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.

Full numerical simulation of coflowing, axisymmetric jet diffusion flames

NASA Technical Reports Server (NTRS)

Mahalingam, S.; Cantwell, B. J.; Ferziger, J. H.

1990-01-01

The near field of a non-premixed flame in a low speed, coflowing axisymmetric jet is investigated numerically using full simulation. The time-dependent governing equations are solved by a second-order, explicit finite difference scheme and a single-step, finite rate model is used to represent the chemistry. Steady laminar flame results show the correct dependence of flame height on Peclet number and reaction zone thickness on Damkoehler number. Forced simulations reveal a large difference in the instantaneous structure of scalar dissipation fields between nonbuoyant and buoyant cases. In the former, the scalar dissipation marks intense reaction zones, supporting the flamelet concept; however, results suggest that flamelet modeling assumptions need to be reexamined. In the latter, this correspondence breaks down, suggesting that modifications to the flamelet modeling approach are needed in buoyant turbulent diffusion flames.

The least-squares finite element method for low-mach-number compressible viscous flows

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao

1994-01-01

The present paper reports the development of the Least-Squares Finite Element Method (LSFEM) for simulating compressible viscous flows at low Mach numbers in which the incompressible flows pose as an extreme. Conventional approach requires special treatments for low-speed flows calculations: finite difference and finite volume methods are based on the use of the staggered grid or the preconditioning technique; and, finite element methods rely on the mixed method and the operator-splitting method. In this paper, however, we show that such difficulty does not exist for the LSFEM and no special treatment is needed. The LSFEM always leads to a symmetric, positive-definite matrix through which the compressible flow equations can be effectively solved. Two numerical examples are included to demonstrate the method: first, driven cavity flows at various Reynolds numbers; and, buoyancy-driven flows with significant density variation. Both examples are calculated by using full compressible flow equations.

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 finite element beam propagation method for simulation of liquid crystal devices.

PubMed

Vanbrabant, Pieter J M; Beeckman, Jeroen; Neyts, Kristiaan; James, Richard; Fernandez, F Anibal

2009-06-22

An efficient full-vectorial finite element beam propagation method is presented that uses higher order vector elements to calculate the wide angle propagation of an optical field through inhomogeneous, anisotropic optical materials such as liquid crystals. The full dielectric permittivity tensor is considered in solving Maxwell's equations. The wide applicability of the method is illustrated with different examples: the propagation of a laser beam in a uniaxial medium, the tunability of a directional coupler based on liquid crystals and the near-field diffraction of a plane wave in a structure containing micrometer scale variations in the transverse refractive index, similar to the pixels of a spatial light modulator.

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

NASA Astrophysics Data System (ADS)

Yi, Tae-Hyeong; Park, Ja-Rin

2017-06-01

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

A conservative finite difference algorithm for the unsteady transonic potential equation in generalized coordinates

NASA Technical Reports Server (NTRS)

Bridgeman, J. O.; Steger, J. L.; Caradonna, F. X.

1982-01-01

An implicit, approximate-factorization, finite-difference algorithm has been developed for the computation of unsteady, inviscid transonic flows in two and three dimensions. The computer program solves the full-potential equation in generalized coordinates in conservation-law form in order to properly capture shock-wave position and speed. A body-fitted coordinate system is employed for the simple and accurate treatment of boundary conditions on the body surface. The time-accurate algorithm is modified to a conventional ADI relaxation scheme for steady-state computations. Results from two- and three-dimensional steady and two-dimensional unsteady calculations are compared with existing methods.

Models and finite element approximations for interacting nanosized piezoelectric bodies and acoustic medium

NASA Astrophysics Data System (ADS)

Nasedkin, A. V.

2017-01-01

This research presents the new size-dependent models of piezoelectric materials oriented to finite element applications. The proposed models include the facilities of taking into account different mechanisms of damping for mechanical and electric fields. The coupled models also incorporate the equations of the theory of acoustics for viscous fluids. In particular cases, these models permit to use the mode superposition method with full separation of the finite element systems into independent equations for the independent modes for transient and harmonic problems. The main boundary conditions were supplemented with the facilities of taking into account the coupled surface effects, allowing to explore the nanoscale piezoelectric materials in the framework of theories of continuous media with surface stresses and their generalizations. For the considered problems we have implemented the finite element technologies and various numerical algorithms to maintain a symmetrical structure of the finite element quasi-definite matrices (matrix structure for the problems with a saddle point).

Detailed puncture analyses tank cars : analysis of different impactor threats and impact conditions.

DOT National Transportation Integrated Search

2013-03-01

There has been significant research in recent years to analyze and improve the impact behavior and puncture resistance of railroad tank cars. Much of this research has been performed using detailed nonlinear finite element analyses supported by full ...

Dynamic finite element method modeling of the upper shelf energy of precracked Charpy specimens of neutron irradiated weld metal 72W

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

Kumar, A.S.; Sidener, S.E.; Hamilton, M.L.

1999-10-01

Dynamic finite element modeling of the fracture behavior of fatigue-precracked Charpy specimens in both unirradiated and irradiated conditions was performed using a computer code, ABAQUS Explicit, to predict the upper shelf energy of precracked specimens of a given size from experimental data obtained for a different size. A tensile fracture-strain based method for modeling crack extension and propagation was used. It was found that the predicted upper shelf energies of full and half size precracked specimens based on third size data were in reasonable agreement with their respective experimental values. Similar success was achieved for predicting the upper shelf energymore » of subsize precracked specimens based on full size data.« less

Assessment of the measurement performance of the in-vessel system of gap 6 of the ITER plasma position reflectometer using a finite-difference time-domain Maxwell full-wave code.

PubMed

da Silva, F; Heuraux, S; Ricardo, E; Quental, P; Ferreira, J

2016-11-01

We conducted a first assessment of the measurement performance of the in-vessel components at gap 6 of the ITER plasma position reflectometry with the aid of a synthetic Ordinary Mode (O-mode) broadband frequency-modulated continuous-wave reflectometer implemented with REFMUL, a 2D finite-difference time-domain full-wave Maxwell code. These simulations take into account the system location within the vacuum vessel as well as its access to the plasma. The plasma case considered is a baseline scenario from Fusion for Energy. We concluded that for the analyzed scenario, (i) the plasma curvature and non-equatorial position of the antenna have neglectable impact on the measurements; (ii) the cavity-like space surrounding the antenna can cause deflection and splitting of the probing beam; and (iii) multi-reflections on the blanket wall cause a substantial error preventing the system from operating within the required error margin.

Application of a finite-element model to low-frequency sound insulation in dwellings.

PubMed

Maluski, S P; Gibbs, B M

2000-10-01

The sound transmission between adjacent rooms has been modeled using a finite-element method. Predicted sound-level difference gave good agreement with experimental data using a full-scale and a quarter-scale model. Results show that the sound insulation characteristics of a party wall at low frequencies strongly depend on the modal characteristics of the sound field of both rooms and of the partition. The effect of three edge conditions of the separating wall on the sound-level difference at low frequencies was examined: simply supported, clamped, and a combination of clamped and simply supported. It is demonstrated that a clamped partition provides greater sound-level difference at low frequencies than a simply supported. It also is confirmed that the sound-pressure level difference is lower in equal room than in unequal room configurations.

Thermodynamics of Gas Turbine Cycles with Analytic Derivatives in OpenMDAO

NASA Technical Reports Server (NTRS)

Gray, Justin; Chin, Jeffrey; Hearn, Tristan; Hendricks, Eric; Lavelle, Thomas; Martins, Joaquim R. R. A.

2016-01-01

A new equilibrium thermodynamics analysis tool was built based on the CEA method using the OpenMDAO framework. The new tool provides forward and adjoint analytic derivatives for use with gradient based optimization algorithms. The new tool was validated against the original CEA code to ensure an accurate analysis and the analytic derivatives were validated against finite-difference approximations. Performance comparisons between analytic and finite difference methods showed a significant speed advantage for the analytic methods. To further test the new analysis tool, a sample optimization was performed to find the optimal air-fuel equivalence ratio, , maximizing combustion temperature for a range of different pressures. Collectively, the results demonstrate the viability of the new tool to serve as the thermodynamic backbone for future work on a full propulsion modeling tool.

Effect of Framework in an Implant-Supported Full-Arch Fixed Prosthesis: 3D Finite Element Analysis.

PubMed

Menini, Maria; Pesce, Paolo; Bevilacqua, Marco; Pera, Francesco; Tealdo, Tiziano; Barberis, Fabrizio; Pera, Paolo

2015-01-01

The aim of this study was to analyze through a three-dimensional finite element analysis (3D-FEA) stress distribution on four implants supporting a full-arch implant-supported fixed prosthesis (FFP) using different prosthesis designs. A 3D edentulous maxillary model was created and four implants were virtually placed into the maxilla and splinted, simulating an FFP without framework, with a cast metal framework, and with a carbon fiber framework. An occlusal load of 150 N was applied, stresses were transmitted into peri-implant bone, and prosthodontic components were recorded. 3D-FEA revealed higher stresses on the implants (up to +55.16%), on peri-implant bone (up to +56.93%), and in the prosthesis (up to +70.71%) when the full-acrylic prosthesis was simulated. The prosthesis with a carbon fiber framework showed an intermediate behavior between that of the other two configurations. This study suggests that the presence of a rigid framework in full-arch fixed prostheses provides a better load distribution that decreases the maximum values of stress at the levels of implants, prosthesis, and maxillary bone.

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

Giunta, G.; Belouettar, S.

In this paper, the static response of three-dimensional beams made of functionally graded materials is investigated through a family of hierarchical one-dimensional finite elements. A wide variety of elements is proposed differing by the kinematic formulation and the number of nodes per elements along the beam axis. Elements’ stiffness matrix and load vector are derived in a unified nuclear form that does not depend upon the a priori expansion order over the cross-section nor the finite element approximation along the beam axis. Results are validated towards three-dimensional finite element models as well as equivalent Navier-type analytical solutions. The numerical investigationsmore » show that accurate and efficient solutions (when compared with full three-dimensional FEM solutions) can be obtained by the proposed family of hierarchical one-dimensional elements’ family.« less

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.

An implicit finite-difference solution to the viscous shock layer, including the effects of radiation and strong blowing

NASA Technical Reports Server (NTRS)

Garrett, L. B.; Smith, G. L.; Perkins, J. N.

1972-01-01

An implicit finite-difference scheme is developed for the fully coupled solution of the viscous, radiating stagnation-streamline equations, including strong blowing. Solutions are presented for both air injection and injection of carbon-phenolic ablation products into air at conditions near the peak radiative heating point in an earth entry trajectory from interplanetary return missions. A detailed radiative-transport code that accounts for the important radiative exchange processes for gaseous mixtures in local thermodynamic and chemical equilibrium is utilized in the study. With minimum number of assumptions for the initially unknown parameters and profile distributions, convergent solutions to the full stagnation-line equations are rapidly obtained by a method of successive approximations. Damping of selected profiles is required to aid convergence of the solutions for massive blowing. It is shown that certain finite-difference approximations to the governing differential equations stabilize and improve the solutions. Detailed comparisons are made with the numerical results of previous investigations. Results of the present study indicate lower radiative heat fluxes at the wall for carbonphenolic ablation than previously predicted.

The Method of Fundamental Solutions using the Vector Magnetic Dipoles for Calculation of the Magnetic Fields in the Diagnostic Problems Based on Full-Scale Modelling Experiment

NASA Astrophysics Data System (ADS)

Bakhvalov, Yu A.; Grechikhin, V. V.; Yufanova, A. L.

2016-04-01

The article describes the calculation of the magnetic fields in the problems diagnostic of technical systems based on the full-scale modeling experiment. Use of gridless fundamental solution method and its variants in combination with grid methods (finite differences and finite elements) are allowed to considerably reduce the dimensionality task of the field calculation and hence to reduce calculation time. When implementing the method are used fictitious magnetic charges. In addition, much attention is given to the calculation accuracy. Error occurs when wrong choice of the distance between the charges. The authors are proposing to use vector magnetic dipoles to improve the accuracy of magnetic fields calculation. Examples of this approacharegiven. The article shows the results of research. They are allowed to recommend the use of this approach in the method of fundamental solutions for the full-scale modeling tests of technical systems.

Finite spaces and schemes

NASA Astrophysics Data System (ADS)

Sancho de Salas, Fernando

2017-12-01

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed space, endowed with a finite open covering, produces a ringed finite space. We introduce the notions of schematic finite space and schematic morphism, showing that they behave, with respect to quasi-coherence, like schemes and morphisms of schemes do. Finally, we construct a fully faithful and essentially surjective functor from a localization of a full subcategory of the category of schematic finite spaces and schematic morphisms to the category of quasi-compact and quasi-separated schemes.

Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation

NASA Technical Reports Server (NTRS)

Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E.; Melvin, Robin G.; Young, David P.

1996-01-01

We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact finite-difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner. We demonstrate that NKS, combined with a density upwinding continuation strategy for problems with weak shocks, is robust and, economical for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributed-memory parallel computer.

Full-wave Moment Tensor and Tomographic Inversions Based on 3D Strain Green Tensor

DTIC Science & Technology

2010-01-31

propagation in three-dimensional (3D) earth, linearizes the inverse problem by iteratively updating the earth model , and provides an accurate way to...self-consistent FD-SGT databases constructed from finite-difference simulations of wave propagation in full-wave tomographic models can be used to...determine the moment tensors within minutes after a seismic event, making it possible for real time monitoring using 3D models . 15. SUBJECT TERMS

Linear and nonlinear pattern selection in Rayleigh-Benard stability problems

NASA Technical Reports Server (NTRS)

Davis, Sanford S.

1993-01-01

A new algorithm is introduced to compute finite-amplitude states using primitive variables for Rayleigh-Benard convection on relatively coarse meshes. The algorithm is based on a finite-difference matrix-splitting approach that separates all physical and dimensional effects into one-dimensional subsets. The nonlinear pattern selection process for steady convection in an air-filled square cavity with insulated side walls is investigated for Rayleigh numbers up to 20,000. The internalization of disturbances that evolve into coherent patterns is investigated and transient solutions from linear perturbation theory are compared with and contrasted to the full numerical simulations.

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

Kim, K.; Petersson, N. A.; Rodgers, A.

Acoustic waveform modeling is a computationally intensive task and full three-dimensional simulations are often impractical for some geophysical applications such as long-range wave propagation and high-frequency sound simulation. In this study, we develop a two-dimensional high-order accurate finite-difference code for acoustic wave modeling. We solve the linearized Euler equations by discretizing them with the sixth order accurate finite difference stencils away from the boundary and the third order summation-by-parts (SBP) closure near the boundary. Non-planar topographic boundary is resolved by formulating the governing equation in curvilinear coordinates following the interface. We verify the implementation of the algorithm by numerical examplesmore » and demonstrate the capability of the proposed method for practical acoustic wave propagation problems in the atmosphere.« less

User's Guide for ENSAERO_FE Parallel Finite Element Solver

NASA Technical Reports Server (NTRS)

Eldred, Lloyd B.; Guruswamy, Guru P.

1999-01-01

A high fidelity parallel static structural analysis capability is created and interfaced to the multidisciplinary analysis package ENSAERO-MPI of Ames Research Center. This new module replaces ENSAERO's lower fidelity simple finite element and modal modules. Full aircraft structures may be more accurately modeled using the new finite element capability. Parallel computation is performed by breaking the full structure into multiple substructures. This approach is conceptually similar to ENSAERO's multizonal fluid analysis capability. The new substructure code is used to solve the structural finite element equations for each substructure in parallel. NASTRANKOSMIC is utilized as a front end for this code. Its full library of elements can be used to create an accurate and realistic aircraft model. It is used to create the stiffness matrices for each substructure. The new parallel code then uses an iterative preconditioned conjugate gradient method to solve the global structural equations for the substructure boundary nodes.

A Finite-Orbit-Width Fokker-Planck solver for modeling of energetic particle interactions with waves, with application to Helicons in ITER

NASA Astrophysics Data System (ADS)

Petrov, Yuri V.; Harvey, R. W.

2017-10-01

The bounce-average (BA) finite-difference Fokker-Planck (FP) code CQL3D [1,2] now includes the essential physics to describe the RF heating of Finite-Orbit-Width (FOW) ions in tokamaks. The FP equation is reformulated in terms of Constants-Of-Motion coordinates, which we select to be particle speed, pitch angle, and major radius on the equatorial plane thus obtaining the distribution function directly at this location. Full-orbit, low collisionality neoclassical radial transport emerges from averaging the local friction and diffusion coefficients along guiding center orbits. Similarly, the BA of local quasilinear RF diffusion terms gives rise to additional radial transport. The local RF electric field components needed for the BA operator are usually obtained by a ray-tracing code, such as GENRAY, or in conjunction with full-wave codes. As a new, practical application, the CQL3D-FOW version is used for simulation of alpha-particle heating by high-harmonic waves in ITER. Coupling of high harmonic or helicon fast waves power to electrons is a promising current drive (CD) scenario for high beta plasmas. However, the efficiency of current drive can be diminished by parasitic channeling of RF power into fast ions, such as alphas, through finite Larmor-radius effects. We investigate possibilities to reduce the fast ion heating in CD scenarios.

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.

A Locally Modal B-Spline Based Full-Vector Finite-Element Method with PML for Nonlinear and Lossy Plasmonic Waveguide

NASA Astrophysics Data System (ADS)

Karimi, Hossein; Nikmehr, Saeid; Khodapanah, Ehsan

2016-09-01

In this paper, we develop a B-spline finite-element method (FEM) based on a locally modal wave propagation with anisotropic perfectly matched layers (PMLs), for the first time, to simulate nonlinear and lossy plasmonic waveguides. Conventional approaches like beam propagation method, inherently omit the wave spectrum and do not provide physical insight into nonlinear modes especially in the plasmonic applications, where nonlinear modes are constructed by linear modes with very close propagation constant quantities. Our locally modal B-spline finite element method (LMBS-FEM) does not suffer from the weakness of the conventional approaches. To validate our method, first, propagation of wave for various kinds of linear, nonlinear, lossless and lossy materials of metal-insulator plasmonic structures are simulated using LMBS-FEM in MATLAB and the comparisons are made with FEM-BPM module of COMSOL Multiphysics simulator and B-spline finite-element finite-difference wide angle beam propagation method (BSFEFD-WABPM). The comparisons show that not only our developed numerical approach is computationally more accurate and efficient than conventional approaches but also it provides physical insight into the nonlinear nature of the propagation modes.

Methodologies for validating ray-based forward model using finite element method in ultrasonic array data simulation

NASA Astrophysics Data System (ADS)

Zhang, Jie; Nixon, Andrew; Barber, Tom; Budyn, Nicolas; Bevan, Rhodri; Croxford, Anthony; Wilcox, Paul

2018-04-01

In this paper, a methodology of using finite element (FE) model to validate a ray-based model in the simulation of full matrix capture (FMC) ultrasonic array data set is proposed. The overall aim is to separate signal contributions from different interactions in FE results for easier comparing each individual component in the ray-based model results. This is achieved by combining the results from multiple FE models of the system of interest that include progressively more geometrical features while preserving the same mesh structure. It is shown that the proposed techniques allow the interactions from a large number of different ray-paths to be isolated in FE results and compared directly to the results from a ray-based forward model.

Failure analysis of various monolithic posterior aesthetic dental crowns using finite element method

NASA Astrophysics Data System (ADS)

Porojan, Liliana; Topală, Florin

2017-08-01

The aim of the study was to assess the effect of material stiffness and load on the biomechanical performance of the monolithic full-coverage posterior aesthetic dental crowns using finite element analysis. Three restorative materials for monolithic dental crowns were selected for the study: zirconia; lithium disilicate glass-ceramic, and resin-based composite. Stresses were calculated in the crowns for all materials and in the teeth structures, under different load values. The experiments show that dental crowns made from all this new aesthetic materials processed by CAD/CAM technologies would be indicated as monolithic dental crowns for posterior areas.

On the structure of viscous flow about the afterbody of hull

NASA Astrophysics Data System (ADS)

Yoshida, Osamu; Zhu, Ming; Miyata, Hideaki

1993-09-01

A finite-volume method is applied to a flow about full ship models in the curvilinear coordinate system. Simulations are carried out for SR196 frame-line series. The simulated results show the difference of the wake and the longitudinal vorticity between the different hull forms. The comparisons between simulated and measured results show qualitative agreements in the wake distributions near the propeller disk circumference.

System-Integrated Finite Element Analysis of a Full-Scale Helicopter Crash Test with Deployable Energy Absorbers

NASA Technical Reports Server (NTRS)

Annett, Martin S.; Polanco, Michael A.

2010-01-01

A full-scale crash test of an MD-500 helicopter was conducted in December 2009 at NASA Langley's Landing and Impact Research facility (LandIR). The MD-500 helicopter was fitted with a composite honeycomb Deployable Energy Absorber (DEA) and tested under vertical and horizontal impact velocities of 26-ft/sec and 40-ft/sec, respectively. The objectives of the test were to evaluate the performance of the DEA concept under realistic crash conditions and to generate test data for validation of a system integrated finite element model. In preparation for the full-scale crash test, a series of sub-scale and MD-500 mass simulator tests was conducted to evaluate the impact performances of various components, including a new crush tube and the DEA blocks. Parameters defined within the system integrated finite element model were determined from these tests. The objective of this paper is to summarize the finite element models developed and analyses performed, beginning with pre-test predictions and continuing through post-test validation.

Insights into the Behavior of Potential Structural Failures Originating from Localized High Stress Regions in Configurations Relevant to Solid Rocket Motor Nozzles

NASA Technical Reports Server (NTRS)

McCutcheon, David Matthew

2017-01-01

During the structural certification effort for the Space Launch System solid rocket booster nozzle, it was identified that no consistent method for addressing local negative margins of safety in non-metallic materials had been developed. Relevant areas included bond-line terminations and geometric features in the composite nozzle liners. In order to gain understanding, analog test specimens were designed that very closely mimic the conditions in the actual full scale hardware. Different locations in the nozzle were represented by different analog specimen designs. This paper describes those tests and corresponding results. Finite element analysis results for the tests are presented. Strain gage correlation of the analysis to the test results is addressed. Furthermore, finite fracture mechanics (a coupled stress and energy failure criterion) is utilized to predict the observed crack pop-in loads for the different configurations. The finite fracture mechanics predictions are found to be within a 10% error relative to the average measured pop-in load for each of four configurations. Initiation locations, arrest behaviors, and resistances to further post-arrest crack propagation are also discussed.

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

NASA Astrophysics Data System (ADS)

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

2009-04-01

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

Single Polygon Counting on Cayley Tree of Order 3

NASA Astrophysics Data System (ADS)

Pah, Chin Hee

2010-07-01

We showed that one form of generalized Catalan numbers is the solution to the problem of finding different connected component with finite vertices containing a fixed root for the semi-infinite Cayley tree of order 3. We give the formula for the full graph, Cayley tree of order 3 which is derived from the generalized Catalan numbers. Using ratios of Gamma functions, two upper bounds are given for problem defined on semi-infinite Cayley tree of order 3 as well as the full graph.

Viscoelastic Finite Difference Modeling Using Graphics Processing Units

NASA Astrophysics Data System (ADS)

Fabien-Ouellet, G.; Gloaguen, E.; Giroux, B.

2014-12-01

Full waveform seismic modeling requires a huge amount of computing power that still challenges today's technology. This limits the applicability of powerful processing approaches in seismic exploration like full-waveform inversion. This paper explores the use of Graphics Processing Units (GPU) to compute a time based finite-difference solution to the viscoelastic wave equation. The aim is to investigate whether the adoption of the GPU technology is susceptible to reduce significantly the computing time of simulations. The code presented herein is based on the freely accessible software of Bohlen (2002) in 2D provided under a General Public License (GNU) licence. This implementation is based on a second order centred differences scheme to approximate time differences and staggered grid schemes with centred difference of order 2, 4, 6, 8, and 12 for spatial derivatives. The code is fully parallel and is written using the Message Passing Interface (MPI), and it thus supports simulations of vast seismic models on a cluster of CPUs. To port the code from Bohlen (2002) on GPUs, the OpenCl framework was chosen for its ability to work on both CPUs and GPUs and its adoption by most of GPU manufacturers. In our implementation, OpenCL works in conjunction with MPI, which allows computations on a cluster of GPU for large-scale model simulations. We tested our code for model sizes between 1002 and 60002 elements. Comparison shows a decrease in computation time of more than two orders of magnitude between the GPU implementation run on a AMD Radeon HD 7950 and the CPU implementation run on a 2.26 GHz Intel Xeon Quad-Core. The speed-up varies depending on the order of the finite difference approximation and generally increases for higher orders. Increasing speed-ups are also obtained for increasing model size, which can be explained by kernel overheads and delays introduced by memory transfers to and from the GPU through the PCI-E bus. Those tests indicate that the GPU memory size and the slow memory transfers are the limiting factors of our GPU implementation. Those results show the benefits of using GPUs instead of CPUs for time based finite-difference seismic simulations. The reductions in computation time and in hardware costs are significant and open the door for new approaches in seismic inversion.

Determination of temperature dependence of full matrix material constants of PZT-8 piezoceramics using only one sample.

PubMed

Zhang, Yang; Tang, Liguo; Tian, Hua; Wang, Jiyang; Cao, Wenwu; Zhang, Zhongwu

2017-08-15

Resonant ultrasound spectroscopy (RUS) was used to determine the temperature dependence of full matrix material constants of PZT-8 piezoceramics from room temperature to 100 °C. Property variations from sample to samples can be eliminated by using only one sample, so that data self-consistency can be guaranteed. The RUS measurement system error was estimated to be lower than 2.35%. The obtained full matrix material constants at different temperatures all have excellent self-consistency, which can help accurately predict device performance at high temperatures using finite element simulations.

Effect of platform switching on the peri-implant bone: A finite element study

PubMed Central

Martínez-González, Amparo; Peiró, Germán; Ródenas, Juan-José; López-Mollá, María-Victoria

2015-01-01

Background There exists a relation between the presence and location of the micro-gap and the loss of peri implant bone. Several authors have shown that the treatments based on the use of platform switching result in less peri-implant bone loss and an increased tissue stability. The purpose of this study was to analyse the effect of the platform switching on the distribution of stresses on the peri-implant bone using the finite element method. Material and Methods A realistic 3D full-mandible finite element model representing cortical bone and trabecular bone was used to study the distribution of the stress on the bone induced by an implant of diameter 4.1 mm. Two abutments were modelled. The first one, of diameter 4.1 mm, was used in the reference model to represent a conventional implant. The second one, of diameter 3.2 mm, was used to represent the implant with platform switching. Both models were subjected to axial and oblique masticatory loads. Results The analyses showed that, although no relevant differences can be found for the trabecular bone, the use of platform switching reduces the maximum stress level in the cortical bone by almost 36% with axial loads and by 40% with oblique loads. Conclusions The full 3D Finite Element model, that can be used to investigate the influence of other parameters (implant diameter, connexion type, …) on the biomechanical behaviour of the implant, showed that this stress reduction can be a biomechanical reasons to explain why the platform switching seems to reduce or eliminate crestal bone resorption after the prosthetic restoration. Key words:Dental implant, platform switching, finite element method. PMID:26535094

Quantitative magneto-optical analysis of the role of finite temperatures on the critical state in YBCO thin films

NASA Astrophysics Data System (ADS)

Albrecht, Joachim; Brück, Sebastian; Stahl, Claudia; Ruoß, Stephen

2016-11-01

We use quantitative magneto-optical microscopy to investigate the influence of finite temperatures on the critical state of thin YBCO films. In particular, temperature and time dependence of supercurrents in inhomogeneous and anisotropic films are analyzed to extract the role of temperature on the supercurrents themselves and the influence of thermally activated relaxation. We find that inhomogeneities and anisotropies of the current density distribution correspond to a different temperature dependence of local supercurrents. In addition, the thermally activated decay of supercurrents can be used to extract local vortex pinning energies. With these results the modification of vortex pinning introduced by substrate structures is studied. In summary the local investigation of supercurrent densities allows the full description of the vortex pinning landscape with respect to pinning forces and energies in superconducting films with complex properties under the influence of finite temperatures.

Identification of material parameters for plasticity models: A comparative study on the finite element model updating and the virtual fields method

NASA Astrophysics Data System (ADS)

Martins, J. M. P.; Thuillier, S.; Andrade-Campos, A.

2018-05-01

The identification of material parameters, for a given constitutive model, can be seen as the first step before any practical application. In the last years, the field of material parameters identification received an important boost with the development of full-field measurement techniques, such as Digital Image Correlation. These techniques enable the use of heterogeneous displacement/strain fields, which contain more information than the classical homogeneous tests. Consequently, different techniques have been developed to extract material parameters from full-field measurements. In this study, two of these techniques are addressed, the Finite Element Model Updating (FEMU) and the Virtual Fields Method (VFM). The main idea behind FEMU is to update the parameters of a constitutive model implemented in a finite element model until both numerical and experimental results match, whereas VFM makes use of the Principle of Virtual Work and does not require any finite element simulation. Though both techniques proved their feasibility in linear and non-linear constitutive models, it is rather difficult to rank their robustness in plasticity. The purpose of this work is to perform a comparative study in the case of elasto-plastic models. Details concerning the implementation of each strategy are presented. Moreover, a dedicated code for VFM within a large strain framework is developed. The reconstruction of the stress field is performed through a user subroutine. A heterogeneous tensile test is considered to compare FEMU and VFM strategies.

Application of an asymmetric finite element model of the C2-T1 cervical spine for evaluating the role of soft tissues in stability.

PubMed

Erbulut, D U; Zafarparandeh, I; Lazoglu, I; Ozer, A F

2014-07-01

Different finite element models of the cervical spine have been suggested for evaluating the roles of ligaments, facet joints, and disks in the stability of cervical spine under sagittal moments. However, no comprehensive study on the response of the full cervical spine that has used a detailed finite element (FE) model (C2-T1) that considers the asymmetry about the mid-sagittal plane has been reported. The aims of this study were to consider asymmetry in a FE model of the full cervical spine and to investigate the influences of ligaments, facet joints, and disk nucleus on the stability of the asymmetric model during flexion and extension. The model was validated against various published in vitro studies and FE studies for the three main loading planes. Next, the C4-C5 level was modified to simulate different cases to investigate the role of the soft tissues in segmental stability. The FE model predicted that excluding the interspinous ligament (ISL) from the index level would cause excessive instability during flexion and that excluding the posterior longitudinal ligament (PLL) or the ligamentum flavum (LF) would not affect segmental rotation. During extension, motion increased when the facet joints were excluded. The model without disk nucleus was unstable compared to the intact model at lower loads and exhibited a similar rotation response at higher loads. Copyright © 2014 IPEM. Published by Elsevier Ltd. All rights reserved.

Divergence correction schemes in finite difference method for 3D tensor CSAMT in axial anisotropic media

NASA Astrophysics Data System (ADS)

Wang, Kunpeng; Tan, Handong; Zhang, Zhiyong; Li, Zhiqiang; Cao, Meng

2017-05-01

Resistivity anisotropy and full-tensor controlled-source audio-frequency magnetotellurics (CSAMT) have gradually become hot research topics. However, much of the current anisotropy research for tensor CSAMT only focuses on the one-dimensional (1D) solution. As the subsurface is rarely 1D, it is necessary to study three-dimensional (3D) model response. The staggered-grid finite difference method is an effective simulation method for 3D electromagnetic forward modelling. Previous studies have suggested using the divergence correction to constrain the iterative process when using a staggered-grid finite difference model so as to accelerate the 3D forward speed and enhance the computational accuracy. However, the traditional divergence correction method was developed assuming an isotropic medium. This paper improves the traditional isotropic divergence correction method and derivation process to meet the tensor CSAMT requirements for anisotropy using the volume integral of the divergence equation. This method is more intuitive, enabling a simple derivation of a discrete equation and then calculation of coefficients related to the anisotropic divergence correction equation. We validate the result of our 3D computational results by comparing them to the results computed using an anisotropic, controlled-source 2.5D program. The 3D resistivity anisotropy model allows us to evaluate the consequences of using the divergence correction at different frequencies and for two orthogonal finite length sources. Our results show that the divergence correction plays an important role in 3D tensor CSAMT resistivity anisotropy research and offers a solid foundation for inversion of CSAMT data collected over an anisotropic body.

Finite T spectral function of a single carrier injected into an Ising chain: a comparison of 3 different models

NASA Astrophysics Data System (ADS)

Moeller, Mirko; Berciu, Mona

2015-03-01

When studying the properties of complex, magnetic materials it is often necessary to work with effective Hamiltonians. In many cases the effective Hamiltonian is obtained by mapping the full, multiband Hamiltonian onto a simpler, single band model. A prominent example is the use of Zhang-Rice singlets to map the multiband Emery model for cuprates onto the single band t - J -model. Such mappings are usually done at zero temperature (T) and it is implicitly assumed that they are justified at finite T, as well. We present results on 3 different models of a single charge carrier (electron or hole) injected into a ferromagnetic Ising chain. Model I is a two band, two sublattice model, Model II is a two band, single sublattice model, and Model III is a single band model, the so called t -Jz -model. Due to the absence of spin-flip terms, a numerically exact solution of all 3 Models is possible, even at finite T. At zero T a mapping between all 3 models results in the same low energy physics. However, this is no longer true at finite T. Here the low energy behavior of Model III is significantly different from that of Models I and II. The reasons for this discrepancy and its implications for more realistic models (higher dimension, inclusion of spin-flip terms) are discussed. This work was supported by NSERC, QMI and the UBC 4YF (M.M.).

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.

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.

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.

Directions for computational mechanics in automotive crashworthiness

NASA Technical Reports Server (NTRS)

Bennett, James A.; Khalil, T. B.

1993-01-01

The automotive industry has used computational methods for crashworthiness since the early 1970's. These methods have ranged from simple lumped parameter models to full finite element models. The emergence of the full finite element models in the mid 1980's has significantly altered the research direction. However, there remains a need for both simple, rapid modeling methods and complex detailed methods. Some directions for continuing research are discussed.

Directions for computational mechanics in automotive crashworthiness

NASA Astrophysics Data System (ADS)

Bennett, James A.; Khalil, T. B.

1993-08-01

The automotive industry has used computational methods for crashworthiness since the early 1970's. These methods have ranged from simple lumped parameter models to full finite element models. The emergence of the full finite element models in the mid 1980's has significantly altered the research direction. However, there remains a need for both simple, rapid modeling methods and complex detailed methods. Some directions for continuing research are discussed.

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size.

PubMed

Schwalger, Tilo; Deger, Moritz; Gerstner, Wulfram

2017-04-01

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50-2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations.

Determination of aerodynamic sensitivity coefficients based on the three-dimensional full potential equation

NASA Technical Reports Server (NTRS)

Elbanna, Hesham M.; Carlson, Leland A.

1992-01-01

The quasi-analytical approach is applied to the three-dimensional full potential equation to compute wing aerodynamic sensitivity coefficients in the transonic regime. Symbolic manipulation is used to reduce the effort associated with obtaining the sensitivity equations, and the large sensitivity system is solved using 'state of the art' routines. Results are compared to those obtained by the direct finite difference approach and both methods are evaluated to determine their computational accuracy and efficiency. The quasi-analytical approach is shown to be accurate and efficient for large aerodynamic systems.

CMS-Wave

DTIC Science & Technology

2015-10-30

Coastal Inlets Research Program CMS -Wave CMS -Wave is a two-dimensional spectral wind-wave generation and transformation model that employs a forward...marching, finite-difference method to solve the wave action conservation equation. Capabilities of CMS -Wave include wave shoaling, refraction... CMS -Wave can be used in either on a half- or full-plane mode, with primary waves propagating from the seaward boundary toward shore. It can

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

Gyrokinetic water-bag modeling of a plasma column: Magnetic moment distribution and finite Larmor radius effects

NASA Astrophysics Data System (ADS)

Klein, R.; Gravier, E.; Morel, P.; Besse, N.; Bertrand, P.

2009-08-01

Describing turbulent transport in fusion plasmas is a major concern in magnetic confinement fusion. It is now widely known that kinetic and fluid descriptions can lead to significantly different properties. Although more accurate, the kinetic calculation of turbulent transport is much more demanding of computer resources than fluid simulations. An alternative approach is based on a water-bag representation of the distribution function that is not an approximation but rather a special class of initial conditions, allowing one to reduce the full kinetic Vlasov equation into a set of hydrodynamics equations while keeping its kinetic character [P. Morel, E. Gravier, N. Besse et al., Phys. Plasmas 14, 112109 (2007)]. In this paper, the water-bag concept is used in a gyrokinetic context to study finite Larmor radius effects with the possibility of using the full Larmor radius distribution instead of an averaged Larmor radius. The resulting model is used to study the ion temperature gradient (ITG) instability.

Correlation of finite-element structural dynamic analysis with measured free vibration characteristics for a full-scale helicopter fuselage

NASA Technical Reports Server (NTRS)

Kenigsberg, I. J.; Dean, M. W.; Malatino, R.

1974-01-01

The correlation achieved with each program provides the material for a discussion of modeling techniques developed for general application to finite-element dynamic analyses of helicopter airframes. Included are the selection of static and dynamic degrees of freedom, cockpit structural modeling, and the extent of flexible-frame modeling in the transmission support region and in the vicinity of large cut-outs. The sensitivity of predicted results to these modeling assumptions are discussed. Both the Sikorsky Finite-Element Airframe Vibration analysis Program (FRAN/Vibration Analysis) and the NASA Structural Analysis Program (NASTRAN) have been correlated with data taken in full-scale vibration tests of a modified CH-53A helicopter.

Vibration effect on the Soret-induced convection of ternary mixture in a rectangular cavity heated from below

NASA Astrophysics Data System (ADS)

Lyubimova, T. P.; Zubova, N. A.

2017-06-01

This paper presents the results of numerical simulation of the Soret-induced convection of ternary mixture in the rectangular cavity elongated in horizontal direction in gravity field. The cavity has rigid impermeable boundaries. It is heated from the bellow and undergoes translational linearly polarized vibrations of finite amplitude and frequency in the horizontal direction. The problem is solved by finite difference method in the framework of full unsteady non-linear approach. The procedure of diagonalization of the molecular diffusion coefficient matrix is applied, allowing to eliminate cross-diffusion components in the equations and to reduce the number of the governing parameters. The calculations are performed for model ternary mixture with positive separation ratios of the components. The data on the vibration effect on temporal evolution of instantaneous and average fields and integral characteristics of the flow and heat and mass transfer at different levels of gravity are obtained.

Spiral vortices and Taylor vortices in the annulus between rotating cylinders and the effect of an axial flow.

