequency of tests vary accordingly. The experimental results show that there is significant decrease in the fatigue life with the increase in strain rate. LCF behavior of AA 5754 is also simulated at different strain rates by finite element method. Chaboche kinematic hardening cyclic plasticity model is used for simulating the hardening behavior of the material. Axisymmetric finite element model is created to reduce the computational cost of the simulation. The material coefficients used for “Chaboche Model” are determined by experimentally obtained stabilized hysteresis loop. The results obtained from finite element simulation are compared with those obtained through LCF experiments.

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for Aircraft Acoustic Nacelle Design

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1996-01-01

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Discrete conservation laws and the convergence of long time simulations of the mkdv equation

NASA Astrophysics Data System (ADS)

Gorria, C.; Alejo, M. A.; Vega, L.

2013-02-01

Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solutions present a structural instability which make difficult to approximate their evolution in long time intervals with enough accuracy. The standard numerical methods do not guarantee the convergence to the proper solution of the initial value problem and often fail by approaching solutions associated to different initial conditions. In this frame the numerical schemes that preserve the discrete invariants related to some conservation laws of this equation produce better results than the methods which only take care of a high consistency order. Pseudospectral spatial discretization appear as the most robust of the numerical methods, but finite difference schemes are useful in order to analyze the rule played by the conservation of the invariants in the convergence.

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.

Skewness and kurtosis analysis for non-Gaussian distributions

NASA Astrophysics Data System (ADS)

Celikoglu, Ahmet; Tirnakli, Ugur

2018-06-01

In this paper we address a number of pitfalls regarding the use of kurtosis as a measure of deviations from the Gaussian. We treat kurtosis in both its standard definition and that which arises in q-statistics, namely q-kurtosis. We have recently shown that the relation proposed by Cristelli et al. (2012) between skewness and kurtosis can only be verified for relatively small data sets, independently of the type of statistics chosen; however it fails for sufficiently large data sets, if the fourth moment of the distribution is finite. For infinite fourth moments, kurtosis is not defined as the size of the data set tends to infinity. For distributions with finite fourth moments, the size, N, of the data set for which the standard kurtosis saturates to a fixed value, depends on the deviation of the original distribution from the Gaussian. Nevertheless, using kurtosis as a criterion for deciding which distribution deviates further from the Gaussian can be misleading for small data sets, even for finite fourth moment distributions. Going over to q-statistics, we find that although the value of q-kurtosis is finite in the range of 0 < q < 3, this quantity is not useful for comparing different non-Gaussian distributed data sets, unless the appropriate q value, which truly characterizes the data set of interest, is chosen. Finally, we propose a method to determine the correct q value and thereby to compute the q-kurtosis of q-Gaussian distributed data sets.

Transient finite element modeling of functional electrical stimulation.

PubMed

Filipovic, Nenad D; Peulic, Aleksandar S; Zdravkovic, Nebojsa D; Grbovic-Markovic, Vesna M; Jurisic-Skevin, Aleksandra J

2011-03-01

Transcutaneous functional electrical stimulation is commonly used for strengthening muscle. However, transient effects during stimulation are not yet well explored. The effect of an amplitude change of the stimulation can be described by static model, but there is no differency for different pulse duration. The aim of this study is to present the finite element (FE) model of a transient electrical stimulation on the forearm. Discrete FE equations were derived by using a standard Galerkin procedure. Different tissue conductive and dielectric properties are fitted using least square method and trial and error analysis from experimental measurement. This study showed that FE modeling of electrical stimulation can give the spatial-temporal distribution of applied current in the forearm. Three different cases were modeled with the same geometry but with different input of the current pulse, in order to fit the tissue properties by using transient FE analysis. All three cases were compared with experimental measurements of intramuscular voltage on one volunteer.

Tools for Designing and Analyzing Structures

NASA Technical Reports Server (NTRS)

Luz, Paul L.

2005-01-01

Structural Design and Analysis Toolset is a collection of approximately 26 Microsoft Excel spreadsheet programs, each of which performs calculations within a different subdiscipline of structural design and analysis. These programs present input and output data in user-friendly, menu-driven formats. Although these programs cannot solve complex cases like those treated by larger finite element codes, these programs do yield quick solutions to numerous common problems more rapidly than the finite element codes, thereby making it possible to quickly perform multiple preliminary analyses - e.g., to establish approximate limits prior to detailed analyses by the larger finite element codes. These programs perform different types of calculations, as follows: 1. determination of geometric properties for a variety of standard structural components; 2. analysis of static, vibrational, and thermal- gradient loads and deflections in certain structures (mostly beams and, in the case of thermal-gradients, mirrors); 3. kinetic energies of fans; 4. detailed analysis of stress and buckling in beams, plates, columns, and a variety of shell structures; and 5. temperature dependent properties of materials, including figures of merit that characterize strength, stiffness, and deformation response to thermal gradients

Turbine Engine Research Center (TERC) Data System Enhancement and Test Article Evaluation. Delivery Order 0002: TERC Aeromechanical Characterization

DTIC Science & Technology

2005-06-01

test, the entire turbulence model was changed from standard k- epsilon to Spalart- Allmaras. Using these different tools of turbulence models, a few...this research, leaving only pre-existing finite element models to be used. At some point a NASTRAN model was developed for vibrations analysis but

Simulated BRDF based on measured surface topography of metal

NASA Astrophysics Data System (ADS)

Yang, Haiyue; Haist, Tobias; Gronle, Marc; Osten, Wolfgang

2017-06-01

The radiative reflective properties of a calibration standard rough surface were simulated by ray tracing and the Finite-difference time-domain (FDTD) method. The simulation results have been used to compute the reflectance distribution functions (BRDF) of metal surfaces and have been compared with experimental measurements. The experimental and simulated results are in good agreement.

Simulation of one-sided heating of boiler unit membrane-type water walls

NASA Astrophysics Data System (ADS)

Kurepin, M. P.; Serbinovskiy, M. Yu.

2017-03-01

This study describes the results of simulation of the temperature field and the stress-strain state of membrane-type gastight water walls of boiler units using the finite element method. The methods of analytical and standard calculation of one-sided heating of fin-tube water walls by a radiative heat flux are analyzed. The methods and software for input data calculation in the finite-element simulation, including thermoelastic moments in welded panels that result from their one-sided heating, are proposed. The method and software modules are used for water wall simulation using ANSYS. The results of simulation of the temperature field, stress field, deformations and displacement of the membrane-type panel for the boiler furnace water wall using the finite-element method, as well as the results of calculation of the panel tube temperature, stresses and deformations using the known methods, are presented. The comparison of the known experimental results on heating and bending by given moments of membrane-type water walls and numerical simulations is performed. It is demonstrated that numerical results agree with high accuracy with the experimental data. The relative temperature difference does not exceed 1%. The relative difference of the experimental fin mutual turning angle caused by one-sided heating by radiative heat flux and the results obtained in the finite element simulation does not exceed 8.5% for nondisplaced fins and 7% for fins with displacement. The same difference for the theoretical results and the simulation using the finite-element method does not exceed 3% and 7.1%, respectively. The proposed method and software modules for simulation of the temperature field and stress-strain state of the water walls are verified and the feasibility of their application in practical design is proven.

Electromagnetic plasma simulation in realistic geometries

NASA Astrophysics Data System (ADS)

Brandon, S.; Ambrosiano, J. J.; Nielsen, D.

1991-08-01

Particle-in-Cell (PIC) calculations have become an indispensable tool to model the nonlinear collective behavior of charged particle species in electromagnetic fields. Traditional finite difference codes, such as CONDOR (2-D) and ARGUS (3-D), are used extensively to design experiments and develop new concepts. A wide variety of physical processes can be modeled simply and efficiently by these codes. However, experiments have become more complex. Geometrical shapes and length scales are becoming increasingly more difficult to model. Spatial resolution requirements for the electromagnetic calculation force large grids and small time steps. Many hours of CRAY YMP time may be required to complete 2-D calculation -- many more for 3-D calculations. In principle, the number of mesh points and particles need only to be increased until all relevant physical processes are resolved. In practice, the size of a calculation is limited by the computer budget. As a result, experimental design is being limited by the ability to calculate, not by the experimenters ingenuity or understanding of the physical processes involved. Several approaches to meet these computational demands are being pursued. Traditional PIC codes continue to be the major design tools. These codes are being actively maintained, optimized, and extended to handle large and more complex problems. Two new formulations are being explored to relax the geometrical constraints of the finite difference codes. A modified finite volume test code, TALUS, uses a data structure compatible with that of standard finite difference meshes. This allows a basic conformal boundary/variable grid capability to be retrofitted to CONDOR. We are also pursuing an unstructured grid finite element code, MadMax. The unstructured mesh approach provides maximum flexibility in the geometrical model while also allowing local mesh refinement.

Recurrent Artificial Neural Networks and Finite State Natural Language Processing.

ERIC Educational Resources Information Center

Moisl, Hermann

It is argued that pessimistic assessments of the adequacy of artificial neural networks (ANNs) for natural language processing (NLP) on the grounds that they have a finite state architecture are unjustified, and that their adequacy in this regard is an empirical issue. First, arguments that counter standard objections to finite state NLP on the…

Flame trench analysis of NLS vehicles

NASA Technical Reports Server (NTRS)

Zeytinoglu, Nuri

1993-01-01

The present study takes the initial steps of establishing a better flame trench design criteria for future National Launch System vehicles. A three-dimensional finite element computer model for predicting the transient thermal and structural behavior of the flame trench walls was developed using both I-DEAS and MSC/NASTRAN software packages. The results of JANNAF Standardized Plume flowfield calculations of sea-level exhaust plume of the Space Shuttle Main Engine (SSME), Space Transportation Main Engine (STME), and Advanced Solid Rocket Motors (ASRM) were analyzed for different axial distances. The results of sample calculations, using the developed finite element model, are included. The further suggestions are also reported for enhancing the overall analysis of the flame trench model.

[Research progress on mechanical performance evaluation of artificial intervertebral disc].

PubMed

Li, Rui; Wang, Song; Liao, Zhenhua; Liu, Weiqiang

2018-03-01

The mechanical properties of artificial intervertebral disc (AID) are related to long-term reliability of prosthesis. There are three testing methods involved in the mechanical performance evaluation of AID based on different tools: the testing method using mechanical simulator, in vitro specimen testing method and finite element analysis method. In this study, the testing standard, testing equipment and materials of AID were firstly introduced. Then, the present status of AID static mechanical properties test (static axial compression, static axial compression-shear), dynamic mechanical properties test (dynamic axial compression, dynamic axial compression-shear), creep and stress relaxation test, device pushout test, core pushout test, subsidence test, etc. were focused on. The experimental techniques using in vitro specimen testing method and testing results of available artificial discs were summarized. The experimental methods and research status of finite element analysis were also summarized. Finally, the research trends of AID mechanical performance evaluation were forecasted. The simulator, load, dynamic cycle, motion mode, specimen and test standard would be important research fields in the future.

A well-balanced meshless tsunami propagation and inundation model

NASA Astrophysics Data System (ADS)

Brecht, Rüdiger; Bihlo, Alexander; MacLachlan, Scott; Behrens, Jörn

2018-05-01

We present a novel meshless tsunami propagation and inundation model. We discretize the nonlinear shallow-water equations using a well-balanced scheme relying on radial basis function based finite differences. For the inundation model, radial basis functions are used to extrapolate the dry region from nearby wet points. Numerical results against standard one- and two-dimensional benchmarks are presented.

Quantifying Cartilage Contact Modulus, Tension Modulus, and Permeability With Hertzian Biphasic Creep

PubMed Central

Moore, A. C.; DeLucca, J. F.; Elliott, D. M.; Burris, D. L.

2016-01-01

This paper describes a new method, based on a recent analytical model (Hertzian biphasic theory (HBT)), to simultaneously quantify cartilage contact modulus, tension modulus, and permeability. Standard Hertzian creep measurements were performed on 13 osteochondral samples from three mature bovine stifles. Each creep dataset was fit for material properties using HBT. A subset of the dataset (N = 4) was also fit using Oyen's method and FEBio, an open-source finite element package designed for soft tissue mechanics. The HBT method demonstrated statistically significant sensitivity to differences between cartilage from the tibial plateau and cartilage from the femoral condyle. Based on the four samples used for comparison, no statistically significant differences were detected between properties from the HBT and FEBio methods. While the finite element method is considered the gold standard for analyzing this type of contact, the expertise and time required to setup and solve can be prohibitive, especially for large datasets. The HBT method agreed quantitatively with FEBio but also offers ease of use by nonexperts, rapid solutions, and exceptional fit quality (R2 = 0.999 ± 0.001, N = 13). PMID:27536012

Comparison of Damage Path Predictions for Composite Laminates by Explicit and Standard Finite Element Analysis Tools

NASA Technical Reports Server (NTRS)

Bogert, Philip B.; Satyanarayana, Arunkumar; Chunchu, Prasad B.

2006-01-01

Splitting, ultimate failure load and the damage path in center notched composite specimens subjected to in-plane tension loading are predicted using progressive failure analysis methodology. A 2-D Hashin-Rotem failure criterion is used in determining intra-laminar fiber and matrix failures. This progressive failure methodology has been implemented in the Abaqus/Explicit and Abaqus/Standard finite element codes through user written subroutines "VUMAT" and "USDFLD" respectively. A 2-D finite element model is used for predicting the intra-laminar damages. Analysis results obtained from the Abaqus/Explicit and Abaqus/Standard code show good agreement with experimental results. The importance of modeling delamination in progressive failure analysis methodology is recognized for future studies. The use of an explicit integration dynamics code for simple specimen geometry and static loading establishes a foundation for future analyses where complex loading and nonlinear dynamic interactions of damage and structure will necessitate it.

On the mechanics of growing thin biological membranes

NASA Astrophysics Data System (ADS)

Rausch, Manuel K.; Kuhl, Ellen

2014-02-01

Despite their seemingly delicate appearance, thin biological membranes fulfill various crucial roles in the human body and can sustain substantial mechanical loads. Unlike engineering structures, biological membranes are able to grow and adapt to changes in their mechanical environment. Finite element modeling of biological growth holds the potential to better understand the interplay of membrane form and function and to reliably predict the effects of disease or medical intervention. However, standard continuum elements typically fail to represent thin biological membranes efficiently, accurately, and robustly. Moreover, continuum models are typically cumbersome to generate from surface-based medical imaging data. Here we propose a computational model for finite membrane growth using a classical midsurface representation compatible with standard shell elements. By assuming elastic incompressibility and membrane-only growth, the model a priori satisfies the zero-normal stress condition. To demonstrate its modular nature, we implement the membrane growth model into the general-purpose non-linear finite element package Abaqus/Standard using the concept of user subroutines. To probe efficiently and robustness, we simulate selected benchmark examples of growing biological membranes under different loading conditions. To demonstrate the clinical potential, we simulate the functional adaptation of a heart valve leaflet in ischemic cardiomyopathy. We believe that our novel approach will be widely applicable to simulate the adaptive chronic growth of thin biological structures including skin membranes, mucous membranes, fetal membranes, tympanic membranes, corneoscleral membranes, and heart valve membranes. Ultimately, our model can be used to identify diseased states, predict disease evolution, and guide the design of interventional or pharmaceutic therapies to arrest or revert disease progression.

On the mechanics of growing thin biological membranes

PubMed Central

Rausch, Manuel K.; Kuhl, Ellen

2013-01-01

Despite their seemingly delicate appearance, thin biological membranes fulfill various crucial roles in the human body and can sustain substantial mechanical loads. Unlike engineering structures, biological membranes are able to grow and adapt to changes in their mechanical environment. Finite element modeling of biological growth holds the potential to better understand the interplay of membrane form and function and to reliably predict the effects of disease or medical intervention. However, standard continuum elements typically fail to represent thin biological membranes efficiently, accurately, and robustly. Moreover, continuum models are typically cumbersome to generate from surface-based medical imaging data. Here we propose a computational model for finite membrane growth using a classical midsurface representation compatible with standard shell elements. By assuming elastic incompressibility and membrane-only growth, the model a priori satisfies the zero-normal stress condition. To demonstrate its modular nature, we implement the membrane growth model into the general-purpose non-linear finite element package Abaqus/Standard using the concept of user subroutines. To probe efficiently and robustness, we simulate selected benchmark examples of growing biological membranes under different loading conditions. To demonstrate the clinical potential, we simulate the functional adaptation of a heart valve leaflet in ischemic cardiomyopathy. We believe that our novel approach will be widely applicable to simulate the adaptive chronic growth of thin biological structures including skin membranes, mucous membranes, fetal membranes, tympanic membranes, corneoscleral membranes, and heart valve membranes. Ultimately, our model can be used to identify diseased states, predict disease evolution, and guide the design of interventional or pharmaceutic therapies to arrest or revert disease progression. PMID:24563551

Improving a complex finite-difference ground water flow model through the use of an analytic element screening model

USGS Publications Warehouse

Hunt, R.J.; Anderson, M.P.; Kelson, V.A.

1998-01-01

This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

NASA Astrophysics Data System (ADS)

Gyrya, V.; Lipnikov, K.

2017-11-01

We present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, we observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

DOE PAGES

Gyrya, V.; Lipnikov, K.

2017-07-18

Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, wemore » observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.« less

The mimetic finite difference method for the Landau–Lifshitz equation

DOE PAGES

Kim, Eugenia Hail; Lipnikov, Konstantin Nikolayevich

2017-01-01

The Landau–Lifshitz equation describes the dynamics of the magnetization inside ferromagnetic materials. This equation is highly nonlinear and has a non-convex constraint (the magnitude of the magnetization is constant) which poses interesting challenges in developing numerical methods. We develop and analyze explicit and implicit mimetic finite difference schemes for this equation. These schemes work on general polytopal meshes which provide enormous flexibility to model magnetic devices with various shapes. A projection on the unit sphere is used to preserve the magnitude of the magnetization. We also provide a proof that shows the exchange energy is decreasing in certain conditions. Themore » developed schemes are tested on general meshes that include distorted and randomized meshes. As a result, the numerical experiments include a test proposed by the National Institute of Standard and Technology and a test showing formation of domain wall structures in a thin film.« less

A 3D finite-difference BiCG iterative solver with the Fourier-Jacobi preconditioner for the anisotropic EIT/EEG forward problem.

PubMed

Turovets, Sergei; Volkov, Vasily; Zherdetsky, Aleksej; Prakonina, Alena; Malony, Allen D

2014-01-01

The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique.

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

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

Gyrya, V.; Lipnikov, K.

Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, wemore » observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.« less

The mimetic finite difference method for the Landau–Lifshitz equation

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

Kim, Eugenia Hail; Lipnikov, Konstantin Nikolayevich

The Landau–Lifshitz equation describes the dynamics of the magnetization inside ferromagnetic materials. This equation is highly nonlinear and has a non-convex constraint (the magnitude of the magnetization is constant) which poses interesting challenges in developing numerical methods. We develop and analyze explicit and implicit mimetic finite difference schemes for this equation. These schemes work on general polytopal meshes which provide enormous flexibility to model magnetic devices with various shapes. A projection on the unit sphere is used to preserve the magnitude of the magnetization. We also provide a proof that shows the exchange energy is decreasing in certain conditions. Themore » developed schemes are tested on general meshes that include distorted and randomized meshes. As a result, the numerical experiments include a test proposed by the National Institute of Standard and Technology and a test showing formation of domain wall structures in a thin film.« less

Modeling Sound Propagation Through Non-Axisymmetric Jets

NASA Technical Reports Server (NTRS)

Leib, Stewart J.

2014-01-01

A method for computing the far-field adjoint Green's function of the generalized acoustic analogy equations under a locally parallel mean flow approximation is presented. The method is based on expanding the mean-flow-dependent coefficients in the governing equation and the scalar Green's function in truncated Fourier series in the azimuthal direction and a finite difference approximation in the radial direction in circular cylindrical coordinates. The combined spectral/finite difference method yields a highly banded system of algebraic equations that can be efficiently solved using a standard sparse system solver. The method is applied to test cases, with mean flow specified by analytical functions, corresponding to two noise reduction concepts of current interest: the offset jet and the fluid shield. Sample results for the Green's function are given for these two test cases and recommendations made as to the use of the method as part of a RANS-based jet noise prediction code.

High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains

NASA Technical Reports Server (NTRS)

Fisher, Travis C.; Carpenter, Mark H.

2013-01-01

Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.

Numerical simulation of conservation laws

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; To, Wai-Ming

1992-01-01

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially from the well established methods, i.e., finite difference, finite volume, finite element and spectral methods, in both concept and methodology. The key features of the current scheme include: (1) direct discretization of the integral forms of conservation laws, (2) treating space and time on the same footing, (3) flux conservation in space and time, and (4) unified treatment of the convection and diffusion fluxes. The model equation considered in the initial study is the standard one dimensional unsteady constant-coefficient convection-diffusion equation. In a stability study, it is shown that the principal and spurious amplification factors of the current scheme, respectively, are structurally similar to those of the leapfrog/DuFort-Frankel scheme. As a result, the current scheme has no numerical diffusion in the special case of pure convection and is unconditionally stable in the special case of pure diffusion. Assuming smooth initial data, it will be shown theoretically and numerically that, by using an easily determined optimal time step, the accuracy of the current scheme may reach a level which is several orders of magnitude higher than that of the MacCormack scheme, with virtually identical operation count.

The accurate solution of Poisson's equation by expansion in Chebyshev polynomials

NASA Technical Reports Server (NTRS)

Haidvogel, D. B.; Zang, T.

1979-01-01

A Chebyshev expansion technique is applied to Poisson's equation on a square with homogeneous Dirichlet boundary conditions. The spectral equations are solved in two ways - by alternating direction and by matrix diagonalization methods. Solutions are sought to both oscillatory and mildly singular problems. The accuracy and efficiency of the Chebyshev approach compare favorably with those of standard second- and fourth-order finite-difference methods.

An efficient numerical technique for calculating thermal spreading resistance

NASA Technical Reports Server (NTRS)

Gale, E. H., Jr.

1977-01-01

An efficient numerical technique for solving the equations resulting from finite difference analyses of fields governed by Poisson's equation is presented. The method is direct (noniterative)and the computer work required varies with the square of the order of the coefficient matrix. The computational work required varies with the cube of this order for standard inversion techniques, e.g., Gaussian elimination, Jordan, Doolittle, etc.

Comparison of FDNS liquid rocket engine plume computations with SPF/2

NASA Technical Reports Server (NTRS)

Kumar, G. N.; Griffith, D. O., II; Warsi, S. A.; Seaford, C. M.

1993-01-01

Prediction of a plume's shape and structure is essential to the evaluation of base region environments. The JANNAF standard plume flowfield analysis code SPF/2 predicts plumes well, but cannot analyze base regions. Full Navier-Stokes CFD codes can calculate both zones; however, before they can be used, they must be validated. The CFD code FDNS3D (Finite Difference Navier-Stokes Solver) was used to analyze the single plume of a Space Transportation Main Engine (STME) and comparisons were made with SPF/2 computations. Both frozen and finite rate chemistry models were employed as well as two turbulence models in SPF/2. The results indicate that FDNS3D plume computations agree well with SPF/2 predictions for liquid rocket engine plumes.

Suggested notation conventions for rotational seismology

USGS Publications Warehouse

Evans, J.R.

2009-01-01

We note substantial inconsistency among authors discussing rotational motions observed with inertial seismic sensors (and much more so in the broader topic of rotational phenomena). Working from physics and other precedents, we propose standard terminology and a preferred reference frame for inertial sensors (Fig. 1) that may be consistently used in discussions of both finite and infinitesimal observed rotational and translational motions in seismology and earthquake engineering. The scope of this article is limited to observations because there are significant differences in the analysis of finite and infinitesimal rotations, though such discussions should remain compatible with those presented here where possible. We recommend the general use of the notation conventions presented in this tutorial, and we recommend that any deviations or alternatives be explicitly defined.

The P1-RKDG method for two-dimensional Euler equations of gas dynamics

NASA Technical Reports Server (NTRS)

Cockburn, Bernardo; Shu, Chi-Wang

1991-01-01

A class of nonlinearly stable Runge-Kutta local projection discontinuous Galerkin (RKDG) finite element methods for conservation laws is investigated. Two dimensional Euler equations for gas dynamics are solved using P1 elements. The generalization of the local projections, which for scalar nonlinear conservation laws was designed to satisfy a local maximum principle, to systems of conservation laws such as the Euler equations of gas dynamics using local characteristic decompositions is discussed. Numerical examples include the standard regular shock reflection problem, the forward facing step problem, and the double Mach reflection problem. These preliminary numerical examples are chosen to show the capacity of the approach to obtain nonlinearly stable results comparable with the modern nonoscillatory finite difference methods.

Mixed-RKDG Finite Element Methods for the 2-D Hydrodynamic Model for Semiconductor Device Simulation

DOE PAGES

Chen, Zhangxin; Cockburn, Bernardo; Jerome, Joseph W.; ...

1995-01-01

In this paper we introduce a new method for numerically solving the equations of the hydrodynamic model for semiconductor devices in two space dimensions. The method combines a standard mixed finite element method, used to obtain directly an approximation to the electric field, with the so-called Runge-Kutta Discontinuous Galerkin (RKDG) method, originally devised for numerically solving multi-dimensional hyperbolic systems of conservation laws, which is applied here to the convective part of the equations. Numerical simulations showing the performance of the new method are displayed, and the results compared with those obtained by using Essentially Nonoscillatory (ENO) finite difference schemes. Frommore » the perspective of device modeling, these methods are robust, since they are capable of encompassing broad parameter ranges, including those for which shock formation is possible. The simulations presented here are for Gallium Arsenide at room temperature, but we have tested them much more generally with considerable success.« less

Three-dimensional finite element modelling of muscle forces during mastication.

PubMed

Röhrle, Oliver; Pullan, Andrew J

2007-01-01

This paper presents a three-dimensional finite element model of human mastication. Specifically, an anatomically realistic model of the masseter muscles and associated bones is used to investigate the dynamics of chewing. A motion capture system is used to track the jaw motion of a subject chewing standard foods. The three-dimensional nonlinear deformation of the masseter muscles are calculated via the finite element method, using the jaw motion data as boundary conditions. Motion-driven muscle activation patterns and a transversely isotropic material law, defined in a muscle-fibre coordinate system, are used in the calculations. Time-force relationships are presented and analysed with respect to different tasks during mastication, e.g. opening, closing, and biting, and are also compared to a more traditional one-dimensional model. The results strongly suggest that, due to the complex arrangement of muscle force directions, modelling skeletal muscles as conventional one-dimensional lines of action might introduce a significant source of error.

Efficient discretization in finite difference method

NASA Astrophysics Data System (ADS)

Rozos, Evangelos; Koussis, Antonis; Koutsoyiannis, Demetris

2015-04-01

Finite difference method (FDM) is a plausible and simple method for solving partial differential equations. The standard practice is to use an orthogonal discretization to form algebraic approximate formulations of the derivatives of the unknown function and a grid, much like raster maps, to represent the properties of the function domain. For example, for the solution of the groundwater flow equation, a raster map is required for the characterization of the discretization cells (flow cell, no-flow cell, boundary cell, etc.), and two raster maps are required for the hydraulic conductivity and the storage coefficient. Unfortunately, this simple approach to describe the topology comes along with the known disadvantages of the FDM (rough representation of the geometry of the boundaries, wasted computational resources in the unavoidable expansion of the grid refinement in all cells of the same column and row, etc.). To overcome these disadvantages, Hunt has suggested an alternative approach to describe the topology, the use of an array of neighbours. This limits the need for discretization nodes only for the representation of the boundary conditions and the flow domain. Furthermore, the geometry of the boundaries is described more accurately using a vector representation. Most importantly, graded meshes can be employed, which are capable of restricting grid refinement only in the areas of interest (e.g. regions where hydraulic head varies rapidly, locations of pumping wells, etc.). In this study, we test the Hunt approach against MODFLOW, a well established finite difference model, and the Finite Volume Method with Simplified Integration (FVMSI). The results of this comparison are examined and critically discussed.

A partially penalty immersed Crouzeix-Raviart finite element method for interface problems.

PubMed

An, Na; Yu, Xijun; Chen, Huanzhen; Huang, Chaobao; Liu, Zhongyan

2017-01-01

The elliptic equations with discontinuous coefficients are often used to describe the problems of the multiple materials or fluids with different densities or conductivities or diffusivities. In this paper we develop a partially penalty immersed finite element (PIFE) method on triangular grids for anisotropic flow models, in which the diffusion coefficient is a piecewise definite-positive matrix. The standard linear Crouzeix-Raviart type finite element space is used on non-interface elements and the piecewise linear Crouzeix-Raviart type immersed finite element (IFE) space is constructed on interface elements. The piecewise linear functions satisfying the interface jump conditions are uniquely determined by the integral averages on the edges as degrees of freedom. The PIFE scheme is given based on the symmetric, nonsymmetric or incomplete interior penalty discontinuous Galerkin formulation. The solvability of the method is proved and the optimal error estimates in the energy norm are obtained. Numerical experiments are presented to confirm our theoretical analysis and show that the newly developed PIFE method has optimal-order convergence in the [Formula: see text] norm as well. In addition, numerical examples also indicate that this method is valid for both the isotropic and the anisotropic elliptic interface problems.

A finite nonlinear hyper-viscoelastic model for soft biological tissues.

PubMed

Panda, Satish Kumar; Buist, Martin Lindsay

2018-03-01

Soft tissues exhibit highly nonlinear rate and time-dependent stress-strain behaviour. Strain and strain rate dependencies are often modelled using a hyperelastic model and a discrete (standard linear solid) or continuous spectrum (quasi-linear) viscoelastic model, respectively. However, these models are unable to properly capture the materials characteristics because hyperelastic models are unsuited for time-dependent events, whereas the common viscoelastic models are insufficient for the nonlinear and finite strain viscoelastic tissue responses. The convolution integral based models can demonstrate a finite viscoelastic response; however, their derivations are not consistent with the laws of thermodynamics. The aim of this work was to develop a three-dimensional finite hyper-viscoelastic model for soft tissues using a thermodynamically consistent approach. In addition, a nonlinear function, dependent on strain and strain rate, was adopted to capture the nonlinear variation of viscosity during a loading process. To demonstrate the efficacy and versatility of this approach, the model was used to recreate the experimental results performed on different types of soft tissues. In all the cases, the simulation results were well matched (R 2 ⩾0.99) with the experimental data. Copyright © 2018 Elsevier Ltd. All rights reserved.

Improving the Process of Adjusting the Parameters of Finite Element Models of Healthy Human Intervertebral Discs by the Multi-Response Surface Method.

PubMed

Gómez, Fátima Somovilla; Lorza, Rubén Lostado; Bobadilla, Marina Corral; García, Rubén Escribano

2017-09-21

The kinematic behavior of models that are based on the finite element method (FEM) for modeling the human body depends greatly on an accurate estimate of the parameters that define such models. This task is complex, and any small difference between the actual biomaterial model and the simulation model based on FEM can be amplified enormously in the presence of nonlinearities. The current paper attempts to demonstrate how a combination of the FEM and the MRS methods with desirability functions can be used to obtain the material parameters that are most appropriate for use in defining the behavior of Finite Element (FE) models of the healthy human lumbar intervertebral disc (IVD). The FE model parameters were adjusted on the basis of experimental data from selected standard tests (compression, flexion, extension, shear, lateral bending, and torsion) and were developed as follows: First, three-dimensional parameterized FE models were generated on the basis of the mentioned standard tests. Then, 11 parameters were selected to define the proposed parameterized FE models. For each of the standard tests, regression models were generated using MRS to model the six stiffness and nine bulges of the healthy IVD models that were created by changing the parameters of the FE models. The optimal combination of the 11 parameters was based on three different adjustment criteria. The latter, in turn, were based on the combination of stiffness and bulges that were obtained from the standard test FE simulations. The first adjustment criteria considered stiffness and bulges to be equally important in the adjustment of FE model parameters. The second adjustment criteria considered stiffness as most important, whereas the third considered the bulges to be most important. The proposed adjustment methods were applied to a medium-sized human IVD that corresponded to the L3-L4 lumbar level with standard dimensions of width = 50 mm, depth = 35 mm, and height = 10 mm. Agreement between the kinematic behavior that was obtained with the optimized parameters and that obtained from the literature demonstrated that the proposed method is a powerful tool with which to adjust healthy IVD FE models when there are many parameters, stiffnesses, and bulges to which the models must adjust.

Improving the Process of Adjusting the Parameters of Finite Element Models of Healthy Human Intervertebral Discs by the Multi-Response Surface Method

PubMed Central

Somovilla Gómez, Fátima

2017-01-01

The kinematic behavior of models that are based on the finite element method (FEM) for modeling the human body depends greatly on an accurate estimate of the parameters that define such models. This task is complex, and any small difference between the actual biomaterial model and the simulation model based on FEM can be amplified enormously in the presence of nonlinearities. The current paper attempts to demonstrate how a combination of the FEM and the MRS methods with desirability functions can be used to obtain the material parameters that are most appropriate for use in defining the behavior of Finite Element (FE) models of the healthy human lumbar intervertebral disc (IVD). The FE model parameters were adjusted on the basis of experimental data from selected standard tests (compression, flexion, extension, shear, lateral bending, and torsion) and were developed as follows: First, three-dimensional parameterized FE models were generated on the basis of the mentioned standard tests. Then, 11 parameters were selected to define the proposed parameterized FE models. For each of the standard tests, regression models were generated using MRS to model the six stiffness and nine bulges of the healthy IVD models that were created by changing the parameters of the FE models. The optimal combination of the 11 parameters was based on three different adjustment criteria. The latter, in turn, were based on the combination of stiffness and bulges that were obtained from the standard test FE simulations. The first adjustment criteria considered stiffness and bulges to be equally important in the adjustment of FE model parameters. The second adjustment criteria considered stiffness as most important, whereas the third considered the bulges to be most important. The proposed adjustment methods were applied to a medium-sized human IVD that corresponded to the L3–L4 lumbar level with standard dimensions of width = 50 mm, depth = 35 mm, and height = 10 mm. Agreement between the kinematic behavior that was obtained with the optimized parameters and that obtained from the literature demonstrated that the proposed method is a powerful tool with which to adjust healthy IVD FE models when there are many parameters, stiffnesses, and bulges to which the models must adjust. PMID:28934161

ICASE Semiannual Report, October 1, 1992 through March 31, 1993

DTIC Science & Technology

1993-06-01

NUMERICAL MATHEMATICS Saul Abarbanel Further results have been obtained regarding long time integration of high order compact finite difference schemes...overall accuracy. These problems are common to all numerical methods: finite differences , finite elements and spectral methods. It should be noted that...fourth order finite difference scheme. * In the same case, the D6 wavelets provide a sixth order finite difference , noncompact formula. * The wavelets

COMGEN - A PROGRAM FOR GENERATING FINITE ELEMENT MODELS OF COMPOSITE MATERIALS AT THE MICRO LEVEL (SGI IRIS VERSION)

NASA Technical Reports Server (NTRS)

Melis, M. E.

1994-01-01

A significant percentage of time spent in a typical finite element analysis is taken up in the modeling and assignment of loads and constraints. This process not only requires the analyst to be well-versed in the art of finite element modeling, but also demands familiarity with some sort of preprocessing software in order to complete the task expediently. COMGEN (COmposite Model GENerator) is an interactive FORTRAN program which can be used to create a wide variety of finite element models of continuous fiber composite materials at the micro level. It quickly generates batch or "session files" to be submitted to the finite element pre- and post-processor program, PATRAN. (PDA Engineering, Costa Mesa, CA.) In modeling a composite material, COMGEN assumes that its constituents can be represented by a "unit cell" of a fiber surrounded by matrix material. Two basic cell types are available. The first is a square packing arrangement where the fiber is positioned in the center of a square matrix cell. The second type, hexagonal packing, has the fiber centered in a hexagonal matrix cell. Different models can be created using combinations of square and hexagonal packing schemes. Variations include two- and three- dimensional cases, models with a fiber-matrix interface, and different constructions of unit cells. User inputs include fiber diameter and percent fiber-volume of the composite to be analyzed. In addition, various mesh densities, boundary conditions, and loads can be assigned to the models within COMGEN. The PATRAN program then uses a COMGEN session file to generate finite element models and their associated loads which can then be translated to virtually any finite element analysis code such as NASTRAN or MARC. COMGEN is written in FORTRAN 77 and has been implemented on DEC VAX series computers under VMS and SGI IRIS series workstations under IRIX. If the user has the PATRAN package available, the output can be graphically displayed. Without PATRAN, the output is tabular. The VAX VMS version is available on a 5.25 inch 360K MS-DOS format diskette (standard distribution media) or a 9-track 1600 BPI DEC VAX FILES-11 format magnetic tape, and it requires about 124K of main memory. The standard distribution media for the IRIS version is a .25 inch streaming magnetic tape cartridge in UNIX tar format. The memory requirement for the IRIS version is 627K. COMGEN was developed in 1990. DEC, VAX and VMS are trademarks of Digital Equipment Corporation. PATRAN is a registered trademark of PDA Engineering. SGI IRIS and IRIX are trademarks of Silicon Graphics, Inc. MS-DOS is a registered trademark of Microsoft Corporation. UNIX is a registered trademark of AT&T.

The Influence of Reconstruction Kernel on Bone Mineral and Strength Estimates Using Quantitative Computed Tomography and Finite Element Analysis.

PubMed

Michalski, Andrew S; Edwards, W Brent; Boyd, Steven K

2017-10-17

Quantitative computed tomography has been posed as an alternative imaging modality to investigate osteoporosis. We examined the influence of computed tomography convolution back-projection reconstruction kernels on the analysis of bone quantity and estimated mechanical properties in the proximal femur. Eighteen computed tomography scans of the proximal femur were reconstructed using both a standard smoothing reconstruction kernel and a bone-sharpening reconstruction kernel. Following phantom-based density calibration, we calculated typical bone quantity outcomes of integral volumetric bone mineral density, bone volume, and bone mineral content. Additionally, we performed finite element analysis in a standard sideways fall on the hip loading configuration. Significant differences for all outcome measures, except integral bone volume, were observed between the 2 reconstruction kernels. Volumetric bone mineral density measured using images reconstructed by the standard kernel was significantly lower (6.7%, p < 0.001) when compared with images reconstructed using the bone-sharpening kernel. Furthermore, the whole-bone stiffness and the failure load measured in images reconstructed by the standard kernel were significantly lower (16.5%, p < 0.001, and 18.2%, p < 0.001, respectively) when compared with the image reconstructed by the bone-sharpening kernel. These data suggest that for future quantitative computed tomography studies, a standardized reconstruction kernel will maximize reproducibility, independent of the use of a quantitative calibration phantom. Copyright © 2017 The International Society for Clinical Densitometry. Published by Elsevier Inc. All rights reserved.

The h-p Version of the Finite Element Method for Problems with Nonhomogeneous Essential Boundary Condition.

DTIC Science & Technology

1987-09-01

one commercial code based on the p and h-p version of the finite element, the program PROBE of NOETIC Technologies (St. Louis, MO). PROBE deals with two...Standards. o To be an international center of study and research for foreign students in numerical mathematics who are supported by foreign govern- ments or...ment agencies such as the National Bureau of Standards. o To be an international center of study and research for foreign students in numerical

Otto engine beyond its standard quantum limit.

PubMed

Leggio, Bruno; Antezza, Mauro

2016-02-01

We propose a quantum Otto cycle based on the properties of a two-level system in a realistic out-of-thermal-equilibrium electromagnetic field acting as its sole reservoir. This steady configuration is produced without the need of active control over the state of the environment, which is a noncoherent thermal radiation, sustained only by external heat supplied to macroscopic objects. Remarkably, even for nonideal finite-time transformations, it largely over-performs the standard ideal Otto cycle and asymptotically achieves unit efficiency at finite power.

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

Jones, J E; Vassilevski, P S; Woodward, C S

This paper provides extensions of an element agglomeration AMG method to nonlinear elliptic problems discretized by the finite element method on general unstructured meshes. The method constructs coarse discretization spaces and corresponding coarse nonlinear operators as well as their Jacobians. We introduce both standard (fairly quasi-uniformly coarsened) and non-standard (coarsened away) coarse meshes and respective finite element spaces. We use both kind of spaces in FAS type coarse subspace correction (or Schwarz) algorithms. Their performance is illustrated on a number of model problems. The coarsened away spaces seem to perform better than the standard spaces for problems with nonlinearities inmore » the principal part of the elliptic operator.« less

Computer-Aided Engineering of Semiconductor Integrated Circuits

DTIC Science & Technology

1979-07-01

equation using a five point finite difference approximation. Section 4.3.6 describes the numerical techniques and iterative algorithms which are used...neighbor points. This is generally referred to as a five point finite difference scheme on a rectangular grid, as described below. The finite difference ...problems in steady state have been analyzed by the finite difference method [4. 16 ] [4.17 3 or finite element method [4. 18 3, [4. 19 3 as reported last

Summary Report of Working Group 2: Computation

NASA Astrophysics Data System (ADS)

Stoltz, P. H.; Tsung, R. S.

2009-01-01

The working group on computation addressed three physics areas: (i) plasma-based accelerators (laser-driven and beam-driven), (ii) high gradient structure-based accelerators, and (iii) electron beam sources and transport [1]. Highlights of the talks in these areas included new models of breakdown on the microscopic scale, new three-dimensional multipacting calculations with both finite difference and finite element codes, and detailed comparisons of new electron gun models with standard models such as PARMELA. The group also addressed two areas of advances in computation: (i) new algorithms, including simulation in a Lorentz-boosted frame that can reduce computation time orders of magnitude, and (ii) new hardware architectures, like graphics processing units and Cell processors that promise dramatic increases in computing power. Highlights of the talks in these areas included results from the first large-scale parallel finite element particle-in-cell code (PIC), many order-of-magnitude speedup of, and details of porting the VPIC code to the Roadrunner supercomputer. The working group featured two plenary talks, one by Brian Albright of Los Alamos National Laboratory on the performance of the VPIC code on the Roadrunner supercomputer, and one by David Bruhwiler of Tech-X Corporation on recent advances in computation for advanced accelerators. Highlights of the talk by Albright included the first one trillion particle simulations, a sustained performance of 0.3 petaflops, and an eight times speedup of science calculations, including back-scatter in laser-plasma interaction. Highlights of the talk by Bruhwiler included simulations of 10 GeV accelerator laser wakefield stages including external injection, new developments in electromagnetic simulations of electron guns using finite difference and finite element approaches.

Summary Report of Working Group 2: Computation

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

Stoltz, P. H.; Tsung, R. S.

2009-01-22

The working group on computation addressed three physics areas: (i) plasma-based accelerators (laser-driven and beam-driven), (ii) high gradient structure-based accelerators, and (iii) electron beam sources and transport [1]. Highlights of the talks in these areas included new models of breakdown on the microscopic scale, new three-dimensional multipacting calculations with both finite difference and finite element codes, and detailed comparisons of new electron gun models with standard models such as PARMELA. The group also addressed two areas of advances in computation: (i) new algorithms, including simulation in a Lorentz-boosted frame that can reduce computation time orders of magnitude, and (ii) newmore » hardware architectures, like graphics processing units and Cell processors that promise dramatic increases in computing power. Highlights of the talks in these areas included results from the first large-scale parallel finite element particle-in-cell code (PIC), many order-of-magnitude speedup of, and details of porting the VPIC code to the Roadrunner supercomputer. The working group featured two plenary talks, one by Brian Albright of Los Alamos National Laboratory on the performance of the VPIC code on the Roadrunner supercomputer, and one by David Bruhwiler of Tech-X Corporation on recent advances in computation for advanced accelerators. Highlights of the talk by Albright included the first one trillion particle simulations, a sustained performance of 0.3 petaflops, and an eight times speedup of science calculations, including back-scatter in laser-plasma interaction. Highlights of the talk by Bruhwiler included simulations of 10 GeV accelerator laser wakefield stages including external injection, new developments in electromagnetic simulations of electron guns using finite difference and finite element approaches.« less

On the dynamics of approximating schemes for dissipative nonlinear equations

NASA Technical Reports Server (NTRS)

Jones, Donald A.

1993-01-01

Since one can rarely write down the analytical solutions to nonlinear dissipative partial differential equations (PDE's), it is important to understand whether, and in what sense, the behavior of approximating schemes to these equations reflects the true dynamics of the original equations. Further, because standard error estimates between approximations of the true solutions coming from spectral methods - finite difference or finite element schemes, for example - and the exact solutions grow exponentially in time, this analysis provides little value in understanding the infinite time behavior of a given approximating scheme. The notion of the global attractor has been useful in quantifying the infinite time behavior of dissipative PDEs, such as the Navier-Stokes equations. Loosely speaking, the global attractor is all that remains of a sufficiently large bounded set in phase space mapped infinitely forward in time under the evolution of the PDE. Though the attractor has been shown to have some nice properties - it is compact, connected, and finite dimensional, for example - it is in general quite complicated. Nevertheless, the global attractor gives a way to understand how the infinite time behavior of approximating schemes such as the ones coming from a finite difference, finite element, or spectral method relates to that of the original PDE. Indeed, one can often show that such approximations also have a global attractor. We therefore only need to understand how the structure of the attractor for the PDE behaves under approximation. This is by no means a trivial task. Several interesting results have been obtained in this direction. However, we will not go into the details. We mention here that approximations generally lose information about the system no matter how accurate they are. There are examples that show certain parts of the attractor may be lost by arbitrary small perturbations of the original equations.

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...

External Boundary Conditions for Three-Dimensional Problems of Computational Aerodynamics

NASA Technical Reports Server (NTRS)

Tsynkov, Semyon V.

1997-01-01

We consider an unbounded steady-state flow of viscous fluid over a three-dimensional finite body or configuration of bodies. For the purpose of solving this flow problem numerically, we discretize the governing equations (Navier-Stokes) on a finite-difference grid. The grid obviously cannot stretch from the body up to infinity, because the number of the discrete variables in that case would not be finite. Therefore, prior to the discretization we truncate the original unbounded flow domain by introducing some artificial computational boundary at a finite distance of the body. Typically, the artificial boundary is introduced in a natural way as the external boundary of the domain covered by the grid. The flow problem formulated only on the finite computational domain rather than on the original infinite domain is clearly subdefinite unless some artificial boundary conditions (ABC's) are specified at the external computational boundary. Similarly, the discretized flow problem is subdefinite (i.e., lacks equations with respect to unknowns) unless a special closing procedure is implemented at this artificial boundary. The closing procedure in the discrete case is called the ABC's as well. In this paper, we present an innovative approach to constructing highly accurate ABC's for three-dimensional flow computations. The approach extends our previous technique developed for the two-dimensional case; it employs the finite-difference counterparts to Calderon's pseudodifferential boundary projections calculated in the framework of the difference potentials method (DPM) by Ryaben'kii. The resulting ABC's appear spatially nonlocal but particularly easy to implement along with the existing solvers. The new boundary conditions have been successfully combined with the NASA-developed production code TLNS3D and used for the analysis of wing-shaped configurations in subsonic (including incompressible limit) and transonic flow regimes. As demonstrated by the computational experiments and comparisons with the standard (local) methods, the DPM-based ABC's allow one to greatly reduce the size of the computational domain while still maintaining high accuracy of the numerical solution. Moreover, they may provide for a noticeable increase of the convergence rate of multigrid iterations.

Revisiting Yasinsky and Henry`s benchmark using modern nodal codes

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

Feltus, M.A.; Becker, M.W.

1995-12-31

The numerical experiments analyzed by Yasinsky and Henry are quite trivial by comparison with today`s standards because they used the finite difference code WIGLE for their benchmark. Also, this problem is a simple slab (one-dimensional) case with no feedback mechanisms. This research attempts to obtain STAR (Ref. 2) and NEM (Ref. 3) code results in order to produce a more modern kinetics benchmark with results comparable WIGLE.

The order of the quantum chromodynamics transition predicted by the standard model of particle physics.

PubMed

Aoki, Y; Endrodi, G; Fodor, Z; Katz, S D; Szabó, K K

2006-10-12

Quantum chromodynamics (QCD) is the theory of the strong interaction, explaining (for example) the binding of three almost massless quarks into a much heavier proton or neutron--and thus most of the mass of the visible Universe. The standard model of particle physics predicts a QCD-related transition that is relevant for the evolution of the early Universe. At low temperatures, the dominant degrees of freedom are colourless bound states of hadrons (such as protons and pions). However, QCD is asymptotically free, meaning that at high energies or temperatures the interaction gets weaker and weaker, causing hadrons to break up. This behaviour underlies the predicted cosmological transition between the low-temperature hadronic phase and a high-temperature quark-gluon plasma phase (for simplicity, we use the word 'phase' to characterize regions with different dominant degrees of freedom). Despite enormous theoretical effort, the nature of this finite-temperature QCD transition (that is, first-order, second-order or analytic crossover) remains ambiguous. Here we determine the nature of the QCD transition using computationally demanding lattice calculations for physical quark masses. Susceptibilities are extrapolated to vanishing lattice spacing for three physical volumes, the smallest and largest of which differ by a factor of five. This ensures that a true transition should result in a dramatic increase of the susceptibilities. No such behaviour is observed: our finite-size scaling analysis shows that the finite-temperature QCD transition in the hot early Universe was not a real phase transition, but an analytic crossover (involving a rapid change, as opposed to a jump, as the temperature varied). As such, it will be difficult to find experimental evidence of this transition from astronomical observations.

