Multigrid finite element method in stress analysis of three-dimensional elastic bodies of heterogeneous structure

NASA Astrophysics Data System (ADS)

Matveev, A. D.

2016-11-01

To calculate the three-dimensional elastic body of heterogeneous structure under static loading, a method of multigrid finite element is provided, when implemented on the basis of algorithms of finite element method (FEM), using homogeneous and composite threedimensional multigrid finite elements (MFE). Peculiarities and differences of MFE from the currently available finite elements (FE) are to develop composite MFE (without increasing their dimensions), arbitrarily small basic partition of composite solids consisting of single-grid homogeneous FE of the first order can be used, i.e. in fact, to use micro approach in finite element form. These small partitions allow one to take into account in MFE, i.e. in the basic discrete models of composite solids, complex heterogeneous and microscopically inhomogeneous structure, shape, the complex nature of the loading and fixation and describe arbitrarily closely the stress and stain state by the equations of three-dimensional elastic theory without any additional simplifying hypotheses. When building the m grid FE, m of nested grids is used. The fine grid is generated by a basic partition of MFE, the other m —1 large grids are applied to reduce MFE dimensionality, when m is increased, MFE dimensionality becomes smaller. The procedures of developing MFE of rectangular parallelepiped, irregular shape, plate and beam types are given. MFE generate the small dimensional discrete models and numerical solutions with a high accuracy. An example of calculating the laminated plate, using three-dimensional 3-grid FE and the reference discrete model is given, with that having 2.2 milliards of FEM nodal unknowns.

NASTRAN analysis for the Airmass Sunburst model 'C' Ultralight Aircraft

NASA Technical Reports Server (NTRS)

Verbestel, John; Smith, Howard W.

1993-01-01

The purpose of this project was to create a three dimensional NASTRAN model of the Airmass Sunburst Ultralight comparable to one made for finite element analysis. A two dimensional sample problem will be calculated by hand and by NASTRAN to make sure that NASTRAN finds similar results. A three dimensional model, similar to the one analyzed by the finite element program, will be run on NASTRAN. A comparison will be done between the NASTRAN results and the finite element program results. This study will deal mainly with the aerodynamic loads on the wing and surrounding support structure at an attack angle of 10 degrees.

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.

Unsteady solute-transport simulation in streamflow using a finite-difference model

USGS Publications Warehouse

Land, Larry F.

1978-01-01

This report documents a rather simple, general purpose, one-dimensional, one-parameter, mass-transport model for field use. The model assumes a well-mixed conservative solute that may be coming from an unsteady source and is moving in unsteady streamflow. The quantity of solute being transported is in the units of concentration. Results are reported as such. An implicit finite-difference technique is used to solve the mass transport equation. It consists of creating a tridiagonal matrix and using the Thomas algorithm to solve the matrix for the unknown concentrations at the new time step. The computer program pesented is designed to compute the concentration of a water-quality constituent at any point and at any preselected time in a one-dimensional stream. The model is driven by the inflowing concentration of solute at the upstream boundary and is influenced by the solute entering the stream from tributaries and lateral ground-water inflow and from a source or sink. (Woodard-USGS)

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 development of an explicit thermochemical nonequilibrium algorithm and its application to compute three dimensional AFE flowfields

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

This study presents a three-dimensional explicit, finite-difference, shock-capturing numerical algorithm applied to viscous hypersonic flows in thermochemical nonequilibrium. The algorithm employs a two-temperature physical model. Equations governing the finite-rate chemical reactions are fully-coupled to the gas dynamic equations using a novel coupling technique. The new coupling method maintains stability in the explicit, finite-rate formulation while allowing relatively large global time steps. The code uses flux-vector accuracy. Comparisons with experimental data and other numerical computations verify the accuracy of the present method. The code is used to compute the three-dimensional flowfield over the Aeroassist Flight Experiment (AFE) vehicle at one of its trajectory points.

A 2-D Interface Element for Coupled Analysis of Independently Modeled 3-D Finite Element Subdomains

NASA Technical Reports Server (NTRS)

Kandil, Osama A.

1998-01-01

Over the past few years, the development of the interface technology has provided an analysis framework for embedding detailed finite element models within finite element models which are less refined. This development has enabled the use of cascading substructure domains without the constraint of coincident nodes along substructure boundaries. The approach used for the interface element is based on an alternate variational principle often used in deriving hybrid finite elements. The resulting system of equations exhibits a high degree of sparsity but gives rise to a non-positive definite system which causes difficulties with many of the equation solvers in general-purpose finite element codes. Hence the global system of equations is generally solved using, a decomposition procedure with pivoting. The research reported to-date for the interface element includes the one-dimensional line interface element and two-dimensional surface interface element. Several large-scale simulations, including geometrically nonlinear problems, have been reported using the one-dimensional interface element technology; however, only limited applications are available for the surface interface element. In the applications reported to-date, the geometry of the interfaced domains exactly match each other even though the spatial discretization within each domain may be different. As such, the spatial modeling of each domain, the interface elements and the assembled system is still laborious. The present research is focused on developing a rapid modeling procedure based on a parametric interface representation of independently defined subdomains which are also independently discretized.

Numerical aerodynamic simulation facility. [for flows about three-dimensional configurations

NASA Technical Reports Server (NTRS)

Bailey, F. R.; Hathaway, A. W.

1978-01-01

Critical to the advancement of computational aerodynamics capability is the ability to simulate flows about three-dimensional configurations that contain both compressible and viscous effects, including turbulence and flow separation at high Reynolds numbers. Analyses were conducted of two solution techniques for solving the Reynolds averaged Navier-Stokes equations describing the mean motion of a turbulent flow with certain terms involving the transport of turbulent momentum and energy modeled by auxiliary equations. The first solution technique is an implicit approximate factorization finite-difference scheme applied to three-dimensional flows that avoids the restrictive stability conditions when small grid spacing is used. The approximate factorization reduces the solution process to a sequence of three one-dimensional problems with easily inverted matrices. The second technique is a hybrid explicit/implicit finite-difference scheme which is also factored and applied to three-dimensional flows. Both methods are applicable to problems with highly distorted grids and a variety of boundary conditions and turbulence models.

Influence of Regional Difference in Bone Mineral Density on Hip Fracture Site in Elderly Females by Finite Element Analysis.

PubMed

Lin, Z L; Li, P F; Pang, Z H; Zheng, X H; Huang, F; Xu, H H; Li, Q L

2015-11-01

Hip fracture is a kind of osteoporotic fractures in elderly patients. Its important monitoring indicator is to measure bone mineral density (BMD) using DXA. The stress characteristics and material distribution in different parts of the bones can be well simulated by three-dimensional finite element analysis. Our previous studies have demonstrated a linear positive correlation between clinical BMD and the density of three-dimensional finite element model of the femur. However, the correlation between the density variation between intertrochanteric region and collum femoris region of the model and the fracture site has not been studied yet. The present study intends to investigate whether the regional difference in the density of three-dimensional finite element model of the femur can be used to predict hip fracture site in elderly females. The CT data of both hip joints were collected from 16 cases of elderly female patients with hip fractures. Mimics 15.01 software was used to reconstruct the model of proximal femur on the healthy side. Ten kinds of material properties were assigned. In Abaqus 6.12 software, the collum femoris region and intertrochanteric region were, respectively, drawn for calculating the corresponding regional density of the model, followed by prediction of hip fracture site and final comparison with factual fracture site. The intertrochanteric region/collum femoris region density was [(1.20 ± 0.02) × 10(6)] on the fracture site and [(1.22 ± 0.03) × 10(6)] on the non-fracture site, and the difference was statistically significant (P = 0.03). Among 16 established models of proximal femur on the healthy side, 14 models were consistent with the actual fracture sites, one model was inconsistent, and one model was unpredictable, with the coincidence rate of 87.5 %. The intertrochanteric region or collum femoris region with lower BMD is more prone to hip fracture of the type on the corresponding site.

Evaluation of HFIR LEU Fuel Using the COMSOL Multiphysics Platform

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

Primm, Trent; Ruggles, Arthur; Freels, James D

2009-03-01

A finite element computational approach to simulation of the High Flux Isotope Reactor (HFIR) Core Thermal-Fluid behavior is developed. These models were developed to facilitate design of a low enriched core for the HFIR, which will have different axial and radial flux profiles from the current HEU core and thus will require fuel and poison load optimization. This report outlines a stepwise implementation of this modeling approach using the commercial finite element code, COMSOL, with initial assessment of fuel, poison and clad conduction modeling capability, followed by assessment of mating of the fuel conduction models to a one dimensional fluidmore » model typical of legacy simulation techniques for the HFIR core. The model is then extended to fully couple 2-dimensional conduction in the fuel to a 2-dimensional thermo-fluid model of the coolant for a HFIR core cooling sub-channel with additional assessment of simulation outcomes. Finally, 3-dimensional simulations of a fuel plate and cooling channel are presented.« less

A one-dimensional stochastic approach to the study of cyclic voltammetry with adsorption effects

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

Samin, Adib J.