PubMed

Hoffmann, Ch; Lücke, M; Pinter, A

2004-05-01

We present numerical simulations of vortices that appear via primary bifurcations out of the unstructured circular Couette flow in the Taylor-Couette system with counter rotating as well as with corotating cylinders. The full, time dependent Navier Stokes equations are solved with a combination of a finite difference and a Galerkin method for a fixed axial periodicity length of the vortex patterns and for a finite system of aspect ratio 12 with rigid nonrotating ends in a setup with radius ratio eta=0.5. Differences in structure, dynamics, symmetry properties, bifurcation, and stability behavior between spiral vortices with azimuthal wave numbers M=+/-1 and M=0 Taylor vortices are elucidated and compared in quantitative detail. Simulations in axially periodic systems and in finite systems with stationary rigid ends are compared with experimental spiral data. In a second part of the paper we determine how the above listed properties of the M=-1, 0, and 1 vortex structures are changed by an externally imposed axial through flow with Reynolds numbers in the range -40< or =Re< or =40. Among other things we investigate when left handed or right handed spirals or toroidally closed vortices are preferred.

Modeling of NiTiHf using finite difference method

NASA Astrophysics Data System (ADS)

Farjam, Nazanin; Mehrabi, Reza; Karaca, Haluk; Mirzaeifar, Reza; Elahinia, Mohammad

2018-03-01

NiTiHf is a high temperature and high strength shape memory alloy with transformation temperatures above 100oC. A constitutive model based on Gibbs free energy is developed to predict the behavior of this material. Two different irrecoverable strains including transformation induced plastic strain (TRIP) and viscoplastic strain (VP) are considered when using high temperature shape memory alloys (HTSMAs). The first one happens during transformation at high levels of stress and the second one is related to the creep which is rate-dependent. The developed model is implemented for NiTiHf under uniaxial loading. Finite difference method is utilized to solve the proposed equations. The material parameters in the equations are calibrated from experimental data. Simulation results are captured to investigate the superelastic behavior of NiTiHf. The extracted results are compared with experimental tests of isobaric heating and cooling at different levels of stress and also superelastic tests at different levels of temperature. More results are generated to investigate the capability of the proposed model in the prediction of the irrecoverable strain after full transformation in HTSMAs.

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

A time accurate finite volume high resolution scheme for three dimensional Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing; Hsu, Andrew T.

1989-01-01

A time accurate, three-dimensional, finite volume, high resolution scheme for solving the compressible full Navier-Stokes equations is presented. The present derivation is based on the upwind split formulas, specifically with the application of Roe's (1981) flux difference splitting. A high-order accurate (up to the third order) upwind interpolation formula for the inviscid terms is derived to account for nonuniform meshes. For the viscous terms, discretizations consistent with the finite volume concept are described. A variant of second-order time accurate method is proposed that utilizes identical procedures in both the predictor and corrector steps. Avoiding the definition of midpoint gives a consistent and easy procedure, in the framework of finite volume discretization, for treating viscous transport terms in the curvilinear coordinates. For the boundary cells, a new treatment is introduced that not only avoids the use of 'ghost cells' and the associated problems, but also satisfies the tangency conditions exactly and allows easy definition of viscous transport terms at the first interface next to the boundary cells. Numerical tests of steady and unsteady high speed flows show that the present scheme gives accurate solutions.

Efficient calculation of higher-order optical waveguide dispersion.

PubMed

Mores, J A; Malheiros-Silveira, G N; Fragnito, H L; Hernández-Figueroa, H E

2010-09-13

An efficient numerical strategy to compute the higher-order dispersion parameters of optical waveguides is presented. For the first time to our knowledge, a systematic study of the errors involved in the higher-order dispersions' numerical calculation process is made, showing that the present strategy can accurately model those parameters. Such strategy combines a full-vectorial finite element modal solver and a proper finite difference differentiation algorithm. Its performance has been carefully assessed through the analysis of several key geometries. In addition, the optimization of those higher-order dispersion parameters can also be carried out by coupling to the present scheme a genetic algorithm, as shown here through the design of a photonic crystal fiber suitable for parametric amplification applications.

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.

Three-dimensional viscous rotor flow calculations using a viscous-inviscid interaction approach

NASA Technical Reports Server (NTRS)

Chen, Ching S.; Bridgeman, John O.

1990-01-01

A three-dimensional viscous-inviscid interaction analysis was developed to predict the performance of rotors in hover and in forward flight at subsonic and transonic tip speeds. The analysis solves the full-potential and boundary-layer equations by finite-difference numerical procedures. Calculations were made for several different model rotor configurations. The results were compared with predictions from a two-dimensional integral method and with experimental data. The comparisons show good agreement between predictions and test data.

Load Testing, Finite Element Analysis, and Design of Steel Traffic-Signal Poles

DOT National Transportation Integrated Search

1993-07-01

At request of the Structures Design and Construction Division, the Engineering Research and Development Bureau performed full-scale testing and finite element analysis (FEA) of span-wire traffic-signal poles to evaluate their structural adequacy. Res...

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

Finite-frequency sensitivity kernels for head waves

NASA Astrophysics Data System (ADS)

Zhang, Zhigang; Shen, Yang; Zhao, Li

2007-11-01

Head waves are extremely important in determining the structure of the predominantly layered Earth. While several recent studies have shown the diffractive nature and the 3-D Fréchet kernels of finite-frequency turning waves, analogues of head waves in a continuous velocity structure, the finite-frequency effects and sensitivity kernels of head waves are yet to be carefully examined. We present the results of a numerical study focusing on the finite-frequency effects of head waves. Our model has a low-velocity layer over a high-velocity half-space and a cylindrical-shaped velocity perturbation placed beneath the interface at different locations. A 3-D finite-difference method is used to calculate synthetic waveforms. Traveltime and amplitude anomalies are measured by the cross-correlation of synthetic seismograms from models with and without the velocity perturbation and are compared to the 3-D sensitivity kernels constructed from full waveform simulations. The results show that the head wave arrival-time and amplitude are influenced by the velocity structure surrounding the ray path in a pattern that is consistent with the Fresnel zones. Unlike the `banana-doughnut' traveltime sensitivity kernels of turning waves, the traveltime sensitivity of the head wave along the ray path below the interface is weak, but non-zero. Below the ray path, the traveltime sensitivity reaches the maximum (absolute value) at a depth that depends on the wavelength and propagation distance. The sensitivity kernels vary with the vertical velocity gradient in the lower layer, but the variation is relatively small at short propagation distances when the vertical velocity gradient is within the range of the commonly accepted values. Finally, the depression or shoaling of the interface results in increased or decreased sensitivities, respectively, beneath the interface topography.

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size

PubMed Central

Gerstner, Wulfram

2017-01-01

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50–2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations. PMID:28422957

The Application of COMSOL Multiphysics Package on the Modelling of Complex 3-D Lithospheric Electrical Resistivity Structures - A Case Study from the Proterozoic Orogenic belt within the North China Craton

NASA Astrophysics Data System (ADS)

Guo, L.; Yin, Y.; Deng, M.; Guo, L.; Yan, J.

2017-12-01

At present, most magnetotelluric (MT) forward modelling and inversion codes are based on finite difference method. But its structured mesh gridding cannot be well adapted for the conditions with arbitrary topography or complex tectonic structures. By contrast, the finite element method is more accurate in calculating complex and irregular 3-D region and has lower requirement of function smoothness. However, the complexity of mesh gridding and limitation of computer capacity has been affecting its application. COMSOL Multiphysics is a cross-platform finite element analysis, solver and multiphysics full-coupling simulation software. It achieves highly accurate numerical simulations with high computational performance and outstanding multi-field bi-directional coupling analysis capability. In addition, its AC/DC and RF module can be used to easily calculate the electromagnetic responses of complex geological structures. Using the adaptive unstructured grid, the calculation is much faster. In order to improve the discretization technique of computing area, we use the combination of Matlab and COMSOL Multiphysics to establish a general procedure for calculating the MT responses for arbitrary resistivity models. The calculated responses include the surface electric and magnetic field components, impedance components, magnetic transfer functions and phase tensors. Then, the reliability of this procedure is certificated by 1-D, 2-D and 3-D and anisotropic forward modeling tests. Finally, we establish the 3-D lithospheric resistivity model for the Proterozoic Wutai-Hengshan Mts. within the North China Craton by fitting the real MT data collected there. The reliability of the model is also verified by induced vectors and phase tensors. Our model shows more details and better resolution, compared with the previously published 3-D model based on the finite difference method. In conclusion, COMSOL Multiphysics package is suitable for modeling the 3-D lithospheric resistivity structures under complex tectonic deformation backgrounds, which could be a good complement to the existing finite-difference inversion algorithms.

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.

Photonic crystal based 1-bit full-adder optical circuit by using ring resonators in a nonlinear structure

NASA Astrophysics Data System (ADS)

Alipour-Banaei, Hamed; Seif-Dargahi, Hamed

2017-05-01

In this paper we proposed a novel design for realizing all optical 1*bit full-adder based on photonic crystals. The proposed structure was realized by cascading two optical 1-bit half-adders. The final structure is consisted of eight optical waveguides and two nonlinear resonant rings, created inside rod type two dimensional photonic crystal with square lattice. The structure has ;X;, ;Y; and ;Z; as input and ;SUM; and ;CARRY; as output ports. The performance and functionality of the proposed structure was validated by means of finite difference time domain method.

Propagation of Finite Amplitude Sound in Multiple Waveguide Modes.

NASA Astrophysics Data System (ADS)

van Doren, Thomas Walter

1993-01-01

This dissertation describes a theoretical and experimental investigation of the propagation of finite amplitude sound in multiple waveguide modes. Quasilinear analytical solutions of the full second order nonlinear wave equation, the Westervelt equation, and the KZK parabolic wave equation are obtained for the fundamental and second harmonic sound fields in a rectangular rigid-wall waveguide. It is shown that the Westervelt equation is an acceptable approximation of the full nonlinear wave equation for describing guided sound waves of finite amplitude. A system of first order equations based on both a modal and harmonic expansion of the Westervelt equation is developed for waveguides with locally reactive wall impedances. Fully nonlinear numerical solutions of the system of coupled equations are presented for waveguides formed by two parallel planes which are either both rigid, or one rigid and one pressure release. These numerical solutions are compared to finite -difference solutions of the KZK equation, and it is shown that solutions of the KZK equation are valid only at frequencies which are high compared to the cutoff frequencies of the most important modes of propagation (i.e., for which sound propagates at small grazing angles). Numerical solutions of both the Westervelt and KZK equations are compared to experiments performed in an air-filled, rigid-wall, rectangular waveguide. Solutions of the Westervelt equation are in good agreement with experiment for low source frequencies, at which sound propagates at large grazing angles, whereas solutions of the KZK equation are not valid for these cases. At higher frequencies, at which sound propagates at small grazing angles, agreement between numerical solutions of the Westervelt and KZK equations and experiment is only fair, because of problems in specifying the experimental source condition with sufficient accuracy.

A total variation diminishing finite difference algorithm for sonic boom propagation models

NASA Technical Reports Server (NTRS)

Sparrow, Victor W.

1993-01-01

It is difficult to accurately model the rise phases of sonic boom waveforms with traditional finite difference algorithms because of finite difference phase dispersion. This paper introduces the concept of a total variation diminishing (TVD) finite difference method as a tool for accurately modeling the rise phases of sonic booms. A standard second order finite difference algorithm and its TVD modified counterpart are both applied to the one-way propagation of a square pulse. The TVD method clearly outperforms the non-TVD method, showing great potential as a new computational tool in the analysis of sonic boom propagation.

Development and application of a technique for reducing airframe finite element models for dynamics analysis

NASA Technical Reports Server (NTRS)

Hashemi-Kia, Mostafa; Toossi, Mostafa

1990-01-01

A computational procedure for the reduction of large finite element models was developed. This procedure is used to obtain a significantly reduced model while retaining the essential global dynamic characteristics of the full-size model. This reduction procedure is applied to the airframe finite element model of AH-64A Attack Helicopter. The resulting reduced model is then validated by application to a vibration reduction study.

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.

Effect of influx on the free surface transport within a hollow ampule

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

Chen, S.C.; Vafai, K.

1994-07-01

A numerical investigation of free surface transport within a hollow glass ampule with feed-in boundary conditions is presented. The glass ampule is treated as a vertical film with a finite pressure difference across the film, with applied influx on the upper boundary, and with applied heat flux at the outer free surface. Two different sizes of glass ampules, along with different influx values are investigated. A finite element method with full consideration of surface tension and viscosity effects is used to solve the transient Navier-Stokes equations in cylindrical coordinates. Radiative and convective boundary conditions are incorporated when solving the energymore » equation. The movement of the inner and outer free surfaces with the specified feed-in velocity for different dimensions and temporal temperature distribution are analyzed. It is found that the feed-in mechanism rather than the pressure difference provides the more dominant driving forces. Also studied is the effect of using different feed-in velocities on the flow and temperature fields. The results presented in this work illustrate the basic effects of the feed-in mechanism of the free surface transport phenomenon.« less

Effects of Earth's curvature in full-wave modeling of VLF propagation

NASA Astrophysics Data System (ADS)

Qiu, L.; Lehtinen, N. G.; Inan, U. S.; Stanford VLF Group

2011-12-01

We show how to include curvature in the full-wave finite element approach to calculate ELF/VLF wave propagation in horizontally stratified earth-ionosphere waveguide. A general curvilinear stratified system is considered, and the numerical solutions of full-wave method in curvilinear system are compared with the analytic solutions in the cylindrical and spherical waveguides filled with an isotropic medium. We calculate the attenuation and height gain for modes in the Earth-ionosphere waveguide, taking into account the anisotropicity of ionospheric plasma, for different assumptions about the Earth's curvature, and quantify the corrections due to the curvature. The results are compared with the results of previous models, such as LWPC, as well as with ground and satellite observations, and show improved accuracy compared with full-wave method without including the curvature effect.

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

Strauss, H.R.

This paper describes the code FEMHD, an adaptive finite element MHD code, which is applied in a number of different manners to model MHD behavior and edge plasma phenomena on a diverted tokamak. The code uses an unstructured triangular mesh in 2D and wedge shaped mesh elements in 3D. The code has been adapted to look at neutral and charged particle dynamics in the plasma scrape off region, and into a full MHD-particle code.

[Researches on biomechanics of micro-implant-bone interface and optimum design of micro implant's neck].

PubMed

Deng, Feng; Zhang, Lei; Zhang, Yi; Song, Jin-lin; Fan, Yuboa

2007-07-01

To compare and analyze the stress distribution at the micro-implant-bone interface based on the different micro-implant-bone conditioned under orthodontic load, and to optimize the design of micro implant's neck. An adult skull with all tooth was scanned by spiral CT, and the data were imported into computer for three-dimensional reconstruction with software Mimics 9.0. The three dimensional finite element models of three micro-implant-bone interfaces(initial stability, full osseointegration and fibrous integration) were analyzed by finite element analysis software ABAQUS6.5. The primary stress distributions of different micro-implant-bone conditions were evaluated when 2N force was loaded. Then the diameter less than 1.5 mm of the micro implant's neck was added with 0.2 mm, to compare the stress distribution of the modified micro-implant-bone interface with traditional type. The stress mostly concentrated on the neck of micro implant and the full osseointegration interface in all models showed the lowest strain level. Compared with the traditional type, the increasing diameter neck of the micro implant obviously decreased the stress level in all the three conditions. The micro-implant-bone interface and the diameter of micro implant's neck both are the important influence factors to the stress distribution of micro implant.

Finite Size Corrections to the Parisi Overlap Function in the GREM

NASA Astrophysics Data System (ADS)

Derrida, Bernard; Mottishaw, Peter

2018-01-01

We investigate the effects of finite size corrections on the overlap probabilities in the Generalized Random Energy Model in two situations where replica symmetry is broken in the thermodynamic limit. Our calculations do not use replicas, but shed some light on what the replica method should give for finite size corrections. In the gradual freezing situation, which is known to exhibit full replica symmetry breaking, we show that the finite size corrections lead to a modification of the simple relations between the sample averages of the overlaps Y_k between k configurations predicted by replica theory. This can be interpreted as fluctuations in the replica block size with a negative variance. The mechanism is similar to the one we found recently in the random energy model in Derrida and Mottishaw (J Stat Mech 2015(1): P01021, 2015). We also consider a simultaneous freezing situation, which is known to exhibit one step replica symmetry breaking. We show that finite size corrections lead to full replica symmetry breaking and give a more complete derivation of the results presented in Derrida and Mottishaw (Europhys Lett 115(4): 40005, 2016) for the directed polymer on a tree.

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.

LS-DYNA Analysis of a Full-Scale Helicopter Crash Test

NASA Technical Reports Server (NTRS)

Annett, Martin S.

2010-01-01

A full-scale crash test of an MD-500 helicopter was conducted in December 2009 at NASA Langley's Landing and Impact Research facility (LandIR). The MD-500 helicopter was fitted with a composite honeycomb Deployable Energy Absorber (DEA) and tested under vertical and horizontal impact velocities of 26 ft/sec and 40 ft/sec, respectively. The objectives of the test were to evaluate the performance of the DEA concept under realistic crash conditions and to generate test data for validation of a system integrated LS-DYNA finite element model. In preparation for the full-scale crash test, a series of sub-scale and MD-500 mass simulator tests was conducted to evaluate the impact performances of various components, including a new crush tube and the DEA blocks. Parameters defined within the system integrated finite element model were determined from these tests. The objective of this paper is to summarize the finite element models developed and analyses performed, beginning with pre-test and continuing through post test validation.

A staggered-grid finite-difference scheme optimized in the time–space domain for modeling scalar-wave propagation in geophysical problems

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

Tan, Sirui, E-mail: siruitan@hotmail.com; Huang, Lianjie, E-mail: ljh@lanl.gov

For modeling scalar-wave propagation in geophysical problems using finite-difference schemes, optimizing the coefficients of the finite-difference operators can reduce numerical dispersion. Most optimized finite-difference schemes for modeling seismic-wave propagation suppress only spatial but not temporal dispersion errors. We develop a novel optimized finite-difference scheme for numerical scalar-wave modeling to control dispersion errors not only in space but also in time. Our optimized scheme is based on a new stencil that contains a few more grid points than the standard stencil. We design an objective function for minimizing relative errors of phase velocities of waves propagating in all directions within amore » given range of wavenumbers. Dispersion analysis and numerical examples demonstrate that our optimized finite-difference scheme is computationally up to 2.5 times faster than the optimized schemes using the standard stencil to achieve the similar modeling accuracy for a given 2D or 3D problem. Compared with the high-order finite-difference scheme using the same new stencil, our optimized scheme reduces 50 percent of the computational cost to achieve the similar modeling accuracy. This new optimized finite-difference scheme is particularly useful for large-scale 3D scalar-wave modeling and inversion.« less

Modeling and Design of a Full-Scale Rotor Blade with Embedded Piezocomposite Actuators

NASA Astrophysics Data System (ADS)

Kovalovs, A.; Barkanov, E.; Ruchevskis, S.; Wesolowski, M.

2017-05-01

An optimization methodology for the design of a full-scale rotor blade with an active twist in order to enhance its ability to reduce vibrations and noise is presented. It is based on a 3D finite-element model, the planning of experiments, and the response surface technique to obtain high piezoelectric actuation forces and displacements with a minimum actuator weight and energy applied. To investigate an active twist of the helicopter rotor blade, a structural static analysis using a 3D finite-element model was carried out. Optimum results were obtained at two possible applications of macrofiber composite actuators. The torsion angle found from the finite-element simulation of helicopter rotor blades was successfully validated by its experimental values, which confirmed the modeling accuracy.

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.

Predicting Rediated Noise With Power Flow Finite Element Analysis

DTIC Science & Technology

2007-02-01

Defence R&D Canada – Atlantic DEFENCE DÉFENSE & Predicting Rediated Noise With Power Flow Finite Element Analysis D. Brennan T.S. Koko L. Jiang J...PREDICTING RADIATED NOISE WITH POWER FLOW FINITE ELEMENT ANALYSIS D.P. Brennan T.S. Koko L. Jiang J.C. Wallace Martec Limited Martec Limited...model- or full-scale data before it is available for general use. Brennan, D.P., Koko , T.S., Jiang, L., Wallace, J.C. 2007. Predicting Radiated

Efficiency trade-offs of steady-state methods using FEM and FDM. [iterative solutions for nonlinear flow equations

NASA Technical Reports Server (NTRS)

Gartling, D. K.; Roache, P. J.

1978-01-01

The efficiency characteristics of finite element and finite difference approximations for the steady-state solution of the Navier-Stokes equations are examined. The finite element method discussed is a standard Galerkin formulation of the incompressible, steady-state Navier-Stokes equations. The finite difference formulation uses simple centered differences that are O(delta x-squared). Operation counts indicate that a rapidly converging Newton-Raphson-Kantorovitch iteration scheme is generally preferable over a Picard method. A split NOS Picard iterative algorithm for the finite difference method was most efficient.

Distance Constraint Satisfaction Problems

NASA Astrophysics Data System (ADS)

Bodirsky, Manuel; Dalmau, Victor; Martin, Barnaby; Pinsker, Michael

We study the complexity of constraint satisfaction problems for templates Γ that are first-order definable in ({ Z}; {suc}), the integers with the successor relation. Assuming a widely believed conjecture from finite domain constraint satisfaction (we require the tractability conjecture by Bulatov, Jeavons and Krokhin in the special case of transitive finite templates), we provide a full classification for the case that Γ is locally finite (i.e., the Gaifman graph of Γ has finite degree). We show that one of the following is true: The structure Γ is homomorphically equivalent to a structure with a certain majority polymorphism (which we call modular median) and CSP(Γ) can be solved in polynomial time, or Γ is homomorphically equivalent to a finite transitive structure, or CSP(Γ) is NP-complete.

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.

Assessment of a hybrid finite element-transfer matrix model for flat structures with homogeneous acoustic treatments.

PubMed

Alimonti, Luca; Atalla, Noureddine; Berry, Alain; Sgard, Franck

2014-05-01

Modeling complex vibroacoustic systems including poroelastic materials using finite element based methods can be unfeasible for practical applications. For this reason, analytical approaches such as the transfer matrix method are often preferred to obtain a quick estimation of the vibroacoustic parameters. However, the strong assumptions inherent within the transfer matrix method lead to a lack of accuracy in the description of the geometry of the system. As a result, the transfer matrix method is inherently limited to the high frequency range. Nowadays, hybrid substructuring procedures have become quite popular. Indeed, different modeling techniques are typically sought to describe complex vibroacoustic systems over the widest possible frequency range. As a result, the flexibility and accuracy of the finite element method and the efficiency of the transfer matrix method could be coupled in a hybrid technique to obtain a reduction of the computational burden. In this work, a hybrid methodology is proposed. The performances of the method in predicting the vibroacoutic indicators of flat structures with attached homogeneous acoustic treatments are assessed. The results prove that, under certain conditions, the hybrid model allows for a reduction of the computational effort while preserving enough accuracy with respect to the full finite element solution.

Test problems for inviscid transonic flow

NASA Technical Reports Server (NTRS)

Carlson, L. A.

1979-01-01

Solving of test problems with the TRANDES program is discussed. This method utilizes the full, inviscid, perturbation potential flow equation in a Cartesian grid system that is stretched to infinity. This equation is represented by a nonconservative system of finite difference equations that includes at supersonic points a rotated difference scheme and is solved by column relaxation. The solution usually starts from a zero perturbation potential on a very coarse grid (typically 13 by 7) followed by several grid halvings until a final solution is obtained on a fine grid (97 by 49).

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.

Angulated Dental Implants in Posterior Maxilla FEA and Experimental Verification.

PubMed

Hamed, Hamed A; Marzook, Hamdy A; Ghoneem, Nahed E; El-Anwar, Mohamed I

2018-02-15

This study aimed to evaluate the effect of different implant angulations in posterior maxilla on stress distribution by finite element analysis and verify its results experimentally. Two simplified models were prepared for an implant placed vertically and tilted 25° piercing the maxillary sinus. Geometric models' components were prepared by Autodesk Inventor then assembled in ANSYS for finite element analysis. The results of finite element analysis were verified against experimental trials results which were statistically analysed using student t-test (level of significance p < 0.05). Implant - abutment complex absorbed the load energy in case of vertical implant better than the case of angulated one. That was reflected on cortical bone stress, while both cases showed stress levels within the physiological limits. Comparing results between FEA and experiment trials showed full agreement. It was found that the tilted implant by 25° can be utilised in the posterior region maxilla for replacing maxillary first molar avoiding sinus penetration. The implant-bone interface and peri-implant bones received the highest Von Mises stress. Implant - bone interface with angulated implant received about 66% more stresses than the straight one.

An exploratory study of a finite difference method for calculating unsteady transonic potential flow

NASA Technical Reports Server (NTRS)

Bennett, R. M.; Bland, S. R.

1979-01-01

A method for calculating transonic flow over steady and oscillating airfoils was developed by Isogai. The full potential equation is solved with a semi-implicit, time-marching, finite difference technique. Steady flow solutions are obtained from time asymptotic solutions for a steady airfoil. Corresponding oscillatory solutions are obtained by initiating an oscillation and marching in time for several cycles until a converged periodic solution is achieved. The method is described in general terms and results for the case of an airfoil with an oscillating flap are presented for Mach numbers 0.500 and 0.875. Although satisfactory results are obtained for some reduced frequencies, it is found that the numerical technique generates spurious oscillations in the indicial response functions and in the variation of the aerodynamic coefficients with reduced frequency. These oscillations are examined with a dynamic data reduction method to evaluate their effects and trends with reduced frequency and Mach number. Further development of the numerical method is needed to eliminate these oscillations.

Principles of Considering the Effect of the Limited Volume of a System on Its Thermodynamic State

NASA Astrophysics Data System (ADS)

Tovbin, Yu. K.

2018-01-01

The features of a system with a finite volume that affect its thermodynamic state are considered in comparison to describing small bodies in macroscopic phases. Equations for unary and pair distribution functions are obtained using difference derivatives of a discrete statistical sum. The structure of the equation for the free energy of a system consisting of an ensemble of volume-limited regions with different sizes and a full set of equations describing a macroscopic polydisperse system are discussed. It is found that the equations can be applied to molecular adsorption on small faces of microcrystals, to bound and isolated pores of a polydisperse material, and to describe the spinodal decomposition of a fluid in brief periods of time and high supersaturations of the bulk phase when each local region functions the same on average. It is shown that as the size of a system diminishes, corrections must be introduced for the finiteness of the system volume and fluctuations of the unary and pair distribution functions.

Rolling Element Bearing Stiffness Matrix Determination (Presentation)

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

Guo, Y.; Parker, R.

2014-01-01

Current theoretical bearing models differ in their stiffness estimates because of different model assumptions. In this study, a finite element/contact mechanics model is developed for rolling element bearings with the focus of obtaining accurate bearing stiffness for a wide range of bearing types and parameters. A combined surface integral and finite element method is used to solve for the contact mechanics between the rolling elements and races. This model captures the time-dependent characteristics of the bearing contact due to the orbital motion of the rolling elements. A numerical method is developed to determine the full bearing stiffness matrix corresponding tomore » two radial, one axial, and two angular coordinates; the rotation about the shaft axis is free by design. This proposed stiffness determination method is validated against experiments in the literature and compared to existing analytical models and widely used advanced computational methods. The fully-populated stiffness matrix demonstrates the coupling between bearing radial, axial, and tilting bearing deflections.« less

Experiences with explicit finite-difference schemes for complex fluid dynamics problems on STAR-100 and CYBER-203 computers

NASA Technical Reports Server (NTRS)

Kumar, A.; Rudy, D. H.; Drummond, J. P.; Harris, J. E.

1982-01-01

Several two- and three-dimensional external and internal flow problems solved on the STAR-100 and CYBER-203 vector processing computers are described. The flow field was described by the full Navier-Stokes equations which were then solved by explicit finite-difference algorithms. Problem results and computer system requirements are presented. Program organization and data base structure for three-dimensional computer codes which will eliminate or improve on page faulting, are discussed. Storage requirements for three-dimensional codes are reduced by calculating transformation metric data in each step. As a result, in-core grid points were increased in number by 50% to 150,000, with a 10% execution time increase. An assessment of current and future machine requirements shows that even on the CYBER-205 computer only a few problems can be solved realistically. Estimates reveal that the present situation is more storage limited than compute rate limited, but advancements in both storage and speed are essential to realistically calculate three-dimensional flow.

A finite element conjugate gradient FFT method for scattering

NASA Technical Reports Server (NTRS)

Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.

1991-01-01

Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.

Investigation of Heat and Mass Transfer and Irreversibility Phenomena Within a Three-Dimensional Tilted Enclosure for Different Shapes

NASA Astrophysics Data System (ADS)

Oueslati, F.; Ben-Beya, B.

2018-01-01

Three-dimensional thermosolutal natural convection and entropy generation within an inclined enclosure is investigated in the current study. A numerical method based on the finite volume method and a full multigrid technique is implemented to solve the governing equations. Effects of various parameters, namely, the aspect ratio, buoyancy ratio, and tilt angle on the flow patterns and entropy generation are predicted and discussed.

Impact of carotid stent cell design on vessel scaffolding: a case study comparing experimental investigation and numerical simulations.

PubMed

Conti, Michele; Van Loo, Denis; Auricchio, Ferdinando; De Beule, Matthieu; De Santis, Gianluca; Verhegghe, Benedict; Pirrelli, Stefano; Odero, Attilio

2011-06-01

To quantitatively evaluate the impact of carotid stent cell design on vessel scaffolding by using patient-specific finite element analysis of carotid artery stenting (CAS). The study was organized in 2 parts: (1) validation of a patient-specific finite element analysis of CAS and (2) evaluation of vessel scaffolding. Micro-computed tomography (CT) images of an open-cell stent deployed in a patient-specific silicone mock artery were compared with the corresponding finite element analysis results. This simulation was repeated for the closed-cell counterpart. In the second part, the stent strut distribution, as reflected by the inter-strut angles, was evaluated for both cell types in different vessel cross sections as a measure of scaffolding. The results of the patient-specific finite element analysis of CAS matched well with experimental stent deployment both qualitatively and quantitatively, demonstrating the reliability of the numerical approach. The measured inter-strut angles suggested that the closed-cell design provided superior vessel scaffolding compared to the open-cell counterpart. However, the full strut interconnection of the closed-cell design reduced the stent's ability to accommodate to the irregular eccentric profile of the vessel cross section, leading to a gap between the stent surface and the vessel wall. Even though this study was limited to a single stent design and one vascular anatomy, the study confirmed the capability of dedicated computer simulations to predict differences in scaffolding by open- and closed-cell carotid artery stents. These simulations have the potential to be used in the design of novel carotid stents or for procedure planning.

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

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.

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

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…

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.

Finiteness Marking in Boys with Fragile X Syndrome

ERIC Educational Resources Information Center

Sterling, Audra M.; Rice, Mabel L.; Warren, Steven F.

2012-01-01

Purpose: The current study investigated finiteness marking (e.g., he walk "s", he walk "ed") in boys with fragile X syndrome (FXS); the boys were grouped based on receptive vocabulary (i.e., borderline, impaired). Method: Twenty-one boys with the full mutation of fragile X, between the ages of 8 and 16 years participated. The…

Bayesian Finite Mixtures for Nonlinear Modeling of Educational Data.

ERIC Educational Resources Information Center

Tirri, Henry; And Others

A Bayesian approach for finding latent classes in data is discussed. The approach uses finite mixture models to describe the underlying structure in the data and demonstrate that the possibility of using full joint probability models raises interesting new prospects for exploratory data analysis. The concepts and methods discussed are illustrated…

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.

Comparison of finite element and transfer matrix methods for numerical investigation of surface plasmon waveguides

NASA Astrophysics Data System (ADS)

Haddouche, Issam; Cherbi, Lynda

2017-01-01

In this paper, we investigate Surface Plasmon Polaritons (SPPs) in the visible regime at a metal/dielectric interface within two different waveguide structures, the first is a Photonic Crystal Fiber where the Full Vector Finite Element Method (FVFEM) is used and the second is a slab waveguide where the transfer matrix method (TMM) is used. Knowing the diversities between the two methods in terms of speed, simplicity, and scope of application, computation is implemented with respect to wavelength and metal layer thickness in order to analyze and compare the performances of the two methods. Simulation results show that the TMM can be a good approximation for the FVFEM and that SPPs behave more like modes propagating in a semi infinite metal/dielectric structure as metal thickness increases from about 150 nm.

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

3D Tensorial Elastodynamics for Isotropic Media on Vertically Deformed Meshes

NASA Astrophysics Data System (ADS)

Shragge, J. C.

2017-12-01

Solutions of the 3D elastodynamic wave equation are sometimes required in industrial and academic applications of elastic reverse-time migration (E-RTM) and full waveform inversion (E-FWI) that involve vertically deformed meshes. Examples include incorporating irregular free-surface topography and handling internal boundaries (e.g., water bottom) directly into the computational meshes. In 3D E-RTM and E-FWI applications, the number of forward modeling simulations can number in the tens of thousands (per iteration), which necessitates the development of stable, accurate and efficient 3D elastodynamics solvers. For topographic scenarios, most finite-difference solution approaches use a change-of-variable strategy that has a number of associated computational challenges, including difficulties in handling of the free-surface boundary condition. In this study, I follow a tensorial approach and use a generalized family of analytic transforms to develop a set of analytic equations for 3D elastodynamics that directly incorporates vertical grid deformations. Importantly, this analytic approach allows for the specification of an analytic free-surface boundary condition appropriate for vertically deformed meshes. These equations are both straightforward and efficient to solve using a velocity-stress formulation with finite-difference (MFD) operators implemented on a fully staggered grid. Moreover, I demonstrate that the use of mimetic finite difference (MFD) methods allows stable, accurate, and efficient numerical solutions to be simulated for typical topographic scenarios. Examples demonstrate that high-quality elastic wavefields can be generated for topographic surfaces exhibiting significant topographic relief.

3D digital image correlation methods for full-field vibration measurement

NASA Astrophysics Data System (ADS)

Helfrick, Mark N.; Niezrecki, Christopher; Avitabile, Peter; Schmidt, Timothy

2011-04-01

In the area of modal test/analysis/correlation, significant effort has been expended over the past twenty years in order to make reduced models and to expand test data for correlation and eventual updating of the finite element models. This has been restricted by vibration measurements which are traditionally limited to the location of relatively few applied sensors. Advances in computers and digital imaging technology have allowed 3D digital image correlation (DIC) methods to measure the shape and deformation of a vibrating structure. This technique allows for full-field measurement of structural response, thus providing a wealth of simultaneous test data. This paper presents some preliminary results for the test/analysis/correlation of data measured using the DIC approach along with traditional accelerometers and a scanning laser vibrometer for comparison to a finite element model. The results indicate that all three approaches correlated well with the finite element model and provide validation for the DIC approach for full-field vibration measurement. Some of the advantages and limitations of the technique are presented and discussed.

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.

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

Higher-order ice-sheet modelling accelerated by multigrid on graphics cards

NASA Astrophysics Data System (ADS)

Brædstrup, Christian; Egholm, David

2013-04-01

Higher-order ice flow modelling is a very computer intensive process owing primarily to the nonlinear influence of the horizontal stress coupling. When applied for simulating long-term glacial landscape evolution, the ice-sheet models must consider very long time series, while both high temporal and spatial resolution is needed to resolve small effects. The use of higher-order and full stokes models have therefore seen very limited usage in this field. However, recent advances in graphics card (GPU) technology for high performance computing have proven extremely efficient in accelerating many large-scale scientific computations. The general purpose GPU (GPGPU) technology is cheap, has a low power consumption and fits into a normal desktop computer. It could therefore provide a powerful tool for many glaciologists working on ice flow models. Our current research focuses on utilising the GPU as a tool in ice-sheet and glacier modelling. To this extent we have implemented the Integrated Second-Order Shallow Ice Approximation (iSOSIA) equations on the device using the finite difference method. To accelerate the computations, the GPU solver uses a non-linear Red-Black Gauss-Seidel iterator coupled with a Full Approximation Scheme (FAS) multigrid setup to further aid convergence. The GPU finite difference implementation provides the inherent parallelization that scales from hundreds to several thousands of cores on newer cards. We demonstrate the efficiency of the GPU multigrid solver using benchmark experiments.

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.

Cross-ply laminates with holes in compression - Straight free-edge stresses determined by two- to three-dimensional global/local finite element analysis

NASA Technical Reports Server (NTRS)

Thompson, Danniella Muheim; Griffin, O. Hayden, Jr.; Vidussoni, Marco A.

1990-01-01

A practical example of applying two- to three-dimensional (2- to 3-D) global/local finite element analysis to laminated composites is presented. Cross-ply graphite/epoxy laminates of 0.1-in. (0.254-cm) thickness with central circular holes ranging from 1 to 6 in. (2.54 to 15.2 cm) in diameter, subjected to in-plane compression were analyzed. Guidelines for full three-dimensional finite element analysis and two- to three-dimensional global/local analysis of interlaminar stresses at straight free edges of laminated composites are included. The larger holes were found to reduce substantially the interlaminar stresses at the straight free-edge in proximity to the hole. Three-dimensional stress results were obtained for thin laminates which require prohibitive computer resources for full three-dimensional analyses of comparative accuracy.

Transport Modeling of Hydrogen in Metals for Application to Hydrogen Assisted Cracking of Metals.

DTIC Science & Technology

1995-04-04

34 consists of a Fortran "user element" subroutine for use with the ABAQUS 2 finite element program. Documentation of the 1-D user element subroutine is...trapping theory. The use of the ABAQUS finite element "User Element" subroutines for solving 1-D problems is then outlined in full detail. This is followed...reflect the new ordering given by Eq. (57). ABAOUS User Element Subroutines ABAQUS executes a Fortran subroutine named UEL for each "user defined" finite

Finite element analyses of wood laminated composite poles

Treesearch

Cheng Piao; Todd F. Shupe; R.C. Tang; Chung Y. Hse

2005-01-01

Finite element analyses using ANSYS were conducted on orthotropic, polygonal, wood laminated composite poles subjected to a body force and a concentrated load at the free end. Deflections and stress distributions of small-scale and full-size composite poles were analyzed and compared to the results obtained in an experimental study. The predicted deflection for both...

Using a multifrontal sparse solver in a high performance, finite element code

NASA Technical Reports Server (NTRS)

King, Scott D.; Lucas, Robert; Raefsky, Arthur

1990-01-01

We consider the performance of the finite element method on a vector supercomputer. The computationally intensive parts of the finite element method are typically the individual element forms and the solution of the global stiffness matrix both of which are vectorized in high performance codes. To further increase throughput, new algorithms are needed. We compare a multifrontal sparse solver to a traditional skyline solver in a finite element code on a vector supercomputer. The multifrontal solver uses the Multiple-Minimum Degree reordering heuristic to reduce the number of operations required to factor a sparse matrix and full matrix computational kernels (e.g., BLAS3) to enhance vector performance. The net result in an order-of-magnitude reduction in run time for a finite element application on one processor of a Cray X-MP.

Basic research on design analysis methods for rotorcraft vibrations

NASA Technical Reports Server (NTRS)

Hanagud, S.