Moisture Transport in Composites during Repair Work,

DTIC Science & Technology

1983-09-01

4 * FINITE DIFFERENCE EQUATIONS. .. . . .. . .. .. .. .. .. 6 INI I A ANBOUNAAYYCONDITIONS................ 7 REASONABLE FIRST...DURING DRYING AND CURING . . . ........ 9 5 CONVERGENCE OF FINITE DIFFERENCE METHOD USING DIFFERENT At . . .. 12 6 CONVERGENCE OF FDA METHOD FOR SAME At...transport we will use a finite difference approach, changing the Fickian equation to a finite number of linear algebraic equations that can be solved by

A direct Primitive Variable Recovery Scheme for hyperbolic conservative equations: The case of relativistic hydrodynamics.

PubMed

Aguayo-Ortiz, A; Mendoza, S; Olvera, D

2018-01-01

In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and "Rankine-Hugoniot" jump conditions. The time evolution is then computed using a forward finite difference scheme. This numerical technique evades the recovery of the primitive vector by solving an algebraic system of equations as it is often used and so, it generalises standard techniques to solve these kind of coupled systems. The article is presented bearing in mind special relativistic hydrodynamic numerical schemes with an added pedagogical view in the appendix section in order to easily comprehend the PVRS. We present the convergence of the method for standard shock-tube problems of special relativistic hydrodynamics and a graphical visualisation of the errors using the fluctuations of the numerical values with respect to exact analytic solutions. The PVRS circumvents the sometimes arduous computation that arises from standard numerical methods techniques, which obtain the desired primitive vector solution through an algebraic polynomial of the charges.

A direct Primitive Variable Recovery Scheme for hyperbolic conservative equations: The case of relativistic hydrodynamics

PubMed Central

Mendoza, S.; Olvera, D.

2018-01-01

In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and “Rankine-Hugoniot” jump conditions. The time evolution is then computed using a forward finite difference scheme. This numerical technique evades the recovery of the primitive vector by solving an algebraic system of equations as it is often used and so, it generalises standard techniques to solve these kind of coupled systems. The article is presented bearing in mind special relativistic hydrodynamic numerical schemes with an added pedagogical view in the appendix section in order to easily comprehend the PVRS. We present the convergence of the method for standard shock-tube problems of special relativistic hydrodynamics and a graphical visualisation of the errors using the fluctuations of the numerical values with respect to exact analytic solutions. The PVRS circumvents the sometimes arduous computation that arises from standard numerical methods techniques, which obtain the desired primitive vector solution through an algebraic polynomial of the charges. PMID:29659602

On the thermal efficiency of power cycles in finite time thermodynamics

NASA Astrophysics Data System (ADS)

Momeni, Farhang; Morad, Mohammad Reza; Mahmoudi, Ashkan

2016-09-01

The Carnot, Diesel, Otto, and Brayton power cycles are reconsidered endoreversibly in finite time thermodynamics (FTT). In particular, the thermal efficiency of these standard power cycles is compared to the well-known results in classical thermodynamics. The present analysis based on FTT modelling shows that a reduction in both the maximum and minimum temperatures of the cycle causes the thermal efficiency to increase. This is antithetical to the existing trend in the classical references. Under the assumption of endoreversibility, the relation between the efficiencies is also changed to {η }{{Carnot}}\\gt {η }{{Brayton}}\\gt {η }{{Diesel}}\\gt {η }{{Otto}}, which is again very different from the corresponding classical results. The present results benefit a better understanding of the important role of irreversibility on heat engines in classical thermodynamics.

Celeris: A GPU-accelerated open source software with a Boussinesq-type wave solver for real-time interactive simulation and visualization

NASA Astrophysics Data System (ADS)

Tavakkol, Sasan; Lynett, Patrick

2017-08-01

In this paper, we introduce an interactive coastal wave simulation and visualization software, called Celeris. Celeris is an open source software which needs minimum preparation to run on a Windows machine. The software solves the extended Boussinesq equations using a hybrid finite volume-finite difference method and supports moving shoreline boundaries. The simulation and visualization are performed on the GPU using Direct3D libraries, which enables the software to run faster than real-time. Celeris provides a first-of-its-kind interactive modeling platform for coastal wave applications and it supports simultaneous visualization with both photorealistic and colormapped rendering capabilities. We validate our software through comparison with three standard benchmarks for non-breaking and breaking waves.

Influence of Finite Element Software on Energy Release Rates Computed Using the Virtual Crack Closure Technique

NASA Technical Reports Server (NTRS)

Krueger, Ronald; Goetze, Dirk; Ransom, Jonathon (Technical Monitor)

2006-01-01

Strain energy release rates were computed along straight delamination fronts of Double Cantilever Beam, End-Notched Flexure and Single Leg Bending specimens using the Virtual Crack Closure Technique (VCCT). Th e results were based on finite element analyses using ABAQUS# and ANSYS# and were calculated from the finite element results using the same post-processing routine to assure a consistent procedure. Mixed-mode strain energy release rates obtained from post-processing finite elem ent results were in good agreement for all element types used and all specimens modeled. Compared to previous studies, the models made of s olid twenty-node hexahedral elements and solid eight-node incompatible mode elements yielded excellent results. For both codes, models made of standard brick elements and elements with reduced integration did not correctly capture the distribution of the energy release rate acr oss the width of the specimens for the models chosen. The results suggested that element types with similar formulation yield matching results independent of the finite element software used. For comparison, m ixed-mode strain energy release rates were also calculated within ABAQUS#/Standard using the VCCT for ABAQUS# add on. For all specimens mod eled, mixed-mode strain energy release rates obtained from ABAQUS# finite element results using post-processing were almost identical to re sults calculated using the VCCT for ABAQUS# add on.

Comparison of finite-difference schemes for analysis of shells of revolution. [stress and free vibration analysis

NASA Technical Reports Server (NTRS)

Noor, A. K.; Stephens, W. B.

1973-01-01

Several finite difference schemes are applied to the stress and free vibration analysis of homogeneous isotropic and layered orthotropic shells of revolution. The study is based on a form of the Sanders-Budiansky first-approximation linear shell theory modified such that the effects of shear deformation and rotary inertia are included. A Fourier approach is used in which all the shell stress resultants and displacements are expanded in a Fourier series in the circumferential direction, and the governing equations reduce to ordinary differential equations in the meridional direction. While primary attention is given to finite difference schemes used in conjunction with first order differential equation formulation, comparison is made with finite difference schemes used with other formulations. These finite difference discretization models are compared with respect to simplicity of application, convergence characteristics, and computational efficiency. Numerical studies are presented for the effects of variations in shell geometry and lamination parameters on the accuracy and convergence of the solutions obtained by the different finite difference schemes. On the basis of the present study it is shown that the mixed finite difference scheme based on the first order differential equation formulation and two interlacing grids for the different fundamental unknowns combines a number of advantages over other finite difference schemes previously reported in the literature.

Divergence Free High Order Filter Methods for Multiscale Non-ideal MHD Flows

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjoegreen, Bjoern

2003-01-01

Low-dissipative high order filter finite difference methods for long time wave propagation of shock/turbulence/combustion compressible viscous MHD flows has been constructed. Several variants of the filter approach that cater to different flow types are proposed. These filters provide a natural and efficient way for the minimization of the divergence of the magnetic field (Delta . B) numerical error in the sense that no standard divergence cleaning is required. For certain 2-D MHD test problems, divergence free preservation of the magnetic fields of these filter schemes has been achieved.

Ambient Vibration Tests of an Arch Dam with Different Reservoir Water Levels: Experimental Results and Comparison with Finite Element Modelling

PubMed Central

Ranieri, Gaetano

2014-01-01

This paper deals with the ambient vibration tests performed in an arch dam in two different working conditions in order to assess the effect produced by two different reservoir water levels on the structural vibration properties. The study consists of an experimental part and a numerical part. The experimental tests were carried out in two different periods of the year, at the beginning of autumn (October 2012) and at the end of winter (March 2013), respectively. The measurements were performed using a fast technique based on asynchronous records of microtremor time-series. In-contact single-station measurements were done by means of one single high resolution triaxial tromometer and two low-frequency seismometers, placed in different points of the structure. The Standard Spectral Ratio method has been used to evaluate the natural frequencies of vibration of the structure. A 3D finite element model of the arch dam-reservoir-foundation system has been developed to verify analytically determined vibration properties, such as natural frequencies and mode shapes, and their changes linked to water level with the experimental results. PMID:25003146

Finite Volume Algorithms for Heat Conduction

DTIC Science & Technology

2010-05-01

scalar quantity). Although (3) is relatively easy to discretize by using finite differences , its form in generalized coordinates is not. Later, we...familiar with the finite difference method for discretizing differential equations. In fact, the Newton divided difference is the numerical analog for a...expression (8) for the average derivative matches the Newton divided difference formula, so for uniform one-dimensional meshes, the finite volume and

A Kirchhoff Approach to Seismic Modeling and Prestack Depth Migration

DTIC Science & Technology

1993-05-01

continuation of sources and geophones by finite difference (S-G finite - difference migration ), are relatively slow and dip-limited. Compared to S-G... finite - difference migration , the Kirchhoff integral implements prestack migration relatively efficiently and has no dip limitation. Liu .Mlodeling and...for modeling and migration . In this paper, a finite - difference algorithm is used to calculate traveltimes and amplitudes. With the help of

Evaluation of finite difference and FFT-based solutions of the transport of intensity equation.

PubMed

Zhang, Hongbo; Zhou, Wen-Jing; Liu, Ying; Leber, Donald; Banerjee, Partha; Basunia, Mahmudunnabi; Poon, Ting-Chung

2018-01-01

A finite difference method is proposed for solving the transport of intensity equation. Simulation results show that although slower than fast Fourier transform (FFT)-based methods, finite difference methods are able to reconstruct the phase with better accuracy due to relaxed assumptions for solving the transport of intensity equation relative to FFT methods. Finite difference methods are also more flexible than FFT methods in dealing with different boundary conditions.

A spectral, quasi-cylindrical and dispersion-free Particle-In-Cell algorithm

DOE PAGES

Lehe, Remi; Kirchen, Manuel; Andriyash, Igor A.; ...

2016-02-17

We propose a spectral Particle-In-Cell (PIC) algorithm that is based on the combination of a Hankel transform and a Fourier transform. For physical problems that have close-to-cylindrical symmetry, this algorithm can be much faster than full 3D PIC algorithms. In addition, unlike standard finite-difference PIC codes, the proposed algorithm is free of spurious numerical dispersion, in vacuum. This algorithm is benchmarked in several situations that are of interest for laser-plasma interactions. These benchmarks show that it avoids a number of numerical artifacts, that would otherwise affect the physics in a standard PIC algorithm - including the zero-order numerical Cherenkov effect.

Finite elements and finite differences for transonic flow calculations

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Murman, E. M.; Wellford, L. C.

1978-01-01

The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

NASA Technical Reports Server (NTRS)

Burns, John A.; Marrekchi, Hamadi

1993-01-01

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

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.

COMPARISONS OF THE FINITE-ELEMENT-WITH-DISCONTIGUOUS-SUPPORT METHOD TO CONTINUOUS-ENERGY MONTE CARLO FOR PIN-CELL PROBLEMS

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

A. T. Till; M. Hanuš; J. Lou

The standard multigroup (MG) method for energy discretization of the transport equation can be sensitive to approximations in the weighting spectrum chosen for cross-section averaging. As a result, MG often inaccurately treats important phenomena such as self-shielding variations across a material. From a finite-element viewpoint, MG uses a single fixed basis function (the pre-selected spectrum) within each group, with no mechanism to adapt to local solution behavior. In this work, we introduce the Finite-Element-with-Discontiguous-Support (FEDS) method, whose only approximation with respect to energy is that the angular flux is a linear combination of unknowns multiplied by basis functions. A basismore » function is non-zero only in the discontiguous set of energy intervals associated with its energy element. Discontiguous energy elements are generalizations of bands and are determined by minimizing a norm of the difference between snapshot spectra and their averages over the energy elements. We begin by presenting the theory of the FEDS method. We then compare to continuous-energy Monte Carlo for one-dimensional slab and two-dimensional pin-cell problem. We find FEDS to be accurate and efficient at producing quantities of interest such as reaction rates and eigenvalues. Results show that FEDS converges at a rate that is approximately first-order in the number of energy elements and that FEDS is less sensitive to weighting spectrum than standard MG.« less

Improved Boundary Layer Module (BLM) for the Solid Performance Program (SPP)

NASA Astrophysics Data System (ADS)

Coats, D. E.; Cebeci, T.

1982-03-01

The requirements for a replacement to the Bartz boundary layer code, the standard method of computing the performance loss due to viscous effects by the solid performance program, were discussed by the propulsion community along with four nationally recognized boundary layer experts. A consensus was reached regarding the preferred features for the analysis of the replacement code. The major points that were agreed upon are: (1) finite difference methods are preferred over integral methods; (2) a single equation eddy viscosity model was considered to be adequate for the purpose of computing performance loss; (3) a variable grid capability in both coordinate directions would be required; (4) a proven finite difference algorithm which is not stability restricted should be used, that is, an implicit numerical scheme would be required; and (5) the replacement code should be able to compute both turbulent and laminar flows. The program should treat mass addition at the wall as well as being able to calculate a stagnation point starting line.

Finite difference time domain implementation of surface impedance boundary conditions

NASA Technical Reports Server (NTRS)

Beggs, John H.; Luebbers, Raymond J.; Yee, Kane S.; Kunz, Karl S.

1991-01-01

Surface impedance boundary conditions are employed to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In the finite difference solution, they also can be utilized to avoid using small cells, made necessary by shorter wavelengths in conducting media throughout the solution volume. The standard approach is to approximate the surface impedance over a very small bandwidth by its value at the center frequency, and then use that result in the boundary condition. Here, two implementations of the surface impedance boundary condition are presented. One implementation is a constant surface impedance boundary condition and the other is a dispersive surface impedance boundary condition that is applicable over a very large frequency bandwidth and over a large range of conductivities. Frequency domain results are presented in one dimension for two conductivity values and are compared with exact results. Scattering width results from an infinite square cylinder are presented as a two dimensional demonstration. Extensions to three dimensions should be straightforward.

A solution to neural field equations by a recurrent neural network method

NASA Astrophysics Data System (ADS)

Alharbi, Abir

2012-09-01

Neural field equations (NFE) are used to model the activity of neurons in the brain, it is introduced from a single neuron 'integrate-and-fire model' starting point. The neural continuum is spatially discretized for numerical studies, and the governing equations are modeled as a system of ordinary differential equations. In this article the recurrent neural network approach is used to solve this system of ODEs. This consists of a technique developed by combining the standard numerical method of finite-differences with the Hopfield neural network. The architecture of the net, energy function, updating equations, and algorithms are developed for the NFE model. A Hopfield Neural Network is then designed to minimize the energy function modeling the NFE. Results obtained from the Hopfield-finite-differences net show excellent performance in terms of accuracy and speed. The parallelism nature of the Hopfield approaches may make them easier to implement on fast parallel computers and give them the speed advantage over the traditional methods.

Spallation studies in Estane

NASA Astrophysics Data System (ADS)

Johnson, J. N.; Dick, J. J.

2000-04-01

Data are presented for the spall fracture of Estane. Estane has been studied previously to determine its low-pressure Hugoniot properties and high-rate viscoelastic response [J.N. Johnson, J.J. Dick and R.S. Hixson, J. Appl. Phys. 84, 2520-2529, 1998]. These results are used in the current analysis of spall fracture data for this material. Calculations are carried out with the characteristics code CHARADE and the finite-difference code FIDO. Comparison of model calculations with experimental data show the onset of spall failure to occur when the longitudinal stress reaches approximately 130 MPa in tension. At this point complete material separation does not occur, but rather the tensile strength in the material falls to approximately one-half the value at onset, as determined by CHARADE calculations. Finite-difference calculations indicate that the standard void-growth model (used previously to describe spall in metals) gives a reasonable approximation to the dynamic failure process in Estane. [Research supported by the USDOE under contract W-7405-ENG-36

Finite difference time domain implementation of surface impedance boundary conditions

NASA Technical Reports Server (NTRS)

Beggs, John H.; Luebbers, Raymond J.; Yee, Kane S.; Kunz, Karl S.

1991-01-01

Surface impedance boundary conditions are employed to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In a finite difference solution, they also can be utilized to avoid using small cells, made necessary by shorter wavelengths in conducting media throughout the solution volume. The standard approach is to approximate the surface impedance over a very small bandwidth by its value at the center frequency, and then use that result in the boundary condition. Two implementations of the surface impedance boundary condition are presented. One implementation is a constant surface impedance boundary condition and the other is a dispersive surface impedance boundary condition that is applicable over a very large frequency bandwidth and over a large range of conductivities. Frequency domain results are presented in one dimension for two conductivity values and are compared with exact results. Scattering width results from an infinite square cylinder are presented as a 2-D demonstration. Extensions to 3-D should be straightforward.

Applications of numerical methods to simulate the movement of contaminants in groundwater.

PubMed Central

Sun, N Z

1989-01-01

This paper reviews mathematical models and numerical methods that have been extensively used to simulate the movement of contaminants through the subsurface. The major emphasis is placed on the numerical methods of advection-dominated transport problems and inverse problems. Several mathematical models that are commonly used in field problems are listed. A variety of numerical solutions for three-dimensional models are introduced, including the multiple cell balance method that can be considered a variation of the finite element method. The multiple cell balance method is easy to understand and convenient for solving field problems. When the advection transport dominates the dispersion transport, two kinds of numerical difficulties, overshoot and numerical dispersion, are always involved in solving standard, finite difference methods and finite element methods. To overcome these numerical difficulties, various numerical techniques are developed, such as upstream weighting methods and moving point methods. A complete review of these methods is given and we also mention the problems of parameter identification, reliability analysis, and optimal-experiment design that are absolutely necessary for constructing a practical model. PMID:2695327

Characterization of a plasma photonic crystal using a multi-fluid plasma model

NASA Astrophysics Data System (ADS)

Thomas, W. R.; Shumlak, U.; Wang, B.; Righetti, F.; Cappelli, M. A.; Miller, S. T.

2017-10-01

Plasma photonic crystals have the potential to significantly expand the capabilities of current microwave filtering and switching technologies by providing high speed (μs) control of energy band-gap/pass characteristics in the GHz through low THz range. While photonic crystals consisting of dielectric, semiconductor, and metallic matrices have seen thousands of articles published over the last several decades, plasma-based photonic crystals remain a relatively unexplored field. Numerical modeling efforts so far have largely used the standard methods of analysis for photonic crystals (the Plane Wave Expansion Method, Finite Difference Time Domain, and ANSYS finite element electromagnetic code HFSS), none of which capture nonlinear plasma-radiation interactions. In this study, a 5N-moment multi-fluid plasma model is implemented using University of Washington's WARPXM finite element multi-physics code. A two-dimensional plasma-vacuum photonic crystal is simulated and its behavior is characterized through the generation of dispersion diagrams and transmission spectra. These results are compared with theory, experimental data, and ANSYS HFSS simulation results. This research is supported by a Grant from United States Air Force Office of Scientific Research.

QCD nature of dark energy at finite temperature: Cosmological implications

NASA Astrophysics Data System (ADS)

Azizi, K.; Katırcı, N.

2016-05-01

The Veneziano ghost field has been proposed as an alternative source of dark energy, whose energy density is consistent with the cosmological observations. In this model, the energy density of the QCD ghost field is expressed in terms of QCD degrees of freedom at zero temperature. We extend this model to finite temperature to search the model predictions from late time to early universe. We depict the variations of QCD parameters entering the calculations, dark energy density, equation of state, Hubble and deceleration parameters on temperature from zero to a critical temperature. We compare our results with the observations and theoretical predictions existing at different eras. It is found that this model safely defines the universe from quark condensation up to now and its predictions are not in tension with those of the standard cosmology. The EoS parameter of dark energy is dynamical and evolves from -1/3 in the presence of radiation to -1 at late time. The finite temperature ghost dark energy predictions on the Hubble parameter well fit to those of Λ CDM and observations at late time.

A Second Order Semi-Discrete Cosserat Rod Model Suitable for Dynamic Simulations in Real Time

NASA Astrophysics Data System (ADS)

Lang, Holger; Linn, Joachim

2009-09-01

We present an alternative approach for a semi-discrete viscoelastic Cosserat rod model that allows both fast dynamic computations within milliseconds and accurate results compared to detailed finite element solutions. The model is able to represent extension, shearing, bending and torsion. For inner dissipation, a consistent damping potential from Antman is chosen. The continuous equations of motion, which consist a system of nonlinear hyperbolic partial differential algebraic equations, are derived from a two dimensional variational principle. The semi-discrete balance equations are obtained by spatial finite difference schemes on a staggered grid and standard index reduction techniques. The right-hand side of the model and its Jacobian can be chosen free of higher algebraic (e.g. root) or transcendent (e.g. trigonometric or exponential) functions and is therefore extremely cheap to evaluate numerically. For the time integration of the system, we use well established stiff solvers. As our model yields computational times within milliseconds, it is suitable for interactive manipulation. It reflects structural mechanics solutions sufficiently correct, as comparison with detailed finite element results shows.

Phase Transitions in Finite Systems

NASA Astrophysics Data System (ADS)

Chomaz, Philippe; Gulminelli, Francesca

In this series of lectures we will first review the general theory of phase transition in the framework of information theory and briefly address some of the well known mean field solutions of three dimensional problems. The theory of phase transitions in finite systems will then be discussed, with a special emphasis to the conceptual problems linked to a thermodynamical description for small, short-lived, open systems as metal clusters and data samples coming from nuclear collisions. The concept of negative heat capacity developed in the early seventies in the context of self-gravitating systems will be reinterpreted in the general framework of convexity anomalies of thermostatistical potentials. The connection with the distribution of the order parameter will lead us to a definition of first order phase transitions in finite systems based on topology anomalies of the event distribution in the space of observations. Finally a careful study of the thermodynamical limit will provide a bridge with the standard theory of phase transitions and show that in a wide class of physical situations the different statistical ensembles are irreducibly inequivalent.

Finite-dimensional approximation for optimal fixed-order compensation of distributed parameter systems

NASA Technical Reports Server (NTRS)

Bernstein, Dennis S.; Rosen, I. G.

1988-01-01

In controlling distributed parameter systems it is often desirable to obtain low-order, finite-dimensional controllers in order to minimize real-time computational requirements. Standard approaches to this problem employ model/controller reduction techniques in conjunction with LQG theory. In this paper we consider the finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory. This approach yields fixed-finite-order controllers which are optimal with respect to high-order, approximating, finite-dimensional plant models. The technique is illustrated by computing a sequence of first-order controllers for one-dimensional, single-input/single-output, parabolic (heat/diffusion) and hereditary systems using spline-based, Ritz-Galerkin, finite element approximation. Numerical studies indicate convergence of the feedback gains with less than 2 percent performance degradation over full-order LQG controllers for the parabolic system and 10 percent degradation for the hereditary system.

Dislocation dynamics in non-convex domains using finite elements with embedded discontinuities

NASA Astrophysics Data System (ADS)

Romero, Ignacio; Segurado, Javier; LLorca, Javier

2008-04-01

The standard strategy developed by Van der Giessen and Needleman (1995 Modelling Simul. Mater. Sci. Eng. 3 689) to simulate dislocation dynamics in two-dimensional finite domains was modified to account for the effect of dislocations leaving the crystal through a free surface in the case of arbitrary non-convex domains. The new approach incorporates the displacement jumps across the slip segments of the dislocations that have exited the crystal within the finite element analysis carried out to compute the image stresses on the dislocations due to the finite boundaries. This is done in a simple computationally efficient way by embedding the discontinuities in the finite element solution, a strategy often used in the numerical simulation of crack propagation in solids. Two academic examples are presented to validate and demonstrate the extended model and its implementation within a finite element program is detailed in the appendix.

Finite-time and finite-size scalings in the evaluation of large-deviation functions: Numerical approach in continuous time.

PubMed

Guevara Hidalgo, Esteban; Nemoto, Takahiro; Lecomte, Vivien

2017-06-01

Rare trajectories of stochastic systems are important to understand because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provides a numerical tool allowing their study, by means of simulating a large number of copies of the system, which are subjected to selection rules that favor the rare trajectories of interest. Such algorithms are plagued by finite simulation time and finite population size, effects that can render their use delicate. In this paper, we present a numerical approach which uses the finite-time and finite-size scalings of estimators of the large deviation functions associated to the distribution of rare trajectories. The method we propose allows one to extract the infinite-time and infinite-size limit of these estimators, which-as shown on the contact process-provides a significant improvement of the large deviation function estimators compared to the standard one.

Application of a trigonometric finite difference procedure to numerical analysis of compressive and shear buckling of orthotropic panels

NASA Technical Reports Server (NTRS)

Stein, M.; Housner, J. D.

1978-01-01

A numerical analysis developed for the buckling of rectangular orthotropic layered panels under combined shear and compression is described. This analysis uses a central finite difference procedure based on trigonometric functions instead of using the conventional finite differences which are based on polynomial functions. Inasmuch as the buckle mode shape is usually trigonometric in nature, the analysis using trigonometric finite differences can be made to exhibit a much faster convergence rate than that using conventional differences. Also, the trigonometric finite difference procedure leads to difference equations having the same form as conventional finite differences; thereby allowing available conventional finite difference formulations to be converted readily to trigonometric form. For two-dimensional problems, the procedure introduces two numerical parameters into the analysis. Engineering approaches for the selection of these parameters are presented and the analysis procedure is demonstrated by application to several isotropic and orthotropic panel buckling problems. Among these problems is the shear buckling of stiffened isotropic and filamentary composite panels in which the stiffener is broken. Results indicate that a break may degrade the effect of the stiffener to the extent that the panel will not carry much more load than if the stiffener were absent.

Arbitrary-order corrections for finite-time drift and diffusion coefficients

NASA Astrophysics Data System (ADS)

Anteneodo, C.; Riera, R.

2009-09-01

We address a standard class of diffusion processes with linear drift and quadratic diffusion coefficients. These contributions to dynamic equations can be directly drawn from data time series. However, real data are constrained to finite sampling rates and therefore it is crucial to establish a suitable mathematical description of the required finite-time corrections. Based on Itô-Taylor expansions, we present the exact corrections to the finite-time drift and diffusion coefficients. These results allow to reconstruct the real hidden coefficients from the empirical estimates. We also derive higher-order finite-time expressions for the third and fourth conditional moments that furnish extra theoretical checks for this class of diffusion models. The analytical predictions are compared with the numerical outcomes of representative artificial time series.

Application of the Finite Element Method to Rotary Wing Aeroelasticity

NASA Technical Reports Server (NTRS)

Straub, F. K.; Friedmann, P. P.

1982-01-01

A finite element method for the spatial discretization of the dynamic equations of equilibrium governing rotary-wing aeroelastic problems is presented. Formulation of the finite element equations is based on weighted Galerkin residuals. This Galerkin finite element method reduces algebraic manipulative labor significantly, when compared to the application of the global Galerkin method in similar problems. The coupled flap-lag aeroelastic stability boundaries of hingeless helicopter rotor blades in hover are calculated. The linearized dynamic equations are reduced to the standard eigenvalue problem from which the aeroelastic stability boundaries are obtained. The convergence properties of the Galerkin finite element method are studied numerically by refining the discretization process. Results indicate that four or five elements suffice to capture the dynamics of the blade with the same accuracy as the global Galerkin method.

A Analysis of the Low Frequency Sound Field in Non-Rectangular Enclosures Using the Finite Element Method.

NASA Astrophysics Data System (ADS)

Geddes, Earl Russell

The details of the low frequency sound field for a rectangular room can be studied by the use of an established analytic technique--separation of variables. The solution is straightforward and the results are well-known. A non -rectangular room has boundary conditions which are not separable and therefore other solution techniques must be used. This study shows that the finite element method can be adapted for use in the study of sound fields in arbitrary shaped enclosures. The finite element acoustics problem is formulated and the modification of a standard program, which is necessary for solving acoustic field problems, is examined. The solution of the semi-non-rectangular room problem (one where the floor and ceiling remain parallel) is carried out by a combined finite element/separation of variables approach. The solution results are used to construct the Green's function for the low frequency sound field in five rooms (or data cases): (1) a rectangular (Louden) room; (2) The smallest wall of the Louden room canted 20 degrees from normal; (3) The largest wall of the Louden room canted 20 degrees from normal; (4) both the largest and the smallest walls are canted 20 degrees; and (5) a five-sided room variation of Case 4. Case 1, the rectangular room was calculated using both the finite element method and the separation of variables technique. The results for the two methods are compared in order to access the accuracy of the finite element method models. The modal damping coefficient are calculated and the results examined. The statistics of the source and receiver average normalized RMS P('2) responses in the 80 Hz, 100 Hz, and 125 Hz one-third octave bands are developed. The receiver averaged pressure response is developed to determine the effect of the source locations on the response. Twelve source locations are examined and the results tabulated for comparison. The effect of a finite sized source is looked at briefly. Finally, the standard deviation of the spatial pressure response is studied. The results for this characteristic show that it not significantly different in any of the rooms. The conclusions of the study are that only the frequency variations of the pressure response are affected by a room's shape. Further, in general, the simplest modification of a rectangular room (i.e., changing the angle of only one of the smallest walls), produces the most pronounced decrease of the pressure response variations in the low frequency region.

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.

Equilibrium charge distribution on a finite straight one-dimensional wire

NASA Astrophysics Data System (ADS)

Batle, Josep; Ciftja, Orion; Abdalla, Soliman; Elhoseny, Mohamed; Alkhambashi, Majid; Farouk, Ahmed

2017-09-01

The electrostatic properties of uniformly charged regular bodies are prominently discussed on college-level electromagnetism courses. However, one of the most basic problems of electrostatics that deals with how a continuous charge distribution reaches equilibrium is rarely mentioned at this level. In this work we revisit the problem of equilibrium charge distribution on a straight one-dimensional (1D) wire with finite length. The majority of existing treatments in the literature deal with the 1D wire as a limiting case of a higher-dimensional structure that can be treated analytically for a Coulomb interaction potential between point charges. Surprisingly, different models (for instance, an ellipsoid or a cylinder model) may lead to different results, thus there is even some ambiguity on whether the problem is well-posed. In this work we adopt a different approach where we do not start with any higher-dimensional body that reduces to a 1D wire in the appropriate limit. Instead, our starting point is the obvious one, a finite straight 1D wire that contains charge. However, the new tweak in the model is the assumption that point charges interact with each other via a non-Coulomb power-law interaction potential. This potential is well-behaved, allows exact analytical results and approaches the standard Coulomb interaction potential as a limit. The results originating from this approach suggest that the equilibrium charge distribution for a finite straight 1D wire is a uniform charge density when the power-law interaction potential approaches the Coulomb interaction potential as a suitable limit. We contrast such a finding to results obtained using a different regularised logarithmic interaction potential which allows exact treatment in 1D. The present self-contained material may be of interest to instructors teaching electromagnetism as well as students who will discover that simple-looking problems may sometimes pose important scientific challenges.

Acoustic Parametric Array for Identifying Standoff Targets

NASA Astrophysics Data System (ADS)

Hinders, M. K.; Rudd, K. E.

2010-02-01

An integrated simulation method for investigating nonlinear sound beams and 3D acoustic scattering from any combination of complicated objects is presented. A standard finite-difference simulation method is used to model pulsed nonlinear sound propagation from a source to a scattering target via the KZK equation. Then, a parallel 3D acoustic simulation method based on the finite integration technique is used to model the acoustic wave interaction with the target. Any combination of objects and material layers can be placed into the 3D simulation space to study the resulting interaction. Several example simulations are presented to demonstrate the simulation method and 3D visualization techniques. The combined simulation method is validated by comparing experimental and simulation data and a demonstration of how this combined simulation method assisted in the development of a nonlinear acoustic concealed weapons detector is also presented.

Effect of grid transparency and finite collector size on determining ion temperature and density by the retarding potential analyzer

NASA Technical Reports Server (NTRS)

Troy, B. E., Jr.; Maier, E. J.

1975-01-01

The effects of the grid transparency and finite collector size on the values of thermal ion density and temperature determined by the standard RPA (retarding potential analyzer) analysis method are investigated. The current-voltage curves calculated for varying RPA parameters and a given ion mass, temperature, and density are analyzed by the standard RPA method. It is found that only small errors in temperature and density are introduced for an RPA with typical dimensions, and that even when the density error is substantial for nontypical dimensions, the temperature error remains minimum.

Conservative properties of finite difference schemes for incompressible flow

NASA Technical Reports Server (NTRS)

Morinishi, Youhei

1995-01-01

The purpose of this research is to construct accurate finite difference schemes for incompressible unsteady flow simulations such as LES (large-eddy simulation) or DNS (direct numerical simulation). In this report, conservation properties of the continuity, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discretized equations. Existing finite difference schemes in staggered grid systems are checked for satisfaction of the requirements. Proper higher order accurate finite difference schemes in a staggered grid system are then proposed. Plane channel flow is simulated using the proposed fourth order accurate finite difference scheme and the results compared with those of the second order accurate Harlow and Welch algorithm.

Calculation of transonic flows using an extended integral equation method

NASA Technical Reports Server (NTRS)

Nixon, D.

1976-01-01

An extended integral equation method for transonic flows is developed. In the extended integral equation method velocities in the flow field are calculated in addition to values on the aerofoil surface, in contrast with the less accurate 'standard' integral equation method in which only surface velocities are calculated. The results obtained for aerofoils in subcritical flow and in supercritical flow when shock waves are present compare satisfactorily with the results of recent finite difference methods.

Investigation into the Impacts of Migration to Emergent NSA Suite B Encryption Standards

DTIC Science & Technology

2009-06-01

detailed statistical information on the difference between the 1024-bit keys and 2048-bit keys. D. ENCRYPTION TAXONOMY The modern field of...because they had already published their ideas globally and most 6 countries bar retroactive patenting of open source concepts. In September 2000, the...order of p operations in a finite field of numbers as large as p itself. If exhaustive search were the best attack on these systems, then bit

Numerical evaluation of moiré pattern in touch sensor module with electrode mesh structure in oblique view

NASA Astrophysics Data System (ADS)

Pournoury, M.; Zamiri, A.; Kim, T. Y.; Yurlov, V.; Oh, K.

2016-03-01

Capacitive touch sensor screen with the metal materials has recently become qualified for substitution of ITO; however several obstacles still have to be solved. One of the most important issues is moiré phenomenon. The visibility problem of the metal-mesh, in touch sensor module (TSM) is numerically considered in this paper. Based on human eye contract sensitivity function (CSF), moiré pattern of TSM electrode mesh structure is simulated with MATLAB software for 8 inch screen display in oblique view. Standard deviation of the generated moiré by the superposition of electrode mesh and screen image is calculated to find the optimal parameters which provide the minimum moiré visibility. To create the screen pixel array and mesh electrode, rectangular function is used. The filtered image, in frequency domain, is obtained by multiplication of Fourier transform of the finite mesh pattern (product of screen pixel and mesh electrode) with the calculated CSF function for three different observer distances (L=200, 300 and 400 mm). It is observed that the discrepancy between analytical and numerical results is less than 0.6% for 400 mm viewer distance. Moreover, in the case of oblique view due to considering the thickness of the finite film between mesh electrodes and screen, different points of minimum standard deviation of moiré pattern are predicted compared to normal view.

Observational constraints on finite scale factor singularities

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

Denkiewicz, Tomasz, E-mail: atomekd@wmf.univ.szczecin.pl

2012-07-01

We discuss the combined constraints on a Finite Scale Factor Singularity (FSF) universe evolution scenario, which come from the shift parameter R, baryon acoustic oscillations (BAO) A, and from the type Ia supernovae. We show that observations allow existence of such singularities in the 2 × 10{sup 9} years in future (at 1σ CL) which is much farther than a Sudden Future Singularity (SFS), and that at the present moment of the cosmic evolution, one cannot differentiate between cosmological scenario which allow finite scale factor singularities and the standard ΛCDM dark energy models. We also show that there is anmore » allowed value of m = 2/3 within 1σ CL, which corresponds to a dust-filled Einstein-de-Sitter universe limit of the early time evolution and so it is pasted into a standard early-time scenario.« less

Stimulus-Response Theory of Finite Automata, Technical Report No. 133.

ERIC Educational Resources Information Center

Suppes, Patrick

The central aim of this paper and its projected successors is to prove in detail that stimulus-response theory, or at least a mathematically precise version, can give an account of the learning of many phrase-structure grammars. Section 2 is concerned with standard notions of finite and probabilistic automata. An automaton is defined as a device…

The p-Version of the Finite Element Method for Domains with Corners and for Infinite Domains

DTIC Science & Technology

1988-11-01

Finite Element Method, Prenticw-Hall, 1973. [24] Szabo, B. A. :PROBE : The Theoretical Manual(Release 1.0), Noetic Tech. Cor. St Louis, MO., 1985...National Bureau of Standards. " To be an international center of study and research for foreign students in numerical mathematics who are supported by

Finite-size corrections to the excitation energy transfer in a massless scalar interaction model

NASA Astrophysics Data System (ADS)

Maeda, Nobuki; Yabuki, Tetsuo; Tobita, Yutaka; Ishikawa, Kenzo

2017-05-01

We study the excitation energy transfer (EET) for a simple model in which a massless scalar particle is exchanged between two molecules. We show that a finite-size effect appears in EET by the interaction energy due to overlapping of the quantum waves in a short time interval. The effect generates finite-size corrections to Fermi's golden rule and modifies EET probability from the standard formula in the Förster mechanism. The correction terms come from transition modes outside the resonance energy region and enhance EET probability substantially.

Practical aspects of prestack depth migration with finite differences

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

Ober, C.C.; Oldfield, R.A.; Womble, D.E.

1997-07-01

Finite-difference, prestack, depth migrations offers significant improvements over Kirchhoff methods in imaging near or under salt structures. The authors have implemented a finite-difference prestack depth migration algorithm for use on massively parallel computers which is discussed. The image quality of the finite-difference scheme has been investigated and suggested improvements are discussed. In this presentation, the authors discuss an implicit finite difference migration code, called Salvo, that has been developed through an ACTI (Advanced Computational Technology Initiative) joint project. This code is designed to be efficient on a variety of massively parallel computers. It takes advantage of both frequency and spatialmore » parallelism as well as the use of nodes dedicated to data input/output (I/O). Besides giving an overview of the finite-difference algorithm and some of the parallelism techniques used, migration results using both Kirchhoff and finite-difference migration will be presented and compared. The authors start out with a very simple Cartoon model where one can intuitively see the multiple travel paths and some of the potential problems that will be encountered with Kirchhoff migration. More complex synthetic models as well as results from actual seismic data from the Gulf of Mexico will be shown.« less

Preclinical evaluation of posterior spine stabilization devices: can the current standards represent basic everyday life activities?

PubMed

La Barbera, Luigi; Galbusera, Fabio; Wilke, Hans-Joachim; Villa, Tomaso

2016-09-01

To discuss whether the available standard methods for preclinical evaluation of posterior spine stabilization devices can represent basic everyday life activities and how to compare the results obtained with different procedures. A comparative finite element study compared ASTM F1717 and ISO 12189 standards to validated instrumented L2-L4 segments undergoing standing, upper body flexion and extension. The internal loads on the spinal rod and the maximum stress on the implant are analysed. ISO recommended anterior support stiffness and force allow for reproducing bending moments measured in vivo on an instrumented physiological segment during upper body flexion. Despite the significance of ASTM model from an engineering point of view, the overly conservative vertebrectomy model represents an unrealistic worst case scenario. A method is proposed to determine the load to apply on assemblies with different anterior support stiffnesses to guarantee a comparable bending moment and reproduce specific everyday life activities. The study increases our awareness on the use of the current standards to achieve meaningful results easy to compare and interpret.

Finite-Difference Solutions for Compressible Laminar Boundary-Layer Flows of a Dusty Gas over a Semi-Infinite Flat Plate.

DTIC Science & Technology

1986-08-01

AD-A174 952 FINITE - DIFFERENCE SOLUTIONS FOR CONPRESSIBLE LANINAR 1/2 BOUNDARY-LAYER FLOUS (U) TORONTO UNIV DOWNSVIEW (ONTARIO) INST FOR AEROSPACE...dilute dusty gas over a semi-infinite flat plate. Details are given of the impliit finite , difference schemes as well as the boundary conditions... FINITE - DIFFERENCE SOLUTIONS FOR COMPRESSIBLE LAMINAR BOUNDARY-LAYER FLOWS OF A DUSTY GAS OVER A SEMI-INFINITE FLAT PLATE by B. Y. Wang and I. I

The NASA/Industry Design Analysis Methods for Vibrations (DAMVIBS) Program - A government overview. [of rotorcraft technology development using finite element method

NASA Technical Reports Server (NTRS)

Kvaternik, Raymond G.

1992-01-01

An overview is presented of government contributions to the program called Design Analysis Methods for Vibrations (DAMV) which attempted to develop finite-element-based analyses of rotorcraft vibrations. NASA initiated the program with a finite-element modeling program for the CH-47D tandem-rotor helicopter. The DAMV program emphasized four areas including: airframe finite-element modeling, difficult components studies, coupled rotor-airframe vibrations, and airframe structural optimization. Key accomplishments of the program include industrywide standards for modeling metal and composite airframes, improved industrial designs for vibrations, and the identification of critical structural contributors to airframe vibratory responses. The program also demonstrated the value of incorporating secondary modeling details to improving correlation, and the findings provide the basis for an improved finite-element-based dynamics design-analysis capability.

Influence of Finite Span and Sweep on Active Flow Control Efficacy

NASA Technical Reports Server (NTRS)

Greenblatt, David; Washburn, Anthony E.

2008-01-01

Active flow control efficacy was investigated by means of leading-edge and flap-shoulder zero mass-flux blowing slots on a semispan wing model that was tested in unswept (standard) and swept configurations. On the standard configuration, stall commenced inboard, but with sweep the wing stalled initially near the tip. On both configurations, leading-edge perturbations increased CL,max and post stall lift, both with and without deflected flaps. Without sweep, the effect of control was approximately uniform across the wing span but remained effective to high angles of attack near the tip; when sweep was introduced a significant effect was noted inboard, but this effect degraded along the span and produced virtually no meaningful lift enhancement near the tip, irrespective of the tip configuration. In the former case, control strengthened the wingtip vortex; in the latter case, a simple semi-empirical model, based on the trajectory or "streamline" of the evolving perturbation, served to explain the observations. In the absence of sweep, control on finite-span flaps did not differ significantly from their nominally twodimensional counterpart. Control from the flap produced expected lift enhancement and CL,max improvements in the absence of sweep, but these improvements degraded with the introduction of sweep.

Finite Mathematics and Discrete Mathematics: Is There a Difference?

ERIC Educational Resources Information Center

Johnson, Marvin L.

Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…

Adaptive Low Dissipative High Order Filter Methods for Multiscale MHD Flows

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjoegreen, Bjoern

2004-01-01

Adaptive low-dissipative high order filter finite difference methods for long time wave propagation of shock/turbulence/combustion compressible viscous MHD flows has been constructed. Several variants of the filter approach that cater to different flow types are proposed. These filters provide a natural and efficient way for the minimization of the divergence of the magnetic field [divergence of B] numerical error in the sense that no standard divergence cleaning is required. For certain 2-D MHD test problems, divergence free preservation of the magnetic fields of these filter schemes has been achieved.

Improved methods of vibration analysis of pretwisted, airfoil blades

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.

1984-01-01

Vibration analysis of pretwisted blades of asymmetric airfoil cross section is performed by using two mixed variational approaches. Numerical results obtained from these two methods are compared to those obtained from an improved finite difference method and also to those given by the ordinary finite difference method. The relative merits, convergence properties and accuracies of all four methods are studied and discussed. The effects of asymmetry and pretwist on natural frequencies and mode shapes are investigated. The improved finite difference method is shown to be far superior to the conventional finite difference method in several respects. Close lower bound solutions are provided by the improved finite difference method for untwisted blades with a relatively coarse mesh while the mixed methods have not indicated any specific bound.

Calculation of unsteady aerodynamics for four AGARD standard aeroelastic configurations

NASA Technical Reports Server (NTRS)

Bland, S. R.; Seidel, D. A.

1984-01-01

Calculated unsteady aerodynamic characteristics for four Advisory Group for Aeronautical Research Development (AGARD) standard aeroelastic two-dimensional airfoils and for one of the AGARD three-dimensional wings are reported. Calculations were made using the finite-difference codes XTRAN2L (two-dimensional flow) and XTRAN3S (three-dimensional flow) which solve the transonic small disturbance potential equations. Results are given for the 36 AGARD cases for the NACA 64A006, NACA 64A010, and NLR 7301 airfoils with experimental comparisons for most of these cases. Additionally, six of the MBB-A3 airfoil cases are included. Finally, results are given for three of the cases for the rectangular wing.

Improving sub-grid scale accuracy of boundary features in regional finite-difference models

USGS Publications Warehouse

Panday, Sorab; Langevin, Christian D.

2012-01-01

As an alternative to grid refinement, the concept of a ghost node, which was developed for nested grid applications, has been extended towards improving sub-grid scale accuracy of flow to conduits, wells, rivers or other boundary features that interact with a finite-difference groundwater flow model. The formulation is presented for correcting the regular finite-difference groundwater flow equations for confined and unconfined cases, with or without Newton Raphson linearization of the nonlinearities, to include the Ghost Node Correction (GNC) for location displacement. The correction may be applied on the right-hand side vector for a symmetric finite-difference Picard implementation, or on the left-hand side matrix for an implicit but asymmetric implementation. The finite-difference matrix connectivity structure may be maintained for an implicit implementation by only selecting contributing nodes that are a part of the finite-difference connectivity. Proof of concept example problems are provided to demonstrate the improved accuracy that may be achieved through sub-grid scale corrections using the GNC schemes.

Plasma Theory and Simulation

DTIC Science & Technology

1988-06-30

equation using finite difference methods. The distribution function is represented by a large number of particles. The particle’s velocities change as a...Small angle Coulomb collisions The FP equation for describing small angle Coulomb collisions can be solved numerically using finite difference techniques...A finite Fourrier transform (FT) is made in z, then we can solve for each k using the following finite difference scheme [5]: 2{r 1 +l1 2 (,,+ 1 - fj

Application of 'steady' state finite element and transient finite difference theory to sound propagation in a variable duct - A comparison with experiment

NASA Technical Reports Server (NTRS)

Baumeister, K. J.; Eversman, W.; Astley, R. J.; White, J. W.

1981-01-01

Experimental data are presented for sound propagation in a simulated infinite hard wall duct with a large change in duct cross sectional area. The data are conveniently tabulated for further use. The 'steady' state finite element theory of Astley and Eversman (1981) and the transient finite difference theory of White (1981) are in good agreement with the data for both the axial and transverse pressure profiles and the axial phase angle. Therefore, numerical finite difference and finite element theories appear to be ideally suited for handling duct propagation problems which encounter large axial gradients in acoustic parameters. The measured energy reflection coefficient agrees with the values from the Astley-Eversman modal coupling model.

Performance of concrete members subjected to large hydrocarbon pool fires

DOE PAGES

Zwiers, Renata I.; Morgan, Bruce J.

1989-01-01

The authors discuss an investigation to determine analytically if the performance of concrete beams and columns in a hydrocarbon pool test fire would differ significantly from their performance in a standard test fire. The investigation consisted of a finite element analysis to obtain temperature distributions in typical cross sections, a comparison of the resulting temperature distribution in the cross section, and a strength analysis of a beam based on temperature distribution data. Results of the investigation are reported.

Tool Efficiency Analysis model research in SEMI industry

NASA Astrophysics Data System (ADS)

Lei, Ma; Nana, Zhang; Zhongqiu, Zhang

2018-06-01

One of the key goals in SEMI industry is to improve equipment through put and ensure equipment production efficiency maximization. This paper is based on SEMI standards in semiconductor equipment control, defines the transaction rules between different tool states, and presents a TEA system model which is to analysis tool performance automatically based on finite state machine. The system was applied to fab tools and verified its effectiveness successfully, and obtained the parameter values used to measure the equipment performance, also including the advices of improvement.

Recent Developments in Computational Techniques for Applied Hydrodynamics.

DTIC Science & Technology

1979-12-07

by block number) Numerical Method Fluids Incompressible Flow Finite Difference Methods Poisson Equation Convective Equations -MABSTRACT (Continue on...weaknesses of the different approaches are analyzed. Finite - difference techniques have particularly attractive properties in this framework. Hence it will...be worthwhile to correct, at least partially, the difficulties from which Eulerian and Lagrangian finite - difference techniques suffer, discussed in

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.

Analytical Computation of Effective Grid Parameters for the Finite-Difference Seismic Waveform Modeling With the PREM, IASP91, SP6, and AK135

NASA Astrophysics Data System (ADS)

Toyokuni, G.; Takenaka, H.