In this study, a one-dimensional stochastic model based on the random walk approach is used to simulate cyclic voltammetry. The model takes into account mass transport, kinetics of the redox reactions, adsorption effects and changes in the morphology of the electrode. The model is shown to display the expected behavior. Furthermore, the model shows consistent qualitative agreement with a finite difference solution. This approach allows for an understanding of phenomena on a microscopic level and may be useful for analyzing qualitative features observed in experimentally recorded signals.

A one-dimensional stochastic approach to the study of cyclic voltammetry with adsorption effects

NASA Astrophysics Data System (ADS)

Samin, Adib J.

2016-05-01

In this study, a one-dimensional stochastic model based on the random walk approach is used to simulate cyclic voltammetry. The model takes into account mass transport, kinetics of the redox reactions, adsorption effects and changes in the morphology of the electrode. The model is shown to display the expected behavior. Furthermore, the model shows consistent qualitative agreement with a finite difference solution. This approach allows for an understanding of phenomena on a microscopic level and may be useful for analyzing qualitative features observed in experimentally recorded signals.

On One-Dimensional Stretching Functions for Finite-Difference Calculations

NASA Technical Reports Server (NTRS)

Vinokur, M.

1980-01-01

The class of one dimensional stretching function used in finite difference calculations is studied. For solutions containing a highly localized region of rapid variation, simple criteria for a stretching function are derived using a truncation error analysis. These criteria are used to investigate two types of stretching functions. One is an interior stretching function, for which the location and slope of an interior clustering region are specified. The simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine. The other type of function is a two sided stretching function, for which the arbitrary slopes at the two ends of the one dimensional interval are specified. The simplest such general function is found to be one based on the inverse tangent. The general two sided function has many applications in the construction of finite difference grids.

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.

User's manual for the one-dimensional hypersonic experimental aero-thermodynamic (1DHEAT) data reduction code

NASA Technical Reports Server (NTRS)

Hollis, Brian R.

1995-01-01

A FORTRAN computer code for the reduction and analysis of experimental heat transfer data has been developed. This code can be utilized to determine heat transfer rates from surface temperature measurements made using either thin-film resistance gages or coaxial surface thermocouples. Both an analytical and a numerical finite-volume heat transfer model are implemented in this code. The analytical solution is based on a one-dimensional, semi-infinite wall thickness model with the approximation of constant substrate thermal properties, which is empirically corrected for the effects of variable thermal properties. The finite-volume solution is based on a one-dimensional, implicit discretization. The finite-volume model directly incorporates the effects of variable substrate thermal properties and does not require the semi-finite wall thickness approximation used in the analytical model. This model also includes the option of a multiple-layer substrate. Fast, accurate results can be obtained using either method. This code has been used to reduce several sets of aerodynamic heating data, of which samples are included in this report.

ENHANCED STREAM WATER QUALITY MODEL (QUAL2EU)

EPA Science Inventory

The enhanced stream water quality model QUAL2E and QUAL2E-UNCAS (37) permits simulation of several water quality constituents in a branching stream system using a finite difference solution to the one-dimensional advective-dispersive mass transport and reaction equation. The con...

Three-dimensional finite element analysis for high velocity impact. [of projectiles from space debris

NASA Technical Reports Server (NTRS)

Chan, S. T. K.; Lee, C. H.; Brashears, M. R.

1975-01-01

A finite element algorithm for solving unsteady, three-dimensional high velocity impact problems is presented. A computer program was developed based on the Eulerian hydroelasto-viscoplastic formulation and the utilization of the theorem of weak solutions. The equations solved consist of conservation of mass, momentum, and energy, equation of state, and appropriate constitutive equations. The solution technique is a time-dependent finite element analysis utilizing three-dimensional isoparametric elements, in conjunction with a generalized two-step time integration scheme. The developed code was demonstrated by solving one-dimensional as well as three-dimensional impact problems for both the inviscid hydrodynamic model and the hydroelasto-viscoplastic model.

An Integrated Magnetic Circuit Model and Finite Element Model Approach to Magnetic Bearing Design

NASA Technical Reports Server (NTRS)

Provenza, Andrew J.; Kenny, Andrew; Palazzolo, Alan B.

2003-01-01

A code for designing magnetic bearings is described. The code generates curves from magnetic circuit equations relating important bearing performance parameters. Bearing parameters selected from the curves by a designer to meet the requirements of a particular application are input directly by the code into a three-dimensional finite element analysis preprocessor. This means that a three-dimensional computer model of the bearing being developed is immediately available for viewing. The finite element model solution can be used to show areas of magnetic saturation and make more accurate predictions of the bearing load capacity, current stiffness, position stiffness, and inductance than the magnetic circuit equations did at the start of the design process. In summary, the code combines one-dimensional and three-dimensional modeling methods for designing magnetic bearings.

Finite-difference interblock transmissivity for unconfined aquifers and for aquifers having smoothly varying transmissivity

USGS Publications Warehouse

Goode, D.J.; Appel, C.A.

1992-01-01

More accurate alternatives to the widely used harmonic mean interblock transmissivity are proposed for block-centered finite-difference models of ground-water flow in unconfined aquifers and in aquifers having smoothly varying transmissivity. The harmonic mean is the exact interblock transmissivity for steady-state one-dimensional flow with no recharge if the transmissivity is assumed to be spatially uniform over each finite-difference block, changing abruptly at the block interface. However, the harmonic mean may be inferior to other means if transmissivity varies in a continuous or smooth manner between nodes. Alternative interblock transmissivity functions are analytically derived for the case of steady-state one-dimensional flow with no recharge. The second author has previously derived the exact interblock transmissivity, the logarithmic mean, for one-dimensional flow when transmissivity is a linear function of distance in the direction of flow. We show that the logarithmic mean transmissivity is also exact for uniform flow parallel to the direction of changing transmissivity in a two- or three-dimensional model, regardless of grid orientation relative to the flow vector. For the case of horizontal flow in a homogeneous unconfined or water-table aquifer with a horizontal bottom and with areally distributed recharge, the exact interblock transmissivity is the unweighted arithmetic mean of transmissivity at the nodes. This mean also exhibits no grid-orientation effect for unidirectional flow in a two-dimensional model. For horizontal flow in an unconfined aquifer with no recharge where hydraulic conductivity is a linear function of distance in the direction of flow the exact interblock transmissivity is the product of the arithmetic mean saturated thickness and the logarithmic mean hydraulic conductivity. For several hypothetical two- and three-dimensional cases with smoothly varying transmissivity or hydraulic conductivity, the harmonic mean is shown to yield the least accurate solution to the flow equation of the alternatives considered. Application of the alternative interblock transmissivities to a regional aquifer system model indicates that the changes in computed heads and fluxes are typically small, relative to model calibration error. For this example, the use of alternative interblock transmissivities resulted in an increase in computational effort of less than 3 percent. Numerical algorithms to compute alternative interblock transmissivity functions in a modular three-dimensional flow model are presented and documented.

Posttest analysis of a 1:6-scale reinforced concrete reactor containment building

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

Weatherby, J.R.

In an experiment conducted at Sandia National Laboratories, 1:6-scale model of a reinforced concrete light water reactor containment building was pressurized with nitrogen gas to more than three times its design pressure. The pressurization produced one large tear and several smaller tears in the steel liner plate that functioned as the primary pneumatic seal for the structure. The data collected from the overpressurization test have been used to evaluate and further refine methods of structural analysis that can be used to predict the performance of containment buildings under conditions produced by a severe accident. This report describes posttest finite elementmore » analyses of the 1:6-scale model tests and compares pretest predictions of the structural response to the experimental results. Strain and displacements calculated in axisymmetric finite element analyses of the 1:6-scale model are compared to strains and displacement measured in the experiment. Detailed analyses of the liner plate are also described in the report. The region of the liner surrounding the large tear was analyzed using two different two-dimensional finite elements model. The results from these analyzed indicate that the primary mechanisms that initiated the tear can be captured in a two- dimensional finite element model. Furthermore, the analyses show that studs used to anchor the liner to the concrete wall, played an important role in initiating the liner tear. Three-dimensional finite element analyses of liner plates loaded by studs are also presented. Results from the three-dimensional analyses are compared to results from two-dimensional analyses of the same problems. 12 refs., 56 figs., 1 tab.« less

A three-dimensional multiphase flow model for assessing NAPL contamination in porous and fractured media, 2. Porous medium simulation examples

NASA Astrophysics Data System (ADS)

Panday, S.; Wu, Y. S.; Huyakorn, P. S.; Springer, E. P.