1991-01-01

The objective of the present work was to develop a method for identifying physically plausible finite element system models of airframe structures from test data. The assumed models were based on linear elastic behavior with general (nonproportional) damping. Physical plausibility of the identified system matrices was insured by restricting the identification process to designated physical parameters only and not simply to the elements of the system matrices themselves. For example, in a large finite element model the identified parameters might be restricted to the moduli for each of the different materials used in the structure. In the case of damping, a restricted set of damping values might be assigned to finite elements based on the material type and on the fabrication processes used. In this case, different damping values might be associated with riveted, bolted and bonded elements. The method itself is developed first, and several approaches are outlined for computing the identified parameter values. The method is applied first to a simple structure for which the 'measured' response is actually synthesized from an assumed model. Both stiffness and damping parameter values are accurately identified. The true test, however, is the application to a full-scale airframe structure. In this case, a NASTRAN model and actual measured modal parameters formed the basis for the identification of a restricted set of physically plausible stiffness and damping parameters.

Finite temperature m=0 Bernstein modes in a non-neutral plasma, theory and simulation

NASA Astrophysics Data System (ADS)

Hart, Grant W.; Spencer, Ross L.; Takeshi Nakata, M.

2008-11-01

Axisymmetric upper-hybrid oscillations have been known to exist in non-neutral plasmas and FTICR/MS devices for a number of years. However, because they are electrostatic in nature and axisymmetric, they are self-shielding and therefore difficult to detect in long systems. Previous theoretical studies have assumed a zero temperature plasma. In the zero temperature limit these oscillations are not properly represented as a mode, because the frequency at a given radius depends only on the local density and is not coupled to neighboring radii, much like the zero temperature plasma oscillation. Finite temperature provides the coupling which links the oscillation into a coherent mode. We have analyzed the finite-temperature theory of these modes and find that they form an infinite set of modes with frequencies above 2̂c- 2̂p. We have simulated these modes in our r-θ particle-in-cell code that includes a full Lorentz-force mover and find that in a mostly flat-top plasma there are two eigenmodes that have essentially the same shape in the bulk of the plasma, but different frequencies. It appears likely that they have different boundary conditions in the boundary region. J.J. Bollinger, et al., Phys. Rev. A 48, 525 (1993). S.E. Barlow, et al., Int. J. Mass Spectrom. Ion Processes 74, 97 (1986). M. Takeshi Nakata, et al., Bull. Am. Phys. Soc. 51, 245 (2006).

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.

TranAir: A full-potential, solution-adaptive, rectangular grid code for predicting subsonic, transonic, and supersonic flows about arbitrary configurations. Theory document

NASA Technical Reports Server (NTRS)

Johnson, F. T.; Samant, S. S.; Bieterman, M. B.; Melvin, R. G.; Young, D. P.; Bussoletti, J. E.; Hilmes, C. L.

1992-01-01

A new computer program, called TranAir, for analyzing complex configurations in transonic flow (with subsonic or supersonic freestream) was developed. This program provides accurate and efficient simulations of nonlinear aerodynamic flows about arbitrary geometries with the ease and flexibility of a typical panel method program. The numerical method implemented in TranAir is described. The method solves the full potential equation subject to a set of general boundary conditions and can handle regions with differing total pressure and temperature. The boundary value problem is discretized using the finite element method on a locally refined rectangular grid. The grid is automatically constructed by the code and is superimposed on the boundary described by networks of panels; thus no surface fitted grid generation is required. The nonlinear discrete system arising from the finite element method is solved using a preconditioned Krylov subspace method embedded in an inexact Newton method. The solution is obtained on a sequence of successively refined grids which are either constructed adaptively based on estimated solution errors or are predetermined based on user inputs. Many results obtained by using TranAir to analyze aerodynamic configurations are presented.

The influence of computational assumptions on analysing abdominal aortic aneurysm haemodynamics.

PubMed

Ene, Florentina; Delassus, Patrick; Morris, Liam

2014-08-01

The variation in computational assumptions for analysing abdominal aortic aneurysm haemodynamics can influence the desired output results and computational cost. Such assumptions for abdominal aortic aneurysm modelling include static/transient pressures, steady/transient flows and rigid/compliant walls. Six computational methods and these various assumptions were simulated and compared within a realistic abdominal aortic aneurysm model with and without intraluminal thrombus. A full transient fluid-structure interaction was required to analyse the flow patterns within the compliant abdominal aortic aneurysms models. Rigid wall computational fluid dynamics overestimates the velocity magnitude by as much as 40%-65% and the wall shear stress by 30%-50%. These differences were attributed to the deforming walls which reduced the outlet volumetric flow rate for the transient fluid-structure interaction during the majority of the systolic phase. Static finite element analysis accurately approximates the deformations and von Mises stresses when compared with transient fluid-structure interaction. Simplifying the modelling complexity reduces the computational cost significantly. In conclusion, the deformation and von Mises stress can be approximately found by static finite element analysis, while for compliant models a full transient fluid-structure interaction analysis is required for acquiring the fluid flow phenomenon. © IMechE 2014.

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.

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

Motion analysis study on sensitivity of finite element model of the cervical spine to geometry.

PubMed

Zafarparandeh, Iman; Erbulut, Deniz U; Ozer, Ali F

2016-07-01

Numerous finite element models of the cervical spine have been proposed, with exact geometry or with symmetric approximation in the geometry. However, few researches have investigated the sensitivity of predicted motion responses to the geometry of the cervical spine. The goal of this study was to evaluate the effect of symmetric assumption on the predicted motion by finite element model of the cervical spine. We developed two finite element models of the cervical spine C2-C7. One model was based on the exact geometry of the cervical spine (asymmetric model), whereas the other was symmetric (symmetric model) about the mid-sagittal plane. The predicted range of motion of both models-main and coupled motions-was compared with published experimental data for all motion planes under a full range of loads. The maximum differences between the asymmetric model and symmetric model predictions for the principal motion were 31%, 78%, and 126% for flexion-extension, right-left lateral bending, and right-left axial rotation, respectively. For flexion-extension and lateral bending, the minimum difference was 0%, whereas it was 2% for axial rotation. The maximum coupled motions predicted by the symmetric model were 1.5° axial rotation and 3.6° lateral bending, under applied lateral bending and axial rotation, respectively. Those coupled motions predicted by the asymmetric model were 1.6° axial rotation and 4° lateral bending, under applied lateral bending and axial rotation, respectively. In general, the predicted motion response of the cervical spine by the symmetric model was in the acceptable range and nonlinearity of the moment-rotation curve for the cervical spine was properly predicted. © IMechE 2016.

Three-phase compositional modeling of CO2 injection by higher-order finite element methods with CPA equation of state for aqueous phase

NASA Astrophysics Data System (ADS)

Moortgat, Joachim; Li, Zhidong; Firoozabadi, Abbas

2012-12-01

Most simulators for subsurface flow of water, gas, and oil phases use empirical correlations, such as Henry's law, for the CO2 composition in the aqueous phase, and equations of state (EOS) that do not represent the polar interactions between CO2and water. Widely used simulators are also based on lowest-order finite difference methods and suffer from numerical dispersion and grid sensitivity. They may not capture the viscous and gravitational fingering that can negatively affect hydrocarbon (HC) recovery, or aid carbon sequestration in aquifers. We present a three-phase compositional model based on higher-order finite element methods and incorporate rigorous and efficient three-phase-split computations for either three HC phases or water-oil-gas systems. For HC phases, we use the Peng-Robinson EOS. We allow solubility of CO2in water and adopt a new cubic-plus-association (CPA) EOS, which accounts for cross association between H2O and CO2 molecules, and association between H2O molecules. The CPA-EOS is highly accurate over a broad range of pressures and temperatures. The main novelty of this work is the formulation of a reservoir simulator with new EOS-based unique three-phase-split computations, which satisfy both the equalities of fugacities in all three phases and the global minimum of Gibbs free energy. We provide five examples that demonstrate twice the convergence rate of our method compared with a finite difference approach, and compare with experimental data and other simulators. The examples consider gravitational fingering during CO2sequestration in aquifers, viscous fingering in water-alternating-gas injection, and full compositional modeling of three HC phases.

Realistic full wave modeling of focal plane array pixels

DOE PAGES

Campione, Salvatore; Warne, Larry K.; Jorgenson, Roy E.; ...

2017-11-01

Here, we investigate full-wave simulations of realistic implementations of multifunctional nanoantenna enabled detectors (NEDs). We focus on a 2x2 pixelated array structure that supports two wavelengths of operation. We design each resonating structure independently using full-wave simulations with periodic boundary conditions mimicking the whole infinite array. We then construct a supercell made of a 2x2 pixelated array with periodic boundary conditions mimicking the full NED; in this case, however, each pixel comprises 10-20 antennas per side. In this way, the cross-talk between contiguous pixels is accounted for in our simulations. We observe that, even though there are finite extent effects,more » the pixels work as designed, each responding at the respective wavelength of operation. This allows us to stress that realistic simulations of multifunctional NEDs need to be performed to verify the design functionality by taking into account finite extent and cross-talk effects.« less

Three-dimensional numerical modeling of full-space transient electromagnetic responses of water in goaf

NASA Astrophysics Data System (ADS)

Chang, Jiang-Hao; Yu, Jing-Cun; Liu, Zhi-Xin

2016-09-01

The full-space transient electromagnetic response of water-filled goaves in coal mines were numerically modeled. Traditional numerical modeling methods cannot be used to simulate the underground full-space transient electromagnetic field. We used multiple transmitting loops instead of the traditional single transmitting loop to load the transmitting loop into Cartesian grids. We improved the method for calculating the z-component of the magnetic field based on the characteristics of full space. Then, we established the fullspace 3D geoelectrical model using geological data for coalmines. In addition, the transient electromagnetic responses of water-filled goaves of variable shape at different locations were simulated by using the finite-difference time-domain (FDTD) method. Moreover, we evaluated the apparent resistivity results. The numerical modeling results suggested that the resistivity differences between the coal seam and its roof and floor greatly affect the distribution of apparent resistivity, resulting in nearly circular contours with the roadway head at the center. The actual distribution of apparent resistivity for different geoelectrical models of water in goaves was consistent with the models. However, when the goaf water was located in one side, a false low-resistivity anomaly would appear on the other side owing to the full-space effect but the response was much weaker. Finally, the modeling results were subsequently confirmed by drilling, suggesting that the proposed method was effective.

A Pseudo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

White, J. A.; Morrison, J. H.

1999-01-01

A multi-grid, flux-difference-split, finite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting flows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extensions to the class of implicit pseudo-time iterative, upwind space-marching schemes. A full approximate storage, full multi-grid scheme is also described which is used to accelerate the convergence of a Gauss-Seidel relaxation method. The multi-grid algorithm is shown to significantly improve convergence on high aspect ratio grids.

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.

Dynamic characteristics of a wind turbine blade using 3D digital image correlation

NASA Astrophysics Data System (ADS)

Baqersad, Javad; Carr, Jennifer; Lundstrom, Troy; Niezrecki, Christopher; Avitabile, Peter; Slattery, Micheal

2012-04-01

Digital image correlation (DIC) has been becoming increasingly popular as a means to perform structural health monitoring because of its full-field, non-contacting measurement ability. In this paper, 3D DIC techniques are used to identify the mode shapes of a wind turbine blade. The blade containing a handful of optical targets is excited at different frequencies using a shaker as well as a pluck test. The response is recorded using two PHOTRON™ high speed cameras. Time domain data is transferred to the frequency domain to extract mode shapes and natural frequencies using an Operational Modal Approach. A finite element model of the blade is also used to compare the mode shapes. Furthermore, a modal hammer impact test is performed using a more conventional approach with an accelerometer. A comparison of mode shapes from the photogrammetric, finite element, and impact test approaches are presented to show the accuracy of the DIC measurement approach.

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.

Robust optimization of front members in a full frontal car impact

NASA Astrophysics Data System (ADS)

Aspenberg (né Lönn), David; Jergeus, Johan; Nilsson, Larsgunnar

2013-03-01

In the search for lightweight automobile designs, it is necessary to assure that robust crashworthiness performance is achieved. Structures that are optimized to handle a finite number of load cases may perform poorly when subjected to various dispersions. Thus, uncertainties must be accounted for in the optimization process. This article presents an approach to optimization where all design evaluations include an evaluation of the robustness. Metamodel approximations are applied both to the design space and the robustness evaluations, using artifical neural networks and polynomials, respectively. The features of the robust optimization approach are displayed in an analytical example, and further demonstrated in a large-scale design example of front side members of a car. Different optimization formulations are applied and it is shown that the proposed approach works well. It is also concluded that a robust optimization puts higher demands on the finite element model performance than normally.

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

Opening complete band gaps in two dimensional locally resonant phononic crystals

NASA Astrophysics Data System (ADS)

Zhou, Xiaoling; Wang, Longqi

2018-05-01

Locally resonant phononic crystals (LRPCs) which have low frequency band gaps attract a growing attention in both scientific and engineering field recently. Wide complete locally resonant band gaps are the goal for researchers. In this paper, complete band gaps are achieved by carefully designing the geometrical properties of the inclusions in two dimensional LRPCs. The band structures and mechanisms of different types of models are investigated by the finite element method. The translational vibration patterns in both the in-plane and out-of-plane directions contribute to the full band gaps. The frequency response of the finite periodic structures demonstrate the attenuation effects in the complete band gaps. Moreover, it is found that the complete band gaps can be further widened and lowered by increasing the height of the inclusions. The tunable properties by changing the geometrical parameters provide a good way to open wide locally resonant band gaps.

The Inclusion of In-Plane Stresses in Delamination Criteria

NASA Technical Reports Server (NTRS)

Fenske, Matthew T.

1999-01-01

A study of delamination failure was conducted with emphasis on delamination criteria. Evidence is presented which supports the inclusion of the in-plane stresses in addition to the interlaminar stress terms in delamination criteria. The delamination is characterized as the failure of a resin rich region in between ply sets. The entire six component stress state in this resin layer is calculated through a finite element analysis, averaged over a dimension of 1.75 ply thicknesses, and used in a Modified von Mises Delamination Criterion. This criterion builds onto previous criteria by including all six stress components in the interply resin layer. The MVMDC shows good correlation to experimental data. The results show that the treatment of delamination as the failure of a finite interply resin layer is a valid method and that the MVMDC, considering the full stress state, accurately indicates delamination for different laminate families.

Modal loss mechanism of micro-structured VCSELs studied using full vector FDTD method.

PubMed

Jo, Du-Ho; Vu, Ngoc Hai; Kim, Jin-Tae; Hwang, In-Kag

2011-09-12

Modal properties of vertical cavity surface-emitting lasers (VCSELs) with holey structures are studied using a finite difference time domain (FDTD) method. We investigate loss behavior with respect to the variation of structural parameters, and explain the loss mechanism of VCSELs. We also propose an effective method to estimate the modal loss based on mode profiles obtained using FDTD simulation. Our results could provide an important guideline for optimization of the microstructures of high-power single-mode VCSELs.

Angulated Dental Implants in Posterior Maxilla FEA and Experimental Verification

PubMed Central

Hamed, Hamed A.; Marzook, Hamdy A.; Ghoneem, Nahed E.; El–Anwar, Mohamed I.

2018-01-01

AIM: This study aimed to evaluate the effect of different implant angulations in posterior maxilla on stress distribution by finite element analysis and verify its results experimentally. METHODS: Two simplified models were prepared for an implant placed vertically and tilted 25° piercing the maxillary sinus. Geometric models’ components were prepared by Autodesk Inventor then assembled in ANSYS for finite element analysis. The results of finite element analysis were verified against experimental trials results which were statistically analysed using student t-test (level of significance p < 0.05). RESULTS: Implant - abutment complex absorbed the load energy in case of vertical implant better than the case of angulated one. That was reflected on cortical bone stress, while both cases showed stress levels within the physiological limits. Comparing results between FEA and experiment trials showed full agreement. CONCLUSION: It was found that the tilted implant by 25° can be utilised in the posterior region maxilla for replacing maxillary first molar avoiding sinus penetration. The implant-bone interface and peri-implant bones received the highest Von Mises stress. Implant - bone interface with angulated implant received about 66% more stresses than the straight one. PMID:29531612

Comparison of 2D Finite Element Modeling Assumptions with Results From 3D Analysis for Composite Skin-Stiffener Debonding

NASA Technical Reports Server (NTRS)

Krueger, Ronald; Paris, Isbelle L.; OBrien, T. Kevin; Minguet, Pierre J.

2004-01-01

The influence of two-dimensional finite element modeling assumptions on the debonding prediction for skin-stiffener specimens was investigated. Geometrically nonlinear finite element analyses using two-dimensional plane-stress and plane-strain elements as well as three different generalized plane strain type approaches were performed. The computed skin and flange strains, transverse tensile stresses and energy release rates were compared to results obtained from three-dimensional simulations. The study showed that for strains and energy release rate computations the generalized plane strain assumptions yielded results closest to the full three-dimensional analysis. For computed transverse tensile stresses the plane stress assumption gave the best agreement. Based on this study it is recommended that results from plane stress and plane strain models be used as upper and lower bounds. The results from generalized plane strain models fall between the results obtained from plane stress and plane strain models. Two-dimensional models may also be used to qualitatively evaluate the stress distribution in a ply and the variation of energy release rates and mixed mode ratios with delamination length. For more accurate predictions, however, a three-dimensional analysis is required.

Influence of 2D Finite Element Modeling Assumptions on Debonding Prediction for Composite Skin-stiffener Specimens Subjected to Tension and Bending

NASA Technical Reports Server (NTRS)

Krueger, Ronald; Minguet, Pierre J.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The influence of two-dimensional finite element modeling assumptions on the debonding prediction for skin-stiffener specimens was investigated. Geometrically nonlinear finite element analyses using two-dimensional plane-stress and plane strain elements as well as three different generalized plane strain type approaches were performed. The computed deflections, skin and flange strains, transverse tensile stresses and energy release rates were compared to results obtained from three-dimensional simulations. The study showed that for strains and energy release rate computations the generalized plane strain assumptions yielded results closest to the full three-dimensional analysis. For computed transverse tensile stresses the plane stress assumption gave the best agreement. Based on this study it is recommended that results from plane stress and plane strain models be used as upper and lower bounds. The results from generalized plane strain models fall between the results obtained from plane stress and plane strain models. Two-dimensional models may also be used to qualitatively evaluate the stress distribution in a ply and the variation of energy release rates and mixed mode ratios with lamination length. For more accurate predictions, however, a three-dimensional analysis is required.

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

Computational fluid dynamics and frequency-dependent finite-difference time-domain method coupling for the interaction between microwaves and plasma in rocket plumes

NASA Astrophysics Data System (ADS)

Kinefuchi, K.; Funaki, I.; Shimada, T.; Abe, T.

2012-10-01

Under certain conditions during rocket flights, ionized exhaust plumes from solid rocket motors may interfere with radio frequency transmissions. To understand the relevant physical processes involved in this phenomenon and establish a prediction process for in-flight attenuation levels, we attempted to measure microwave attenuation caused by rocket exhaust plumes in a sea-level static firing test for a full-scale solid propellant rocket motor. The microwave attenuation level was calculated by a coupling simulation of the inviscid-frozen-flow computational fluid dynamics of an exhaust plume and detailed analysis of microwave transmissions by applying a frequency-dependent finite-difference time-domain method with the Drude dispersion model. The calculated microwave attenuation level agreed well with the experimental results, except in the case of interference downstream the Mach disk in the exhaust plume. It was concluded that the coupling estimation method based on the physics of the frozen plasma flow with Drude dispersion would be suitable for actual flight conditions, although the mixing and afterburning in the plume should be considered depending on the flow condition.

Methods for finding transition states on reduced potential energy surfaces

NASA Astrophysics Data System (ADS)

Burger, Steven K.; Ayers, Paul W.

2010-06-01

Three new algorithms are presented for determining transition state (TS) structures on the reduced potential energy surface, that is, for problems in which a few important degrees of freedom can be isolated. All three methods use constrained optimization to rapidly find the TS without an initial Hessian evaluation. The algorithms highlight how efficiently the TS can be located on a reduced surface, where the rest of the degrees of freedom are minimized. The first method uses a nonpositive definite quasi-Newton update for the reduced degrees of freedom. The second uses Shepard interpolation to fit the Hessian and starts from a set of points that bound the TS. The third directly uses a finite difference scheme to calculate the reduced degrees of freedom of the Hessian of the entire system, and searches for the TS on the full potential energy surface. All three methods are tested on an epoxide hydrolase cluster, and the ring formations of cyclohexane and cyclobutenone. The results indicate that all the methods are able to converge quite rapidly to the correct TS, but that the finite difference approach is the most efficient.

Methods for finding transition states on reduced potential energy surfaces.

PubMed

Burger, Steven K; Ayers, Paul W

2010-06-21

Three new algorithms are presented for determining transition state (TS) structures on the reduced potential energy surface, that is, for problems in which a few important degrees of freedom can be isolated. All three methods use constrained optimization to rapidly find the TS without an initial Hessian evaluation. The algorithms highlight how efficiently the TS can be located on a reduced surface, where the rest of the degrees of freedom are minimized. The first method uses a nonpositive definite quasi-Newton update for the reduced degrees of freedom. The second uses Shepard interpolation to fit the Hessian and starts from a set of points that bound the TS. The third directly uses a finite difference scheme to calculate the reduced degrees of freedom of the Hessian of the entire system, and searches for the TS on the full potential energy surface. All three methods are tested on an epoxide hydrolase cluster, and the ring formations of cyclohexane and cyclobutenone. The results indicate that all the methods are able to converge quite rapidly to the correct TS, but that the finite difference approach is the most efficient.

Evaluation of Test Methods for Triaxially Braided Composites using a Meso-Scale Finite Element Model

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

Zhang, Chao

The characterization of triaxially braided composite is complicate due to the nonuniformity of deformation within the unit cell as well as the possibility of the freeedge effect related to the large size of the unit cell. Extensive experimental investigation has been conducted to develop more accurate test approaches in characterizing the actual mechanical properties of the material we are studying. In this work, a meso-scale finite element model is utilized to simulate two complex specimens: notched tensile specimen and tube tensile specimen, which are designed to avoid the free-edge effect and free-edge effect induced premature edge damage. The full fieldmore » strain data is predicted numerically and compared with experimental data obtained by Digit Image Correlation. The numerically predicted tensile strength values are compared with experimentally measured results. The discrepancy between numerically predicted and experimentally measured data, the capability of different test approaches are analyzed and discussed. The presented numerical model could serve as assistance to the evaluation of different test methods, and is especially useful in identifying potential local damage events.« less

High-Modulation-Speed LEDs Based on III-Nitride

NASA Astrophysics Data System (ADS)

Chen, Hong

III-nitride InGaN light-emitting diodes (LEDs) enable wide range of applications in solid-state lighting, full-color displays, and high-speed visible-light communication. Conventional InGaN quantum well LEDs grown on polar c-plane substrate suffer from quantum confined Stark effect due to the large internal polarization-related fields, leading to a reduced radiative recombination rate and device efficiency, which limits the performance of InGaN LEDs in high-speed communication applications. To circumvent these negative effects, non-trivial-cavity designs such as flip-chip LEDs, metallic grating coated LEDs are proposed. This oral defense will show the works on the high-modulation-speed LEDs from basic ideas to applications. Fundamental principles such as rate equations for LEDs/laser diodes (LDs), plasmonic effects, Purcell effects will be briefly introduced. For applications, the modal properties of flip-chip LEDs are solved by implementing finite difference method in order to study the modulation response. The emission properties of highly polarized InGaN LEDs coated by metallic gratings are also investigated by finite difference time domain method.

Three-dimensional wave field modeling by a collocated-grid finite-difference method in the anelastic model with surface topography

NASA Astrophysics Data System (ADS)

Wang, N.; Li, J.; Borisov, D.; Gharti, H. N.; Shen, Y.; Zhang, W.; Savage, B. K.

2016-12-01

We incorporate 3D anelastic attenuation into the collocated-grid finite-difference method on curvilinear grids (Zhang et al., 2012), using the rheological model of the generalized Maxwell body (Emmerich and Korn, 1987; Moczo and Kristek, 2005; Käser et al., 2007). We follow a conventional procedure to calculate the anelastic coefficients (Emmerich and Korn, 1987) determined by the Q(ω)-law, with a modification in the choice of frequency band and thus the relaxation frequencies that equidistantly cover the logarithmic frequency range. We show that such an optimization of anelastic coefficients is more accurate when using a fixed number of relaxation mechanisms to fit the frequency independent Q-factors. We use curvilinear grids to represent the surface topography. The velocity-stress form of the 3D isotropic anelastic wave equation is solved with a collocated-grid finite-difference method. Compared with the elastic case, we need to solve additional material-independent anelastic functions (Kristek and Moczo, 2003) for the mechanisms at each relaxation frequency. Based on the stress-strain relation, we calculate the spatial partial derivatives of the anelastic functions indirectly thereby saving computational storage and improving computational efficiency. The complex-frequency-shifted perfectly matched layer (CFS-PML) is used for the absorbing boundary condition based on the auxiliary difference equation (Zhang and Shen, 2010). The traction image method (Zhang and Chen, 2006) is employed for the free-surface boundary condition. We perform several numerical experiments including homogeneous full-space models and layered half-space models, considering both flat and 3D Gaussian-shape hill surfaces. The results match very well with those of the spectral-element method (Komatitisch and Tromp, 2002; Savage et al., 2010), verifying the simulations by our method in the anelastic model with surface topography.

Comparative study of BCS-BEC crossover theories above T{sub c}: The nature of the pseudogap in ultracold atomic Fermi gases

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

Chien, C.-C.; Guo Hao; He Yan

2010-02-15

This article presents a comparison of two finite-temperature BCS-Bose-Einstein condensation (BEC) crossover theories above the transition temperature: Nozieres-Schmitt-Rink (NSR) theory and finite-T extended BCS-Leggett theory. The comparison is cast in the form of numerical studies of the behavior of the fermionic spectral function both theoretically and as constrained by (primarily) radio frequency (rf) experiments. Both theories include pair fluctuations and exhibit pseudogap effects, although the nature of this pseudogap is very different. The pseudogap in finite-T extended BCS-Leggett theory is found to follow a BCS-like dispersion which, in turn, is associated with a broadened BCS-like self-energy, rather more similar tomore » what is observed in high-temperature superconductors (albeit, for a d-wave case). The fermionic quasiparticle dispersion is different in NSR theory and the damping is considerably larger. We argue that the two theories are appropriate in different temperature regimes with the BCS-Leggett approach being more suitable nearer to condensation. There should, in effect, be little difference at higher T as the pseudogap becomes weaker and where the simplifying approximations used in the BCS-Leggett approach break down. On the basis of momentum-integrated rf studies of unpolarized gases, it would be difficult to distinguish which theory is the better one. A full comparison for polarized gases is not possible since it is claimed that there are inconsistencies in the NSR approach (not found in the BCS-Leggett scheme). Future experiments along the lines of momentum-resolved experiments look to be very promising in distinguishing the two theories.« less

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.

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

NASA Astrophysics Data System (ADS)

Song, Huimin

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

Full particle simulations of quasi-perpendicular shocks

NASA Astrophysics Data System (ADS)

Lembège, B.

This tutorial-style review is dedicated to the different strategies and constraints used for analysing the dynamics of a collisionless shocks with full particle simulations. Main results obtained with such simulations can be found in published materials (recent references are provided in this text); these will be only quoted herein in order to illustrate a few aspects of these simulations. Thanks to the large improvement of super computers, full particle simulations reveal to be quite helpful for analyzing in details the dynamics of collisionless shocks. The main characteristics of such codes can be shortly reminded as follows: one resolves the full set of Poisson and Maxwell's equations without any approximation. Two approaches are commonly used for resolving this equation's set, more precisely the space derivatives: (i) the finite difference approach and (ii) the use of FFT's (Fast Fourier Transform). Two advantages of approach (ii) are that FFT's are highly optimized in supercomputers libraries, and these allow to separate all fields components into two groups: the longitudinal electrostatic component El (solution of Poisson equation) and the transverse electromagnetic components Et and Bt solutions of the Maxwell's equations (so called "fields pusher"). Such a separation is quite helpful in the post processing stage necessary for the data analysis, as will be explained in the presentation. both ions and electrons populations are treated as individual finite-size particles and suffer the effects of all fields via the Lorentz force, so called "particle pusher", which is applied to each particle. Because of the large number of particles commonly used, the particle pusher represents the most expensive part of the calculations on which most efforts of optimisation needs to be performed (in terms of "vectorisation" or of "parallelism"). Relativistic effects may be included in this force via the use of particle momemtum. Each particle has three velocity components (vx, vy, vz), but may have 1, 2 or 3 space coordinates (x, y, z) according to the dimension of the code of concern.

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…

Predicting Long-term Temperature Increase for Time-Dependent SAR Levels with a Single Short-term Temperature Response

PubMed Central

Carluccio, Giuseppe; Bruno, Mary; Collins, Christopher M.

2015-01-01

Purpose Present a novel method for rapid prediction of temperature in vivo for a series of pulse sequences with differing levels and distributions of specific energy absorption rate (SAR). Methods After the temperature response to a brief period of heating is characterized, a rapid estimate of temperature during a series of periods at different heating levels is made using a linear heat equation and Impulse-Response (IR) concepts. Here the initial characterization and long-term prediction for a complete spine exam are made with the Pennes’ bioheat equation where, at first, core body temperature is allowed to increase and local perfusion is not. Then corrections through time allowing variation in local perfusion are introduced. Results The fast IR-based method predicted maximum temperature increase within 1% of that with a full finite difference simulation, but required less than 3.5% of the computation time. Even higher accelerations are possible depending on the time step size chosen, with loss in temporal resolution. Correction for temperature-dependent perfusion requires negligible additional time, and can be adjusted to be more or less conservative than the corresponding finite difference simulation. Conclusion With appropriate methods, it is possible to rapidly predict temperature increase throughout the body for actual MR examinations. (200/200 words) PMID:26096947

Predicting long-term temperature increase for time-dependent SAR levels with a single short-term temperature response.

PubMed

Carluccio, Giuseppe; Bruno, Mary; Collins, Christopher M

2016-05-01

Present a novel method for rapid prediction of temperature in vivo for a series of pulse sequences with differing levels and distributions of specific energy absorption rate (SAR). After the temperature response to a brief period of heating is characterized, a rapid estimate of temperature during a series of periods at different heating levels is made using a linear heat equation and impulse-response (IR) concepts. Here the initial characterization and long-term prediction for a complete spine exam are made with the Pennes' bioheat equation where, at first, core body temperature is allowed to increase and local perfusion is not. Then corrections through time allowing variation in local perfusion are introduced. The fast IR-based method predicted maximum temperature increase within 1% of that with a full finite difference simulation, but required less than 3.5% of the computation time. Even higher accelerations are possible depending on the time step size chosen, with loss in temporal resolution. Correction for temperature-dependent perfusion requires negligible additional time and can be adjusted to be more or less conservative than the corresponding finite difference simulation. With appropriate methods, it is possible to rapidly predict temperature increase throughout the body for actual MR examinations. © 2015 Wiley Periodicals, Inc.

Nonlinear transient analysis via energy minimization

NASA Technical Reports Server (NTRS)

Kamat, M. P.; Knight, N. F., Jr.

1978-01-01

The formulation basis for nonlinear transient analysis of finite element models of structures using energy minimization is provided. Geometric and material nonlinearities are included. The development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. The results indicate the effectiveness of the technique as a viable tool for this purpose.

Finite Element Model to Reduce Fire and Blast Vulnerability

DTIC Science & Technology

2013-01-01

4 Figure 4. Scapula, Clavicle and Arm Models Attached to the Larger Model .............................. 5 Figure 5. The Full Body...Finite Element Model of the Lower Limbs UNCLASSIFIED 4 UNCLASSIFIED Anatomical surfaces of the scapula and clavicle were obtained and...ulna and hand bones. For the arms, hands, scapula and clavicle , the materials were made to be rigid and joints created using computational constraints

Flexible Models for Solar Sail Control

NASA Technical Reports Server (NTRS)

Weaver Smith, Suzanne; Song, Haiping; Baker, John R.; Black, Jonathan; Muheim, Danniella M.

2005-01-01

Solar sails employ a unique form of propulsion, gaining momentum from incident and reflected photons. However, the momentum transferred by an individual photon is extremely small. Consequently, a solar sail must have an extremely large surface area and also be extremely light. The flexibility of the sail then must be considered when designing or evaluating control laws. In this paper, solar sail flexibility and its influence on control effectiveness is considered using idealized two-dimensional models to represent physical phenomena rather than a specific design. Differential equations of motion are derived for a distributed parameter model of a flexible solar sail idealized as a rotating central hub with two opposing flexible booms. This idealization is appropriate for solar sail designs in which the vibrational modes of the sail and supporting booms move together allowing the sail mass to be distributed along the booms in the idealized model. A reduced analytical model of the flexible response is considered. Linear feedback torque control is applied at the central hub. Two translational disturbances and a torque disturbance also act at the central hub representing the equivalent effect of deflecting sail shape about a reference line. Transient simulations explore different control designs and their effectiveness for controlling orientation, for reducing flexible motion and for disturbance rejection. A second model also is developed as a two-dimensional "pathfinder" model to calculate the effect of solar sail shape on the resultant thrust, in-plane force and torque at the hub. The analysis is then extended to larger models using the finite element method. The finite element modeling approach is verified by comparing results from a two-dimensional finite element model with those from the analytical model. The utility of the finite element modeling approach for this application is then illustrated through examples based on a full finite element model.

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.

One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Blackwell, Ben F.; Edwards, Jack R.

2007-01-01

The development and verification of a one-dimensional material thermal response code with ablation is presented. The implicit time integrator, control volume finite element spatial discretization, and Newton's method for nonlinear iteration on the entire system of residual equations have been implemented and verified for the thermochemical ablation of internally decomposing materials. This study is a continuation of the work presented in "One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure" (AIAA-2006-2910), which described the derivation, implementation, and verification of the constant density solid energy equation terms and boundary conditions. The present study extends the model to decomposing materials including decomposition kinetics, pyrolysis gas flow through the porous char layer, and a mixture (solid and gas) energy equation. Verification results are presented for the thermochemical ablation of a carbon-phenolic ablator which involves the solution of the entire system of governing equations.

Electromagnetic pulse excitation of finite- and infinitely-long lossy conductors over a lossy ground plane

DOE PAGES

Campione, Salvatore; Warne, Larry K.; Basilio, Lorena I.; ...

2017-01-13

This study details a model for the response of a finite- or an infinite-length wire interacting with a conducting ground to an electromagnetic pulse excitation. We develop a frequency–domain method based on transmission line theory that we name ATLOG – Analytic Transmission Line Over Ground. This method is developed as an alternative to full-wave methods, as it delivers a fast and reliable solution. It allows for the treatment of finite or infinite lossy, coated wires, and lossy grounds. The cases of wire above ground, as well as resting on the ground and buried beneath the ground are treated. The reportedmore » method is general and the time response of the induced current is obtained using an inverse Fourier transform of the current in the frequency domain. The focus is on the characteristics and propagation of the transmission line mode. Comparisons with full-wave simulations strengthen the validity of the proposed method.« less

Electromagnetic pulse excitation of finite- and infinitely-long lossy conductors over a lossy ground plane

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

Campione, Salvatore; Warne, Larry K.; Basilio, Lorena I.

This study details a model for the response of a finite- or an infinite-length wire interacting with a conducting ground to an electromagnetic pulse excitation. We develop a frequency–domain method based on transmission line theory that we name ATLOG – Analytic Transmission Line Over Ground. This method is developed as an alternative to full-wave methods, as it delivers a fast and reliable solution. It allows for the treatment of finite or infinite lossy, coated wires, and lossy grounds. The cases of wire above ground, as well as resting on the ground and buried beneath the ground are treated. The reportedmore » method is general and the time response of the induced current is obtained using an inverse Fourier transform of the current in the frequency domain. The focus is on the characteristics and propagation of the transmission line mode. Comparisons with full-wave simulations strengthen the validity of the proposed method.« less

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.

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

Monte Carlo simulation of a near-continuum shock-shock interaction problem

NASA Technical Reports Server (NTRS)

Carlson, Ann B.; Wilmoth, Richard G.

1992-01-01

A complex shock interaction is calculated with direct simulation Monte Carlo (DSMC). The calculation is performed for the near-continuum flow produced when an incident shock impinges on the bow shock of a 0.1 in. radius cowl lip for freestream conditions of approximately Mach 15 and 35 km altitude. Solutions are presented both for a full finite-rate chemistry calculation and for a case with chemical reactions suppressed. In each case, both the undisturbed flow about the cowl lip and the full shock interaction flowfields are calculated. Good agreement has been obtained between the no-chemistry simulation of the undisturbed flow and a perfect gas solution obtained with the viscous shock-layer method. Large differences in calculated surface properties when different chemical models are used demonstrate the necessity of adequately representing the chemistry when making surface property predictions. Preliminary grid refinement studies make it possible to estimate the accuracy of the solutions.

Fast downscaled inverses for images compressed with M-channel lapped transforms.

PubMed

de Queiroz, R L; Eschbach, R

1997-01-01

Compressed images may be decompressed and displayed or printed using different devices at different resolutions. Full decompression and rescaling in space domain is a very expensive method. We studied downscaled inverses where the image is decompressed partially, and a reduced inverse transform is used to recover the image. In this fashion, fewer transform coefficients are used and the synthesis process is simplified. We studied the design of fast inverses, for a given forward transform. General solutions are presented for M-channel finite impulse response (FIR) filterbanks, of which block and lapped transforms are a subset. Designs of faster inverses are presented for popular block and lapped transforms.

Critical Nucleation Length for Accelerating Frictional Slip

NASA Astrophysics Data System (ADS)

Aldam, Michael; Weikamp, Marc; Spatschek, Robert; Brener, Efim A.; Bouchbinder, Eran

2017-11-01

The spontaneous nucleation of accelerating slip along slowly driven frictional interfaces is central to a broad range of geophysical, physical, and engineering systems, with particularly far-reaching implications for earthquake physics. A common approach to this problem associates nucleation with an instability of an expanding creep patch upon surpassing a critical length Lc. The critical nucleation length Lc is conventionally obtained from a spring-block linear stability analysis extended to interfaces separating elastically deformable bodies using model-dependent fracture mechanics estimates. We propose an alternative approach in which the critical nucleation length is obtained from a related linear stability analysis of homogeneous sliding along interfaces separating elastically deformable bodies. For elastically identical half-spaces and rate-and-state friction, the two approaches are shown to yield Lc that features the same scaling structure, but with substantially different numerical prefactors, resulting in a significantly larger Lc in our approach. The proposed approach is also shown to be naturally applicable to finite-size systems and bimaterial interfaces, for which various analytic results are derived. To quantitatively test the proposed approach, we performed inertial Finite-Element-Method calculations for a finite-size two-dimensional elastically deformable body in rate-and-state frictional contact with a rigid body under sideway loading. We show that the theoretically predicted Lc and its finite-size dependence are in reasonably good quantitative agreement with the full numerical solutions, lending support to the proposed approach. These results offer a theoretical framework for predicting rapid slip nucleation along frictional interfaces.