2007-12-01

We propose a method to obtain effective grid parameters for the finite-difference (FD) method with standard Earth models using analytical ways. In spite of the broad use of the heterogeneous FD formulation for seismic waveform modeling, accurate treatment of material discontinuities inside the grid cells has been a serious problem for many years. One possible way to solve this problem is to introduce effective grid elastic moduli and densities (effective parameters) calculated by the volume harmonic averaging of elastic moduli and volume arithmetic averaging of density in grid cells. This scheme enables us to put a material discontinuity into an arbitrary position in the spatial grids. Most of the methods used for synthetic seismogram calculation today receives the blessing of the standard Earth models, such as the PREM, IASP91, SP6, and AK135, represented as functions of normalized radius. For the FD computation of seismic waveform with such models, we first need accurate treatment of material discontinuities in radius. This study provides a numerical scheme for analytical calculations of the effective parameters for an arbitrary spatial grids in radial direction as to these major four standard Earth models making the best use of their functional features. This scheme can analytically obtain the integral volume averages through partial fraction decompositions (PFDs) and integral formulae. We have developed a FORTRAN subroutine to perform the computations, which is opened to utilization in a large variety of FD schemes ranging from 1-D to 3-D, with conventional- and staggered-grids. In the presentation, we show some numerical examples displaying the accuracy of the FD synthetics simulated with the analytical effective parameters.

Mixed finite-difference scheme for free vibration analysis of noncircular cylinders

NASA Technical Reports Server (NTRS)

Noor, A. K.; Stephens, W. B.

1973-01-01

A mixed finite-difference scheme is presented for the free-vibration analysis of simply supported closed noncircular cylindrical shells. The problem is formulated in terms of eight first-order differential equations in the circumferential coordinate which possess a symmetric coefficient matrix and are free of the derivatives of the elastic and geometric characteristics of the shell. In the finite-difference discretization, two interlacing grids are used for the different fundamental unknowns in such a way as to avoid averaging in the difference-quotient expressions used for the first derivative. The resulting finite-difference equations are symmetric. The inverse-power method is used for obtaining the eigenvalues and eigenvectors.

Parametric optimization and design validation based on finite element analysis of hybrid socket adapter for transfemoral prosthetic knee.

PubMed

Kumar, Neelesh

2014-10-01

Finite element analysis has been universally employed for the stress and strain analysis in lower extremity prosthetics. The socket adapter was the principal subject of interest due to its importance in deciding the knee motion range. This article focused on the static and dynamic stress analysis of the designed hybrid adapter developed by the authors. A standard mechanical design validation approach using von Mises was followed. Four materials were considered for the analysis, namely, carbon fiber, oil-filled nylon, Al-6061, and mild steel. The paper analyses the static and dynamic stress on designed hybrid adapter which incorporates features of conventional male and female socket adapters. The finite element analysis was carried out for possible different angles of knee flexion simulating static and dynamic gait situation. Research was carried out on available design of socket adapter. Mechanical design of hybrid adapter was conceptualized and a CAD model was generated using Inventor modelling software. Static and dynamic stress analysis was carried out on different materials for optimization. The finite element analysis was carried out on the software Autodesk Inventor Professional Ver. 2011. The peak value of von Mises stress occurred in the neck region of the adapter and in the lower face region at rod eye-adapter junction in static and dynamic analyses, respectively. Oil-filled nylon was found to be the best material among the four with respect to strength, weight, and cost. Research investigations on newer materials for development of improved prosthesis will immensely benefit the amputees. The study analyze the static and dynamic stress on the knee joint adapter to provide better material used for hybrid design of adapter. © The International Society for Prosthetics and Orthotics 2013.

Predicting financial market crashes using ghost singularities.

PubMed

Smug, Damian; Ashwin, Peter; Sornette, Didier

2018-01-01

We analyse the behaviour of a non-linear model of coupled stock and bond prices exhibiting periodically collapsing bubbles. By using the formalism of dynamical system theory, we explain what drives the bubbles and how foreshocks or aftershocks are generated. A dynamical phase space representation of that system coupled with standard multiplicative noise rationalises the log-periodic power law singularity pattern documented in many historical financial bubbles. The notion of 'ghosts of finite-time singularities' is introduced and used to estimate the end of an evolving bubble, using finite-time singularities of an approximate normal form near the bifurcation point. We test the forecasting skill of this method on different stochastic price realisations and compare with Monte Carlo simulations of the full system. Remarkably, the approximate normal form is significantly more precise and less biased. Moreover, the method of ghosts of singularities is less sensitive to the noise realisation, thus providing more robust forecasts.

Predicting financial market crashes using ghost singularities

PubMed Central

2018-01-01

We analyse the behaviour of a non-linear model of coupled stock and bond prices exhibiting periodically collapsing bubbles. By using the formalism of dynamical system theory, we explain what drives the bubbles and how foreshocks or aftershocks are generated. A dynamical phase space representation of that system coupled with standard multiplicative noise rationalises the log-periodic power law singularity pattern documented in many historical financial bubbles. The notion of ‘ghosts of finite-time singularities’ is introduced and used to estimate the end of an evolving bubble, using finite-time singularities of an approximate normal form near the bifurcation point. We test the forecasting skill of this method on different stochastic price realisations and compare with Monte Carlo simulations of the full system. Remarkably, the approximate normal form is significantly more precise and less biased. Moreover, the method of ghosts of singularities is less sensitive to the noise realisation, thus providing more robust forecasts. PMID:29596485

Influence of fine threads and platform-switching on crestal bone stress around implant-a three-dimensional finite element analysis.

PubMed

Khurana, Pardeep; Sharma, Arun; Sodhi, Kiranmeet Kaur

2013-12-01

The aims of this study were to investigate the effect of implant fine threads on crestal bone stress compared to a standard smooth implant collar and to analyze how different abutment diameters influenced the crestal bone stress level. Three-dimensional finite element imaging was used to create a cross-sectional model in SolidWorks 2007 software of an implant (5-mm platform and 10 mm in length) placed in the premolar region of the mandible. The implant model was created to resemble a commercially available fine thread implant. Abutments of different diameters (5.0 mm: standard, 4.5 mm, 4.0 mm, and 3.5 mm) were loaded with a force of 100 N at 90° vertical and 40° oblique angles. Finite element analysis was done in COSMOSWorks software, which was used to analyze the stress patterns in bone, especially in the crestal region. Upon loading, the fine thread implant model had greater stress at the crestal bone adjacent to the implant than the smooth neck implant in both vertical and oblique loading. When the abutment diameter decreased progressively from 5.0 mm to 4.5 mm to 4 mm and to 3.5 mm the thread model showed a reduction of stress at the crestal bone level from 23.2 MPa to 15.02 MPa for fine thread and from 22.7 to 13.5 MPa for smooth collar implant group after vertical loading and from 43.7 MPa to 33.1 MPa in fine thread model and from 36.9 to 20.5 MPa in smooth collar implant model after oblique loading. Fine threads increase crestal stress upon loading. Reduced abutment diameter that is platform switching resulted in less stress translated to the crestal bone in the fine thread and smooth neck.

Stable finite element approximations of two-phase flow with soluble surfactant

NASA Astrophysics Data System (ADS)

Barrett, John W.; Garcke, Harald; Nürnberg, Robert

2015-09-01

A parametric finite element approximation of incompressible two-phase flow with soluble surfactants is presented. The Navier-Stokes equations are coupled to bulk and surfaces PDEs for the surfactant concentrations. At the interface adsorption, desorption and stress balances involving curvature effects and Marangoni forces have to be considered. A parametric finite element approximation for the advection of the interface, which maintains good mesh properties, is coupled to the evolving surface finite element method, which is used to discretize the surface PDE for the interface surfactant concentration. The resulting system is solved together with standard finite element approximations of the Navier-Stokes equations and of the bulk parabolic PDE for the surfactant concentration. Semidiscrete and fully discrete approximations are analyzed with respect to stability, conservation and existence/uniqueness issues. The approach is validated for simple test cases and for complex scenarios, including colliding drops in a shear flow, which are computed in two and three space dimensions.

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

Vay, Jean-Luc, E-mail: jlvay@lbl.gov; Haber, Irving; Godfrey, Brendan B.

Pseudo-spectral electromagnetic solvers (i.e. representing the fields in Fourier space) have extraordinary precision. In particular, Haber et al. presented in 1973 a pseudo-spectral solver that integrates analytically the solution over a finite time step, under the usual assumption that the source is constant over that time step. Yet, pseudo-spectral solvers have not been widely used, due in part to the difficulty for efficient parallelization owing to global communications associated with global FFTs on the entire computational domains. A method for the parallelization of electromagnetic pseudo-spectral solvers is proposed and tested on single electromagnetic pulses, and on Particle-In-Cell simulations of themore » wakefield formation in a laser plasma accelerator. The method takes advantage of the properties of the Discrete Fourier Transform, the linearity of Maxwell’s equations and the finite speed of light for limiting the communications of data within guard regions between neighboring computational domains. Although this requires a small approximation, test results show that no significant error is made on the test cases that have been presented. The proposed method opens the way to solvers combining the favorable parallel scaling of standard finite-difference methods with the accuracy advantages of pseudo-spectral methods.« less

Finite Volume Numerical Methods for Aeroheating Rate Calculations from Infrared Thermographic Data

NASA Technical Reports Server (NTRS)

Daryabeigi, Kamran; Berry, Scott A.; Horvath, Thomas J.; Nowak, Robert J.

2006-01-01

The use of multi-dimensional finite volume heat conduction techniques for calculating aeroheating rates from measured global surface temperatures on hypersonic wind tunnel models was investigated. Both direct and inverse finite volume techniques were investigated and compared with the standard one-dimensional semi-infinite technique. Global transient surface temperatures were measured using an infrared thermographic technique on a 0.333-scale model of the Hyper-X forebody in the NASA Langley Research Center 20-Inch Mach 6 Air tunnel. In these tests the effectiveness of vortices generated via gas injection for initiating hypersonic transition on the Hyper-X forebody was investigated. An array of streamwise-orientated heating striations was generated and visualized downstream of the gas injection sites. In regions without significant spatial temperature gradients, one-dimensional techniques provided accurate aeroheating rates. In regions with sharp temperature gradients caused by striation patterns multi-dimensional heat transfer techniques were necessary to obtain more accurate heating rates. The use of the one-dimensional technique resulted in differences of 20% in the calculated heating rates compared to 2-D analysis because it did not account for lateral heat conduction in the model.

Mass-corrections for the conservative coupling of flow and transport on collocated meshes

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

Waluga, Christian, E-mail: waluga@ma.tum.de; Wohlmuth, Barbara; Rüde, Ulrich

2016-01-15

Buoyancy-driven flow models demand a careful treatment of the mass-balance equation to avoid spurious source and sink terms in the non-linear coupling between flow and transport. In the context of finite-elements, it is therefore commonly proposed to employ sufficiently rich pressure spaces, containing piecewise constant shape functions to obtain local or even strong mass-conservation. In three-dimensional computations, this usually requires nonconforming approaches, special meshes or higher order velocities, which make these schemes prohibitively expensive for some applications and complicate the implementation into legacy code. In this paper, we therefore propose a lean and conservatively coupled scheme based on standard stabilizedmore » linear equal-order finite elements for the Stokes part and vertex-centered finite volumes for the energy equation. We show that in a weak mass-balance it is possible to recover exact conservation properties by a local flux-correction which can be computed efficiently on the control volume boundaries of the transport mesh. We discuss implementation aspects and demonstrate the effectiveness of the flux-correction by different two- and three-dimensional examples which are motivated by geophysical applications.« less

Long-Time Numerical Integration of the Three-Dimensional Wave Equation in the Vicinity of a Moving Source

NASA Technical Reports Server (NTRS)

Ryabenkii, V. S.; Turchaninov, V. I.; Tsynkov, S. V.

1999-01-01

We propose a family of algorithms for solving numerically a Cauchy problem for the three-dimensional wave equation. The sources that drive the equation (i.e., the right-hand side) are compactly supported in space for any given time; they, however, may actually move in space with a subsonic speed. The solution is calculated inside a finite domain (e.g., sphere) that also moves with a subsonic speed and always contains the support of the right-hand side. The algorithms employ a standard consistent and stable explicit finite-difference scheme for the wave equation. They allow one to calculate tile solution for arbitrarily long time intervals without error accumulation and with the fixed non-growing amount of tile CPU time and memory required for advancing one time step. The algorithms are inherently three-dimensional; they rely on the presence of lacunae in the solutions of the wave equation in oddly dimensional spaces. The methodology presented in the paper is, in fact, a building block for constructing the nonlocal highly accurate unsteady artificial boundary conditions to be used for the numerical simulation of waves propagating with finite speed over unbounded domains.

Variability analysis of SAR from 20 MHz to 2.4 GHz for different adult and child models using finite-difference time-domain

NASA Astrophysics Data System (ADS)

Conil, E.; Hadjem, A.; Lacroux, F.; Wong, M. F.; Wiart, J.

2008-03-01

This paper deals with the variability of body models used in numerical dosimetry studies. Six adult anthropomorphic voxel models have been collected and used to build 5-, 8- and 12-year-old children using a morphing method respecting anatomical parameters. Finite-difference time-domain calculations of a specific absorption rate (SAR) have been performed for a range of frequencies from 20 MHz to 2.4 GHz for isolated models illuminated by plane waves. A whole-body-averaged SAR is presented as well as the average on specific tissues such as skin, muscles, fat or bones and the average on specific parts of the body such as head, legs, arms or torso. Results point out the variability of adult models. The standard deviation of whole-body-averaged SAR of adult models can reach 40%. All phantoms are exposed to the ICNIRP reference levels. Results show that for adults, compliance with reference levels ensures compliance with basic restrictions, but concerning children models involved in this study, the whole-body-averaged SAR goes over the fundamental safety limits up to 40%. For more information on this article, see medicalphysicsweb.org

Ghost-free, finite, fourth-order D = 3 gravity.

PubMed

Deser, S

2009-09-04

Canonical analysis of a recently proposed linear + quadratic curvature gravity model in D = 3 establishes its pure, irreducibly fourth derivative, quadratic curvature limit as both ghost-free and power-counting UV finite, thereby maximally violating standard folklore. This limit is representative of a generic class whose kinetic terms are conformally invariant in any dimension, but it is unique in simultaneously avoiding the transverse-traceless graviton ghosts plaguing D > 3 quadratic actions as well as double pole propagators in its other variables. While the two-term model is also unitary, its additional mode's second-derivative nature forfeits finiteness.

Finite difference and Runge-Kutta methods for solving vibration problems

NASA Astrophysics Data System (ADS)

Lintang Renganis Radityani, Scolastika; Mungkasi, Sudi

2017-11-01

The vibration of a storey building can be modelled into a system of second order ordinary differential equations. If the number of floors of a building is large, then the result is a large scale system of second order ordinary differential equations. The large scale system is difficult to solve, and if it can be solved, the solution may not be accurate. Therefore, in this paper, we seek for accurate methods for solving vibration problems. We compare the performance of numerical finite difference and Runge-Kutta methods for solving large scale systems of second order ordinary differential equations. The finite difference methods include the forward and central differences. The Runge-Kutta methods include the Euler and Heun methods. Our research results show that the central finite difference and the Heun methods produce more accurate solutions than the forward finite difference and the Euler methods do.

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

NASA Astrophysics Data System (ADS)

Lai, Wencong; Khan, Abdul A.

2018-04-01

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

Finite difference time domain modeling of steady state scattering from jet engines with moving turbine blades

NASA Technical Reports Server (NTRS)

Ryan, Deirdre A.; Langdon, H. Scott; Beggs, John H.; Steich, David J.; Luebbers, Raymond J.; Kunz, Karl S.

1992-01-01

The approach chosen to model steady state scattering from jet engines with moving turbine blades is based upon the Finite Difference Time Domain (FDTD) method. The FDTD method is a numerical electromagnetic program based upon the direct solution in the time domain of Maxwell's time dependent curl equations throughout a volume. One of the strengths of this method is the ability to model objects with complicated shape and/or material composition. General time domain functions may be used as source excitations. For example, a plane wave excitation may be specified as a pulse containing many frequencies and at any incidence angle to the scatterer. A best fit to the scatterer is accomplished using cubical cells in the standard cartesian implementation of the FDTD method. The material composition of the scatterer is determined by specifying its electrical properties at each cell on the scatterer. Thus, the FDTD method is a suitable choice for problems with complex geometries evaluated at multiple frequencies. It is assumed that the reader is familiar with the FDTD method.

Numerical analysis of a main crack interactions with micro-defects/inhomogeneities using two-scale generalized/extended finite element method

NASA Astrophysics Data System (ADS)

Malekan, Mohammad; Barros, Felício B.

2017-12-01

Generalized or extended finite element method (G/XFEM) models the crack by enriching functions of partition of unity type with discontinuous functions that represent well the physical behavior of the problem. However, this enrichment functions are not available for all problem types. Thus, one can use numerically-built (global-local) enrichment functions to have a better approximate procedure. This paper investigates the effects of micro-defects/inhomogeneities on a main crack behavior by modeling the micro-defects/inhomogeneities in the local problem using a two-scale G/XFEM. The global-local enrichment functions are influenced by the micro-defects/inhomogeneities from the local problem and thus change the approximate solution of the global problem with the main crack. This approach is presented in detail by solving three different linear elastic fracture mechanics problems for different cases: two plane stress and a Reissner-Mindlin plate problems. The numerical results obtained with the two-scale G/XFEM are compared with the reference solutions from the analytical, numerical solution using standard G/XFEM method and ABAQUS as well, and from the literature.

Radiative decay rate of excitons in square quantum wells: Microscopic modeling and experiment

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

Khramtsov, E. S.; Grigoryev, P. S.; Ignatiev, I. V.

The binding energy and the corresponding wave function of excitons in GaAs-based finite square quantum wells (QWs) are calculated by the direct numerical solution of the three-dimensional Schrödinger equation. The precise results for the lowest exciton state are obtained by the Hamiltonian discretization using the high-order finite-difference scheme. The microscopic calculations are compared with the results obtained by the standard variational approach. The exciton binding energies found by two methods coincide within 0.1 meV for the wide range of QW widths. The radiative decay rate is calculated for QWs of various widths using the exciton wave functions obtained by direct andmore » variational methods. The radiative decay rates are confronted with the experimental data measured for high-quality GaAs/AlGaAs and InGaAs/GaAs QW heterostructures grown by molecular beam epitaxy. The calculated and measured values are in good agreement, though slight differences with earlier calculations of the radiative decay rate are observed.« less

Finite-key security analyses on passive decoy-state QKD protocols with different unstable sources.

PubMed

Song, Ting-Ting; Qin, Su-Juan; Wen, Qiao-Yan; Wang, Yu-Kun; Jia, Heng-Yue

2015-10-16

In quantum communication, passive decoy-state QKD protocols can eliminate many side channels, but the protocols without any finite-key analyses are not suitable for in practice. The finite-key securities of passive decoy-state (PDS) QKD protocols with two different unstable sources, type-II parametric down-convention (PDC) and phase randomized weak coherent pulses (WCPs), are analyzed in our paper. According to the PDS QKD protocols, we establish an optimizing programming respectively and obtain the lower bounds of finite-key rates. Under some reasonable values of quantum setup parameters, the lower bounds of finite-key rates are simulated. The simulation results show that at different transmission distances, the affections of different fluctuations on key rates are different. Moreover, the PDS QKD protocol with an unstable PDC source can resist more intensity fluctuations and more statistical fluctuation.

Nonlinear Computational Aeroelasticity: Formulations and Solution Algorithms

DTIC Science & Technology

2003-03-01

problem is proposed. Fluid-structure coupling algorithms are then discussed with some emphasis on distributed computing strategies. Numerical results...the structure and the exchange of structure motion to the fluid. The computational fluid dynamics code PFES is our finite element code for the numerical ...unstructured meshes). It was numerically demonstrated [1-3] that EBS can be less diffusive than SUPG [4-6] and the standard Finite Volume schemes

The Standard Model in noncommutative geometry: fundamental fermions as internal forms

NASA Astrophysics Data System (ADS)

Dąbrowski, Ludwik; D'Andrea, Francesco; Sitarz, Andrzej

2018-05-01

Given the algebra, Hilbert space H, grading and real structure of the finite spectral triple of the Standard Model, we classify all possible Dirac operators such that H is a self-Morita equivalence bimodule for the associated Clifford algebra.

Recent Developments in the Formability of Aluminum Alloys

NASA Astrophysics Data System (ADS)

Banabic, Dorel; Cazacu, Oana; Paraianu, Liana; Jurco, Paul

2005-08-01

The paper presents a few recent contributions brought by the authors in the field of the formability of aluminum alloys. A new concept for calculating Forming Limit Diagrams (FLD) using the finite element method is presented. The article presents a new strategy for calculating both branches of an FLD, using a Hutchinson - Neale model implemented in a finite element code. The simulations have been performed with Abaqus/Standard. The constitutive model has been implemented using a UMAT subroutine. The plastic anisotropy of the sheet metal is described by the Cazacu-Barlat and the BBC2003 yield criteria. The theoretical predictions have been compared with the results given by the classical Hutchinson - Neale method and also with experimental data for different aluminum alloys. The comparison proves the capability of the finite element method to predict the strain localization. A computer program used for interactive calculation and graphical representation of different Yield Loci and Forming Limit Diagrams has also been developed. The program is based on a Hutchinson-Neale model. Different yield criteria (Hill 1948, Barlat-Lian and BBC 2003) are implemented in this model. The program consists in three modules: a graphical interface for input, a module for the identification and visualization of the yield surfaces, and a module for calculating and visualizing the forming limit curves. A useful facility offered by the program is the possibility to perform the sensitivity analysis both for the yield surface and the forming limit curves. The numerical results can be compared with experimental data, using the import/export facilities included in the program.

Recent Developments in the Formability of Aluminum Alloys

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

Banabic, Dorel; Paraianu, Liana; Jurco, Paul

The paper presents a few recent contributions brought by the authors in the field of the formability of aluminum alloys. A new concept for calculating Forming Limit Diagrams (FLD) using the finite element method is presented. The article presents a new strategy for calculating both branches of an FLD, using a Hutchinson - Neale model implemented in a finite element code. The simulations have been performed with Abaqus/Standard. The constitutive model has been implemented using a UMAT subroutine. The plastic anisotropy of the sheet metal is described by the Cazacu-Barlat and the BBC2003 yield criteria. The theoretical predictions have beenmore » compared with the results given by the classical Hutchinson - Neale method and also with experimental data for different aluminum alloys. The comparison proves the capability of the finite element method to predict the strain localization. A computer program used for interactive calculation and graphical representation of different Yield Loci and Forming Limit Diagrams has also been developed. The program is based on a Hutchinson-Neale model. Different yield criteria (Hill 1948, Barlat-Lian and BBC 2003) are implemented in this model. The program consists in three modules: a graphical interface for input, a module for the identification and visualization of the yield surfaces, and a module for calculating and visualizing the forming limit curves. A useful facility offered by the program is the possibility to perform the sensitivity analysis both for the yield surface and the forming limit curves. The numerical results can be compared with experimental data, using the import/export facilities included in the program.« less

Technical Feasibility of Centrifugal Techniques for Evaluating Hazardous Waste Migration

DTIC Science & Technology

1987-12-01

direct evaluation of the -influence of acceleration on soil moisture movement. A fully implicit finite difference solution scheme was used. The...using the finite difference scheme mentioned earlier. 2. The soil test apparatus for the centrifuge tests was designed and constructed. 110 3...npcr3 f~nJPX 115 S.. 0i U 4 I3 u cc/ U) C~j tC LL~~*- Lý u ’ uiu ’ 4-’ Uju x~j~r3np~~r~tj~jpU W3= 116 Finite Difference Model The finite difference

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 study of the response of nonlinear springs

NASA Technical Reports Server (NTRS)

Hyer, M. W.; Knott, T. W.; Johnson, E. R.

1991-01-01

The various phases to developing a methodology for studying the response of a spring-reinforced arch subjected to a point load are discussed. The arch is simply supported at its ends with both the spring and the point load assumed to be at midspan. The spring is present to off-set the typical snap through behavior normally associated with arches, and to provide a structure that responds with constant resistance over a finite displacement. The various phases discussed consist of the following: (1) development of the closed-form solution for the shallow arch case; (2) development of a finite difference analysis to study (shallow) arches; and (3) development of a finite element analysis for studying more general shallow and nonshallow arches. The two numerical analyses rely on a continuation scheme to move the solution past limit points, and to move onto bifurcated paths, both characteristics being common to the arch problem. An eigenvalue method is used for a continuation scheme. The finite difference analysis is based on a mixed formulation (force and displacement variables) of the governing equations. The governing equations for the mixed formulation are in first order form, making the finite difference implementation convenient. However, the mixed formulation is not well-suited for the eigenvalue continuation scheme. This provided the motivation for the displacement based finite element analysis. Both the finite difference and the finite element analyses are compared with the closed form shallow arch solution. Agreement is excellent, except for the potential problems with the finite difference analysis and the continuation scheme. Agreement between the finite element analysis and another investigator's numerical analysis for deep arches is also good.

Optimization of finite difference forward modeling for elastic waves based on optimum combined window functions

NASA Astrophysics Data System (ADS)

Jian, Wang; Xiaohong, Meng; Hong, Liu; Wanqiu, Zheng; Yaning, Liu; Sheng, Gui; Zhiyang, Wang

2017-03-01

Full waveform inversion and reverse time migration are active research areas for seismic exploration. Forward modeling in the time domain determines the precision of the results, and numerical solutions of finite difference have been widely adopted as an important mathematical tool for forward modeling. In this article, the optimum combined of window functions was designed based on the finite difference operator using a truncated approximation of the spatial convolution series in pseudo-spectrum space, to normalize the outcomes of existing window functions for different orders. The proposed combined window functions not only inherit the characteristics of the various window functions, to provide better truncation results, but also control the truncation error of the finite difference operator manually and visually by adjusting the combinations and analyzing the characteristics of the main and side lobes of the amplitude response. Error level and elastic forward modeling under the proposed combined system were compared with outcomes from conventional window functions and modified binomial windows. Numerical dispersion is significantly suppressed, which is compared with modified binomial window function finite-difference and conventional finite-difference. Numerical simulation verifies the reliability of the proposed method.

Minimizing tooth bending stress in spur gears with simplified shapes of fillet and tool shape determination

NASA Astrophysics Data System (ADS)

Pedersen, N. L.

2015-06-01

The strength of a gear is typically defined relative to durability (pitting) and load capacity (tooth-breakage). Tooth-breakage is controlled by the root shape and this gear part can be designed because there is no contact between gear pairs here. The shape of gears is generally defined by different standards, with the ISO standard probably being the most common one. Gears are manufactured using two principally different tools: rack tools and gear tools. In this work, the bending stress of involute teeth is minimized by shape optimization made directly on the final gear. This optimized shape is then used to find the cutting tool (the gear envelope) that can create this optimized gear shape. A simple but sufficiently flexible root parameterization is applied and emphasis is put on the importance of separating the shape parameterization from the finite element analysis of stresses. Large improvements in the stress level are found.

Full Wave Analysis of Passive Microwave Monolithic Integrated Circuit Devices Using a Generalized Finite Difference Time Domain (GFDTD) Algorithm

NASA Technical Reports Server (NTRS)

Lansing, Faiza S.; Rascoe, Daniel L.

1993-01-01

This paper presents a modified Finite-Difference Time-Domain (FDTD) technique using a generalized conformed orthogonal grid. The use of the Conformed Orthogonal Grid, Finite Difference Time Domain (GFDTD) enables the designer to match all the circuit dimensions, hence eliminating a major source o error in the analysis.

Combination of the discontinuous Galerkin method with finite differences for simulation of seismic wave propagation

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

Lisitsa, Vadim, E-mail: lisitsavv@ipgg.sbras.ru; Novosibirsk State University, Novosibirsk; Tcheverda, Vladimir

We present an algorithm for the numerical simulation of seismic wave propagation in models with a complex near surface part and free surface topography. The approach is based on the combination of finite differences with the discontinuous Galerkin method. The discontinuous Galerkin method can be used on polyhedral meshes; thus, it is easy to handle the complex surfaces in the models. However, this approach is computationally intense in comparison with finite differences. Finite differences are computationally efficient, but in general, they require rectangular grids, leading to the stair-step approximation of the interfaces, which causes strong diffraction of the wavefield. Inmore » this research we present a hybrid algorithm where the discontinuous Galerkin method is used in a relatively small upper part of the model and finite differences are applied to the main part of the model.« less

Finite-key security analyses on passive decoy-state QKD protocols with different unstable sources

PubMed Central

Song, Ting-Ting; Qin, Su-Juan; Wen, Qiao-Yan; Wang, Yu-Kun; Jia, Heng-Yue

2015-01-01

In quantum communication, passive decoy-state QKD protocols can eliminate many side channels, but the protocols without any finite-key analyses are not suitable for in practice. The finite-key securities of passive decoy-state (PDS) QKD protocols with two different unstable sources, type-II parametric down-convention (PDC) and phase randomized weak coherent pulses (WCPs), are analyzed in our paper. According to the PDS QKD protocols, we establish an optimizing programming respectively and obtain the lower bounds of finite-key rates. Under some reasonable values of quantum setup parameters, the lower bounds of finite-key rates are simulated. The simulation results show that at different transmission distances, the affections of different fluctuations on key rates are different. Moreover, the PDS QKD protocol with an unstable PDC source can resist more intensity fluctuations and more statistical fluctuation. PMID:26471947

An Embedded Statistical Method for Coupling Molecular Dynamics and Finite Element Analyses

NASA Technical Reports Server (NTRS)

Saether, E.; Glaessgen, E.H.; Yamakov, V.

2008-01-01

The coupling of molecular dynamics (MD) simulations with finite element methods (FEM) yields computationally efficient models that link fundamental material processes at the atomistic level with continuum field responses at higher length scales. The theoretical challenge involves developing a seamless connection along an interface between two inherently different simulation frameworks. Various specialized methods have been developed to solve particular classes of problems. Many of these methods link the kinematics of individual MD atoms with FEM nodes at their common interface, necessarily requiring that the finite element mesh be refined to atomic resolution. Some of these coupling approaches also require simulations to be carried out at 0 K and restrict modeling to two-dimensional material domains due to difficulties in simulating full three-dimensional material processes. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the standard boundary value problem used to define a coupled domain. The method replaces a direct linkage of individual MD atoms and finite element (FE) nodes with a statistical averaging of atomistic displacements in local atomic volumes associated with each FE node in an interface region. The FEM and MD computational systems are effectively independent and communicate only through an iterative update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM). ESCM provides an enhanced coupling methodology that is inherently applicable to three-dimensional domains, avoids discretization of the continuum model to atomic scale resolution, and permits finite temperature states to be applied.

A New Concurrent Multiscale Methodology for Coupling Molecular Dynamics and Finite Element Analyses

NASA Technical Reports Server (NTRS)

Yamakov, Vesselin; Saether, Erik; Glaessgen, Edward H/.

2008-01-01

The coupling of molecular dynamics (MD) simulations with finite element methods (FEM) yields computationally efficient models that link fundamental material processes at the atomistic level with continuum field responses at higher length scales. The theoretical challenge involves developing a seamless connection along an interface between two inherently different simulation frameworks. Various specialized methods have been developed to solve particular classes of problems. Many of these methods link the kinematics of individual MD atoms with FEM nodes at their common interface, necessarily requiring that the finite element mesh be refined to atomic resolution. Some of these coupling approaches also require simulations to be carried out at 0 K and restrict modeling to two-dimensional material domains due to difficulties in simulating full three-dimensional material processes. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the standard boundary value problem used to define a coupled domain. The method replaces a direct linkage of individual MD atoms and finite element (FE) nodes with a statistical averaging of atomistic displacements in local atomic volumes associated with each FE node in an interface region. The FEM and MD computational systems are effectively independent and communicate only through an iterative update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM). ESCM provides an enhanced coupling methodology that is inherently applicable to three-dimensional domains, avoids discretization of the continuum model to atomic scale resolution, and permits finite temperature states to be applied.

A finite element method for solving the shallow water equations on the sphere

NASA Astrophysics Data System (ADS)

Comblen, Richard; Legrand, Sébastien; Deleersnijder, Eric; Legat, Vincent

Within the framework of ocean general circulation modeling, the present paper describes an efficient way to discretize partial differential equations on curved surfaces by means of the finite element method on triangular meshes. Our approach benefits from the inherent flexibility of the finite element method. The key idea consists in a dialog between a local coordinate system defined for each element in which integration takes place, and a nodal coordinate system in which all local contributions related to a vectorial degree of freedom are assembled. Since each element of the mesh and each degree of freedom are treated in the same way, the so-called pole singularity issue is fully circumvented. Applied to the shallow water equations expressed in primitive variables, this new approach has been validated against the standard test set defined by [Williamson, D.L., Drake, J.B., Hack, J.J., Jakob, R., Swarztrauber, P.N., 1992. A standard test set for numerical approximations to the shallow water equations in spherical geometry. Journal of Computational Physics 102, 211-224]. Optimal rates of convergence for the P1NC-P1 finite element pair are obtained, for both global and local quantities of interest. Finally, the approach can be extended to three-dimensional thin-layer flows in a straightforward manner.

Finite-difference computations of rotor loads

NASA Technical Reports Server (NTRS)

Caradonna, F. X.; Tung, C.

1985-01-01

This paper demonstrates the current and future potential of finite-difference methods for solving real rotor problems which now rely largely on empiricism. The demonstration consists of a simple means of combining existing finite-difference, integral, and comprehensive loads codes to predict real transonic rotor flows. These computations are performed for hover and high-advance-ratio flight. Comparisons are made with experimental pressure data.

Finite-difference computations of rotor loads

NASA Technical Reports Server (NTRS)

Caradonna, F. X.; Tung, C.

1985-01-01

The current and future potential of finite difference methods for solving real rotor problems which now rely largely on empiricism are demonstrated. The demonstration consists of a simple means of combining existing finite-difference, integral, and comprehensive loads codes to predict real transonic rotor flows. These computations are performed for hover and high-advanced-ratio flight. Comparisons are made with experimental pressure data.

Verification of a non-hydrostatic dynamical core using the horizontal spectral element method and vertical finite difference method: 2-D aspects

NASA Astrophysics Data System (ADS)

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

2014-11-01

The non-hydrostatic (NH) compressible Euler equations for dry atmosphere were 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. By using horizontal SEM, which decomposes the physical domain into smaller pieces with a small communication stencil, a high level of scalability can be achieved. By using vertical FDM, an easy method for coupling the dynamics and existing physics packages can be provided. 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 and integral terms. For temporal integration, a time-split, third-order Runge-Kutta (RK3) integration technique was applied. The Euler equations that were used here are in flux form based on the hydrostatic pressure vertical coordinate. The equations are the same as those used in the Weather Research and Forecasting (WRF) model, but a hybrid sigma-pressure vertical coordinate was implemented in this model. We validated the model by conducting the widely used standard tests: linear hydrostatic mountain wave, tracer advection, and gravity wave over the Schär-type mountain, as well as density current, inertia-gravity wave, and rising thermal bubble. The results from these tests demonstrated that the model using the horizontal SEM and the vertical FDM is accurate and robust provided sufficient diffusion is applied. The results with various horizontal resolutions also showed convergence of second-order accuracy due to the accuracy of the time integration scheme and that of the vertical direction, although high-order basis functions were used in the horizontal. By using the 2-D slice model, we effectively showed that the combined spatial discretization method of the spectral element and finite difference methods in the horizontal and vertical directions, respectively, offers a viable method for development of an NH dynamical core.

Numerical time-domain electromagnetics based on finite-difference and convolution

NASA Astrophysics Data System (ADS)

Lin, Yuanqu

Time-domain methods posses a number of advantages over their frequency-domain counterparts for the solution of wideband, nonlinear, and time varying electromagnetic scattering and radiation phenomenon. Time domain integral equation (TDIE)-based methods, which incorporate the beneficial properties of integral equation method, are thus well suited for solving broadband scattering problems for homogeneous scatterers. Widespread adoption of TDIE solvers has been retarded relative to other techniques by their inefficiency, inaccuracy and instability. Moreover, two-dimensional (2D) problems are especially problematic, because 2D Green's functions have infinite temporal support, exacerbating these difficulties. This thesis proposes a finite difference delay modeling (FDDM) scheme for the solution of the integral equations of 2D transient electromagnetic scattering problems. The method discretizes the integral equations temporally using first- and second-order finite differences to map Laplace-domain equations into the Z domain before transforming to the discrete time domain. The resulting procedure is unconditionally stable because of the nature of the Laplace- to Z-domain mapping. The first FDDM method developed in this thesis uses second-order Lagrange basis functions with Galerkin's method for spatial discretization. The second application of the FDDM method discretizes the space using a locally-corrected Nystrom method, which accelerates the precomputation phase and achieves high order accuracy. The Fast Fourier Transform (FFT) is applied to accelerate the marching-on-time process in both methods. While FDDM methods demonstrate impressive accuracy and stability in solving wideband scattering problems for homogeneous scatterers, they still have limitations in analyzing interactions between several inhomogenous scatterers. Therefore, this thesis devises a multi-region finite-difference time-domain (MR-FDTD) scheme based on domain-optimal Green's functions for solving sparsely-populated problems. The scheme uses a discrete Green's function (DGF) on the FDTD lattice to truncate the local subregions, and thus reduces reflection error on the local boundary. A continuous Green's function (CGF) is implemented to pass the influence of external fields into each FDTD region which mitigates the numerical dispersion and anisotropy of standard FDTD. Numerical results will illustrate the accuracy and stability of the proposed techniques.

Direct phase projection and transcranial focusing of ultrasound for brain therapy.

PubMed

Pinton, Gianmarco F; Aubry, Jean-Francois; Tanter, Mickaël

2012-06-01

Ultrasound can be used to noninvasively treat the human brain with hyperthermia by focusing through the skull. To obtain an accurate focus, especially at high frequencies (>500 kHz), the phase of the transmitted wave must be modified to correct the aberrations introduced by the patient's individual skull morphology. Currently, three-dimensional finite-difference time-domain simulations are used to model a point source at the target. The outward-propagating wave crosses the measured representation of the human skull and is recorded at the therapy array transducer locations. The signal is then time reversed and experimentally transmitted back to its origin. These simulations are resource intensive and add a significant delay to treatment planning. Ray propagation is computationally efficient because it neglects diffraction and only describes two propagation parameters: the wave's direction and the phase. We propose a minimal method that is based only on the phase. The phase information is projected from the external skull surface to the array locations. This replaces computationally expensive finite-difference computations with an almost instantaneous direct phase projection calculation. For the five human skull samples considered, the phase distribution outside of the skull is shown to vary by less than λ/20 as it propagates over a 5 cm distance and the validity of phase projection is established over these propagation distances. The phase aberration introduced by the skull is characterized and is shown to have a good correspondence with skull morphology. The shape of this aberration is shown to have little variation with propagation distance. The focusing quality with the proposed phase-projection algorithm is shown to be indistinguishable from the gold-standard full finite-difference simulation. In conclusion, a spherical wave that is aberrated by the skull has a phase propagation that can be accurately described as radial, even after it has been distorted. By combining finite-difference simulations with a phase-projection algorithm, the time required for treatment planning is significantly reduced. The correlation length of the phase is used to validate the algorithm and it can also be used to provide guiding parameters for clinical array transducer design in terms of transducer spacing and phase error.

An energy-based equilibrium contact angle boundary condition on jagged surfaces for phase-field methods.

PubMed

Frank, Florian; Liu, Chen; Scanziani, Alessio; Alpak, Faruk O; Riviere, Beatrice

2018-08-01

We consider an energy-based boundary condition to impose an equilibrium wetting angle for the Cahn-Hilliard-Navier-Stokes phase-field model on voxel-set-type computational domains. These domains typically stem from μCT (micro computed tomography) imaging of porous rock and approximate a (on μm scale) smooth domain with a certain resolution. Planar surfaces that are perpendicular to the main axes are naturally approximated by a layer of voxels. However, planar surfaces in any other directions and curved surfaces yield a jagged/topologically rough surface approximation by voxels. For the standard Cahn-Hilliard formulation, where the contact angle between the diffuse interface and the domain boundary (fluid-solid interface/wall) is 90°, jagged surfaces have no impact on the contact angle. However, a prescribed contact angle smaller or larger than 90° on jagged voxel surfaces is amplified. As a remedy, we propose the introduction of surface energy correction factors for each fluid-solid voxel face that counterbalance the difference of the voxel-set surface area with the underlying smooth one. The discretization of the model equations is performed with the discontinuous Galerkin method. However, the presented semi-analytical approach of correcting the surface energy is equally applicable to other direct numerical methods such as finite elements, finite volumes, or finite differences, since the correction factors appear in the strong formulation of the model. Copyright © 2018 Elsevier Inc. All rights reserved.

One-loop topological expansion for spin glasses in the large connectivity limit

NASA Astrophysics Data System (ADS)

Chiara Angelini, Maria; Parisi, Giorgio; Ricci-Tersenghi, Federico

2018-01-01

We apply for the first time a new one-loop topological expansion around the Bethe solution to the spin-glass model with a field in the high connectivity limit, following the methodological scheme proposed in a recent work. The results are completely equivalent to the well-known ones, found by standard field-theoretical expansion around the fully connected model (Bray and Roberts 1980, and following works). However this method has the advantage that the starting point is the original Hamiltonian of the model, with no need to define an associated field theory, nor to know the initial values of the couplings, and the computations have a clear and simple physical meaning. Moreover this new method can also be applied in the case of zero temperature, when the Bethe model has a transition in field, contrary to the fully connected model that is always in the spin-glass phase. Sharing with finite-dimensional model the finite connectivity properties, the Bethe lattice is clearly a better starting point for an expansion with respect to the fully connected model. The present work is a first step towards the generalization of this new expansion to more difficult and interesting cases as the zero-temperature limit, where the expansion could lead to different results with respect to the standard one.

Two Perspectives on the Origin of the Standard Genetic Code

NASA Astrophysics Data System (ADS)

Sengupta, Supratim; Aggarwal, Neha; Bandhu, Ashutosh Vishwa

2014-12-01

The origin of a genetic code made it possible to create ordered sequences of amino acids. In this article we provide two perspectives on code origin by carrying out simulations of code-sequence coevolution in finite populations with the aim of examining how the standard genetic code may have evolved from more primitive code(s) encoding a small number of amino acids. We determine the efficacy of the physico-chemical hypothesis of code origin in the absence and presence of horizontal gene transfer (HGT) by allowing a diverse collection of code-sequence sets to compete with each other. We find that in the absence of horizontal gene transfer, natural selection between competing codes distinguished by differences in the degree of physico-chemical optimization is unable to explain the structure of the standard genetic code. However, for certain probabilities of the horizontal transfer events, a universal code emerges having a structure that is consistent with the standard genetic code.

Solving the incompressible surface Navier-Stokes equation by surface finite elements

NASA Astrophysics Data System (ADS)

Reuther, Sebastian; Voigt, Axel

2018-01-01

We consider a numerical approach for the incompressible surface Navier-Stokes equation on surfaces with arbitrary genus g (S ) . The approach is based on a reformulation of the equation in Cartesian coordinates of the embedding R3, penalization of the normal component, a Chorin projection method, and discretization in space by surface finite elements for each component. The approach thus requires only standard ingredients which most finite element implementations can offer. We compare computational results with discrete exterior calculus simulations on a torus and demonstrate the interplay of the flow field with the topology by showing realizations of the Poincaré-Hopf theorem on n-tori.

Group iterative methods for the solution of two-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Balasim, Alla Tareq; Ali, Norhashidah Hj. Mohd.

2016-06-01

Variety of problems in science and engineering may be described by fractional partial differential equations (FPDE) in relation to space and/or time fractional derivatives. The difference between time fractional diffusion equations and standard diffusion equations lies primarily in the time derivative. Over the last few years, iterative schemes derived from the rotated finite difference approximation have been proven to work well in solving standard diffusion equations. However, its application on time fractional diffusion counterpart is still yet to be investigated. In this paper, we will present a preliminary study on the formulation and analysis of new explicit group iterative methods in solving a two-dimensional time fractional diffusion equation. These methods were derived from the standard and rotated Crank-Nicolson difference approximation formula. Several numerical experiments were conducted to show the efficiency of the developed schemes in terms of CPU time and iteration number. At the request of all authors of the paper an updated version of this article was published on 7 July 2016. The original version supplied to AIP Publishing contained an error in Table 1 and References 15 and 16 were incomplete. These errors have been corrected in the updated and republished article.

Parity oscillations and photon correlation functions in the Z2-U (1 ) Dicke model at a finite number of atoms or qubits

NASA Astrophysics Data System (ADS)

Yi-Xiang, Yu; Ye, Jinwu; Zhang, CunLin

2016-08-01

Four standard quantum optics models, that is, the Rabi, Dicke, Jaynes-Cummings, and Tavis-Cummings models, were proposed by physicists many decades ago. Despite their relative simple forms and many previous theoretical works, their physics at a finite N , especially inside the superradiant regime, remain unknown. In this work, by using the strong-coupling expansion and exact diagonalization (ED), we study the Z2-U(1 ) Dicke model with independent rotating-wave coupling g and counterrotating-wave coupling g' at a finite N . This model includes the four standard quantum optics models as its various special limits. We show that in the superradiant phase, the system's energy levels are grouped into doublets with even and odd parity. Any anisotropy β =g'/g ≠1 leads to the oscillation of parities in both the ground and excited doublets as the atom-photon coupling strength increases. The oscillations will be pushed to the infinite coupling strength in the isotropic Z2 limit β =1 . We find nearly perfect agreement between the strong-coupling expansion and the ED in the superradiant regime when β is not too small. We also compute the photon correlation functions, squeezing spectrum, and number correlation functions that can be measured by various standard optical techniques.

Kalman filters for assimilating near-surface observations into the Richards equation - Part 1: Retrieving state profiles with linear and nonlinear numerical schemes

NASA Astrophysics Data System (ADS)

Chirico, G. B.; Medina, H.; Romano, N.

2014-07-01

This paper examines the potential of different algorithms, based on the Kalman filtering approach, for assimilating near-surface observations into a one-dimensional Richards equation governing soil water flow in soil. Our specific objectives are: (i) to compare the efficiency of different Kalman filter algorithms in retrieving matric pressure head profiles when they are implemented with different numerical schemes of the Richards equation; (ii) to evaluate the performance of these algorithms when nonlinearities arise from the nonlinearity of the observation equation, i.e. when surface soil water content observations are assimilated to retrieve matric pressure head values. The study is based on a synthetic simulation of an evaporation process from a homogeneous soil column. Our first objective is achieved by implementing a Standard Kalman Filter (SKF) algorithm with both an explicit finite difference scheme (EX) and a Crank-Nicolson (CN) linear finite difference scheme of the Richards equation. The Unscented (UKF) and Ensemble Kalman Filters (EnKF) are applied to handle the nonlinearity of a backward Euler finite difference scheme. To accomplish the second objective, an analogous framework is applied, with the exception of replacing SKF with the Extended Kalman Filter (EKF) in combination with a CN numerical scheme, so as to handle the nonlinearity of the observation equation. While the EX scheme is computationally too inefficient to be implemented in an operational assimilation scheme, the retrieval algorithm implemented with a CN scheme is found to be computationally more feasible and accurate than those implemented with the backward Euler scheme, at least for the examined one-dimensional problem. The UKF appears to be as feasible as the EnKF when one has to handle nonlinear numerical schemes or additional nonlinearities arising from the observation equation, at least for systems of small dimensionality as the one examined in this study.

Computer-Oriented Calculus Courses Using Finite Differences.

ERIC Educational Resources Information Center

Gordon, Sheldon P.

The so-called discrete approach in calculus instruction involves introducing topics from the calculus of finite differences and finite sums, both for motivation and as useful tools for applications of the calculus. In particular, it provides an ideal setting in which to incorporate computers into calculus courses. This approach has been…

Backscatter Correction Algorithm for TBI Treatment Conditions

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

Sanchez-Nieto, B.; Sanchez-Doblado, F.; Arrans, R.

2015-01-15

The accuracy requirements in target dose delivery is, according to ICRU, ±5%. This is so not only in standard radiotherapy but also in total body irradiation (TBI). Physical dosimetry plays an important role in achieving this recommended level. The semi-infinite phantoms, customarily used for dosimetry purposes, give scatter conditions different to those of the finite thickness of the patient. So dose calculated in patient’s points close to beam exit surface may be overestimated. It is then necessary to quantify the backscatter factor in order to decrease the uncertainty in this dose calculation. The backward scatter has been well studied atmore » standard distances. The present work intends to evaluate the backscatter phenomenon under our particular TBI treatment conditions. As a consequence of this study, a semi-empirical expression has been derived to calculate (within 0.3% uncertainty) the backscatter factor. This factor depends lineally on the depth and exponentially on the underlying tissue. Differences found in the qualitative behavior with respect to standard distances are due to scatter in the bunker wall close to the measurement point.« less

ADAPTION OF NONSTANDARD PIPING COMPONENTS INTO PRESENT DAY SEISMIC CODES

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

D. T. Clark; M. J. Russell; R. E. Spears

2009-07-01

With spiraling energy demand and flat energy supply, there is a need to extend the life of older nuclear reactors. This sometimes requires that existing systems be evaluated to present day seismic codes. Older reactors built in the 1960s and early 1970s often used fabricated piping components that were code compliant during their initial construction time period, but are outside the standard parameters of present-day piping codes. There are several approaches available to the analyst in evaluating these non-standard components to modern codes. The simplest approach is to use the flexibility factors and stress indices for similar standard components withmore » the assumption that the non-standard component’s flexibility factors and stress indices will be very similar. This approach can require significant engineering judgment. A more rational approach available in Section III of the ASME Boiler and Pressure Vessel Code, which is the subject of this paper, involves calculation of flexibility factors using finite element analysis of the non-standard component. Such analysis allows modeling of geometric and material nonlinearities. Flexibility factors based on these analyses are sensitive to the load magnitudes used in their calculation, load magnitudes that need to be consistent with those produced by the linear system analyses where the flexibility factors are applied. This can lead to iteration, since the magnitude of the loads produced by the linear system analysis depend on the magnitude of the flexibility factors. After the loading applied to the nonstandard component finite element model has been matched to loads produced by the associated linear system model, the component finite element model can then be used to evaluate the performance of the component under the loads with the nonlinear analysis provisions of the Code, should the load levels lead to calculated stresses in excess of Allowable stresses. This paper details the application of component-level finite element modeling to account for geometric and material nonlinear component behavior in a linear elastic piping system model. Note that this technique can be applied to the analysis of B31 piping systems.« less

Computation of Nonlinear Backscattering Using a High-Order Numerical Method

NASA Technical Reports Server (NTRS)

Fibich, G.; Ilan, B.; Tsynkov, S.