1994-06-01

This paper discusses the verification and application of the three-dimensional (3-D) multiphase flow model presented by Huyakorn et al. (Part 1 in this issue) for assessing contamination due to subsurface releases of non-aqueous-phase liquids (NAPL's). Attention is focussed on situations involving one-, two- and three-dimensional flow through porous media. The model formulations and numerical schemes are tested for highly nonlinear field conditions. The utility and accuracy of various simplifications to certain simulation scenarios are assessed. Five simulation examples are included for demonstrative purposes. The first example verifies the model for vertical flow and compares the performance of the fully three-phase and the passive-air-phase formulations. Air-phase boundary conditions are noted to have considerable effects on simulation results. The second example verifies the model for cross-sectional analyses involving LNAPL and DNAPL migration. Finite-difference (5-point) and finite-element (9-point) spatial approximations are compared for different grid aspect ratios. Unless corrected, negative-transmissivity conditions were found to have undesirable impact on the finite-element solutions. The third example provides a model validation against laboratory experimental data on 5-spot water-flood treatment of oil reservoirs. The sensitivity to grid orientation is noted for the finite-difference schemes. The fourth example demonstrates model utility in characterizing the 3-D migration of LNAPL and DNAPL from surface sources. The final example present a modeling study of air sparging. Critical parameters affecting the performance of air-sparging system are examined. In general, the modeling results indicate sparging is more effective in water-retentive soils, and larger values of sparge influence radius may be achieved for certain anisotropic conditions.

[Three dimensional finite element model of a modified posterior cervical single open-door laminoplasty].

PubMed

Wang, Q; Yang, Y; Fei, Q; Li, D; Li, J J; Meng, H; Su, N; Fan, Z H; Wang, B Q

2017-06-06

Objective: To build a three-dimensional finite element models of a modified posterior cervical single open-door laminoplasty with short-segmental lateral mass screws fusion. Methods: The C(2)-C(7) segmental data were obtained from computed tomography (CT) scans of a male patient with cervical spondylotic myelopathy and spinal stenosis.Three-dimensional finite element models of a modified cervical single open-door laminoplasty (before and after surgery) were constructed by the combination of software package MIMICS, Geomagic and ABAQUS.The models were composed of bony vertebrae, articulating facets, intervertebral disc and associated ligaments.The loads of moments 1.5Nm at different directions (flexion, extension, lateral bending and axial rotation)were applied at preoperative model to calculate intersegmental ranges of motion.The results were compared with the previous studies to verify the validation of the models. Results: Three-dimensional finite element models of the modified cervical single open- door laminoplasty had 102258 elements (preoperative model) and 161 892 elements (postoperative model) respectively, including C(2-7) six bony vertebraes, C(2-3)-C(6-7) five intervertebral disc, main ligaments and lateral mass screws.The intersegmental responses at the preoperative model under the loads of moments 1.5 Nm at different directions were similar to the previous published data. Conclusion: Three-dimensional finite element models of the modified cervical single open- door laminoplasty were successfully established and had a good biological fidelity, which can be used for further study.

Mechanical modeling of self-expandable stent fabricated using braiding technology.

PubMed

Kim, Ju Hyun; Kang, Tae Jin; Yu, Woong-Ryeol

2008-11-14

The mechanical behavior of a stent is one of the important factors involved in ensuring its opening within arterial conduits. This study aimed to develop a mechanical model for designing self-expandable stents fabricated using braiding technology. For this purpose, a finite element model was constructed by developing a preprocessing program for the three-dimensional geometrical modeling of the braiding structure inside stents, and validated for various stents with different braiding structures. The constituent wires (Nitinol) in the braided stents were assumed to be superelastic material and their mechanical behavior was incorporated into the finite element software through a user material subroutine (VUMAT in ABAQUS) employing a one-dimensional superelastic model. For the verification of the model, several braided stents were manufactured using an automated braiding machine and characterized focusing on their compressive behavior. It was observed that the braided stents showed a hysteresis between their loading and unloading behavior when a compressive load was applied to the braided tube. Through the finite element analysis, it was concluded that the current mechanical model can appropriately predict the mechanical behavior of braided stents including such hysteretic behavior, and that the hysteresis was caused by the slippage between the constituent wires and their superelastic property.

Bistatic scattering from a three-dimensional object above a two-dimensional randomly rough surface modeled with the parallel FDTD approach.

PubMed

Guo, L-X; Li, J; Zeng, H

2009-11-01

We present an investigation of the electromagnetic scattering from a three-dimensional (3-D) object above a two-dimensional (2-D) randomly rough surface. A Message Passing Interface-based parallel finite-difference time-domain (FDTD) approach is used, and the uniaxial perfectly matched layer (UPML) medium is adopted for truncation of the FDTD lattices, in which the finite-difference equations can be used for the total computation domain by properly choosing the uniaxial parameters. This makes the parallel FDTD algorithm easier to implement. The parallel performance with different number of processors is illustrated for one rough surface realization and shows that the computation time of our parallel FDTD algorithm is dramatically reduced relative to a single-processor implementation. Finally, the composite scattering coefficients versus scattered and azimuthal angle are presented and analyzed for different conditions, including the surface roughness, the dielectric constants, the polarization, and the size of the 3-D object.

Data-Adaptive Bias-Reduced Doubly Robust Estimation.

PubMed

Vermeulen, Karel; Vansteelandt, Stijn

2016-05-01

Doubly robust estimators have now been proposed for a variety of target parameters in the causal inference and missing data literature. These consistently estimate the parameter of interest under a semiparametric model when one of two nuisance working models is correctly specified, regardless of which. The recently proposed bias-reduced doubly robust estimation procedure aims to partially retain this robustness in more realistic settings where both working models are misspecified. These so-called bias-reduced doubly robust estimators make use of special (finite-dimensional) nuisance parameter estimators that are designed to locally minimize the squared asymptotic bias of the doubly robust estimator in certain directions of these finite-dimensional nuisance parameters under misspecification of both parametric working models. In this article, we extend this idea to incorporate the use of data-adaptive estimators (infinite-dimensional nuisance parameters), by exploiting the bias reduction estimation principle in the direction of only one nuisance parameter. We additionally provide an asymptotic linearity theorem which gives the influence function of the proposed doubly robust estimator under correct specification of a parametric nuisance working model for the missingness mechanism/propensity score but a possibly misspecified (finite- or infinite-dimensional) outcome working model. Simulation studies confirm the desirable finite-sample performance of the proposed estimators relative to a variety of other doubly robust estimators.

3-D thermal analysis using finite difference technique with finite element model for improved design of components of rocket engine turbomachines for Space Shuttle Main Engine SSME

NASA Technical Reports Server (NTRS)

Sohn, Kiho D.; Ip, Shek-Se P.

1988-01-01

Three-dimensional finite element models were generated and transferred into three-dimensional finite difference models to perform transient thermal analyses for the SSME high pressure fuel turbopump's first stage nozzles and rotor blades. STANCOOL was chosen to calculate the heat transfer characteristics (HTCs) around the airfoils, and endwall effects were included at the intersections of the airfoils and platforms for the steady-state boundary conditions. Free and forced convection due to rotation effects were also considered in hollow cores. Transient HTCs were calculated by taking ratios of the steady-state values based on the flow rates and fluid properties calculated at each time slice. Results are presented for both transient plots and three-dimensional color contour isotherm plots; they were also converted into universal files to be used for FEM stress analyses.

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Adamian, A.

1988-01-01

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

PRZM-2, A MODEL FOR PREDICTING PESTICIDE FATE IN THE CROP ROOT AND UNSATURATED SOIL ZONES: USERS MANUAL FOR RELEASE 2.0

EPA Science Inventory

PRZM-2 links two subordinate models--PRZM and VADOFT--in order to predict pesticide transport and transformation down through the crop root and unsaturated zones. RZM is a one-dimensional, finite difference model that accounts for pesticide fate in the crop root zone. his release...

Recurrence relations in one-dimensional Ising models.

PubMed

da Conceição, C M Silva; Maia, R N P

2017-09-01

The exact finite-size partition function for the nonhomogeneous one-dimensional (1D) Ising model is found through an approach using algebra operators. Specifically, in this paper we show that the partition function can be computed through a trace from a linear second-order recurrence relation with nonconstant coefficients in matrix form. A relation between the finite-size partition function and the generalized Lucas polynomials is found for the simple homogeneous model, thus establishing a recursive formula for the partition function. This is an important property and it might indicate the possible existence of recurrence relations in higher-dimensional Ising models. Moreover, assuming quenched disorder for the interactions within the model, the quenched averaged magnetic susceptibility displays a nontrivial behavior due to changes in the ferromagnetic concentration probability.

Pressure distribution under flexible polishing tools. II - Cylindrical (conical) optics

NASA Astrophysics Data System (ADS)

Mehta, Pravin K.

1990-10-01

A previously developed eigenvalue model is extended to determine polishing pressure distribution by rectangular tools with unequal stiffness in two directions on cylindrical optics. Tool misfit is divided into two simplified one-dimensional problems and one simplified two-dimensional problem. Tools with nonuniform cross-sections are treated with a new one-dimensional eigenvalue algorithm, permitting evaluation of tool designs where the edge is more flexible than the interior. This maintains edge pressure variations within acceptable parameters. Finite element modeling is employed to resolve upper bounds, which handle pressure changes in the two-dimensional misfit element. Paraboloids and hyperboloids from the NASA AXAF system are treated with the AXAFPOD software for this method, and are verified with NASTRAN finite element analyses. The maximum deviation from the one-dimensional azimuthal pressure variation is predicted to be 10 percent and 20 percent for paraboloids and hyperboloids, respectively.