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

Three-dimensional long-period groundmotion simulations in the upper Mississippi embayment

USGS Publications Warehouse

Macpherson, K.A.; Woolery, E.W.; Wang, Z.; Liu, P.

2010-01-01

We employed a 3D velocity model and 3D wave propagation code to simulate long-period ground motions in the upper Mississippi embayment. This region is at risk from large earthquakes in the New Madrid seismic zone (NMSZ) and observational data are sparse, making simulation a valuable tool for predicting the effects of large events. We undertook these simulations to estimate the magnitude of shaking likely to occur and to investigate the influence of the 3D embayment structure and finite-fault mechanics on ground motions. There exist three primary fault zones in the NMSZ, each of which was likely associated with one of the main shocks of the 1811-12 earthquake triplet. For this study, three simulations have been conducted on each major segment, exploring the impact of different epicentral locations and rupture directions on ground motions. The full wave field up to a frequency of 0.5 Hz is computed on a 200 ?? 200 ?? 50-km 3 volume using a staggered-grid finite-difference code. Peak horizontal velocity and bracketed durations were calculated at the free surface. The NMSZ simulations indicate that for the considered bandwidth, finite-fault mechanics such as fault proximity, directivity effect, and slip distribution exert the most control on ground motions. The 3D geologic structure of the upper Mississippi embayment also influences ground motion with indications that amplification is induced by the sharp velocity contrast at the basin edge.

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

SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES

PubMed Central

Wan, Xiaohai; Li, Zhilin

2012-01-01

Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size. PMID:22701346

SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES.

PubMed

Wan, Xiaohai; Li, Zhilin

2012-06-01

Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size.

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

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)

MC21 analysis of the MIT PWR benchmark: Hot zero power results

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

Kelly Iii, D. J.; Aviles, B. N.; Herman, B. R.

2013-07-01

MC21 Monte Carlo results have been compared with hot zero power measurements from an operating pressurized water reactor (PWR), as specified in a new full core PWR performance benchmark from the MIT Computational Reactor Physics Group. Included in the comparisons are axially integrated full core detector measurements, axial detector profiles, control rod bank worths, and temperature coefficients. Power depressions from grid spacers are seen clearly in the MC21 results. Application of Coarse Mesh Finite Difference (CMFD) acceleration within MC21 has been accomplished, resulting in a significant reduction of inactive batches necessary to converge the fission source. CMFD acceleration has alsomore » been shown to work seamlessly with the Uniform Fission Site (UFS) variance reduction method. (authors)« less

Progress on the development of FullWave, a Hot and Cold Plasma Parallel Full Wave Code

NASA Astrophysics Data System (ADS)

Spencer, J. Andrew; Svidzinski, Vladimir; Zhao, Liangji; Kim, Jin-Soo

2017-10-01

FullWave is being developed at FAR-TECH, Inc. to simulate RF waves in hot inhomogeneous magnetized plasmas without making small orbit approximations. FullWave is based on a meshless formulation in configuration space on non-uniform clouds of computational points (CCP) adapted to better resolve plasma resonances, antenna structures and complex boundaries. The linear frequency domain wave equation is formulated using two approaches: for cold plasmas the local cold plasma dielectric tensor is used (resolving resonances by particle collisions), while for hot plasmas the conductivity kernel is calculated. The details of FullWave and some preliminary results will be presented, including: 1) a monitor function based on analytic solutions of the cold-plasma dispersion relation; 2) an adaptive CCP based on the monitor function; 3) construction of the finite differences for approximation of derivatives on adaptive CCP; 4) results of 2-D full wave simulations in the cold plasma model in tokamak geometry using the formulated approach for ECRH, ICRH and Lower Hybrid range of frequencies. Work is supported by the U.S. DOE SBIR program.

Manual for automatic generation of finite element models of spiral bevel gears in mesh

NASA Technical Reports Server (NTRS)

Bibel, G. D.; Reddy, S.; Kumar, A.

1994-01-01

The goal of this research is to develop computer programs that generate finite element models suitable for doing 3D contact analysis of faced milled spiral bevel gears in mesh. A pinion tooth and a gear tooth are created and put in mesh. There are two programs: Points.f and Pat.f to perform the analysis. Points.f is based on the equation of meshing for spiral bevel gears. It uses machine tool settings to solve for an N x M mesh of points on the four surfaces, pinion concave and convex, and gear concave and convex. Points.f creates the file POINTS.OUT, an ASCI file containing N x M points for each surface. (N is the number of node points along the length of the tooth, and M is nodes along the height.) Pat.f reads POINTS.OUT and creates the file tl.out. Tl.out is a series of PATRAN input commands. In addition to the mesh density on the tooth face, additional user specified variables are the number of finite elements through the thickness, and the number of finite elements along the tooth full fillet. A full fillet is assumed to exist for both the pinion and gear.

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.

Finite-temperature fluid–insulator transition of strongly interacting 1D disordered bosons

PubMed Central

Michal, Vincent P.; Aleiner, Igor L.; Altshuler, Boris L.; Shlyapnikov, Georgy V.

2016-01-01

We consider the many-body localization–delocalization transition for strongly interacting one-dimensional disordered bosons and construct the full picture of finite temperature behavior of this system. This picture shows two insulator–fluid transitions at any finite temperature when varying the interaction strength. At weak interactions, an increase in the interaction strength leads to insulator → fluid transition, and, for large interactions, there is a reentrance to the insulator regime. It is feasible to experimentally verify these predictions by tuning the interaction strength with the use of Feshbach or confinement-induced resonances, for example, in 7Li or 39K. PMID:27436894

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.

Three-dimensional finite element analysis of the stress distribution pattern in a mandibular first molar tooth restored with five different restorative materials.

PubMed

D'souza, Kathleen Manuela; Aras, Meena Ajay

2017-01-01

Badly broken or structurally compromised posterior teeth are frequently associated with crown/root fracture. Numerous restorative materials have been used to fabricate indirect full-coverage restorations for such teeth. This study aims to evaluate and compare the effect of restorative materials on the stress distribution pattern in a mandibular first molar tooth, under varying loading conditions and to compare the stress distribution pattern in five commonly used indirect restorative materials. Five three-dimensional finite element models representing a mandibular first molar tooth restored with crowns of gold, porcelain fused to metal, composite (Artglass), alumina-based zirconia (In-Ceram Zirconia [ICZ]), and double-layered zirconia-based materials (zirconia core veneered with porcelain, Lava) were constructed, using a Finite Element Analysis Software (ANSYS version 10; ANSYS Inc., Canonsburg, PA, USA). Two loading conditions were applied, simulating maximum bite force of 600 N axially and normal masticatory bite force of 225 N axially and nonaxially. Both all-ceramic crowns allowed the least amount of stress distribution to the surrounding tooth structure. In maximum bite force-simulation test, alumina-based all-ceramic crown displayed the highest von Mises stresses (123.745 MPa). In the masticatory bite force-simulation test, both all-ceramic crowns (122.503-133.13 MPa) displayed the highest von Mises stresses. ICZ crown displayed the highest peak von Mises stress values under maximum and masticatory bite forces. ICZ and Lava crowns also allowed the least amount of stress distribution to the surrounding tooth structure, which is indicative of a favorable response of the underlying tooth structure to the overlying full-coverage indirect restorative material. These results suggest that ICZ and Lava crowns can be recommended for clinical use in cases of badly damaged teeth.

Effect of Carreau-Yasuda rheological parameters on subcritical Lapwood convection in horizontal porous cavity saturated by shear-thinning fluid

NASA Astrophysics Data System (ADS)

Khechiba, Khaled; Mamou, Mahmoud; Hachemi, Madjid; Delenda, Nassim; Rebhi, Redha

2017-06-01

The present study is focused on Lapwood convection in isotropic porous media saturated with non-Newtonian shear thinning fluid. The non-Newtonian rheological behavior of the fluid is modeled using the general viscosity model of Carreau-Yasuda. The convection configuration consists of a shallow porous cavity with a finite aspect ratio and subject to a vertical constant heat flux, whereas the vertical walls are maintained impermeable and adiabatic. An approximate analytical solution is developed on the basis of the parallel flow assumption, and numerical solutions are obtained by solving the full governing equations. The Darcy model with the Boussinesq approximation and energy transport equations are solved numerically using a finite difference method. The results are obtained in terms of the Nusselt number and the flow fields as functions of the governing parameters. A good agreement is obtained between the analytical approximation and the numerical solution of the full governing equations. The effects of the rheological parameters of the Carreau-Yasuda fluid and Rayleigh number on the onset of subcritical convection thresholds are demonstrated. Regardless of the aspect ratio of the enclosure and thermal boundary condition type, the subcritical convective flows are seen to occur below the onset of stationary convection. Correlations are proposed to estimate the subcritical Rayleigh number for the onset of finite amplitude convection as a function of the fluid rheological parameters. Linear stability of the convective motion, predicted by the parallel flow approximation, is studied, and the onset of Hopf bifurcation, from steady convective flow to oscillatory behavior, is found to depend strongly on the rheological parameters. In general, Hopf bifurcation is triggered earlier as the fluid becomes more and more shear-thinning.

Iterative Addition of Kinetic Effects to Cold Plasma RF Wave Solvers

NASA Astrophysics Data System (ADS)

Green, David; Berry, Lee; RF-SciDAC Collaboration

2017-10-01

The hot nature of fusion plasmas requires a wave vector dependent conductivity tensor for accurate calculation of wave heating and current drive. Traditional methods for calculating the linear, kinetic full-wave plasma response rely on a spectral method such that the wave vector dependent conductivity fits naturally within the numerical method. These methods have seen much success for application to the well-confined core plasma of tokamaks. However, quantitative prediction of high power RF antenna designs for fusion applications has meant a requirement of resolving the geometric details of the antenna and other plasma facing surfaces for which the Fourier spectral method is ill-suited. An approach to enabling the addition of kinetic effects to the more versatile finite-difference and finite-element cold-plasma full-wave solvers was presented by where an operator-split iterative method was outlined. Here we expand on this approach, examine convergence and present a simplified kinetic current estimator for rapidly updating the right-hand side of the wave equation with kinetic corrections. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725.

Finite Macro-Element Mesh Deformation in a Structured Multi-Block Navier-Stokes Code

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2005-01-01

A mesh deformation scheme is developed for a structured multi-block Navier-Stokes code consisting of two steps. The first step is a finite element solution of either user defined or automatically generated macro-elements. Macro-elements are hexagonal finite elements created from a subset of points from the full mesh. When assembled, the finite element system spans the complete flow domain. Macro-element moduli vary according to the distance to the nearest surface, resulting in extremely stiff elements near a moving surface and very pliable elements away from boundaries. Solution of the finite element system for the imposed boundary deflections generally produces smoothly varying nodal deflections. The manner in which distance to the nearest surface has been found to critically influence the quality of the element deformation. The second step is a transfinite interpolation which distributes the macro-element nodal deflections to the remaining fluid mesh points. The scheme is demonstrated for several two-dimensional applications.

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.

Towards a Full Waveform Ambient Noise Inversion

NASA Astrophysics Data System (ADS)

Sager, K.; Ermert, L. A.; Boehm, C.; Fichtner, A.

2015-12-01

Noise tomography usually works under the assumption that the inter-station ambient noise correlation is equal to a scaled version of the Green's function between the two receivers. This assumption, however, is only met under specific conditions, for instance, wavefield diffusivity and equipartitioning, zero attenuation, etc., that are typically not satisfied in the Earth. This inconsistency inhibits the exploitation of the full waveform information contained in noise correlations regarding Earth structure and noise generation. To overcome this limitation we attempt to develop a method that consistently accounts for noise distribution, 3D heterogeneous Earth structure and the full seismic wave propagation physics in order to improve the current resolution of tomographic images of the Earth. As an initial step towards a full waveform ambient noise inversion we develop a preliminary inversion scheme based on a 2D finite-difference code simulating correlation functions and on adjoint techniques. With respect to our final goal, a simultaneous inversion for noise distribution and Earth structure, we address the following two aspects: (1) the capabilities of different misfit functionals to image wave speed anomalies and source distribution and (2) possible source-structure trade-offs, especially to what extent unresolvable structure could be mapped into the inverted noise source distribution and vice versa.

Diffraction modeling of finite subband EFC probing on dark hole contrast with WFIRST-CGI shaped pupil coronagraph

NASA Astrophysics Data System (ADS)

Zhou, Hanying; Krist, John; Nemati, Bijan

2016-08-01

Current coronagraph instrument design (CGI), as a part of a proposed NASA WFIRST (Wide-Field InfraRed Survey Telescope) mission, allocates two subband filters per full science band in order to contain system complexity and cost. We present our detailed investigation results on the adequacy of such limited number of finite subband filters in achieving full band dark hole contrast with shaped pupil coronagraph. The study is based on diffraction propagation modeling with realistic WFIRST optics, where each subband's complex field estimation is obtained, using Electric Field Conjugation (EFC) wavefront sensing / control algorithm, from pairwise pupil plane deformable mirror (DM) probing and image plane intensity averaging of the resulting fields of multiple (subband) wavelengths. Multiple subband choices and probing and control strategies are explored, including standard subband probing; mixed wavelength and/or weighted Jacobian matrix; subband probing with intensity subtraction; and extended subband probing with intensity subtraction. Overall, the investigation shows that the achievable contrast with limited number of finite subband EFC probing is about 2 2.5x worse than the designed post-EFC contrast for current SPC design. The result suggests that for future shaped pupil design, slightly larger over intended full bandwidth should be considered if it will be used with limited subbands for probing.

Calcul numérique des ondes de surface par une méthode de projection avec un maillage eulérien adaptatif

NASA Astrophysics Data System (ADS)

Guillou, Sylvain; Barbry, Nathaly; Nguyen, Kim Dan

A non hydrostatic vertical two-dimensional numerical model is proposed to calculate free-surface flows. This model is based on resolving the full Navier-Stokes equations by a finite-difference method coupled with Chorin's projection method. An adaptative-Eulerian grid in the sigma-coordinate system is used. The model permits the calculation of surface-waves in estuarine and coastal zones. A benchmark test relative to the soliton propagation is realised to validate the model.

Applying CASE Tools for On-Board Software Development

NASA Astrophysics Data System (ADS)

Brammer, U.; Hönle, A.

For many space projects the software development is facing great pressure with respect to quality, costs and schedule. One way to cope with these challenges is the application of CASE tools for automatic generation of code and documentation. This paper describes two CASE tools: Rhapsody (I-Logix) featuring UML and ISG (BSSE) that provides modeling of finite state machines. Both tools have been used at Kayser-Threde in different space projects for the development of on-board software. The tools are discussed with regard to the full software development cycle.

Full-scale locomotive dynamic collision testing and correlations : offset collisions between a locomotive and a covered hopper car (test 4).

DOT National Transportation Integrated Search

2011-09-01

This report presents the test results and finite element correlations of a full-scale dynamic collision test with rail vehicles as part of the Federal Railroad Administrations research program on improved crashworthiness of locomotive structures. ...

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

Campione, Salvatore; Warne, Larry K.; Jorgenson, Roy E.

Here, we investigate full-wave simulations of realistic implementations of multifunctional nanoantenna enabled detectors (NEDs). We focus on a 2x2 pixelated array structure that supports two wavelengths of operation. We design each resonating structure independently using full-wave simulations with periodic boundary conditions mimicking the whole infinite array. We then construct a supercell made of a 2x2 pixelated array with periodic boundary conditions mimicking the full NED; in this case, however, each pixel comprises 10-20 antennas per side. In this way, the cross-talk between contiguous pixels is accounted for in our simulations. We observe that, even though there are finite extent effects,more » the pixels work as designed, each responding at the respective wavelength of operation. This allows us to stress that realistic simulations of multifunctional NEDs need to be performed to verify the design functionality by taking into account finite extent and cross-talk effects.« less

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.

Modified Displacement Transfer Functions for Deformed Shape Predictions of Slender Curved Structures with Varying Curvatives

NASA Technical Reports Server (NTRS)

Ko, William L.; Fleischer, Van Tran

2014-01-01

To eliminate the need to use finite-element modeling for structure shape predictions, a new method was invented. This method is to use the Displacement Transfer Functions to transform the measured surface strains into deflections for mapping out overall structural deformed shapes. The Displacement Transfer Functions are expressed in terms of rectilinearly distributed surface strains, and contain no material properties. This report is to apply the patented method to the shape predictions of non-symmetrically loaded slender curved structures with different curvatures up to a full circle. Because the measured surface strains are not available, finite-element analysis had to be used to analytically generate the surface strains. Previously formulated straight-beam Displacement Transfer Functions were modified by introducing the curvature-effect correction terms. Through single-point or dual-point collocations with finite-elementgenerated deflection curves, functional forms of the curvature-effect correction terms were empirically established. The resulting modified Displacement Transfer Functions can then provide quite accurate shape predictions. Also, the uniform straight-beam Displacement Transfer Function was applied to the shape predictions of a section-cut of a generic capsule (GC) outer curved sandwich wall. The resulting GC shape predictions are quite accurate in partial regions where the radius of curvature does not change sharply.

Effects of finite pulse width on two-dimensional Fourier transform electron spin resonance.

PubMed

Liang, Zhichun; Crepeau, Richard H; Freed, Jack H

2005-12-01

Two-dimensional (2D) Fourier transform ESR techniques, such as 2D-ELDOR, have considerably improved the resolution of ESR in studies of molecular dynamics in complex fluids such as liquid crystals and membrane vesicles and in spin labeled polymers and peptides. A well-developed theory based on the stochastic Liouville equation (SLE) has been successfully employed to analyze these experiments. However, one fundamental assumption has been utilized to simplify the complex analysis, viz. the pulses have been treated as ideal non-selective ones, which therefore provide uniform irradiation of the whole spectrum. In actual experiments, the pulses are of finite width causing deviations from the theoretical predictions, a problem that is exacerbated by experiments performed at higher frequencies. In the present paper we provide a method to deal with the full SLE including the explicit role of the molecular dynamics, the spin Hamiltonian and the radiation field during the pulse. The computations are rendered more manageable by utilizing the Trotter formula, which is adapted to handle this SLE in what we call a "Split Super-Operator" method. Examples are given for different motional regimes, which show how 2D-ELDOR spectra are affected by the finite pulse widths. The theory shows good agreement with 2D-ELDOR experiments performed as a function of pulse width.

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.

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.

Topological order, entanglement, and quantum memory at finite temperature

NASA Astrophysics Data System (ADS)

Mazáč, Dalimil; Hamma, Alioscia

2012-09-01

We compute the topological entropy of the toric code models in arbitrary dimension at finite temperature. We find that the critical temperatures for the existence of full quantum (classical) topological entropy correspond to the confinement-deconfinement transitions in the corresponding Z2 gauge theories. This implies that the thermal stability of topological entropy corresponds to the stability of quantum (classical) memory. The implications for the understanding of ergodicity breaking in topological phases are discussed.

Advances and future directions of research on spectral methods

NASA Technical Reports Server (NTRS)

Patera, A. T.

1986-01-01

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

Design of a Modular Monolithic Implicit Solver for Multi-Physics Applications

NASA Technical Reports Server (NTRS)

Carton De Wiart, Corentin; Diosady, Laslo T.; Garai, Anirban; Burgess, Nicholas; Blonigan, Patrick; Ekelschot, Dirk; Murman, Scott M.

2018-01-01

The design of a modular multi-physics high-order space-time finite-element framework is presented together with its extension to allow monolithic coupling of different physics. One of the main objectives of the framework is to perform efficient high- fidelity simulations of capsule/parachute systems. This problem requires simulating multiple physics including, but not limited to, the compressible Navier-Stokes equations, the dynamics of a moving body with mesh deformations and adaptation, the linear shell equations, non-re effective boundary conditions and wall modeling. The solver is based on high-order space-time - finite element methods. Continuous, discontinuous and C1-discontinuous Galerkin methods are implemented, allowing one to discretize various physical models. Tangent and adjoint sensitivity analysis are also targeted in order to conduct gradient-based optimization, error estimation, mesh adaptation, and flow control, adding another layer of complexity to the framework. The decisions made to tackle these challenges are presented. The discussion focuses first on the "single-physics" solver and later on its extension to the monolithic coupling of different physics. The implementation of different physics modules, relevant to the capsule/parachute system, are also presented. Finally, examples of coupled computations are presented, paving the way to the simulation of the full capsule/parachute system.

Finite element method framework for RF-based through-the-wall mapping

NASA Astrophysics Data System (ADS)

Campos, Rafael Saraiva; Lovisolo, Lisandro; de Campos, Marcello Luiz R.

2017-05-01

Radiofrequency (RF) Through-the-Wall Mapping (TWM) employs techniques originally applied in X-Ray Computerized Tomographic Imaging to map obstacles behind walls. It aims to provide valuable information for rescuing efforts in damaged buildings, as well as for military operations in urban scenarios. This work defines a Finite Element Method (FEM) based framework to allow fast and accurate simulations of the reconstruction of floors blueprints, using Ultra High-Frequency (UHF) signals at three different frequencies (500 MHz, 1 GHz and 2 GHz). To the best of our knowledge, this is the first use of FEM in a TWM scenario. This framework allows quick evaluation of different algorithms without the need to assemble a full test setup, which might not be available due to budgetary and time constraints. Using this, the present work evaluates a collection of reconstruction methods (Filtered Backprojection Reconstruction, Direct Fourier Reconstruction, Algebraic Reconstruction and Simultaneous Iterative Reconstruction) under a parallel-beam acquisition geometry for different spatial sampling rates, number of projections, antenna gains and operational frequencies. The use of multiple frequencies assesses the trade-off between higher resolution at shorter wavelengths and lower through-the-wall penetration. Considering all the drawbacks associated with such a complex problem, a robust and reliable computational setup based on a flexible method such as FEM can be very useful.

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

Finite element simulation of structural performance on flexible pavements with stabilized base/treated sub-base materials under accelerated loading : research project capsule.

DOT National Transportation Integrated Search

2008-12-01

PROBLEM: The full-scale accelerated pavement testing (APT) provides a unique tool for pavement : engineers to directly collect pavement performance and failure data under heavy : wheel loading. However, running a full-scale APT experiment is very exp...

Quark-Meson-Coupling (QMC) model for finite nuclei, nuclear matter and beyond

NASA Astrophysics Data System (ADS)

Guichon, P. A. M.; Stone, J. R.; Thomas, A. W.

2018-05-01

The Quark-Meson-Coupling model, which self-consistently relates the dynamics of the internal quark structure of a hadron to the relativistic mean fields arising in nuclear matter, provides a natural explanation to many open questions in low energy nuclear physics, including the origin of many-body nuclear forces and their saturation, the spin-orbit interaction and properties of hadronic matter at a wide range of densities up to those occurring in the cores of neutron stars. Here we focus on four aspects of the model (i) a full comprehensive survey of the theory, including the latest developments, (ii) extensive application of the model to ground state properties of finite nuclei and hypernuclei, with a discussion of similarities and differences between the QMC and Skyrme energy density functionals, (iii) equilibrium conditions and composition of hadronic matter in cold and warm neutron stars and their comparison with the outcome of relativistic mean-field theories and, (iv) tests of the fundamental idea that hadron structure changes in-medium.

Progress with the COGENT Edge Kinetic Code: Implementing the Fokker-Plank Collision Operator

DOE PAGES

Dorf, M. A.; Cohen, R. H.; Dorr, M.; ...

2014-06-20

Here, COGENT is a continuum gyrokinetic code for edge plasma simulations being developed by the Edge Simulation Laboratory collaboration. The code is distinguished by application of a fourth-order finite-volume (conservative) discretization, and mapped multiblock grid technology to handle the geometric complexity of the tokamak edge. The distribution function F is discretized in v∥ – μ (parallel velocity – magnetic moment) velocity coordinates, and the code presently solves an axisymmetric full-f gyro-kinetic equation coupled to the long-wavelength limit of the gyro-Poisson equation. COGENT capabilities are extended by implementing the fully nonlinear Fokker-Plank operator to model Coulomb collisions in magnetized edge plasmas.more » The corresponding Rosenbluth potentials are computed by making use of a finite-difference scheme and multipole-expansion boundary conditions. Details of the numerical algorithms and results of the initial verification studies are discussed. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)« less

Auto-ignition of methane-air mixtures flowing along an array of thin catalytic plates

NASA Astrophysics Data System (ADS)

Treviño, C.

2010-12-01

In this paper, the heterogeneous ignition of a methane-air mixture flowing along an infinite array of catalytic parallel plates has been studied by inclusion of gas expansion effects and the finite heat conduction on the plates. The system of equations considers the full compressible Navier-Stokes equations coupled with the energy equations of the plates. The gas expansion effects which arise from temperature changes have been considered. The heterogeneous kinetics considers the adsorption and desorption reactions for both reactants. The limits of large and small longitudinal thermal conductance of the plate material are analyzed and the critical conditions for ignition are obtained in closed form. The governing equations are solved numerically using finite differences. The results show that ignition is more easily produced as the longitudinal wall thermal conductance increases, and the effects of the gas expansion on the catalytic ignition process are rather small due to the large value of the activation energy of the desorption reaction of adsorbed oxygen atoms.

Fatigue Life Methodology for Tapered Hybrid Composite Flexbeams

NASA Technical Reports Server (NTRS)

urri, Gretchen B.; Schaff, Jeffery R.

2006-01-01

Nonlinear-tapered flexbeam specimens from a full-size composite helicopter rotor hub flexbeam were tested under combined constant axial tension and cyclic bending loads. Two different graphite/glass hybrid configurations tested under cyclic loading failed by delamination in the tapered region. A 2-D finite element model was developed which closely approximated the flexbeam geometry, boundary conditions, and loading. The analysis results from two geometrically nonlinear finite element codes, ANSYS and ABAQUS, are presented and compared. Strain energy release rates (G) associated with simulated delamination growth in the flexbeams are presented from both codes. These results compare well with each other and suggest that the initial delamination growth from the tip of the ply-drop toward the thick region of the flexbeam is strongly mode II. The peak calculated G values were used with material characterization data to calculate fatigue life curves for comparison with test data. A curve relating maximum surface strain to number of loading cycles at delamination onset compared well with the test results.

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

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

Preston, Leiph

Although using standard Taylor series coefficients for finite-difference operators is optimal in the sense that in the limit of infinitesimal space and time discretization, the solution approaches the correct analytic solution to the acousto-dynamic system of differential equations, other finite-difference operators may provide optimal computational run time given certain error bounds or source bandwidth constraints. This report describes the results of investigation of alternative optimal finite-difference coefficients based on several optimization/accuracy scenarios and provides recommendations for minimizing run time while retaining error within given error bounds.

High-speed GPU-based finite element simulations for NDT

NASA Astrophysics Data System (ADS)

Huthwaite, P.; Shi, F.; Van Pamel, A.; Lowe, M. J. S.

2015-03-01

The finite element method solved with explicit time increments is a general approach which can be applied to many ultrasound problems. It is widely used as a powerful tool within NDE for developing and testing inspection techniques, and can also be used in inversion processes. However, the solution technique is computationally intensive, requiring many calculations to be performed for each simulation, so traditionally speed has been an issue. For maximum speed, an implementation of the method, called Pogo [Huthwaite, J. Comp. Phys. 2014, doi: 10.1016/j.jcp.2013.10.017], has been developed to run on graphics cards, exploiting the highly parallelisable nature of the algorithm. Pogo typically demonstrates speed improvements of 60-90x over commercial CPU alternatives. Pogo is applied to three NDE examples, where the speed improvements are important: guided wave tomography, where a full 3D simulation must be run for each source transducer and every different defect size; scattering from rough cracks, where many simulations need to be run to build up a statistical model of the behaviour; and ultrasound propagation within coarse-grained materials where the mesh must be highly refined and many different cases run.

Electromagnetic Wave Propagation in Body Area Networks Using the Finite-Difference-Time-Domain Method

PubMed Central

Bringuier, Jonathan N.; Mittra, Raj

2012-01-01

A rigorous full-wave solution, via the Finite-Difference-Time-Domain (FDTD) method, is performed in an attempt to obtain realistic communication channel models for on-body wireless transmission in Body-Area-Networks (BANs), which are local data networks using the human body as a propagation medium. The problem of modeling the coupling between body mounted antennas is often not amenable to attack by hybrid techniques owing to the complex nature of the human body. For instance, the time-domain Green's function approach becomes more involved when the antennas are not conformal. Furthermore, the human body is irregular in shape and has dispersion properties that are unique. One consequence of this is that we must resort to modeling the antenna network mounted on the body in its entirety, and the number of degrees of freedom (DoFs) can be on the order of billions. Even so, this type of problem can still be modeled by employing a parallel version of the FDTD algorithm running on a cluster. Lastly, we note that the results of rigorous simulation of BANs can serve as benchmarks for comparison with the abundance of measurement data. PMID:23012575

Influence of hole shape on sound absorption of underwater anechoic layers

NASA Astrophysics Data System (ADS)

Ye, Changzheng; Liu, Xuewei; Xin, Fengxian; Lu, Tian Jian

2018-07-01

A theoretical model is established to evaluate the sound absorption performance of underwater anechoic layers containing periodically distributed axial holes. Based on the concept for homogenized equivalent layer and on the theory of wave propagation in viscoelastic cylindrical tubes, the transfer function method is used to obtain the absorption coefficient of the anechoic layer adhered on the rigid plate. Three different types of axial holes are considered, the cylindrical, the conical and the horn shaped one. Results obtained with full finite element simulations are used to validate the model predictions. For each hole type, the vibration characteristics of the anechoic layer as well as the propagation of longitudinal and transverse waves in the layer are analyzed in detail to explore the physical mechanisms underlying its absorption performance. Furthermore, a three-dimensional finite element model for oblique incidence is developed to study the effect of hole shape at different incidence angles. The results show that two new absorption peaks appear since the oblique incidence excites two horizontal modes. Among the three hole types, the horn one achieves the best absorption performance at relatively low frequencies both in normal incidence and in oblique incidence.

Damage identification in beams using speckle shearography and an optimal spatial sampling

NASA Astrophysics Data System (ADS)

Mininni, M.; Gabriele, S.; Lopes, H.; Araújo dos Santos, J. V.

2016-10-01

Over the years, the derivatives of modal displacement and rotation fields have been used to localize damage in beams. Usually, the derivatives are computed by applying finite differences. The finite differences propagate and amplify the errors that exist in real measurements, and thus, it is necessary to minimize this problem in order to get reliable damage localizations. A way to decrease the propagation and amplification of the errors is to select an optimal spatial sampling. This paper presents a technique where an optimal spatial sampling of modal rotation fields is computed and used to obtain the modal curvatures. Experimental measurements of modal rotation fields of a beam with single and multiple damages are obtained with shearography, which is an optical technique allowing the measurement of full-fields. These measurements are used to test the validity of the optimal sampling technique for the improvement of damage localization in real structures. An investigation on the ability of a model updating technique to quantify the damage is also reported. The model updating technique is defined by the variations of measured natural frequencies and measured modal rotations and aims at calibrating the values of the second moment of area in the damaged areas, which were previously localized.

Performance of Nonlinear Finite-Difference Poisson-Boltzmann Solvers

PubMed Central

Cai, Qin; Hsieh, Meng-Juei; Wang, Jun; Luo, Ray

2014-01-01

We implemented and optimized seven finite-difference solvers for the full nonlinear Poisson-Boltzmann equation in biomolecular applications, including four relaxation methods, one conjugate gradient method, and two inexact Newton methods. The performance of the seven solvers was extensively evaluated with a large number of nucleic acids and proteins. Worth noting is the inexact Newton method in our analysis. We investigated the role of linear solvers in its performance by incorporating the incomplete Cholesky conjugate gradient and the geometric multigrid into its inner linear loop. We tailored and optimized both linear solvers for faster convergence rate. In addition, we explored strategies to optimize the successive over-relaxation method to reduce its convergence failures without too much sacrifice in its convergence rate. Specifically we attempted to adaptively change the relaxation parameter and to utilize the damping strategy from the inexact Newton method to improve the successive over-relaxation method. Our analysis shows that the nonlinear methods accompanied with a functional-assisted strategy, such as the conjugate gradient method and the inexact Newton method, can guarantee convergence in the tested molecules. Especially the inexact Newton method exhibits impressive performance when it is combined with highly efficient linear solvers that are tailored for its special requirement. PMID:24723843

An efficient flexible-order model for 3D nonlinear water waves

NASA Astrophysics Data System (ADS)

Engsig-Karup, A. P.; Bingham, H. B.; Lindberg, O.

2009-04-01

The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature.

Frequency-domain Green's functions for radar waves in heterogeneous 2.5D media

USGS Publications Warehouse

Ellefsen, K.J.; Croize, D.; Mazzella, A.T.; McKenna, J.R.

2009-01-01

Green's functions for radar waves propagating in heterogeneous 2.5D media might be calculated in the frequency domain using a hybrid method. The model is defined in the Cartesian coordinate system, and its electromagnetic properties might vary in the x- and z-directions, but not in the y-direction. Wave propagation in the x- and z-directions is simulated with the finite-difference method, and wave propagation in the y-direction is simulated with an analytic function. The absorbing boundaries on the finite-difference grid are perfectly matched layers that have been modified to make them compatible with the hybrid method. The accuracy of these numerical Greens functions is assessed by comparing them with independently calculated Green's functions. For a homogeneous model, the magnitude errors range from -4.16% through 0.44%, and the phase errors range from -0.06% through 4.86%. For a layered model, the magnitude errors range from -2.60% through 2.06%, and the phase errors range from -0.49% through 2.73%. These numerical Green's functions might be used for forward modeling and full waveform inversion. ?? 2009 Society of Exploration Geophysicists. All rights reserved.

Computational fluid dynamics and frequency-dependent finite-difference time-domain method coupling for the interaction between microwaves and plasma in rocket plumes

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

Kinefuchi, K.; Funaki, I.; Shimada, T.

Under certain conditions during rocket flights, ionized exhaust plumes from solid rocket motors may interfere with radio frequency transmissions. To understand the relevant physical processes involved in this phenomenon and establish a prediction process for in-flight attenuation levels, we attempted to measure microwave attenuation caused by rocket exhaust plumes in a sea-level static firing test for a full-scale solid propellant rocket motor. The microwave attenuation level was calculated by a coupling simulation of the inviscid-frozen-flow computational fluid dynamics of an exhaust plume and detailed analysis of microwave transmissions by applying a frequency-dependent finite-difference time-domain method with the Drude dispersion model.more » The calculated microwave attenuation level agreed well with the experimental results, except in the case of interference downstream the Mach disk in the exhaust plume. It was concluded that the coupling estimation method based on the physics of the frozen plasma flow with Drude dispersion would be suitable for actual flight conditions, although the mixing and afterburning in the plume should be considered depending on the flow condition.« less

Vibration analysis of angle-ply laminated composite plates with an embedded piezoceramic layer.

PubMed

Lin, Hsien-Yang; Huang, Jin-Hung; Ma, Chien-Ching

2003-09-01

An optical full-field technique, called amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), is used in this study to investigate the force-induced transverse vibration of an angle-ply laminated composite embedded with a piezoceramic layer (piezolaminated plates). The piezolaminated plates are excited by applying time-harmonic voltages to the embedded piezoceramic layer. Because clear fringe patterns will appear only at resonant frequencies, both the resonant frequencies and mode shapes of the vibrating piezolaminated plates with five different fiber orientation angles are obtained by the proposed AF-ESPI method. A laser Doppler vibrometer (LDV) system that has the advantage of high resolution and broad dynamic range also is applied to measure the frequency response of piezolaminated plates. In addition to the two proposed optical techniques, numerical computations based on a commercial finite element package are presented for comparison with the experimental results. Three different numerical formulations are used to evaluate the vibration characteristics of piezolaminated plates. Good agreements of the measured data by the optical method and the numerical results predicted by the finite element method (FEM) demonstrate that the proposed methodology in this study is a powerful tool for the vibration analysis of piezolaminated plates.

Full Wave Analysis of RF Signal Attenuation in a Lossy Cave using a High Order Time Domain Vector Finite Element Method

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

Pingenot, J; Rieben, R; White, D

2004-12-06

We present a computational study of signal propagation and attenuation of a 200 MHz dipole antenna in a cave environment. The cave is modeled as a straight and lossy random rough wall. To simulate a broad frequency band, the full wave Maxwell equations are solved directly in the time domain via a high order vector finite element discretization using the massively parallel CEM code EMSolve. The simulation is performed for a series of random meshes in order to generate statistical data for the propagation and attenuation properties of the cave environment. Results for the power spectral density and phase ofmore » the electric field vector components are presented and discussed.« less

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.

Measurement-based quantum teleportation on finite AKLT chains

NASA Astrophysics Data System (ADS)

Fujii, Akihiko; Feder, David

In the measurement-based model of quantum computation, universal quantum operations are effected by making repeated local measurements on resource states which contain suitable entanglement. Resource states include two-dimensional cluster states and the ground state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) state on the honeycomb lattice. Recent studies suggest that measurements on one-dimensional systems in the Haldane phase teleport perfect single-qubit gates in the correlation space, protected by the underlying symmetry. As laboratory realizations of symmetry-protected states will necessarily be finite, we investigate the potential for quantum gate teleportation in finite chains of a bilinear-biquadratic Hamiltonian which is a generalization of the AKLT model representing the full Haldane phase.

Holographic QCD in the Veneziano Limit at a Finite Magnetic Field and Chemical Potential

NASA Astrophysics Data System (ADS)

Gürsoy, Umut; Järvinen, Matti; Nijs, Govert

2018-06-01

We investigate QCD-like gauge theories at strong coupling at a finite magnetic field B , temperature T , and quark chemical potential μ using the improved holographic QCD model, including the full backreaction of the quarks in the plasma. In addition to the phase diagram, we study the behavior of the quark condensate as a function of T , B , and μ and discuss the fate of (inverse) magnetic catalysis at a finite μ . In particular, we observe that inverse magnetic catalysis exists only for small values of the chemical potential. The speed of sound in this holographic quark-gluon plasma exhibits interesting dependence on the thermodynamic parameters.