2001-01-01

The nonlinear Schrodinger equation (NLS) is the standard model for propagation of intense laser beams in Kerr media. The NLS is derived from the nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. In this study we use a fourth-order finite-difference method supplemented by special two-way artificial boundary conditions (ABCs) to solve the NLH as a boundary value problem. Our numerical methodology allows for a direct comparison of the NLH and NLS models and for an accurate quantitative assessment of the backscattered signal.

Non-Abelian gauge preheating

NASA Astrophysics Data System (ADS)

Adshead, Peter; Giblin, John T.; Weiner, Zachary J.

2017-12-01

We study preheating in models where a scalar inflaton is directly coupled to a non-Abelian S U (2 ) gauge field. In particular, we examine m2ϕ2 inflation with a conformal, dilatonlike coupling to the non-Abelian sector. We describe a numerical scheme that combines lattice gauge theory with standard finite difference methods applied to the scalar field. We show that a significant tachyonic instability allows for efficient preheating, which is parametrically suppressed by increasing the non-Abelian self-coupling. Additionally, we comment on the technical implementation of the evolution scheme and setting initial conditions.

A fast direct solver for a class of two-dimensional separable elliptic equations on the sphere

NASA Technical Reports Server (NTRS)

Moorthi, Shrinivas; Higgins, R. Wayne

1992-01-01

An efficient, direct, second-order solver for the discrete solution of two-dimensional separable elliptic equations on the sphere is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wavenumber and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

High Order Filter Methods for the Non-ideal Compressible MHD Equations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjoegreen, Bjoern

2003-01-01

The generalization of a class of low-dissipative high order filter finite difference methods for long time wave propagation of shock/turbulence/combustion compressible viscous gas dynamic flows to compressible MHD equations for structured curvilinear grids has been achieved. The new scheme is shown to provide a natural and efficient way for the minimization of the divergence of the magnetic field numerical error. Standard divergence cleaning is not required by the present filter approach. For certain non-ideal MHD test cases, divergence free preservation of the magnetic fields has been achieved.

Divergence Free High Order Filter Methods for the Compressible MHD Equations

NASA Technical Reports Server (NTRS)

Yea, H. C.; Sjoegreen, Bjoern

2003-01-01

The generalization of a class of low-dissipative high order filter finite difference methods for long time wave propagation of shock/turbulence/combustion compressible viscous gas dynamic flows to compressible MHD equations for structured curvilinear grids has been achieved. The new scheme is shown to provide a natural and efficient way for the minimization of the divergence of the magnetic field numerical error. Standard diver- gence cleaning is not required by the present filter approach. For certain MHD test cases, divergence free preservation of the magnetic fields has been achieved.

Extended Finite Element Method with Simplified Spherical Harmonics Approximation for the Forward Model of Optical Molecular Imaging

PubMed Central

Li, Wei; Yi, Huangjian; Zhang, Qitan; Chen, Duofang; Liang, Jimin

2012-01-01

An extended finite element method (XFEM) for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SPN). In XFEM scheme of SPN equations, the signed distance function is employed to accurately represent the internal tissue boundary, and then it is used to construct the enriched basis function of the finite element scheme. Therefore, the finite element calculation can be carried out without the time-consuming internal boundary mesh generation. Moreover, the required overly fine mesh conforming to the complex tissue boundary which leads to excess time cost can be avoided. XFEM conveniences its application to tissues with complex internal structure and improves the computational efficiency. Phantom and digital mouse experiments were carried out to validate the efficiency of the proposed method. Compared with standard finite element method and classical Monte Carlo (MC) method, the validation results show the merits and potential of the XFEM for optical imaging. PMID:23227108

Extended finite element method with simplified spherical harmonics approximation for the forward model of optical molecular imaging.

PubMed

Li, Wei; Yi, Huangjian; Zhang, Qitan; Chen, Duofang; Liang, Jimin

2012-01-01

An extended finite element method (XFEM) for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SP(N)). In XFEM scheme of SP(N) equations, the signed distance function is employed to accurately represent the internal tissue boundary, and then it is used to construct the enriched basis function of the finite element scheme. Therefore, the finite element calculation can be carried out without the time-consuming internal boundary mesh generation. Moreover, the required overly fine mesh conforming to the complex tissue boundary which leads to excess time cost can be avoided. XFEM conveniences its application to tissues with complex internal structure and improves the computational efficiency. Phantom and digital mouse experiments were carried out to validate the efficiency of the proposed method. Compared with standard finite element method and classical Monte Carlo (MC) method, the validation results show the merits and potential of the XFEM for optical imaging.

Navier-Stokes Solutions for Spin-Up from Rest in a Cylindrical Container

DTIC Science & Technology

1979-09-01

CONDITIONS The calculations employ a finite - difference analog of the unsteady axisyimetric Navier-Stokes equations formulated in cylindrical coordinates...derivatives are approximated by second- order accurate one-sided difference formulae involving three time levels. * The following finite - difference ...equation are identical in form to Equations (13). The finite - difference representations for the ?-equation are: "(i)[aJ~lk " /i’,J-l2k] T (14a) •g I

Real-time and rapid GNSS solutions from the M8.2 September 2017 Tehuantepec Earthquake and implications for Earthquake and Tsunami Early Warning Systems

NASA Astrophysics Data System (ADS)

Mencin, D.; Hodgkinson, K. M.; Mattioli, G. S.

2017-12-01

In support of hazard research and Earthquake Early Warning (EEW) Systems UNAVCO operates approximately 800 RT-GNSS stations throughout western North America and Alaska (EarthScope Plate Boundary Observatory), Mexico (TLALOCNet), and the pan-Caribbean region (COCONet). Our system produces and distributes raw data (BINEX and RTCM3) and real-time Precise Point Positions via the Trimble PIVOT Platform (RTX). The 2017-09-08 earthquake M8.2 located 98 km SSW of Tres Picos, Mexico is the first great earthquake to occur within the UNAVCO RT-GNSS footprint, which allows for a rigorous analysis of our dynamic and static processing methods. The need for rapid geodetic solutions ranges from seconds (EEW systems) to several minutes (Tsunami Warning and NEIC moment tensor and finite fault models). Here, we compare and quantify the relative processing strategies for producing static offsets, moment tensors and geodetically determined finite fault models using data recorded during this event. We also compare the geodetic solutions with the USGS NEIC seismically derived moment tensors and finite fault models, including displacement waveforms generated from these models. We define kinematic post-processed solutions from GIPSY-OASISII (v6.4) with final orbits and clocks as a "best" case reference to evaluate the performance of our different processing strategies. We find that static displacements of a few centimeters or less are difficult to resolve in the real-time GNSS position estimates. The standard daily 24-hour solutions provide the highest-quality data-set to determine coseismic offsets, but these solutions are delayed by at least 48 hours after the event. Dynamic displacements, estimated in real-time, however, show reasonable agreement with final, post-processed position estimates, and while individual position estimates have large errors, the real-time solutions offer an excellent operational option for EEW systems, including the use of estimated peak-ground displacements or directly inverting for finite-fault solutions. In the near-field, we find that the geodetically-derived moment tensors and finite fault models differ significantly with seismically-derived models, highlighting the utility of using geodetic data in hazard applications.

An Exponential Finite Difference Technique for Solving Partial Differential Equations. M.S. Thesis - Toledo Univ., Ohio

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.

exponential finite difference technique for solving partial differential equations

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

Handschuh, R.F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that weremore » more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.« less

3D Gaussian Beam Modeling

DTIC Science & Technology

2011-09-01

optimized building blocks such as a parallelized tri-diagonal linear solver (used in the “implicit finite differences ” and split-step Pade PE models...and Ding Lee. “A finite - difference treatment of interface conditions for the parabolic wave equation: The horizontal interface.” The Journal of the...Acoustical Society of America, 71(4):855, 1982. 3. Ding Lee and Suzanne T. McDaniel. “A finite - difference treatment of interface conditions for

A Finite Difference Numerical Model for the Propagation of Finite Amplitude Acoustical Blast Waves Outdoors Over Hard and Porous Surfaces

DTIC Science & Technology

1991-09-01

Difference Numerical Model for the Propagation of Finite Amplitude Acoustical Blast Waves Outdoors Over Hard and Porous Surfaces by Victor W. Sparrow...The nonlinear acoustic propagation effects require a numerical solution in the time domain. To model a porous ground surface, which in the frequency...incident on the hard and porous surfaces were produced. The model predicted that near grazing finite amplitude acoustic blast waves decay with distance

Computational modeling of chemo-electro-mechanical coupling: A novel implicit monolithic finite element approach

PubMed Central

Wong, J.; Göktepe, S.; Kuhl, E.

2014-01-01

Summary Computational modeling of the human heart allows us to predict how chemical, electrical, and mechanical fields interact throughout a cardiac cycle. Pharmacological treatment of cardiac disease has advanced significantly over the past decades, yet it remains unclear how the local biochemistry of an individual heart cell translates into global cardiac function. Here we propose a novel, unified strategy to simulate excitable biological systems across three biological scales. To discretize the governing chemical, electrical, and mechanical equations in space, we propose a monolithic finite element scheme. We apply a highly efficient and inherently modular global-local split, in which the deformation and the transmembrane potential are introduced globally as nodal degrees of freedom, while the chemical state variables are treated locally as internal variables. To ensure unconditional algorithmic stability, we apply an implicit backward Euler finite difference scheme to discretize the resulting system in time. To increase algorithmic robustness and guarantee optimal quadratic convergence, we suggest an incremental iterative Newton-Raphson scheme. The proposed algorithm allows us to simulate the interaction of chemical, electrical, and mechanical fields during a representative cardiac cycle on a patient-specific geometry, robust and stable, with calculation times on the order of four days on a standard desktop computer. PMID:23798328

Finite element analysis of a condylar support prosthesis to replace the temporomandibular joint.

PubMed

Abel, Eric W; Hilgers, André; McLoughlin, Philip M

2015-04-01

This paper presents a finite element study of a temporomandibular joint (TMJ) prosthesis in which the mandibular component sits on the condyle after removal of only the diseased articular surface and minimal amount of condylar bone. The condylar support prosthesis (CSP) is customised to fit the patient and allows a large part of the joint force to be transmitted through the condyle to the ramus, rather than relying only on transfer of the load by the screws that fix the prosthesis to the ramus. The 3-dimensional structural finite element analysis compared a design of CSP with a standard commercial prosthesis and one that was modified to fit the ramus, to relate the findings to the different designs and geometrical features. The models simulated an incisal bite under high loading. In the CSP and in its fixation screws, the stresses were much lower than those in the other 2 prostheses and the bone strains were at physiological levels. The CSP gives a more physiological form of load transfer than is possible without the condylar contact, and considerably reduces the amount of strain on the bone around the screws. Copyright © 2015 The British Association of Oral and Maxillofacial Surgeons. Published by Elsevier Ltd. All rights reserved.

Solution of the advection-dispersion equation in two dimensions by a finite-volume Eulerian-Lagrangian localized adjoint method

USGS Publications Warehouse

Healy, R.W.; Russell, T.F.

1998-01-01

We extend the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) for solution of the advection-dispersion equation to two dimensions. The method can conserve mass globally and is not limited by restrictions on the size of the grid Peclet or Courant number. Therefore, it is well suited for solution of advection-dominated ground-water solute transport problems. In test problem comparisons with standard finite differences, FVELLAM is able to attain accurate solutions on much coarser space and time grids. On fine grids, the accuracy of the two methods is comparable. A critical aspect of FVELLAM (and all other ELLAMs) is evaluation of the mass storage integral from the preceding time level. In FVELLAM this may be accomplished with either a forward or backtracking approach. The forward tracking approach conserves mass globally and is the preferred approach. The backtracking approach is less computationally intensive, but not globally mass conservative. Boundary terms are systematically represented as integrals in space and time which are evaluated by a common integration scheme in conjunction with forward tracking through time. Unlike the one-dimensional case, local mass conservation cannot be guaranteed, so slight oscillations in concentration can develop, particularly in the vicinity of inflow or outflow boundaries. Published by Elsevier Science Ltd.

A progress report on estuary modeling by the finite-element method

USGS Publications Warehouse

Gray, William G.

1978-01-01

Various schemes are investigated for finite-element modeling of two-dimensional surface-water flows. The first schemes investigated combine finite-element spatial discretization with split-step time stepping schemes that have been found useful in finite-difference computations. Because of the large number of numerical integrations performed in space and the large sparse matrices solved, these finite-element schemes were found to be economically uncompetitive with finite-difference schemes. A very promising leapfrog scheme is proposed which, when combined with a novel very fast spatial integration procedure, eliminates the need to solve any matrices at all. Additional problems attacked included proper propagation of waves and proper specification of the normal flow-boundary condition. This report indicates work in progress and does not come to a definitive conclusion as to the best approach for finite-element modeling of surface-water problems. The results presented represent findings obtained between September 1973 and July 1976. (Woodard-USGS)

Fourier/Chebyshev methods for the incompressible Navier-Stokes equations in finite domains

NASA Technical Reports Server (NTRS)

Corral, Roque; Jimenez, Javier

1992-01-01

A fully spectral numerical scheme for the incompressible Navier-Stokes equations in domains which are infinite or semi-infinite in one dimension. The domain is not mapped, and standard Fourier or Chebyshev expansions can be used. The handling of the infinite domain does not introduce any significant overhead. The scheme assumes that the vorticity in the flow is essentially concentrated in a finite region, which is represented numerically by standard spectral collocation methods. To accomodate the slow exponential decay of the velocities at infinity, extra expansion functions are introduced, which are handled analytically. A detailed error analysis is presented, and two applications to Direct Numerical Simulation of turbulent flows are discussed in relation with the numerical performance of the scheme.

A Matlab-based finite-difference solver for the Poisson problem with mixed Dirichlet-Neumann boundary conditions

NASA Astrophysics Data System (ADS)

Reimer, Ashton S.; Cheviakov, Alexei F.

2013-03-01

A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers. Catalogue identifier: AENQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v3.0 No. of lines in distributed program, including test data, etc.: 102793 No. of bytes in distributed program, including test data, etc.: 369378 Distribution format: tar.gz Programming language: Matlab 2010a. Computer: PC, Macintosh. Operating system: Windows, OSX, Linux. RAM: 8 GB (8, 589, 934, 592 bytes) Classification: 4.3. Nature of problem: To solve the Poisson problem in a standard domain with “patchy surface”-type (strongly heterogeneous) Neumann/Dirichlet boundary conditions. Solution method: Finite difference with mesh refinement. Restrictions: Spherical domain in 3D; rectangular domain or a disk in 2D. Unusual features: Choice between mldivide/iterative solver for the solution of large system of linear algebraic equations that arise. Full user control of Neumann/Dirichlet boundary conditions and mesh refinement. Running time: Depending on the number of points taken and the geometry of the domain, the routine may take from less than a second to several hours to execute.

Effects of foot posture on fifth metatarsal fracture healing: a finite element study.

PubMed

Brilakis, Emmanuel; Kaselouris, Evaggelos; Xypnitos, Frank; Provatidis, Christopher G; Efstathopoulos, Nicolas

2012-01-01

The goal of this study was to evaluate the effects of maintaining different foot postures during healing of proximal fifth metatarsal fractures for each of 3 common fracture types. A 3-dimensional (3D) finite element model of a human foot was developed and 3 loading situations were evaluated, including the following: (1) normal weightbearing, (2) standing with the affected foot in dorsiflexion at the ankle, and (3) standing with the affected foot in eversion. Three different stages of the fracture-healing process were studied, including: stage 1, wherein the material interposed between the fractured edges was the initial connective tissue; stage 2, wherein connective tissue had been replaced by soft callus; and stage 3, wherein soft callus was replaced by mature bone. Thus, 30 3D finite element models were analyzed that took into account fracture type, foot posture, and healing stage. Different foot postures did not statistically significantly affect the peak-developed strains on the fracture site. When the fractured foot was everted or dorsiflexed, it developed a slightly higher strain within the fracture than when it was in the normal weightbearing position. In Jones fractures, eversion of the foot caused further torsional strain and we believe that this position should be avoided during foot immobilization during the treatment of fifth metatarsal base fractures. Tuberosity avulsion fractures and Jones fractures seem to be biomechanically stable fractures, as compared with shaft fractures. Our understanding of the literature and experience indicate that current clinical observations and standard therapeutic options are in accordance with the results that we observed in this investigation, with the exception of Jones fractures. Copyright © 2012 American College of Foot and Ankle Surgeons. Published by Elsevier Inc. All rights reserved.

Face-based smoothed finite element method for real-time simulation of soft tissue

NASA Astrophysics Data System (ADS)

Mendizabal, Andrea; Bessard Duparc, Rémi; Bui, Huu Phuoc; Paulus, Christoph J.; Peterlik, Igor; Cotin, Stéphane

2017-03-01

In soft tissue surgery, a tumor and other anatomical structures are usually located using the preoperative CT or MR images. However, due to the deformation of the concerned tissues, this information suffers from inaccuracy when employed directly during the surgery. In order to account for these deformations in the planning process, the use of a bio-mechanical model of the tissues is needed. Such models are often designed using the finite element method (FEM), which is, however, computationally expensive, in particular when a high accuracy of the simulation is required. In our work, we propose to use a smoothed finite element method (S-FEM) in the context of modeling of the soft tissue deformation. This numerical technique has been introduced recently to overcome the overly stiff behavior of the standard FEM and to improve the solution accuracy and the convergence rate in solid mechanics problems. In this paper, a face-based smoothed finite element method (FS-FEM) using 4-node tetrahedral elements is presented. We show that in some cases, the method allows for reducing the number of degrees of freedom, while preserving the accuracy of the discretization. The method is evaluated on a simulation of a cantilever beam loaded at the free end and on a simulation of a 3D cube under traction and compression forces. Further, it is applied to the simulation of the brain shift and of the kidney's deformation. The results demonstrate that the method outperforms the standard FEM in a bending scenario and that has similar accuracy as the standard FEM in the simulations of the brain-shift and of the kidney's deformation.

Theory and simulation of time-fractional fluid diffusion in porous media

NASA Astrophysics Data System (ADS)

Carcione, José M.; Sanchez-Sesma, Francisco J.; Luzón, Francisco; Perez Gavilán, Juan J.

2013-08-01

We simulate a fluid flow in inhomogeneous anisotropic porous media using a time-fractional diffusion equation and the staggered Fourier pseudospectral method to compute the spatial derivatives. A fractional derivative of the order of 0 < ν < 2 replaces the first-order time derivative in the classical diffusion equation. It implies a time-dependent permeability tensor having a power-law time dependence, which describes memory effects and accounts for anomalous diffusion. We provide a complete analysis of the physics based on plane waves. The concepts of phase, group and energy velocities are analyzed to describe the location of the diffusion front, and the attenuation and quality factors are obtained to quantify the amplitude decay. We also obtain the frequency-domain Green function. The time derivative is computed with the Grünwald-Letnikov summation, which is a finite-difference generalization of the standard finite-difference operator to derivatives of fractional order. The results match the analytical solution obtained from the Green function. An example of the pressure field generated by a fluid injection in a heterogeneous sandstone illustrates the performance of the algorithm for different values of ν. The calculation requires storing the whole pressure field in the computer memory since anomalous diffusion ‘recalls the past’.

Algorithm XXX : functions to support the IEEE standard for binary floating-point arithmetic.

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

Cody, W. J.; Mathematics and Computer Science

1993-12-01

This paper describes C programs for the support functions copysign(x,y), logb(x), scalb(x,n), nextafter(x,y), finite(x), and isnan(x) recommended in the Appendix to the IEEE Standard for Binary Floating-Point Arithmetic. In the case of logb, the modified definition given in the later IEEE Standard for Radix-Independent Floating-Point Arithmetic is followed. These programs should run without modification on most systems conforming to the binary standard.

Asymptotic analysis of numerical wave propagation in finite difference equations

NASA Technical Reports Server (NTRS)

Giles, M.; Thompkins, W. T., Jr.

1983-01-01

An asymptotic technique is developed for analyzing the propagation and dissipation of wave-like solutions to finite difference equations. It is shown that for each fixed complex frequency there are usually several wave solutions with different wavenumbers and the slowly varying amplitude of each satisfies an asymptotic amplitude equation which includes the effects of smoothly varying coefficients in the finite difference equations. The local group velocity appears in this equation as the velocity of convection of the amplitude. Asymptotic boundary conditions coupling the amplitudes of the different wave solutions are also derived. A wavepacket theory is developed which predicts the motion, and interaction at boundaries, of wavepackets, wave-like disturbances of finite length. Comparison with numerical experiments demonstrates the success and limitations of the theory. Finally an asymptotic global stability analysis is developed.

Selected engineering properties and applications of EPS geofoam

NASA Astrophysics Data System (ADS)

Elragi, Ahmed Fouad

Expanded polystyrene (EPS) geofoam is a lightweight material that has been used in engineering applications since at least the 1950s. Its density is about a hundredth of that of soil. It has good thermal insulation properties with stiffness and compression strength comparable to medium clay. It is utilized in reducing settlement below embankments, sound and vibration damping, reducing lateral pressure on substructures, reducing stresses on rigid buried conduits and related applications. This study starts with an overview on EPS geofoam. EPS manufacturing processes are described followed by a review of engineering properties found in previous research work done so far. Standards and design manuals applicable to EPS are presented. Selected EPS geofoam-engineering applications are discussed with examples. State-of-the-art of experimental work is done on different sizes of EPS specimens under different loading rates for better understanding of the behavior of the material. The effects of creep, sample size, strain rate and cyclic loading on the stress strain response are studied. Equations for the initial modulus and the strength of the material under compression for different strain rates are presented. The initial modulus and Poisson's ratio are discussed in detail. Sample size effect on creep behavior is examined. Three EPS projects are shown in this study. The creep behavior of the largest EPS geofoam embankment fill is shown. Results from laboratory tests, mathematical modeling and field records are compared to each other. Field records of a geofoam-stabilized slope are compared to finite difference analysis results. Lateral stress reduction on an EPS backfill retaining structure is analyzed. The study ends with a discussion on two promising properties of EPS geofoam. These are the damping ability and the compressibility of this material. Finite element analysis, finite difference analysis and lab results are included in this discussion. The discussion with the rest of the study points towards the main conclusion that EPS geofoam is the future material of promise in various civil engineering applications.

A biomechanical comparison of four fixed-angle dorsal plates in a finite element model of dorsally-unstable radius fracture.

PubMed

Knežević, Josip; Kodvanj, Janoš; Čukelj, Fabijan; Pamuković, Frane; Pavić, Arsen

2017-11-01

To compare the finite element models of two different composite radius fracture patterns, reduced and stabilised with four different fixed-angle dorsal plates during axial, dorsal and volar loading conditions. Eight different plastic models representing four AO/ASIF type 23-A3 distal radius fractures and four AO/ASIF 23-C2 distal radius fractures were obtained and fixed each with 1 of 4 methods: a standard dorsal non-anatomical fixed angle T-plate (3.5mm Dorsal T-plate, Synthes), anatomical fixed-angle double plates (2.4mm LCP Dorsal Distal Radius, Synthes), anatomical fixed angle T-plate (2.4mm Acu-Loc Dorsal Plate, Acumed) or anatomical variable-angle dorsal T-plate (3.5mm, Dorsal Plate, Zrinski). Composite radius with plate and screws were scanned with a 3D optical scanner and later processed in Abaqus Software to generate the finite element model. All models were axially loaded at 3 points (centrally, volarly and dorsally) with 50 N forces to avoid the appearance of plastic deformations of the models. Total displacements at the end of the bone and the stresses in the bones and plates were determined and compared. Maximal von Mises stress in bone for 3-part fracture models was very similar to that in 2-part fracture models. The biggest difference between models and the largest displacements were seen during volar loading. The stresses in all models were the highest above the fracture gap. The best performance in all parameters tested was with the Zrinski plate and the most modest results were with the Synthes T-plate. There was no significant difference between 2-part (AO/ASIF type 23-A3) and 3-part (AO/ASIF 23-C2) fracture models. Maximal stresses in the plates appeared above the fracture gap; therefore, it is worth considering the development of plates without screw holes above the gap. © 2017 Elsevier Ltd. All rights reserved.

Mixed finite-difference scheme for analysis of simply supported thick plates.

NASA Technical Reports Server (NTRS)

Noor, A. K.

1973-01-01

A mixed finite-difference scheme is presented for the stress and free vibration analysis of simply supported nonhomogeneous and layered orthotropic thick plates. The analytical formulation is based on the linear, three-dimensional theory of orthotropic elasticity and a Fourier approach is used to reduce the governing equations to six first-order ordinary differential equations in the thickness coordinate. The governing equations possess a symmetric coefficient matrix and are free of derivatives of the elastic characteristics of the plate. In the finite difference discretization two interlacing grids are used for the different fundamental unknowns in such a way as to reduce both the local discretization error and the bandwidth of the resulting finite-difference field equations. Numerical studies are presented for the effects of reducing the interior and boundary discretization errors and of mesh refinement on the accuracy and convergence of solutions. It is shown that the proposed scheme, in addition to a number of other advantages, leads to highly accurate results, even when a small number of finite difference intervals is used.

The MV model of the color glass condensate for a finite number of sources including Coulomb interactions

DOE PAGES

McLerran, Larry; Skokov, Vladimir V.

2016-09-19

We modify the McLerran–Venugopalan model to include only a finite number of sources of color charge. In the effective action for such a system of a finite number of sources, there is a point-like interaction and a Coulombic interaction. The point interaction generates the standard fluctuation term in the McLerran–Venugopalan model. The Coulomb interaction generates the charge screening originating from well known evolution in x. Such a model may be useful for computing angular harmonics of flow measured in high energy hadron collisions for small systems. In this study we provide a basic formulation of the problem on a lattice.

Reduction of parameters in Finite Unified Theories and the MSSM

NASA Astrophysics Data System (ADS)

Heinemeyer, Sven; Mondragón, Myriam; Tracas, Nicholas; Zoupanos, George

2018-02-01

The method of reduction of couplings developed by W. Zimmermann, combined with supersymmetry, can lead to realistic quantum field theories, where the gauge and Yukawa sectors are related. It is the basis to find all-loop Finite Unified Theories, where the β-function vanishes to all-loops in perturbation theory. It can also be applied to the Minimal Supersymmetric Standard Model, leading to a drastic reduction in the number of parameters. Both Finite Unified Theories and the reduced MSSM lead to successful predictions for the masses of the third generation of quarks and the Higgs boson, and also predict a heavy supersymmetric spectrum, consistent with the non-observation of supersymmetry so far.

Domain decomposition methods for nonconforming finite element spaces of Lagrange-type

NASA Technical Reports Server (NTRS)

Cowsar, Lawrence C.

1993-01-01

In this article, we consider the application of three popular domain decomposition methods to Lagrange-type nonconforming finite element discretizations of scalar, self-adjoint, second order elliptic equations. The additive Schwarz method of Dryja and Widlund, the vertex space method of Smith, and the balancing method of Mandel applied to nonconforming elements are shown to converge at a rate no worse than their applications to the standard conforming piecewise linear Galerkin discretization. Essentially, the theory for the nonconforming elements is inherited from the existing theory for the conforming elements with only modest modification by constructing an isomorphism between the nonconforming finite element space and a space of continuous piecewise linear functions.

A rocket engine design expert system

NASA Technical Reports Server (NTRS)

Davidian, Kenneth J.

1989-01-01

The overall structure and capabilities of an expert system designed to evaluate rocket engine performance are described. The expert system incorporates a JANNAF standard reference computer code to determine rocket engine performance and a state-of-the-art finite element computer code to calculate the interactions between propellant injection, energy release in the combustion chamber, and regenerative cooling heat transfer. Rule-of-thumb heuristics were incorporated for the hydrogen-oxygen coaxial injector design, including a minimum gap size constraint on the total number of injector elements. One-dimensional equilibrium chemistry was employed in the energy release analysis of the combustion chamber and three-dimensional finite-difference analysis of the regenerative cooling channels was used to calculate the pressure drop along the channels and the coolant temperature as it exits the coolant circuit. Inputting values to describe the geometry and state properties of the entire system is done directly from the computer keyboard. Graphical display of all output results from the computer code analyses is facilitated by menu selection of up to five dependent variables per plot.

Exact finite difference schemes for the non-linear unidirectional wave equation

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1985-01-01

Attention is given to the construction of exact finite difference schemes for the nonlinear unidirectional wave equation that describes the nonlinear propagation of a wave motion in the positive x-direction. The schemes constructed for these equations are compared with those obtained by using the usual procedures of numerical analysis. It is noted that the order of the exact finite difference models is equal to the order of the differential equation.

Application of finite element approach to transonic flow problems

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Murman, E. M.; Wellford, L. C., Jr.

1976-01-01

A variational finite element model for transonic small disturbance calculations is described. Different strategy is adopted in subsonic and supersonic regions, and blending elements are introduced between different regions. In the supersonic region, no upstream effect is allowed. If rectangular elements with linear shape functions are used, the model is similar to Murman's finite difference operators. Higher order shape functions, nonrectangular elements, and discontinuous approximation of shock waves are also discussed.

Phase shifts in I = 2 ππ-scattering from two lattice approaches

NASA Astrophysics Data System (ADS)

Kurth, T.; Ishii, N.; Doi, T.; Aoki, S.; Hatsuda, T.

2013-12-01

We present a lattice QCD study of the phase shift of I = 2 ππ scattering on the basis of two different approaches: the standard finite volume approach by Lüscher and the recently introduced HAL QCD potential method. Quenched QCD simulations are performed on lattices with extents N s = 16 , 24 , 32 , 48 and N t = 128 as well as lattice spacing a ~ 0 .115 fm and a pion mass of m π ~ 940 MeV. The phase shift and the scattering length are calculated in these two methods. In the potential method, the error is dominated by the systematic uncertainty associated with the violation of rotational symmetry due to finite lattice spacing. In Lüscher's approach, such systematic uncertainty is difficult to be evaluated and thus is not included in this work. A systematic uncertainty attributed to the quenched approximation, however, is not evaluated in both methods. In case of the potential method, the phase shift can be calculated for arbitrary energies below the inelastic threshold. The energy dependence of the phase shift is also obtained from Lüscher's method using different volumes and/or nonrest-frame extension of it. The results are found to agree well with the potential method.

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

Kuprat, A.P.; Glasser, A.H.

The authors discuss unstructured grids for application to transport in the tokamak edge SOL. They have developed a new metric with which to judge element elongation and resolution requirements. Using this method, the authors apply a standard moving finite element technique to advance the SOL equations while inserting/deleting dynamically nodes that violate an elongation criterion. In a tokamak plasma, this method achieves a more uniform accuracy, and results in highly stretched triangular finite elements, except near separatrix X-point where transport is more isotropic.

SMAUMAT_ITI

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

Jannetti, C.; Becker, R.

The software is an ABAQUS/Standard UMAT (user defined material behavior subroutine) that implements the constitutive model for shape-memory alloy materials developed by Jannetti et. al. (2003a) using a fully implicit time integration scheme to integrate the constitutive equations. The UMAT is used in conjunction with ABAQUS/Standard to perform a finite-element analysis of SMA materials.

Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Bertola, Marco; El, Gennady A.; Tovbis, Alexander

2016-10-01

Rogue waves appearing on deep water or in optical fibres are often modelled by certain breather solutions of the focusing nonlinear Schrödinger (fNLS) equation which are referred to as solitons on finite background (SFBs). A more general modelling of rogue waves can be achieved via the consideration of multiphase, or finite-band, fNLS solutions of whom the standard SFBs and the structures forming due to their collisions represent particular, degenerate, cases. A generalized rogue wave notion then naturally enters as a large-amplitude localized coherent structure occurring within a finite-band fNLS solution. In this paper, we use the winding of real tori to show the mechanism of the appearance of such generalized rogue waves and derive an analytical criterion distinguishing finite-band potentials of the fNLS equation that exhibit generalized rogue waves.

Testing Linear Temporal Logic Formulae on Finite Execution Traces

NASA Technical Reports Server (NTRS)

Havelund, Klaus; Rosu, Grigore; Norvig, Peter (Technical Monitor)

2001-01-01

We present an algorithm for efficiently testing Linear Temporal Logic (LTL) formulae on finite execution traces. The standard models of LTL are infinite traces, reflecting the behavior of reactive and concurrent systems which conceptually may be continuously alive. In most past applications of LTL. theorem provers and model checkers have been used to formally prove that down-scaled models satisfy such LTL specifications. Our goal is instead to use LTL for up-scaled testing of real software applications. Such tests correspond to analyzing the conformance of finite traces against LTL formulae. We first describe what it means for a finite trace to satisfy an LTL property. We then suggest an optimized algorithm based on transforming LTL formulae. The work is done using the Maude rewriting system. which turns out to provide a perfect notation and an efficient rewriting engine for performing these experiments.

A Floating Node Method for the Modelling of Discontinuities Within a Finite Element

NASA Technical Reports Server (NTRS)

Pinho, Silvestre T.; Chen, B. Y.; DeCarvalho, Nelson V.; Baiz, P. M.; Tay, T. E.

2013-01-01

This paper focuses on the accurate numerical representation of complex networks of evolving discontinuities in solids, with particular emphasis on cracks. The limitation of the standard finite element method (FEM) in approximating discontinuous solutions has motivated the development of re-meshing, smeared crack models, the eXtended Finite Element Method (XFEM) and the Phantom Node Method (PNM). We propose a new method which has some similarities to the PNM, but crucially: (i) does not introduce an error on the crack geometry when mapping to natural coordinates; (ii) does not require numerical integration over only part of a domain; (iii) can incorporate weak discontinuities and cohesive cracks more readily; (iv) is ideally suited for the representation of multiple and complex networks of (weak, strong and cohesive) discontinuities; (v) leads to the same solution as a finite element mesh where the discontinuity is represented explicitly; and (vi) is conceptually simpler than the PNM.

Finite element analysis on influence of implant surface treatments, connection and bone types.

PubMed

Santiago Junior, Joel Ferreira; Verri, Fellippo Ramos; Almeida, Daniel Augusto de Faria; de Souza Batista, Victor Eduardo; Lemos, Cleidiel Aparecido Araujo; Pellizzer, Eduardo Piza

2016-06-01

The aim of this study is to assess the effect of different dental implant designs, bone type, loading, and surface treatment on the stress distribution around the implant by using the 3D finite-element method. Twelve 3D models were developed with Invesalius 3.0, Rhinoceros 4.0, and Solidworks 2010 software. The analysis was processed using the FEMAP 10.2 and NeiNastran 10.0 software. The applied oblique forces were 200 N and 100 N. The results were analyzed using maps of maximum principal stress and bone microstrain. Statistical analysis was performed using ANOVA and Tukey's test. The results showed that the Morse taper design was most efficient in terms of its distribution of stresses (p<0.05); the external hexagon with platform switching did not show a significant difference from an external hexagon with a standard platform (p>0.05). The different bone types did not show a significant difference in the stress/strain distribution (p>0.05). The surface treatment increased areas of stress concentration under axial loading (p<0.05) and increased areas of microstrain under axial and oblique loading (p<0.05) on the cortical bone. The Morse taper design behaved better biomechanically in relation to the bone tissue. The treated surface increased areas of stress and strain on the cortical bone tissue. Copyright © 2016 Elsevier B.V. All rights reserved.

Validation of predicted patellofemoral mechanics in a finite element model of the healthy and cruciate-deficient knee.

PubMed

Ali, Azhar A; Shalhoub, Sami S; Cyr, Adam J; Fitzpatrick, Clare K; Maletsky, Lorin P; Rullkoetter, Paul J; Shelburne, Kevin B

2016-01-25

Healthy patellofemoral (PF) joint mechanics are critical to optimal function of the knee joint. Patellar maltracking may lead to large joint reaction loads and high stresses on the articular cartilage, increasing the risk of cartilage wear and the onset of osteoarthritis. While the mechanical sources of PF joint dysfunction are not well understood, links have been established between PF tracking and abnormal kinematics of the tibiofemoral (TF) joint, specifically following cruciate ligament injury and repair. The objective of this study was to create a validated finite element (FE) representation of the PF joint in order to predict PF kinematics and quadriceps force across healthy and pathological specimens. Measurements from a series of dynamic in-vitro cadaveric experiments were used to develop finite element models of the knee for three specimens. Specimens were loaded under intact, ACL-resected and both ACL and PCL-resected conditions. Finite element models of each specimen were constructed and calibrated to the outputs of the intact knee condition, and subsequently used to predict PF kinematics, contact mechanics, quadriceps force, patellar tendon moment arm and patellar tendon angle of the cruciate resected conditions. Model results for the intact and cruciate resected trials successfully matched experimental kinematics (avg. RMSE 4.0°, 3.1mm) and peak quadriceps forces (avg. difference 5.6%). Cruciate resections demonstrated either increased patellar tendon loads or increased joint reaction forces. The current study advances the standard for evaluation of PF mechanics through direct validation of cruciate-resected conditions including specimen-specific representations of PF anatomy. Copyright © 2015 Elsevier Ltd. All rights reserved.

Probabilistic treatment of the uncertainty from the finite size of weighted Monte Carlo data

NASA Astrophysics Data System (ADS)

Glüsenkamp, Thorsten

2018-06-01

Parameter estimation in HEP experiments often involves Monte Carlo simulation to model the experimental response function. A typical application are forward-folding likelihood analyses with re-weighting, or time-consuming minimization schemes with a new simulation set for each parameter value. Problematically, the finite size of such Monte Carlo samples carries intrinsic uncertainty that can lead to a substantial bias in parameter estimation if it is neglected and the sample size is small. We introduce a probabilistic treatment of this problem by replacing the usual likelihood functions with novel generalized probability distributions that incorporate the finite statistics via suitable marginalization. These new PDFs are analytic, and can be used to replace the Poisson, multinomial, and sample-based unbinned likelihoods, which covers many use cases in high-energy physics. In the limit of infinite statistics, they reduce to the respective standard probability distributions. In the general case of arbitrary Monte Carlo weights, the expressions involve the fourth Lauricella function FD, for which we find a new finite-sum representation in a certain parameter setting. The result also represents an exact form for Carlson's Dirichlet average Rn with n > 0, and thereby an efficient way to calculate the probability generating function of the Dirichlet-multinomial distribution, the extended divided difference of a monomial, or arbitrary moments of univariate B-splines. We demonstrate the bias reduction of our approach with a typical toy Monte Carlo problem, estimating the normalization of a peak in a falling energy spectrum, and compare the results with previously published methods from the literature.

Multi-scale finite element modeling of strain localization in geomaterials with strong discontinuity

NASA Astrophysics Data System (ADS)

Lai, Timothy Yu

2002-01-01

Geomaterials such as soils and rocks undergo strain localization during various loading conditions. Strain localization manifests itself in the form of a shear band, a narrow zone of intense straining. It is now generally recognized that these localized deformations lead to an accelerated softening response and influence the response of structures at or near failure. In order to accurately predict the behavior of geotechnical structures, the effects of strain localization must be included in any model developed. In this thesis, a multi-scale Finite Element (FE) model has been developed that captures the macro- and micro-field deformation patterns present during strain localization. The FE model uses a strong discontinuity approach where a jump in the displacement field is assumed. The onset of strain localization is detected using bifurcation theory that checks when the governing equations lose ellipticity. Two types of bifurcation, continuous and discontinuous are considered. Precise conditions for plane strain loading conditions are reported for each type of bifurcation. Post-localization behavior is governed by the traction relations on the band. Different plasticity models such as Mohr-Coulomb, Drucker-Prager and a Modified Mohr-Coulomb yield were implemented together with cohesion softening and cutoff for the post-localization behavior. The FE model is implemented into a FORTRAN code SPIN2D-LOC using enhanced constant strain triangular (CST) elements. The model is formulated using standard Galerkin finite element method, applicable to problems under undrained conditions and small deformation theory. A band-tracing algorithm is implemented to track the propagation of the shear band. To validate the model, several simulations are performed from simple compression test of soft rock to simulation of a full-scale geosynthetic reinforced soil wall model undergoing strain localization. Results from both standard and enhanced FE method are included for comparison. The resulting load-displacement curves show that the model can represent the softening behavior of geomaterials once strain localization is detected. The orientation of the shear band is found to depend on both the friction and dilation angle of the geomaterial. For most practical problems, slight mesh dependency can be expected but is associated with the standard FE interpolation rather than the strong discontinuity enhancements.

Ideal orthodontic alignment load relationships based on periodontal ligament stress.

PubMed

Viecilli, R F; Burstone, C J

2015-04-01

To test the hypothesis that periodontal ligament (PDL) stress relationships that yield resistance numbers representing load proportions between different teeth depend on alignment load type. Finite element models of all teeth, except the third molars, were produced. Four different types of loads were applied, and the third principal stresses of different teeth in standardized areas of most compression were calculated. Based on these results, resistance numbers, representing the load proportions for each tooth derived from PDL stress, were determined. The third principal stress values for typical alignment loads in the areas of most stress were very different for different load types for each tooth. Differences in resistance numbers between teeth also varied with different loads. Resistance numbers, that is, load proportion numbers between teeth to achieve similar stress at the compressive PDL zone, depend on the type of applied load. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

A comparison of the finite difference and finite element methods for heat transfer calculations

NASA Technical Reports Server (NTRS)

Emery, A. F.; Mortazavi, H. R.

1982-01-01

The finite difference method and finite element method for heat transfer calculations are compared by describing their bases and their application to some common heat transfer problems. In general it is noted that neither method is clearly superior, and in many instances, the choice is quite arbitrary and depends more upon the codes available and upon the personal preference of the analyst than upon any well defined advantages of one method. Classes of problems for which one method or the other is better suited are defined.

Electron-phonon coupling from finite differences

NASA Astrophysics Data System (ADS)

Monserrat, Bartomeu

2018-02-01

The interaction between electrons and phonons underlies multiple phenomena in physics, chemistry, and materials science. Examples include superconductivity, electronic transport, and the temperature dependence of optical spectra. A first-principles description of electron-phonon coupling enables the study of the above phenomena with accuracy and material specificity, which can be used to understand experiments and to predict novel effects and functionality. In this topical review, we describe the first-principles calculation of electron-phonon coupling from finite differences. The finite differences approach provides several advantages compared to alternative methods, in particular (i) any underlying electronic structure method can be used, and (ii) terms beyond the lowest order in the electron-phonon interaction can be readily incorporated. But these advantages are associated with a large computational cost that has until recently prevented the widespread adoption of this method. We describe some recent advances, including nondiagonal supercells and thermal lines, that resolve these difficulties, and make the calculation of electron-phonon coupling from finite differences a powerful tool. We review multiple applications of the calculation of electron-phonon coupling from finite differences, including the temperature dependence of optical spectra, superconductivity, charge transport, and the role of defects in semiconductors. These examples illustrate the advantages of finite differences, with cases where semilocal density functional theory is not appropriate for the calculation of electron-phonon coupling and many-body methods such as the GW approximation are required, as well as examples in which higher-order terms in the electron-phonon interaction are essential for an accurate description of the relevant phenomena. We expect that the finite difference approach will play a central role in future studies of the electron-phonon interaction.

Accuracy of finite-difference modeling of seismic waves : Simulation versus laboratory measurements

NASA Astrophysics Data System (ADS)

Arntsen, B.

2017-12-01

The finite-difference technique for numerical modeling of seismic waves is still important and for some areas extensively used.For exploration purposes is finite-difference simulation at the core of both traditional imaging techniques such as reverse-time migration and more elaborate Full-Waveform Inversion techniques.The accuracy and fidelity of finite-difference simulation of seismic waves are hard to quantify and meaningfully error analysis is really onlyeasily available for simplistic media. A possible alternative to theoretical error analysis is provided by comparing finite-difference simulated data with laboratory data created using a scale model. The advantage of this approach is the accurate knowledge of the model, within measurement precision, and the location of sources and receivers.We use a model made of PVC immersed in water and containing horizontal and tilted interfaces together with several spherical objects to generateultrasonic pressure reflection measurements. The physical dimensions of the model is of the order of a meter, which after scaling represents a model with dimensions of the order of 10 kilometer and frequencies in the range of one to thirty hertz.We find that for plane horizontal interfaces the laboratory data can be reproduced by the finite-difference scheme with relatively small error, but for steeply tilted interfaces the error increases. For spherical interfaces the discrepancy between laboratory data and simulated data is sometimes much more severe, to the extent that it is not possible to simulate reflections from parts of highly curved bodies. The results are important in view of the fact that finite-difference modeling is often at the core of imaging and inversion algorithms tackling complicatedgeological areas with highly curved interfaces.

Convergence Rates of Finite Difference Stochastic Approximation Algorithms

DTIC Science & Technology

2016-06-01

dfferences as gradient approximations. It is shown that the convergence of these algorithms can be accelerated by controlling the implementation of the...descent algorithm, under various updating schemes using finite dfferences as gradient approximations. It is shown that the convergence of these...the Kiefer-Wolfowitz algorithm and the mirror descent algorithm, under various updating schemes using finite differences as gradient approximations. It

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

Wiley, J.C.

The author describes a general `hp` finite element method with adaptive grids. The code was based on the work of Oden, et al. The term `hp` refers to the method of spatial refinement (h), in conjunction with the order of polynomials used as a part of the finite element discretization (p). This finite element code seems to handle well the different mesh grid sizes occuring between abuted grids with different resolutions.

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1976-01-01

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Boundary and Interface Conditions for High Order Finite Difference Methods Applied to the Euler and Navier-Strokes Equations

NASA Technical Reports Server (NTRS)

Nordstrom, Jan; Carpenter, Mark H.

1998-01-01

Boundary and interface conditions for high order finite difference methods applied to the constant coefficient Euler and Navier-Stokes equations are derived. The boundary conditions lead to strict and strong stability. The interface conditions are stable and conservative even if the finite difference operators and mesh sizes vary from domain to domain. Numerical experiments show that the new conditions also lead to good results for the corresponding nonlinear problems.

A Numerical Model for Predicting Shoreline Changes.

DTIC Science & Technology

1980-07-01

minimal shorelines for finite - difference scheme of time lAt (B) . . . 27 11 Transport function Q(ao) = cos ao sin za o for selected values of z . 28 12...generate the preceding examples was based on the use of implicit finite differences . Such schemes, whether implicit or ex- plicit (or both), are...10(A) shows an initially straight shoreline. In any finite - difference scheme, after one time increment At, the shoreline is bounded below by the solid

Experimental Investigation of Hydrodynamic Self-Acting Gas Bearings at High Knudsen Numbers.

DTIC Science & Technology

1980-07-01

Reynolds equation. Two finite - difference algorithms were used to solve the equation. Numerical results - the predicted load and pitch angle - from the two...that should be used. The majority of the numerical solution are still based on the finite difference approximation of the governing equation. But in... finite difference method. Reddi and Chu [26) also noted that it is very difficult to compare the two techniques on the same level since the solution

Numerical Methods for Analysis of Charged Vacancy Diffusion in Dielectric Solids

DTIC Science & Technology

2006-12-01

theory for charged vacancy diffusion in elastic dielectric materials is formulated and implemented numerically in a finite difference code. The...one of the co-authors on neutral vacancy kinetics (Grinfeld and Hazzledine, 1997). The theory is implemented numerically in a finite difference code...accuracy of order ( )2x∆ , using a finite difference approximation (Hoffman, 1992) for the second spatial derivative of φ : ( )21 1 0ˆ2 /i i i i Rxφ

Impacts of Ocean Waves on the Atmospheric Surface Layer: Simulations and Observations

DTIC Science & Technology

2008-06-06

energy and pressure described in § 4 are solved using a mixed finite - difference pseudospectral scheme with a third-order Runge-Kutta time stepping with a...to that in our DNS code (Sullivan and McWilliams 2002; Sullivan et al. 2000). For our mixed finite - difference pseudospec- tral differencing scheme a...Poisson equation. The spatial discretization is pseu- dospectral along lines of constant or and second- order finite difference in the vertical

A Calculation Method for Convective Heat and Mass Transfer in Multiply-Slotted Film-Cooling Applications.