Lax-Wendroff and TVD finite volume methods for unidimensional thermomechanical numerical simulations of impacts on elastic-plastic solids

NASA Astrophysics Data System (ADS)

Heuzé, Thomas

2017-10-01

We present in this work two finite volume methods for the simulation of unidimensional impact problems, both for bars and plane waves, on elastic-plastic solid media within the small strain framework. First, an extension of Lax-Wendroff to elastic-plastic constitutive models with linear and nonlinear hardenings is presented. Second, a high order TVD method based on flux-difference splitting [1] and Superbee flux limiter [2] is coupled with an approximate elastic-plastic Riemann solver for nonlinear hardenings, and follows that of Fogarty [3] for linear ones. Thermomechanical coupling is accounted for through dissipation heating and thermal softening, and adiabatic conditions are assumed. This paper essentially focuses on one-dimensional problems since analytical solutions exist or can easily be developed. Accordingly, these two numerical methods are compared to analytical solutions and to the explicit finite element method on test cases involving discontinuous and continuous solutions. This allows to study in more details their respective performance during the loading, unloading and reloading stages. Particular emphasis is also paid to the accuracy of the computed plastic strains, some differences being found according to the numerical method used. Lax-Wendoff two-dimensional discretization of a one-dimensional problem is also appended at the end to demonstrate the extensibility of such numerical scheme to multidimensional problems.

Numerical simulation of one-dimensional heat transfer in composite bodies with phase change. M.S. Thesis, 1980 Final Report; [wing deicing pads

NASA Technical Reports Server (NTRS)

Dewitt, K. J.; Baliga, G.

1982-01-01

A numerical simulation was developed to investigate the one dimensional heat transfer occurring in a system composed of a layered aircraft blade having an ice deposit on its surface. The finite difference representation of the heat conduction equations was done using the Crank-Nicolson implicit finite difference formulation. The simulation considers uniform or time dependent heat sources, from heaters which can be either point sources or of finite thickness. For the ice water phase change, a numerical method which approximates the latent heat effect by a large heat capacity over a small temperature interval was applied. The simulation describes the temperature profiles within the various layers of the de-icer pad, as well as the movement of the ice water interface. The simulation could also be used to predict the one dimensional temperature profiles in any composite slab having different boundary conditions.

An Implicit Characteristic Based Method for Electromagnetics

NASA Technical Reports Server (NTRS)

Beggs, John H.; Briley, W. Roger

2001-01-01

An implicit characteristic-based approach for numerical solution of Maxwell's time-dependent curl equations in flux conservative form is introduced. This method combines a characteristic based finite difference spatial approximation with an implicit lower-upper approximate factorization (LU/AF) time integration scheme. This approach is advantageous for three-dimensional applications because the characteristic differencing enables a two-factor approximate factorization that retains its unconditional stability in three space dimensions, and it does not require solution of tridiagonal systems. Results are given both for a Fourier analysis of stability, damping and dispersion properties, and for one-dimensional model problems involving propagation and scattering for free space and dielectric materials using both uniform and nonuniform grids. The explicit Finite Difference Time Domain Method (FDTD) algorithm is used as a convenient reference algorithm for comparison. The one-dimensional results indicate that for low frequency problems on a highly resolved uniform or nonuniform grid, this LU/AF algorithm can produce accurate solutions at Courant numbers significantly greater than one, with a corresponding improvement in efficiency for simulating a given period of time. This approach appears promising for development of dispersion optimized LU/AF schemes for three dimensional applications.

Hubbard physics in the symmetric half-filled periodic anderson-hubbard model

NASA Astrophysics Data System (ADS)

Hagymási, I.; Itai, K.; Sólyom, J.

2013-05-01

Two very different methods — exact diagonalization on finite chains and a variational method — are used to study the possibility of a metal-insulator transition in the symmetric half-filled periodic Anderson-Hubbard model. With this aim we calculate the density of doubly occupied d sites ( gn d ) as a function of various parameters. In the absence of on-site Coulomb interaction ( U f ) between f electrons, the two methods yield similar results. The double occupancy of d levels remains always finite just as in the one-dimensional Hubbard model. Exact diagonalization on finite chains gives the same result for finite U f , while the Gutzwiller method leads to a Brinkman-Rice transition at a critical value ( U {/d c }), which depends on U f and V.

3DHYDROGEOCHEM: A 3-DIMENSIONAL MODEL OF DENSITY-DEPENDENT SUBSURFACE FLOW AND THERMAL MULTISPECIES-MULTICOMPONENT HYDROGEOCHEMICAL TRANSPORT

EPA Science Inventory

This report presents a three-dimensional finite-element numerical model designed to simulate chemical transport in subsurface systems with temperature effect taken into account. The three-dimensional model is developed to provide (1) a tool of application, with which one is able...

A quasi two-dimensional model for sound attenuation by the sonic crystals.

PubMed

Gupta, A; Lim, K M; Chew, C H

2012-10-01

Sound propagation in the sonic crystal (SC) along the symmetry direction is modeled by sound propagation through a variable cross-sectional area waveguide. A one-dimensional (1D) model based on the Webster horn equation is used to obtain sound attenuation through the SC. This model is compared with two-dimensional (2D) finite element simulation and experiment. The 1D model prediction of frequency band for sound attenuation is found to be shifted by around 500 Hz with respect to the finite element simulation. The reason for this shift is due to the assumption involved in the 1D model. A quasi 2D model is developed for sound propagation through the waveguide. Sound pressure profiles from the quasi 2D model are compared with the finite element simulation and the 1D model. The result shows significant improvement over the 1D model and is in good agreement with the 2D finite element simulation. Finally, sound attenuation through the SC is computed based on the quasi 2D model and is found to be in good agreement with the finite element simulation. The quasi 2D model provides an improved method to calculate sound attenuation through the SC.

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.

A numerical solution for thermoacoustic convection of fluids in low gravity

NASA Technical Reports Server (NTRS)

Spradley, L. W.; Bourgeois, S. V., Jr.; Fan, C.; Grodzka, P. G.

1973-01-01

A finite difference numerical technique for solving the differential equations which describe thermal convection of compressible fluids in low gravity are reported. Results of one-dimensional calculations are presented, and comparisons are made to previous solutions. The primary result presented is a one-dimensional radial model of the Apollo 14 heat flow and convection demonstration flight experiment. The numerical calculations show that thermally induced convective motion in a confined fluid can have significant effects on heat transfer in a low gravity environment.

Computer model of one-dimensional equilibrium controlled sorption processes

USGS Publications Warehouse

Grove, D.B.; Stollenwerk, K.G.

1984-01-01

A numerical solution to the one-dimensional solute-transport equation with equilibrium-controlled sorption and a first-order irreversible-rate reaction is presented. The computer code is written in FORTRAN language, with a variety of options for input and output for user ease. Sorption reactions include Langmuir, Freundlich, and ion-exchange, with or without equal valance. General equations describing transport and reaction processes are solved by finite-difference methods, with nonlinearities accounted for by iteration. Complete documentation of the code, with examples, is included. (USGS)

Fourier analysis of finite element preconditioned collocation schemes

NASA Technical Reports Server (NTRS)

Deville, Michel O.; Mund, Ernest H.

1990-01-01

The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.

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.

Application of the finite element groundwater model FEWA to the engineered test facility

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

Craig, P.M.; Davis, E.C.

1985-09-01

A finite element model for water transport through porous media (FEWA) has been applied to the unconfined aquifer at the Oak Ridge National Laboratory Solid Waste Storage Area 6 Engineered Test Facility (ETF). The model was developed in 1983 as part of the Shallow Land Burial Technology - Humid Task (ONL-WL14) and was previously verified using several general hydrologic problems for which an analytic solution exists. Model application and calibration, as described in this report, consisted of modeling the ETF water table for three specialized cases: a one-dimensional steady-state simulation, a one-dimensional transient simulation, and a two-dimensional transient simulation. Inmore » the one-dimensional steady-state simulation, the FEWA output accurately predicted the water table during a long period in which there were no man-induced or natural perturbations to the system. The input parameters of most importance for this case were hydraulic conductivity and aquifer bottom elevation. In the two transient cases, the FEWA output has matched observed water table responses to a single rainfall event occurring in February 1983, yielding a calibrated finite element model that is useful for further study of additional precipitation events as well as contaminant transport at the experimental site.« less

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 well-balanced meshless tsunami propagation and inundation model

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

[Comparison between one-step and two-step space closing methods of sliding mechanics using three-dimensional finite element].