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)

Neutron star mergers as a probe of modifications of general relativity with finite-range scalar forces

NASA Astrophysics Data System (ADS)

Sagunski, Laura; Zhang, Jun; Johnson, Matthew C.; Lehner, Luis; Sakellariadou, Mairi; Liebling, Steven L.; Palenzuela, Carlos; Neilsen, David

2018-03-01

Observations of gravitational radiation from compact binary systems provide an unprecedented opportunity to test general relativity in the strong field dynamical regime. In this paper, we investigate how future observations of gravitational radiation from binary neutron star mergers might provide constraints on finite-range forces from a universally coupled massive scalar field. Such scalar degrees of freedom (d.o.f.) are a characteristic feature of many extensions of general relativity. For concreteness, we work in the context of metric f (R ) gravity, which is equivalent to general relativity and a universally coupled scalar field with a nonlinear potential whose form is fixed by the choice of f (R ). In theories where neutron stars (or other compact objects) obtain a significant scalar charge, the resulting attractive finite-range scalar force has implications for both the inspiral and merger phases of binary systems. We first present an analysis of the inspiral dynamics in Newtonian limit, and forecast the constraints on the mass of the scalar and charge of the compact objects for the Advanced LIGO gravitational wave observatory. We then perform a comparative study of binary neutron star mergers in general relativity with those of a one-parameter model of f (R ) gravity using fully relativistic hydrodynamical simulations. These simulations elucidate the effects of the scalar on the merger and postmerger dynamics. We comment on the utility of the full waveform (inspiral, merger, postmerger) to probe different regions of parameter space for both the particular model of f (R ) gravity studied here and for finite-range scalar forces more generally.

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.

Finite-Time Destruction of Entanglement and Non-Locality by Environmental Influences

NASA Astrophysics Data System (ADS)

Ann, Kevin; Jaeger, Gregg

2009-07-01

Entanglement and non-locality are non-classical global characteristics of quantum states important to the foundations of quantum mechanics. Recent investigations have shown that environmental noise, even when it is entirely local in influence, can destroy both of these properties in finite time despite giving rise to full quantum state decoherence only in the infinite time limit. These investigations, which have been carried out in a range of theoretical and experimental situations, are reviewed here.

Development of a finite element based delamination analysis for laminates subject to extension, bending, and torsion

NASA Technical Reports Server (NTRS)

Hooper, Steven J.

1989-01-01

Delamination is a common failure mode of laminated composite materials. This type of failure frequently occurs at the free edges of laminates where singular interlaminar stresses are developed due to the difference in Poisson's ratios between adjacent plies. Typically the delaminations develop between 90 degree plies and adjacent angle plies. Edge delamination has been studied by several investigators using a variety of techniques. Recently, Chan and Ochoa applied the quasi-three-dimensional finite element model to the analysis of a laminate subject to bending, extension, and torsion. This problem is of particular significance relative to the structural integrity of composite helicopter rotors. The task undertaken was to incorporate Chan and Ochoa's formulation into a Raju Q3DG program. The resulting program is capable of modeling extension, bending, and torsional mechanical loadings as well as thermal and hygroscopic loadings. The addition of the torsional and bending loading capability will provide the capability to perform a delamination analysis of a general unsymmetric laminate containing four cracks, each of a different length. The solutions obtained using this program are evaluated by comparing them with solutions from a full three-dimensional finite element solution. This comparison facilitates the assessment of three dimensional affects such as the warping constraint imposed by the load frame grips. It wlso facilitates the evaluation of the external load representation employed in the Q3D formulation. Finally, strain energy release rates computed from the three-dimensional results are compared with those predicted using the quasi-three-dimensional formulation.

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.

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

Full-scale locomotive dynamic crash testing and correlations : locomotive consist colliding with steel coil truck at grade crossing (test 3).

DOT National Transportation Integrated Search

2011-09-01

This report presents the test results and finite element correlations of a full-scale dynamic collision between a locomotive and a highway truck loaded with two heavy steel coils. The locomotive consist was moving at 58 miles per hour before it struc...

Finite Element Simulation of Three Full-Scale Crash Tests for Cessna 172 Aircraft

NASA Technical Reports Server (NTRS)

Mason, Brian H.; Warren, Jerry E., Jr.

2017-01-01

The NASA Emergency Locator Transmitter Survivability and Reliability (ELT-SAR) project was initiated in 2013 to assess the crash performance standards for the next generation of emergency locator transmitter (ELT) systems. Three Cessna 172 aircraft were acquired to perform crash testing at NASA Langley Research Center's Landing and Impact Research Facility. Full-scale crash tests were conducted in the summer of 2015 and each test article was subjected to severe, but survivable, impact conditions including a flare-to-stall during emergency landing, and two controlled-flight-into-terrain scenarios. Full-scale finite element analyses were performed using a commercial explicit solver, ABAQUS. The first test simulated impacting a concrete surface represented analytically by a rigid plane. Tests 2 and 3 simulated impacting a dirt surface represented analytically by an Eulerian grid of brick elements using a Mohr-Coulomb material model. The objective of this paper is to summarize the test and analysis results for the three full-scale crash tests. Simulation models of the airframe which correlate well with the tests are needed for future studies of alternate ELT mounting configurations.

Simulating the Response of a Composite Honeycomb Energy Absorber. Part 2; Full-Scale Impact Testing

NASA Technical Reports Server (NTRS)

Fasanella, Edwin L.; Annett, Martin S.; Jackson, Karen E.; Polanco, Michael A.

2012-01-01

NASA has sponsored research to evaluate an externally deployable composite honeycomb designed to attenuate loads in the event of a helicopter crash. The concept, designated the Deployable Energy Absorber (DEA), is an expandable Kevlar(Registered TradeMark) honeycomb. The DEA has a flexible hinge that allows the honeycomb to be stowed collapsed until needed during an emergency. Evaluation of the DEA began with material characterization of the Kevlar(Registered TradeMark)-129 fabric/epoxy, and ended with a full-scale crash test of a retrofitted MD-500 helicopter. During each evaluation phase, finite element models of the test articles were developed and simulations were performed using the dynamic finite element code, LS-DYNA(Registered TradeMark). The paper will focus on simulations of two full-scale impact tests involving the DEA, a mass-simulator and a full-scale crash of an instrumented MD-500 helicopter. Isotropic (MAT24) and composite (MAT58) material models, which were assigned to DEA shell elements, were compared. Based on simulations results, the MAT58 model showed better agreement with test.

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.

Predicting full-field dynamic strain on a three-bladed wind turbine using three dimensional point tracking and expansion techniques

NASA Astrophysics Data System (ADS)

Baqersad, Javad; Niezrecki, Christopher; Avitabile, Peter

2014-03-01

As part of a project to predict the full-field dynamic strain in rotating structures (e.g. wind turbines and helicopter blades), an experimental measurement was performed on a wind turbine attached to a 500-lb steel block and excited using a mechanical shaker. In this paper, the dynamic displacement of several optical targets mounted to a turbine placed in a semi-built-in configuration was measured by using three-dimensional point tracking. Using an expansion algorithm in conjunction with a finite element model of the blades, the measured displacements were expanded to all finite element degrees of freedom. The calculated displacements were applied to the finite element model to extract dynamic strain on the surface as well as within the interior points of the structure. To validate the technique for dynamic strain prediction, the physical strain at eight locations on the blades was measured during excitation using strain-gages. The expansion was performed by using both structural modes of an individual cantilevered blade and using modes of the entire structure (three-bladed wind turbine and the fixture) and the predicted strain was compared to the physical strain-gage measurements. The results demonstrate the ability of the technique to predict full-field dynamic strain from limited sets of measurements and can be used as a condition based monitoring tool to help provide damage prognosis of structures during operation.

A non-contacting approach for full field dynamic strain monitoring of rotating structures using the photogrammetry, finite element, and modal expansion techniques

NASA Astrophysics Data System (ADS)

Baqersad, Javad

Health monitoring of rotating structures such as wind turbines and helicopter rotors is generally performed using conventional sensors that provide a limited set of data at discrete locations near or on the hub. These sensors usually provide no data on the blades or interior locations where failures may occur. Within this work, an unique expansion algorithm was extended and combined with finite element (FE) modeling and an optical measurement technique to identify the dynamic strain in rotating structures. The merit of the approach is shown by using the approach to predict the dynamic strain on a small non-rotating and rotating wind turbine. A three-bladed wind turbine having 2.3-meter long blades was placed in a semi-built-in boundary condition using a hub, a machining chuck, and a steel block. A finite element model of the three wind turbine blades assembled to the hub was created and used to extract resonant frequencies and mode shapes. The FE model was validated and updated using experimental modal tests. For the non-rotating optical test, the turbine was excited using a sinusoidal excitation, a pluck test, arbitrary impacts on three blades, and random force excitations with a mechanical shaker. The response of the structure to the excitations was measured using three-dimensional point tracking. A pair of high-speed cameras was used to measure the displacement of optical targets on the structure when the blades were vibrating. The measured displacements at discrete locations were expanded and applied to the finite element model of the structure to extract the full-field dynamic strain. The results of the work show an excellent correlation between the strain predicted using the proposed approach and the strain measured with strain-gages for all of the three loading conditions. Similar to the non-rotating case, optical measurements were also preformed on a rotating wind turbine. The point tracking technique measured both rigid body displacement and flexible deformation of the blades at target locations. The measured displacements were expanded and applied to the finite element model of the turbine to extract full-field dynamic strain on the structure. In order to validate the results for the rotating turbine, the predicted strain was compared to strain measured at four locations on the spinning blades using a wireless strain-gage system. The approach used in this work to predict the strain showed higher accuracy than measurements obtainable by using the digital image correlation technique. The new expansion approach is able to extract dynamic strain all over the entire structure, even inside the structure beyond the line of sight of the measurement system. Because the method is based on a non-contacting measurement approach, it can be readily applied to a variety of structures having different boundary and operating conditions, including rotating blades.

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.

Three dimensional full-wave nonlinear acoustic simulations: Applications to ultrasound imaging

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

Pinton, Gianmarco

Characterization of acoustic waves that propagate nonlinearly in an inhomogeneous medium has significant applications to diagnostic and therapeutic ultrasound. The generation of an ultrasound image of human tissue is based on the complex physics of acoustic wave propagation: diffraction, reflection, scattering, frequency dependent attenuation, and nonlinearity. The nonlinearity of wave propagation is used to the advantage of diagnostic scanners that use the harmonic components of the ultrasonic signal to improve the resolution and penetration of clinical scanners. One approach to simulating ultrasound images is to make approximations that can reduce the physics to systems that have a low computational cost.more » Here a maximalist approach is taken and the full three dimensional wave physics is simulated with finite differences. This paper demonstrates how finite difference simulations for the nonlinear acoustic wave equation can be used to generate physically realistic two and three dimensional ultrasound images anywhere in the body. A specific intercostal liver imaging scenario for two cases: with the ribs in place, and with the ribs removed. This configuration provides an imaging scenario that cannot be performed in vivo but that can test the influence of the ribs on image quality. Several imaging properties are studied, in particular the beamplots, the spatial coherence at the transducer surface, the distributed phase aberration, and the lesion detectability for imaging at the fundamental and harmonic frequencies. The results indicate, counterintuitively, that at the fundamental frequency the beamplot improves due to the apodization effect of the ribs but at the same time there is more degradation from reverberation clutter. At the harmonic frequency there is significantly less improvement in the beamplot and also significantly less degradation from reverberation. It is shown that even though simulating the full propagation physics is computationally challenging it is necessary to quantify ultrasound image quality and its sources of degradation.« less

Discovery of the "RNA continent" through a contrarian's research strategy.

PubMed

Hayashizaki, Yoshihide

2011-01-01

The International Human Genome Sequencing Consortium completed the decoding of the human genome sequence in 2003. Readers will be aware of the paradigm shift which has occurred since then in the field of life science research. At last, mankind has been able to focus on a complete picture of the full extent of the genome, on which is recorded the basic information that controls all life. Meanwhile, another genome project, centered on Japan and known as the mouse genome encyclopedia project, was progressing with participation from around the world. Led by our research group at RIKEN, it was a full-length cDNA project which aimed to decode the whole RNA (transcriptome) using the mouse as a model. The basic information that controls all life is recorded on the genome, but in order to obtain a complete picture of this extensive information, the decoding of the genome alone is far from sufficient. These two genome projects established that the number of letters in the genome, which is the blueprint of life, is finite, that the number of RNA molecules derived from it is also finite, and that the number of protein molecules derived from the RNA is probably finite too. A massive number of combinations is still involved, but we are now able to understand one section of the network formed by these data. Once an object of study has been understood to be finite, establishing an image of the whole is certain to lead us to an understanding of the whole. Omics is an approach that views the information controlling life as finite and seeks to assemble and analyze it as a whole. Here, I would like to present our transcriptome research while making reference to our unique research strategy.

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.

A training rule which guarantees finite-region stability for a class of closed-loop neural-network control systems.

PubMed

Kuntanapreeda, S; Fullmer, R R

1996-01-01

A training method for a class of neural network controllers is presented which guarantees closed-loop system stability. The controllers are assumed to be nonlinear, feedforward, sampled-data, full-state regulators implemented as single hidden-layer neural networks. The controlled systems must be locally hermitian and observable. Stability of the closed-loop system is demonstrated by determining a Lyapunov function, which can be used to identify a finite stability region about the regulator point.

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.

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.

Simulation of reflectometry Bragg backscattering spectral responses in the absence of a cutoff layer.

PubMed

da Silva, F; da Graça, S; Heuraux, S; Conway, G D

2010-10-01

Experimental reflectometry signals obtained in the absence of a cutoff layer, with the possibility of interferometric operation excluded, show a coherent and recurrent frequency spectrum signature similar to an Alfvén cascade signature. A possible explanation resides in the modulation of a resonant Bragg backscattering response by an Alfvén mode structure located at the center of the plasma whose frequency of oscillation modulates the backscattered signal in a conformable way. This situation is modeled and simulated using an O-mode full-wave Maxwell finite-difference time-domain code and the resulting signatures are discussed.

On the removal of boundary errors caused by Runge-Kutta integration of non-linear partial differential equations

NASA Technical Reports Server (NTRS)

Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H.

1994-01-01

It has been previously shown that the temporal integration of hyperbolic partial differential equations (PDE's) may, because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic (PDE's) (linear and non-linear) whose boundary treatment is done via the SAT-procedure. A methodology is present for recovery of the full order of accuracy, and has been applied to the case of a 4th order explicit finite difference scheme.

Structural tailoring of advanced turboprops

NASA Technical Reports Server (NTRS)

Brown, K. W.; Hopkins, Dale A.

1988-01-01

The Structural Tailoring of Advanced Turboprops (STAT) computer program was developed to perform numerical optimization on highly swept propfan blades. The optimization procedure seeks to minimize an objective function defined as either: (1) direct operating cost of full scale blade or, (2) aeroelastic differences between a blade and its scaled model, by tuning internal and external geometry variables that must satisfy realistic blade design constraints. The STAT analysis system includes an aerodynamic efficiency evaluation, a finite element stress and vibration analysis, an acoustic analysis, a flutter analysis, and a once-per-revolution forced response life prediction capability. STAT includes all relevant propfan design constraints.

Illusion media: Generating virtual objects using realizable metamaterials

NASA Astrophysics Data System (ADS)

Jiang, Wei Xiang; Ma, Hui Feng; Cheng, Qiang; Cui, Tie Jun

2010-03-01

We propose a class of optical transformation media, illusion media, which render the enclosed object invisible and generate one or more virtual objects as desired. We apply the proposed media to design a microwave device, which transforms an actual object into two virtual objects. Such an illusion device exhibits unusual electromagnetic behavior as verified by full-wave simulations. Different from the published illusion devices which are composed of left-handed materials with simultaneously negative permittivity and permeability, the proposed illusion media have finite and positive permittivity and permeability. Hence the designed device could be realizable using artificial metamaterials.

The finite element method in low speed aerodynamics

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.

1975-01-01

The finite element procedure is shown to be of significant impact in design of the 'computational wind tunnel' for low speed aerodynamics. The uniformity of the mathematical differential equation description, for viscous and/or inviscid, multi-dimensional subsonic flows about practical aerodynamic system configurations, is utilized to establish the general form of the finite element algorithm. Numerical results for inviscid flow analysis, as well as viscous boundary layer, parabolic, and full Navier Stokes flow descriptions verify the capabilities and overall versatility of the fundamental algorithm for aerodynamics. The proven mathematical basis, coupled with the distinct user-orientation features of the computer program embodiment, indicate near-term evolution of a highly useful analytical design tool to support computational configuration studies in low speed aerodynamics.

Application of Probability Methods to Assess Crash Modeling Uncertainty

NASA Technical Reports Server (NTRS)

Lyle, Karen H.; Stockwell, Alan E.; Hardy, Robin C.

2003-01-01

Full-scale aircraft crash simulations performed with nonlinear, transient dynamic, finite element codes can incorporate structural complexities such as: geometrically accurate models; human occupant models; and advanced material models to include nonlinear stress-strain behaviors, and material failure. Validation of these crash simulations is difficult due to a lack of sufficient information to adequately determine the uncertainty in the experimental data and the appropriateness of modeling assumptions. This paper evaluates probabilistic approaches to quantify the effects of finite element modeling assumptions on the predicted responses. The vertical drop test of a Fokker F28 fuselage section will be the focus of this paper. The results of a probabilistic analysis using finite element simulations will be compared with experimental data.

Application of Probability Methods to Assess Crash Modeling Uncertainty

NASA Technical Reports Server (NTRS)

Lyle, Karen H.; Stockwell, Alan E.; Hardy, Robin C.

2007-01-01

Full-scale aircraft crash simulations performed with nonlinear, transient dynamic, finite element codes can incorporate structural complexities such as: geometrically accurate models; human occupant models; and advanced material models to include nonlinear stress-strain behaviors, and material failure. Validation of these crash simulations is difficult due to a lack of sufficient information to adequately determine the uncertainty in the experimental data and the appropriateness of modeling assumptions. This paper evaluates probabilistic approaches to quantify the effects of finite element modeling assumptions on the predicted responses. The vertical drop test of a Fokker F28 fuselage section will be the focus of this paper. The results of a probabilistic analysis using finite element simulations will be compared with experimental data.

Controlling the sign problem in finite-density quantum field theory

NASA Astrophysics Data System (ADS)

Garron, Nicolas; Langfeld, Kurt

2017-07-01

Quantum field theories at finite matter densities generically possess a partition function that is exponentially suppressed with the volume compared to that of the phase quenched analog. The smallness arises from an almost uniform distribution for the phase of the fermion determinant. Large cancellations upon integration is the origin of a poor signal to noise ratio. We study three alternatives for this integration: the Gaussian approximation, the "telegraphic" approximation, and a novel expansion in terms of theory-dependent moments and universal coefficients. We have tested the methods for QCD at finite densities of heavy quarks. We find that for two of the approximations the results are extremely close—if not identical—to the full answer in the strong sign-problem regime.

Development and validation of a computational model of the knee joint for the evaluation of surgical treatments for osteoarthritis

PubMed Central

Mootanah, R.; Imhauser, C.W.; Reisse, F.; Carpanen, D.; Walker, R.W.; Koff, M.F.; Lenhoff, M.W.; Rozbruch, S.R.; Fragomen, A.T.; Dewan, Z.; Kirane, Y.M.; Cheah, Pamela A.; Dowell, J.K.; Hillstrom, H.J.

2014-01-01

A three-dimensional (3D) knee joint computational model was developed and validated to predict knee joint contact forces and pressures for different degrees of malalignment. A 3D computational knee model was created from high-resolution radiological images to emulate passive sagittal rotation (full-extension to 65°-flexion) and weight acceptance. A cadaveric knee mounted on a six-degree-of-freedom robot was subjected to matching boundary and loading conditions. A ligament-tuning process minimised kinematic differences between the robotically loaded cadaver specimen and the finite element (FE) model. The model was validated by measured intra-articular force and pressure measurements. Percent full scale error between EE-predicted and in vitro-measured values in the medial and lateral compartments were 6.67% and 5.94%, respectively, for normalised peak pressure values, and 7.56% and 4.48%, respectively, for normalised force values. The knee model can accurately predict normalised intra-articular pressure and forces for different loading conditions and could be further developed for subject-specific surgical planning. PMID:24786914

Development and validation of a computational model of the knee joint for the evaluation of surgical treatments for osteoarthritis.

PubMed

Mootanah, R; Imhauser, C W; Reisse, F; Carpanen, D; Walker, R W; Koff, M F; Lenhoff, M W; Rozbruch, S R; Fragomen, A T; Dewan, Z; Kirane, Y M; Cheah, K; Dowell, J K; Hillstrom, H J

2014-01-01

A three-dimensional (3D) knee joint computational model was developed and validated to predict knee joint contact forces and pressures for different degrees of malalignment. A 3D computational knee model was created from high-resolution radiological images to emulate passive sagittal rotation (full-extension to 65°-flexion) and weight acceptance. A cadaveric knee mounted on a six-degree-of-freedom robot was subjected to matching boundary and loading conditions. A ligament-tuning process minimised kinematic differences between the robotically loaded cadaver specimen and the finite element (FE) model. The model was validated by measured intra-articular force and pressure measurements. Percent full scale error between FE-predicted and in vitro-measured values in the medial and lateral compartments were 6.67% and 5.94%, respectively, for normalised peak pressure values, and 7.56% and 4.48%, respectively, for normalised force values. The knee model can accurately predict normalised intra-articular pressure and forces for different loading conditions and could be further developed for subject-specific surgical planning.

Partition of unity finite element method for quantum mechanical materials calculations

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

Pask, J. E.; Sukumar, N.

The current state of the art for large-scale quantum-mechanical simulations is the planewave (PW) pseudopotential method, as implemented in codes such as VASP, ABINIT, and many others. However, since the PW method uses a global Fourier basis, with strictly uniform resolution at all points in space, it suffers from substantial inefficiencies in calculations involving atoms with localized states, such as first-row and transition-metal atoms, and requires significant nonlocal communications, which limit parallel efficiency. Real-space methods such as finite-differences (FD) and finite-elements (FE) have partially addressed both resolution and parallel-communications issues but have been plagued by one key disadvantage relative tomore » PW: excessive number of degrees of freedom (basis functions) needed to achieve the required accuracies. In this paper, we present a real-space partition of unity finite element (PUFE) method to solve the Kohn–Sham equations of density functional theory. In the PUFE method, we build the known atomic physics into the solution process using partition-of-unity enrichment techniques in finite element analysis. The method developed herein is completely general, applicable to metals and insulators alike, and particularly efficient for deep, localized potentials, as occur in calculations at extreme conditions of pressure and temperature. Full self-consistent Kohn–Sham calculations are presented for LiH, involving light atoms, and CeAl, involving heavy atoms with large numbers of atomic-orbital enrichments. We find that the new PUFE approach attains the required accuracies with substantially fewer degrees of freedom, typically by an order of magnitude or more, than the PW method. As a result, we compute the equation of state of LiH and show that the computed lattice constant and bulk modulus are in excellent agreement with reference PW results, while requiring an order of magnitude fewer degrees of freedom to obtain.« less

Finite Element Analysis of Grouting Compactness Monitoring in a Post-Tensioning Tendon Duct Using Piezoceramic Transducers

PubMed Central

Jiang, Tianyong; Song, Gangbing

2017-01-01

With the development of the post-tensioning technique, prestressed concrete structures have been widely used in civil engineering. To ensure the long-term effectiveness of the prestressed tendon, the grouting quality of the tendon duct is one of the important factors. However, it is still a challenge to monitor the grouting quality of post-tensioning tendon ducts, due to the invisibility of the grouting. The authors’ previous work proposed a real-time method that employed a stress wave-based active sensing approach with piezoceramic transducers to monitor the grouting compactness of a Post-Tensioning Tendon Duct (PTTD). To further understand the piezoceramic induced stress wave propagation in the PTTD with different grouting levels, this paper develops a two-dimensional finite element model for monitoring the grouting compactness of the tendon duct with a piezoceramic transducer. A smart aggregate (SA) developed to utilize one Lead Zirconate Titanate (PZT) transducer with marble protection is installed in the center location of the tendon duct as an actuator. Two PZT patches are bonded on the bottom and top surface of the tendon duct as the sensors. The analysis results show that the finite element analysis results are in good agreement with the experimental results, which demonstrates that the finite element analysis is feasible and reliable. For the top half of the specimen, not much stress wave could be detected before the full grouting level, except for negligible signals that may propagate through the walls of the tendon duct. When the tendon duct grouting is at 100%, the stress wave propagates to the top of the specimen, and the displacements are symmetric in both left-right and top-bottom directions before the stress waves reach the boundary. The proposed two-dimensional finite element model has the potential to be implemented to simulate the stress wave propagation principle for monitoring grouting compaction of the post-tensioning tendon duct. PMID:28961173

Finite Element Analysis of Grouting Compactness Monitoring in a Post-Tensioning Tendon Duct Using Piezoceramic Transducers.

PubMed

Jiang, Tianyong; Zheng, Junbo; Huo, Linsheng; Song, Gangbing

2017-09-29

With the development of the post-tensioning technique, prestressed concrete structures have been widely used in civil engineering. To ensure the long-term effectiveness of the prestressed tendon, the grouting quality of the tendon duct is one of the important factors. However, it is still a challenge to monitor the grouting quality of post-tensioning tendon ducts, due to the invisibility of the grouting. The authors' previous work proposed a real-time method that employed a stress wave-based active sensing approach with piezoceramic transducers to monitor the grouting compactness of a Post-Tensioning Tendon Duct (PTTD). To further understand the piezoceramic induced stress wave propagation in the PTTD with different grouting levels, this paper develops a two-dimensional finite element model for monitoring the grouting compactness of the tendon duct with a piezoceramic transducer. A smart aggregate (SA) developed to utilize one Lead Zirconate Titanate (PZT) transducer with marble protection is installed in the center location of the tendon duct as an actuator. Two PZT patches are bonded on the bottom and top surface of the tendon duct as the sensors. The analysis results show that the finite element analysis results are in good agreement with the experimental results, which demonstrates that the finite element analysis is feasible and reliable. For the top half of the specimen, not much stress wave could be detected before the full grouting level, except for negligible signals that may propagate through the walls of the tendon duct. When the tendon duct grouting is at 100%, the stress wave propagates to the top of the specimen, and the displacements are symmetric in both left-right and top-bottom directions before the stress waves reach the boundary. The proposed two-dimensional finite element model has the potential to be implemented to simulate the stress wave propagation principle for monitoring grouting compaction of the post-tensioning tendon duct.

Partition of unity finite element method for quantum mechanical materials calculations

DOE PAGES

Pask, J. E.; Sukumar, N.

2016-11-09

The current state of the art for large-scale quantum-mechanical simulations is the planewave (PW) pseudopotential method, as implemented in codes such as VASP, ABINIT, and many others. However, since the PW method uses a global Fourier basis, with strictly uniform resolution at all points in space, it suffers from substantial inefficiencies in calculations involving atoms with localized states, such as first-row and transition-metal atoms, and requires significant nonlocal communications, which limit parallel efficiency. Real-space methods such as finite-differences (FD) and finite-elements (FE) have partially addressed both resolution and parallel-communications issues but have been plagued by one key disadvantage relative tomore » PW: excessive number of degrees of freedom (basis functions) needed to achieve the required accuracies. In this paper, we present a real-space partition of unity finite element (PUFE) method to solve the Kohn–Sham equations of density functional theory. In the PUFE method, we build the known atomic physics into the solution process using partition-of-unity enrichment techniques in finite element analysis. The method developed herein is completely general, applicable to metals and insulators alike, and particularly efficient for deep, localized potentials, as occur in calculations at extreme conditions of pressure and temperature. Full self-consistent Kohn–Sham calculations are presented for LiH, involving light atoms, and CeAl, involving heavy atoms with large numbers of atomic-orbital enrichments. We find that the new PUFE approach attains the required accuracies with substantially fewer degrees of freedom, typically by an order of magnitude or more, than the PW method. As a result, we compute the equation of state of LiH and show that the computed lattice constant and bulk modulus are in excellent agreement with reference PW results, while requiring an order of magnitude fewer degrees of freedom to obtain.« less

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.

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.

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...

Recent applications of the transonic wing analysis computer code, TWING

NASA Technical Reports Server (NTRS)

Subramanian, N. R.; Holst, T. L.; Thomas, S. D.

1982-01-01

An evaluation of the transonic-wing-analysis computer code TWING is given. TWING utilizes a fully implicit approximate factorization iteration scheme to solve the full potential equation in conservative form. A numerical elliptic-solver grid-generation scheme is used to generate the required finite-difference mesh. Several wing configurations were analyzed, and the limits of applicability of this code was evaluated. Comparisons of computed results were made with available experimental data. Results indicate that the code is robust, accurate (when significant viscous effects are not present), and efficient. TWING generally produces solutions an order of magnitude faster than other conservative full potential codes using successive-line overrelaxation. The present method is applicable to a wide range of isolated wing configurations including high-aspect-ratio transport wings and low-aspect-ratio, high-sweep, fighter configurations.

Full wave simulations of helicon wave losses in the scrape-off-layer of the DIII-D tokamak

NASA Astrophysics Data System (ADS)

Lau, Cornwall; Jaeger, Fred; Berry, Lee; Bertelli, Nicola; Pinsker, Robert

2017-10-01

Helicon waves have been recently proposed as an off-axis current drive actuator for DIII-D. Previous modeling using the hot plasma, full wave code AORSA, has shown good agreement with the ray tracing code GENRAY for helicon wave propagation and absorption in the core plasma. AORSA, and a new, reduced finite-element-model show discrepancies between ray tracing and full wave occur in the scrape-off-layer (SOL), especially at high densities. The reduced model is much faster than AORSA, and reproduces most of the important features of the AORSA model. The reduced model also allows for larger parametric scans and for the easy use of arbitrary tokamak geometry. Results of the full wave codes, AORSA and COMSOL, will be shown for helicon wave losses in the SOL are shown for a large range of parameters, such as SOL density profiles, n||, radial and vertical locations of the antenna, and different tokamak vessel geometries. This work was supported by DE-AC05-00OR22725, DE-AC02-09CH11466, and DE-FC02-04ER54698.

Mechanical response of silk crystalline units from force-distribution analysis.

PubMed

Xiao, Senbo; Stacklies, Wolfram; Cetinkaya, Murat; Markert, Bernd; Gräter, Frauke

2009-05-20

The outstanding mechanical toughness of silk fibers is thought to be caused by embedded crystalline units acting as cross links of silk proteins in the fiber. Here, we examine the robustness of these highly ordered beta-sheet structures by molecular dynamics simulations and finite element analysis. Structural parameters and stress-strain relationships of four different models, from spider and Bombyx mori silk peptides, in antiparallel and parallel arrangement, were determined and found to be in good agreement with x-ray diffraction data. Rupture forces exceed those of any previously examined globular protein many times over, with spider silk (poly-alanine) slightly outperforming Bombyx mori silk ((Gly-Ala)(n)). All-atom force distribution analysis reveals both intrasheet hydrogen-bonding and intersheet side-chain interactions to contribute to stability to similar extent. In combination with finite element analysis of simplified beta-sheet skeletons, we could ascribe the distinct force distribution pattern of the antiparallel and parallel silk crystalline units to the difference in hydrogen-bond geometry, featuring an in-line or zigzag arrangement, respectively. Hydrogen-bond strength was higher in antiparallel models, and ultimately resulted in higher stiffness of the crystal, compensating the effect of the mechanically disadvantageous in-line hydrogen-bond geometry. Atomistic and coarse-grained force distribution patterns can thus explain differences in mechanical response of silk crystals, opening up the road to predict full fiber mechanics.

Numerical investigation of hydrodynamic flow over an AUV moving in the water-surface vicinity considering the laminar-turbulent transition

NASA Astrophysics Data System (ADS)

Salari, Mahmoud; Rava, Amin

2017-09-01

Nowadays, Autonomous Underwater Vehicles (AUVs) are frequently used for exploring the oceans. The hydrodynamics of AUVs moving in the vicinity of the water surface are significantly different at higher depths. In this paper, the hydrodynamic coefficients of an AUV in non-dimensional depths of 0.75, 1, 1.5, 2, and 4D are obtained for movement close to the free-surface. Reynolds Averaged Navier Stokes Equations (RANS) are discretized using the finite volume approach and the water-surface effects modeled using the Volume of Fraction (VOF) method. As the operating speeds of AUVs are usually low, the boundary layer over them is not fully laminar or fully turbulent, so the effect of boundary layer transition from laminar to turbulent flow was considered in the simulations. Two different turbulence/transition models were used: 1) a full-turbulence model, the k-ɛ model, and 2) a turbulence/transition model, Menter's Transition-SST model. The results show that the Menter's Transition-SST model has a better consistency with experimental results. In addition, the wave-making effects of these bodies are studied at different immersion depths in the sea-surface vicinity or at finite depths. It is observed that the relevant pitch moments and lift coefficients are non-zero for these axi-symmetric bodies when they move close to the sea-surface. This is not expected for greater depths.

Investigation of graphene-on-metal substrates for SPR-based sensor using finite-difference time domain.

PubMed

Said, Fairus Atida; Menon, Pulliyaseri Susthitha; Rajendran, Venkatachalam; Shaari, Sahbudin; Majlis, Burhanuddin Y

2017-12-01

In this study, the authors investigated the effects of a single layer graphene as a coating layer on top of metal thin films such as silver, gold, aluminum and copper using finite-difference time domain method. To enhance the resolution of surface plasmon resonance (SPR) sensor, it is necessary to increase the SPR reflectivity and decrease the full-width-half maximum (FWHM) of the SPR curve so that there is minimum uncertainty in the determination of the resonance dip. Numerical data was verified with analytical and experimental data where all the data were in good agreement with resonance angle differing in <10% due to noise present in components such as humidity and temperature. In further analysis, reflectivity and FWHM were compared among four types of metal with various thin film thicknesses where graphene was applied on top of the metal layers, and data was compared against pure conventional metal thin films. A 60 nm-thick Au thin film results in higher performance with reflectivity of 92.4% and FWHM of 0.88° whereas single layer graphene-on-60 nm-thick Au gave reflectivity of 91.7% and FWHM of 1.32°. However, a graphene-on-40 nm-thick Ag also gave good performance with narrower FWHM of 0.88° and reflection spectra of 89.2%.

Stress distribution difference between Lava Ultimate full crowns and IPS e.max CAD full crowns on a natural tooth and on tooth-shaped implant abutments.

PubMed

Krejci, Ivo; Daher, René

2017-04-01

The goal of this short communication is to present finite element analysis comparison of the stress distribution between CAD/CAM full crowns made of Lava Ultimate and of IPS e.max CAD, adhesively luted to natural teeth and to implant abutments with the shape of natural teeth. Six 3D models were prepared using a 3D content-creating software, based on a micro-CT scan of a human mandibular molar. The geometry of the full crown and of the abutment was the same for all models representing Lava Ultimate full crowns (L) and IPS e.max CAD full crowns (E) on three different abutments: prepared natural tooth (n), titanium abutment (t) and zirconia abutment (z). A static load of 400 N was applied on the vestibular and lingual cusps, and fixtures were applied to the base of the models. After running the static linear analysis, the post-processing data we analyzed. The stress values at the interface between the crown and the abutment of the Lt and Lz groups were significantly higher than the stress values at the same interface of all the other models. The high stress concentration in the adhesive at the interface between the crown and the abutment of the Lava Ultimate group on implants might be one of the factors contributing to the reported debondings of crowns.

MITHRA 1.0: A full-wave simulation tool for free electron lasers

NASA Astrophysics Data System (ADS)

Fallahi, Arya; Yahaghi, Alireza; Kärtner, Franz X.

2018-07-01

Free Electron Lasers (FELs) are a solution for providing intense, coherent and bright radiation in the hard X-ray regime. Due to the low wall-plug efficiency of FEL facilities, it is crucial and additionally very useful to develop complete and accurate simulation tools for better optimizing a FEL interaction. The highly sophisticated dynamics involved in a FEL process was the main obstacle hindering the development of general simulation tools for this problem. We present a numerical algorithm based on finite difference time domain/Particle in cell (FDTD/PIC) in a Lorentz boosted coordinate system which is able to fulfill a full-wave simulation of a FEL process. The developed software offers a suitable tool for the analysis of FEL interactions without considering any of the usual approximations. A coordinate transformation to bunch rest frame makes the very different length scales of bunch size, optical wavelengths and the undulator period transform to values with the same order. Consequently, FDTD/PIC simulations in conjunction with efficient parallelization techniques make the full-wave simulation feasible using the available computational resources. Several examples of free electron lasers are analyzed using the developed software, the results are benchmarked based on standard FEL codes and discussed in detail.

Shear Heating-Induced Thermal Pressurization During the Nucleation of Earthquakes

NASA Astrophysics Data System (ADS)

Schmitt, S. V.; Segall, P.

2008-12-01

Shear heating-induced thermal pressurization has long been posited as a weakening mechanism during earthquakes. It is often assumed that thermal pressurization does not become important until earthquakes become moderate to large in magnitude. Schmitt et al. [AGU, 2007] confirmed the estimate of Segall and Rice [JGR, 2006] that thermal pressurization becomes dominant during the quasi-static nucleation phase by conducting 2D numerical simulations that account for full thermomechanical coupling, with rate and state dependent friction. In that work, thermal pressurization becomes the dominant weakening mechanism at slip rates of 10-5 to 10-3 m/s, depending on the fault zone hydraulic diffusivity. Interestingly, the thermal pressurization process leads to a contraction of the nucleation zone, rather than the growing crack (aging law) or unidirectional slip pulse (slip law) associated with drained rate- and state-dependent frictional nucleation. The results of Schmitt et al. [AGU, 2007] had a shortcoming in that the principal slip surface was treated as a zero-width feature, while in reality it should be a finite-width shear zone. We address that shortcoming with a new set of numerical simulations. We assume a finite-width fault governed by rate and state friction with the radiation damping approximation to simulate inertial effects. Both thermal and hydraulic diffusion are computed via finite differences on separate, coupled grids that adaptively remesh to minimize computational expense while maintaining accuracy. New results suggest that the thermal pressurization effect is modestly reduced by including the finite thickness of the shear zone. Despite the reduction in the effect, the new results still indicate that (1) thermal pressurization is important before seismic slip and (2) thermal pressurization restricts growth of the nucleation zone.

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).

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...

The Penn State Safety Floor: Part I--Design parameters associated with walking deflections.

PubMed

Casalena, J A; Ovaert, T C; Cavanagh, P R; Streit, D A

1998-08-01

A new flooring system has been developed to reduce peak impact forces to the hips when humans fall. The new safety floor is designed to remain relatively rigid under normal walking conditions, but to deform elastically when impacted during a fall. Design objectives included minimizing peak force experienced by the femur during a fall-induced impact, while maintaining a maximum of 2 mm of floor deflection during walking. Finite Element Models (FEMs) were developed to capture the complex dynamics of impact response between two deformable bodies. Validation of the finite element models included analytical calculations of theoretical buckling column response, experimental quasi-static loading of full-scale flooring prototypes, and flooring response during walking trials. Finite Element Method results compared well with theoretical and experimental data. Both finite element and experimental data suggest that the proposed safety floor can effectively meet the design goal of 2 mm maximum deflection during walking, while effectively reducing impact forces during a fall.

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.

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.

Modeling of Sensor Placement Strategy for Shape Sensing and Structural Health Monitoring of a Wing-Shaped Sandwich Panel Using Inverse Finite Element Method.