DTIC Science & Technology

1980-01-01

Transport of Heat ..... .......... 8 3. THE SOLUTION PROCEDURE ..... .. ................. 8 3.1 The Finite-Difference Grid Network ... .......... 8 3.2...The Finite-Difference Grid Network. Figure 4: The Iterative Solution Procedure used at each Streamwise Station. Figure 5: Velocity Profiles in the...the finite-difference grid in the y-direction. I is the mixing length. L is the distance in the x-direction from the injection slot entrance to the

Group foliation of finite difference equations

NASA Astrophysics Data System (ADS)

Thompson, Robert; Valiquette, Francis

2018-06-01

Using the theory of equivariant moving frames, a group foliation method for invariant finite difference equations is developed. This method is analogous to the group foliation of differential equations and uses the symmetry group of the equation to decompose the solution process into two steps, called resolving and reconstruction. Our constructions are performed algorithmically and symbolically by making use of discrete recurrence relations among joint invariants. Applications to invariant finite difference equations that approximate differential equations are given.

Error analysis of finite difference schemes applied to hyperbolic initial boundary value problems

NASA Technical Reports Server (NTRS)

Skollermo, G.

1979-01-01

Finite difference methods for the numerical solution of mixed initial boundary value problems for hyperbolic equations are studied. The reported investigation has the objective to develop a technique for the total error analysis of a finite difference scheme, taking into account initial approximations, boundary conditions, and interior approximation. Attention is given to the Cauchy problem and the initial approximation, the homogeneous problem in an infinite strip with inhomogeneous boundary data, the reflection of errors in the boundaries, and two different boundary approximations for the leapfrog scheme with a fourth order accurate difference operator in space.

Pion properties at finite isospin chemical potential with isospin symmetry breaking

NASA Astrophysics Data System (ADS)

Wu, Zuqing; Ping, Jialun; Zong, Hongshi

2017-12-01

Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU(2) NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons, we calculate the pion mass, the decay constant and the phase diagram with different quark masses for the u quark and d quark, related to QCD corrections, for the first time. Our results show an asymmetry between μI <0 and μI >0 in the phase diagram, and different values for the charged pion mass (or decay constant) and neutral pion mass (or decay constant) at finite temperature and finite isospin chemical potential. This is caused by the effect of isospin symmetry breaking, which is from different quark masses. Supported by National Natural Science Foundation of China (11175088, 11475085, 11535005, 11690030) and the Fundamental Research Funds for the Central Universities (020414380074)

Convergence of finite difference transient response computations for thin shells.

NASA Technical Reports Server (NTRS)

Sobel, L. H.; Geers, T. L.

1973-01-01

Numerical studies pertaining to the limits of applicability of the finite difference method in the solution of linear transient shell response problems are performed, and a computational procedure for the use of the method is recommended. It is found that the only inherent limitation of the finite difference method is its inability to reproduce accurately response discontinuities. This is not a serious limitation in view of natural constraints imposed by the extension of Saint Venant's principle to transient response problems. It is also found that the short wavelength limitations of thin shell (Bernoulli-Euler) theory create significant convergence difficulties in computed response to certain types of transverse excitations. These difficulties may be overcome, however, through proper selection of finite difference mesh dimensions and temporal smoothing of the excitation.

Analysis of transient, linear wave propagation in shells by the finite difference method

NASA Technical Reports Server (NTRS)

Geers, T. L.; Sobel, L. H.

1971-01-01

The applicability of the finite difference method to propagation problems in shells, and the response of a cylindrical shell with cutouts to both longitudinal and radial transient excitations are investigated. It is found that the only inherent limitation of the finite difference method is its inability to reproduce accurately response discontinuities. The short wave length limitations of thin shell theory create significant convergence difficulties may often be overcome through proper selection of finite difference mesh dimensions and temporal or spatial smoothing of the excitation. Cutouts produce moderate changes in early and intermediate time response of a cylindrical shell to axisymmetric pulse loads applied at one end. The cutouts may facilitate the undesirable late-time transfer of load-injected extensional energy into nonaxisymmetric flexural response.

Variational finite-difference methods in linear and nonlinear problems of the deformation of metallic and composite shells (review)

NASA Astrophysics Data System (ADS)

Maksimyuk, V. A.; Storozhuk, E. A.; Chernyshenko, I. S.

2012-11-01

Variational finite-difference methods of solving linear and nonlinear problems for thin and nonthin shells (plates) made of homogeneous isotropic (metallic) and orthotropic (composite) materials are analyzed and their classification principles and structure are discussed. Scalar and vector variational finite-difference methods that implement the Kirchhoff-Love hypotheses analytically or algorithmically using Lagrange multipliers are outlined. The Timoshenko hypotheses are implemented in a traditional way, i.e., analytically. The stress-strain state of metallic and composite shells of complex geometry is analyzed numerically. The numerical results are presented in the form of graphs and tables and used to assess the efficiency of using the variational finite-difference methods to solve linear and nonlinear problems of the statics of shells (plates)

Development of low-frequency kernel-function aerodynamics for comparison with time-dependent finite-difference methods

NASA Technical Reports Server (NTRS)

Bland, S. R.

1982-01-01

Finite difference methods for unsteady transonic flow frequency use simplified equations in which certain of the time dependent terms are omitted from the governing equations. Kernel functions are derived for two dimensional subsonic flow, and provide accurate solutions of the linearized potential equation with the same time dependent terms omitted. These solutions make possible a direct evaluation of the finite difference codes for the linear problem. Calculations with two of these low frequency kernel functions verify the accuracy of the LTRAN2 and HYTRAN2 finite difference codes. Comparisons of the low frequency kernel function results with the Possio kernel function solution of the complete linear equations indicate the adequacy of the HYTRAN approximation for frequencies in the range of interest for flutter calculations.

Effects of finite volume on the K L – K S mass difference

DOE PAGES

Christ, N.  H.; Feng, X.; Martinelli, G.; ...

2015-06-24

Phenomena that involve two or more on-shell particles are particularly sensitive to the effects of finite volume and require special treatment when computed using lattice QCD. In this paper we generalize the results of Lüscher and Lellouch and Lüscher, which determine the leading-order effects of finite volume on the two-particle spectrum and two-particle decay amplitudes to determine the finite-volume effects in the second-order mixing of the K⁰ and K⁰⁻ states. We extend the methods of Kim, Sachrajda, and Sharpe to provide a direct, uniform treatment of these three, related, finite-volume corrections. In particular, the leading, finite-volume corrections to the Kmore » L – K S mass difference ΔM K and the CP-violating parameter εK are determined, including the potentially large effects which can arise from the near degeneracy of the kaon mass and the energy of a finite-volume, two-pion state.« less

Fatigue assessment of an existing steel bridge by finite element modelling and field measurements

NASA Astrophysics Data System (ADS)

Kwad, J.; Alencar, G.; Correia, J.; Jesus, A.; Calçada, R.; Kripakaran, P.

2017-05-01

The evaluation of fatigue life of structural details in metallic bridges is a major challenge for bridge engineers. A reliable and cost-effective approach is essential to ensure appropriate maintenance and management of these structures. Typically, local stresses predicted by a finite element model of the bridge are employed to assess the fatigue life of fatigue-prone details. This paper illustrates an approach for fatigue assessment based on measured data for a connection in an old bascule steel bridge located in Exeter (UK). A finite element model is first developed from the design information. The finite element model of the bridge is calibrated using measured responses from an ambient vibration test. The stress time histories are calculated through dynamic analysis of the updated finite element model. Stress cycles are computed through the rainflow counting algorithm, and the fatigue prone details are evaluated using the standard SN curves approach and the Miner’s rule. Results show that the proposed approach can estimate the fatigue damage of a fatigue prone detail in a structure using measured strain data.

Automated finite element modeling of the lumbar spine: Using a statistical shape model to generate a virtual population of models.

PubMed

Campbell, J Q; Petrella, A J

2016-09-06

Population-based modeling of the lumbar spine has the potential to be a powerful clinical tool. However, developing a fully parameterized model of the lumbar spine with accurate geometry has remained a challenge. The current study used automated methods for landmark identification to create a statistical shape model of the lumbar spine. The shape model was evaluated using compactness, generalization ability, and specificity. The primary shape modes were analyzed visually, quantitatively, and biomechanically. The biomechanical analysis was performed by using the statistical shape model with an automated method for finite element model generation to create a fully parameterized finite element model of the lumbar spine. Functional finite element models of the mean shape and the extreme shapes (±3 standard deviations) of all 17 shape modes were created demonstrating the robust nature of the methods. This study represents an advancement in finite element modeling of the lumbar spine and will allow population-based modeling in the future. Copyright © 2016 Elsevier Ltd. All rights reserved.

Higgs decays to Z Z and Z γ in the standard model effective field theory: An NLO analysis

NASA Astrophysics Data System (ADS)

Dawson, S.; Giardino, P. P.

2018-05-01

We calculate the complete one-loop electroweak corrections to the inclusive H →Z Z and H →Z γ decays in the dimension-6 extension of the Standard Model Effective Field Theory (SMEFT). The corrections to H →Z Z are computed for on-shell Z bosons and are a precursor to the physical H →Z f f ¯ calculation. We present compact numerical formulas for our results and demonstrate that the logarithmic contributions that result from the renormalization group evolution of the SMEFT coefficients are larger than the finite next-to-leading-order contributions to the decay widths. As a byproduct of our calculation, we obtain the first complete result for the finite corrections to Gμ in the SMEFT.

Towards Improved Finite Element Modelling of the Interaction of Elastic Waves with Complex Defect Geometries

NASA Astrophysics Data System (ADS)

Rajagopal, P.; Drozdz, M.; Lowe, M. J. S.

2009-03-01

A solution to the problem of improving the finite element (FE) modeling of elastic wave-defect interaction is sought by reconsidering the conventional opinion on meshing strategy. The standard approach using uniform square elements imposes severe limitations in representing complex defect outlines but this is thought to improve when the mesh is made finer. Free meshing algorithms available widely in commercial packages of late can cope with difficult features well but they are thought to cause scattering by the irregular mesh itself. This paper examines whether the benefits offered by free meshing in representing defects better outweigh the inaccuracies due to mesh scattering. If using the standard mesh, the questions whether mesh refinement leads to improved results and whether a practical strategy can be constructed are considered.

On Replacing "Quantum Thinking" with Counterfactual Reasoning

NASA Astrophysics Data System (ADS)

Narens, Louis

The probability theory used in quantum mechanics is currently being employed by psychologists to model the impact of context on decision. Its event space consists of closed subspaces of a Hilbert space, and its probability function sometimes violate the law of the finite additivity of probabilities. Results from the quantum mechanics literature indicate that such a "Hilbert space probability theory" cannot be extended in a useful way to standard, finitely additive, probability theory by the addition of new events with specific probabilities. This chapter presents a new kind of probability theory that shares many fundamental algebraic characteristics with Hilbert space probability theory but does extend to standard probability theory by adjoining new events with specific probabilities. The new probability theory arises from considerations about how psychological experiments are related through counterfactual reasoning.

[Three dimensional mathematical model of tooth for finite element analysis].

PubMed

Puskar, Tatjana; Vasiljević, Darko; Marković, Dubravka; Jevremović, Danimir; Pantelić, Dejan; Savić-Sević, Svetlana; Murić, Branka

2010-01-01

The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects) in programmes for solid modeling. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analysing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body) into simple geometric bodies (cylinder, cone, pyramid,...). Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.

Hierarchical Material Properties in Finite Element Analysis: The Oilfield Infrastructure Problem.

NASA Astrophysics Data System (ADS)

Weiss, C. J.; Wilson, G. A.

2017-12-01

Geophysical simulation of low-frequency electromagnetic signals within built environments such as urban centers and industrial landscapes facilities is a challenging computational problem because strong conductors (e.g., pipes, fences, rail lines, rebar, etc.) are not only highly conductive and/or magnetic relative to the surrounding geology, but they are very small in one or more of their physical length coordinates. Realistic modeling of such structures as idealized conductors has long been the standard approach; however this strategy carries with it computational burdens such as cumbersome implementation of internal boundary conditions, and limited flexibility for accommodating realistic geometries. Another standard approach is "brute force" discretization (often coupled with an equivalent medium model) whereby 100's of millions of voxels are used to represent these strong conductors, but at the cost of extreme computation times (and mesh design) for a simulation result when possible. To minimize these burdens, a new finite element scheme (Weiss, Geophysics, 2017) has been developed in which the material properties reside on a hierarchy of geometric simplicies (i.e., edges, facets and volumes) within an unstructured tetrahedral mesh. This allows thin sheet—like structures, such as subsurface fractures, to be economically represented by a connected set of triangular facets, for example, that freely conform to arbitrary "real world" geometries. The same holds thin pipe/wire-like structures, such as casings or pipelines. The hierarchical finite element scheme has been applied to problems in electro- and magnetostatics for oilfield problems where the elevated, but finite, conductivity and permeability of the steel-cased oil wells must be properly accounted for, yielding results that are otherwise unobtainable, with run times as low as a few 10s of seconds. Extension of the hierarchical finite element concept to broadband electromagnetics is presently underway, as are its implications for geophysical inversion.

Einstein's equations and a cosmology with finite matter

NASA Astrophysics Data System (ADS)

Clavelli, L.; Goldstein, Gary R.

2015-05-01

We discuss various space-time metrics which are compatible with Einstein's equations and a previously suggested cosmology with a finite total mass.1 In this alternative cosmology, the matter density was postulated to be a spatial delta function at the time of the big bang thereafter diffusing outward with constant total mass. This proposal explores a departure from standard assumptions that the big bang occurred everywhere at once or was just one of an infinite number of previous and later transitions.

Eigenvalue asymptotics for the damped wave equation on metric graphs

NASA Astrophysics Data System (ADS)

Freitas, Pedro; Lipovský, Jiří

2017-09-01

We consider the linear damped wave equation on finite metric graphs and analyse its spectral properties with an emphasis on the asymptotic behaviour of eigenvalues. In the case of equilateral graphs and standard coupling conditions we show that there is only a finite number of high-frequency abscissas, whose location is solely determined by the averages of the damping terms on each edge. We further describe some of the possible behaviour when the edge lengths are no longer necessarily equal but remain commensurate.

Localization and Spreading of Diseases in Complex Networks

NASA Astrophysics Data System (ADS)

Goltsev, A. V.; Dorogovtsev, S. N.; Oliveira, J. G.; Mendes, J. F. F.

2012-09-01

Using the susceptible-infected-susceptible model on unweighted and weighted networks, we consider the disease localization phenomenon. In contrast to the well-recognized point of view that diseases infect a finite fraction of vertices right above the epidemic threshold, we show that diseases can be localized on a finite number of vertices, where hubs and edges with large weights are centers of localization. Our results follow from the analysis of standard models of networks and empirical data for real-world networks.

A unified heteronuclear decoupling strategy for magic-angle-spinning solid-state NMR spectroscopy

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

Equbal, Asif; Bjerring, Morten; Nielsen, Niels Chr., E-mail: madhu@tifr.res.in, E-mail: ncn@inano.au.dk

2015-05-14

A unified strategy of two-pulse based heteronuclear decoupling for solid-state magic-angle spinning nuclear magnetic resonance is presented. The analysis presented here shows that different decoupling sequences like two-pulse phase-modulation (TPPM), X-inverse-X (XiX), and finite pulse refocused continuous wave (rCW{sup A}) are basically specific solutions of a more generalized decoupling scheme which incorporates the concept of time-modulation along with phase-modulation. A plethora of other good decoupling conditions apart from the standard, TPPM, XiX, and rCW{sup A} decoupling conditions are available from the unified decoupling approach. The importance of combined time- and phase-modulation in order to achieve the best decoupling conditions ismore » delineated. The consequences of different indirect dipolar interactions arising from cross terms comprising of heteronuclear and homonuclear dipolar coupling terms and also those between heteronuclear dipolar coupling and chemical-shift anisotropy terms are presented in order to unfold the effects of anisotropic interactions under different decoupling conditions. Extensive numerical simulation results are corroborated with experiments on standard amino acids.« less

Accuracy of dynamical-decoupling-based spectroscopy of Gaussian noise

NASA Astrophysics Data System (ADS)

Szańkowski, Piotr; Cywiński, Łukasz

2018-03-01

The fundamental assumption of dynamical-decoupling-based noise spectroscopy is that the coherence decay rate of qubit (or qubits) driven with a sequence of many pulses, is well approximated by the environmental noise spectrum spanned on frequency comb defined by the sequence. Here we investigate the precise conditions under which this commonly used spectroscopic approach is quantitatively correct. To this end we focus on two representative examples of spectral densities: the long-tailed Lorentzian, and finite-ranged Gaussian—both expected to be encountered when using the qubit for nanoscale nuclear resonance imaging. We have found that, in contrast to Lorentz spectrum, for which the corrections to the standard spectroscopic formulas can easily be made negligible, the spectra with finite range are more challenging to reconstruct accurately. For Gaussian line shape of environmental spectral density, direct application of the standard dynamical-decoupling-based spectroscopy leads to erroneous attribution of long-tail behavior to the reconstructed spectrum. Fortunately, artifacts such as this, can be completely avoided with the simple extension to standard reconstruction method.

Coordinated Research Program in Pulsed Power Physics.

DTIC Science & Technology

1981-12-01

Ref. C11, this problem may be elimi- nated by factoring the tridiagonal , 2nd order, finite difference equation, Eq. (1), into two ist order finite ...13)Ti,o where 1h 2 /2 h2 = 2 - g + / -h g (1- - g) (14) 1+ h This solution to the finite difference equations consists of expo- nentially growing...December 1, 1981fl j,/,,- //,CJ’ .* ., .) - 13. NUMBEROF PAGES - A.)6 2 /’ij250 14. MONITORING AGENCY NAME & ADDRESS(iI different from Controlling

ɛ-connectedness, finite approximations, shape theory and coarse graining in hyperspaces

NASA Astrophysics Data System (ADS)

Alonso-Morón, Manuel; Cuchillo-Ibanez, Eduardo; Luzón, Ana

2008-12-01

We use upper semifinite hyperspaces of compacta to describe ε-connectedness and to compute homology from finite approximations. We find a new connection between ε-connectedness and the so-called Shape Theory. We construct a geodesically complete R-tree, by means of ε-components at different resolutions, whose behavior at infinite captures the topological structure of the space of components of a given compact metric space. We also construct inverse sequences of finite spaces using internal finite approximations of compact metric spaces. These sequences can be converted into inverse sequences of polyhedra and simplicial maps by means of what we call the Alexandroff-McCord correspondence. This correspondence allows us to relate upper semifinite hyperspaces of finite approximation with the Vietoris-Rips complexes of such approximations at different resolutions. Two motivating examples are included in the introduction. We propose this procedure as a different mathematical foundation for problems on data analysis. This process is intrinsically related to the methodology of shape theory. This paper reinforces Robins’s idea of using methods from shape theory to compute homology from finite approximations.

High-contrast grating hollow-core waveguide splitter applied to optical phased array

NASA Astrophysics Data System (ADS)

Zhao, Che; Xue, Ping; Zhang, Hanxing; Chen, Te; Peng, Chao; Hu, Weiwei

2014-11-01

A novel hollow-core (HW) Y-branch waveguide splitter based on high-contrast grating (HCG) is presented. We calculated and designed the HCG-HW splitter using Rigorous Coupled Wave Analysis (RCWA). Finite-different timedomain (FDTD) simulation shows that the splitter has a broad bandwidth and the branching loss is as low as 0.23 dB. Fabrication is accomplished with standard Silicon-On-Insulator (SOI) process. The experimental measurement results indicate its good performance on beam splitting near the central wavelength λ = 1550 nm with a total insertion loss of 7.0 dB.

Explaining the harmonic sequence paradox.

PubMed

Schmidt, Ulrich; Zimper, Alexander

2012-05-01

According to the harmonic sequence paradox, an expected utility decision maker's willingness to pay for a gamble whose expected payoffs evolve according to the harmonic series is finite if and only if his marginal utility of additional income becomes zero for rather low payoff levels. Since the assumption of zero marginal utility is implausible for finite payoff levels, expected utility theory - as well as its standard generalizations such as cumulative prospect theory - are apparently unable to explain a finite willingness to pay. This paper presents first an experimental study of the harmonic sequence paradox. Additionally, it demonstrates that the theoretical argument of the harmonic sequence paradox only applies to time-patient decision makers, whereas the paradox is easily avoided if time-impatience is introduced. ©2011 The British Psychological Society.

Weak Gravitational Lensing of Finite Beams.

PubMed

Fleury, Pierre; Larena, Julien; Uzan, Jean-Philippe

2017-11-10

The standard theory of weak gravitational lensing relies on the infinitesimal light beam approximation. In this context, images are distorted by convergence and shear, the respective sources of which unphysically depend on the resolution of the distribution of matter-the so-called Ricci-Weyl problem. In this Letter, we propose a strong-lensing-inspired formalism to describe the lensing of finite beams. We address the Ricci-Weyl problem by showing explicitly that convergence is caused by the matter enclosed by the beam, regardless of its distribution. Furthermore, shear turns out to be systematically enhanced by the finiteness of the beam. This implies, in particular, that the Kaiser-Squires relation between shear and convergence is violated, which could have profound consequences on the interpretation of weak-lensing surveys.

The use of Galerkin finite-element methods to solve mass-transport equations

USGS Publications Warehouse

Grove, David B.

1977-01-01

The partial differential equation that describes the transport and reaction of chemical solutes in porous media was solved using the Galerkin finite-element technique. These finite elements were superimposed over finite-difference cells used to solve the flow equation. Both convection and flow due to hydraulic dispersion were considered. Linear and Hermite cubic approximations (basis functions) provided satisfactory results: however, the linear functions were computationally more efficient for two-dimensional problems. Successive over relaxation (SOR) and iteration techniques using Tchebyschef polynomials were used to solve the sparce matrices generated using the linear and Hermite cubic functions, respectively. Comparisons of the finite-element methods to the finite-difference methods, and to analytical results, indicated that a high degree of accuracy may be obtained using the method outlined. The technique was applied to a field problem involving an aquifer contaminated with chloride, tritium, and strontium-90. (Woodard-USGS)

Finite-difference modeling with variable grid-size and adaptive time-step in porous media

NASA Astrophysics Data System (ADS)

Liu, Xinxin; Yin, Xingyao; Wu, Guochen

2014-04-01

Forward modeling of elastic wave propagation in porous media has great importance for understanding and interpreting the influences of rock properties on characteristics of seismic wavefield. However, the finite-difference forward-modeling method is usually implemented with global spatial grid-size and time-step; it consumes large amounts of computational cost when small-scaled oil/gas-bearing structures or large velocity-contrast exist underground. To overcome this handicap, combined with variable grid-size and time-step, this paper developed a staggered-grid finite-difference scheme for elastic wave modeling in porous media. Variable finite-difference coefficients and wavefield interpolation were used to realize the transition of wave propagation between regions of different grid-size. The accuracy and efficiency of the algorithm were shown by numerical examples. The proposed method is advanced with low computational cost in elastic wave simulation for heterogeneous oil/gas reservoirs.

Order of accuracy of QUICK and related convection-diffusion schemes

NASA Technical Reports Server (NTRS)

Leonard, B. P.

1993-01-01

This report attempts to correct some misunderstandings that have appeared in the literature concerning the order of accuracy of the QUICK scheme for steady-state convective modeling. Other related convection-diffusion schemes are also considered. The original one-dimensional QUICK scheme written in terms of nodal-point values of the convected variable (with a 1/8-factor multiplying the 'curvature' term) is indeed a third-order representation of the finite volume formulation of the convection operator average across the control volume, written naturally in flux-difference form. An alternative single-point upwind difference scheme (SPUDS) using node values (with a 1/6-factor) is a third-order representation of the finite difference single-point formulation; this can be written in a pseudo-flux difference form. These are both third-order convection schemes; however, the QUICK finite volume convection operator is 33 percent more accurate than the single-point implementation of SPUDS. Another finite volume scheme, writing convective fluxes in terms of cell-average values, requires a 1/6-factor for third-order accuracy. For completeness, one can also write a single-point formulation of the convective derivative in terms of cell averages, and then express this in pseudo-flux difference form; for third-order accuracy, this requires a curvature factor of 5/24. Diffusion operators are also considered in both single-point and finite volume formulations. Finite volume formulations are found to be significantly more accurate. For example, classical second-order central differencing for the second derivative is exactly twice as accurate in a finite volume formulation as it is in single-point.

Stability Analysis of Finite Difference Schemes for Hyperbolic Systems, and Problems in Applied and Computational Linear Algebra.

DTIC Science & Technology

FINITE DIFFERENCE THEORY, * LINEAR ALGEBRA , APPLIED MATHEMATICS, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, COMPUTATIONS, HYPERBOLAS, MATHEMATICAL MODELS, NUMERICAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, STABILITY.

Enhancing the thermal conductivity of ethylene-vinyl acetate (EVA) in a photovoltaic thermal collector

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

Allan, J., E-mail: james.p.allan14@gmail.com; ChapmanBDSP, Saffron House, 6-10 Kirby Street, London, EC1N 8EQ; Pinder, H.

2016-03-15

Samples of Ethylene-Vinyl Acetate (EVA) were doped with particles of Boron Nitride (BN) in concentrations ranging from 0-60% w/w. Thermal conductivity was measured using a Differential Scanning Calorimetery (DSC) technique. The thermal conductivity of parent EVA was increased from 0.24 W/m ⋅ K to 0.80 W/m ⋅ K for the 60% w/w sample. Two PV laminates were made; one using the parent EVA the other using EVA doped with 50% BN. When exposed to a one directional heat flux the doped laminate was, on average, 6% cooler than the standard laminate. A finite difference model had good agreement with experimentalmore » results and showed that the use of 60% BN composite achieved a PV performance increase of 0.3% compared to the standard laminate.« less

Time-domain representation of frequency-dependent foundation impedance functions

USGS Publications Warehouse

Safak, E.

2006-01-01

Foundation impedance functions provide a simple means to account for soil-structure interaction (SSI) when studying seismic response of structures. Impedance functions represent the dynamic stiffness of the soil media surrounding the foundation. The fact that impedance functions are frequency dependent makes it difficult to incorporate SSI in standard time-history analysis software. This paper introduces a simple method to convert frequency-dependent impedance functions into time-domain filters. The method is based on the least-squares approximation of impedance functions by ratios of two complex polynomials. Such ratios are equivalent, in the time-domain, to discrete-time recursive filters, which are simple finite-difference equations giving the relationship between foundation forces and displacements. These filters can easily be incorporated into standard time-history analysis programs. Three examples are presented to show the applications of the method.

Radiation boundary condition and anisotropy correction for finite difference solutions of the Helmholtz equation

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Webb, Jay C.

1994-01-01

In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompability between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevita bly introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The effectiveness of the correction factor in providing improvements to the computed solution is demonstrated in this paper.

Time-domain finite-difference based analysis of induced crosstalk in multiwall carbon nanotube interconnects

NASA Astrophysics Data System (ADS)

Kumar, Amit; Nehra, Vikas; Kaushik, Brajesh Kumar

2017-08-01

Graphene rolled-up cylindrical sheets i.e. carbon nanotubes (CNTs) is one of the finest and emerging research area. This paper presents the investigation of induced crosstalk in coupled on-chip multiwalled carbon nanotube (MWCNT) interconnects using finite-difference analysis (FDA) in time-domain i.e. the finite-difference time-domain (FDTD) method. The exceptional properties of versatile MWCNTs profess their candidacy to replace conventional on-chip copper interconnects. Time delay and crosstalk noise have been evaluated for coupled on-chip MWCNT interconnects. With a decrease in CNT length, the obtained results for an MWCNT shows that transmission performance improves as the number of shells increases. It has been observed that the obtained results using the finite-difference time domain (FDTD) technique shows a very close match with the HSPICE simulated results.

A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

NASA Astrophysics Data System (ADS)

Wu, Zedong; Alkhalifah, Tariq

2018-07-01

Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is highly accurate and efficient.

Selection of finite-element mesh parameters in modeling the growth of hydraulic fracturing cracks

NASA Astrophysics Data System (ADS)

Kurguzov, V. D.

2016-12-01

The effect of the mesh geometry on the accuracy of solutions obtained by the finite-element method for problems of linear fracture mechanics is investigated. The guidelines have been formulated for constructing an optimum mesh for several routine problems involving elements with linear and quadratic approximation of displacements. The accuracy of finite-element solutions is estimated based on the degree of the difference between the calculated stress-intensity factor (SIF) and its value obtained analytically. In problems of hydrofracturing of oil-bearing formation, the pump-in pressure of injected water produces a distributed load on crack flanks as opposed to standard fracture mechanics problems that have analytical solutions, where a load is applied to the external boundaries of the computational region and the cracks themselves are kept free from stresses. Some model pressure profiles, as well as pressure profiles taken from real hydrodynamic computations, have been considered. Computer models of cracks with allowance for the pre-stressed state, fracture toughness, and elastic properties of materials are developed in the MSC.Marc 2012 finite-element analysis software. The Irwin force criterion is used as a criterion of brittle fracture and the SIFs are computed using the Cherepanov-Rice invariant J-integral. The process of crack propagation in a linearly elastic isotropic body is described in terms of the elastic energy release rate G and modeled using the VCCT (Virtual Crack Closure Technique) approach. It has been found that the solution accuracy is sensitive to the mesh configuration. Several parameters that are decisive in constructing effective finite-element meshes, namely, the minimum element size, the distance between mesh nodes in the vicinity of a crack tip, and the ratio of the height of an element to its length, have been established. It has been shown that a mesh that consists of only small elements does not improve the accuracy of the solution.

Biomechanical Evaluation of Different Fixation Methods for Mandibular Anterior Segmental Osteotomy Using Finite Element Analysis, Part Two: Superior Repositioning Surgery With Bone Allograft.

PubMed

Kilinç, Yeliz; Erkmen, Erkan; Kurt, Ahmet

2016-01-01

In this study, the biomechanical behavior of different fixation methods used to fix the mandibular anterior segment following various amounts of superior repositioning was evaluated by using Finite Element Analysis (FEA). The three-dimensional finite element models representing 3 and 5 mm superior repositioning were generated. The gap in between segments was assumed to be filled by block bone allograft and resignated to be in perfect contact with the mandible and segmented bone. Six different finite element models with 2 distinct mobilization rate including 3 different fixation configurations, double right L (DRL), double left L (DLL), or double I (DI) miniplates with monocortical screws, correspondingly were created. A comparative evaluation has been made under vertical, horizontal and oblique loads. The von Mises and principal maximum stress (Pmax) values were calculated by finite element solver programme. The first part of our ongoing Finite Element Analysis research has been addressed to the mechanical behavior of the same fixation configurations in nongrafted models. In comparison with the findings of the first part of the study, it was concluded that bone graft offers superior mechanical stability without any limitation of mobilization and less stress on the fixative appliances as well as in the bone.

Effects of Verb Familiarity on Finiteness Marking in Children With Specific Language Impairment

PubMed Central

Rice, Mabel L.; Bontempo, Daniel E.

2015-01-01

Purpose Children with specific language impairment (SLI) have known deficits in the verb lexicon and finiteness marking. This study investigated a potential relationship between these 2 variables in children with SLI and 2 control groups considering predictions from 2 different theoretical perspectives, morphosyntactic versus morphophonological. Method Children with SLI, age-equivalent, and language-equivalent (LE) control children (n = 59) completed an experimental sentence imitation task that generated estimates of children's finiteness accuracy under 2 levels of verb familiarity—familiar real verbs versus unfamiliar real verbs—in clausal sites marked for finiteness. Imitations were coded and analyzed for overall accuracy as well as finiteness marking and verb root imitation accuracy. Results Statistical comparisons revealed that children with SLI did not differ from LE children and were less accurate than age-equivalent children on all dependent variables: overall imitation, finiteness marking imitation, and verb root imitation accuracy. A significant Group × Condition interaction for finiteness marking revealed lower levels of accuracy on unfamiliar verbs for the SLI and LE groups only. Conclusions Findings indicate a relationship between verb familiarity and finiteness marking in children with SLI and younger controls and help clarify the roles of morphosyntax, verb lexicon, and morphophonology. PMID:25611349

Microscope Resolution.

ERIC Educational Resources Information Center

Higbie, J.

1981-01-01

Describes problems using the Jenkins and White approach and standard diffraction theory when dealing with the topic of finite conjugate, point-source resolution and how they may be resolved using the relatively obscure Abbe's sine theorem. (JN)

Finite Element Stress Analysis of Spent Nuclear Fuel Disposal Canister in a Deep Geological Repository

NASA Astrophysics Data System (ADS)

Kwon, Young Joo; Choi, Jong Won

This paper presents the finite element stress analysis of a spent nuclear fuel disposal canister to provide basic information for dimensioning the canister and configuration of canister components and consequently to suggest the structural analysis methodology for the disposal canister in a deep geological repository which is nowadays very important in the environmental waste treatment technology. Because of big differences in the pressurized water reactor (PWR) and the Canadian deuterium and uranium reactor (CANDU) fuel properties, two types of canisters are conceived. For manufacturing, operational reasons and standardization, however, both canisters have the same outer diameter and length. The construction type of canisters introduced here is a solid structure with a cast insert and a corrosion resistant overpack. The structural stress analysis is carried out using a finite element analysis code, NISA, and focused on the structural strength of the canister against the expected external pressures due to the swelling of the bentonite buffer and the hydrostatic head. The canister must withstand these large pressure loads. Consequently, canisters presented here contain 4 PWR fuel assemblies and 33×9 CANDU fuel bundles. The outside diameter of the canister for both fuels is 122cm and the cast insert diameter is 112cm. The total length of the canister is 483cm with the lid/bottom and the outer shell of 5cm.

Effect of Finite Particle Size on Convergence of Point Particle Models in Euler-Lagrange Multiphase Dispersed Flow

NASA Astrophysics Data System (ADS)

Nili, Samaun; Park, Chanyoung; Haftka, Raphael T.; Kim, Nam H.; Balachandar, S.

2017-11-01

Point particle methods are extensively used in simulating Euler-Lagrange multiphase dispersed flow. When particles are much smaller than the Eulerian grid the point particle model is on firm theoretical ground. However, this standard approach of evaluating the gas-particle coupling at the particle center fails to converge as the Eulerian grid is reduced below particle size. We present an approach to model the interaction between particles and fluid for finite size particles that permits convergence. We use the generalized Faxen form to compute the force on a particle and compare the results against traditional point particle method. We apportion the different force components on the particle to fluid cells based on the fraction of particle volume or surface in the cell. The application is to a one-dimensional model of shock propagation through a particle-laden field at moderate volume fraction, where the convergence is achieved for a well-formulated force model and back coupling for finite size particles. Comparison with 3D direct fully resolved numerical simulations will be used to check if the approach also improves accuracy compared to the point particle model. Work supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA0002378.

Numerical calculation of thermo-mechanical problems at large strains based on complex step derivative approximation of tangent stiffness matrices

NASA Astrophysics Data System (ADS)

Balzani, Daniel; Gandhi, Ashutosh; Tanaka, Masato; Schröder, Jörg

2015-05-01

In this paper a robust approximation scheme for the numerical calculation of tangent stiffness matrices is presented in the context of nonlinear thermo-mechanical finite element problems and its performance is analyzed. The scheme extends the approach proposed in Kim et al. (Comput Methods Appl Mech Eng 200:403-413, 2011) and Tanaka et al. (Comput Methods Appl Mech Eng 269:454-470, 2014 and bases on applying the complex-step-derivative approximation to the linearizations of the weak forms of the balance of linear momentum and the balance of energy. By incorporating consistent perturbations along the imaginary axis to the displacement as well as thermal degrees of freedom, we demonstrate that numerical tangent stiffness matrices can be obtained with accuracy up to computer precision leading to quadratically converging schemes. The main advantage of this approach is that contrary to the classical forward difference scheme no round-off errors due to floating-point arithmetics exist within the calculation of the tangent stiffness. This enables arbitrarily small perturbation values and therefore leads to robust schemes even when choosing small values. An efficient algorithmic treatment is presented which enables a straightforward implementation of the method in any standard finite-element program. By means of thermo-elastic and thermo-elastoplastic boundary value problems at finite strains the performance of the proposed approach is analyzed.

Signals of strong electronic correlation in ion scattering processes

NASA Astrophysics Data System (ADS)

Bonetto, F.; Gonzalez, C.; Goldberg, E. C.

2016-05-01

Previous measurements of neutral atom fractions for S r+ scattered by gold polycrystalline surfaces show a singular dependence with the target temperature. There is still not a theoretical model that can properly describe the magnitude and the temperature dependence of the neutralization probabilities found. Here, we applied a first-principles quantum-mechanical theoretical formalism to describe the time-dependent scattering process. Three different electronic correlation approaches consistent with the system analyzed are used: (i) the spinless approach, where two charge channels are considered (S r0 and S r+ ) and the spin degeneration is neglected; (ii) the infinite-U approach, with the same charge channels (S r0 and S r+ ) but considering the spin degeneration; and (iii) the finite-U approach, where the first ionization and second ionization energy levels are considered very, but finitely, separated. Neutral fraction magnitudes and temperature dependence are better described by the finite-U approach, indicating that e -correlation plays a significant role in charge-transfer processes. However, none of them is able to explain the nonmonotonous temperature dependence experimentally obtained. Here, we suggest that small changes in the surface work function introduced by the target heating, and possibly not detected by experimental standard methods, could be responsible for that singular behavior. Additionally, we apply the same theoretical model using the infinite-U approximation for the Mg-Au system, obtaining an excellent description of the experimental neutral fractions measured.

Finite Temperature Densities via the S-Function Method with Application to Electron Screening in Plasmas

NASA Astrophysics Data System (ADS)

Watrous, Mitchell James

1997-12-01

A new approach to the Green's-function method for the calculation of equilibrium densities within the finite temperature, Kohn-Sham formulation of density functional theory is presented, which extends the method to all temperatures. The contour of integration in the complex energy plane is chosen such that the density is given by a sum of Green's function differences evaluated at the Matsubara frequencies, rather than by the calculation and summation of Kohn-Sham single-particle wave functions. The Green's functions are written in terms of their spectral representation and are calculated as the solutions of their defining differential equations. These differential equations are boundary value problems as opposed to the standard eigenvalue problems. For large values of the complex energy, the differential equations are further simplified from second to first-order by writing the Green's functions in terms of logarithmic derivatives. An asymptotic expression for the Green's functions is derived, which allows the sum over Matsubara poles to be approximated. The method is applied to the screening of nuclei by electrons in finite temperature plasmas. To demonstrate the method's utility, and to illustrate its advantages, the results of previous wave function type calculations for protons and neon nuclei are reproduced. The method is also used to formulate a new screening model for fusion reactions in the solar core, and the predicted reaction rate enhancements factors are compared with existing models.

Nonuniform grid implicit spatial finite difference method for acoustic wave modeling in tilted transversely isotropic media

NASA Astrophysics Data System (ADS)

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

Discrete earth models are commonly represented by uniform structured grids. In order to ensure accurate numerical description of all wave components propagating through these uniform grids, the grid size must be determined by the slowest velocity of the entire model. Consequently, high velocity areas are always oversampled, which inevitably increases the computational cost. A practical solution to this problem is to use nonuniform grids. We propose a nonuniform grid implicit spatial finite difference method which utilizes nonuniform grids to obtain high efficiency and relies on implicit operators to achieve high accuracy. We present a simple way of deriving implicit finite difference operators of arbitrary stencil widths on general nonuniform grids for the first and second derivatives and, as a demonstration example, apply these operators to the pseudo-acoustic wave equation in tilted transversely isotropic (TTI) media. We propose an efficient gridding algorithm that can be used to convert uniformly sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced efficiency, compared to uniform grid explicit finite difference implementations.

Realized Volatility Analysis in A Spin Model of Financial Markets

NASA Astrophysics Data System (ADS)

Takaishi, Tetsuya

We calculate the realized volatility of returns in the spin model of financial markets and examine the returns standardized by the realized volatility. We find that moments of the standardized returns agree with the theoretical values of standard normal variables. This is the first evidence that the return distributions of the spin financial markets are consistent with a finite-variance of mixture of normal distributions that is also observed empirically in real financial markets.

Applications of an exponential finite difference technique

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

Handschuh, R.F.; Keith, T.G. Jr.

1988-07-01

An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.

Development of digital phantoms based on a finite element model to simulate low-attenuation areas in CT imaging for pulmonary emphysema quantification.

PubMed

Diciotti, Stefano; Nobis, Alessandro; Ciulli, Stefano; Landini, Nicholas; Mascalchi, Mario; Sverzellati, Nicola; Innocenti, Bernardo

2017-09-01

To develop an innovative finite element (FE) model of lung parenchyma which simulates pulmonary emphysema on CT imaging. The model is aimed to generate a set of digital phantoms of low-attenuation areas (LAA) images with different grades of emphysema severity. Four individual parameter configurations simulating different grades of emphysema severity were utilized to generate 40 FE models using ten randomizations for each setting. We compared two measures of emphysema severity (relative area (RA) and the exponent D of the cumulative distribution function of LAA clusters size) between the simulated LAA images and those computed directly on the models output (considered as reference). The LAA images obtained from our model output can simulate CT-LAA images in subjects with different grades of emphysema severity. Both RA and D computed on simulated LAA images were underestimated as compared to those calculated on the models output, suggesting that measurements in CT imaging may not be accurate in the assessment of real emphysema extent. Our model is able to mimic the cluster size distribution of LAA on CT imaging of subjects with pulmonary emphysema. The model could be useful to generate standard test images and to design physical phantoms of LAA images for the assessment of the accuracy of indexes for the radiologic quantitation of emphysema.

Structural Crashworthiness Standards Comparison: Grade Crossing Collision Scenarios

DOT National Transportation Integrated Search

2009-10-20

In support of the Federal Railroad Administrations (FRA) : Railroad Equipment Safety Program, American and European : grade-crossing collision scenarios were evaluated and : compared. Finite element analyses (FEA) were employed to : subject an FRA...

Estimation of Standard Error of Regression Effects in Latent Regression Models Using Binder's Linearization. Research Report. ETS RR-07-09

ERIC Educational Resources Information Center

Li, Deping; Oranje, Andreas

2007-01-01

Two versions of a general method for approximating standard error of regression effect estimates within an IRT-based latent regression model are compared. The general method is based on Binder's (1983) approach, accounting for complex samples and finite populations by Taylor series linearization. In contrast, the current National Assessment of…

Computational Aspects of Sensitivity Calculations in Linear Transient Structural Analysis. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Greene, William H.

1989-01-01

A study has been performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semianalytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models.

Simulation of variation of apparent resistivity in resistivity surveys using finite difference modelling with Monte Carlo analysis

NASA Astrophysics Data System (ADS)

Aguirre, E. E.; Karchewski, B.

2017-12-01

DC resistivity surveying is a geophysical method that quantifies the electrical properties of the subsurface of the earth by applying a source current between two electrodes and measuring potential differences between electrodes at known distances from the source. Analytical solutions for a homogeneous half-space and simple subsurface models are well known, as the former is used to define the concept of apparent resistivity. However, in situ properties are heterogeneous meaning that simple analytical models are only an approximation, and ignoring such heterogeneity can lead to misinterpretation of survey results costing time and money. The present study examines the extent to which random variations in electrical properties (i.e. electrical conductivity) affect potential difference readings and therefore apparent resistivities, relative to an assumed homogeneous subsurface model. We simulate the DC resistivity survey using a Finite Difference (FD) approximation of an appropriate simplification of Maxwell's equations implemented in Matlab. Electrical resistivity values at each node in the simulation were defined as random variables with a given mean and variance, and are assumed to follow a log-normal distribution. The Monte Carlo analysis for a given variance of electrical resistivity was performed until the mean and variance in potential difference measured at the surface converged. Finally, we used the simulation results to examine the relationship between variance in resistivity and variation in surface potential difference (or apparent resistivity) relative to a homogeneous half-space model. For relatively low values of standard deviation in the material properties (<10% of mean), we observed a linear correlation between variance of resistivity and variance in apparent resistivity.

Quasi-finite-time control for high-order nonlinear systems with mismatched disturbances via mapping filtered forwarding technique

NASA Astrophysics Data System (ADS)

Zhang, X.; Huang, X. L.; Lu, H. Q.

2017-02-01

In this study, a quasi-finite-time control method for designing stabilising control laws is developed for high-order strict-feedback nonlinear systems with mismatched disturbances. By using mapping filtered forwarding technique, a virtual control is designed to force the off-the-manifold coordinate to converge to zero in quasi-finite time at each step of the design; at the same time, the manifold is rendered insensitive to time-varying, bounded and unknown disturbances. In terms of standard forwarding methodology, the algorithm proposed here not only does not require the Lyapunov function for controller design, but also avoids to calculate the derivative of sign function. As far as the dynamic performance of closed-loop systems is concerned, we essentially obtain the finite-time performances, which is typically reflected in the following aspects: fast and accurate responses, high tracking precision, and robust disturbance rejection. Spring, mass, and damper system and flexible joints robot are tested to demonstrate the proposed controller performance.

Discontinuous dual-primal mixed finite elements for elliptic problems

NASA Technical Reports Server (NTRS)

Bottasso, Carlo L.; Micheletti, Stefano; Sacco, Riccardo

2000-01-01

We propose a novel discontinuous mixed finite element formulation for the solution of second-order elliptic problems. Fully discontinuous piecewise polynomial finite element spaces are used for the trial and test functions. The discontinuous nature of the test functions at the element interfaces allows to introduce new boundary unknowns that, on the one hand enforce the weak continuity of the trial functions, and on the other avoid the need to define a priori algorithmic fluxes as in standard discontinuous Galerkin methods. Static condensation is performed at the element level, leading to a solution procedure based on the sole interface unknowns. The resulting family of discontinuous dual-primal mixed finite element methods is presented in the one and two-dimensional cases. In the one-dimensional case, we show the equivalence of the method with implicit Runge-Kutta schemes of the collocation type exhibiting optimal behavior. Numerical experiments in one and two dimensions demonstrate the order accuracy of the new method, confirming the results of the analysis.

Evaluation of the Ross fast solution of Richards’ equation in unfavourable conditions for standard finite element methods

NASA Astrophysics Data System (ADS)

Crevoisier, David; Chanzy, André; Voltz, Marc

2009-06-01

Ross [Ross PJ. Modeling soil water and solute transport - fast, simplified numerical solutions. Agron J 2003;95:1352-61] developed a fast, simplified method for solving Richards' equation. This non-iterative 1D approach, using Brooks and Corey [Brooks RH, Corey AT. Hydraulic properties of porous media. Hydrol. papers, Colorado St. Univ., Fort Collins; 1964] hydraulic functions, allows a significant reduction in computing time while maintaining the accuracy of the results. The first aim of this work is to confirm these results in a more extensive set of problems, including those that would lead to serious numerical difficulties for the standard numerical method. The second aim is to validate a generalisation of the Ross method to other mathematical representations of hydraulic functions. The Ross method is compared with the standard finite element model, Hydrus-1D [Simunek J, Sejna M, Van Genuchten MTh. The HYDRUS-1D and HYDRUS-2D codes for estimating unsaturated soil hydraulic and solutes transport parameters. Agron Abstr 357; 1999]. Computing time, accuracy of results and robustness of numerical schemes are monitored in 1D simulations involving different types of homogeneous soils, grids and hydrological conditions. The Ross method associated with modified Van Genuchten hydraulic functions [Vogel T, Cislerova M. On the reliability of unsaturated hydraulic conductivity calculated from the moisture retention curve. Transport Porous Media 1988;3:1-15] proves in every tested scenario to be more robust numerically, and the compromise of computing time/accuracy is seen to be particularly improved on coarse grids. Ross method run from 1.25 to 14 times faster than Hydrus-1D.

Equivalent circuit modeling of a piezo-patch energy harvester on a thin plate with AC-DC conversion

NASA Astrophysics Data System (ADS)

Bayik, B.; Aghakhani, A.; Basdogan, I.; Erturk, A.

2016-05-01

As an alternative to beam-like structures, piezoelectric patch-based energy harvesters attached to thin plates can be readily integrated to plate-like structures in automotive, marine, and aerospace applications, in order to directly exploit structural vibration modes of the host system without mass loading and volumetric occupancy of cantilever attachments. In this paper, a multi-mode equivalent circuit model of a piezo-patch energy harvester integrated to a thin plate is developed and coupled with a standard AC-DC conversion circuit. Equivalent circuit parameters are obtained in two different ways: (1) from the modal analysis solution of a distributed-parameter analytical model and (2) from the finite-element numerical model of the harvester by accounting for two-way coupling. After the analytical modeling effort, multi-mode equivalent circuit representation of the harvester is obtained via electronic circuit simulation software SPICE. Using the SPICE software, electromechanical response of the piezoelectric energy harvester connected to linear and nonlinear circuit elements are computed. Simulation results are validated for the standard AC-AC and AC-DC configurations. For the AC input-AC output problem, voltage frequency response functions are calculated for various resistive loads, and they show excellent agreement with modal analysis-based analytical closed-form solution and with the finite-element model. For the standard ideal AC input-DC output case, a full-wave rectifier and a smoothing capacitor are added to the harvester circuit for conversion of the AC voltage to a stable DC voltage, which is also validated against an existing solution by treating the single-mode plate dynamics as a single-degree-of-freedom system.