PubMed

Han, Yaohui; Mou, Lan; Xu, Gengchi; Yang, Yiqiang; Ge, Zhenlin

2015-03-01

To construct a three-dimensional finite element model comparing between one-step and two-step methods in torque control of anterior teeth during space closure. Dicom image data including maxilla and upper teeth were obtained though cone-beam CT. A three-dimensional model was set up and the maxilla, upper teeth and periodontium were separated using Mimics software. The models were instantiated using Pro/Engineer software, and Abaqus finite element analysis software was used to simulate the sliding mechanics by loading 1.47 Nforce on traction hooks with different heights (2, 4, 6, 8, 10, 12 and 14 mm, respectively) in order to compare the initial displacement between six maxillary anterior teeth (one-step method) and four maxillary anterior teeth (two-step method). When moving anterior teeth bodily, initial displacements of central incisors in two-step method and in one-step method were 29.26 × 10⁻⁶ mm and 15.75 × 10⁻⁶ mm, respectively. The initial displacements of lateral incisors in two-step method and in one-step method were 46.76 × 10(-6) mm and 23.18 × 10(-6) mm, respectively. Under the same amount of light force, the initial displacement of anterior teeth in two-step method was doubled compared with that in one-step method. The root and crown of the canine couldn't obtain the same amount of displacement in one-step method. Two-step method could produce more initial displacement than one-step method. Therefore, two-step method was easier to achieve torque control of the anterior teeth during space closure.

The MUSIC algorithm for impedance tomography of small inclusions from discrete data

NASA Astrophysics Data System (ADS)

Lechleiter, A.

2015-09-01

We consider a point-electrode model for electrical impedance tomography and show that current-to-voltage measurements from finitely many electrodes are sufficient to characterize the positions of a finite number of point-like inclusions. More precisely, we consider an asymptotic expansion with respect to the size of the small inclusions of the relative Neumann-to-Dirichlet operator in the framework of the point electrode model. This operator is naturally finite-dimensional and models difference measurements by finitely many small electrodes of the electric potential with and without the small inclusions. Moreover, its leading-order term explicitly characterizes the centers of the small inclusions if the (finite) number of point electrodes is large enough. This characterization is based on finite-dimensional test vectors and leads naturally to a MUSIC algorithm for imaging the inclusion centers. We show both the feasibility and limitations of this imaging technique via two-dimensional numerical experiments, considering in particular the influence of the number of point electrodes on the algorithm’s images.

Finite Element Analysis of Folded Airbag in Frontal Impact of Adapted Vehicles for Disabled Drivers

NASA Astrophysics Data System (ADS)

Masiá, J.; Eixerés, B.; Dols, J. F.; Esquerdo, T. V.

2009-11-01

The car control adaptations are used in vehicles in order to facilitate the driving to persons with physical handicaps. This does not have to suppose a decrease of the passive safety that is required to the vehicles. In order to analyze this relation there will be characterized the different control adaptations that are in use together with the different devices of passive safety that can be mounted in the vehicles in diverse cases of impact in order to generate models of simulation. The methodology used to generate this simulation consists of the first phase in which there develops the three-dimensional model of the driving place. For it, there has been used a commercial software of three-dimensional design. Once realized this one divides, the model is imported to the finite elements software in which meshing is generated. Finally, dynamic simulation software is used to assign the most important characteristics like material properties, contact interfaces, gas expansion models, airbag fold types, etc.

[Analysis of a three-dimensional finite element model of atlas and axis complex fracture].

PubMed

Tang, X M; Liu, C; Huang, K; Zhu, G T; Sun, H L; Dai, J; Tian, J W

2018-05-22

Objective: To explored the clinical application of the three-dimensional finite element model of atlantoaxial complex fracture. Methods: A three-dimensional finite element model of cervical spine (FEM/intact) was established by software of Abaqus6.12.On the basis of this model, a three-dimensional finite element model of four types of atlantoaxial complex fracture was established: C(1) fracture (Jefferson)+ C(2) fracture (type Ⅱfracture), Jefferson+ C(2) fracture(type Ⅲfracture), Jefferson+ C(2) fracture(Hangman), Jefferson+ stable C(2) fracture (FEM/fracture). The range of motion under flexion, extension, lateral bending and axial rotation were measured and compared with the model of cervical spine. Results: The three-dimensional finite element model of four types of atlantoaxial complex fracture had the same similarity and profile.The range of motion (ROM) of different segments had different changes.Compared with those in the normal model, the ROM of C(0/1) and C(1/2) in C(1) combined Ⅱ odontoid fracture model in flexion/extension, lateral bending and rotation increased by 57.45%, 29.34%, 48.09% and 95.49%, 88.52%, 36.71%, respectively.The ROM of C(0/1) and C(1/2) in C(1) combined Ⅲodontoid fracture model in flexion/extension, lateral bending and rotation increased by 47.01%, 27.30%, 45.31% and 90.38%, 27.30%, 30.0%.The ROM of C(0/1) and C(1/2) in C(1) combined Hangman fracture model in flexion/extension, lateral bending and rotation increased by 32.68%, 79.34%, 77.62% and 60.53%, 81.20%, 21.48%, respectively.The ROM of C(0/1) and C(1/2) in C(1) combined axis fracture model in flexion/extension, lateral bending and rotation increased by 15.00%, 29.30%, 8.47% and 37.87%, 75.57%, 8.30%, respectively. Conclusions: The three-dimensional finite element model can be used to simulate the biomechanics of atlantoaxial complex fracture.The ROM of atlantoaxial complex fracture is larger than nomal model, which indicates that surgical treatment should be performed.

[Construction and validation of a three-dimensional finite element model of cranio-maxillary complex with sutures in unilateral cleft lip and palate patient].

PubMed

Wu, Zhi-fang; Lei, Yong-hua; Li, Wen-jie; Liao, Sheng-hui; Zhao, Zi-jin

2013-02-01

To explore an effective method to construct and validate a finite element model of the unilateral cleft lip and palate(UCLP) craniomaxillary complex with sutures, which could be applied in further three-dimensional finite element analysis (FEA). One male patient aged 9 with left complete lip and palate cleft was selected and CT scan was taken at 0.75mm intervals on the skull. The CT data was saved in Dicom format, which was, afterwards, imported into Software Mimics 10.0 to generate a three-dimensional anatomic model. Then Software Geomagic Studio 12.0 was used to match, smoothen and transfer the anatomic model into a CAD model with NURBS patches. Then, 12 circum-maxillary sutures were integrated into the CAD model by Solidworks (2011 version). Finally meshing by E-feature Biomedical Modeler was done and a three-dimensional finite element model with sutures was obtained. A maxillary protraction force (500 g per side, 20° downward and forward from the occlusal plane) was applied. Displacement and stress distribution of some important craniofacial structures were measured and compared with the results of related researches in the literature. A three-dimensional finite element model of UCLP craniomaxillary complex with 12 sutures was established from the CT scan data. This simulation model consisted of 206 753 individual elements with 260 662 nodes, which was a more precise simulation and a better representation of human craniomaxillary complex than the formerly available FEA models. By comparison, this model was proved to be valid. It is an effective way to establish the three-dimensional finite element model of UCLP cranio-maxillary complex with sutures from CT images with the help of the following softwares: Mimics 10.0, Geomagic Studio 12.0, Solidworks and E-feature Biomedical Modeler.

One-dimensional transient finite difference model of an operational salinity gradient solar pond

NASA Technical Reports Server (NTRS)

Hicks, Michael C.; Golding, Peter

1992-01-01

This paper describes the modeling approach used to simulate the transient behavior of a salinity gradient solar pond. A system of finite difference equations are used to generate the time dependent temperature and salinity profiles within the pond. The stability of the pond, as determined by the capacity of the resulting salinity profile to suppress thermal convection within the primary gradient region of the pond, is continually monitored and when necessary adjustments are made to the thickness of the gradient zone. Results of the model are then compared to measurements taken during two representative seasonal periods at the University of Texas at El Paso's (UTEP's) research solar pond.

Development of an energy storage tank model

NASA Astrophysics Data System (ADS)

Buckley, Robert Christopher

A linearized, one-dimensional finite difference model employing an implicit finite difference method for energy storage tanks is developed, programmed with MATLAB, and demonstrated for different applications. A set of nodal energy equations is developed by considering the energy interactions on a small control volume. The general method of solving these equations is described as are other features of the simulation program. Two modeling applications are presented: the first using a hot water storage tank with a solar collector and an absorption chiller to cool a building in the summer, the second using a molten salt storage system with a solar collector and steam power plant to generate electricity. Recommendations for further study as well as all of the source code generated in the project are also provided.

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 ...

Heat transfer analysis of the Bridgman-Stockbarger configuration for crystal growth. Part 1: Analytical treatment of the axial temperature distribution

NASA Technical Reports Server (NTRS)

Jasinski, T. J.; Rohsenow, W. M.; Witt, A. F.