PubMed

Kefal, Adnan; Yildiz, Mehmet

2017-11-30

This paper investigated the effect of sensor density and alignment for three-dimensional shape sensing of an airplane-wing-shaped thick panel subjected to three different loading conditions, i.e., bending, torsion, and membrane loads. For shape sensing analysis of the panel, the Inverse Finite Element Method (iFEM) was used together with the Refined Zigzag Theory (RZT), in order to enable accurate predictions for transverse deflection and through-the-thickness variation of interfacial displacements. In this study, the iFEM-RZT algorithm is implemented by utilizing a novel three-node C°-continuous inverse-shell element, known as i3-RZT. The discrete strain data is generated numerically through performing a high-fidelity finite element analysis on the wing-shaped panel. This numerical strain data represents experimental strain readings obtained from surface patched strain gauges or embedded fiber Bragg grating (FBG) sensors. Three different sensor placement configurations with varying density and alignment of strain data were examined and their corresponding displacement contours were compared with those of reference solutions. The results indicate that a sparse distribution of FBG sensors (uniaxial strain measurements), aligned in only the longitudinal direction, is sufficient for predicting accurate full-field membrane and bending responses (deformed shapes) of the panel, including a true zigzag representation of interfacial displacements. On the other hand, a sparse deployment of strain rosettes (triaxial strain measurements) is essentially enough to produce torsion shapes that are as accurate as those of predicted by a dense sensor placement configuration. Hence, the potential applicability and practical aspects of i3-RZT/iFEM methodology is proven for three-dimensional shape-sensing of future aerospace structures.

Effect of Integration Patterns Around Implant Neck on Stress Distribution in Peri-Implant Bone: A Finite Element Analysis.

PubMed

Han, Jingyun; Sun, Yuchun; Wang, Chao

2017-08-01

To investigate the biomechanical performance of different osseointegration patterns between cortical bone and implants using finite element analysis. Fifteen finite element models were constructed of the mandibular fixed prosthesis supported by implants. Masticatory loads (200 N axial, 100 N oblique, 40 N horizontal) were applied. The cortical bone/implant interface was divided equally into four layers: upper, upper-middle, lower-middle, and lower. The bone stress and implant displacement were calculated for 5 degrees of uniform integration (0, 20%, 40%, 60%, and 100%) and 10 integration patterns. The stress was concentrated in the bone margin and gradually decreased as osseointegration progressed, when the integrated and nonintegrated areas were alternated on the bone-implant surface. Compared with full integration, the integration of only the lower-middle layer or lower half layers significantly decreased von Mises, tensile, and compressive stresses in cortical bone under oblique and horizontal loads, and these patterns did not induce higher stress in the cancellous bone. For the integration of only the upper or upper-middle layer, stress in the cortical and cancellous bones significantly increased and was considerably higher than in the case of nonintegration. In addition, the maximum stress in the cortical bone was sensitive to the quantity of integrated nodes at the bone margin; lower quantity was associated with higher stress. There was no significant difference in the displacement of implants among 15 models. Integration patterns of cortical bone significantly affect stress distribution in peri-implant bone. The integration of only the lower-middle or lower half layers helps to increase the load-bearing capacity of peri-implant bone and decrease the risk of overloading, while upper integration may further increase the risk of bone resorption. © 2016 by the American College of Prosthodontists.

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.

Structural Anomaly Detection Using Fiber Optic Sensors and Inverse Finite Element Method

NASA Technical Reports Server (NTRS)

Quach, Cuong C.; Vazquez, Sixto L.; Tessler, Alex; Moore, Jason P.; Cooper, Eric G.; Spangler, Jan. L.

2005-01-01

NASA Langley Research Center is investigating a variety of techniques for mitigating aircraft accidents due to structural component failure. One technique under consideration combines distributed fiber optic strain sensing with an inverse finite element method for detecting and characterizing structural anomalies anomalies that may provide early indication of airframe structure degradation. The technique identifies structural anomalies that result in observable changes in localized strain but do not impact the overall surface shape. Surface shape information is provided by an Inverse Finite Element Method that computes full-field displacements and internal loads using strain data from in-situ fiberoptic sensors. This paper describes a prototype of such a system and reports results from a series of laboratory tests conducted on a test coupon subjected to increasing levels of damage.

A time-domain finite element boundary integral approach for elastic wave scattering

NASA Astrophysics Data System (ADS)

Shi, F.; Lowe, M. J. S.; Skelton, E. A.; Craster, R. V.

2018-04-01

The response of complex scatterers, such as rough or branched cracks, to incident elastic waves is required in many areas of industrial importance such as those in non-destructive evaluation and related fields; we develop an approach to generate accurate and rapid simulations. To achieve this we develop, in the time domain, an implementation to efficiently couple the finite element (FE) method within a small local region, and the boundary integral (BI) globally. The FE explicit scheme is run in a local box to compute the surface displacement of the scatterer, by giving forcing signals to excitation nodes, which can lie on the scatterer itself. The required input forces on the excitation nodes are obtained with a reformulated FE equation, according to the incident displacement field. The surface displacements computed by the local FE are then projected, through time-domain BI formulae, to calculate the scattering signals with different modes. This new method yields huge improvements in the efficiency of FE simulations for scattering from complex scatterers. We present results using different shapes and boundary conditions, all simulated using this approach in both 2D and 3D, and then compare with full FE models and theoretical solutions to demonstrate the efficiency and accuracy of this numerical approach.

Simulation of ultrasonic NCF composites testing using 3D finite element model

NASA Astrophysics Data System (ADS)

Liu, Z.; Saffari, N.; Fromme, P.

2012-04-01

Composite materials offer many advantages for aerospace applications, e.g., good strength to weight ratio. Different types of composites, such as non-crimp fabrics (NCF), are currently being investigated as they offer reduced manufacturing costs and improved damage tolerance as compared to traditional pre-impregnated composite materials. NCF composites are made from stitched fiber bundles (tows), which typically have a width and thickness in the order of millimeter. This results in strongly inhomogeneous and anisotropic material properties. Different types of manufacturing imperfections, such as porosity, resin pockets, tow crimp and misalignment can lead to reduced material strength and thus to defects following excessive loads or impact, e.g. fracture and delaminations. The ultrasonic non-destructive testing of NCF composites is difficult, as the tow size is comparable to the wavelength, leading to multiple scattering in this inherently three-dimensional structure. For typical material properties and geometry of an NCF composite, a full three-dimensional Finite Element (FE) model has been developed in ABAQUS. The propagation of longitudinal ultrasonic waves has been simulated and the effect of multiple scattering at the fiber tows investigated. The effect of porosity as a typical manufacturing imperfection has been considered. The potential for the detection and quantification of such defects is discussed based on the observed influence on the ultrasonic wave propagation and attenuation.

Numerical Characterization of Piezoceramics Using Resonance Curves

PubMed Central

Pérez, Nicolás; Buiochi, Flávio; Brizzotti Andrade, Marco Aurélio; Adamowski, Julio Cezar

2016-01-01

Piezoelectric materials characterization is a challenging problem involving physical concepts, electrical and mechanical measurements and numerical optimization techniques. Piezoelectric ceramics such as Lead Zirconate Titanate (PZT) belong to the 6 mm symmetry class, which requires five elastic, three piezoelectric and two dielectric constants to fully represent the material properties. If losses are considered, the material properties can be represented by complex numbers. In this case, 20 independent material constants are required to obtain the full model. Several numerical methods have been used to adjust the theoretical models to the experimental results. The continuous improvement of the computer processing ability has allowed the use of a specific numerical method, the Finite Element Method (FEM), to iteratively solve the problem of finding the piezoelectric constants. This review presents the recent advances in the numerical characterization of 6 mm piezoelectric materials from experimental electrical impedance curves. The basic strategy consists in measuring the electrical impedance curve of a piezoelectric disk, and then combining the Finite Element Method with an iterative algorithm to find a set of material properties that minimizes the difference between the numerical impedance curve and the experimental one. Different methods to validate the results are also discussed. Examples of characterization of some common piezoelectric ceramics are presented to show the practical application of the described methods. PMID:28787875

Applications of a General Finite-Difference Method for Calculating Bending Deformations of Solid Plates

NASA Technical Reports Server (NTRS)

Walton, William C., Jr.

1960-01-01

This paper reports the findings of an investigation of a finite - difference method directly applicable to calculating static or simple harmonic flexures of solid plates and potentially useful in other problems of structural analysis. The method, which was proposed in doctoral thesis by John C. Houbolt, is based on linear theory and incorporates the principle of minimum potential energy. Full realization of its advantages requires use of high-speed computing equipment. After a review of Houbolt's method, results of some applications are presented and discussed. The applications consisted of calculations of the natural modes and frequencies of several uniform-thickness cantilever plates and, as a special case of interest, calculations of the modes and frequencies of the uniform free-free beam. Computed frequencies and nodal patterns for the first five or six modes of each plate are compared with existing experiments, and those for one plate are compared with another approximate theory. Beam computations are compared with exact theory. On the basis of the comparisons it is concluded that the method is accurate and general in predicting plate flexures, and additional applications are suggested. An appendix is devoted t o computing procedures which evolved in the progress of the applications and which facilitate use of the method in conjunction with high-speed computing equipment.

Numerical Characterization of Piezoceramics Using Resonance Curves.

PubMed

Pérez, Nicolás; Buiochi, Flávio; Brizzotti Andrade, Marco Aurélio; Adamowski, Julio Cezar

2016-01-27

Piezoelectric materials characterization is a challenging problem involving physical concepts, electrical and mechanical measurements and numerical optimization techniques. Piezoelectric ceramics such as Lead Zirconate Titanate (PZT) belong to the 6 mm symmetry class, which requires five elastic, three piezoelectric and two dielectric constants to fully represent the material properties. If losses are considered, the material properties can be represented by complex numbers. In this case, 20 independent material constants are required to obtain the full model. Several numerical methods have been used to adjust the theoretical models to the experimental results. The continuous improvement of the computer processing ability has allowed the use of a specific numerical method, the Finite Element Method (FEM), to iteratively solve the problem of finding the piezoelectric constants. This review presents the recent advances in the numerical characterization of 6 mm piezoelectric materials from experimental electrical impedance curves. The basic strategy consists in measuring the electrical impedance curve of a piezoelectric disk, and then combining the Finite Element Method with an iterative algorithm to find a set of material properties that minimizes the difference between the numerical impedance curve and the experimental one. Different methods to validate the results are also discussed. Examples of characterization of some common piezoelectric ceramics are presented to show the practical application of the described methods.

3D finite element simulation of non-crimp fabric composites ultrasonic testing

NASA Astrophysics Data System (ADS)

Liu, Z.; Saffari, N.; Fromme, P.

2012-05-01

Composite materials offer many advantages for aerospace applications, e.g., good strength to weight ratio. Different types of composites, such as non-crimp fabrics (NCF), are currently being investigated as they offer reduced manufacturing costs and improved damage tolerance as compared to traditional pre-impregnated composite materials. NCF composites are made from stitched fiber bundles (tows), which typically have a width and thickness of less than a millimeter. This results in strongly inhomogeneous and anisotropic material properties. Different types of manufacturing imperfections, such as porosity, resin pockets, tow crimp and misalignment can lead to reduced material strength and thus to defects following excessive loads or impact, e.g., fracture and delaminations. The ultrasonic non-destructive testing of NCF composites is difficult, as the tow size is comparable to the wavelength, leading to multiple scattering in this inherently three-dimensional structure. For typical material properties and geometry of an NCF composite, a full three-dimensional Finite Element (FE) model has been developed in ABAQUS. The propagation of longitudinal ultrasonic waves has been simulated and the effect of multiple scattering at the fiber tows investigated. The influence of porosity in the epoxy matrix as a typical manufacturing defect on the ultrasonic wave propagation and attenuation has been studied.

77 FR 75833 - Airworthiness Directives; Airbus Airplanes

Federal Register 2010, 2011, 2012, 2013, 2014

2012-12-26

... accordance with Airbus SB A300-57-6053 (Mod. 10453). Therefore and pending completion of the full analysis using a refined Finite Element Model, EASA [European Aviation Safety Agency] issued AD 2009-0094 [which...

Simulating the interaction of the heliosphere with the local interstellar medium: MHD results from a finite volume approach, first bidimensional results

NASA Technical Reports Server (NTRS)

Chanteur, G.; Khanfir, R.

1995-01-01

We have designed a full compressible MHD code working on unstructured meshes in order to be able to compute accurately sharp structures embedded in large scale simulations. The code is based on a finite volume method making use of a kinetic flux splitting. A bidimensional version of the code has been used to simulate the interaction of a moving interstellar medium, magnetized or unmagnetized with a rotating and magnetized heliopspheric plasma source. Being aware that these computations are not realistic due to the restriction to two dimensions, we present it to demonstrate the ability of this new code to handle this problem. An axisymetric version, now under development, will be operational in a few months. Ultimately we plan to run a full 3d version.

Full-vectorial finite element method in a cylindrical coordinate system for loss analysis of photonic wire bends

NASA Astrophysics Data System (ADS)

Kakihara, Kuniaki; Kono, Naoya; Saitoh, Kunimasa; Koshiba, Masanori

2006-11-01

This paper presents a new full-vectorial finite-element method in a local cylindrical coordinate system, to effectively analyze bending losses in photonic wires. The discretization is performed in the cross section of a three-dimensional curved waveguide, using hybrid edge/nodal elements. The solution region is truncated by anisotropic, perfectly matched layers in the cylindrical coordinate system, to deal properly with leaky modes of the waveguide. This approach is used to evaluate bending losses in silicon wire waveguides. The numerical results of the present approach are compared with results calculated with an equivalent straight waveguide approach and with reported experimental data. These comparisons together demonstrate the validity of the present approach based on the cylindrical coordinate system and also clarifies the limited validity of the equivalent straight waveguide approximation.

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II

NASA Technical Reports Server (NTRS)

Shertzer, J.; Temkin, A.

2003-01-01

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE) can be reduced to a 2d partial differential equation (pde), and was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation. The resultant equation can be reduced to a pair of coupled pde's, to which the finite element method can still be applied. The resultant scattering amplitudes, both singlet and triplet, as a function of angle can be calculated for various energies. The results are in excellent agreement with converged partial wave results.

Discrete variable representation in electronic structure theory: quadrature grids for least-squares tensor hypercontraction.

PubMed

Parrish, Robert M; Hohenstein, Edward G; Martínez, Todd J; Sherrill, C David

2013-05-21

We investigate the application of molecular quadratures obtained from either standard Becke-type grids or discrete variable representation (DVR) techniques to the recently developed least-squares tensor hypercontraction (LS-THC) representation of the electron repulsion integral (ERI) tensor. LS-THC uses least-squares fitting to renormalize a two-sided pseudospectral decomposition of the ERI, over a physical-space quadrature grid. While this procedure is technically applicable with any choice of grid, the best efficiency is obtained when the quadrature is tuned to accurately reproduce the overlap metric for quadratic products of the primary orbital basis. Properly selected Becke DFT grids can roughly attain this property. Additionally, we provide algorithms for adopting the DVR techniques of the dynamics community to produce two different classes of grids which approximately attain this property. The simplest algorithm is radial discrete variable representation (R-DVR), which diagonalizes the finite auxiliary-basis representation of the radial coordinate for each atom, and then combines Lebedev-Laikov spherical quadratures and Becke atomic partitioning to produce the full molecular quadrature grid. The other algorithm is full discrete variable representation (F-DVR), which uses approximate simultaneous diagonalization of the finite auxiliary-basis representation of the full position operator to produce non-direct-product quadrature grids. The qualitative features of all three grid classes are discussed, and then the relative efficiencies of these grids are compared in the context of LS-THC-DF-MP2. Coarse Becke grids are found to give essentially the same accuracy and efficiency as R-DVR grids; however, the latter are built from explicit knowledge of the basis set and may guide future development of atom-centered grids. F-DVR is found to provide reasonable accuracy with markedly fewer points than either Becke or R-DVR schemes.

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.

Solving the critical thermal bowing in 3C-SiC/Si(111) by a tilting Si pillar architecture

NASA Astrophysics Data System (ADS)

Albani, Marco; Marzegalli, Anna; Bergamaschini, Roberto; Mauceri, Marco; Crippa, Danilo; La Via, Francesco; von Känel, Hans; Miglio, Leo

2018-05-01

The exceptionally large thermal strain in few-micrometers-thick 3C-SiC films on Si(111), causing severe wafer bending and cracking, is demonstrated to be elastically quenched by substrate patterning in finite arrays of Si micro-pillars, sufficiently large in aspect ratio to allow for lateral pillar tilting, both by simulations and by preliminary experiments. In suspended SiC patches, the mechanical problem is addressed by finite element method: both the strain relaxation and the wafer curvature are calculated at different pillar height, array size, and film thickness. Patches as large as required by power electronic devices (500-1000 μm in size) show a remarkable residual strain in the central area, unless the pillar aspect ratio is made sufficiently large to allow peripheral pillars to accommodate the full film retraction. A sublinear relationship between the pillar aspect ratio and the patch size, guaranteeing a minimal curvature radius, as required for wafer processing and micro-crack prevention, is shown to be valid for any heteroepitaxial system.

Finite Element Analysis of Wrinkled Membrane Structures for Sunshield Applications

NASA Technical Reports Server (NTRS)

Johnston, John D.; Brodeur, Stephen J. (Technical Monitor)

2002-01-01

The deployable sunshield is an example of a gossamer structure envisioned for use on future space telescopes. The basic structure consists of multiple layers of pretensioned, thin-film membranes supported by deployable booms. The prediction and verification of sunshield dynamics has been identified as an area in need of technology development due to the difficulties inherent in predicting nonlinear structural behavior of the membranes and because of the challenges involved. in ground testing of the full-scale structure. This paper describes a finite element analysis of a subscale sunshield that has been subjected to ground testing in support of the Next Generation Space Telescope (NGST) program. The analysis utilizes a nonlinear material model that accounts for wrinkling of the membranes. Results are presented from a nonlinear static preloading analysis and subsequent dynamics analyses to illustrate baseline sunshield structural characteristics. Studies are then described which provide further insight into the effect of membrane. preload on sunshield dynamics and the performance of different membrane modeling techniques. Lastly, a comparison of analytical predictions and ground test results is presented.

Overview of the DAEDALOS project

NASA Astrophysics Data System (ADS)

Bisagni, Chiara

2015-10-01

The "Dynamics in Aircraft Engineering Design and Analysis for Light Optimized Structures" (DAEDALOS) project aimed to develop methods and procedures to determine dynamic loads by considering the effects of dynamic buckling, material damping and mechanical hysteresis during aircraft service. Advanced analysis and design principles were assessed with the scope of partly removing the uncertainty and the conservatism of today's design and certification procedures. To reach these objectives a DAEDALOS aircraft model representing a mid-size business jet was developed. Analysis and in-depth investigation of the dynamic response were carried out on full finite element models and on hybrid models. Material damping was experimentally evaluated, and different methods for damping evaluation were developed, implemented in finite element codes and experimentally validated. They include a strain energy method, a quasi-linear viscoelastic material model, and a generalized Maxwell viscous material damping. Panels and shells representative of typical components of the DAEDALOS aircraft model were experimentally tested subjected to static as well as dynamic loads. Composite and metallic components of the aircraft model were investigated to evaluate the benefit in terms of weight saving.

Tetrahedral Finite-Volume Solutions to the Navier-Stokes Equations on Complex Configurations

NASA Technical Reports Server (NTRS)

Frink, Neal T.; Pirzadeh, Shahyar Z.

1998-01-01

A review of the algorithmic features and capabilities of the unstructured-grid flow solver USM3Dns is presented. This code, along with the tetrahedral grid generator, VGRIDns, is being extensively used throughout the U.S. for solving the Euler and Navier-Stokes equations on complex aerodynamic problems. Spatial discretization is accomplished by a tetrahedral cell-centered finite-volume formulation using Roe's upwind flux difference splitting. The fluxes are limited by either a Superbee or MinMod limiter. Solution reconstruction within the tetrahedral cells is accomplished with a simple, but novel, multidimensional analytical formula. Time is advanced by an implicit backward-Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the near-wall region of the boundary layer. The issues of accuracy and robustness of USM3Dns Navier-Stokes capabilities are addressed for a flat-plate boundary layer, and a full F-16 aircraft with external stores at transonic speed.

Extension of Ko Straight-Beam Displacement Theory to Deformed Shape Predictions of Slender Curved Structures

NASA Technical Reports Server (NTRS)

Ko, William L.; Fleischer, Van Tran

2011-01-01

The Ko displacement theory originally developed for shape predictions of straight beams is extended to shape predictions of curved beams. The surface strains needed for shape predictions were analytically generated from finite-element nodal stress outputs. With the aid of finite-element displacement outputs, mathematical functional forms for curvature-effect correction terms are established and incorporated into straight-beam deflection equations for shape predictions of both cantilever and two-point supported curved beams. The newly established deflection equations for cantilever curved beams could provide quite accurate shape predictions for different cantilever curved beams, including the quarter-circle cantilever beam. Furthermore, the newly formulated deflection equations for two-point supported curved beams could provide accurate shape predictions for a range of two-point supported curved beams, including the full-circular ring. Accuracy of the newly developed curved-beam deflection equations is validated through shape prediction analysis of curved beams embedded in the windward shallow spherical shell of a generic crew exploration vehicle. A single-point collocation method for optimization of shape predictions is discussed in detail

Microstructured optical fibers for terahertz waveguiding regime by using an analytical field model

NASA Astrophysics Data System (ADS)

Sharma, Dinesh Kumar; Sharma, Anurag; Tripathi, Saurabh Mani

2017-12-01

Microstructured optical fibres (MOFs) are seen as novel optical waveguide for the potential applications in the terahertz (THz) band as they provide a flexible route towards THz waveguiding. Using the analytical field model (Sharma et al., 2014) developed for index-guiding MOFs with hexagonal lattice of circular air-holes in the photonic crystal cladding; we aim to study the propagation characteristics such as effective index, near and the far-field radiation patterns and its evolution from near-to-far-field domain, spot size, effective mode area, and the numerical aperture at the THz regime. Further, we present an analytical field expression for the next higher-order mode of the MOF for studying the modal properties at terahertz frequencies. Also, we investigate the mode cut-off conditions for identifying the single-mode operation range at THz frequencies. Emphasis is put on studying the coupling characteristics of MOF geometries for efficient mode coupling. Comparisons with available experimental and numerical simulation results, e.g., those based on the full-vector finite element method (FEM) and the finite-difference frequency-domain (FDFD) method have been included.

Convective hydromagnetic instabilities of a power-law liquid saturating a porous medium: Flux conditions

NASA Astrophysics Data System (ADS)

Chahtour, C.; Ben Hamed, H.; Beji, H.; Guizani, A.; Alimi, W.

2018-01-01

We investigate how an external imposed magnetic field affects thermal instability in a horizontal shallow porous cavity saturated by a non-Newtonian power-law liquid. The magnetic field is assumed to be constant and parallel to the gravity. A uniform heat flux is applied to the horizontal walls of the layer while the vertical walls are adiabatic. We use linear stability analysis to find expressions for the critical Rayleigh number as a function of the power-law index and the intensity of the magnetic field. We use nonlinear parallel flow theory to find some explicit solutions of the problem, and we use finite difference numerical simulations to solve the full nonlinear equations. We show how the presence of magnetic field alters the known hydrodynamical result of Newtonian flows and power-law flows and how it causes the presence of subcritical finite amplitude convection for both pseudoplastic and dilatant fluids. We also show that in the limit of very strong magnetic field, the dissipation of energy by Joule effect dominates the dissipation of energy by shear stress and gives to the liquid an inviscid character.

Fatigue Life Analysis of Tapered Hybrid Composite Flexbeams

NASA Technical Reports Server (NTRS)

Murri, Gretchen B.; Schaff, Jeffery R.; Dobyns, Alan L.

2002-01-01

Nonlinear-tapered flexbeam laminates from a full-size composite helicopter rotor hub flexbeam were tested under combined constant axial tension and cyclic bending loads. The two different graphite/glass hybrid configurations tested under cyclic loading failed by delamination in the tapered region. A 2-D finite element model was developed which closely approximated the flexbeam geometry, boundary conditions, and loading. The analysis results from two geometrically nonlinear finite element codes, ANSYS and ABAQUS, are presented and compared. Strain energy release rates (G) obtained from the above codes using the virtual crack closure technique (VCCT) at a resin crack location in the flexbeams are presented for both hybrid material types. These results compare well with each other and suggest that the initial delamination growth from the resin crack toward the thick region of the flexbeam is strongly mode II. The peak calculated G values were used with material characterization data to calculate fatigue life curves and compared with test data. A curve relating maximum surface strain to number of loading cycles at delamination onset compared reasonably well with the test results.

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.

Entanglement entropy in Fermi gases and Anderson's orthogonality catastrophe.

PubMed

Ossipov, A

2014-09-26

We study the ground-state entanglement entropy of a finite subsystem of size L of an infinite system of noninteracting fermions scattered by a potential of finite range a. We derive a general relation between the scattering matrix and the overlap matrix and use it to prove that for a one-dimensional symmetric potential the von Neumann entropy, the Rényi entropies, and the full counting statistics are robust against potential scattering, provided that L/a≫1. The results of numerical calculations support the validity of this conclusion for a generic potential.

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,…

Modelling water uptake efficiency of root systems

NASA Astrophysics Data System (ADS)

Leitner, Daniel; Tron, Stefania; Schröder, Natalie; Bodner, Gernot; Javaux, Mathieu; Vanderborght, Jan; Vereecken, Harry; Schnepf, Andrea

2016-04-01

Water uptake is crucial for plant productivity. Trait based breeding for more water efficient crops will enable a sustainable agricultural management under specific pedoclimatic conditions, and can increase drought resistance of plants. Mathematical modelling can be used to find suitable root system traits for better water uptake efficiency defined as amount of water taken up per unit of root biomass. This approach requires large simulation times and large number of simulation runs, since we test different root systems under different pedoclimatic conditions. In this work, we model water movement by the 1-dimensional Richards equation with the soil hydraulic properties described according to the van Genuchten model. Climatic conditions serve as the upper boundary condition. The root system grows during the simulation period and water uptake is calculated via a sink term (after Tron et al. 2015). The goal of this work is to compare different free software tools based on different numerical schemes to solve the model. We compare implementations using DUMUX (based on finite volumes), Hydrus 1D (based on finite elements), and a Matlab implementation of Van Dam, J. C., & Feddes 2000 (based on finite differences). We analyse the methods for accuracy, speed and flexibility. Using this model case study, we can clearly show the impact of various root system traits on water uptake efficiency. Furthermore, we can quantify frequent simplifications that are introduced in the modelling step like considering a static root system instead of a growing one, or considering a sink term based on root density instead of considering the full root hydraulic model (Javaux et al. 2008). References Tron, S., Bodner, G., Laio, F., Ridolfi, L., & Leitner, D. (2015). Can diversity in root architecture explain plant water use efficiency? A modeling study. Ecological modelling, 312, 200-210. Van Dam, J. C., & Feddes, R. A. (2000). Numerical simulation of infiltration, evaporation and shallow groundwater levels with the Richards equation. Journal of Hydrology, 233(1), 72-85. Javaux, M., Schröder, T., Vanderborght, J., & Vereecken, H. (2008). Use of a three-dimensional detailed modeling approach for predicting root water uptake. Vadose Zone Journal, 7(3), 1079-1088.

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.

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.

Interactions of skin thickness and physicochemical properties of test compounds in percutaneous penetration studies.

PubMed

Wilkinson, Simon C; Maas, Wilfred J M; Nielsen, Jesper Bo; Greaves, Laura C; van de Sandt, Johannes J M; Williams, Faith M

2006-05-01

To determine the effect of skin thickness on the percutaneous penetration and distribution of test compounds with varying physicochemical properties using in vitro systems. Studies were carried out in accordance with OECD guidelines on skin absorption tests. Percutaneous penetration of caffeine (log P -0.01), testosterone (log P 3.32), propoxur (log P 1.52) (finite dose in ethanol to water vehicle ratio) and butoxyethanol (log P 0.83) (undiluted finite dose or as an infinite dose 50% [v/v] aqueous solution) through skin of varying thicknesses under occluded conditions was measured using flow through cells for 8-24 h. Saline (adjusted to pH 7.4) was used as receptor fluid, with BSA added for studies with testosterone and propoxur. Following exposure, the remaining surface dose was removed by swabbing and the skin digested prior to scintillation counting. The maximum flux of caffeine was increased with decreasing skin thickness, although these differences were found to be non-significant. The presence of caffeine in the skin membrane was not altered by skin thickness. Maximum flux and cumulative dose absorbed of testosterone and butoxyethanol (in both finite and infinite doses) were markedly reduced with full thickness (about 1 mm thick) skin compared with split thickness skin (about 0.5 mm). Maximum flux of propoxur (dissolved in 60% ethanol) was clearly higher through skin of 0.71 mm than through skin of 1.36 mm, but no difference was found between 0.56 and 0.71 mm. The proportion of propoxur present in the membrane after 24 h increased significantly over the complete range of thicknesses tested (0.56-1.36 mm). A complex relationship exists between skin thickness, lipophilicity and percutaneous penetration and distribution. This has implications for risk assessment studies and for the validation of models with data from different sources.

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.

Solutal separation in a binary nanofluid due to thermodiffusion

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

Saghir, M.Z.; Yousefi, T.; Farahbakhsh, B.

2015-03-10

Transport phenomena in porous media have received considerable attention due to an increasing interest in geothermal processes, chemical catalytic reactors, waste storage (especially geological or ocean storage of carbon dioxide), etc. Among others, oil industry has shown an increasing interest in studying diffusion phenomenon. Nanofluid is a term used to describe the suspension of low concentration of metallic and non-metallic nanoparticles in a base fluid. The size of a nanoparticle ranges from 10 to 100nm, and the conventional fluids used are water, ethylene glycol (C{sub 2}H{sub 6}O{sub 2}) or engine oil. Various studies have proven that nanoparticles improve the heatmore » transfer of a base fluid. However, using various nanofluids it has been shown that the results could vary depending on different initial concentrations. The main objective of this paper is to study the diffusion and the thermodiffusion effect in a nanofluid for different fluid/porous media configurations. In this configuration, a liquid layer surrounds a porous layer. The full Brinkman equation coupled with the heat and mass transfer equations have been solved numerically for the porous layer using the finite element technique. The full Navier stokes equation coupled with heat and mass transfer equations have been solved for the liquid layer using the finite element method. A constraint between the liquid and porous layer has been applied to ensure heat flow and mass transfer continuity is maintained. A square cavity filled with hydrocarbon nanofluid of a mixture of fullerene-toluene with varying concentration of fullerene has been subject to different heating conditions. The entire cavity has been considered to be fully wetted with nanofluid. Results have confirmed that in the presence of a nanofluid a heat transfer enhancement is present up to certain initial concentration of the fullerene. The heat convection coefficient has been found to be 16% higher when a nanofluid is used as the working fluid.« less

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.

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.

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.

Numerical solutions of 2-D multi-stage rotor/stator unsteady flow interactions

NASA Astrophysics Data System (ADS)

Yang, R.-J.; Lin, S.-J.

1991-01-01

The Rai method of single-stage rotor/stator flow interaction is extended to handle multistage configurations. In this study, a two-dimensional Navier-Stokes multi-zone approach was used to investigate unsteady flow interactions within two multistage axial turbines. The governing equations are solved by an iterative, factored, implicit finite-difference, upwind algorithm. Numerical accuracy is checked by investigating the effect of time step size, the effect of subiteration in the Newton-Raphson technique, and the effect of full viscous versus thin-layer approximation. Computer results compared well with experimental data. Unsteady flow interactions, wake cutting, and the associated evolution of vortical entities are discussed.

Supersonic quasi-axisymmetric vortex breakdown

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; Kandil, Hamdy A.; Liu, C. H.

1991-01-01

An extensive computational study of supersonic quasi-axisymmetric vortex breakdown in a configured circular duct is presented. The unsteady, compressible, full Navier-Stokes (NS) equations are used. The NS equations are solved for the quasi-axisymmetric flows using an implicit, upwind, flux difference splitting, finite volume scheme. The quasi-axisymmetric solutions are time accurate and are obtained by forcing the components of the flowfield vector to be equal on two axial planes, which are in close proximity of each other. The effect of Reynolds number, for laminar flows, on the evolution and persistence of vortex breakdown, is studied. Finally, the effect of swirl ration at the duct inlet is investigated.

Analysis of viscous transonic flow over airfoil sections

NASA Technical Reports Server (NTRS)

Huff, Dennis L.; Wu, Jiunn-Chi; Sankar, L. N.

1987-01-01

A full Navier-Stokes solver has been used to model transonic flow over three airfoil sections. The method uses a two-dimensional, implicit, conservative finite difference scheme for solving the compressible Navier-Stokes equations. Results are presented as prescribed for the Viscous Transonic Airfoil Workshop to be held at the AIAA 25th Aerospace Sciences Meeting. The NACA 0012, RAE 2822 and Jones airfoils have been investigated for both attached and separated transonic flows. Predictions for pressure distributions, loads, skin friction coefficients, boundary layer displacement thickness and velocity profiles are included and compared with experimental data when possible. Overall, the results are in good agreement with experimental data.

The Spectral Element Method for Geophysical Flows

NASA Astrophysics Data System (ADS)

Taylor, Mark

1998-11-01

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

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.

Numerical Simulation of Partially-Coherent Broadband Optical Imaging Using the FDTD Method

PubMed Central

Çapoğlu, İlker R.; White, Craig A.; Rogers, Jeremy D.; Subramanian, Hariharan; Taflove, Allen; Backman, Vadim

2012-01-01

Rigorous numerical modeling of optical systems has attracted interest in diverse research areas ranging from biophotonics to photolithography. We report the full-vector electromagnetic numerical simulation of a broadband optical imaging system with partially-coherent and unpolarized illumination. The scattering of light from the sample is calculated using the finite-difference time-domain (FDTD) numerical method. Geometrical optics principles are applied to the scattered light to obtain the intensity distribution at the image plane. Multilayered object spaces are also supported by our algorithm. For the first time, numerical FDTD calculations are directly compared to and shown to agree well with broadband experimental microscopy results. PMID:21540939

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.

Development and Calibration of a System-Integrated Rotorcraft Finite Element Model for Impact Scenarios

NASA Technical Reports Server (NTRS)

Annett, Martin S.; Horta, Lucas G.; Jackson, Karen E.; Polanco, Michael A.; Littell, Justin D.

2012-01-01

Two full-scale crash tests of an MD-500 helicopter were conducted in 2009 and 2010 at NASA Langley's Landing and Impact Research Facility in support of NASA s Subsonic Rotary Wing Crashworthiness Project. The first crash test was conducted to evaluate the performance of an externally mounted composite deployable energy absorber (DEA) under combined impact conditions. In the second crash test, the energy absorber was removed to establish baseline loads that are regarded as severe but survivable. The presence of this energy absorbing device reduced the peak impact acceleration levels by a factor of three. Accelerations and kinematic data collected from the crash tests were compared to a system-integrated finite element model of the test article developed in parallel with the test program. In preparation for the full-scale crash test, a series of sub-scale and MD-500 mass simulator tests were conducted to evaluate the impact performances of various components and subsystems, including new crush tubes and the DEA blocks. Parameters defined for the system-integrated finite element model were determined from these tests. Results from 19 accelerometers placed throughout the airframe were compared to finite element model responses. The model developed for the purposes of predicting acceleration responses from the first crash test was inadequate when evaluating more severe conditions seen in the second crash test. A newly developed model calibration approach that includes uncertainty estimation, parameter sensitivity, impact shape orthogonality, and numerical optimization was used to calibrate model results for the full-scale crash test without the DEA. This combination of heuristic and quantitative methods identified modeling deficiencies, evaluated parameter importance, and proposed required model changes. The multidimensional calibration techniques presented here are particularly effective in identifying model adequacy. Acceleration results for the calibrated model were compared to test results and the original model results. There was a noticeable improvement in the pilot and copilot region, a slight improvement in the occupant model response, and an over-stiffening effect in the passenger region. One lesson learned was that this approach should be adopted early on, in combination with the building-block approaches that are customarily used, for model development and pretest predictions. Complete crash simulations with validated finite element models can be used to satisfy crash certification requirements, potentially reducing overall development costs.

Erratum: Sources of Image Degradation in Fundamental and Harmonic Ultrasound Imaging: A Nonlinear, Full-Wave, Simulation Study

PubMed Central

Pinton, Gianmarco F.; Trahey, Gregg E.; Dahl, Jeremy J.

2015-01-01

A full-wave equation that describes nonlinear propagation in a heterogeneous attenuating medium is solved numerically with finite differences in the time domain. This numerical method is used to simulate propagation of a diagnostic ultrasound pulse through a measured representation of the human abdomen with heterogeneities in speed of sound, attenuation, density, and nonlinearity. Conventional delay-and-sum beamforming is used to generate point spread functions (PSFs) that display the effects of these heterogeneities. For the particular imaging configuration that is modeled, these PSFs reveal that the primary source of degradation in fundamental imaging is due to reverberation from near-field structures. Compared with fundamental imaging, reverberation clutter in harmonic imaging is 27.1 dB lower. Simulated tissue with uniform velocity but unchanged impedance characteristics indicates that for harmonic imaging, the primary source of degradation is phase aberration. PMID:21693410

Full self-consistency in the Fermi-orbital self-interaction correction

NASA Astrophysics Data System (ADS)

Yang, Zeng-hui; Pederson, Mark R.; Perdew, John P.

2017-05-01

The Perdew-Zunger self-interaction correction cures many common problems associated with semilocal density functionals, but suffers from a size-extensivity problem when Kohn-Sham orbitals are used in the correction. Fermi-Löwdin-orbital self-interaction correction (FLOSIC) solves the size-extensivity problem, allowing its use in periodic systems and resulting in better accuracy in finite systems. Although the previously published FLOSIC algorithm Pederson et al., J. Chem. Phys. 140, 121103 (2014)., 10.1063/1.4869581 appears to work well in many cases, it is not fully self-consistent. This would be particularly problematic for systems where the occupied manifold is strongly changed by the correction. In this paper, we demonstrate a different algorithm for FLOSIC to achieve full self-consistency with only marginal increase of computational cost. The resulting total energies are found to be lower than previously reported non-self-consistent results.

Surface Profile and Stress Field Evaluation using Digital Gradient Sensing Method

DOE PAGES

Miao, C.; Sundaram, B. M.; Huang, L.; ...

2016-08-09

Shape and surface topography evaluation from measured orthogonal slope/gradient data is of considerable engineering significance since many full-field optical sensors and interferometers readily output accurate data of that kind. This has applications ranging from metrology of optical and electronic elements (lenses, silicon wafers, thin film coatings), surface profile estimation, wave front and shape reconstruction, to name a few. In this context, a new methodology for surface profile and stress field determination based on a recently introduced non-contact, full-field optical method called digital gradient sensing (DGS) capable of measuring small angular deflections of light rays coupled with a robust finite-difference-based least-squaresmore » integration (HFLI) scheme in the Southwell configuration is advanced here. The method is demonstrated by evaluating (a) surface profiles of mechanically warped silicon wafers and (b) stress gradients near growing cracks in planar phase objects.« less

A Kosloff/Basal method, 3D migration program implemented on the CYBER 205 supercomputer

NASA Technical Reports Server (NTRS)

Pyle, L. D.; Wheat, S. R.