Dielectric properties and Raman spectra of ZnO from a first principles finite-differences/finite-fields approach

PubMed Central

Calzolari, Arrigo; Nardelli, Marco Buongiorno

2013-01-01

Using first principles calculations based on density functional theory and a coupled finite-fields/finite-differences approach, we study the dielectric properties, phonon dispersions and Raman spectra of ZnO, a material whose internal polarization fields require special treatment to correctly reproduce the ground state electronic structure and the coupling with external fields. Our results are in excellent agreement with existing experimental measurements and provide an essential reference for the characterization of crystallinity, composition, piezo- and thermo-electricity of the plethora of ZnO-derived nanostructured materials used in optoelectronics and sensor devices. PMID:24141391

A Multifunctional Interface Method for Coupling Finite Element and Finite Difference Methods: Two-Dimensional Scalar-Field Problems

NASA Technical Reports Server (NTRS)

Ransom, Jonathan B.

2002-01-01

A multifunctional interface method with capabilities for variable-fidelity modeling and multiple method analysis is presented. The methodology provides an effective capability by which domains with diverse idealizations can be modeled independently to exploit the advantages of one approach over another. The multifunctional method is used to couple independently discretized subdomains, and it is used to couple the finite element and the finite difference methods. The method is based on a weighted residual variational method and is presented for two-dimensional scalar-field problems. A verification test problem and a benchmark application are presented, and the computational implications are discussed.

Stable Artificial Dissipation Operators for Finite Volume Schemes on Unstructured Grids

NASA Technical Reports Server (NTRS)

Svard, Magnus; Gong, Jing; Nordstrom, Jan

2006-01-01

Our objective is to derive stable first-, second- and fourth-order artificial dissipation operators for node based finite volume schemes. Of particular interest are general unstructured grids where the strength of the finite volume method is fully utilized. A commonly used finite volume approximation of the Laplacian will be the basis in the construction of the artificial dissipation. Both a homogeneous dissipation acting in all directions with equal strength and a modification that allows different amount of dissipation in different directions are derived. Stability and accuracy of the new operators are proved and the theoretical results are supported by numerical computations.

A new finite element and finite difference hybrid method for computing electrostatics of ionic solvated biomolecule

NASA Astrophysics Data System (ADS)

Ying, Jinyong; Xie, Dexuan

2015-10-01

The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model for calculating electrostatics of ionic solvated biomolecule. In this paper, a new finite element and finite difference hybrid method is presented to solve PBE efficiently based on a special seven-overlapped box partition with one central box containing the solute region and surrounded by six neighboring boxes. In particular, an efficient finite element solver is applied to the central box while a fast preconditioned conjugate gradient method using a multigrid V-cycle preconditioning is constructed for solving a system of finite difference equations defined on a uniform mesh of each neighboring box. Moreover, the PBE domain, the box partition, and an interface fitted tetrahedral mesh of the central box can be generated adaptively for a given PQR file of a biomolecule. This new hybrid PBE solver is programmed in C, Fortran, and Python as a software tool for predicting electrostatics of a biomolecule in a symmetric 1:1 ionic solvent. Numerical results on two test models with analytical solutions and 12 proteins validate this new software tool, and demonstrate its high performance in terms of CPU time and memory usage.

An object-oriented, coprocessor-accelerated model for ice sheet simulations

NASA Astrophysics Data System (ADS)

Seddik, H.; Greve, R.

2013-12-01

Recently, numerous models capable of modeling the thermo-dynamics of ice sheets have been developed within the ice sheet modeling community. Their capabilities have been characterized by a wide range of features with different numerical methods (finite difference or finite element), different implementations of the ice flow mechanics (shallow-ice, higher-order, full Stokes) and different treatments for the basal and coastal areas (basal hydrology, basal sliding, ice shelves). Shallow-ice models (SICOPOLIS, IcIES, PISM, etc) have been widely used for modeling whole ice sheets (Greenland and Antarctica) due to the relatively low computational cost of the shallow-ice approximation but higher order (ISSM, AIF) and full Stokes (Elmer/Ice) models have been recently used to model the Greenland ice sheet. The advance in processor speed and the decrease in cost for accessing large amount of memory and storage have undoubtedly been the driving force in the commoditization of models with higher capabilities, and the popularity of Elmer/Ice (http://elmerice.elmerfem.com) with an active user base is a notable representation of this trend. Elmer/Ice is a full Stokes model built on top of the multi-physics package Elmer (http://www.csc.fi/english/pages/elmer) which provides the full machinery for the complex finite element procedure and is fully parallel (mesh partitioning with OpenMPI communication). Elmer is mainly written in Fortran 90 and targets essentially traditional processors as the code base was not initially written to run on modern coprocessors (yet adding support for the recently introduced x86 based coprocessors is possible). Furthermore, a truly modular and object-oriented implementation is required for quick adaptation to fast evolving capabilities in hardware (Fortran 2003 provides an object-oriented programming model while not being clean and requiring a tricky refactoring of Elmer code). In this work, the object-oriented, coprocessor-accelerated finite element code Sainou is introduced. Sainou is an Elmer fork which is reimplemented in Objective C and used for experimenting with ice sheet models running on coprocessors, essentially GPU devices. GPUs are highly parallel processors that provide opportunities for fine-grained parallelization of the full Stokes problem using the standard OpenCL language (http://www.khronos.org/opencl/) to access the device. Sainou is built upon a collection of Objective C base classes that service a modular kernel (itself a base class) which provides the core methods to solve the finite element problem. An early implementation of Sainou will be presented with emphasis on the object architecture and the strategies of parallelizations. The computation of a simple heat conduction problem is used to test the implementation which also provides experimental support for running the global matrix assembly on GPU.

A comparative study of computational solutions to flow over a backward-facing step

NASA Technical Reports Server (NTRS)

Mizukami, M.; Georgiadis, N. J.; Cannon, M. R.

1993-01-01

A comparative study was conducted for computational fluid dynamic solutions to flow over a backward-facing step. This flow is a benchmark problem, with a simple geometry, but involves complicated flow physics such as free shear layers, reattaching flow, recirculation, and high turbulence intensities. Three Reynolds-averaged Navier-Stokes flow solvers with k-epsilon turbulence models were used, each using a different solution algorithm: finite difference, finite element, and hybrid finite element - finite difference. Comparisons were made with existing experimental data. Results showed that velocity profiles and reattachment lengths were predicted reasonably well by all three methods, while the skin friction coefficients were more difficult to predict accurately. It was noted that, in general, selecting an appropriate solver for each problem to be considered is important.

Estimating finite-population reproductive numbers in heterogeneous populations.

PubMed

Keegan, Lindsay T; Dushoff, Jonathan

2016-05-21

The basic reproductive number, R0, is one of the most important epidemiological quantities. R0 provides a threshold for elimination and determines when a disease can spread or when a disease will die out. Classically, R0 is calculated assuming an infinite population of identical hosts. Previous work has shown that heterogeneity in the host mixing rate increases R0 in an infinite population. However, it has been suggested that in a finite population, heterogeneity in the mixing rate may actually decrease the finite-population reproductive numbers. Here, we outline a framework for discussing different types of heterogeneity in disease parameters, and how these affect disease spread and control. We calculate "finite-population reproductive numbers" with different types of heterogeneity, and show that in a finite population, heterogeneity has complicated effects on the reproductive number. We find that simple heterogeneity decreases the finite-population reproductive number, whereas heterogeneity in the intrinsic mixing rate (which affects both infectiousness and susceptibility) increases the finite-population reproductive number when R0 is small relative to the size of the population and decreases the finite-population reproductive number when R0 is large relative to the size of the population. Although heterogeneity has complicated effects on the finite-population reproductive numbers, its implications for control are straightforward: when R0 is large relative to the size of the population, heterogeneity decreases the finite-population reproductive numbers, making disease control or elimination easier than predicted by R0. Copyright © 2016 Elsevier Ltd. All rights reserved.

1r2dinv: A finite-difference model for inverse analysis of two dimensional linear or radial groundwater flow

USGS Publications Warehouse

Bohling, Geoffrey C.; Butler, J.J.

2001-01-01

We have developed a program for inverse analysis of two-dimensional linear or radial groundwater flow problems. The program, 1r2dinv, uses standard finite difference techniques to solve the groundwater flow equation for a horizontal or vertical plane with heterogeneous properties. In radial mode, the program simulates flow to a well in a vertical plane, transforming the radial flow equation into an equivalent problem in Cartesian coordinates. The physical parameters in the model are horizontal or x-direction hydraulic conductivity, anisotropy ratio (vertical to horizontal conductivity in a vertical model, y-direction to x-direction in a horizontal model), and specific storage. The program allows the user to specify arbitrary and independent zonations of these three parameters and also to specify which zonal parameter values are known and which are unknown. The Levenberg-Marquardt algorithm is used to estimate parameters from observed head values. Particularly powerful features of the program are the ability to perform simultaneous analysis of heads from different tests and the inclusion of the wellbore in the radial mode. These capabilities allow the program to be used for analysis of suites of well tests, such as multilevel slug tests or pumping tests in a tomographic format. The combination of information from tests stressing different vertical levels in an aquifer provides the means for accurately estimating vertical variations in conductivity, a factor profoundly influencing contaminant transport in the subsurface. ?? 2001 Elsevier Science Ltd. All rights reserved.

The Use of Non-Standard Devices in Finite Element Analysis

NASA Technical Reports Server (NTRS)

Schur, Willi W.; Broduer, Steve (Technical Monitor)

2001-01-01

A general mathematical description of the response behavior of thin-skin pneumatic envelopes and many other membrane and cable structures produces under-constrained systems that pose severe difficulties to analysis. These systems are mobile, and the general mathematical description exposes the mobility. Yet the response behavior of special under-constrained structures under special loadings can be accurately predicted using a constrained mathematical description. The static response behavior of systems that are infinitesimally mobile, such as a non-slack membrane subtended from a rigid or elastic boundary frame, can be easily analyzed using such general mathematical description as afforded by the non-linear, finite element method using an implicit solution scheme if the incremental uploading is guided through a suitable path. Similarly, if such structures are assembled with structural lack of fit that provides suitable self-stress, then dynamic response behavior can be predicted by the non-linear, finite element method and an implicit solution scheme. An explicit solution scheme is available for evolution problems. Such scheme can be used via the method of dynamic relaxation to obtain the solution to a static problem. In some sense, pneumatic envelopes and many other compliant structures can be said to have destiny under a specified loading system. What that means to the analyst is that what happens on the evolution path of the solution is irrelevant as long as equilibrium is achieved at destiny under full load and that the equilibrium is stable in the vicinity of that load. The purpose of this paper is to alert practitioners to the fact that non-standard procedures in finite element analysis are useful and can be legitimate although they burden their users with the requirement to use special caution. Some interesting findings that are useful to the US Scientific Balloon Program and that could not be obtained without non-standard techniques are presented.

Micro-scale finite element modeling of ultrasound propagation in aluminum trabecular bone-mimicking phantoms: A comparison between numerical simulation and experimental results.

PubMed

Vafaeian, B; Le, L H; Tran, T N H T; El-Rich, M; El-Bialy, T; Adeeb, S

2016-05-01

The present study investigated the accuracy of micro-scale finite element modeling for simulating broadband ultrasound propagation in water-saturated trabecular bone-mimicking phantoms. To this end, five commercially manufactured aluminum foam samples as trabecular bone-mimicking phantoms were utilized for ultrasonic immersion through-transmission experiments. Based on micro-computed tomography images of the same physical samples, three-dimensional high-resolution computational samples were generated to be implemented in the micro-scale finite element models. The finite element models employed the standard Galerkin finite element method (FEM) in time domain to simulate the ultrasonic experiments. The numerical simulations did not include energy dissipative mechanisms of ultrasonic attenuation; however, they expectedly simulated reflection, refraction, scattering, and wave mode conversion. The accuracy of the finite element simulations were evaluated by comparing the simulated ultrasonic attenuation and velocity with the experimental data. The maximum and the average relative errors between the experimental and simulated attenuation coefficients in the frequency range of 0.6-1.4 MHz were 17% and 6% respectively. Moreover, the simulations closely predicted the time-of-flight based velocities and the phase velocities of ultrasound with maximum relative errors of 20 m/s and 11 m/s respectively. The results of this study strongly suggest that micro-scale finite element modeling can effectively simulate broadband ultrasound propagation in water-saturated trabecular bone-mimicking structures. Copyright © 2016 Elsevier B.V. All rights reserved.

Assessing behind armor blunt trauma (BABT) under NIJ standard-0101.04 conditions using human torso models.

PubMed

Merkle, Andrew C; Ward, Emily E; O'Connor, James V; Roberts, Jack C

2008-06-01

Although soft armor vests serve to prevent penetrating wounds and dissipate impact energy, the potential of nonpenetrating injury to the thorax, termed behind armor blunt trauma, does exist. Currently, the ballistic resistance of personal body armor is determined by impacting a soft armor vest over a clay backing and measuring the resulting clay deformation as specified in National Institute of Justice (NIJ) Standard-0101.04. This research effort evaluated the efficacy of a physical Human Surrogate Torso Model (HSTM) as a device for determining thoracic response when exposed to impact conditions specified in the NIJ Standard. The HSTM was subjected to a series of ballistic impacts over the sternum and stomach. The pressure waves propagating through the torso were measured with sensors installed in the organs. A previously developed Human Torso Finite Element Model (HTFEM) was used to analyze the amount of tissue displacement during impact and compared with the amount of clay deformation predicted by a validated finite element model. All experiments and simulations were conducted at NIJ Standard test conditions. When normalized by the response at the lowest threat level (Level I), the clay deformations for the higher levels are relatively constant and range from 2.3 to 2.7 times that of the base threat level. However, the pressures in the HSTM increase with each test level and range from three to seven times greater than Level I depending on the organ. The results demonstrate the abilities of the HSTM to discriminate between threat levels, impact conditions, and impact locations. The HTFEM and HSTM are capable of realizing pressure and displacement differences because of the level of protection, surrounding tissue, and proximity to the impact point. The results of this research provide insight into the transfer of energy and pressure wave propagation during ballistic impacts using a physical surrogate and computational model of the human torso.

Predator-prey Encounter Rates in Turbulent Environments: Consequences of Inertia Effects and Finite Sizes

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

Pecseli, H. L.; Trulsen, J.

2009-10-08

Experimental as well as theoretical studies have demonstrated that turbulence can play an important role for the biosphere in marine environments, in particular also by affecting prey-predator encounter rates. Reference models for the encounter rates rely on simplifying assumptions of predators and prey being described as point particles moving passively with the local flow velocity. Based on simple arguments that can be tested experimentally we propose corrections for the standard expression for the encounter rates, where now finite sizes and Stokes drag effects are included.

The Crank Nicolson Time Integrator for EMPHASIS.

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

McGregor, Duncan Alisdair Odum; Love, Edward; Kramer, Richard Michael Jack

2018-03-01

We investigate the use of implicit time integrators for finite element time domain approxi- mations of Maxwell's equations in vacuum. We discretize Maxwell's equations in time using Crank-Nicolson and in 3D space using compatible finite elements. We solve the system by taking a single step of Newton's method and inverting the Eddy-Current Schur complement allowing for the use of standard preconditioning techniques. This approach also generalizes to more complex material models that can include the Unsplit PML. We present verification results and demonstrate performance at CFL numbers up to 1000.

On the Use of a Mixed Gaussian/Finite-Element Basis Set for the Calculation of Rydberg States

NASA Technical Reports Server (NTRS)

Thuemmel, Helmar T.; Langhoff, Stephen (Technical Monitor)

1996-01-01

Configuration-interaction studies are reported for the Rydberg states of the helium atom using mixed Gaussian/finite-element (GTO/FE) one particle basis sets. Standard Gaussian valence basis sets are employed, like those, used extensively in quantum chemistry calculations. It is shown that the term values for high-lying Rydberg states of the helium atom can be obtained accurately (within 1 cm -1), even for a small GTO set, by augmenting the n-particle space with configurations, where orthonormalized interpolation polynomials are singly occupied.

The Theory and Practice of the h-p Version of Finite Element Method.

DTIC Science & Technology

1987-04-01

1Wr-194 ’The problem with none-hmogeneous Dirichlet problem is to find the finite element solution u. £ data was studied by Babuika, Guo.im- 4401 The h...implemented in the coasmercial code PROOE . by Noetic Tech., St. Louis. See (27,281. The commer- IuS -u 01 1 C(SIS2)Z(u0,HI,S1) (2.3) cial program FIESTA...collaboration with govern- ment agencies such as the National Bureau of Standards. o To be an international center of study and research for foreign

Program design by a multidisciplinary team. [for structural finite element analysis on STAR-100 computer

NASA Technical Reports Server (NTRS)

Voigt, S.

1975-01-01

The use of software engineering aids in the design of a structural finite-element analysis computer program for the STAR-100 computer is described. Nested functional diagrams to aid in communication among design team members were used, and a standardized specification format to describe modules designed by various members was adopted. This is a report of current work in which use of the functional diagrams provided continuity and helped resolve some of the problems arising in this long-running part-time project.

The biomechanical behavior on the interface of tumor arthrosis/allograft prosthetic composite by finite element analysis

NASA Astrophysics Data System (ADS)

Chen, H. Z.; Jiang, W.; Zou, W.; Luo, J. M.; Chen, J. Y.; Tu, C. Q.; Xing, B. B.; Gu, Z. W.; Zhang, X. D.

2008-11-01

The biomechanical behavior of the uniting interface between the allograft bone and the autogenetic bone plays an important role in the treatment of the proximal femur massive defects with artificial tumor arthrosis/allograft prosthetic composite (TAAPC). According to the CT data of a patient, a 3D medical treatment model of TAAPC was established. Under the loads of 1.5 and 2.5 times standard body weight (70 kg), the mechanical behavior of the treatment model was analyzed by finite element analysis (FEA) for three typical healing periods. The results show that there are significant differences in the stress values and distribution in different healing periods. With healing of osteotomy, the hardness of the tissue of the uniting interface increases, the stress in uniting area was increased greatly and the stress concentration decreased. After cured the stress almost reached the level of normal bone. In the initial stage of healing, the healing training is not encouraged because there is an obvious risk of fracture of prosthesis and bone cement. In addition, porous hydroxyapatite (HA) ceramic used as bone tissue scaffold for this case, not only facilitates the generation of new bone, but also can avoid this risk caused by the non-uniting interface.

Quasi-disjoint pentadiagonal matrix systems for the parallelization of compact finite-difference schemes and filters

NASA Astrophysics Data System (ADS)

Kim, Jae Wook

2013-05-01

This paper proposes a novel systematic approach for the parallelization of pentadiagonal compact finite-difference schemes and filters based on domain decomposition. The proposed approach allows a pentadiagonal banded matrix system to be split into quasi-disjoint subsystems by using a linear-algebraic transformation technique. As a result the inversion of pentadiagonal matrices can be implemented within each subdomain in an independent manner subject to a conventional halo-exchange process. The proposed matrix transformation leads to new subdomain boundary (SB) compact schemes and filters that require three halo terms to exchange with neighboring subdomains. The internode communication overhead in the present approach is equivalent to that of standard explicit schemes and filters based on seven-point discretization stencils. The new SB compact schemes and filters demand additional arithmetic operations compared to the original serial ones. However, it is shown that the additional cost becomes sufficiently low by choosing optimal sizes of their discretization stencils. Compared to earlier published results, the proposed SB compact schemes and filters successfully reduce parallelization artifacts arising from subdomain boundaries to a level sufficiently negligible for sophisticated aeroacoustic simulations without degrading parallel efficiency. The overall performance and parallel efficiency of the proposed approach are demonstrated by stringent benchmark tests.

Development and analysis of a finite element model to simulate pulmonary emphysema in CT imaging.

PubMed

Diciotti, Stefano; Nobis, Alessandro; Ciulli, Stefano; Landini, Nicholas; Mascalchi, Mario; Sverzellati, Nicola; Innocenti, Bernardo

2015-01-01

In CT imaging, pulmonary emphysema appears as lung regions with Low-Attenuation Areas (LAA). In this study we propose a finite element (FE) model of lung parenchyma, based on a 2-D grid of beam elements, which simulates pulmonary emphysema related to smoking in CT imaging. Simulated LAA images were generated through space sampling of the model output. We employed two measurements of emphysema extent: Relative Area (RA) and the exponent D of the cumulative distribution function of LAA clusters size. The model has been used to compare RA and D computed on the simulated LAA images with those computed on the models output. Different mesh element sizes and various model parameters, simulating different physiological/pathological conditions, have been considered and analyzed. A proper mesh element size has been determined as the best trade-off between reliable results and reasonable computational cost. Both RA and D computed on simulated LAA images were underestimated with respect to those calculated on the models output. Such underestimations were larger for RA (≈ -44 ÷ -26%) as compared to those for D (≈ -16 ÷ -2%). Our FE model could be useful to generate standard test images and to design realistic physical phantoms of LAA images for the assessment of the accuracy of descriptors for quantifying emphysema in CT imaging.

Non-linear 3D evaluation of different oral implant-abutment connections.

PubMed

Streckbein, P; Streckbein, R G; Wilbrand, J F; Malik, C Y; Schaaf, H; Howaldt, H P; Flach, M

2012-12-01

Micro-gaps and osseous overload in the implant-abutment connection are the most common causes of peri-implant bone resorption and implant failure. These undesirable events can be visualized on standardized three-dimensional finite element models and by radiographic methods. The present study investigated the influence of 7 available implant systems (Ankylos, Astra, Bego, Brånemark, Camlog, Straumann, and Xive) with different implant-abutment connections on bone overload and the appearance of micro-gaps in vitro. The individual geometries of the implants were transferred to three-dimensional finite element models. In a non-linear analysis considering the pre-loading of the occlusion screw, friction between the implant and abutment, the influence of the cone angle on bone strain, and the appearance of micro-gaps were determined. Increased bone strains were correlated with small (< 15°) cone angles. Conical implant-abutment connections efficiently avoided micro-gaps but had a negative effect on peri-implant bone strain. Bone strain was reduced in implants with greater wall thickness (Ankylos) or a smaller cone angle (Bego). The results of our in silico study provide a solid basis for the reduction of peri-implant bone strain and micro-gaps in the implant-abutment connection to improve long-term stability.

Scalable direct Vlasov solver with discontinuous Galerkin method on unstructured mesh.

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

Xu, J.; Ostroumov, P. N.; Mustapha, B.

2010-12-01

This paper presents the development of parallel direct Vlasov solvers with discontinuous Galerkin (DG) method for beam and plasma simulations in four dimensions. Both physical and velocity spaces are in two dimesions (2P2V) with unstructured mesh. Contrary to the standard particle-in-cell (PIC) approach for kinetic space plasma simulations, i.e., solving Vlasov-Maxwell equations, direct method has been used in this paper. There are several benefits to solving a Vlasov equation directly, such as avoiding noise associated with a finite number of particles and the capability to capture fine structure in the plasma. The most challanging part of a direct Vlasov solvermore » comes from higher dimensions, as the computational cost increases as N{sup 2d}, where d is the dimension of the physical space. Recently, due to the fast development of supercomputers, the possibility has become more realistic. Many efforts have been made to solve Vlasov equations in low dimensions before; now more interest has focused on higher dimensions. Different numerical methods have been tried so far, such as the finite difference method, Fourier Spectral method, finite volume method, and spectral element method. This paper is based on our previous efforts to use the DG method. The DG method has been proven to be very successful in solving Maxwell equations, and this paper is our first effort in applying the DG method to Vlasov equations. DG has shown several advantages, such as local mass matrix, strong stability, and easy parallelization. These are particularly suitable for Vlasov equations. Domain decomposition in high dimensions has been used for parallelization; these include a highly scalable parallel two-dimensional Poisson solver. Benchmark results have been shown and simulation results will be reported.« less

Single-spin observables and orbital structures in hadronic distributions

NASA Astrophysics Data System (ADS)

Sivers, Dennis

2006-11-01

Single-spin observables in scattering processes (either analyzing powers or polarizations) are highly constrained by rotational invariance and finite symmetries. For example, it is possible to demonstrate that all single-spin observables are odd under the finite transformation O=PAτ where P is parity and Aτ is a finite symmetry that can be designated “artificial time reversal”. The operators P, O and Aτ all have eigenvalues ±1 so that all single-spin observables can be classified into two distinct categories: (1) P-odd and Aτ-even, (2) P-even and Aτ-odd. Within the light-quark sector of the standard model, P-odd observables are generated from pointlike electroweak processes while Aτ-odd observables (neglecting quark mass parameters) come from dynamic spin-orbit correlations within hadrons or within larger composite systems, such as nuclei. The effects of Aτ-odd dynamics can be inserted into transverse-momentum dependent constituent distribution functions and, in this paper, we construct the contribution from an orbital quark to the Aτ-odd quark parton distribution ΔNGq/p↑front(x,kTN;μ2). Using this distribution, we examine the crucial role of initial- and final-state interactions in the observation of the scattering asymmetries in different hard-scattering processes. This construction provides a geometrical and dynamical interpretation of the Collins conjugation relation between single-spin asymmetries in semi-inclusive deep inelastic scattering and the asymmetries in Drell-Yan production. Finally, our construction allows us to display a significant difference between the calculation of a spin asymmetry generated by a hard-scattering mechanism involving color-singlet exchange (such as a photon) and a calculation of an asymmetry with a hard-scattering exchange involving gluons. This leads to an appreciation of the process-dependence inherent in measurements of single-spin observables.

Tools for Modeling & Simulation of Molecular and Nanoelectronics Devices

DTIC Science & Technology

2012-06-14

implemented a prototype DFT simulation software using two different open source Finite Element (FE) libraries: DEALII and FENICS . These two libraries have been...ATK. In the first part of this Phase I project we investigated two different candidate finite element libraries, DEAL II and FENICS . Although both...element libraries, Deal.II and FEniCS /dolfin, for use as back-ends to a finite element DFT in ATK, Quantum Insight and QuantumWise A/S, October 2011.

Codifference as a practical tool to measure interdependence

NASA Astrophysics Data System (ADS)

Wyłomańska, Agnieszka; Chechkin, Aleksei; Gajda, Janusz; Sokolov, Igor M.

2015-03-01

Correlation and spectral analysis represent the standard tools to study interdependence in statistical data. However, for the stochastic processes with heavy-tailed distributions such that the variance diverges, these tools are inadequate. The heavy-tailed processes are ubiquitous in nature and finance. We here discuss codifference as a convenient measure to study statistical interdependence, and we aim to give a short introductory review of its properties. By taking different known stochastic processes as generic examples, we present explicit formulas for their codifferences. We show that for the Gaussian processes codifference is equivalent to covariance. For processes with finite variance these two measures behave similarly with time. For the processes with infinite variance the covariance does not exist, however, the codifference is relevant. We demonstrate the practical importance of the codifference by extracting this function from simulated as well as real data taken from turbulent plasma of fusion device and financial market. We conclude that the codifference serves as a convenient practical tool to study interdependence for stochastic processes with both infinite and finite variances as well.

Fracture mechanics life analytical methods verification testing

NASA Technical Reports Server (NTRS)

Favenesi, J. A.; Clemmons, T. G.; Lambert, T. J.

1994-01-01

Verification and validation of the basic information capabilities in NASCRAC has been completed. The basic information includes computation of K versus a, J versus a, and crack opening area versus a. These quantities represent building blocks which NASCRAC uses in its other computations such as fatigue crack life and tearing instability. Several methods were used to verify and validate the basic information capabilities. The simple configurations such as the compact tension specimen and a crack in a finite plate were verified and validated versus handbook solutions for simple loads. For general loads using weight functions, offline integration using standard FORTRAN routines was performed. For more complicated configurations such as corner cracks and semielliptical cracks, NASCRAC solutions were verified and validated versus published results and finite element analyses. A few minor problems were identified in the basic information capabilities of the simple configurations. In the more complicated configurations, significant differences between NASCRAC and reference solutions were observed because NASCRAC calculates its solutions as averaged values across the entire crack front whereas the reference solutions were computed for a single point.

Computation of turbulent boundary layer flows with an algebraic stress turbulence model

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook; Chen, Yen-Sen

1986-01-01

An algebraic stress turbulence model is presented, characterized by the following: (1) the eddy viscosity expression is derived from the Reynolds stress turbulence model; (2) the turbulent kinetic energy dissipation rate equation is improved by including a production range time scale; and (3) the diffusion coefficients for turbulence equations are adjusted so that the kinetic energy profile extends further into the free stream region found in most experimental data. The turbulent flow equations were solved using a finite element method. Examples include: fully developed channel flow, fully developed pipe flow, flat plate boundary layer flow, plane jet exhausting into a moving stream, circular jet exhausting into a moving stream, and wall jet flow. Computational results compare favorably with experimental data for most of the examples considered. Significantly improved results were obtained for the plane jet flow, the circular jet flow, and the wall jet flow; whereas the remainder are comparable to those obtained by finite difference methods using the standard kappa-epsilon turbulence model. The latter seems to be promising with further improvement of the expression for the eddy viscosity coefficient.

Electro-optical modeling of bulk heterojunction solar cells

NASA Astrophysics Data System (ADS)

Kirchartz, Thomas; Pieters, Bart E.; Taretto, Kurt; Rau, Uwe

2008-11-01

We introduce a model for charge separation in bulk heterojunction solar cells that combines exciton transport to the interface between donor and acceptor phases with the dissociation of the bound electron/hole pair. We implement this model into a standard semiconductor device simulator, thereby creating a convenient method to simulate the optical and electrical characteristics of a bulk heterojunction solar cell with a commercially available program. By taking into account different collection probabilities for the excitons in the polymer and the fullerene, we are able to reproduce absorptance, internal and external quantum efficiency, as well as current/voltage curves of bulk heterojunction solar cells. We further investigate the influence of mobilities of the free excitons as well as the mobilities of the free charge carriers on the performance of bulk heterojunction solar cells. We find that, in general, the highest efficiencies are achieved with the highest mobilities. However, an optimum finite mobility of free charge carriers can result from a large recombination velocity at the contacts. In contrast, Langevin-type of recombination cannot lead to finite optimum mobilities even though this mechanism has a strong dependence on the free carrier mobilities.

An ultra-accurate numerical method in the design of liquid phononic crystals with hard inclusion

NASA Astrophysics Data System (ADS)

Li, Eric; He, Z. C.; Wang, G.; Liu, G. R.

2017-12-01

The phononics crystals (PCs) are periodic man-made composite materials. In this paper, a mass-redistributed finite element method (MR-FEM) is formulated to study the wave propagation within liquid PCs with hard inclusion. With a perfect balance between stiffness and mass in the MR-FEM model, the dispersion error of longitudinal wave is minimized by redistribution of mass. Such tuning can be easily achieved by adjusting the parameter r that controls the location of integration points of mass matrix. More importantly, the property of mass conservation in the MR-FEM model indicates that the locations of integration points inside or outside the element are immaterial. Four numerical examples are studied in this work, including liquid PCs with cross and circle hard inclusions, different size of inclusion and defect. Compared with standard finite element method, the numerical results have verified the accuracy and effectiveness of MR-FEM. The proposed MR-FEM is a unique and innovative numerical approach with its outstanding features, which has strong potentials to study the stress wave within multi-physics PCs.

Frequency-difference MIT imaging of cerebral haemorrhage with a hemispherical coil array: numerical modelling.

PubMed

Zolgharni, M; Griffiths, H; Ledger, P D

2010-08-01

The feasibility of detecting a cerebral haemorrhage with a hemispherical MIT coil array consisting of 56 exciter/sensor coils of 10 mm radius and operating at 1 and 10 MHz was investigated. A finite difference method combined with an anatomically realistic head model comprising 12 tissue types was used to simulate the strokes. Frequency-difference images were reconstructed from the modelled data with different levels of the added phase noise and two types of a priori boundary errors: a displacement of the head and a size scaling error. The results revealed that a noise level of 3 m degrees (standard deviation) was adequate for obtaining good visualization of a peripheral stroke (volume approximately 49 ml). The simulations further showed that the displacement error had to be within 3-4 mm and the scaling error within 3-4% so as not to cause unacceptably large artefacts on the images.

An evaluation of objective rating methods for full-body finite element model comparison to PMHS tests.

PubMed

Vavalle, Nicholas A; Jelen, Benjamin C; Moreno, Daniel P; Stitzel, Joel D; Gayzik, F Scott

2013-01-01

Objective evaluation methods of time history signals are used to quantify how well simulated human body responses match experimental data. As the use of simulations grows in the field of biomechanics, there is a need to establish standard approaches for comparisons. There are 2 aims of this study. The first is to apply 3 objective evaluation methods found in the literature to a set of data from a human body finite element model. The second is to compare the results of each method, examining how they are correlated to each other and the relative strengths and weaknesses of the algorithms. In this study, the methods proposed by Sprague and Geers (magnitude and phase error, SGM and SGP), Rhule et al. (cumulative standard deviation, CSD), and Gehre et al. (CORrelation and Analysis, or CORA, size, phase, shape, corridor) were compared. A 40 kph frontal sled test presented by Shaw et al. was simulated using the Global Human Body Models Consortium midsized male full-body finite element model (v. 3.5). Mean and standard deviation experimental data (n = 5) from Shaw et al. were used as the benchmark. Simulated data were output from the model at the appropriate anatomical locations for kinematic comparison. Force data were output at the seat belts, seat pan, knee, and foot restraints. Objective comparisons from 53 time history data channels were compared to the experimental results. To compare the different methods, all objective comparison metrics were cross-plotted and linear regressions were calculated. The following ratings were found to be statistically significantly correlated (P < .01): SGM and CORrelation and Analysis (CORA) size, R (2) = 0.73; SGP and CORA shape, R (2) = 0.82; and CSD and CORA's corridor factor, R (2) = 0.59. Relative strengths of the correlated ratings were then investigated. For example, though correlated to CORA size, SGM carries a sign to indicate whether the simulated response is greater than or less than the benchmark signal. A further analysis of the advantages and drawbacks of each method is discussed. The results demonstrate that a single metric is insufficient to provide a complete assessment of how well the simulated results match the experiments. The CORA method provided the most comprehensive evaluation of the signal. Regardless of the method selected, one primary recommendation of this work is that for any comparison, the results should be reported to provide separate assessments of a signal's match to experimental variance, magnitude, phase, and shape. Future work planned includes implementing any forthcoming International Organization for Standardization standards for objective evaluations. Supplemental materials are available for this article. Go to the publisher's online edition of Traffic Injury Prevention to view the supplemental file.

Applications of discrete element method in modeling of grain postharvest operations

USDA-ARS?s Scientific Manuscript database

Grain kernels are finite and discrete materials. Although flowing grain can behave like a continuum fluid at times, the discontinuous behavior exhibited by grain kernels cannot be simulated solely with conventional continuum-based computer modeling such as finite-element or finite-difference methods...

An investigation of several factors involved in a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings

NASA Technical Reports Server (NTRS)

Ehlers, F. E.; Sebastian, J. D.; Weatherill, W. H.

1979-01-01

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. Since sinusoidal motion is assumed, the unsteady equation is independent of time. Three finite difference investigations are discussed including a new operator for mesh points with supersonic flow, the effects on relaxation solution convergence of adding a viscosity term to the original differential equation, and an alternate and relatively simple downstream boundary condition. A method is developed which uses a finite difference procedure over a limited inner region and an approximate analytical procedure for the remaining outer region. Two investigations concerned with three-dimensional flow are presented. The first is the development of an oblique coordinate system for swept and tapered wings. The second derives the additional terms required to make row relaxation solutions converge when mixed flow is present. A finite span flutter analysis procedure is described using the two-dimensional unsteady transonic program with a full three-dimensional steady velocity potential.

Optical absorption enhancement by inserting ZnO optical spacer in plasmonic organic solar cells

NASA Astrophysics Data System (ADS)

N'Konou, Kekeli; Torchio, Philippe

2018-01-01

Optical absorption enhancement (AE) using coupled optical spacer and plasmonic effects in standard and inverted organic solar cells (OSCs) are demonstrated using the finite-difference time-domain numerical method. The influence of an added zinc oxide (ZnO) optical spacer layer inserted below the active layer in standard architecture is first theoretically investigated while the influence of varying the ZnO cathodic buffer layer thickness in inverted design is studied on AE. Then, the embedding of a square periodic array of core-shell silver-silica nanospheres (Ag@SiO2 NSs) at different positions in standard and inverted OSCs is performed while AE and short-circuit current density (Jsc) are calculated. As a result of previous combined effects, the optimized standard plasmonic OSCs present 15% and 79.45% enhancement in J over the reference with and without ZnO optical spacer layer, respectively, and a 16% increase of AE when Ag@SiO2 NSs are placed on top of the PEDOT:PSS layer. Compared to the inverted OSC reference, the plasmonic OSCs present 26% and 27% enhancement in J and AE, respectively, when the Ag@SiO2 NSs are located on top of the ZnO layer. Furthermore, the spatial position of these NSs in such OSCs is a key parameter for increasing light absorption via enhanced electromagnetic field distribution.

Interference between light and heavy neutrinos for 0 νββ decay in the left–right symmetric model

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

Ahmed, Fahim; Neacsu, Andrei; Horoi, Mihai

Neutrinoless double-beta decay is proposed as an important low energy phenomenon that could test beyond the Standard Model physics. There are several potentially competing beyond the Standard Model mechanisms that can induce the process. It thus becomes important to disentangle the different processes. In the present study we consider the interference effect between the light left-handed and heavy right-handed Majorana neutrino exchange mechanisms. The decay rate, and consequently, the phase-space factors for the interference term are derived, based on the left–right symmetric model. The numerical values for the interference phase-space factors for several nuclides are calculated, taking into consideration themore » relativistic Coulomb distortion of the electron wave function and finite-size of the nucleus. As a result, the variation of the interference effect with the Q-value of the process is studied.« less

Interference between light and heavy neutrinos for 0 νββ decay in the left–right symmetric model

DOE PAGES

Ahmed, Fahim; Neacsu, Andrei; Horoi, Mihai

2017-03-31

Neutrinoless double-beta decay is proposed as an important low energy phenomenon that could test beyond the Standard Model physics. There are several potentially competing beyond the Standard Model mechanisms that can induce the process. It thus becomes important to disentangle the different processes. In the present study we consider the interference effect between the light left-handed and heavy right-handed Majorana neutrino exchange mechanisms. The decay rate, and consequently, the phase-space factors for the interference term are derived, based on the left–right symmetric model. The numerical values for the interference phase-space factors for several nuclides are calculated, taking into consideration themore » relativistic Coulomb distortion of the electron wave function and finite-size of the nucleus. As a result, the variation of the interference effect with the Q-value of the process is studied.« less

Phase Transition in Protocols Minimizing Work Fluctuations

NASA Astrophysics Data System (ADS)

Solon, Alexandre P.; Horowitz, Jordan M.

2018-05-01

For two canonical examples of driven mesoscopic systems—a harmonically trapped Brownian particle and a quantum dot—we numerically determine the finite-time protocols that optimize the compromise between the standard deviation and the mean of the dissipated work. In the case of the oscillator, we observe a collection of protocols that smoothly trade off between average work and its fluctuations. However, for the quantum dot, we find that as we shift the weight of our optimization objective from average work to work standard deviation, there is an analog of a first-order phase transition in protocol space: two distinct protocols exchange global optimality with mixed protocols akin to phase coexistence. As a result, the two types of protocols possess qualitatively different properties and remain distinct even in the infinite duration limit: optimal-work-fluctuation protocols never coalesce with the minimal-work protocols, which therefore never become quasistatic.

A stochastic-field description of finite-size spiking neural networks

PubMed Central

Longtin, André

2017-01-01

Neural network dynamics are governed by the interaction of spiking neurons. Stochastic aspects of single-neuron dynamics propagate up to the network level and shape the dynamical and informational properties of the population. Mean-field models of population activity disregard the finite-size stochastic fluctuations of network dynamics and thus offer a deterministic description of the system. Here, we derive a stochastic partial differential equation (SPDE) describing the temporal evolution of the finite-size refractory density, which represents the proportion of neurons in a given refractory state at any given time. The population activity—the density of active neurons per unit time—is easily extracted from this refractory density. The SPDE includes finite-size effects through a two-dimensional Gaussian white noise that acts both in time and along the refractory dimension. For an infinite number of neurons the standard mean-field theory is recovered. A discretization of the SPDE along its characteristic curves allows direct simulations of the activity of large but finite spiking networks; this constitutes the main advantage of our approach. Linearizing the SPDE with respect to the deterministic asynchronous state allows the theoretical investigation of finite-size activity fluctuations. In particular, analytical expressions for the power spectrum and autocorrelation of activity fluctuations are obtained. Moreover, our approach can be adapted to incorporate multiple interacting populations and quasi-renewal single-neuron dynamics. PMID:28787447

Finite-Strain Fractional-Order Viscoelastic (FOV) Material Models and Numerical Methods for Solving Them

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Diethelm, Kai; Gray, Hugh R. (Technical Monitor)

2002-01-01

Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis.

Explosive synchronization coexists with classical synchronization in the Kuramoto model

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

Danziger, Michael M., E-mail: michael.danziger@biu.ac.il; Havlin, Shlomo; Moskalenko, Olga I.

2016-06-15

Explosive synchronization has recently been reported in a system of adaptively coupled Kuramoto oscillators, without any conditions on the frequency or degree of the nodes. Here, we find that, in fact, the explosive phase coexists with the standard phase of the Kuramoto oscillators. We determine this by extending the mean-field theory of adaptively coupled oscillators with full coupling to the case with partial coupling of a fraction f. This analysis shows that a metastable region exists for all finite values of f > 0, and therefore explosive synchronization is expected for any perturbation of adaptively coupling added to the standard Kuramoto model.more » We verify this theory with GPU-accelerated simulations on very large networks (N ∼ 10{sup 6}) and find that, in fact, an explosive transition with hysteresis is observed for all finite couplings. By demonstrating that explosive transitions coexist with standard transitions in the limit of f → 0, we show that this behavior is far more likely to occur naturally than was previously believed.« less

Bäcklund transformations for the Boussinesq equation and merging solitons

NASA Astrophysics Data System (ADS)

Rasin, Alexander G.; Schiff, Jeremy

2017-08-01

The Bäcklund transformation (BT) for the ‘good’ Boussinesq equation and its superposition principles are presented and applied. Unlike other standard integrable equations, the Boussinesq equation does not have a strictly algebraic superposition principle for 2 BTs, but it does for 3. We present this and discuss associated lattice systems. Applying the BT to the trivial solution generates both standard solitons and what we call ‘merging solitons’—solutions in which two solitary waves (with related speeds) merge into a single one. We use the superposition principles to generate a variety of interesting solutions, including superpositions of a merging soliton with 1 or 2 regular solitons, and solutions that develop a singularity in finite time which then disappears at a later finite time. We prove a Wronskian formula for the solutions obtained by applying a general sequence of BTs on the trivial solution. Finally, we obtain the standard conserved quantities of the Boussinesq equation from the BT, and show how the hierarchy of local symmetries follows in a simple manner from the superposition principle for 3 BTs.

Can a pseudo-Nambu-Goldstone Higgs lead to symmetry non-restoration?

NASA Astrophysics Data System (ADS)

Kilic, Can; Swaminathan, Sivaramakrishnan

2016-01-01

The calculation of finite temperature contributions to the scalar potential in a quantum field theory is similar to the calculation of loop corrections at zero temperature. In natural extensions of the Standard Model where loop corrections to the Higgs potential cancel between Standard Model degrees of freedom and their symmetry partners, it is interesting to contemplate whether finite temperature corrections also cancel, raising the question of whether a broken phase of electroweak symmetry may persist at high temperature. It is well known that this does not happen in supersymmetric theories because the thermal contributions of bosons and fermions do not cancel each other. However, for theories with same spin partners, the answer is less obvious. Using the Twin Higgs model as a benchmark, we show that although thermal corrections do cancel at the level of quadratic divergences, subleading corrections still drive the system to a restored phase. We further argue that our conclusions generalize to other well-known extensions of the Standard Model where the Higgs is rendered natural by being the pseudo-Nambu-Goldstone mode of an approximate global symmetry.

Parallel processing in finite element structural analysis

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.

1987-01-01

A brief review is made of the fundamental concepts and basic issues of parallel processing. Discussion focuses on parallel numerical algorithms, performance evaluation of machines and algorithms, and parallelism in finite element computations. A computational strategy is proposed for maximizing the degree of parallelism at different levels of the finite element analysis process including: 1) formulation level (through the use of mixed finite element models); 2) analysis level (through additive decomposition of the different arrays in the governing equations into the contributions to a symmetrized response plus correction terms); 3) numerical algorithm level (through the use of operator splitting techniques and application of iterative processes); and 4) implementation level (through the effective combination of vectorization, multitasking and microtasking, whenever available).

Experimental test of nonlocal realistic theories without the rotational symmetry assumption.

PubMed

Paterek, Tomasz; Fedrizzi, Alessandro; Gröblacher, Simon; Jennewein, Thomas; Zukowski, Marek; Aspelmeyer, Markus; Zeilinger, Anton

2007-11-23

We analyze the class of nonlocal realistic theories that was originally considered by Leggett [Found. Phys. 33, 1469 (2003)10.1023/A:1026096313729] and tested by us in a recent experiment [Nature (London) 446, 871 (2007)10.1038/nature05677]. We derive an incompatibility theorem that works for finite numbers of polarizer settings and that does not require the previously assumed rotational symmetry of the two-particle correlation functions. The experimentally measured case involves seven different measurement settings. Using polarization-entangled photon pairs, we exclude this broader class of nonlocal realistic models by experimentally violating a new Leggett-type inequality by 80 standard deviations.

Application of fast Fourier transforms to the direct solution of a class of two-dimensional separable elliptic equations on the sphere

NASA Technical Reports Server (NTRS)

Moorthi, Shrinivas; Higgins, R. W.

1993-01-01

An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

Computer simulation of fibrillation threshold measurements and electrophysiologic testing procedures

NASA Technical Reports Server (NTRS)

Grumbach, M. P.; Saxberg, B. E.; Cohen, R. J.

1987-01-01

A finite element model of cardiac conduction was used to simulate two experimental protocols: 1) fibrillation threshold measurements and 2) clinical electrophysiologic (EP) testing procedures. The model consisted of a cylindrical lattice whose properties were determined by four parameters: element length, conduction velocity, mean refractory period, and standard deviation of refractory periods. Different stimulation patterns were applied to the lattice under a given set of lattice parameter values and the response of the model was observed through a simulated electrocardiogram. The studies confirm that the model can account for observations made in experimental fibrillation threshold measurements and in clinical EP testing protocols.

Eliminating the zero spectrum in Fourier transform profilometry using empirical mode decomposition.

PubMed

Li, Sikun; Su, Xianyu; Chen, Wenjing; Xiang, Liqun

2009-05-01

Empirical mode decomposition is introduced into Fourier transform profilometry to extract the zero spectrum included in the deformed fringe pattern without the need for capturing two fringe patterns with pi phase difference. The fringe pattern is subsequently demodulated using a standard Fourier transform profilometry algorithm. With this method, the deformed fringe pattern is adaptively decomposed into a finite number of intrinsic mode functions that vary from high frequency to low frequency by means of an algorithm referred to as a sifting process. Then the zero spectrum is separated from the high-frequency components effectively. Experiments validate the feasibility of this method.

THREE-POINT BACKWARD FINITE DIFFERENCE METHOD FOR SOLVING A SYSTEM OF MIXED HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. (R825549C019)

EPA Science Inventory

A three-point backward finite-difference method has been derived for a system of mixed hyperbolic_¯¯parabolic (convection_¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...

Stability and uncertainty of finite-fault slip inversions: Application to the 2004 Parkfield, California, earthquake

USGS Publications Warehouse

Hartzell, S.; Liu, P.; Mendoza, C.; Ji, C.; Larson, K.M.

2007-01-01

The 2004 Parkfield, California, earthquake is used to investigate stability and uncertainty aspects of the finite-fault slip inversion problem with different a priori model assumptions. We utilize records from 54 strong ground motion stations and 13 continuous, 1-Hz sampled, geodetic instruments. Two inversion procedures are compared: a linear least-squares subfault-based methodology and a nonlinear global search algorithm. These two methods encompass a wide range of the different approaches that have been used to solve the finite-fault slip inversion problem. For the Parkfield earthquake and the inversion of velocity or displacement waveforms, near-surface related site response (top 100 m, frequencies above 1 Hz) is shown to not significantly affect the solution. Results are also insensitive to selection of slip rate functions with similar duration and to subfault size if proper stabilizing constraints are used. The linear and nonlinear formulations yield consistent results when the same limitations in model parameters are in place and the same inversion norm is used. However, the solution is sensitive to the choice of inversion norm, the bounds on model parameters, such as rake and rupture velocity, and the size of the model fault plane. The geodetic data set for Parkfield gives a slip distribution different from that of the strong-motion data, which may be due to the spatial limitation of the geodetic stations and the bandlimited nature of the strong-motion data. Cross validation and the bootstrap method are used to set limits on the upper bound for rupture velocity and to derive mean slip models and standard deviations in model parameters. This analysis shows that slip on the northwestern half of the Parkfield rupture plane from the inversion of strong-motion data is model dependent and has a greater uncertainty than slip near the hypocenter.

Constitutive models for a poly(e-caprolactone) scaffold.