1982-01-01

All first order effects on the axial temperature distribution in a solidifying charge in a Bridgman-Stockbarger configuration for crystal growth are analyzed on the basis of a one dimensional model whose validity can be verified through comparison with published finite difference ana;uses of two dimensional models. The model presented includes an insulated region between axially aligned heat pipes and considers the effects of charge diameter, charge motion, thickness, and thermal conductivity of a confining crucible, thermal conductivity change at the crystal-melt interface, generation of latent heat at the interface, and finite charge length. Results are primarily given in analytical form and can be used without recourse to computer work for both improve furnace design and optimization of growth conditions in a given thermal configuration.

3-D geoelectrical modelling using finite-difference: a new boundary conditions improvement

NASA Astrophysics Data System (ADS)

Maineult, A.; Schott, J.-J.; Ardiot, A.

2003-04-01

Geoelectrical prospecting is a well-known and frequently used method for quantitative and non-destructive subsurface exploration until depths of a few hundreds metres. Thus archeological objects can be efficiently detected as their resistivities often contrast with those of the surrounding media. Nevertheless using the geoelectrical prospecting method has long been restricted due to inhability to model correctly arbitrarily-shaped structures. The one-dimensional modelling and inversion have long been classical, but are of no interest for the majority of field data, since the natural distribution of resistivity is rarely homogeneous or tabular. Since the 1970's some authors developed discrete methods in order to solve the two and three-dimensional problem, using mathematical tools such as finite-element or finite-difference. The finite-difference approach is quite simple, easily understandable and programmable. Since the work of Dey and Morrison (1979), this approach has become quite popular. Nevertheless, one of its major drawbacks is the difficulty to establish satisfying boundary conditions. Recently Lowry et al. (1989) and Zhao and Yedlin (1996) suggested some refinements on the improvement of the boundary problem. We propose a new betterment, based on the splitting of the potential into two terms, the potential due to a reference tabular medium and a secondary potential caused by a disturbance of this medium. The surface response of a tabular medium has long been known (see for example Koefoed 1979). Here we developed the analytical solution for the electrical tabular potential everywhere in the medium, in order to establish more satisfying boundary conditions. The response of the perturbation, that is to say the object of interest, is then solved using volume-difference and preconditioned conjugate gradient. Finally the grid is refined one or more times in the perturbed domain in order to ameliorate the precision. This method of modelling is easy to implement and numerical computations run very fast. Thanks to improved boundary conditions and refinement processes, edges effects are reduced. Moreover, one important conclusion of this work is the necessity to prefer three-dimensional prospecting, since in some cases a unique profile can lead to misinterpretation, as shown by the comparison of transverse profiles through a buried cylinder and through a buried sphere.

Generalized fourier analyses of the advection-diffusion equation - Part II: two-dimensional domains

NASA Astrophysics Data System (ADS)

Voth, Thomas E.; Martinez, Mario J.; Christon, Mark A.

2004-07-01

Part I of this work presents a detailed multi-methods comparison of the spatial errors associated with the one-dimensional finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. In Part II we extend the analysis to two-dimensional domains and also consider the effects of wave propagation direction and grid aspect ratio on the phase speed, and the discrete and artificial diffusivities. The observed dependence of dispersive and diffusive behaviour on propagation direction makes comparison of methods more difficult relative to the one-dimensional results. For this reason, integrated (over propagation direction and wave number) error and anisotropy metrics are introduced to facilitate comparison among the various methods. With respect to these metrics, the consistent mass Galerkin and consistent mass control-volume finite element methods, and their streamline upwind derivatives, exhibit comparable accuracy, and generally out-perform their lumped mass counterparts and finite-difference based schemes. While this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common mathematical framework. Published in 2004 by John Wiley & Sons, Ltd.

A MULTIPLE GRID ALGORITHM FOR ONE-DIMENSIONAL TRANSIENT OPEN CHANNEL FLOWS. (R825200)

EPA Science Inventory

Numerical modeling of open channel flows with shocks using explicit finite difference schemes is constrained by the choice of time step, which is limited by the CFL stability criteria. To overcome this limitation, in this work we introduce the application of a multiple grid al...

On one-dimensional stretching functions for finite-difference calculations. [computational fluid dynamics

NASA Technical Reports Server (NTRS)

Vinokur, M.

1979-01-01

The class of one-dimensional stretching functions used in finite-difference calculations is studied. For solutions containing a highly localized region of rapid variation, simple criteria for a stretching function are derived using a truncation error analysis. These criteria are used to investigate two types of stretching functions. One is an interior stretching function, for which the location and slope of an interior clustering region are specified. The simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine. The other type of function is a two-sided stretching function, for which the arbitrary slopes at the two ends of the one-dimensional interval are specified. The simplest such general function is found to be one based on the inverse tangent.

Computational simulations of vocal fold vibration: Bernoulli versus Navier-Stokes.

PubMed

Decker, Gifford Z; Thomson, Scott L

2007-05-01

The use of the mechanical energy (ME) equation for fluid flow, an extension of the Bernoulli equation, to predict the aerodynamic loading on a two-dimensional finite element vocal fold model is examined. Three steady, one-dimensional ME flow models, incorporating different methods of flow separation point prediction, were compared. For two models, determination of the flow separation point was based on fixed ratios of the glottal area at separation to the minimum glottal area; for the third model, the separation point determination was based on fluid mechanics boundary layer theory. Results of flow rate, separation point, and intraglottal pressure distribution were compared with those of an unsteady, two-dimensional, finite element Navier-Stokes model. Cases were considered with a rigid glottal profile as well as with a vibrating vocal fold. For small glottal widths, the three ME flow models yielded good predictions of flow rate and intraglottal pressure distribution, but poor predictions of separation location. For larger orifice widths, the ME models were poor predictors of flow rate and intraglottal pressure, but they satisfactorily predicted separation location. For the vibrating vocal fold case, all models resulted in similar predictions of mean intraglottal pressure, maximum orifice area, and vibration frequency, but vastly different predictions of separation location and maximum flow rate.

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...

Exact finite elements for conduction and convection

NASA Technical Reports Server (NTRS)

Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.

1981-01-01

An approach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions.

3DHYDROGEOCHEM: A 3-DIMENSIONAL MODEL OF DENSITY-DEPENDENT SUBSURFACE FLOW AND THERMAL MULTISPECIES-MULTICOMPONENT HYDROGEOCHEMICAL TRANSPORT (EPA/600/SR-98/159)

EPA Science Inventory

This report presents a three-dimensional finite-element numerical model designed to simulate chemical transport in subsurface systems with temperature effect taken into account. The three-dimensional model is developed to provide (1) a tool of application, with which one is able ...

Statistics of Lyapunov exponents of quasi-one-dimensional disordered systems

NASA Astrophysics Data System (ADS)

Zhang, Yan-Yang; Xiong, Shi-Jie

2005-10-01

Statistical properties of Lyapunov exponents (LE) are numerically calculated in a quasi-one-dimensional (1D) Anderson model, which is in a 2D or 3D lattice with a finite cross section. The single-parameter scaling (SPS) variable τ relating the Lyapunov exponents γ and their variances σ by τ≡σ2L/⟨γ⟩ is calculated for different lateral coupling t and disorder strength W . In a wide range of t , τ is approximately independent of W , but it has different values for LEs in different channels. For small t , the distribution of the smallest LE is non-Gaussian and τ strongly depends on W , remarkably different from the 1D SPS hypothesis.

Investigation of shock-induced combustion past blunt projectiles

NASA Technical Reports Server (NTRS)

Ahuja, J. K.; Tiwari, S. N.

1996-01-01

A numerical study is conducted to simulate shock-induced combustion in premixed hydrogen-air mixtures at various free-stream conditions and parameters. Two-dimensional axisymmetric, reacting viscous flow over blunt projectiles is computed to study shock-induced combustion at Mach 5.11 and Mach 6.46 in hydrogen-air mixture. A seven-species, seven reactions finite rate hydrogen-air chemical reaction mechanism is used combined with a finite-difference, shock-fitting method to solve the complete set of Navier-Stokes and species conservation equations. The study has allowed an improved understanding of the physics of shock-induced combustion over blunt projectiles and the numerical results can now be explained more readily with one-dimensional wave-interaction model.

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.

[Analysis of the movement of long axis and the distribution of principal stress in abutment tooth retained by conical telescope].

PubMed

Lin, Ying-he; Man, Yi; Qu, Yi-li; Guan, Dong-hua; Lu, Xuan; Wei, Na

2006-01-01

To study the movement of long axis and the distribution of principal stress in the abutment teeth in removable partial denture which is retained by use of conical telescope. An ideal three dimensional finite element model was constructed by using SCT image reconstruction technique, self-programming and ANSYS software. The static loads were applied. The displacement of the long axis and the distribution of the principal stress in the abutment teeth was analyzed. There is no statistic difference of displacenat and stress distribution among different three-dimensional finite element models. Generally, the abutment teeth move along the long axis itself. Similar stress distribution was observed in each three-dimensional finite element model. The maximal principal compressive stress was observed at the distal cervix of the second premolar. The abutment teeth can be well protected by use of conical telescope.