1984-01-01

Conventional finite difference migration has relied on approximations to the acoustic wave equation which allow energy to propagate only downwards. Although generally reliable, such approaches usually do not yield an accurate migration for geological structures with strong lateral velocity variations or with steeply dipping reflectors. An earlier study by D. Kosloff and E. Baysal (Migration with the Full Acoustic Wave Equation) examined an alternative approach based on the full acoustic wave equation. The 2D, Fourier type algorithm which was developed was tested by Kosloff and Baysal against synthetic data and against physical model data. The results indicated that such a scheme gives accurate migration for complicated structures. This paper describes the development and testing of a vectorized, 3D migration program for the CYBER 205 using the Kosloff/Baysal method. The program can accept as many as 65,536 zero offset (stacked) traces.

[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.

Finite volume method and multigrid acceleration in modelling of rapid crack propagation in full-scale pipe test

NASA Astrophysics Data System (ADS)

Ivankovic, A.; Muzaferija, S.; Demirdzic, I.

1997-07-01

Rapid Crack Propagation (RCP) along pressurised plastic pipes is by far the most dangerous pipe failure mode. Despite the economic benefits offered by increasing pipe size and operating pressure, both strategies increase the risk and the potential consequences of RCP. It is therefore extremely important to account for RCP in establishing the safe operational conditions. Combined experimental-numerical study is the only reliable approach of addressing the problem, and extensive research is undertaken by various fracture groups (e.g. Southwest Research Institute - USA, Imperial College - UK). This paper presents numerical results from finite volume modelling of full-scale test on medium density polyethylene gas pressurised pipes. The crack speed and pressure profile are prescribed in the analysis. Both steady-state and transient RCPs are considered, and the comparison between the two shown. The steady-state results are efficiently achieved employing a full multigrid acceleration technique, where sets of progressively finer grids are used in V-cycles. Also, the effect of inelastic behaviour of polyethylene on RCP results is demonstrated.

Study of human phonation in a full-body domain

NASA Astrophysics Data System (ADS)

Saurabh, Shakti; Bodony, Daniel

2015-11-01

The generation and propagation of the human voice is studied in two-dimensions using a full-body domain, using direct numerical simulation. The fluid/air in the vocal tract is modeled as a compressible and viscous fluid interacting with the non-linear, viscoelastic vocal folds (VF). The VF tissue material properties are multi-layered, with varying stiffness, and a finite-strain model is utilized and implemented in a quadratic finite element code. The fluid-solid domains are coupled through a boundary-fitted interface and utilize a Poisson equation-based mesh deformation method. The full-body domain includes the near VF region, the vocal tract, a simplified model of the soft palate and mouth, and extends out into the acoustic far-field. A new kind of inflow boundary condition based upon a quasi-one-dimensional formulation with constant sub-glottal volume velocity, which is linked to the VF movement, has been adopted. The sound pressure levels (SPL) measured are realistic and we analyze their connection to the VF dynamics and glottal and vocal tract geometries. Supported by the National Science Foundation (CAREER award number 1150439).

Simulating the Impact Response of Three Full-Scale Crash Tests of Cessna 172 Aircraft

NASA Technical Reports Server (NTRS)

Jackson, Karen E.; Fasanella, Edwin L.; Littell, Justin D.; Annett, Martin S.; Stimson, Chad M.

2017-01-01

During the summer of 2015, a series of three full-scale crash tests were performed at the Landing and Impact Research Facility located at NASA Langley Research Center of Cessna 172 aircraft. The first test (Test 1) represented a flare-to-stall emergency or hard landing onto a rigid surface. The second test (Test 2) represented a controlled-flight- into-terrain (CFIT) with a nose down pitch attitude of the aircraft, which impacted onto soft soil. The third test (Test 3) also represented a CFIT with a nose up pitch attitude of the aircraft, which resulted in a tail strike condition. Test 3 was also conducted onto soft soil. These crash tests were performed for the purpose of evaluating the performance of Emergency Locator Transmitters and to generate impact test data for model calibration. Finite element models were generated and impact analyses were conducted to simulate the three impact conditions using the commercial nonlinear, transient dynamic finite element code, LS-DYNA®. The objective of this paper is to summarize test-analysis results for the three full-scale crash tests.

Development of a hip joint model for finite volume simulations.

PubMed

Cardiff, P; Karač, A; FitzPatrick, D; Ivanković, A

2014-01-01

This paper establishes a procedure for numerical analysis of a hip joint using the finite volume method. Patient-specific hip joint geometry is segmented directly from computed tomography and magnetic resonance imaging datasets and the resulting bone surfaces are processed into a form suitable for volume meshing. A high resolution continuum tetrahedral mesh has been generated, where a sandwich model approach is adopted; the bones are represented as a stiffer cortical shells surrounding more flexible cancellous cores. Cartilage is included as a uniform thickness extruded layer and the effect of layer thickness is investigated. To realistically position the bones, gait analysis has been performed giving the 3D positions of the bones for the full gait cycle. Three phases of the gait cycle are examined using a finite volume based custom structural contact solver implemented in open-source software OpenFOAM.

Parallelized Three-Dimensional Resistivity Inversion Using Finite Elements And Adjoint State Methods

NASA Astrophysics Data System (ADS)

Schaa, Ralf; Gross, Lutz; Du Plessis, Jaco

2015-04-01

The resistivity method is one of the oldest geophysical exploration methods, which employs one pair of electrodes to inject current into the ground and one or more pairs of electrodes to measure the electrical potential difference. The potential difference is a non-linear function of the subsurface resistivity distribution described by an elliptic partial differential equation (PDE) of the Poisson type. Inversion of measured potentials solves for the subsurface resistivity represented by PDE coefficients. With increasing advances in multichannel resistivity acquisition systems (systems with more than 60 channels and full waveform recording are now emerging), inversion software require efficient storage and solver algorithms. We developed the finite element solver Escript, which provides a user-friendly programming environment in Python to solve large-scale PDE-based problems (see https://launchpad.net/escript-finley). Using finite elements, highly irregular shaped geology and topography can readily be taken into account. For the 3D resistivity problem, we have implemented the secondary potential approach, where the PDE is decomposed into a primary potential caused by the source current and the secondary potential caused by changes in subsurface resistivity. The primary potential is calculated analytically, and the boundary value problem for the secondary potential is solved using nodal finite elements. This approach removes the singularity caused by the source currents and provides more accurate 3D resistivity models. To solve the inversion problem we apply a 'first optimize then discretize' approach using the quasi-Newton scheme in form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method (see Gross & Kemp 2013). The evaluation of the cost function requires the solution of the secondary potential PDE for each source current and the solution of the corresponding adjoint-state PDE for the cost function gradients with respect to the subsurface resistivity. The Hessian of the regularization term is used as preconditioner which requires an additional PDE solution in each iteration step. As it turns out, the relevant PDEs are naturally formulated in the finite element framework. Using the domain decomposition method provided in Escript, the inversion scheme has been parallelized for distributed memory computers with multi-core shared memory nodes. We show numerical examples from simple layered models to complex 3D models and compare with the results from other methods. The inversion scheme is furthermore tested on a field data example to characterise localised freshwater discharge in a coastal environment.. References: L. Gross and C. Kemp (2013) Large Scale Joint Inversion of Geophysical Data using the Finite Element Method in escript. ASEG Extended Abstracts 2013, http://dx.doi.org/10.1071/ASEG2013ab306

Richard P. Feynman and the Feynman Diagrams

Science.gov Websites

available in full-text and on the Web. Documents: A Theorem and Its Application to Finite Tampers, DOE Fermi-Thomas Theory; DOE Technical Report, April 28, 1947 Mathematical Formulation of the Quantum Theory

The Effect of Multigrid Parameters in a 3D Heat Diffusion Equation

NASA Astrophysics Data System (ADS)

Oliveira, F. De; Franco, S. R.; Pinto, M. A. Villela

2018-02-01

The aim of this paper is to reduce the necessary CPU time to solve the three-dimensional heat diffusion equation using Dirichlet boundary conditions. The finite difference method (FDM) is used to discretize the differential equations with a second-order accuracy central difference scheme (CDS). The algebraic equations systems are solved using the lexicographical and red-black Gauss-Seidel methods, associated with the geometric multigrid method with a correction scheme (CS) and V-cycle. Comparisons are made between two types of restriction: injection and full weighting. The used prolongation process is the trilinear interpolation. This work is concerned with the study of the influence of the smoothing value (v), number of mesh levels (L) and number of unknowns (N) on the CPU time, as well as the analysis of algorithm complexity.

Finite Element Modelling Full Vehicle Side Impact with Ultrahigh Strength Hot Stamped Steels

NASA Astrophysics Data System (ADS)

Taylor, T.; Fourlaris, G.; Cafolla, J.

2016-10-01

"Hot stamped boron steel" 22MnB5 has been imperative in meeting the automotive industry's demand for materials exhibiting higher tensile strength in the final component. In this paper, the crash performance of three experimental grades developed for automotive hot stamping technologies, exhibiting wider tensile property ranges than 22MnB5, was validated by finite element modelling full vehicle side impact with the experimental material data applied to the B-pillar reinforcement. The superior anti-intrusive crash performance of grade 38MnB5 was demonstrated, with 11 mm less intrusion of the B-pillar reinforcement compared to 22MnB5. Moreover, the superior "impact-energy absorptive" crash performance of grade 15MnCr5 was demonstrated, with 0.15 kJ greater impact-energy absorption by the B-pillar reinforcement compared to 22MnB5.

Full Wave Analysis of RF Signal Attenuation in a Lossy Rough Surface Cave using a High Order Time Domain Vector Finite Element Method

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

Pingenot, J; Rieben, R; White, D

2005-10-31

We present a computational study of signal propagation and attenuation of a 200 MHz planar loop antenna in a cave environment. The cave is modeled as a straight and lossy random rough wall. To simulate a broad frequency band, the full wave Maxwell equations are solved directly in the time domain via a high order vector finite element discretization using the massively parallel CEM code EMSolve. The numerical technique is first verified against theoretical results for a planar loop antenna in a smooth lossy cave. The simulation is then performed for a series of random rough surface meshes in ordermore » to generate statistical data for the propagation and attenuation properties of the antenna in a cave environment. Results for the mean and variance of the power spectral density of the electric field are presented and discussed.« less

Constitutive Modeling of Porcine Liver in Indentation Using 3D Ultrasound Imaging

PubMed Central

Jordan, P.; Socrate, S.; Zickler, T.E.; Howe, R.D.

2009-01-01

In this work we present an inverse finite-element modeling framework for constitutive modeling and parameter estimation of soft tissues using full-field volumetric deformation data obtained from 3D ultrasound. The finite-element model is coupled to full-field visual measurements by regularization springs attached at nodal locations. The free ends of the springs are displaced according to the locally estimated tissue motion and the normalized potential energy stored in all springs serves as a measure of model-experiment agreement for material parameter optimization. We demonstrate good accuracy of estimated parameters and consistent convergence properties on synthetically generated data. We present constitutive model selection and parameter estimation for perfused porcine liver in indentation and demonstrate that a quasilinear viscoelastic model with shear modulus relaxation offers good model-experiment agreement in terms of indenter displacement (0.19 mm RMS error) and tissue displacement field (0.97 mm RMS error). PMID:19627823

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.

Influence of the implanted pulse generator as reference electrode in finite element model of monopolar deep brain stimulation.

PubMed

Walckiers, Grégoire; Fuchs, Benjamin; Thiran, Jean-Philippe; Mosig, Juan R; Pollo, Claudio

2010-01-30

Electrical deep brain stimulation (DBS) is an efficient method to treat movement disorders. Many models of DBS, based mostly on finite elements, have recently been proposed to better understand the interaction between the electrical stimulation and the brain tissues. In monopolar DBS, clinically widely used, the implanted pulse generator (IPG) is used as reference electrode (RE). In this paper, the influence of the RE model of monopolar DBS is investigated. For that purpose, a finite element model of the full electric loop including the head, the neck and the superior chest is used. Head, neck and superior chest are made of simple structures such as parallelepipeds and cylinders. The tissues surrounding the electrode are accurately modelled from data provided by the diffusion tensor magnetic resonance imaging (DT-MRI). Three different configurations of RE are compared with a commonly used model of reduced size. The electrical impedance seen by the DBS system and the potential distribution are computed for each model. Moreover, axons are modelled to compute the area of tissue activated by stimulation. Results show that these indicators are influenced by the surface and position of the RE. The use of a RE model corresponding to the implanted device rather than the usually simplified model leads to an increase of the system impedance (+48%) and a reduction of the area of activated tissue (-15%). (c) 2009 Elsevier B.V. All rights reserved.

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.

A method for modeling finite-core vortices in wake-flow calculations

NASA Technical Reports Server (NTRS)

Stremel, P. M.

1984-01-01

A numerical method for computing nonplanar vortex wakes represented by finite-core vortices is presented. The approach solves for the velocity on an Eulerian grid, using standard finite-difference techniques; the vortex wake is tracked by Lagrangian methods. In this method, the distribution of continuous vorticity in the wake is replaced by a group of discrete vortices. An axially symmetric distribution of vorticity about the center of each discrete vortex is used to represent the finite-core model. Two distributions of vorticity, or core models, are investigated: a finite distribution of vorticity represented by a third-order polynomial, and a continuous distribution of vorticity throughout the wake. The method provides for a vortex-core model that is insensitive to the mesh spacing. Results for a simplified case are presented. Computed results for the roll-up of a vortex wake generated by wings with different spanwise load distributions are presented; contour plots of the flow-field velocities are included; and comparisons are made of the computed flow-field velocities with experimentally measured velocities.

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.

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.

CAD-FEA modeling and analysis of different full crown monolithic restorations.

PubMed

Dal Piva, Amanda Maria de Oliveira; Tribst, João Paulo Mendes; Borges, Alexandre Luiz Souto; Souza, Rodrigo Othávio de Assunção E; Bottino, Marco Antonio

2018-06-19

To investigate the influence of different materials for monolithic full posterior crowns using 3D-Finite Element Analysis (FEA). Twelve (12) 3D models of adhesively-restored teeth with different crowns according to the material and its elastic modulus were analysed: Acrylic resin, Polyetheretherketone, Composite resin, Hybrid ceramic, pressable and machinable Zirconia reinforced lithium silicate, Feldspathic, Lithium disilicate, Gold alloy, Cobalt-Chromium alloy (Co-Cr), Zirconia tetragonal partially stabilized with yttria, and Alumina. All materials were assumed to behave elastically throughout the entire deformation. Results in restoration and cementing line were obtained using maximum principal stress. In addition, maximum shear stress criteria was used for the cementing line. Restorative materials with higher elastic modulus present higher stress concentration inside the crown, mainly tensile stress on an intaglio surface. On the other hand, materials with lower elastic modulus allow stress passage for cement, increasing shear stress on this layer. Stiffer materials promote higher stress peak values. Materials with higher elastic modulus such as Co-Cr, zirconia and alumina enable higher tensile stress concentration on the crown intaglio surface and higher shear stress on the cement layer, facilitating crown debonding. Copyright © 2018 The Academy of Dental Materials. Published by Elsevier Inc. All rights reserved.

Full-Scale Crash Test and Finite Element Simulation of a Composite Prototype Helicopter

NASA Technical Reports Server (NTRS)

Jackson, Karen E.; Fasanella, Edwin L.; Boitnott, Richard L.; Lyle, Karen H.

2003-01-01

A full-scale crash test of a prototype composite helicopter was performed at the Impact Dynamics Research Facility at NASA Langley Research Center in 1999 to obtain data for validation of a finite element crash simulation. The helicopter was the flight test article built by Sikorsky Aircraft during the Advanced Composite Airframe Program (ACAP). The composite helicopter was designed to meet the stringent Military Standard (MIL-STD-1290A) crashworthiness criteria and was outfitted with two crew and two troop seats and four anthropomorphic dummies. The test was performed at 38-ft/s vertical and 32.5-ft/s horizontal velocity onto a rigid surface. An existing modal-vibration model of the Sikorsky ACAP helicopter was converted into a model suitable for crash simulation. A two-stage modeling approach was implemented and an external user-defined subroutine was developed to represent the complex landing gear response. The crash simulation was executed with a nonlinear, explicit transient dynamic finite element code. Predictions of structural deformation and failure, the sequence of events, and the dynamic response of the airframe structure were generated and the numerical results were correlated with the experimental data to validate the simulation. The test results, the model development, and the test-analysis correlation are described.

Effects of weld residual stresses on crack-opening area analysis of pipes for LBB applications

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

Dong, P.; Rahman, S.; Wilkowski, G.

1997-04-01

This paper summarizes four different studies undertaken to evaluate the effects of weld residual stresses on the crack-opening behavior of a circumferential through-wall crack in the center of a girth weld. The effect of weld residual stress on the crack-opening-area and leak-rate analyses of a pipe is not well understood. There are no simple analyses to account for these effects, and, therefore, they are frequently neglected. The four studies involved the following efforts: (1) Full-field thermoplastic finite element residual stress analyses of a crack in the center of a girth weld, (2) A comparison of the crack-opening displacements from amore » full-field thermoplastic residual stress analysis with a crack-face pressure elastic stress analysis to determine the residual stress effects on the crack-opening displacement, (3) The effects of hydrostatic testing on the residual stresses and the resulting crack-opening displacement, and (4) The effect of residual stresses on crack-opening displacement with different normal operating stresses.« less

Modeling, simulation and optimization approaches for design of lightweight car body structures

NASA Astrophysics Data System (ADS)

Kiani, Morteza

Simulation-based design optimization and finite element method are used in this research to investigate weight reduction of car body structures made of metallic and composite materials under different design criteria. Besides crashworthiness in full frontal, offset frontal, and side impact scenarios, vibration frequencies, static stiffness, and joint rigidity are also considered. Energy absorption at the component level is used to study the effectiveness of carbon fiber reinforced polymer (CFRP) composite material with consideration of different failure criteria. A global-local design strategy is introduced and applied to multi-objective optimization of car body structures with CFRP components. Multiple example problems involving the analysis of full-vehicle crash and body-in-white models are used to examine the effect of material substitution and the choice of design criteria on weight reduction. The results of this study show that car body structures that are optimized for crashworthiness alone may not meet the vibration criterion. Moreover, optimized car body structures with CFRP components can be lighter with superior crashworthiness than the baseline and optimized metallic structures.

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.

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.

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.

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.

Nonlinear probabilistic finite element models of laminated composite shells

NASA Technical Reports Server (NTRS)

Engelstad, S. P.; Reddy, J. N.

1993-01-01

A probabilistic finite element analysis procedure for laminated composite shells has been developed. A total Lagrangian finite element formulation, employing a degenerated 3-D laminated composite shell with the full Green-Lagrange strains and first-order shear deformable kinematics, forms the modeling foundation. The first-order second-moment technique for probabilistic finite element analysis of random fields is employed and results are presented in the form of mean and variance of the structural response. The effects of material nonlinearity are included through the use of a rate-independent anisotropic plasticity formulation with the macroscopic point of view. Both ply-level and micromechanics-level random variables can be selected, the latter by means of the Aboudi micromechanics model. A number of sample problems are solved to verify the accuracy of the procedures developed and to quantify the variability of certain material type/structure combinations. Experimental data is compared in many cases, and the Monte Carlo simulation method is used to check the probabilistic results. In general, the procedure is quite effective in modeling the mean and variance response of the linear and nonlinear behavior of laminated composite shells.

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.

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.

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.

Bubbling in unbounded coflowing liquids.

PubMed

Gañán-Calvo, Alfonso M; Herrada, Miguel A; Garstecki, Piotr

2006-03-31

An investigation of the stability of low density and viscosity fluid jets and spouts in unbounded coflowing liquids is presented. A full parametrical analysis from low to high Weber and Reynolds numbers shows that the presence of any fluid of finite density and viscosity inside the hollow jet elicits a transition from an absolute to a convective instability at a finite value of the Weber number, for any value of the Reynolds number. Below that critical value of the Weber number, the absolute character of the instability leads to local breakup, and consequently to local bubbling. Experimental data support our model.

Dark-soliton dynamics in Bose-Einstein condensates at finite temperature

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

Jackson, B.; Proukakis, N. P.; Barenghi, C. F.

2007-05-15

The dynamics of a dark soliton in an elongated Bose-Einstein condensate is studied at finite temperatures. In addition to accurately reproducing all stages of the decay of the soliton observed in the experiment of Burger et al. [Phys. Rev. Lett. 83, 5198 (1999)], our numerical simulations reveal the existence of an experimentally accessible parameter regime for which phase-imprinted dark solitons can execute at least one full axial oscillation prior to their decay. The dependence of the decay time scale on temperature and initial soliton depth is analyzed and the role of interatomic collisions quantified.

Design of invisibility cloaks with an open tunnel.

PubMed

Ako, Thomas; Yan, Min; Qiu, Min

2010-12-20

In this paper we apply the methodology of transformation optics for design of a novel invisibility cloak which can possess an open tunnel. Such a cloak facilitates the insertion (retrieval) of matter into (from) the cloak's interior without significantly affecting the cloak's performance, overcoming the matter exchange bottleneck inherent to most previously proposed cloak designs.We achieve this by applying a transformation which expands a point at the origin in electromagnetic space to a finite area in physical space in a highly anisotropic manner. The invisibility performance of the proposed cloak is verified by using full-wave finite-element simulations.

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.

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

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.

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).

Crystallization of hard spheres revisited. II. Thermodynamic modeling, nucleation work, and the surface of tension.

PubMed

Richard, David; Speck, Thomas

2018-06-14

Combining three numerical methods (forward flux sampling, seeding of droplets, and finite-size droplets), we probe the crystallization of hard spheres over the full range from close to coexistence to the spinodal regime. We show that all three methods allow us to sample different regimes and agree perfectly in the ranges where they overlap. By combining the nucleation work calculated from forward flux sampling of small droplets and the nucleation theorem, we show how to compute the nucleation work spanning three orders of magnitude. Using a variation of the nucleation theorem, we show how to extract the pressure difference between the solid droplet and ambient liquid. Moreover, combining the nucleation work with the pressure difference allows us to calculate the interfacial tension of small droplets. Our results demonstrate that employing bulk quantities yields inaccurate results for the nucleation rate.

TECHNICAL NOTE: Direct finite-element analysis of the frequency response of a Y-Z lithium niobate SAW filter

NASA Astrophysics Data System (ADS)

Xu, Guanshui

2000-12-01

A direct finite-element model is developed for the full-scale analysis of the electromechanical phenomena involved in surface acoustic wave (SAW) devices. The equations of wave propagation in piezoelectric materials are discretized using the Galerkin method, in which an implicit algorithm of the Newmark family with unconditional stability is implemented. The Rayleigh damping coefficients are included in the elements near the boundary to reduce the influence of the reflection of waves. The performance of the model is demonstrated by the analysis of the frequency response of a Y-Z lithium niobate filter with two uniform ports, with emphasis on the influence of the number of electrodes. The frequency response of the filter is obtained through the Fourier transform of the impulse response, which is solved directly from the finite-element simulation. It shows that the finite-element results are in good agreement with the characteristic frequency response of the filter predicted by the simple phase-matching argument. The ability of the method to evaluate the influence of the bulk waves at the high-frequency end of the filter passband and the influence of the number of electrodes on insertion loss is noteworthy. We conclude that the direct finite-element analysis of SAW devices can be used as an effective tool for the design of high-performance SAW devices. Some practical computational challenges of finite-element modeling of SAW devices are discussed.

An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics

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

Kühnlein, Christian, E-mail: christian.kuehnlein@ecmwf.int; Smolarkiewicz, Piotr K., E-mail: piotr.smolarkiewicz@ecmwf.int

An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-formmore » schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.« less

Development of FullWave : Hot Plasma RF Simulation Tool

NASA Astrophysics Data System (ADS)

Svidzinski, Vladimir; Kim, Jin-Soo; Spencer, J. Andrew; Zhao, Liangji; Galkin, Sergei

2017-10-01

Full wave simulation tool, modeling RF fields in hot inhomogeneous magnetized plasma, is being developed. The wave equations with linearized hot plasma dielectric response are solved in configuration space on adaptive cloud of computational points. The nonlocal hot plasma dielectric response is formulated in configuration space without limiting approximations by calculating the plasma conductivity kernel based on the solution of the linearized Vlasov equation in inhomogeneous magnetic field. This approach allows for better resolution of plasma resonances, antenna structures and complex boundaries. The formulation of FullWave and preliminary results will be presented: construction of the finite differences for approximation of derivatives on adaptive cloud of computational points; model and results of nonlocal conductivity kernel calculation in tokamak geometry; results of 2-D full wave simulations in the cold plasma model in tokamak geometry using the formulated approach; results of self-consistent calculations of hot plasma dielectric response and RF fields in 1-D mirror magnetic field; preliminary results of self-consistent simulations of 2-D RF fields in tokamak using the calculated hot plasma conductivity kernel; development of iterative solver for wave equations. Work is supported by the U.S. DOE SBIR program.

Numerical models of diapiric structures: comparison of the 2D finite deformation field between Rayleigh-Taylor like and down-built like diapirs

NASA Astrophysics Data System (ADS)

Fuchs, Lukas; Schmeling, Harro; Koyi, Hemin

2013-04-01

Magmatic and salt diapirs are common structures in different tectonic regimes. Salt diapirs can act as possible hydrocarbon traps and, moreover, they could be used as repositories for nuclear waste disposal. Understanding the evolution and the dynamics of diapirs as well as their driving mechanisms has fundamental and applied significance. In general, salt diapirs seem to be driven by differential loading of sediments creating an uneven load that drives the salt from high to low pressure areas, e.g. a down-built diapir. Magmatic diapirs, instead, seem to be driven by buoyancy where lighter material rises vertically through a heavier overburden, i.e. a classical Rayleigh-Taylor instability [RTI]. These different driving mechanisms and dynamics strongly govern the internal deformation of the diapirs. In this study, we use a two-dimensional finite difference code (FDCON) in combination with a marker and cell method to calculate the finite deformation within diapiric structures. Thereby, we distinguish between the two different driving mechanisms, i.e. the differential loading and the buoyancy. We calculate the different finite deformation patterns during the evolution of RTI's and down-built diapirs for different viscosity ratios m = -?buoyant- ?overburden. The deformation pattern in the buoyant layer shows similarities for both diapiric structures, like high shear deformation at the bottom, a high finite deformation within the middle of the stem, and an increasing maximum finite deformation for a decreasing m. However, the strain partitioning between the overburden and the source layer is different within down-built diapirs compared to the RTI's, even for down-built diapirs with m = 1. Thus a higher amount of the total strain induced by down-building is concentrated within the buoyant layer. Moreover, in the case of viscosity ratios of m = 0.1 or 1 the sinking overburden units create an internal rotation within the diapiric bulb. This rotation depends indirectly on the sedimentation rate as it determines the width of the sediment basin; the higher the sedimentation rate, the wider the basins and the weaker the internal rotation. In addition, the viscous drag between the sinking overburden and the rising diapir creates a stronger and wider band of finite deformation along the edges of the down-built diapir in comparison to the RTI.

An Integrated Approach to Characterizing Bypassed Oil in Heterogeneous and Fractured Reservoirs Using Partitioning Tracers

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

Akhil Datta-Gupta

2006-12-31

We explore the use of efficient streamline-based simulation approaches for modeling partitioning interwell tracer tests in hydrocarbon reservoirs. Specifically, we utilize the unique features of streamline models to develop an efficient approach for interpretation and history matching of field tracer response. A critical aspect here is the underdetermined and highly ill-posed nature of the associated inverse problems. We have investigated the relative merits of the traditional history matching ('amplitude inversion') and a novel travel time inversion in terms of robustness of the method and convergence behavior of the solution. We show that the traditional amplitude inversion is orders of magnitudemore » more non-linear and the solution here is likely to get trapped in local minimum, leading to inadequate history match. The proposed travel time inversion is shown to be extremely efficient and robust for practical field applications. The streamline approach is generalized to model water injection in naturally fractured reservoirs through the use of a dual media approach. The fractures and matrix are treated as separate continua that are connected through a transfer function, as in conventional finite difference simulators for modeling fractured systems. A detailed comparison with a commercial finite difference simulator shows very good agreement. Furthermore, an examination of the scaling behavior of the computation time indicates that the streamline approach is likely to result in significant savings for large-scale field applications. We also propose a novel approach to history matching finite-difference models that combines the advantage of the streamline models with the versatility of finite-difference simulation. In our approach, we utilize the streamline-derived sensitivities to facilitate history matching during finite-difference simulation. The use of finite-difference model allows us to account for detailed process physics and compressibility effects. The approach is very fast and avoids much of the subjective judgments and time-consuming trial-and-errors associated with manual history matching. We demonstrate the power and utility of our approach using a synthetic example and two field examples. We have also explored the use of a finite difference reservoir simulator, UTCHEM, for field-scale design and optimization of partitioning interwell tracer tests. The finite-difference model allows us to include detailed physics associated with reactive tracer transport, particularly those related with transverse and cross-streamline mechanisms. We have investigated the potential use of downhole tracer samplers and also the use of natural tracers for the design of partitioning tracer tests. Finally, we discuss several alternative ways of using partitioning interwell tracer tests (PITTs) in oil fields for the calculation of oil saturation, swept pore volume and sweep efficiency, and assess the accuracy of such tests under a variety of reservoir conditions.« less

The morphological state space revisited: what do phylogenetic patterns in homoplasy tell us about the number of possible character states?

PubMed Central

Hoyal Cuthill, Jennifer F.

2015-01-01

Biological variety and major evolutionary transitions suggest that the space of possible morphologies may have varied among lineages and through time. However, most models of phylogenetic character evolution assume that the potential state space is finite. Here, I explore what the morphological state space might be like, by analysing trends in homoplasy (repeated derivation of the same character state). Analyses of ten published character matrices are compared against computer simulations with different state space models: infinite states, finite states, ordered states and an ‘inertial' model, simulating phylogenetic constraints. Of these, only the infinite states model results in evolution without homoplasy, a prediction which is not generally met by real phylogenies. Many authors have interpreted the ubiquity of homoplasy as evidence that the number of evolutionary alternatives is finite. However, homoplasy is also predicted by phylogenetic constraints on the morphological distance that can be traversed between ancestor and descendent. Phylogenetic rarefaction (sub-sampling) shows that finite and inertial state spaces do produce contrasting trends in the distribution of homoplasy. Two clades show trends characteristic of phylogenetic inertia, with decreasing homoplasy (increasing consistency index) as we sub-sample more distantly related taxa. One clade shows increasing homoplasy, suggesting exhaustion of finite states. Different clades may, therefore, show different patterns of character evolution. However, when parsimony uninformative characters are excluded (which may occur without documentation in cladistic studies), it may no longer be possible to distinguish inertial and finite state spaces. Interestingly, inertial models predict that homoplasy should be clustered among comparatively close relatives (parallel evolution), whereas finite state models do not. If morphological evolution is often inertial in nature, then homoplasy (false homology) may primarily occur between close relatives, perhaps being replaced by functional analogy at higher taxonomic scales. PMID:26640650

Relaxation and Preconditioning for High Order Discontinuous Galerkin Methods with Applications to Aeroacoustics and High Speed Flows

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

2004-01-01

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. Other related issues in high order WENO finite difference and finite volume methods have also been investigated. methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In [18], we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing. In [3], we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge-Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier-Stokes equations, and Hamilton-Jacobi-like equations.

Applications of Photonic Crystals to Photovoltaic Devices

NASA Astrophysics Data System (ADS)

Foster, Stephen

Photonic crystals are structures that exhibit wavelength-scale spatial periodicity in their dielectric function. They are best known for their ability to exhibit complete photonic band gaps (PBGs) - spectral regions over which no light can propagate within the crystal. PBGs are specific instances of a more general phenomenon, in which the local photonic density of states can be enhanced or suppressed over different frequency ranges by tuning the properties of the crystal. This can be used to redirect, concentrate, or even trap light incident on the crystal. In this thesis, we investigate how photonic crystals can be used to enhance the efficiency of photovoltaic devices by trapping light. Due to the many different types of photovoltaic devices in existence (varying widely in materials used, modes of operation, and internal structure), there is no single light trapping architecture that can be applied to all photovoltaics. In this work we study a number of different devices: dye-sensitized solar cells, polymer solar cells, silicon-perovskite tandem cells, and single-junction silicon cells. We propose novel photonic crystal-based light trapping designs for each type of device, and evaluate these designs numerically to demonstrate their effectiveness. Full-field optical simulations of the cell are performed for each design, using either finite element method (FEM) or finite-difference time-domain (FDTD) techniques. Where appropriate, electrical modelling of the cell is also performed, through either the use of a simple one-diode model, or by obtaining full solutions to the semiconductor drift-diffusion equations within the cell. In all cases we find that the photonic crystal-based designs significantly outperform their non-nanostructured counterparts. In the case of dye-sensitized and polymer cells, enhancements in light absorption of 33% and 40% (respectively) are seen, relative to reference cells with planar geometries. In the case of silicon-perovskite tandem cells and silicon cells, projected power conversion efficiencies of over 30% are obtained, well beyond the current world record for silicon-based cells. We conclude the thesis with a discussion on the overall prospects for photonic crystal-based solar cells, with a focus on the factors that make solar cell technologies amenable to light trapping.

A Discrete Approach to Computer-Oriented Calculus.

ERIC Educational Resources Information Center

Gordon, Sheldon P.

1979-01-01

Some of the implications and advantages of an instructional approach using results from the calculus of finite differences and finite sums, both for motivation and as tools leading to applications, are discussed. (MP)

Effects of Crimped Fiber Paths on Mixed Mode Delamination Behaviors in Woven Fabric Composites

DTIC Science & Technology

2016-09-01

continuum finite - element models. Three variations of a plain-woven fabric architecture—each of which had different crimped fiber paths—were considered... Finite - Element Analysis Fracture Mechanics Fracture Toughness Mixed Modes Strain Energy Release Rate 16. SECURITY...polymer FB Fully balanced laminate FEA Finite - element analysis FTCM Fracture toughness conversion mechanism G Shear modulus GI, GII, GIII Mode

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

NASA Technical Reports Server (NTRS)

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

1972-01-01

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

Newton's method applied to finite-difference approximations for the steady-state compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bailey, Harry E.; Beam, Richard M.

1991-01-01

Finite-difference approximations for steady-state compressible Navier-Stokes equations, whose two spatial dimensions are written in generalized curvilinear coordinates and strong conservation-law form, are presently solved by means of Newton's method in order to obtain a lifting-airfoil flow field under subsonic and transonnic conditions. In addition to ascertaining the computational requirements of an initial guess ensuring convergence and the degree of computational efficiency obtainable via the approximate Newton method's freezing of the Jacobian matrices, attention is given to the need for auxiliary methods assessing the temporal stability of steady-state solutions. It is demonstrated that nonunique solutions of the finite-difference equations are obtainable by Newton's method in conjunction with a continuation method.

Finite element dynamic analysis on CDC STAR-100 computer

NASA Technical Reports Server (NTRS)

Noor, A. K.; Lambiotte, J. J., Jr.

1978-01-01

Computational algorithms are presented for the finite element dynamic analysis of structures on the CDC STAR-100 computer. The spatial behavior is described using higher-order finite elements. The temporal behavior is approximated by using either the central difference explicit scheme or Newmark's implicit scheme. In each case the analysis is broken up into a number of basic macro-operations. Discussion is focused on the organization of the computation and the mode of storage of different arrays to take advantage of the STAR pipeline capability. The potential of the proposed algorithms is discussed and CPU times are given for performing the different macro-operations for a shell modeled by higher order composite shallow shell elements having 80 degrees of freedom.

Transport properties of bilayer graphene due to charged impurity scattering: Temperature-dependent screening and substrate effects

NASA Astrophysics Data System (ADS)

Linh, Dang Khanh; Khanh, Nguyen Quoc

2018-03-01

We calculate the zero-temperature conductivity of bilayer graphene (BLG) impacted by Coulomb impurity scattering using four different screening models: unscreened, Thomas-Fermi (TF), overscreened and random phase approximation (RPA). We also calculate the conductivity and thermal conductance of BLG using TF, zero- and finite-temperature RPA screening functions. We find large differences between the results of the models and show that TF and finite-temperature RPA give similar results for diffusion thermopower Sd. Using the finite-temperature RPA, we calculate temperature and density dependence of Sd in BLG on SiO2, HfO2 substrates and suspended BLG for different values of interlayer distance c and distance between the first layer and the substrate d.

Establishing the 3-D finite element solid model of femurs in partial by volume rendering.

PubMed

Zhang, Yinwang; Zhong, Wuxue; Zhu, Haibo; Chen, Yun; Xu, Lingjun; Zhu, Jianmin

2013-01-01

It remains rare to report three-dimensional (3-D) finite element solid model of femurs in partial by volume rendering method, though several methods of femoral 3-D finite element modeling are already available. We aim to analyze the advantages of the modeling method by establishing the 3-D finite element solid model of femurs in partial by volume rendering. A 3-D finite element model of the normal human femurs, made up of three anatomic structures: cortical bone, cancellous bone and pulp cavity, was constructed followed by pretreatment of the CT original image. Moreover, the finite-element analysis was carried on different material properties, three types of materials given for cortical bone, six assigned for cancellous bone, and single for pulp cavity. The established 3-D finite element of femurs contains three anatomical structures: cortical bone, cancellous bone, and pulp cavity. The compressive stress primarily concentrated in the medial surfaces of femur, especially in the calcar femorale. Compared with whole modeling by volume rendering method, the 3-D finite element solid model created in partial is more real and fit for finite element analysis. Copyright © 2013 Surgical Associates Ltd. Published by Elsevier Ltd. All rights reserved.

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

Modeling a surface-mounted Lamb wave emission-reception system: applications to structural health monitoring.

PubMed

Moulin, Emmanuel; Grondel, Sébastien; Assaad, Jamal; Duquenne, Laurent

2008-12-01

The work described in this paper is intended to present a simple and efficient way of modeling a full Lamb wave emission and reception system. The emitter behavior and the Lamb wave generation are predicted using a two-dimensional (2D) hybrid finite element-normal mode expansion model. Then the receiver electrical response is obtained from a finite element computation with prescribed displacements. A numerical correction is applied to the 2D results in order to account for the in-plane radiation divergence caused by the finite length of the emitter. The advantage of this modular approach is that realistic configurations can be simulated without performing cumbersome modeling and time-consuming computations. It also provides insight into the physical interpretation of the results. A good agreement is obtained between predicted and measured signals. The range of application of the method is discussed.

Application of Interface Technology in Nonlinear Analysis of a Stitched/RFI Composite Wing Stub Box

NASA Technical Reports Server (NTRS)

Wang, John T.; Ransom, Jonathan B.