PubMed

Quinn, T P; Oreskovic, T L; McCowan, C N; Washburn, N R

2004-01-01

We investigate material models for a porous, polymeric scaffold used for bone. The material was made by co-extruding poly(e-caprolactone) (PCL), a biodegradable polyester, and poly(ethylene oxide) (PEO). The water soluble PEO was removed resulting in a porous scaffold. The stress-strain curve in compression was fit with a phenomenological model in hyperbolic form. This material model will be useful for designers for quasi-static analysis as it provides a simple form that can easily be used in finite element models. The ASTM D-1621 standard recommends using a secant modulus based on 10% strain. The resulting modulus has a smaller scatter in its value compared to the coefficients of the hyperbolic model, and it is therefore easier to compare material processing differences and ensure quality of the scaffold. A third material model was constructed from images of the microstructure. Each pixel of the micrographs was represented with a brick finite element and assigned the Young's modulus of bulk PCL or a value of 0 for a pore. A compressive strain was imposed on the model and the resulting stresses were calculated. The elastic constants of the scaffold were then computed using Hooke's law for a linear-elastic isotropic material. The model was able to predict the small strain Young's modulus measured in the experiments to within one standard deviation. Thus, by knowing the microstructure of the scaffold, its bulk properties can be predicted from the material properties of the constituents.

A standard test case suite for two-dimensional linear transport on the sphere: results from a collection of state-of-the-art schemes

NASA Astrophysics Data System (ADS)

Lauritzen, P. H.; Ullrich, P. A.; Jablonowski, C.; Bosler, P. A.; Calhoun, D.; Conley, A. J.; Enomoto, T.; Dong, L.; Dubey, S.; Guba, O.; Hansen, A. B.; Kaas, E.; Kent, J.; Lamarque, J.-F.; Prather, M. J.; Reinert, D.; Shashkin, V. V.; Skamarock, W. C.; Sørensen, B.; Taylor, M. A.; Tolstykh, M. A.

2013-09-01

Recently, a standard test case suite for 2-D linear transport on the sphere was proposed to assess important aspects of accuracy in geophysical fluid dynamics with a "minimal" set of idealized model configurations/runs/diagnostics. Here we present results from 19 state-of-the-art transport scheme formulations based on finite-difference/finite-volume methods as well as emerging (in the context of atmospheric/oceanographic sciences) Galerkin methods. Discretization grids range from traditional regular latitude-longitude grids to more isotropic domain discretizations such as icosahedral and cubed-sphere tessellations of the sphere. The schemes are evaluated using a wide range of diagnostics in idealized flow environments. Accuracy is assessed in single- and two-tracer configurations using conventional error norms as well as novel diagnostics designed for climate and climate-chemistry applications. In addition, algorithmic considerations that may be important for computational efficiency are reported on. The latter is inevitably computing platform dependent, The ensemble of results from a wide variety of schemes presented here helps shed light on the ability of the test case suite diagnostics and flow settings to discriminate between algorithms and provide insights into accuracy in the context of global atmospheric/ocean modeling. A library of benchmark results is provided to facilitate scheme intercomparison and model development. Simple software and data-sets are made available to facilitate the process of model evaluation and scheme intercomparison.

A standard test case suite for two-dimensional linear transport on the sphere: results from a collection of state-of-the-art schemes

NASA Astrophysics Data System (ADS)

Lauritzen, P. H.; Ullrich, P. A.; Jablonowski, C.; Bosler, P. A.; Calhoun, D.; Conley, A. J.; Enomoto, T.; Dong, L.; Dubey, S.; Guba, O.; Hansen, A. B.; Kaas, E.; Kent, J.; Lamarque, J.-F.; Prather, M. J.; Reinert, D.; Shashkin, V. V.; Skamarock, W. C.; Sørensen, B.; Taylor, M. A.; Tolstykh, M. A.

2014-01-01

Recently, a standard test case suite for 2-D linear transport on the sphere was proposed to assess important aspects of accuracy in geophysical fluid dynamics with a "minimal" set of idealized model configurations/runs/diagnostics. Here we present results from 19 state-of-the-art transport scheme formulations based on finite-difference/finite-volume methods as well as emerging (in the context of atmospheric/oceanographic sciences) Galerkin methods. Discretization grids range from traditional regular latitude-longitude grids to more isotropic domain discretizations such as icosahedral and cubed-sphere tessellations of the sphere. The schemes are evaluated using a wide range of diagnostics in idealized flow environments. Accuracy is assessed in single- and two-tracer configurations using conventional error norms as well as novel diagnostics designed for climate and climate-chemistry applications. In addition, algorithmic considerations that may be important for computational efficiency are reported on. The latter is inevitably computing platform dependent. The ensemble of results from a wide variety of schemes presented here helps shed light on the ability of the test case suite diagnostics and flow settings to discriminate between algorithms and provide insights into accuracy in the context of global atmospheric/ocean modeling. A library of benchmark results is provided to facilitate scheme intercomparison and model development. Simple software and data sets are made available to facilitate the process of model evaluation and scheme intercomparison.

Prediction and standard error estimation for a finite universe total when a stratum is not sampled

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

Wright, T.

1994-01-01

In the context of a universe of trucks operating in the United States in 1990, this paper presents statistical methodology for estimating a finite universe total on a second occasion when a part of the universe is sampled and the remainder of the universe is not sampled. Prediction is used to compensate for the lack of data from the unsampled portion of the universe. The sample is assumed to be a subsample of an earlier sample where stratification is used on both occasions before sample selection. Accounting for births and deaths in the universe between the two points in time,more » the detailed sampling plan, estimator, standard error, and optimal sample allocation, are presented with a focus on the second occasion. If prior auxiliary information is available, the methodology is also applicable to a first occasion.« less

The FBI wavelet/scalar quantization standard for gray-scale fingerprint image compression

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

Bradley, J.N.; Brislawn, C.M.; Hopper, T.

1993-05-01

The FBI has recently adopted a standard for the compression of digitized 8-bit gray-scale fingerprint images. The standard is based on scalar quantization of a 64-subband discrete wavelet transform decomposition of the images, followed by Huffman coding. Novel features of the algorithm include the use of symmetric boundary conditions for transforming finite-length signals and a subband decomposition tailored for fingerprint images scanned at 500 dpi. The standard is intended for use in conjunction with ANSI/NBS-CLS 1-1993, American National Standard Data Format for the Interchange of Fingerprint Information, and the FBI`s Integrated Automated Fingerprint Identification System.

The FBI wavelet/scalar quantization standard for gray-scale fingerprint image compression

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

Bradley, J.N.; Brislawn, C.M.; Hopper, T.

1993-01-01

The FBI has recently adopted a standard for the compression of digitized 8-bit gray-scale fingerprint images. The standard is based on scalar quantization of a 64-subband discrete wavelet transform decomposition of the images, followed by Huffman coding. Novel features of the algorithm include the use of symmetric boundary conditions for transforming finite-length signals and a subband decomposition tailored for fingerprint images scanned at 500 dpi. The standard is intended for use in conjunction with ANSI/NBS-CLS 1-1993, American National Standard Data Format for the Interchange of Fingerprint Information, and the FBI's Integrated Automated Fingerprint Identification System.

Finite Difference Schemes as Algebraic Correspondences between Layers

NASA Astrophysics Data System (ADS)

Malykh, Mikhail; Sevastianov, Leonid

2018-02-01

For some differential equations, especially for Riccati equation, new finite difference schemes are suggested. These schemes define protective correspondences between the layers. Calculation using these schemes can be extended to the area beyond movable singularities of exact solution without any error accumulation.

Construction of stable explicit finite-difference schemes for Schroedinger type differential equations

NASA Technical Reports Server (NTRS)

Mickens, Ronald E.

1989-01-01

A family of conditionally stable, forward Euler finite difference equations can be constructed for the simplest equation of Schroedinger type, namely u sub t - iu sub xx. Generalization of this result to physically realistic Schroedinger type equations is presented.

Development of Finite Elements for Two-Dimensional Structural Analysis Using the Integrated Force Method

NASA Technical Reports Server (NTRS)

Kaljevic, Igor; Patnaik, Surya N.; Hopkins, Dale A.

1996-01-01

The Integrated Force Method has been developed in recent years for the analysis of structural mechanics problems. This method treats all independent internal forces as unknown variables that can be calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper a finite element library for analyzing two-dimensional problems by the Integrated Force Method is presented. Triangular- and quadrilateral-shaped elements capable of modeling arbitrary domain configurations are presented. The element equilibrium and flexibility matrices are derived by discretizing the expressions for potential and complementary energies, respectively. The displacement and stress fields within the finite elements are independently approximated. The displacement field is interpolated as it is in the standard displacement method, and the stress field is approximated by using complete polynomials of the correct order. A procedure that uses the definitions of stress components in terms of an Airy stress function is developed to derive the stress interpolation polynomials. Such derived stress fields identically satisfy the equations of equilibrium. Moreover, the resulting element matrices are insensitive to the orientation of local coordinate systems. A method is devised to calculate the number of rigid body modes, and the present elements are shown to be free of spurious zero-energy modes. A number of example problems are solved by using the present library, and the results are compared with corresponding analytical solutions and with results from the standard displacement finite element method. The Integrated Force Method not only gives results that agree well with analytical and displacement method results but also outperforms the displacement method in stress calculations.

Calculation of compressible boundary layer flow about airfoils by a finite element/finite difference method

NASA Technical Reports Server (NTRS)

Strong, Stuart L.; Meade, Andrew J., Jr.

1992-01-01

Preliminary results are presented of a finite element/finite difference method (semidiscrete Galerkin method) used to calculate compressible boundary layer flow about airfoils, in which the group finite element scheme is applied to the Dorodnitsyn formulation of the boundary layer equations. The semidiscrete Galerkin (SDG) method promises to be fast, accurate and computationally efficient. The SDG method can also be applied to any smoothly connected airfoil shape without modification and possesses the potential capability of calculating boundary layer solutions beyond flow separation. Results are presented for low speed laminar flow past a circular cylinder and past a NACA 0012 airfoil at zero angle of attack at a Mach number of 0.5. Also shown are results for compressible flow past a flat plate for a Mach number range of 0 to 10 and results for incompressible turbulent flow past a flat plate. All numerical solutions assume an attached boundary layer.

Dynamical phase transitions at finite temperature from fidelity and interferometric Loschmidt echo induced metrics

NASA Astrophysics Data System (ADS)

Mera, Bruno; Vlachou, Chrysoula; Paunković, Nikola; Vieira, Vítor R.; Viyuela, Oscar

2018-03-01

We study finite-temperature dynamical quantum phase transitions (DQPTs) by means of the fidelity and the interferometric Loschmidt echo (LE) induced metrics. We analyze the associated dynamical susceptibilities (Riemannian metrics), and derive analytic expressions for the case of two-band Hamiltonians. At zero temperature, the two quantities are identical, nevertheless, at finite temperatures they behave very differently. Using the fidelity LE, the zero-temperature DQPTs are gradually washed away with temperature, while the interferometric counterpart exhibits finite-temperature phase transitions. We analyze the physical differences between the two finite-temperature LE generalizations, and argue that, while the interferometric one is more sensitive and can therefore provide more information when applied to genuine quantum (microscopic) systems, when analyzing many-body macroscopic systems, the fidelity-based counterpart is a more suitable quantity to study. Finally, we apply the previous results to two representative models of topological insulators in one and two dimensions.

The finite element method for micro-scale modeling of ultrasound propagation in cancellous bone.

PubMed

Vafaeian, B; El-Rich, M; El-Bialy, T; Adeeb, S

2014-08-01

Quantitative ultrasound for bone assessment is based on the correlations between ultrasonic parameters and the properties (mechanical and physical) of cancellous bone. To elucidate the correlations, understanding the physics of ultrasound in cancellous bone is demanded. Micro-scale modeling of ultrasound propagation in cancellous bone using the finite-difference time-domain (FDTD) method has been so far utilized as one of the approaches in this regard. However, the FDTD method accompanies two disadvantages: staircase sampling of cancellous bone by finite difference grids leads to generation of wave artifacts at the solid-fluid interface inside the bone; additionally, this method cannot explicitly satisfy the needed perfect-slip conditions at the interface. To overcome these disadvantages, the finite element method (FEM) is proposed in this study. Three-dimensional finite element models of six water-saturated cancellous bone samples with different bone volume were created. The values of speed of sound (SOS) and broadband ultrasound attenuation (BUA) were calculated through the finite element simulations of ultrasound propagation in each sample. Comparing the results with other experimental and simulation studies demonstrated the capabilities of the FEM for micro-scale modeling of ultrasound in water-saturated cancellous bone. Copyright © 2014 Elsevier B.V. All rights reserved.

The State-of-the-Art Parabolic Equation Approximation as Applied to Underwater Acoustic Propagation with Discussions on Intensive Computations: An Invited Paper Presented at the Meeting of the Acoustical Society of America (108th) Held in Minneapolis, Minnesota on 8-12 October 1984

DTIC Science & Technology

1984-10-12

MCYwWWm M& de4 l 8.id iW d by N1wk "wt Finite Difference Reference Wavenumber Interface Split-Step Ordinary Difference Equation Wide Angle Parabolic...Problems D. Lee and S. Praiser J. Comp. & Math. with Appls., 7(2), pp. 195-202 (1981) Finite - Difference Solution to the Parabolic Wave Equation D. Lee, G...was incorporated into the ODE and finite difference models. At that time, we did not have a better implementation of the ODE solution, but we

Numerical stability of an explicit finite difference scheme for the solution of transient conduction in composite media

NASA Technical Reports Server (NTRS)

Campbell, W.

1981-01-01

A theoretical evaluation of the stability of an explicit finite difference solution of the transient temperature field in a composite medium is presented. The grid points of the field are assumed uniformly spaced, and media interfaces are either vertical or horizontal and pass through grid points. In addition, perfect contact between different media (infinite interfacial conductance) is assumed. A finite difference form of the conduction equation is not valid at media interfaces; therefore, heat balance forms are derived. These equations were subjected to stability analysis, and a computer graphics code was developed that permitted determination of a maximum time step for a given grid spacing.

Chiral anomaly and anomalous finite-size conductivity in graphene

NASA Astrophysics Data System (ADS)

Shen, Shun-Qing; Li, Chang-An; Niu, Qian

2017-09-01

Graphene is a monolayer of carbon atoms packed into a hexagon lattice to host two spin degenerate pairs of massless two-dimensional Dirac fermions with different chirality. It is known that the existence of non-zero electric polarization in reduced momentum space which is associated with a hidden chiral symmetry will lead to the zero-energy flat band of a zigzag nanoribbon and some anomalous transport properties. Here it is proposed that the Adler-Bell-Jackiw chiral anomaly or non-conservation of chiral charges of Dirac fermions at different valleys can be realized in a confined ribbon of finite width, even in the absence of a magnetic field. In the laterally diffusive regime, the finite-size correction to conductivity is always positive and is inversely proportional to the square of the lateral dimension W, which is different from the finite-size correction inversely proportional to W from the boundary modes. This anomalous finite-size conductivity reveals the signature of the chiral anomaly in graphene, and it is measurable experimentally. This finding provides an alternative platform to explore the purely quantum mechanical effect in graphene.

Transoesophageal detection of heart graft rejection by electrical impedance: Using finite element method simulations

NASA Astrophysics Data System (ADS)

Giovinazzo, G.; Ribas, N.; Cinca, J.; Rosell-Ferrer, J.

2010-04-01

Previous studies have shown that it is possible to evaluate heart graft rejection level using a bioimpedance technique by means of an intracavitary catheter. However, this technique does not present relevant advantages compared to the gold standard for the detection of a heart rejection, which is the biopsy of the endomyocardial tissue. We propose to use a less invasive technique that consists in the use of a transoesophageal catheter and two standard ECG electrodes on the thorax. The aim of this work is to evaluate different parameters affecting the impedance measurement, including: sensitivity to electrical conductivity and permittivity of different organs in the thorax, lung edema and pleural water. From these results, we deduce the best estimator for cardiac rejection detection, and we obtain the tools to identify possible cases of false positive of heart rejection due to other factors. To achieve these objectives we have created a thoracic model and we have simulated, with a FEM program, different situations at the frequencies of 13, 30, 100, 300 and 1000 kHz. Our simulation demonstrates that the phase, at 100 and 300 kHz, has the higher sensitivity to changes in the electrical parameters of the heart muscle.

Graphics processing unit (GPU)-based computation of heat conduction in thermally anisotropic solids

NASA Astrophysics Data System (ADS)

Nahas, C. A.; Balasubramaniam, Krishnan; Rajagopal, Prabhu

2013-01-01

Numerical modeling of anisotropic media is a computationally intensive task since it brings additional complexity to the field problem in such a way that the physical properties are different in different directions. Largely used in the aerospace industry because of their lightweight nature, composite materials are a very good example of thermally anisotropic media. With advancements in video gaming technology, parallel processors are much cheaper today and accessibility to higher-end graphical processing devices has increased dramatically over the past couple of years. Since these massively parallel GPUs are very good in handling floating point arithmetic, they provide a new platform for engineers and scientists to accelerate their numerical models using commodity hardware. In this paper we implement a parallel finite difference model of thermal diffusion through anisotropic media using the NVIDIA CUDA (Compute Unified device Architecture). We use the NVIDIA GeForce GTX 560 Ti as our primary computing device which consists of 384 CUDA cores clocked at 1645 MHz with a standard desktop pc as the host platform. We compare the results from standard CPU implementation for its accuracy and speed and draw implications for simulation using the GPU paradigm.

Calculation of skin-stiffener interface stresses in stiffened composite panels

NASA Technical Reports Server (NTRS)

Cohen, David; Hyer, Michael W.

1987-01-01

A method for computing the skin-stiffener interface stresses in stiffened composite panels is developed. Both geometrically linear and nonlinear analyses are considered. Particular attention is given to the flange termination region where stresses are expected to exhibit unbounded characteristics. The method is based on a finite-element analysis and an elasticity solution. The finite-element analysis is standard, while the elasticity solution is based on an eigenvalue expansion of the stress functions. The eigenvalue expansion is assumed to be valid in the local flange termination region and is coupled with the finite-element analysis using collocation of stresses on the local region boundaries. Accuracy and convergence of the local elasticity solution are assessed using a geometrically linear analysis. Using this analysis procedure, the influence of geometric nonlinearities and stiffener parameters on the skin-stiffener interface stresses is evaluated.

Numerical evaluation of discontinuous and nonconforming finite element methods in nonlinear solid mechanics

NASA Astrophysics Data System (ADS)

Bayat, Hamid Reza; Krämer, Julian; Wunderlich, Linus; Wulfinghoff, Stephan; Reese, Stefanie; Wohlmuth, Barbara; Wieners, Christian

2018-03-01

This work presents a systematic study of discontinuous and nonconforming finite element methods for linear elasticity, finite elasticity, and small strain plasticity. In particular, we consider new hybrid methods with additional degrees of freedom on the skeleton of the mesh and allowing for a local elimination of the element-wise degrees of freedom. We show that this process leads to a well-posed approximation scheme. The quality of the new methods with respect to locking and anisotropy is compared with standard and in addition locking-free conforming methods as well as established (non-) symmetric discontinuous Galerkin methods with interior penalty. For several benchmark configurations, we show that all methods converge asymptotically for fine meshes and that in many cases the hybrid methods are more accurate for a fixed size of the discrete system.

The unstaggered extension to GFDL's FV3 dynamical core on the cubed-sphere

NASA Astrophysics Data System (ADS)

Chen, X.; Lin, S. J.; Harris, L.

2017-12-01

Finite-volume schemes have become popular for atmospheric transport since they provide intrinsic mass conservation to constituent species. Many CFD codes use unstaggered discretizations for finite volume methods with an approximate Riemann solver. However, this approach is inefficient for geophysical flows due to the complexity of the Riemann solver. We introduce a Low Mach number Approximate Riemann Solver (LMARS) simplified using assumptions appropriate for atmospheric flows: the wind speed is much slower than the sound speed, weak discontinuities, and locally uniform sound wave velocity. LMARS makes possible a Riemann-solver-based dynamical core comparable in computational efficiency to many current dynamical cores. We will present a 3D finite-volume dynamical core using LMARS in a cubed-sphere geometry with a vertically Lagrangian discretization. Results from standard idealized test cases will be discussed.

Light scattering microscopy measurements of single nuclei compared with GPU-accelerated FDTD simulations

NASA Astrophysics Data System (ADS)

Stark, Julian; Rothe, Thomas; Kieß, Steffen; Simon, Sven; Kienle, Alwin

2016-04-01

Single cell nuclei were investigated using two-dimensional angularly and spectrally resolved scattering microscopy. We show that even for a qualitative comparison of experimental and theoretical data, the standard Mie model of a homogeneous sphere proves to be insufficient. Hence, an accelerated finite-difference time-domain method using a graphics processor unit and domain decomposition was implemented to analyze the experimental scattering patterns. The measured cell nuclei were modeled as single spheres with randomly distributed spherical inclusions of different size and refractive index representing the nucleoli and clumps of chromatin. Taking into account the nuclear heterogeneity of a large number of inclusions yields a qualitative agreement between experimental and theoretical spectra and illustrates the impact of the nuclear micro- and nanostructure on the scattering patterns.

An easily implemented static condensation method for structural sensitivity analysis

NASA Technical Reports Server (NTRS)

Gangadharan, S. N.; Haftka, R. T.; Nikolaidis, E.

1990-01-01

A black-box approach to static condensation for sensitivity analysis is presented with illustrative examples of a cube and a car structure. The sensitivity of the structural response with respect to joint stiffness parameter is calculated using the direct method, forward-difference, and central-difference schemes. The efficiency of the various methods for identifying joint stiffness parameters from measured static deflections of these structures is compared. The results indicate that the use of static condensation can reduce computation times significantly and the black-box approach is only slightly less efficient than the standard implementation of static condensation. The ease of implementation of the black-box approach recommends it for use with general-purpose finite element codes that do not have a built-in facility for static condensation.

Light scattering microscopy measurements of single nuclei compared with GPU-accelerated FDTD simulations.

PubMed

Stark, Julian; Rothe, Thomas; Kieß, Steffen; Simon, Sven; Kienle, Alwin

2016-04-07

Single cell nuclei were investigated using two-dimensional angularly and spectrally resolved scattering microscopy. We show that even for a qualitative comparison of experimental and theoretical data, the standard Mie model of a homogeneous sphere proves to be insufficient. Hence, an accelerated finite-difference time-domain method using a graphics processor unit and domain decomposition was implemented to analyze the experimental scattering patterns. The measured cell nuclei were modeled as single spheres with randomly distributed spherical inclusions of different size and refractive index representing the nucleoli and clumps of chromatin. Taking into account the nuclear heterogeneity of a large number of inclusions yields a qualitative agreement between experimental and theoretical spectra and illustrates the impact of the nuclear micro- and nanostructure on the scattering patterns.

The role of continuity in residual-based variational multiscale modeling of turbulence

NASA Astrophysics Data System (ADS)

Akkerman, I.; Bazilevs, Y.; Calo, V. M.; Hughes, T. J. R.; Hulshoff, S.

2008-02-01

This paper examines the role of continuity of the basis in the computation of turbulent flows. We compare standard finite elements and non-uniform rational B-splines (NURBS) discretizations that are employed in Isogeometric Analysis (Hughes et al. in Comput Methods Appl Mech Eng, 194:4135 4195, 2005). We make use of quadratic discretizations that are C 0-continuous across element boundaries in standard finite elements, and C 1-continuous in the case of NURBS. The variational multiscale residual-based method (Bazilevs in Isogeometric analysis of turbulence and fluid-structure interaction, PhD thesis, ICES, UT Austin, 2006; Bazilevs et al. in Comput Methods Appl Mech Eng, submitted, 2007; Calo in Residual-based multiscale turbulence modeling: finite volume simulation of bypass transition. PhD thesis, Department of Civil and Environmental Engineering, Stanford University, 2004; Hughes et al. in proceedings of the XXI international congress of theoretical and applied mechanics (IUTAM), Kluwer, 2004; Scovazzi in Multiscale methods in science and engineering, PhD thesis, Department of Mechanical Engineering, Stanford Universty, 2004) is employed as a turbulence modeling technique. We find that C 1-continuous discretizations outperform their C 0-continuous counterparts on a per-degree-of-freedom basis. We also find that the effect of continuity is greater for higher Reynolds number flows.

Application of the finite-field coupled-cluster method to calculate molecular properties relevant to electron electric-dipole-moment searches

NASA Astrophysics Data System (ADS)

Abe, M.; Prasannaa, V. S.; Das, B. P.

2018-03-01

Heavy polar diatomic molecules are currently among the most promising probes of fundamental physics. Constraining the electric dipole moment of the electron (e EDM ), in order to explore physics beyond the standard model, requires a synergy of molecular experiment and theory. Recent advances in experiment in this field have motivated us to implement a finite-field coupled-cluster (FFCC) approach. This work has distinct advantages over the theoretical methods that we had used earlier in the analysis of e EDM searches. We used relativistic FFCC to calculate molecular properties of interest to e EDM experiments, that is, the effective electric field (Eeff) and the permanent electric dipole moment (PDM). We theoretically determine these quantities for the alkaline-earth monofluorides (AEMs), the mercury monohalides (Hg X ), and PbF. The latter two systems, as well as BaF from the AEMs, are of interest to e EDM searches. We also report the calculation of the properties using a relativistic finite-field coupled-cluster approach with single, double, and partial triples' excitations, which is considered to be the gold standard of electronic structure calculations. We also present a detailed error estimate, including errors that stem from our choice of basis sets, and higher-order correlation effects.

APPLICATION OF A FINITE-DIFFERENCE TECHNIQUE TO THE HUMAN RADIOFREQUENCY DOSIMETRY PROBLEM

EPA Science Inventory

A powerful finite difference numerical technique has been applied to the human radiofrequency dosimetry problem. The method possesses inherent advantages over the method of moments approach in that its implementation requires much less computer memory. Consequently, it has the ca...

A FINITE-DIFFERENCE, DISCRETE-WAVENUMBER METHOD FOR CALCULATING RADAR TRACES

EPA Science Inventory

A hybrid of the finite-difference method and the discrete-wavenumber method is developed to calculate radar traces. The method is based on a three-dimensional model defined in the Cartesian coordinate system; the electromagnetic properties of the model are symmetric with respect ...

High Order Finite Difference Methods, Multidimensional Linear Problems and Curvilinear Coordinates

NASA Technical Reports Server (NTRS)

Nordstrom, Jan; Carpenter, Mark H.

1999-01-01

Boundary and interface conditions are derived for high order finite difference methods applied to multidimensional linear problems in curvilinear coordinates. The boundary and interface conditions lead to conservative schemes and strict and strong stability provided that certain metric conditions are met.

A mixed pseudospectral/finite difference method for the axisymmetric flow in a heated, rotating spherical shell. [for experimental atmospheric simulation

NASA Technical Reports Server (NTRS)

Macaraeg, M. G.

1986-01-01

For a Spacelab flight, a model experiment of the earth's atmospheric circulation has been proposed. This experiment is known as the Atmospheric General Circulation Experiment (AGCE). In the experiment concentric spheres will rotate as a solid body, while a dielectric fluid is confined in a portion of the gap between the spheres. A zero gravity environment will be required in the context of the simulation of the gravitational body force on the atmosphere. The present study is concerned with the development of pseudospectral/finite difference (PS/FD) model and its subsequent application to physical cases relevant to the AGCE. The model is based on a hybrid scheme involving a pseudospectral latitudinal formulation, and finite difference radial and time discretization. The advantages of the use of the hybrid PS/FD method compared to a pure second-order accurate finite difference (FD) method are discussed, taking into account the higher accuracy and efficiency of the PS/FD method.

Finite-Difference Lattice Boltzmann Scheme for High-Speed Compressible Flow: Two-Dimensional Case

NASA Astrophysics Data System (ADS)

Gan, Yan-Biao; Xu, Ai-Guo; Zhang, Guang-Cai; Zhang, Ping; Zhang, Lei; Li, Ying-Jun

2008-07-01

Lattice Boltzmann (LB) modeling of high-speed compressible flows has long been attempted by various authors. One common weakness of most of previous models is the instability problem when the Mach number of the flow is large. In this paper we present a finite-difference LB model, which works for flows with flexible ratios of specific heats and a wide range of Mach number, from 0 to 30 or higher. Besides the discrete-velocity-model by Watari [Physica A 382 (2007) 502], a modified Lax Wendroff finite difference scheme and an artificial viscosity are introduced. The combination of the finite-difference scheme and the adding of artificial viscosity must find a balance of numerical stability versus accuracy. The proposed model is validated by recovering results of some well-known benchmark tests: shock tubes and shock reflections. The new model may be used to track shock waves and/or to study the non-equilibrium procedure in the transition between the regular and Mach reflections of shock waves, etc.

The use of spectral methods in bidomain studies.

PubMed

Trayanova, N; Pilkington, T

1992-01-01

A Fourier transform method is developed for solving the bidomain coupled differential equations governing the intracellular and extracellular potentials on a finite sheet of cardiac cells undergoing stimulation. The spectral formulation converts the system of differential equations into a "diagonal" system of algebraic equations. Solving the algebraic equations directly and taking the inverse transform of the potentials proved numerically less expensive than solving the coupled differential equations by means of traditional numerical techniques, such as finite differences; the comparison between the computer execution times showed that the Fourier transform method was about 40 times faster than the finite difference method. By application of the Fourier transform method, transmembrane potential distributions in the two-dimensional myocardial slice were calculated. For a tissue characterized by a ratio of the intra- to extracellular conductivities that is different in all principal directions, the transmembrane potential distribution exhibits a rather complicated geometrical pattern. The influence of the different anisotropy ratios, the finite tissue size, and the stimuli configuration on the pattern of membrane polarization is investigated.

Experimental validation of finite element modelling of a modular metal-on-polyethylene total hip replacement.

PubMed

Hua, Xijin; Wang, Ling; Al-Hajjar, Mazen; Jin, Zhongmin; Wilcox, Ruth K; Fisher, John

2014-07-01

Finite element models are becoming increasingly useful tools to conduct parametric analysis, design optimisation and pre-clinical testing for hip joint replacements. However, the verification of the finite element model is critically important. The purposes of this study were to develop a three-dimensional anatomic finite element model for a modular metal-on-polyethylene total hip replacement for predicting its contact mechanics and to conduct experimental validation for a simple finite element model which was simplified from the anatomic finite element model. An anatomic modular metal-on-polyethylene total hip replacement model (anatomic model) was first developed and then simplified with reasonable accuracy to a simple modular total hip replacement model (simplified model) for validation. The contact areas on the articulating surface of three polyethylene liners of modular metal-on-polyethylene total hip replacement bearings with different clearances were measured experimentally in the Leeds ProSim hip joint simulator under a series of loading conditions and different cup inclination angles. The contact areas predicted from the simplified model were then compared with that measured experimentally under the same conditions. The results showed that the simplification made for the anatomic model did not change the predictions of contact mechanics of the modular metal-on-polyethylene total hip replacement substantially (less than 12% for contact stresses and contact areas). Good agreements of contact areas between the finite element predictions from the simplified model and experimental measurements were obtained, with maximum difference of 14% across all conditions considered. This indicated that the simplification and assumptions made in the anatomic model were reasonable and the finite element predictions from the simplified model were valid. © IMechE 2014.

Computation of confined coflow jets with three turbulence models

NASA Technical Reports Server (NTRS)

Zhu, J.; Shih, T. H.

1993-01-01

A numerical study of confined jets in a cylindrical duct is carried out to examine the performance of two recently proposed turbulence models: an RNG-based K-epsilon model and a realizable Reynolds stress algebraic equation model. The former is of the same form as the standard K-epsilon model but has different model coefficients. The latter uses an explicit quadratic stress-strain relationship to model the turbulent stresses and is capable of ensuring the positivity of each turbulent normal stress. The flow considered involves recirculation with unfixed separation and reattachment points and severe adverse pressure gradients, thereby providing a valuable test of the predictive capability of the models for complex flows. Calculations are performed with a finite-volume procedure. Numerical credibility of the solutions is ensured by using second-order accurate differencing schemes and sufficiently fine grids. Calculations with the standard K-epsilon model are also made for comparison. Detailed comparisons with experiments show that the realizable Reynolds stress algebraic equation model consistently works better than does the standard K-epsilon model in capturing the essential flow features, while the RNG-based K-epsilon model does not seem to give improvements over the standard K-epsilon model under the flow conditions considered.

Relative and Absolute Error Control in a Finite-Difference Method Solution of Poisson's Equation

ERIC Educational Resources Information Center

Prentice, J. S. C.

2012-01-01

An algorithm for error control (absolute and relative) in the five-point finite-difference method applied to Poisson's equation is described. The algorithm is based on discretization of the domain of the problem by means of three rectilinear grids, each of different resolution. We discuss some hardware limitations associated with the algorithm,…

Finite micro-tab system for load control on a wind turbine

NASA Astrophysics Data System (ADS)

Bach, A. B.; Lennie, M.; Pechlivanoglou, G.; Nayeri, C. N.; Paschereit, C. O.

2014-06-01

Finite micro-tabs have been investigated experimentally to evaluate the potential for load control on wind turbines. Two dimensional full span, as well as multiple finite tabs of various aspect ratios have been studied on an AH93W174 airfoil at different chord wise positions. A force balance was used to measure the aerodynamic loads. Furthermore, the wake vortex system consisting of the Karman vortex street as well as the tab tip vortices was analyzed with a 12-hole probe and hot wire anemometry. Finally, conventional oil paint as well as a quantitative digital flow analysis technique called SMARTviz were used to visualize the flow around the finite tab configurations. Results have shown that the devices are an effective solution to alleviate the airfoils overall load. The influence of the tab height, tab position as well as the finite tab aspect ratio on the lift and lift to drag ratio have been evaluated. It could be shown, that the lift difference can either be varied by changing the tab height as well as by altering the aspect ratio of the finite tabs. The drag of a two-dimensional flap is directly associated with the vortex street, while in the case of the finite tab, the solidity ratio of the tabs has the strongest effect on the drag. Therefore, the application of a finite tab system showed to improve the lift to drag ratio.

The effectiveness of element downsizing on a three-dimensional finite element model of bone trabeculae in implant biomechanics.

PubMed

Sato, Y; Wadamoto, M; Tsuga, K; Teixeira, E R

1999-04-01

More validity of finite element analysis in implant biomechanics requires element downsizing. However, excess downsizing needs computer memory and calculation time. To investigate the effectiveness of element downsizing on the construction of a three-dimensional finite element bone trabeculae model, with different element sizes (600, 300, 150 and 75 microm) models were constructed and stress induced by vertical 10 N loading was analysed. The difference in von Mises stress values between the models with 600 and 300 microm element sizes was larger than that between 300 and 150 microm. On the other hand, no clear difference of stress values was detected among the models with 300, 150 and 75 microm element sizes. Downsizing of elements from 600 to 300 microm is suggested to be effective in the construction of a three-dimensional finite element bone trabeculae model for possible saving of computer memory and calculation time in the laboratory.

Comparing the influence of crestal cortical bone and sinus floor cortical bone in posterior maxilla bi-cortical dental implantation: a three-dimensional finite element analysis.

PubMed

Yan, Xu; Zhang, Xinwen; Chi, Weichao; Ai, Hongjun; Wu, Lin

2015-05-01

This study aimed to compare the influence of alveolar ridge cortical bone and sinus floor cortical bone in sinus areabi-cortical dental implantation by means of 3D finite element analysis. Three-dimensional finite element (FE) models in a posterior maxillary region with sinus membrane and the same height of alveolar ridge of 10 mm were generated according to the anatomical data of the sinus area. They were either with fixed thickness of crestal cortical bone and variable thickness of sinus floor cortical bone or vice versa. Ten models were assumed to be under immediate loading or conventional loading. The standard implant model based on the Nobel Biocare implant system was created via computer-aided design software. All materials were assumed to be isotropic and linearly elastic. An inclined force of 129 N was applied. Von Mises stress mainly concentrated on the surface of crestal cortical bone around the implant neck. For all the models, both the axial and buccolingual resonance frequencies of conventional loading were higher than those of immediate loading; however, the difference is less than 5%. The results showed that bi-cortical implant in sinus area increased the stability of the implant, especially for immediately loading implantation. The thickness of both crestal cortical bone and sinus floor cortical bone influenced implant micromotion and stress distribution; however, crestal cortical bone may be more important than sinus floor cortical bone.

Finite element modelling of AA6063T52 thin-walled tubes under quasi-static axial loading

NASA Astrophysics Data System (ADS)

Othman, A.; Ismail, AE

2018-04-01

The behavior of aluminum alloy 6063T52 thin walled tubes have been present in this paper to determine absorbed energy under quasi-static axial loading. The correlation and comparison have been implemented for each experimental and finite element analysis results, respectively. Wall-thickness of 1.6 and 1.9 mm were selected and all specimen tested under room temperature standard. The length of each specimen were fixed at 125 mm as well as diameter as well as a width and diameter of the tube at 50.8 mm. The two types of tubular cross-section were examined whereas a round and square thin-walled profiles. The specific absorbed energy (SEA) and crush force efficiency (CFE) were analyzed for each specimen and model to see the behavior induced to failure under progressive collapse. Result showed that a correlation less than 5% different between both of comparison experimental and finite element model. It has been found that the thin walled round tube absorbed more energy rather than square profile in term of specific energy with both of either 1.6 or 1.9 of 23.93% and 35.36%, respectively. Overall for crush force efficiency (CFE) of each tube profile around 0.42 to 0.58 value. Indicated that the all specimen profile fail under progressive damage. The calibration between deformed model and experimental specimen were examined and discussed. It was found that the similarity failure mechanism observed for each thin walled profiles.

Assessing behind armor blunt trauma in accordance with the National Institute of Justice Standard for Personal Body Armor Protection using finite element modeling.

PubMed

Roberts, Jack C; Ward, Emily E; Merkle, Andrew C; O'Connor, James V

2007-05-01

To assess the possibility of injury as a result of behind armor blunt trauma (BABT), a study was undertaken to determine the conditions necessary to produce the 44-mm clay deformation as set forth in the National Institute of Justice (NIJ) Standard 0101.04. These energy levels were then applied to a three-dimensional Human Torso Finite Element Model (HTFEM) with soft armor vest. An examination will be made of tissue stresses to determine the effects of the increased kinetic energy levels on the probability of injury. A clay finite element model (CFEM) was created with a material model that required nonlinear properties for clay. To determine these properties empirically, the results from the CFEM were matched with experimental drop tests. A soft armor vest was modeled over the clay to create a vest over clay block finite element model (VCFEM) and empirical methods were again used to obtain material properties for the vest from experimental ballistic testing. Once the properties for the vest and clay had been obtained, the kinetic energy required to produce a 44-mm deformation in the VCFEM was determined through ballistic testing. The resulting kinetic energy was then used in the HTFEM to evaluate the probability of BABT. The VCFEM, with determined clay and vest material properties, was exercised with the equivalent of a 9-mm (8-gm) projectile at various impact velocities. The 44-mm clay deformation was produced with a velocity of 785 m/s. This impact condition (9-mm projectile at 785 m/s) was used in ballistic exercises of the HTFEM, which was modeled with high-strain rate human tissue properties for the organs. The impact zones were over the sternum anterior to T6 and over the liver. The principal stresses in both soft and hard tissue at both locations exceeded the tissue tensile strength. This study indicates that although NIJ standard 0101.04 may be a good guide to soft armor failure, it may not be as good a guide in BABT, especially at large projectile kinetic energies. Further studies, both numerical and experimental, are needed to assist in predicting injury using the NIJ standard.

The method of space-time and conservation element and solution element: A new approach for solving the Navier-Stokes and Euler equations

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1995-01-01

A new numerical framework for solving conservation laws is being developed. This new framework differs substantially in both concept and methodology from the well-established methods, i.e., finite difference, finite volume, finite element, and spectral methods. It is conceptually simple and designed to overcome several key limitations of the above traditional methods. A two-level scheme for solving the convection-diffusion equation is constructed and used to illuminate the major differences between the present method and those previously mentioned. This explicit scheme, referred to as the a-mu scheme, has two independent marching variables.

A finite difference solution for the propagation of sound in near sonic flows

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Lester, H. C.

1983-01-01

An explicit time/space finite difference procedure is used to model the propagation of sound in a quasi one-dimensional duct containing high Mach number subsonic flow. Nonlinear acoustic equations are derived by perturbing the time-dependent Euler equations about a steady, compressible mean flow. The governing difference relations are based on a fourth-order, two-step (predictor-corrector) MacCormack scheme. The solution algorithm functions by switching on a time harmonic source and allowing the difference equations to iterate to a steady state. The principal effect of the non-linearities was to shift acoustical energy to higher harmonics. With increased source strengths, wave steepening was observed. This phenomenon suggests that the acoustical response may approach a shock behavior at at higher sound pressure level as the throat Mach number aproaches unity. On a peak level basis, good agreement between the nonlinear finite difference and linear finite element solutions was observed, even through a peak sound pressure level of about 150 dB occurred in the throat region. Nonlinear steady state waveform solutions are shown to be in excellent agreement with a nonlinear asymptotic theory.

A guide to differences between stochastic point-source and stochastic finite-fault simulations

USGS Publications Warehouse

Atkinson, G.M.; Assatourians, K.; Boore, D.M.; Campbell, K.; Motazedian, D.

2009-01-01

Why do stochastic point-source and finite-fault simulation models not agree on the predicted ground motions for moderate earthquakes at large distances? This question was posed by Ken Campbell, who attempted to reproduce the Atkinson and Boore (2006) ground-motion prediction equations for eastern North America using the stochastic point-source program SMSIM (Boore, 2005) in place of the finite-source stochastic program EXSIM (Motazedian and Atkinson, 2005) that was used by Atkinson and Boore (2006) in their model. His comparisons suggested that a higher stress drop is needed in the context of SMSIM to produce an average match, at larger distances, with the model predictions of Atkinson and Boore (2006) based on EXSIM; this is so even for moderate magnitudes, which should be well-represented by a point-source model. Why? The answer to this question is rooted in significant differences between point-source and finite-source stochastic simulation methodologies, specifically as implemented in SMSIM (Boore, 2005) and EXSIM (Motazedian and Atkinson, 2005) to date. Point-source and finite-fault methodologies differ in general in several important ways: (1) the geometry of the source; (2) the definition and application of duration; and (3) the normalization of finite-source subsource summations. Furthermore, the specific implementation of the methods may differ in their details. The purpose of this article is to provide a brief overview of these differences, their origins, and implications. This sets the stage for a more detailed companion article, "Comparing Stochastic Point-Source and Finite-Source Ground-Motion Simulations: SMSIM and EXSIM," in which Boore (2009) provides modifications and improvements in the implementations of both programs that narrow the gap and result in closer agreement. These issues are important because both SMSIM and EXSIM have been widely used in the development of ground-motion prediction equations and in modeling the parameters that control observed ground motions.

THE PSTD ALGORITHM: A TIME-DOMAIN METHOD REQUIRING ONLY TWO CELLS PER WAVELENGTH. (R825225)

EPA Science Inventory

A pseudospectral time-domain (PSTD) method is developed for solutions of Maxwell's equations. It uses the fast Fourier transform (FFT), instead of finite differences on conventional finite-difference-time-domain (FDTD) methods, to represent spatial derivatives. Because the Fourie...

FINITE-DIFFERENCE ELECTROMAGNETIC DEPOSITION/THERMOREGULATORY MODEL: COMPARISON BETWEEN THEORY AND MEASUREMENTS (JOURNAL VERSION)

EPA Science Inventory

The rate of the electromagnetic energy deposition and the resultant thermoregulatory response of a block model of a squirrel monkey exposed to plane-wave fields at 350 MHz were calculated using a finite-difference procedure. Noninvasive temperature measurements in live squirrel m...

A FINITE-DIFFERENCE, DISCRETE-WAVENUMBER METHOD FOR CALCULATING RADAR TRACES

EPA Science Inventory

A hybrid of the finite-difference method and the discrete-wavenumber method is developed to calculate radar traces. The method is based on a three-dimensional model defined in the Cartesian coordinate system; the electromag-netic properties of the model are symmetric with respect...

Finite difference methods for transient signal propagation in stratified dispersive media

NASA Technical Reports Server (NTRS)

Lam, D. H.

1975-01-01

Explicit difference equations are presented for the solution of a signal of arbitrary waveform propagating in an ohmic dielectric, a cold plasma, a Debye model dielectric, and a Lorentz model dielectric. These difference equations are derived from the governing time-dependent integro-differential equations for the electric fields by a finite difference method. A special difference equation is derived for the grid point at the boundary of two different media. Employing this difference equation, transient signal propagation in an inhomogeneous media can be solved provided that the medium is approximated in a step-wise fashion. The solutions are generated simply by marching on in time. It is concluded that while the classical transform methods will remain useful in certain cases, with the development of the finite difference methods described, an extensive class of problems of transient signal propagating in stratified dispersive media can be effectively solved by numerical methods.

Runtime Analysis of Linear Temporal Logic Specifications

NASA Technical Reports Server (NTRS)

Giannakopoulou, Dimitra; Havelund, Klaus

2001-01-01

This report presents an approach to checking a running program against its Linear Temporal Logic (LTL) specifications. LTL is a widely used logic for expressing properties of programs viewed as sets of executions. Our approach consists of translating LTL formulae to finite-state automata, which are used as observers of the program behavior. The translation algorithm we propose modifies standard LTL to B chi automata conversion techniques to generate automata that check finite program traces. The algorithm has been implemented in a tool, which has been integrated with the generic JPaX framework for runtime analysis of Java programs.

Finite elements for the calculation of turbulent flows in three-dimensional complex geometries

NASA Astrophysics Data System (ADS)

Ruprecht, A.

A finite element program for the calculation of incompressible turbulent flows is presented. In order to reduce the required storage an iterative algorithm is used which solves the necessary equations sequentially. The state of turbulence is defined by the k-epsilon model. In addition to the standard k-epsilon model, the modification of Bardina et al., taking into account the rotation of the mean flow, is investigated. With this program, the flow in the draft tube of a Kaplan turbine is examined. Calculations are carried out for swirling and nonswirling entrance flow. The results are compared with measurements.

Automata-Based Verification of Temporal Properties on Running Programs

NASA Technical Reports Server (NTRS)

Giannakopoulou, Dimitra; Havelund, Klaus; Lan, Sonie (Technical Monitor)

2001-01-01

This paper presents an approach to checking a running program against its Linear Temporal Logic (LTL) specifications. LTL is a widely used logic for expressing properties of programs viewed as sets of executions. Our approach consists of translating LTL formulae to finite-state automata, which are used as observers of the program behavior. The translation algorithm we propose modifies standard LTL to Buchi automata conversion techniques to generate automata that check finite program traces. The algorithm has been implemented in a tool, which has been integrated with the generic JPaX framework for runtime analysis of Java programs.

Nemesis I: Parallel Enhancements to ExodusII

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

Hennigan, Gary L.; John, Matthew S.; Shadid, John N.

2006-03-28

NEMESIS I is an enhancement to the EXODUS II finite element database model used to store and retrieve data for unstructured parallel finite element analyses. NEMESIS I adds data structures which facilitate the partitioning of a scalar (standard serial) EXODUS II file onto parallel disk systems found on many parallel computers. Since the NEMESIS I application programming interface (APl)can be used to append information to an existing EXODUS II files can be used on files which contain NEMESIS I information. The NEMESIS I information is written and read via C or C++ callable functions which compromise the NEMESIS I API.

Finite-size effects in Anderson localization of one-dimensional Bose-Einstein condensates

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

Cestari, J. C. C.; Foerster, A.; Gusmao, M. A.

We investigate the disorder-induced localization transition in Bose-Einstein condensates for the Anderson and Aubry-Andre models in the noninteracting limit using exact diagonalization. We show that, in addition to the standard superfluid fraction, other tools such as the entanglement and fidelity can provide clear signatures of the transition. Interestingly, the fidelity exhibits good sensitivity even for small lattices. Effects of the system size on these quantities are analyzed in detail, including the determination of a finite-size-scaling law for the critical disorder strength in the case of the Anderson model.

Quantifying nonergodicity in nonautonomous dissipative dynamical systems: An application to climate change

NASA Astrophysics Data System (ADS)

Drótos, Gábor; Bódai, Tamás; Tél, Tamás

2016-08-01

In nonautonomous dynamical systems, like in climate dynamics, an ensemble of trajectories initiated in the remote past defines a unique probability distribution, the natural measure of a snapshot attractor, for any instant of time, but this distribution typically changes in time. In cases with an aperiodic driving, temporal averages taken along a single trajectory would differ from the corresponding ensemble averages even in the infinite-time limit: ergodicity does not hold. It is worth considering this difference, which we call the nonergodic mismatch, by taking time windows of finite length for temporal averaging. We point out that the probability distribution of the nonergodic mismatch is qualitatively different in ergodic and nonergodic cases: its average is zero and typically nonzero, respectively. A main conclusion is that the difference of the average from zero, which we call the bias, is a useful measure of nonergodicity, for any window length. In contrast, the standard deviation of the nonergodic mismatch, which characterizes the spread between different realizations, exhibits a power-law decrease with increasing window length in both ergodic and nonergodic cases, and this implies that temporal and ensemble averages differ in dynamical systems with finite window lengths. It is the average modulus of the nonergodic mismatch, which we call the ergodicity deficit, that represents the expected deviation from fulfilling the equality of temporal and ensemble averages. As an important finding, we demonstrate that the ergodicity deficit cannot be reduced arbitrarily in nonergodic systems. We illustrate via a conceptual climate model that the nonergodic framework may be useful in Earth system dynamics, within which we propose the measure of nonergodicity, i.e., the bias, as an order-parameter-like quantifier of climate change.