Nonlinear Conservation Laws and Finite Volume Methods

NASA Astrophysics Data System (ADS)

Leveque, Randall J.

Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

Switching synchronization in one-dimensional memristive networks

NASA Astrophysics Data System (ADS)

Slipko, Valeriy A.; Shumovskyi, Mykola; Pershin, Yuriy V.

2015-11-01

We report on a switching synchronization phenomenon in one-dimensional memristive networks, which occurs when several memristive systems with different switching constants are switched from the high- to low-resistance state. Our numerical simulations show that such a collective behavior is especially pronounced when the applied voltage slightly exceeds the combined threshold voltage of memristive systems. Moreover, a finite increase in the network switching time is found compared to the average switching time of individual systems. An analytical model is presented to explain our observations. Using this model, we have derived asymptotic expressions for memory resistances at short and long times, which are in excellent agreement with results of our numerical simulations.

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.

On one-dimensional stretching functions for finite-difference calculations. [computational fluid dynamics

NASA Technical Reports Server (NTRS)

Vinokur, M.

1983-01-01

The class of one-dimensional stretching functions used in finite-difference calculations is studied. For solutions containing a highly localized region of rapid variation, simple criteria for a stretching function are derived using a truncation error analysis. These criteria are used to investigate two types of stretching functions. One an interior stretching function, for which the location and slope of an interior clustering region are specified. The simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine. The other type of function is a two-sided stretching function, for which the arbitrary slopes at the two ends of the one-dimensional interval are specified. The simplest such general function is found to be one based on the inverse tangent. Previously announced in STAR as N80-25055

RISK OF UNSATURATED/SATURATED TRANSPORT AND TRANSFORMATION OF CHEMICAL CONCENTRATIONS (RUSTIC): VOLUME 1. THEORY AND CODE VERIFICATION

EPA Science Inventory

The RUSTIC program links three subordinate models--PRZM, VADOFT, and SAFTMOD--in order to predict pesticide transport and transformation through the crop root zone, the unsaturated zone, and the saturated zone to drinking water wells. PRZM is a one-dimensional finite-difference m...

Entanglement Area Law in Disordered Free Fermion Anderson Model in One, Two, and Three Dimensions

DOE PAGES

Pouranvari, Mohammad; Zhang, Yuhui; Yang, Kun

2015-01-01

We calculate numerically the entanglement entropy of free fermion ground states in one-, two-, and three-dimensional Anderson models and find that it obeys the area law as long as the linear size of the subsystem is sufficiently larger than the mean free path. This result holds in the metallic phase of the three-dimensional Anderson model, where the mean free path is finite although the localization length is infinite. Relation between the present results and earlier ones on area law violation in special one-dimensional models that support metallic phases is discussed.

Entanglement Area Law in Disordered Free Fermion Anderson Model in One, Two, and Three Dimensions

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

Pouranvari, Mohammad; Zhang, Yuhui; Yang, Kun

We calculate numerically the entanglement entropy of free fermion ground states in one-, two-, and three-dimensional Anderson models and find that it obeys the area law as long as the linear size of the subsystem is sufficiently larger than the mean free path. This result holds in the metallic phase of the three-dimensional Anderson model, where the mean free path is finite although the localization length is infinite. Relation between the present results and earlier ones on area law violation in special one-dimensional models that support metallic phases is discussed.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 1: Model Description and User's Manual

USGS Publications Warehouse

Torak, L.J.

1993-01-01

A MODular, Finite-Element digital-computer program (MODFE) was developed to simulate steady or unsteady-state, two-dimensional or axisymmetric ground-water flow. Geometric- and hydrologic-aquifer characteristics in two spatial dimensions are represented by triangular finite elements and linear basis functions; one-dimensional finite elements and linear basis functions represent time. Finite-element matrix equations are solved by the direct symmetric-Doolittle method or the iterative modified, incomplete-Cholesky, conjugate-gradient method. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining beds; (3) specified recharge or discharge at points, along lines, and over areas; (4) flow across specified-flow, specified-head, or bead-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining beds combined with aquifer dewatering, and evapotranspiration. The report describes procedures for applying MODFE to ground-water-flow problems, simulation capabilities, and data preparation. Guidelines for designing the finite-element mesh and for node numbering and determining band widths are given. Tables are given that reference simulation capabilities to specific versions of MODFE. Examples of data input and model output for different versions of MODFE are provided.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems; Part 1, Model description and user's manual

USGS Publications Warehouse

Torak, Lynn J.

1992-01-01

A MODular, Finite-Element digital-computer program (MODFE) was developed to simulate steady or unsteady-state, two-dimensional or axisymmetric ground-water flow. Geometric- and hydrologic-aquifer characteristics in two spatial dimensions are represented by triangular finite elements and linear basis functions; one-dimensional finite elements and linear basis functions represent time. Finite-element matrix equations are solved by the direct symmetric-Doolittle method or the iterative modified, incomplete-Cholesky, conjugate-gradient method. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining beds; (3) specified recharge or discharge at points, along lines, and over areas; (4) flow across specified-flow, specified-head, or head-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining beds combined with aquifer dewatering, and evapotranspiration.The report describes procedures for applying MODFE to ground-water-flow problems, simulation capabilities, and data preparation. Guidelines for designing the finite-element mesh and for node numbering and determining band widths are given. Tables are given that reference simulation capabilities to specific versions of MODFE. Examples of data input and model output for different versions of MODFE are provided.

Source term evaluation for combustion modeling

NASA Technical Reports Server (NTRS)

Sussman, Myles A.

1993-01-01

A modification is developed for application to the source terms used in combustion modeling. The modification accounts for the error of the finite difference scheme in regions where chain-branching chemical reactions produce exponential growth of species densities. The modification is first applied to a one-dimensional scalar model problem. It is then generalized to multiple chemical species, and used in quasi-one-dimensional computations of shock-induced combustion in a channel. Grid refinement studies demonstrate the improved accuracy of the method using this modification. The algorithm is applied in two spatial dimensions and used in simulations of steady and unsteady shock-induced combustion. Comparisons with ballistic range experiments give confidence in the numerical technique and the 9-species hydrogen-air chemistry model.

Approximation of Optimal Infinite Dimensional Compensators for Flexible Structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Mingori, D. L.; Adamian, A.; Jabbari, F.

1985-01-01

The infinite dimensional compensator for a large class of flexible structures, modeled as distributed systems are discussed, as well as an approximation scheme for designing finite dimensional compensators to approximate the infinite dimensional compensator. The approximation scheme is applied to develop a compensator for a space antenna model based on wrap-rib antennas being built currently. While the present model has been simplified, it retains the salient features of rigid body modes and several distributed components of different characteristics. The control and estimator gains are represented by functional gains, which provide graphical representations of the control and estimator laws. These functional gains also indicate the convergence of the finite dimensional compensators and show which modes the optimal compensator ignores.

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.

Exact finite elements for conduction and convection

NASA Technical Reports Server (NTRS)

Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.

1981-01-01

An appproach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions. Previously announced in STAR as N81-31507

Three dimensional finite temperature SU(3) gauge theory near the phase transition

NASA Astrophysics Data System (ADS)

Bialas, P.; Daniel, L.; Morel, A.; Petersson, B.

2013-06-01

We have measured the correlation function of Polyakov loops on the lattice in three dimensional SU(3) gauge theory near its finite temperature phase transition. Using a new and powerful application of finite size scaling, we furthermore extend the measurements of the critical couplings to considerably larger values of the lattice sizes, both in the temperature and space directions, than was investigated earlier in this theory. With the help of these measurements we perform a detailed finite size scaling analysis, showing that for the critical exponents of the two dimensional three state Potts model the mass and the susceptibility fall on unique scaling curves. This strongly supports the expectation that the gauge theory is in the same universality class. The Nambu-Goto string model on the other hand predicts that the exponent ν has the mean field value, which is quite different from the value in the abovementioned Potts model. Using our values of the critical couplings we also determine the continuum limit of the value of the critical temperature in terms of the square root of the zero temperature string tension. This value is very near to the prediction of the Nambu-Goto string model in spite of the different critical behaviour.

Interactions between Magnetically Levitated Vehicles and Elevated Guideway Structures

DOT National Transportation Integrated Search

1992-07-01

The dynamic performance characteristic of magnetically levitated vehicles and vehicle trains relating to ride quality and magnetic gap variations have been determined using computer simulation models for one-dimensional, two-dimensional and finite le...

A dynamic model of the piezoelectric traveling wave rotary ultrasonic motor stator with the finite volume method.