1997-01-01

A recently developed interface technology was successfully employed in the geometrically nonlinear analysis of a full-scale stitched/RFI composite wing box loaded in bending. The technology allows mismatched finite element models to be joined in a variationally consistent manner and reduces the modeling complexity by eliminating transition meshing. In the analysis, local finite element models of nonlinearly deformed wide bays of the wing box are refined without the need for transition meshing to the surrounding coarse mesh. The COMET-AR finite element code, which has the interface technology capability, was used to perform the analyses. The COMET-AR analysis is compared to both a NASTRAN analysis and to experimental data. The interface technology solution is shown to be in good agreement with both. The viability of interface technology for coupled global/local analysis of large scale aircraft structures is demonstrated.

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

NASA Technical Reports Server (NTRS)

Jin, Jian-Ming; Volakis, John L.

1990-01-01

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

Computational aspects of sensitivity calculations in linear transient structural analysis. Ph.D. Thesis - Virginia Polytechnic Inst. and State Univ.

NASA Technical Reports Server (NTRS)

Greene, William H.

1990-01-01

A study was performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal of the study 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 semi-analytical 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. In several cases this fixed mode approach resulted in very poor approximations of the stress sensitivities. Almost all of the original modes were required for an accurate sensitivity and for small numbers of modes, the accuracy was extremely poor. To overcome this poor accuracy, two semi-analytical techniques were developed. The first technique accounts for the change in eigenvectors through approximate eigenvector derivatives. The second technique applies the mode acceleration method of transient analysis to the sensitivity calculations. Both result in accurate values of the stress sensitivities with a small number of modes and much lower computational costs than if the vibration modes were recalculated and then used in an overall finite difference method.

The effect of in situ/in vitro three-dimensional quantitative computed tomography image voxel size on the finite element model of human vertebral cancellous bone.

PubMed

Lu, Yongtao; Engelke, Klaus; Glueer, Claus-C; Morlock, Michael M; Huber, Gerd

2014-11-01

Quantitative computed tomography-based finite element modeling technique is a promising clinical tool for the prediction of bone strength. However, quantitative computed tomography-based finite element models were created from image datasets with different image voxel sizes. The aim of this study was to investigate whether there is an influence of image voxel size on the finite element models. In all 12 thoracolumbar vertebrae were scanned prior to autopsy (in situ) using two different quantitative computed tomography scan protocols, which resulted in image datasets with two different voxel sizes (0.29 × 0.29 × 1.3 mm(3) vs 0.18 × 0.18 × 0.6 mm(3)). Eight of them were scanned after autopsy (in vitro) and the datasets were reconstructed with two voxel sizes (0.32 × 0.32 × 0.6 mm(3) vs. 0.18 × 0.18 × 0.3 mm(3)). Finite element models with cuboid volume of interest extracted from the vertebral cancellous part were created and inhomogeneous bilinear bone properties were defined. Axial compression was simulated. No effect of voxel size was detected on the apparent bone mineral density for both the in situ and in vitro cases. However, the apparent modulus and yield strength showed significant differences in the two voxel size group pairs (in situ and in vitro). In conclusion, the image voxel size may have to be considered when the finite element voxel modeling technique is used in clinical applications. © IMechE 2014.

Full Waveform 2.5D Teleseismic Surface Wave Tomography with Application to the Tien Shan

NASA Astrophysics Data System (ADS)

Roecker, S. W.; Priestley, K. F.; Baker, B. I.

2011-12-01

We adapt the 2.5D spectral domain finite difference waveform tomography algorithm of Roecker et al. (2010) to permit the analysis of teleseismically recorded surface waves. The teleseismic body wave technique of generating synthetic waveforms by specifying an analytic solution for a background wavefield in a 1D model and solving for a scattered field excited by this background is equally applicable to surface waves. We use the locked mode approach of Gomberg and Masters (1988) to calculate the background Greens functions at each point of the finite difference (FD) grid. Because of the much greater concentration of energy at the surface, we adopt the cell-based FD operators of Min et al. (2004) to calculate the free surface boundary conditions, and the generalized stretching function of Komatitch and Martin (2007) to improve the absorption in the PML. We use this algorithm to analyze broad band seismograms of events in Sumatra recorded by the MANAS array in the Tien Shan. Our results show that the upper mantle beneath much of the central Tien Shan has shear wavespeeds at least 10% lower than the lithosphere beneath the Tarim basin to the south or the Kazach shield to the north. At the same time, there appears to be a remnant lithospheric lid beneath the Kyrgyz range in the north, an observation consistent with previous receiver function studies in this area.

Stress distribution of endodontically treated teeth with titanium alloy post and carbon fiber post with different alveolar bone height: A three-dimensional finite element analysis.

PubMed

Singh, S Vijay; Bhat, Manohar; Gupta, Saurabh; Sharma, Deepak; Satija, Harsha; Sharma, Sumeet

2015-01-01

A three-dimensional (3D) finite element analysis (FEA) on the stress distribution of endodontically treated teeth with titanium alloy post and carbon fiber post with different alveolar bone height. The 3D model was fabricated using software to represent an endodontically treated mandibular second premolar with post and restored with a full ceramic crown restoration, which was then analyzed using FEA using FEA ANSYS Workbench V13.0 (ANSYS Inc., Canonsburg, Pennsylvania, U.S.A) software. The FEA showed the maximum stresses of 137.43 Mpa in dentin with alveolar bone height of 4 mm when the titanium post was used, 138.48 Mpa when carbon fiber post was used as compared to 105.91 Mpa in the model with alveolar bone height of 2 mm from the cement enamel junction (CEJ) when the titanium post was used and 107.37 Mpa when the carbon fiber post was used. Stress was observed more in alveolar bone height level of 4 mm from CEJ than 2 mm from CEJ. Stresses in the dentin were almost similar when the carbon fiber post was compared to titanium post. However, stresses in the post and the cement were much higher when titanium post was used as compared to carbon fiber post.

A Newton method for the magnetohydrodynamic equilibrium equations

NASA Astrophysics Data System (ADS)

Oliver, Hilary James

We have developed and implemented a (J, B) space Newton method to solve the full nonlinear three dimensional magnetohydrodynamic equilibrium equations in toroidal geometry. Various cases have been run successfully, demonstrating significant improvement over Picard iteration, including a 3D stellarator equilibrium at β = 2%. The algorithm first solves the equilibrium force balance equation for the current density J, given a guess for the magnetic field B. This step is taken from the Picard-iterative PIES 3D equilibrium code. Next, we apply Newton's method to Ampere's Law by expansion of the functional J(B), which is defined by the first step. An analytic calculation in magnetic coordinates, of how the Pfirsch-Schlüter currents vary in the plasma in response to a small change in the magnetic field, yields the Newton gradient term (analogous to ∇f . δx in Newton's method for f(x) = 0). The algorithm is computationally feasible because we do this analytically, and because the gradient term is flux surface local when expressed in terms of a vector potential in an Ar=0 gauge. The equations are discretized by a hybrid spectral/offset grid finite difference technique, and leading order radial dependence is factored from Fourier coefficients to improve finite- difference accuracy near the polar-like origin. After calculating the Newton gradient term we transfer the equation from the magnetic grid to a fixed background grid, which greatly improves the code's performance.

Analysis of full-scale tank car shell impact tests

DOT National Transportation Integrated Search

2007-09-11

This paper describes analyses of a railroad tank car : impacted at its side by a ram car with a rigid punch. This : generalized collision, referred to as a shell impact, is examined : using nonlinear finite element analysis (FEA) and threedimensional...

Finite element analysis and full-scale testing of locomotive crashworthy components

DOT National Transportation Integrated Search

2013-04-15

The Office of Research and Development of the Federal Railroad Administration (FRA) and the Volpe Center are continuing to evaluate new technologies for increasing the safety of passengers and operators in rail equipment. In recognition of the import...

Structural assessment of highway "N" power substation under earthquake loads.

DOT National Transportation Integrated Search

2009-10-01

In this study, the Highway N Substation was analyzed with a finite element model (FEM) for its vulnerability. The rigid bus and electric switch components were characterized with full scale shake table tests. Each component of the substation wa...

A finite-volume Eulerian-Lagrangian Localized Adjoint Method for solution of the advection-dispersion equation

USGS Publications Warehouse

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

1993-01-01

A new mass-conservative method for solution of the one-dimensional advection-dispersion equation is derived and discussed. Test results demonstrate that the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) outperforms standard finite-difference methods, in terms of accuracy and efficiency, for solute transport problems that are dominated by advection. For dispersion-dominated problems, the performance of the method is similar to that of standard methods. Like previous ELLAM formulations, FVELLAM systematically conserves mass globally with all types of boundary conditions. FVELLAM differs from other ELLAM approaches in that integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking, as used by most characteristic methods, of characteristic lines intersecting inflow boundaries. FVELLAM extends previous ELLAM results by obtaining mass conservation locally on Lagrangian space-time elements. Details of the integration, tracking, and boundary algorithms are presented. Test results are given for problems in Cartesian and radial coordinates.

Energy stable and high-order-accurate finite difference methods on staggered grids

NASA Astrophysics Data System (ADS)

O'Reilly, Ossian; Lundquist, Tomas; Dunham, Eric M.; Nordström, Jan

2017-10-01

For wave propagation over distances of many wavelengths, high-order finite difference methods on staggered grids are widely used due to their excellent dispersion properties. However, the enforcement of boundary conditions in a stable manner and treatment of interface problems with discontinuous coefficients usually pose many challenges. In this work, we construct a provably stable and high-order-accurate finite difference method on staggered grids that can be applied to a broad class of boundary and interface problems. The staggered grid difference operators are in summation-by-parts form and when combined with a weak enforcement of the boundary conditions, lead to an energy stable method on multiblock grids. The general applicability of the method is demonstrated by simulating an explosive acoustic source, generating waves reflecting against a free surface and material discontinuity.

On the wavelet optimized finite difference method

NASA Technical Reports Server (NTRS)

Jameson, Leland

1994-01-01

When one considers the effect in the physical space, Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small scale structure exists. Adding a wavelet basis function at a given scale and location where one has a correspondingly large wavelet coefficient is, essentially, equivalent to adding a grid point, or two, at the same location and at a grid density which corresponds to the wavelet scale. This paper introduces a wavelet optimized finite difference method which is equivalent to a wavelet method in its multiresolution approach but which does not suffer from difficulties with nonlinear terms and boundary conditions, since all calculations are done in the physical space. With this method one can obtain an arbitrarily good approximation to a conservative difference method for solving nonlinear conservation laws.

Quantiles for Finite Mixtures of Normal Distributions

ERIC Educational Resources Information Center

Rahman, Mezbahur; Rahman, Rumanur; Pearson, Larry M.

2006-01-01

Quantiles for finite mixtures of normal distributions are computed. The difference between a linear combination of independent normal random variables and a linear combination of independent normal densities is emphasized. (Contains 3 tables and 1 figure.)

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.

Experiments with explicit filtering for LES using a finite-difference method

NASA Technical Reports Server (NTRS)

Lund, T. S.; Kaltenbach, H. J.

1995-01-01

The equations for large-eddy simulation (LES) are derived formally by applying a spatial filter to the Navier-Stokes equations. The filter width as well as the details of the filter shape are free parameters in LES, and these can be used both to control the effective resolution of the simulation and to establish the relative importance of different portions of the resolved spectrum. An analogous, but less well justified, approach to filtering is more or less universally used in conjunction with LES using finite-difference methods. In this approach, the finite support provided by the computational mesh as well as the wavenumber-dependent truncation errors associated with the finite-difference operators are assumed to define the filter operation. This approach has the advantage that it is also 'automatic' in the sense that no explicit filtering: operations need to be performed. While it is certainly convenient to avoid the explicit filtering operation, there are some practical considerations associated with finite-difference methods that favor the use of an explicit filter. Foremost among these considerations is the issue of truncation error. All finite-difference approximations have an associated truncation error that increases with increasing wavenumber. These errors can be quite severe for the smallest resolved scales, and these errors will interfere with the dynamics of the small eddies if no corrective action is taken. Years of experience at CTR with a second-order finite-difference scheme for high Reynolds number LES has repeatedly indicated that truncation errors must be minimized in order to obtain acceptable simulation results. While the potential advantages of explicit filtering are rather clear, there is a significant cost associated with its implementation. In particular, explicit filtering reduces the effective resolution of the simulation compared with that afforded by the mesh. The resolution requirements for LES are usually set by the need to capture most of the energy-containing eddies, and if explicit filtering is used, the mesh must be enlarged so that these motions are passed by the filter. Given the high cost of explicit filtering, the following interesting question arises. Since the mesh must be expanded in order to perform the explicit filter, might it be better to take advantage of the increased resolution and simply perform an unfiltered simulation on the larger mesh? The cost of the two approaches is roughly the same, but the philosophy is rather different. In the filtered simulation, resolution is sacrificed in order to minimize the various forms of numerical error. In the unfiltered simulation, the errors are left intact, but they are concentrated at very small scales that could be dynamically unimportant from a LES perspective. Very little is known about this tradeoff and the objective of this work is to study this relationship in high Reynolds number channel flow simulations using a second-order finite-difference method.

Explaining negative refraction without negative refractive indices.

PubMed

Talalai, Gregory A; Garner, Timothy J; Weiss, Steven J

2018-03-01

Negative refraction through a triangular prism may be explained without assigning a negative refractive index to the prism by using array theory. For the case of a beam incident upon the wedge, the array theory accurately predicts the beam transmission angle through the prism and provides an estimate of the frequency interval at which negative refraction occurs. The hypotenuse of the prism has a staircase shape because it is built of cubic unit cells. The large phase delay imparted by each unit cell, combined with the staircase shape of the hypotenuse, creates the necessary conditions for negative refraction. Full-wave simulations using the finite-difference time-domain method show that array theory accurately predicts the beam transmission angle.

Beam-splitter switches based on zenithal bistable liquid-crystal gratings.

PubMed

Zografopoulos, Dimitrios C; Beccherelli, Romeo; Kriezis, Emmanouil E

2014-10-01

The tunable optical diffractive properties of zenithal bistable nematic liquid-crystal gratings are theoretically investigated. The liquid-crystal orientation is rigorously solved via a tensorial formulation of the Landau-de Gennes theory and the optical transmission properties of the gratings are investigated via full-wave finite-element frequency-domain simulations. It is demonstrated that by proper design the two stable states of the grating can provide nondiffracting and diffracting operation, the latter with equal power splitting among different diffraction orders. An electro-optic switching mechanism, based on dual-frequency nematic materials, and its temporal dynamics are further discussed. Such gratings provide a solution towards tunable beam-steering and beam-splitting components with extremely low power consumption.

Low-loss ultracompact optical power splitter using a multistep structure.

PubMed

Huang, Zhe; Chan, Hau Ping; Afsar Uddin, Mohammad

2010-04-01

We propose a low-loss ultracompact optical power splitter for broadband passive optical network applications. The design is based on a multistep structure involving a two-material (core/cladding) system. The performance of the proposed device was evaluated through the three-dimensional finite-difference beam propagation method. By using the proposed design, an excess loss of 0.4 dB was achieved at a full branching angle of 24 degrees. The wavelength-dependent loss was found to be less than 0.3 dB, and the polarization-dependent loss was less than 0.05 dB from O to L bands. The device offers the potential of being mass-produced using low-cost polymer-based embossing techniques.

Design of single-polarization wavelength splitter based on photonic crystal fiber.

PubMed

Zhang, Shanshan; Zhang, Weigang; Geng, Pengcheng; Li, Xiaolan; Ruan, Juan

2011-12-20

A new single-polarization wavelength splitter based on the photonic crystal fiber (PCF) has been proposed. The full-vector finite-element method (FEM) is applied to analyze the single-polarization single-mode guiding properties. Splitting of two different wavelengths is realized by adjusting the structural parameters. The semi-vector three-dimensional beam propagation method is employed to confirm the wavelength splitting characteristics of the PCF. Numerical simulations show that the wavelengths of 1.3 μm and 1.55 μm are split for a fiber length of 10.7 mm with single-polarization guiding in each core. The crosstalk between the two cores is low over appreciable optical bandwidths.

Reverse time migration in tilted transversely isotropic media

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

Zhang, Linbing; Rector III, James W.; Hoversten, G. Michael

2004-07-01

This paper presents a reverse time migration (RTM) method for the migration of shot records in tilted transversely isotropic (TTI) media. It is based on the tilted TI acoustic wave equation that was derived from the dispersion relation. The RTM is a full depth migration allowing for velocity to vary laterally as well as vertically and has no dip limitations. The wave equation is solved by a tenth-order finite difference scheme. Using 2D numerical models, we demonstrate that ignoring the tilt angle will introduce both lateral and vertical shifts in imaging. The shifts can be larger than 0.5 wavelength inmore » the vertical direction and 1.5 wavelength in the lateral direction.« less

Design, analysis, and testing of a metal matrix composite web/flange intersection

NASA Technical Reports Server (NTRS)

Biggers, S. B.; Knight, N. F., Jr.; Moran, S. G.; Olliffe, R.

1992-01-01

An experimental and analytical program to study the local design details of a typical T-shaped web/flange intersection made from a metal matrix composite is described. Loads creating flange bending were applied to specimens having different designs and boundary conditions. Finite element analyses were conducted on models of the test specimens to predict the structural response. The analyses correctly predict failure load, mode, and location in the fillet material in the intersection region of the web and the flange when specimen quality is good. The test program shows the importance of fabrication quality in the intersection region. The full-scale test program that led to the investigation of this local detail is also described.

Numerical analysis of flow about a total temperature sensor

NASA Technical Reports Server (NTRS)

Von Lavante, Ernst; Bruns, Russell L., Jr.; Sanetrik, Mark D.; Lam, Tim

1989-01-01

The unsteady flowfield about an airfoil-shaped inlet temperature sensor has been investigated using the thin-layer and full Navier-Stokes equations. A finite-volume formulation of the governing equations was used in conjunction with a Runge-Kutta time stepping scheme to analyze the flow about the sensor. Flow characteristics for this configuration were established at Mach numbers of 0.5 and 0.8 for different Reynolds numbers. The results were obtained for configurations of increasing complexity; important physical phenomena such as shock formation, boundary-layer separation, and unsteady wake formation were noted. Based on the computational results, recommendations for further study and refinement of the inlet temperature sensor were made.

Plasmon confinement in fractal quantum systems

NASA Astrophysics Data System (ADS)

Westerhout, Tom; van Veen, Edo; Katsnelson, Mikhail I.; Yuan, Shengjun

2018-05-01

Recent progress in the fabrication of materials has made it possible to create arbitrary nonperiodic two-dimensional structures in the quantum plasmon regime. This paves the way for exploring the quantum plasmonic properties of electron gases in complex geometries. In this work we study systems with a fractal dimension. We calculate the full dielectric functions of two prototypical fractals with different ramification numbers, namely the Sierpinski carpet and gasket. We show that the Sierpinski carpet has a dispersion comparable to a square lattice, but the Sierpinski gasket features highly localized plasmon modes with a flat dispersion. This strong plasmon confinement in finitely ramified fractals can provide a novel setting for manipulating light at the quantum level.

Tools and techniques for estimating high intensity RF effects

NASA Astrophysics Data System (ADS)

Zacharias, Richard L.; Pennock, Steve T.; Poggio, Andrew J.; Ray, Scott L.

1992-01-01

Tools and techniques for estimating and measuring coupling and component disturbance for avionics and electronic controls are described. A finite-difference-time-domain (FD-TD) modeling code, TSAR, used to predict coupling is described. This code can quickly generate a mesh model to represent the test object. Some recent applications as well as the advantages and limitations of using such a code are described. Facilities and techniques for making low-power coupling measurements and for making direct injection test measurements of device disturbance are also described. Some scaling laws for coupling and device effects are presented. A method for extrapolating these low-power test results to high-power full-system effects are presented.

Computer Generated Pictorial Stores Management Displays for Fighter Aircraft.

DTIC Science & Technology

1983-05-01

questionnaire rating-scale data. KRISHNAIAH FINITE INTERSECTION TESTS (FITs) - A set of tests conducted after significant MANOVA results are found to...the Social Sciences (SPSS) (Reference 2). To further examine significant performance differences, the Krishnaiah Finite Intersection Test (FIT), a...New York: McGraw-Hill Book Company, 1975. 3. C. M. Cox, P. R. Krishnaiah , J. C. Lee, J. M. Reising, and F. J. Schuurman, A study on Finite Intersection

The finite ground plane effect on the microstrip antenna radiation patterns

NASA Technical Reports Server (NTRS)

Huang, J.

1983-01-01

The uniform geometrical theory of diffraction (GTD) is employed for calculating the edge diffracted fields from the finite ground plane of a microstrip antenna. The source field from the radiating patch is calculated by two different methods: the slot theory and the modal expansion theory. Many numerical and measured results are presented to demonstrate the accuracy of the calculations and the finite ground plane edge effect.

Full Stokes finite-element modeling of ice sheets using a graphics processing unit

NASA Astrophysics Data System (ADS)

Seddik, H.; Greve, R.

2016-12-01

Thermo-mechanical simulation of ice sheets is an important approach to understand and predict their evolution in a changing climate. For that purpose, higher order (e.g., ISSM, BISICLES) and full Stokes (e.g., Elmer/Ice, http://elmerice.elmerfem.org) models are increasingly used to more accurately model the flow of entire ice sheets. In parallel to this development, the rapidly improving performance and capabilities of Graphics Processing Units (GPUs) allows to efficiently offload more calculations of complex and computationally demanding problems on those devices. Thus, in order to continue the trend of using full Stokes models with greater resolutions, using GPUs should be considered for the implementation of ice sheet models. We developed the GPU-accelerated ice-sheet model Sainō. Sainō is an Elmer (http://www.csc.fi/english/pages/elmer) derivative implemented in Objective-C which solves the full Stokes equations with the finite element method. It uses the standard OpenCL language (http://www.khronos.org/opencl/) to offload the assembly of the finite element matrix on the GPU. A mesh-coloring scheme is used so that elements with the same color (non-sharing nodes) are assembled in parallel on the GPU without the need for synchronization primitives. The current implementation shows that, for the ISMIP-HOM experiment A, during the matrix assembly in double precision with 8000, 87,500 and 252,000 brick elements, Sainō is respectively 2x, 10x and 14x faster than Elmer/Ice (when both models are run on a single processing unit). In single precision, Sainō is even 3x, 20x and 25x faster than Elmer/Ice. A detailed description of the comparative results between Sainō and Elmer/Ice will be presented, and further perspectives in optimization and the limitations of the current implementation.

Momentum distribution functions in ensembles: the inequivalence of microcannonical and canonical ensembles in a finite ultracold system.

PubMed

Wang, Pei; Xianlong, Gao; Li, Haibin

2013-08-01

It is demonstrated in many thermodynamic textbooks that the equivalence of the different ensembles is achieved in the thermodynamic limit. In this present work we discuss the inequivalence of microcanonical and canonical ensembles in a finite ultracold system at low energies. We calculate the microcanonical momentum distribution function (MDF) in a system of identical fermions (bosons). We find that the microcanonical MDF deviates from the canonical one, which is the Fermi-Dirac (Bose-Einstein) function, in a finite system at low energies where the single-particle density of states and its inverse are finite.

Non-Linear Finite Element Modeling of THUNDER Piezoelectric Actuators

NASA Technical Reports Server (NTRS)

Taleghani, Barmac K.; Campbell, Joel F.

1999-01-01

A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (THin Layer UNimorph Ferroelectric DrivER) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.

Application of numerical methods to heat transfer and thermal stress analysis of aerospace vehicles

NASA Technical Reports Server (NTRS)

Wieting, A. R.

1979-01-01

The paper describes a thermal-structural design analysis study of a fuel-injection strut for a hydrogen-cooled scramjet engine for a supersonic transport, utilizing finite-element methodology. Applications of finite-element and finite-difference codes to the thermal-structural design-analysis of space transports and structures are discussed. The interaction between the thermal and structural analyses has led to development of finite-element thermal methodology to improve the integration between these two disciplines. The integrated thermal-structural analysis capability developed within the framework of a computer code is outlined.

A finite element algorithm for high-lying eigenvalues with Neumann and Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Báez, G.; Méndez-Sánchez, R. A.; Leyvraz, F.; Seligman, T. H.

2014-01-01

We present a finite element algorithm that computes eigenvalues and eigenfunctions of the Laplace operator for two-dimensional problems with homogeneous Neumann or Dirichlet boundary conditions, or combinations of either for different parts of the boundary. We use an inverse power plus Gauss-Seidel algorithm to solve the generalized eigenvalue problem. For Neumann boundary conditions the method is much more efficient than the equivalent finite difference algorithm. We checked the algorithm by comparing the cumulative level density of the spectrum obtained numerically with the theoretical prediction given by the Weyl formula. We found a systematic deviation due to the discretization, not to the algorithm itself.

A numerical solution of a singular boundary value problem arising in boundary layer theory.

PubMed

Hu, Jiancheng

2016-01-01

In this paper, a second-order nonlinear singular boundary value problem is presented, which is equivalent to the well-known Falkner-Skan equation. And the one-dimensional third-order boundary value problem on interval [Formula: see text] is equivalently transformed into a second-order boundary value problem on finite interval [Formula: see text]. The finite difference method is utilized to solve the singular boundary value problem, in which the amount of computational effort is significantly less than the other numerical methods. The numerical solutions obtained by the finite difference method are in agreement with those obtained by previous authors.

Socio-economic applications of finite state mean field games.

PubMed

Gomes, Diogo; Velho, Roberto M; Wolfram, Marie-Therese

2014-11-13

In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments, which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Incremental analysis of large elastic deformation of a rotating cylinder

NASA Technical Reports Server (NTRS)

Buchanan, G. R.

1976-01-01

The effect of finite deformation upon a rotating, orthotropic cylinder was investigated using a general incremental theory. The incremental equations of motion are developed using the variational principle. The governing equations are derived using the principle of virtual work for a body with initial stress. The governing equations are reduced to those for the title problem and a numerical solution is obtained using finite difference approximations. Since the problem is defined in terms of one independent space coordinate, the finite difference grid can be modified as the incremental deformation occurs without serious numerical difficulties. The nonlinear problem is solved incrementally by totaling a series of linear solutions.

A conservative numerical scheme for modeling nonlinear acoustic propagation in thermoviscous homogeneous media

NASA Astrophysics Data System (ADS)

Diaz, Manuel A.; Solovchuk, Maxim A.; Sheu, Tony W. H.

2018-06-01

A nonlinear system of partial differential equations capable of describing the nonlinear propagation and attenuation of finite amplitude perturbations in thermoviscous media is presented. This system constitutes a full nonlinear wave model that has been formulated in the conservation form. Initially, this model is investigated analytically in the inviscid limit where it has been found that the resulting flux function fulfills the Lax-Wendroff theorem, and the scheme can match the solutions of the Westervelt and Burgers equations numerically. Here, high-order numerical descriptions of strongly nonlinear wave propagations become of great interest. For that matter we consider finite difference formulations of the weighted essentially non-oscillatory (WENO) schemes associated with explicit strong stability preserving Runge-Kutta (SSP-RK) time integration methods. Although this strategy is known to be computationally demanding, it is found to be effective when implemented to be solved in graphical processing units (GPUs). As we consider wave propagations in unbounded domains, perfectly matching layers (PML) have been also considered in this work. The proposed system model is validated and illustrated by using one- and two-dimensional benchmark test cases proposed in the literature for nonlinear acoustic propagation in homogeneous thermoviscous media.

Precision of EM Simulation Based Wireless Location Estimation in Multi-Sensor Capsule Endoscopy

PubMed Central

Ye, Yunxing; Aisha, Ain-Ul; Swar, Pranay; Pahlavan, Kaveh

2018-01-01

In this paper, we compute and examine two-way localization limits for an RF endoscopy pill as it passes through an individuals gastrointestinal (GI) tract. We obtain finite-difference time-domain and finite element method-based simulation results position assessment employing time of arrival (TOA). By means of a 3-D human body representation from a full-wave simulation software and lognormal models for TOA propagation from implant organs to body surface, we calculate bounds on location estimators in three digestive organs: stomach, small intestine, and large intestine. We present an investigation of the causes influencing localization precision, consisting of a range of organ properties; peripheral sensor array arrangements, number of pills in cooperation, and the random variations in transmit power of sensor nodes. We also perform a localization precision investigation for the situation where the transmission signal of the antenna is arbitrary with a known probability distribution. The computational solver outcome shows that the number of receiver antennas on the exterior of the body has higher impact on the precision of the location than the amount of capsules in collaboration within the GI region. The large intestine is influenced the most by the transmitter power probability distribution. PMID:29651364

Dispersion characteristics of plasmonic waveguides for THz waves

NASA Astrophysics Data System (ADS)

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

2013-05-01

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

[Towards a sheltered aging in individual and social responsibility].

PubMed

Birkenstock, E; Rentsch, T

2005-08-01

Aging is a slow process, the beginning of which as well as its progress are defined in quite different ways from the biomedical, psychological, or sociological point of view. Philosophy can perform a significant contribution to a sound and human approach to this phenomenon of life: first clarifying the present situation on the background of historic experiences; second improving a fundamental ascertainment of our ontological condition as human beings, characterized by finiteness and vulnerability, while recalling that humans possess the unique capability to reflect on this aspect of their existence; and, always moving from the results of that analysis, lastly suggesting some tentative solutions, conceived as ethical-practical guidelines and values pool, for an overcoming of the individual and social challenges posed by aging. The aim consists in a re-interpretation of aging as a "becoming oneself", without denying hereby the negativity embodied in the finiteness and fragility of our life. To this purpose it is necessary to distinguish the situations where aging, while maintaining full self-consciousness, can be shaped as an autonomous process, from those, mostly near to the edge of death, for which the goal of self-realization cannot be applied, making rather indispensable the resort to concepts of respect and empathy.

Full-Field Reconstruction of Structural Deformations and Loads from Measured Strain Data on a Wing Using the Inverse Finite Element Method

NASA Technical Reports Server (NTRS)

Miller, Eric J.; Manalo, Russel; Tessler, Alexander

2016-01-01

A study was undertaken to investigate the measurement of wing deformation and internal loads using measured strain data. Future aerospace vehicle research depends on the ability to accurately measure the deformation and internal loads during ground testing and in flight. The approach uses the inverse Finite Element Method (iFEM). The iFEM is a robust, computationally efficient method that is well suited for real-time measurement of real-time structural deformation and loads. The method has been validated in previous work, but has yet to be applied to a large-scale test article. This work is in preparation for an upcoming loads test of a half-span test wing in the Flight Loads Laboratory at the National Aeronautics and Space Administration Armstrong Flight Research Center (Edwards, California). The method has been implemented into an efficient MATLAB® (The MathWorks, Inc., Natick, Massachusetts) code for testing different sensor configurations. This report discusses formulation and implementation along with the preliminary results from a representative aerospace structure. The end goal is to investigate the modeling and sensor placement approach so that the best practices can be applied to future aerospace projects.

A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models

DOE PAGES

Guerra, Jorge E.; Ullrich, Paul A.

2016-06-01

Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finite-element method (SNFEM). Our method uses a generalized discrete derivative that consistently combines the discontinuous Galerkin and spectral element methods on a staggered grid. Our combined method leverages the accurate wave propagation and conservation properties of spectral elements with staggered methods that eliminate stationary (2Δ x) modes. Furthermore, high-order accuracymore » also eliminates the need for a reference state to maintain hydrostatic balance. In this work we demonstrate the use of high vertical order as a means of improving simulation quality at relatively coarse resolution. We choose a test case suite that spans the range of atmospheric flows from predominantly hydrostatic to nonlinear in the large-eddy regime. Lastly, our results show that there is a distinct benefit in using the high-order vertical coordinate at low resolutions with the same robust properties as the low-order alternative.« less

A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models

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

Guerra, Jorge E.; Ullrich, Paul A.

Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finite-element method (SNFEM). Our method uses a generalized discrete derivative that consistently combines the discontinuous Galerkin and spectral element methods on a staggered grid. Our combined method leverages the accurate wave propagation and conservation properties of spectral elements with staggered methods that eliminate stationary (2Δ x) modes. Furthermore, high-order accuracymore » also eliminates the need for a reference state to maintain hydrostatic balance. In this work we demonstrate the use of high vertical order as a means of improving simulation quality at relatively coarse resolution. We choose a test case suite that spans the range of atmospheric flows from predominantly hydrostatic to nonlinear in the large-eddy regime. Lastly, our results show that there is a distinct benefit in using the high-order vertical coordinate at low resolutions with the same robust properties as the low-order alternative.« less

Finite Element Analysis of Stresses Developed in the Blood Sac of a Left Ventricular Assist Device

PubMed Central

Haut Donahue, T. L.; Dehlin, W.; Gillespie, J.; Weiss, W.J.; Rosenberg, G.

2009-01-01

The goal of this research is to develop a 3D finite element (FE) model of a left ventricular assist device (LVAD) to predict stresses in the blood sac. The hyperelastic stress-strain curves for the segmented poly(ether polyurethane urea) blood sac were determined in both tension and compression using a servo-hydraulic testing system at various strain rates. Over the range of strain rates studied, the sac was not strain rate sensitive, however the material response was different for tension versus compression. The experimental tension and compression properties were used in a FE model that consisted of the pusher plate, blood sac and pump case. A quasi-static analysis was used to allow for nonlinearities due to contact and material deformation. The 3D FE model showed that blood sac stresses are not adversely affected by the location of the inlet and outlet ports of the device and that over the systolic ejection phase of the simulation the prediction of blood sac stresses from the full 3D model and an axisymmetric model are the same. Minimizing stresses in the blood sac will increase the longevity of the blood sac in vivo. PMID:19131267

Gravity–capillary waves in finite depth on flows of constant vorticity

PubMed Central

Hsu, Hung-Chu; Francius, Marc; Kharif, Christian

2016-01-01

This paper considers two-dimensional periodic gravity–capillary waves propagating steadily in finite depth on a linear shear current (constant vorticity). A perturbation series solution for steady periodic waves, accurate up to the third order, is derived using a classical Stokes expansion procedure, which allows us to include surface tension effects in the analysis of wave–current interactions in the presence of constant vorticity. The analytical results are then compared with numerical computations with the full equations. The main results are (i) the phase velocity is strongly dependent on the value of the vorticity; (ii) the singularities (Wilton singularities) in the Stokes expansion in powers of wave amplitude that correspond to a Bond number of 1/2 and 1/3, which are the consequences of the non-uniformity in the ordering of the Fourier coefficients, are found to be influenced by vorticity; (iii) different surface profiles of capillary–gravity waves are computed and the effect of vorticity on those profiles is shown to be important, in particular that the solutions exhibit type-2-like wave features, characterized by a secondary maximum on the surface profile with a trough between the two maxima. PMID:27956873

Precision of EM Simulation Based Wireless Location Estimation in Multi-Sensor Capsule Endoscopy.

PubMed

Khan, Umair; Ye, Yunxing; Aisha, Ain-Ul; Swar, Pranay; Pahlavan, Kaveh

2018-01-01

In this paper, we compute and examine two-way localization limits for an RF endoscopy pill as it passes through an individuals gastrointestinal (GI) tract. We obtain finite-difference time-domain and finite element method-based simulation results position assessment employing time of arrival (TOA). By means of a 3-D human body representation from a full-wave simulation software and lognormal models for TOA propagation from implant organs to body surface, we calculate bounds on location estimators in three digestive organs: stomach, small intestine, and large intestine. We present an investigation of the causes influencing localization precision, consisting of a range of organ properties; peripheral sensor array arrangements, number of pills in cooperation, and the random variations in transmit power of sensor nodes. We also perform a localization precision investigation for the situation where the transmission signal of the antenna is arbitrary with a known probability distribution. The computational solver outcome shows that the number of receiver antennas on the exterior of the body has higher impact on the precision of the location than the amount of capsules in collaboration within the GI region. The large intestine is influenced the most by the transmitter power probability distribution.

A knowledge engineering approach to recognizing and extracting sequences of nucleic acids from scientific literature.

PubMed

García-Remesal, Miguel; Maojo, Victor; Crespo, José

2010-01-01

In this paper we present a knowledge engineering approach to automatically recognize and extract genetic sequences from scientific articles. To carry out this task, we use a preliminary recognizer based on a finite state machine to extract all candidate DNA/RNA sequences. The latter are then fed into a knowledge-based system that automatically discards false positives and refines noisy and incorrectly merged sequences. We created the knowledge base by manually analyzing different manuscripts containing genetic sequences. Our approach was evaluated using a test set of 211 full-text articles in PDF format containing 3134 genetic sequences. For such set, we achieved 87.76% precision and 97.70% recall respectively. This method can facilitate different research tasks. These include text mining, information extraction, and information retrieval research dealing with large collections of documents containing genetic sequences.

Application of the three-dimensional aperiodic Fourier modal method using arc elements in curvilinear coordinates.

PubMed

Bucci, Davide; Martin, Bruno; Morand, Alain

2012-03-01

This paper deals with a full vectorial generalization of the aperiodic Fourier modal method (AFMM) in cylindrical coordinates. The goal is to predict some key characteristics such as the bending losses of waveguides having an arbitrary distribution of the transverse refractive index. After a description of the method, we compare the results of the cylindrical coordinates AFMM with simulations by the finite-difference time-domain (FDTD) method performed on an S-bend structure made by a 500 nm × 200 nm silicon core (n=3.48) in silica (n=1.44) at a wavelength λ=1550 nm, the bending radius varying from 0.5 up to 2 μm. The FDTD and AFMM results show differences comparable to the variations obtained by changing the parameters of the FDTD simulations.

The Laguerre finite difference one-way equation solver

NASA Astrophysics Data System (ADS)

Terekhov, Andrew V.

2017-05-01

This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of partial differential equations. As opposed to the existing approaches, the integral Laguerre transform instead of Fourier transform is used. After carrying out the approximation of spatial variables it is possible to obtain systems of linear algebraic equations with better computing properties and to reduce computer costs for their solution. High accuracy of calculations is attained at the expense of employing finite difference approximations of higher accuracy order that are based on the dispersion-relationship-preserving method and the Richardson extrapolation in the downward continuation direction. The numerical experiments have verified that as compared to the spectral difference method based on Fourier transform, the new algorithm allows one to calculate wave fields with a higher degree of accuracy and a lower level of numerical noise and artifacts including those for non-smooth velocity models. In the context of solving the geophysical problem the post-stack migration for velocity models of the types Syncline and Sigsbee2A has been carried out. It is shown that the images obtained contain lesser noise and are considerably better focused as compared to those obtained by the known Fourier Finite Difference and Phase-Shift Plus Interpolation methods. There is an opinion that purely finite difference approaches do not allow carrying out the seismic migration procedure with sufficient accuracy, however the results obtained disprove this statement. For the supercomputer implementation it is proposed to use the parallel dichotomy algorithm when solving systems of linear algebraic equations with block-tridiagonal matrices.