Rupture Dynamics Simulation for Non-Planar fault by a Curved Grid Finite Difference Method

NASA Astrophysics Data System (ADS)

Zhang, Z.; Zhu, G.; Chen, X.

2011-12-01

We first implement the non-staggered finite difference method to solve the dynamic rupture problem, with split-node, for non-planar fault. Split-node method for dynamic simulation has been used widely, because of that it's more precise to represent the fault plane than other methods, for example, thick fault, stress glut and so on. The finite difference method is also a popular numeric method to solve kinematic and dynamic problem in seismology. However, previous works focus most of theirs eyes on the staggered-grid method, because of its simplicity and computational efficiency. However this method has its own disadvantage comparing to non-staggered finite difference method at some fact for example describing the boundary condition, especially the irregular boundary, or non-planar fault. Zhang and Chen (2006) proposed the MacCormack high order non-staggered finite difference method based on curved grids to precisely solve irregular boundary problem. Based upon on this non-staggered grid method, we make success of simulating the spontaneous rupture problem. The fault plane is a kind of boundary condition, which could be irregular of course. So it's convinced that we could simulate rupture process in the case of any kind of bending fault plane. We will prove this method is valid in the case of Cartesian coordinate first. In the case of bending fault, the curvilinear grids will be used.

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 Novel Polygonal Finite Element Method: Virtual Node Method

NASA Astrophysics Data System (ADS)

Tang, X. H.; Zheng, C.; Zhang, J. H.

2010-05-01

Polygonal finite element method (PFEM), which can construct shape functions on polygonal elements, provides greater flexibility in mesh generation. However, the non-polynomial form of traditional PFEM, such as Wachspress method and Mean Value method, leads to inexact numerical integration. Since the integration technique for non-polynomial functions is immature. To overcome this shortcoming, a great number of integration points have to be used to obtain sufficiently exact results, which increases computational cost. In this paper, a novel polygonal finite element method is proposed and called as virtual node method (VNM). The features of present method can be list as: (1) It is a PFEM with polynomial form. Thereby, Hammer integral and Gauss integral can be naturally used to obtain exact numerical integration; (2) Shape functions of VNM satisfy all the requirements of finite element method. To test the performance of VNM, intensive numerical tests are carried out. It found that, in standard patch test, VNM can achieve significantly better results than Wachspress method and Mean Value method. Moreover, it is observed that VNM can achieve better results than triangular 3-node elements in the accuracy test.

Semi-analytical discontinuous Galerkin finite element method for the calculation of dispersion properties of guided waves in plates.

PubMed

Hebaz, Salah-Eddine; Benmeddour, Farouk; Moulin, Emmanuel; Assaad, Jamal

2018-01-01

The development of reliable guided waves inspection systems is conditioned by an accurate knowledge of their dispersive properties. The semi-analytical finite element method has been proven to be very practical for modeling wave propagation in arbitrary cross-section waveguides. However, when it comes to computations on complex geometries to a given accuracy, it still has a major drawback: the high consumption of resources. Recently, discontinuous Galerkin finite element method (DG-FEM) has been found advantageous over the standard finite element method when applied as well in the frequency domain. In this work, a high-order method for the computation of Lamb mode characteristics in plates is proposed. The problem is discretised using a class of DG-FEM, namely, the interior penalty methods family. The analytical validation is performed through the homogeneous isotropic case with traction-free boundary conditions. Afterwards, functionally graded material plates are analysed and a numerical example is presented. It was found that the obtained results are in good agreement with those found in the literature.

Anisotropic constitutive model for nickel base single crystal alloys: Development and finite element implementation

NASA Technical Reports Server (NTRS)

Dame, L. T.; Stouffer, D. C.

1986-01-01

A tool for the mechanical analysis of nickel base single crystal superalloys, specifically Rene N4, used in gas turbine engine components is developed. This is achieved by a rate dependent anisotropic constitutive model implemented in a nonlinear three dimensional finite element code. The constitutive model is developed from metallurigical concepts utilizing a crystallographic approach. A non Schmid's law formulation is used to model the tension/compression asymmetry and orientation dependence in octahedral slip. Schmid's law is a good approximation to the inelastic response of the material in cube slip. The constitutive equations model the tensile behavior, creep response, and strain rate sensitivity of these alloys. Methods for deriving the material constants from standard tests are presented. The finite element implementation utilizes an initial strain method and twenty noded isoparametric solid elements. The ability to model piecewise linear load histories is included in the finite element code. The constitutive equations are accurately and economically integrated using a second order Adams-Moulton predictor-corrector method with a dynamic time incrementing procedure. Computed results from the finite element code are compared with experimental data for tensile, creep and cyclic tests at 760 deg C. The strain rate sensitivity and stress relaxation capabilities of the model are evaluated.

In-Vivo Assessment of Femoral Bone Strength Using Finite Element Analysis (FEA) Based on Routine MDCT Imaging: A Preliminary Study on Patients with Vertebral Fractures

PubMed Central

Liebl, Hans; Garcia, Eduardo Grande; Holzner, Fabian; Noel, Peter B.; Burgkart, Rainer; Rummeny, Ernst J.; Baum, Thomas; Bauer, Jan S.

2015-01-01

Purpose To experimentally validate a non-linear finite element analysis (FEA) modeling approach assessing in-vitro fracture risk at the proximal femur and to transfer the method to standard in-vivo multi-detector computed tomography (MDCT) data of the hip aiming to predict additional hip fracture risk in subjects with and without osteoporosis associated vertebral fractures using bone mineral density (BMD) measurements as gold standard. Methods One fresh-frozen human femur specimen was mechanically tested and fractured simulating stance and clinically relevant fall loading configurations to the hip. After experimental in-vitro validation, the FEA simulation protocol was transferred to standard contrast-enhanced in-vivo MDCT images to calculate individual hip fracture risk each for 4 subjects with and without a history of osteoporotic vertebral fractures matched by age and gender. In addition, FEA based risk factor calculations were compared to manual femoral BMD measurements of all subjects. Results In-vitro simulations showed good correlation with the experimentally measured strains both in stance (R2 = 0.963) and fall configuration (R2 = 0.976). The simulated maximum stress overestimated the experimental failure load (4743 N) by 14.7% (5440 N) while the simulated maximum strain overestimated by 4.7% (4968 N). The simulated failed elements coincided precisely with the experimentally determined fracture locations. BMD measurements in subjects with a history of osteoporotic vertebral fractures did not differ significantly from subjects without fragility fractures (femoral head: p = 0.989; femoral neck: p = 0.366), but showed higher FEA based risk factors for additional incident hip fractures (p = 0.028). Conclusion FEA simulations were successfully validated by elastic and destructive in-vitro experiments. In the subsequent in-vivo analyses, MDCT based FEA based risk factor differences for additional hip fractures were not mirrored by according BMD measurements. Our data suggests, that MDCT derived FEA models may assess bone strength more accurately than BMD measurements alone, providing a valuable in-vivo fracture risk assessment tool. PMID:25723187

A mass-conservative adaptive FAS multigrid solver for cell-centered finite difference methods on block-structured, locally-cartesian grids

NASA Astrophysics Data System (ADS)

Feng, Wenqiang; Guo, Zhenlin; Lowengrub, John S.; Wise, Steven M.

2018-01-01

We present a mass-conservative full approximation storage (FAS) multigrid solver for cell-centered finite difference methods on block-structured, locally cartesian grids. The algorithm is essentially a standard adaptive FAS (AFAS) scheme, but with a simple modification that comes in the form of a mass-conservative correction to the coarse-level force. This correction is facilitated by the creation of a zombie variable, analogous to a ghost variable, but defined on the coarse grid and lying under the fine grid refinement patch. We show that a number of different types of fine-level ghost cell interpolation strategies could be used in our framework, including low-order linear interpolation. In our approach, the smoother, prolongation, and restriction operations need never be aware of the mass conservation conditions at the coarse-fine interface. To maintain global mass conservation, we need only modify the usual FAS algorithm by correcting the coarse-level force function at points adjacent to the coarse-fine interface. We demonstrate through simulations that the solver converges geometrically, at a rate that is h-independent, and we show the generality of the solver, applying it to several nonlinear, time-dependent, and multi-dimensional problems. In several tests, we show that second-order asymptotic (h → 0) convergence is observed for the discretizations, provided that (1) at least linear interpolation of the ghost variables is employed, and (2) the mass conservation corrections are applied to the coarse-level force term.

An improved finite-difference analysis of uncoupled vibrations of tapered cantilever beams

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.

1983-01-01

An improved finite difference procedure for determining the natural frequencies and mode shapes of tapered cantilever beams undergoing uncoupled vibrations is presented. Boundary conditions are derived in the form of simple recursive relations involving the second order central differences. Results obtained by using the conventional first order central differences and the present second order central differences are compared, and it is observed that the present second order scheme is more efficient than the conventional approach. An important advantage offered by the present approach is that the results converge to exact values rapidly, and thus the extrapolation of the results is not necessary. Consequently, the basic handicap with the classical finite difference method of solution that requires the Richardson's extrapolation procedure is eliminated. Furthermore, for the cases considered herein, the present approach produces consistent lower bound solutions.

A fast finite-difference algorithm for topology optimization of permanent magnets

NASA Astrophysics Data System (ADS)

Abert, Claas; Huber, Christian; Bruckner, Florian; Vogler, Christoph; Wautischer, Gregor; Suess, Dieter

2017-09-01

We present a finite-difference method for the topology optimization of permanent magnets that is based on the fast-Fourier-transform (FFT) accelerated computation of the stray-field. The presented method employs the density approach for topology optimization and uses an adjoint method for the gradient computation. Comparison to various state-of-the-art finite-element implementations shows a superior performance and accuracy. Moreover, the presented method is very flexible and easy to implement due to various preexisting FFT stray-field implementations that can be used.

A discourse on sensitivity analysis for discretely-modeled structures

NASA Technical Reports Server (NTRS)

Adelman, Howard M.; Haftka, Raphael T.

1991-01-01

A descriptive review is presented of the most recent methods for performing sensitivity analysis of the structural behavior of discretely-modeled systems. The methods are generally but not exclusively aimed at finite element modeled structures. Topics included are: selections of finite difference step sizes; special consideration for finite difference sensitivity of iteratively-solved response problems; first and second derivatives of static structural response; sensitivity of stresses; nonlinear static response sensitivity; eigenvalue and eigenvector sensitivities for both distinct and repeated eigenvalues; and sensitivity of transient response for both linear and nonlinear structural response.

The Development of a Finite Volume Method for Modeling Sound in Coastal Ocean Environment

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

Long, Wen; Yang, Zhaoqing; Copping, Andrea E.

: As the rapid growth of marine renewable energy and off-shore wind energy, there have been concerns that the noises generated from construction and operation of the devices may interfere marine animals’ communication. In this research, a underwater sound model is developed to simulate sound prorogation generated by marine-hydrokinetic energy (MHK) devices or offshore wind (OSW) energy platforms. Finite volume and finite difference methods are developed to solve the 3D Helmholtz equation of sound propagation in the coastal environment. For finite volume method, the grid system consists of triangular grids in horizontal plane and sigma-layers in vertical dimension. A 3Dmore » sparse matrix solver with complex coefficients is formed for solving the resulting acoustic pressure field. The Complex Shifted Laplacian Preconditioner (CSLP) method is applied to efficiently solve the matrix system iteratively with MPI parallelization using a high performance cluster. The sound model is then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound propagation generated by human activities in a range-dependent setting, such as offshore wind energy platform constructions and tidal stream turbines. As a proof of concept, initial validation of the finite difference solver is presented for two coastal wedge problems. Validation of finite volume method will be reported separately.« less

Benchmark model correction of monitoring system based on Dynamic Load Test of Bridge

NASA Astrophysics Data System (ADS)

Shi, Jing-xian; Fan, Jiang

2018-03-01

Structural health monitoring (SHM) is a field of research in the area, and it’s designed to achieve bridge safety and reliability assessment, which needs to be carried out on the basis of the accurate simulation of the finite element model. Bridge finite element model is simplified of the structural section form, support conditions, material properties and boundary condition, which is based on the design and construction drawings, and it gets the calculation models and the results.But according to the design and specification requirements established finite element model due to its cannot fully reflect the true state of the bridge, so need to modify the finite element model to obtain the more accurate finite element model. Based on Da-guan river crossing of Ma - Zhao highway in Yunnan province as the background to do the dynamic load test test, we find that the impact coefficient of the theoretical model of the bridge is very different from the coefficient of the actual test, and the change is different; according to the actual situation, the calculation model is adjusted to get the correct frequency of the bridge, the revised impact coefficient found that the modified finite element model is closer to the real state, and provides the basis for the correction of the finite model.

Nonlinear truncation error analysis of finite difference schemes for the Euler equations

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1983-01-01

It is pointed out that, in general, dissipative finite difference integration schemes have been found to be quite robust when applied to the Euler equations of gas dynamics. The present investigation considers a modified equation analysis of both implicit and explicit finite difference techniques as applied to the Euler equations. The analysis is used to identify those error terms which contribute most to the observed solution errors. A technique for analytically removing the dominant error terms is demonstrated, resulting in a greatly improved solution for the explicit Lax-Wendroff schemes. It is shown that the nonlinear truncation errors are quite large and distributed quite differently for each of the three conservation equations as applied to a one-dimensional shock tube problem.

A vortex wake capturing method for potential flow calculations

NASA Technical Reports Server (NTRS)

Murman, E. M.; Stremel, P. M.

1982-01-01

A method is presented for modifying finite difference solutions of the potential equation to include the calculation of non-planar vortex wake features. The approach is an adaptation of Baker's 'cloud in cell' algorithm developed for the stream function-vorticity equations. The vortex wake is tracked in a Lagrangian frame of reference as a group of discrete vortex filaments. These are distributed to the Eulerian mesh system on which the velocity is calculated by a finite difference solution of the potential equation. An artificial viscosity introduced by the finite difference equations removes the singular nature of the vortex filaments. Computed examples are given for the two-dimensional time dependent roll-up of vortex wakes generated by wings with different spanwise loading distributions.

A compact finite element method for elastic bodies

NASA Technical Reports Server (NTRS)

Rose, M. E.

1984-01-01

A nonconforming finite method is described for treating linear equilibrium problems, and a convergence proof showing second order accuracy is given. The close relationship to a related compact finite difference scheme due to Phillips and Rose is examined. A condensation technique is shown to preserve the compactness property and suggests an approach to a certain type of homogenization.

An analysis of finite-difference and finite-volume formulations of conservation laws

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1986-01-01

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations--potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomeclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

An analysis of finite-difference and finite-volume formulations of conservation laws

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1989-01-01

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

Duality in non-linear programming

NASA Astrophysics Data System (ADS)

Jeyalakshmi, K.

2018-04-01

In this paper we consider duality and converse duality for a programming problem involving convex objective and constraint functions with finite dimensional range. We do not assume any constraint qualification. The dual is presented by reducing the problem to a standard Lagrange multiplier problem.

[Application of finite element method in spinal biomechanics].

PubMed

Liu, Qiang; Zhang, Jun; Sun, Shu-Chun; Wang, Fei

2017-02-25

The finite element model is one of the most important methods in study of modern spinal biomechanics, according to the needs to simulate the various states of the spine, calculate the stress force and strain distribution of the different groups in the state, and explore its principle of mechanics, mechanism of injury, and treatment effectiveness. In addition, in the study of the pathological state of the spine, the finite element is mainly used in the understanding the mechanism of lesion location, evaluating the effects of different therapeutic tool, assisting and completing the selection and improvement of therapeutic tool, in order to provide a theoretical basis for the rehabilitation of spinal lesions. Finite element method can be more provide the service for the patients suffering from spinal correction, operation and individual implant design. Among the design and performance evaluation of the implant need to pay attention to the individual difference and perfect the evaluation system. At present, how to establish a model which is more close to the real situation has been the focus and difficulty of the study of human body's finite element.Although finite element method can better simulate complex working condition, it is necessary to improve the authenticity of the model and the sharing of the group by using many kinds of methods, such as image science, statistics, kinematics and so on. Copyright© 2017 by the China Journal of Orthopaedics and Traumatology Press.

Ablative Thermal Response Analysis Using the Finite Element Method

NASA Technical Reports Server (NTRS)

Dec John A.; Braun, Robert D.

2009-01-01

A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the finite element and finite difference methods are described. As a first step in developing a three dimensional finite element based ablative thermal response capability, a one dimensional computer tool has been developed. The finite element method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the element equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed.

First-Order System Least-Squares for Second-Order Elliptic Problems with Discontinuous Coefficients

NASA Technical Reports Server (NTRS)

Manteuffel, Thomas A.; McCormick, Stephen F.; Starke, Gerhard

1996-01-01

The first-order system least-squares methodology represents an alternative to standard mixed finite element methods. Among its advantages is the fact that the finite element spaces approximating the pressure and flux variables are not restricted by the inf-sup condition and that the least-squares functional itself serves as an appropriate error measure. This paper studies the first-order system least-squares approach for scalar second-order elliptic boundary value problems with discontinuous coefficients. Ellipticity of an appropriately scaled least-squares bilinear form of the size of the jumps in the coefficients leading to adequate finite element approximation results. The occurrence of singularities at interface corners and cross-points is discussed. and a weighted least-squares functional is introduced to handle such cases. Numerical experiments are presented for two test problems to illustrate the performance of this approach.

Finite element analysis of human joints

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

Bossart, P.L.; Hollerbach, K.

1996-09-01

Our work focuses on the development of finite element models (FEMs) that describe the biomechanics of human joints. Finite element modeling is becoming a standard tool in industrial applications. In highly complex problems such as those found in biomechanics research, however, the full potential of FEMs is just beginning to be explored, due to the absence of precise, high resolution medical data and the difficulties encountered in converting these enormous datasets into a form that is usable in FEMs. With increasing computing speed and memory available, it is now feasible to address these challenges. We address the first by acquiringmore » data with a high resolution C-ray CT scanner and the latter by developing semi-automated method for generating the volumetric meshes used in the FEM. Issues related to tomographic reconstruction, volume segmentation, the use of extracted surfaces to generate volumetric hexahedral meshes, and applications of the FEM are described.« less

Chiral Luttinger liquids and a generalized Luttinger's theorem in fractional quantum Hall edges via finite-entanglement scaling

NASA Astrophysics Data System (ADS)

Varjas, Daniel; Zaletel, Michael; Moore, Joel

2014-03-01

We use bosonic field theories and the infinite system density matrix renormalization group (iDMRG) method to study infinite strips of fractional quantum Hall (FQH) states starting from microscopic Hamiltonians. Finite-entanglement scaling allows us to accurately measure chiral central charge, edge mode exponents and momenta without finite-size errors. We analyze states in the first and second level of the standard hierarchy and compare our results to predictions of the chiral Luttinger liquid (χLL) theory. The results confirm the universality of scaling exponents in chiral edges and demonstrate that renormalization is subject to universal relations in the non-chiral case. We prove a generalized Luttinger's theorem involving all singularities in the momentum-resolved density, which naturally arises when mapping Landau levels on a cylinder to a fermion chain and deepens our understanding of non-Fermi liquids in 1D.

Chiral Luttinger liquids and a generalized Luttinger theorem in fractional quantum Hall edges via finite-entanglement scaling

NASA Astrophysics Data System (ADS)

Varjas, Dániel; Zaletel, Michael P.; Moore, Joel E.

2013-10-01

We use bosonic field theories and the infinite system density matrix renormalization group method to study infinite strips of fractional quantum Hall states starting from microscopic Hamiltonians. Finite-entanglement scaling allows us to accurately measure chiral central charge, edge-mode exponents, and momenta without finite-size errors. We analyze states in the first and second levels of the standard hierarchy and compare our results to predictions of the chiral Luttinger liquid theory. The results confirm the universality of scaling exponents in chiral edges and demonstrate that renormalization is subject to universal relations in the nonchiral case. We prove a generalized Luttinger theorem involving all singularities in the momentum-resolved density, which naturally arises when mapping Landau levels on a cylinder to a fermion chain and deepens our understanding of non-Fermi liquids in one dimension.

Dynamical transition for a particle in a squared Gaussian potential

NASA Astrophysics Data System (ADS)

Touya, C.; Dean, D. S.

2007-02-01

We study the problem of a Brownian particle diffusing in finite dimensions in a potential given by ψ = phi2/2 where phi is Gaussian random field. Exact results for the diffusion constant in the high temperature phase are given in one and two dimensions and it is shown to vanish in a power-law fashion at the dynamical transition temperature. Our results are confronted with numerical simulations where the Gaussian field is constructed, in a standard way, as a sum over random Fourier modes. We show that when the number of Fourier modes is finite the low temperature diffusion constant becomes non-zero and has an Arrhenius form. Thus we have a simple model with a fully understood finite size scaling theory for the dynamical transition. In addition we analyse the nature of the anomalous diffusion in the low temperature regime and show that the anomalous exponent agrees with that predicted by a trap model.

A hybrid-stress finite element approach for stress and vibration analysis in linear anisotropic elasticity

NASA Technical Reports Server (NTRS)

Oden, J. Tinsley; Fly, Gerald W.; Mahadevan, L.

1987-01-01

A hybrid stress finite element method is developed for accurate stress and vibration analysis of problems in linear anisotropic elasticity. A modified form of the Hellinger-Reissner principle is formulated for dynamic analysis and an algorithm for the determination of the anisotropic elastic and compliance constants from experimental data is developed. These schemes were implemented in a finite element program for static and dynamic analysis of linear anisotropic two dimensional elasticity problems. Specific numerical examples are considered to verify the accuracy of the hybrid stress approach and compare it with that of the standard displacement method, especially for highly anisotropic materials. It is that the hybrid stress approach gives much better results than the displacement method. Preliminary work on extensions of this method to three dimensional elasticity is discussed, and the stress shape functions necessary for this extension are included.

STARS: An integrated general-purpose finite element structural, aeroelastic, and aeroservoelastic analysis computer program

NASA Technical Reports Server (NTRS)

Gupta, Kajal K.

1991-01-01

The details of an integrated general-purpose finite element structural analysis computer program which is also capable of solving complex multidisciplinary problems is presented. Thus, the SOLIDS module of the program possesses an extensive finite element library suitable for modeling most practical problems and is capable of solving statics, vibration, buckling, and dynamic response problems of complex structures, including spinning ones. The aerodynamic module, AERO, enables computation of unsteady aerodynamic forces for both subsonic and supersonic flow for subsequent flutter and divergence analysis of the structure. The associated aeroservoelastic analysis module, ASE, effects aero-structural-control stability analysis yielding frequency responses as well as damping characteristics of the structure. The program is written in standard FORTRAN to run on a wide variety of computers. Extensive graphics, preprocessing, and postprocessing routines are also available pertaining to a number of terminals.

Affine cellularity of finite type KLR algebras, and homomorphisms between Specht modules for KLR algebras in affine type A

NASA Astrophysics Data System (ADS)

Loubert, Joseph William

This thesis consists of two parts. In the first we prove that the Khovanov-Lauda-Rouquier algebras Ralpha of finite type are (graded) affine cellular in the sense of Koenig and Xi. In fact, we establish a stronger property, namely that the affine cell ideals in Ralpha are generated by idempotents. This in particular implies the (known) result that the global dimension of Ralpha is finite. In the second part we use the presentation of the Specht modules given by Kleshchev-Mathas-Ram to derive results about Specht modules. In particular, we determine all homomorphisms from an arbitrary Specht module to a fixed Specht module corresponding to any hook partition. Along the way, we give a complete description of the action of the standard KLR generators on the hook Specht module. This work generalizes a result of James. This dissertation includes previously published coauthored material.

Stress-intensity factors for small surface and corner cracks in plates

NASA Technical Reports Server (NTRS)

Raju, I. S.; Atluri, S. N.; Newman, J. C., Jr.

1988-01-01

Three-dimensional finite-element and finite-alternating methods were used to obtain the stress-intensity factors for small surface and corner cracked plates subjected to remote tension and bending loads. The crack-depth-to-crack-length ratios (a/c) ranged from 0.2 to 1 and the crack-depth-to-plate-thickness ratios (a/t) ranged from 0.05 to 0.2. The performance of the finite-element alternating method was studied on these crack configurations. A study of the computational effort involved in the finite-element alternating method showed that several crack configurations could be analyzed with a single rectangular mesh idealization, whereas the conventional finite-element method requires a different mesh for each configuration. The stress-intensity factors obtained with the finite-element-alternating method agreed well (within 5 percent) with those calculated from the finite-element method with singularity elements.

A three-dimensional thermal finite element analysis of AISI 304 stainless steel and copper dissimilar weldment

NASA Astrophysics Data System (ADS)

Singh, Gurdeep; Saxena, Ravindra K.; Pandey, Sunil

2018-04-01

The aim of this study to developed a 3-D thermal finite element model for dissimilar material welding of AISI-304 stainless steel and copper. Welding of similar material is widely studied using experimental and numerical methods but the problem becomes trivial for the welding of dissimilar materials especially in ferrous and nonferrous materials. Finite element analysis of dissimilar material welding is a cost-effective method for the understanding and analysis of the process. The finite element analysis has been performed to predict the heat affected zone and temperature distribution in AISI-304 stainless steel and copper dissimilar weldment using MSC Marc 2017®. Due to the difference in physical properties of these materials the behavior of heat affected zone and temperature distribution are perceived to be different. To verify the accuracy of the thermal finite element model, the welding process was simulated with butt-welded joints having same dimensions and parameters from Attarha and Far [1]. It is found from the study that the heat affected zone is larger in copper weld pads than in AISI 304 stainless steel due to large difference in thermal conductivity of these two weld pads.

An Eigenvalue Analysis of finite-difference approximations for hyperbolic IBVPs

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1989-01-01

The eigenvalue spectrum associated with a linear finite-difference approximation plays a crucial role in the stability analysis and in the actual computational performance of the discrete approximation. The eigenvalue spectrum associated with the Lax-Wendroff scheme applied to a model hyperbolic equation was investigated. For an initial-boundary-value problem (IBVP) on a finite domain, the eigenvalue or normal mode analysis is analytically intractable. A study of auxiliary problems (Dirichlet and quarter-plane) leads to asymptotic estimates of the eigenvalue spectrum and to an identification of individual modes as either benign or unstable. The asymptotic analysis establishes an intuitive as well as quantitative connection between the algebraic tests in the theory of Gustafsson, Kreiss, and Sundstrom and Lax-Richtmyer L(sub 2) stability on a finite domain.

OpenSeesPy: Python library for the OpenSees finite element framework

NASA Astrophysics Data System (ADS)

Zhu, Minjie; McKenna, Frank; Scott, Michael H.

2018-01-01

OpenSees, an open source finite element software framework, has been used broadly in the earthquake engineering community for simulating the seismic response of structural and geotechnical systems. The framework allows users to perform finite element analysis with a scripting language and for developers to create both serial and parallel finite element computer applications as interpreters. For the last 15 years, Tcl has been the primary scripting language to which the model building and analysis modules of OpenSees are linked. To provide users with different scripting language options, particularly Python, the OpenSees interpreter interface was refactored to provide multi-interpreter capabilities. This refactoring, resulting in the creation of OpenSeesPy as a Python module, is accomplished through an abstract interface for interpreter calls with concrete implementations for different scripting languages. Through this approach, users are able to develop applications that utilize the unique features of several scripting languages while taking advantage of advanced finite element analysis models and algorithms.

Computing an upper bound on contact stress with surrogate duality

NASA Astrophysics Data System (ADS)

Xuan, Zhaocheng; Papadopoulos, Panayiotis

2016-07-01

We present a method for computing an upper bound on the contact stress of elastic bodies. The continuum model of elastic bodies with contact is first modeled as a constrained optimization problem by using finite elements. An explicit formulation of the total contact force, a fraction function with the numerator as a linear function and the denominator as a quadratic convex function, is derived with only the normalized nodal contact forces as the constrained variables in a standard simplex. Then two bounds are obtained for the sum of the nodal contact forces. The first is an explicit formulation of matrices of the finite element model, derived by maximizing the fraction function under the constraint that the sum of the normalized nodal contact forces is one. The second bound is solved by first maximizing the fraction function subject to the standard simplex and then using Dinkelbach's algorithm for fractional programming to find the maximum—since the fraction function is pseudo concave in a neighborhood of the solution. These two bounds are solved with the problem dimensions being only the number of contact nodes or node pairs, which are much smaller than the dimension for the original problem, namely, the number of degrees of freedom. Next, a scheme for constructing an upper bound on the contact stress is proposed that uses the bounds on the sum of the nodal contact forces obtained on a fine finite element mesh and the nodal contact forces obtained on a coarse finite element mesh, which are problems that can be solved at a lower computational cost. Finally, the proposed method is verified through some examples concerning both frictionless and frictional contact to demonstrate the method's feasibility, efficiency, and robustness.

A user's guide for V174, a program using a finite difference method to analyze transonic flow over oscillating wings

NASA Technical Reports Server (NTRS)

Butler, T. D.; Weatherill, W. H.; Sebastian, J. D.; Ehlers, F. E.

1977-01-01

The design and usage of a pilot program using a finite difference method for calculating the pressure distributions over harmonically oscillating wings in transonic flow are discussed. The procedure used is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The steady velocity potential which must be obtained from some other program, is required for input. The unsteady differential equation is linear, complex in form with spatially varying coefficients. Because sinusoidal motion is assumed, time is not a variable. The numerical solution is obtained through a finite difference formulation and a line relaxation solution method.

Electrostatic bending response of a charged helix

NASA Astrophysics Data System (ADS)

Zampetaki, A. V.; Stockhofe, J.; Schmelcher, P.

2018-04-01

We explore the electrostatic bending response of a chain of charged particles confined on a finite helical filament. We analyze how the energy difference Δ E between the bent and the unbent helical chain scales with the length of the helical segment and the radius of curvature and identify features that are not captured by the standard notion of the bending rigidity, normally used as a measure of bending tendency in the linear response regime. Using Δ E to characterize the bending response of the helical chain we identify two regimes with qualitatively different bending behaviors for the ground state configuration: the regime of small and the regime of large radius-to-pitch ratio, respectively. Within the former regime, Δ E changes smoothly with the variation of the system parameters. Of particular interest are its oscillations with the number of charged particles encountered for commensurate fillings which yield length-dependent oscillations in the preferred bending direction of the helical chain. We show that the origin of these oscillations is the nonuniformity of the charge distribution caused by the long-range character of the Coulomb interactions and the finite length of the helix. In the second regime of large values of the radius-to-pitch ratio, sudden changes in the ground state structure of the charges occur as the system parameters vary, leading to complex and discontinuous variations in the ground state bending response Δ E .

Investigating the effect of tablet thickness and punch curvature on density distribution using finite elements method.

PubMed

Diarra, Harona; Mazel, Vincent; Busignies, Virginie; Tchoreloff, Pierre

2015-09-30

Finite elements method was used to study the influence of tablet thickness and punch curvature on the density distribution inside convex faced (CF) tablets. The modeling of the process was conducted on 2 pharmaceutical excipients (anhydrous calcium phosphate and microcrystalline cellulose) by using Drucker-Prager Cap model in Abaqus(®) software. The parameters of the model were obtained from experimental tests. Several punch shapes based on industrial standards were used. A flat-faced (FF) punch and 3 convex faced (CF) punches (8R11, 8R8 and 8R6) with a diameter of 8mm were chosen. Different tablet thicknesses were studied at a constant compression force. The simulation of the compaction of CF tablets with increasing thicknesses showed an important change on the density distribution inside the tablet. For smaller thicknesses, low density zones are located toward the center. The density is not uniform inside CF tablets and the center of the 2 faces appears with low density whereas the distribution inside FF tablets is almost independent of the tablet thickness. These results showed that FF and CF tablets, even obtained at the same compression force, do not have the same density at the center of the compact. As a consequence differences in tensile strength, as measured by diametral compression, are expected. This was confirmed by experimental tests. Copyright © 2015 Elsevier B.V. All rights reserved.

Shallow-Water Performance of a Planing Boat

DTIC Science & Technology

1969-04-25

coefficient h Finite depth of water, ft Fn Froude number based on length Nomenclature used is ITTC Standard Symbols and that recommended in SNAME T & R...Published by SNAME, 1967. 3. "Systematishe Untersuchungen von Kleinschiffsformen auf flachem Wasser im unter- und Uberuritishen

Integrating Security into the Curriculum

DTIC Science & Technology

1998-12-01

predicate calculus, discrete math , and finite-state machine the- ory. In addition to applying standard mathematical foundations to constructing hardware and...models, specifi- cations, and the use of formal methods for verification and covert channel analysis. The means for analysis is based on discrete math , information

Smooth particle hydrodynamics: theory and application to the origin of the moon

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

Benz, W.

1986-01-01

The origin of the moon is modeled by the so-called smooth particle hydrodynamics (SPH) method (Lucy, 1977, Monaghan 1985) which substitutes to the fluid a finite set of extended particles, the hydrodynamics equations reduce to the equation of motion of individual particles. These equations of motion differ only from the standard gravitational N-body problem insofar that pressure gradients and viscosity terms have to be added to the gradient of the potential to derive the forces between the particles. The numerical tools developed for ''classical'' N-body problems can therefore be readily applied to solve 3 dimensional hydroynamical problems. 12 refs., 1more » fig.« less

Law of corresponding states for open collaborations

NASA Astrophysics Data System (ADS)

Gherardi, Marco; Bassetti, Federico; Cosentino Lagomarsino, Marco

2016-04-01

We study the relation between number of contributors and product size in Wikipedia and GitHub. In contrast to traditional production, this is strongly probabilistic, but is characterized by two quantitative nonlinear laws: a power-law bound to product size for increasing number of contributors, and the universal collapse of rescaled distributions. A variant of the random-energy model shows that both laws are due to the heterogeneity of contributors, and displays an intriguing finite-size scaling property with no equivalent in standard systems. The analysis uncovers the right intensive densities, enabling the comparison of projects with different numbers of contributors on equal grounds. We use this property to expose the detrimental effects of conflicting interactions in Wikipedia.

Finite Mixture Multilevel Multidimensional Ordinal IRT Models for Large Scale Cross-Cultural Research

ERIC Educational Resources Information Center

de Jong, Martijn G.; Steenkamp, Jan-Benedict E. M.

2010-01-01

We present a class of finite mixture multilevel multidimensional ordinal IRT models for large scale cross-cultural research. Our model is proposed for confirmatory research settings. Our prior for item parameters is a mixture distribution to accommodate situations where different groups of countries have different measurement operations, while…

Computational procedure for finite difference solution of one-dimensional heat conduction problems reduces computer time

NASA Technical Reports Server (NTRS)

Iida, H. T.

1966-01-01

Computational procedure reduces the numerical effort whenever the method of finite differences is used to solve ablation problems for which the surface recession is large relative to the initial slab thickness. The number of numerical operations required for a given maximum space mesh size is reduced.

Bone preserving level of osteotomy in short-stem total hip arthroplasty does not influence stress shielding dimensions - a comparing finite elements analysis.

PubMed

Burchard, Rene; Braas, Sabrina; Soost, Christian; Graw, Jan Adriaan; Schmitt, Jan

2017-08-07

The main objective of every new development in total hip arthroplasty (THA) is the longest possible survival of the implant. Periprosthetic stress shielding is a scientifically proven phenomenon which leads to inadvertent bone loss. So far, many studies have analysed whether implanting different hip stem prostheses result in significant preservation of bone stock. The aim of this preclinical study was to investigate design-depended differences of the stress shielding effect after implantation of a selection of short-stem THA-prostheses that are currently available. Based on computerised tomography (CT), a finite elements (FE) model was generated and a virtual THA was performed with different stem designs of the implant. Stems were chosen by osteotomy level at the femoral neck (collum, partial collum, trochanter sparing, trochanter harming). Analyses were performed with previously validated FE models to identify changes in the strain energy density (SED). In the trochanteric region, only the collum-type stem demonstrated a biomechanical behaviour similar to the native femur. In contrast, no difference in biomechanical behaviour was found between partial collum, trochanter harming and trochanter sparing models. All of the short stem-prostheses showed lower stress-shielding than a standard stem. Based on the results of this study, we cannot confirm that the design of current short stem THA-implants leads to a different stress shielding effect with regard to the level of osteotomy. Somehow unexpected, we found a bone stock protection in metadiaphyseal bone by simulating a more distal approach for osteotomy. Further clinical and biomechanical research including long-term results is needed to understand the influence of short-stem THA on bone remodelling and to find the optimal stem-design for a reduction of the stress shielding effect.

Some Finite Difference Solutions of the Laminar Compressible Boundary Layer Showing the Effects of Upstream Transpiration Cooling

NASA Technical Reports Server (NTRS)

Howe, John T.

1959-01-01

Three numerical solutions of the partial differential equations describing the compressible laminar boundary layer are obtained by the finite difference method described in reports by I. Flugge-Lotz, D.C. Baxter, and this author. The solutions apply to steady-state supersonic flow without pressure gradient, over a cold wall and over an adiabatic wall, both having transpiration cooling upstream, and over an adiabatic wall with upstream cooling but without upstream transpiration. It is shown that for a given upstream wall temperature, upstream transpiration cooling affords much better protection to the adiabatic solid wall than does upstream cooling without transpiration. The results of the numerical solutions are compared with those of approximate solutions. The thermal results of the finite difference solution lie between the results of Rubesin and Inouye, and those of Libby and Pallone. When the skin-friction results of one finite difference solution are used in the thermal analysis of Rubesin and Inouye, improved agreement between the thermal results of the two methods of solution is obtained.

Elastic critical moment for bisymmetric steel profiles and its sensitivity by the finite difference method

NASA Astrophysics Data System (ADS)

Kamiński, M.; Supeł, Ł.

2016-02-01

It is widely known that lateral-torsional buckling of a member under bending and warping restraints of its cross-sections in the steel structures are crucial for estimation of their safety and durability. Although engineering codes for steel and aluminum structures support the designer with the additional analytical expressions depending even on the boundary conditions and internal forces diagrams, one may apply alternatively the traditional Finite Element or Finite Difference Methods (FEM, FDM) to determine the so-called critical moment representing this phenomenon. The principal purpose of this work is to compare three different ways of determination of critical moment, also in the context of structural sensitivity analysis with respect to the structural element length. Sensitivity gradients are determined by the use of both analytical and the central finite difference scheme here and contrasted also for analytical, FEM as well as FDM approaches. Computational study is provided for the entire family of the steel I- and H - beams available for the practitioners in this area, and is a basis for further stochastic reliability analysis as well as durability prediction including possible corrosion progress.

A time-spectral approach to numerical weather prediction

NASA Astrophysics Data System (ADS)

Scheffel, Jan; Lindvall, Kristoffer; Yik, Hiu Fai

2018-05-01

Finite difference methods are traditionally used for modelling the time domain in numerical weather prediction (NWP). Time-spectral solution is an attractive alternative for reasons of accuracy and efficiency and because time step limitations associated with causal CFL-like criteria, typical for explicit finite difference methods, are avoided. In this work, the Lorenz 1984 chaotic equations are solved using the time-spectral algorithm GWRM (Generalized Weighted Residual Method). Comparisons of accuracy and efficiency are carried out for both explicit and implicit time-stepping algorithms. It is found that the efficiency of the GWRM compares well with these methods, in particular at high accuracy. For perturbative scenarios, the GWRM was found to be as much as four times faster than the finite difference methods. A primary reason is that the GWRM time intervals typically are two orders of magnitude larger than those of the finite difference methods. The GWRM has the additional advantage to produce analytical solutions in the form of Chebyshev series expansions. The results are encouraging for pursuing further studies, including spatial dependence, of the relevance of time-spectral methods for NWP modelling.

Time dependent wave envelope finite difference analysis of sound propagation

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1984-01-01

A transient finite difference wave envelope formulation is presented for sound propagation, without steady flow. Before the finite difference equations are formulated, the governing wave equation is first transformed to a form whose solution tends not to oscillate along the propagation direction. This transformation reduces the required number of grid points by an order of magnitude. Physically, the transformed pressure represents the amplitude of the conventional sound wave. The derivation for the wave envelope transient wave equation and appropriate boundary conditions are presented as well as the difference equations and stability requirements. To illustrate the method, example solutions are presented for sound propagation in a straight hard wall duct and in a two dimensional straight soft wall duct. The numerical results are in good agreement with exact analytical results.

Validation by numerical simulation of the behaviour of protective structures of machinery cabins subjected to standardized shocks

NASA Astrophysics Data System (ADS)

Dumitrache, P.; Goanţă, A. M.

2017-08-01

The ability of the cabins to insure the operator protection in the case of the shock loading that appears at the roll-over of the machine or when the cab is struck by the falling objects, it’s one of the most important performance criterions that it must comply by the machines and the mobile equipments. The experimental method provides the most accurate information on the behaviour of protective structures, but generates high costs due to experimental installations and structures which may be compromised during the experiments. In these circumstances, numerical simulation of the actual problem (mechanical shock applied to a strength structure) is a perfectly viable alternative, given that the hardware and software current performances provides the necessary support to obtain results with an acceptable level of accuracy. In this context, the paper proposes using FEA platforms for virtual testing of the actual strength structures of the cabins using their finite element models based on 3D models generated in CAD environments. In addition to the economic advantage above mentioned, although the results obtained by simulation using the finite element method are affected by a number of simplifying assumptions, the adequate modelling of the phenomenon can be a successful support in the design process of structures to meet safety performance criteria imposed by current standards. In the first section of the paper is presented the general context of the security performance requirements imposed by current standards on the cabins strength structures. The following section of the paper is dedicated to the peculiarities of finite element modelling in problems that impose simulation of the behaviour of structures subjected to shock loading. The final section of the paper is dedicated to a case study and to the future objectives.

An investigation of several numerical procedures for time-asymptotic compressible Navier-Stokes solutions

NASA Technical Reports Server (NTRS)

Rudy, D. H.; Morris, D. J.; Blanchard, D. K.; Cooke, C. H.; Rubin, S. G.

1975-01-01

The status of an investigation of four numerical techniques for the time-dependent compressible Navier-Stokes equations is presented. Results for free shear layer calculations in the Reynolds number range from 1000 to 81000 indicate that a sequential alternating-direction implicit (ADI) finite-difference procedure requires longer computing times to reach steady state than a low-storage hopscotch finite-difference procedure. A finite-element method with cubic approximating functions was found to require excessive computer storage and computation times. A fourth method, an alternating-direction cubic spline technique which is still being tested, is also described.

LaRC design analysis report for National Transonic Facility for 304 stainless steel tunnel shell. Volume 1S: Finite difference analysis of cone/cylinder junction

NASA Technical Reports Server (NTRS)

Ramsey, J. W., Jr.; Taylor, J. T.; Wilson, J. F.; Gray, C. E., Jr.; Leatherman, A. D.; Rooker, J. R.; Allred, J. W.

1976-01-01

The results of extensive computer (finite element, finite difference and numerical integration), thermal, fatigue, and special analyses of critical portions of a large pressurized, cryogenic wind tunnel (National Transonic Facility) are presented. The computer models, loading and boundary conditions are described. Graphic capability was used to display model geometry, section properties, and stress results. A stress criteria is presented for evaluation of the results of the analyses. Thermal analyses were performed for major critical and typical areas. Fatigue analyses of the entire tunnel circuit are presented.

Wall function treatment for bubbly boundary layers at low void fractions.

PubMed

Soares, Daniel V; Bitencourt, Marcelo C; Loureiro, Juliana B R; Silva Freire, Atila P

2018-01-01

The present work investigates the role of different treatments of the lower boundary condition on the numerical prediction of bubbly flows. Two different wall function formulations are tested against experimental data obtained for bubbly boundary layers: (i) a new analytical solution derived through asymptotic techniques and (ii) the previous formulation of Troshko and Hassan (IJHMT, 44, 871-875, 2001a). A modified k-e model is used to close the averaged Navier-Stokes equations together with the hypothesis that turbulence can be modelled by a linear superposition of bubble and shear induced eddy viscosities. The work shows, in particular, how four corrections must the implemented in the standard single-phase k-e model to account for the effects of bubbles. The numerical implementation of the near wall functions is made through a finite elements code.

Lattice study of finite volume effect in HVP for muon g-2

NASA Astrophysics Data System (ADS)

Izubuchi, Taku; Kuramashi, Yoshinobu; Lehner, Christoph; Shintani, Eigo

2018-03-01

We study the finite volume effect of the hadronic vacuum polarization contribution to muon g-2, aμhvp, in lattice QCD by comparison with two different volumes, L4 = (5.4)4 and (8.1)4 fm4, at physical pion. We perform the lattice computation of highly precise vector-vector current correlator with optimized AMA technique on Nf = 2 + 1 PACS gauge configurations in Wilson-clover fermion and stout smeared gluon action at one lattice cut-off, a-1 = 2.33 GeV. We compare two integrals of aμhvp, momentum integral and time-slice summation, on the lattice and numerically show that the different size of finite volume effect appears between two methods. We also discuss the effect of backward-state propagation into the result of aμhvp with the different boundary condition. Our model-independent study suggest that the lattice computation at physical pion is important for correct estimate of finite volume and other lattice systematics in aμhvp.

A mimetic finite difference method for the Stokes problem with elected edge bubbles

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

Lipnikov, K; Berirao, L

2009-01-01

A new mimetic finite difference method for the Stokes problem is proposed and analyzed. The unstable P{sub 1}-P{sub 0} discretization is stabilized by adding a small number of bubble functions to selected mesh edges. A simple strategy for selecting such edges is proposed and verified with numerical experiments. The discretizations schemes for Stokes and Navier-Stokes equations must satisfy the celebrated inf-sup (or the LBB) stability condition. The stability condition implies a balance between discrete spaces for velocity and pressure. In finite elements, this balance is frequently achieved by adding bubble functions to the velocity space. The goal of this articlemore » is to show that the stabilizing edge bubble functions can be added only to a small set of mesh edges. This results in a smaller algebraic system and potentially in a faster calculations. We employ the mimetic finite difference (MFD) discretization technique that works for general polyhedral meshes and can accomodate non-uniform distribution of stabilizing bubbles.« less

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).

A Kernel-free Boundary Integral Method for Elliptic Boundary Value Problems ⋆

PubMed Central

Ying, Wenjun; Henriquez, Craig S.

2013-01-01

This paper presents a class of kernel-free boundary integral (KFBI) methods for general elliptic boundary value problems (BVPs). The boundary integral equations reformulated from the BVPs are solved iteratively with the GMRES method. During the iteration, the boundary and volume integrals involving Green's functions are approximated by structured grid-based numerical solutions, which avoids the need to know the analytical expressions of Green's functions. The KFBI method assumes that the larger regular domain, which embeds the original complex domain, can be easily partitioned into a hierarchy of structured grids so that fast elliptic solvers such as the fast Fourier transform (FFT) based Poisson/Helmholtz solvers or those based on geometric multigrid iterations are applicable. The structured grid-based solutions are obtained with standard finite difference method (FDM) or finite element method (FEM), where the right hand side of the resulting linear system is appropriately modified at irregular grid nodes to recover the formal accuracy of the underlying numerical scheme. Numerical results demonstrating the efficiency and accuracy of the KFBI methods are presented. It is observed that the number of GM-RES iterations used by the method for solving isotropic and moderately anisotropic BVPs is independent of the sizes of the grids that are employed to approximate the boundary and volume integrals. With the standard second-order FEMs and FDMs, the KFBI method shows a second-order convergence rate in accuracy for all of the tested Dirichlet/Neumann BVPs when the anisotropy of the diffusion tensor is not too strong. PMID:23519600

Material model measurements and predictions for a random pore poly(epsilon-caprolactone) scaffold.

PubMed

Quinn, T P; Oreskovic, T L; Landis, F A; Washburn, N R

2007-07-01

We investigated material models for a polymeric scaffold used for bone. The material was made by co-extruding poly(epsilon-caprolactone) (PCL), a biodegradable polyester, and poly(ethylene oxide) (PEO). The water soluble PEO was removed resulting in a porous scaffold. The stress-strain curve in compression was fit with a phenomenological model in hyperbolic form. This material model will be useful for designers for quasi-static analysis as it provides a simple form that can easily be used in finite element models. The ASTM D-1621 standard recommends using a secant modulus based on 10% strain. The resulting modulus has a smaller scatter in its value compared with the coefficients of the hyperbolic model, and it is therefore easier to compare differences in material processing and ensure quality of the scaffold. A prediction of the small-strain elastic modulus was constructed from images of the microstructure. Each pixel of the micrographs was represented with a brick finite element and assigned the Young's modulus of bulk PCL or a value of 0 for a pore. A compressive strain was imposed on the model and the resulting stresses were calculated. The elastic constants of the scaffold were then computed with Hooke's law for a linear-elastic isotropic material. The model was able to predict the small-strain elastic modulus measured in the experiments to within one standard deviation. Thus, by knowing the microstructure of the scaffold, its bulk properties can be predicted from the material properties of the constituents. Copyright 2006 Wiley Periodicals, Inc.