PubMed

Renteria Marquez, I A; Bolborici, V

2017-05-01

This manuscript presents a method to model in detail the piezoelectric traveling wave rotary ultrasonic motor (PTRUSM) stator response under the action of DC and AC voltages. The stator is modeled with a discrete two dimensional system of equations using the finite volume method (FVM). In order to obtain accurate results, a model of the stator bridge is included into the stator model. The model of the stator under the action of DC voltage is presented first, and the results of the model are compared versus a similar model using the commercial finite element software COMSOL Multiphysics. One can observe that there is a difference of less than 5% between the displacements of the stator using the proposed model and the one with COMSOL Multiphysics. After that, the model of the stator under the action of AC voltages is presented. The time domain analysis shows the generation of the traveling wave in the stator surface. One can use this model to accurately calculate the stator surface velocities, elliptical motion of the stator surface and the amplitude and shape of the stator traveling wave. A system of equations discretized with the finite volume method can easily be transformed into electrical circuits, because of that, FVM may be a better choice to develop a model-based control strategy for the PTRUSM. Copyright © 2017 Elsevier B.V. All rights reserved.

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.

Modeling the curing process of thick-section autoclave cured composites

NASA Technical Reports Server (NTRS)

Loos, A. C.; Dara, P. H.

1985-01-01

Temperature gradients are significant during cure of large area, thick-section composites. Such temperature gradients result in nonuniformly cured parts with high void contents, poor ply compaction, and variations in the fiber/resin distribution. A model was developed to determine the temperature distribution in thick-section autoclave cured composites. Using the model, long with temperature measurements obtained from the thick-section composites, the effects of various processing parameters on the thermal response of the composites were examined. A one-dimensional heat transfer model was constructed for the composite-tool assembly. The governing differential equations and associated boundary conditions describing one-dimensional unsteady heat-conduction in the composite, tool plate, and pressure plate are given. Solution of the thermal model was obtained using an implicit finite difference technique.

An Advanced One-Dimensional Finite Element Model for Incompressible Thermally Expandable Flow

DOE PAGES

Hu, Rui

2017-03-27

Here, this paper provides an overview of a new one-dimensional finite element flow model for incompressible but thermally expandable flow. The flow model was developed for use in system analysis tools for whole-plant safety analysis of sodium fast reactors. Although the pressure-based formulation was implemented, the use of integral equations in the conservative form ensured the conservation laws of the fluid. A stabilization scheme based on streamline-upwind/Petrov-Galerkin and pressure-stabilizing/Petrov-Galerkin formulations is also introduced. The flow model and its implementation have been verified by many test problems, including density wave propagation, steep gradient problems, discharging between tanks, and the conjugate heatmore » transfer in a heat exchanger.« less

An Advanced One-Dimensional Finite Element Model for Incompressible Thermally Expandable Flow

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

Hu, Rui

Here, this paper provides an overview of a new one-dimensional finite element flow model for incompressible but thermally expandable flow. The flow model was developed for use in system analysis tools for whole-plant safety analysis of sodium fast reactors. Although the pressure-based formulation was implemented, the use of integral equations in the conservative form ensured the conservation laws of the fluid. A stabilization scheme based on streamline-upwind/Petrov-Galerkin and pressure-stabilizing/Petrov-Galerkin formulations is also introduced. The flow model and its implementation have been verified by many test problems, including density wave propagation, steep gradient problems, discharging between tanks, and the conjugate heatmore » transfer in a heat exchanger.« less

Thermal conductivity in one-dimensional nonlinear systems

NASA Astrophysics Data System (ADS)

Politi, Antonio; Giardinà, Cristian; Livi, Roberto; Vassalli, Massimo

2000-03-01

Thermal conducitivity of one-dimensional nonlinear systems typically diverges in the thermodynamic limit, whenever the momentum is conserved (i.e. in the absence of interactions with an external substrate). Evidence comes from detailed studies of Fermi-Pasta-Ulam and diatomic Toda chains. Here, we discuss the first example of a one-dimensional system obeying Fourier law : a chain of coupled rotators. Numerical estimates of the thermal conductivity obtained by simulating a chain in contact with two thermal baths at different temperatures are found to be consistent with those ones based on linear response theory. The dynamics of the Fourier modes provides direct evidence of energy diffusion. The finiteness of the conductivity is traced back to the occurrence of phase-jumps. Our conclusions are confirmed by the analysis of two variants of the rotator model.

Finite-difference model for 3-D flow in bays and estuaries

USGS Publications Warehouse

Smith, Peter E.; Larock, Bruce E.; ,

1993-01-01

This paper describes a semi-implicit finite-difference model for the numerical solution of three-dimensional flow in bays and estuaries. The model treats the gravity wave and vertical diffusion terms in the governing equations implicitly, and other terms explicitly. The model achieves essentially second-order accurate and stable solutions in strongly nonlinear problems by using a three-time-level leapfrog-trapezoidal scheme for the time integration.

[Stress analysis of the mandible by 3D FEA in normal human being under three loading conditions].

PubMed

Sun, Jian; Zhang, Fu-qiang; Wang, Dong-wei; Yu, Jia; Wang, Cheng-tao

2004-02-01

The condition and character of stress distribution in the mandibular in normal human being during centric, protrusive, laterotrusive occlusion were analysed. The three-dimensional finite element model of the mandibular was developed by helica CT scanning and CAD/CAM software, and three-dimensional finite element stress analysis was done by ANSYS software. Three-dimensional finite element model of the mandibular was generated. Under these three occlusal conditions, the stress of various regions in the mandible were distributed unequally, and the stress feature was different;while the stress of corresponding region in bilateral mandibular was in symmetric distribution. The stress value of condyle neck, the posterior surface of coronoid process and mandibular angle were high. The material properties of mandible were closely correlated to the value of stress. Stress distribution were similar according to the three different loading patterns, but had different effects on TMJ joint. The concentrated areas of stress were in the condyle neck, the posterior surface of coronoid process and mandibular angle.

Entangled photon pair generation by spontaneous parametric down-conversion in finite-length one-dimensional photonic crystals

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

Centini, M.; Sciscione, L.; Sibilia, C.

A description of spontaneous parametric down-conversion in finite-length one-dimensional nonlinear photonic crystals is developed using semiclassical and quantum approaches. It is shown that if a suitable averaging is added to the semiclassical model, its results are in very good agreement with the quantum approach. We propose two structures made with GaN/AlN that generate both degenerate and nondegenerate entangled photon pairs. Both structures are designed so as to achieve a high efficiency of the nonlinear process.

An efficient semi-implicit method for three-dimensional non-hydrostatic flows in compliant arterial vessels.

PubMed

Fambri, Francesco; Dumbser, Michael; Casulli, Vincenzo

2014-11-01

Blood flow in arterial systems can be described by the three-dimensional Navier-Stokes equations within a time-dependent spatial domain that accounts for the elasticity of the arterial walls. In this article, blood is treated as an incompressible Newtonian fluid that flows through compliant vessels of general cross section. A three-dimensional semi-implicit finite difference and finite volume model is derived so that numerical stability is obtained at a low computational cost on a staggered grid. The key idea of the method consists in a splitting of the pressure into a hydrostatic and a non-hydrostatic part, where first a small quasi-one-dimensional nonlinear system is solved for the hydrostatic pressure and only in a second step the fully three-dimensional non-hydrostatic pressure is computed from a three-dimensional nonlinear system as a correction to the hydrostatic one. The resulting algorithm is robust, efficient, locally and globally mass conservative, and applies to hydrostatic and non-hydrostatic flows in one, two and three space dimensions. These features are illustrated on nontrivial test cases for flows in tubes with circular or elliptical cross section where the exact analytical solution is known. Test cases of steady and pulsatile flows in uniformly curved rigid and elastic tubes are presented. Wherever possible, axial velocity development and secondary flows are shown and compared with previously published results. Copyright © 2014 John Wiley & Sons, Ltd.

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.

A quantitative study on magnesium alloy stent biodegradation.

PubMed

Gao, Yuanming; Wang, Lizhen; Gu, Xuenan; Chu, Zhaowei; Guo, Meng; Fan, Yubo

2018-06-06

Insufficient scaffolding time in the process of rapid corrosion is the main problem of magnesium alloy stent (MAS). Finite element method had been used to investigate corrosion of MAS. However, related researches mostly described all elements suffered corrosion in view of one-dimensional corrosion. Multi-dimensional corrosions significantly influence mechanical integrity of MAS structures such as edges and corners. In this study, the effects of multi-dimensional corrosion were studied using experiment quantitatively, then a phenomenological corrosion model was developed to consider these effects. We implemented immersion test with magnesium alloy (AZ31B) cubes, which had different numbers of exposed surfaces to analyze differences of dimension. It was indicated that corrosion rates of cubes are almost proportional to their exposed-surface numbers, especially when pitting corrosions are not marked. The cubes also represented the hexahedron elements in simulation. In conclusion, corrosion rate of every element accelerates by increasing corrosion-surface numbers in multi-dimensional corrosion. The damage ratios among elements with the same size are proportional to the ratios of corrosion-surface numbers under uniform corrosion. The finite element simulation using proposed model provided more details of changes of morphology and mechanics in scaffolding time by removing 25.7% of elements of MAS. The proposed corrosion model reflected the effects of multi-dimension on corrosions. It would be used to predict degradation process of MAS quantitatively. Copyright © 2018 Elsevier Ltd. All rights reserved.

Geodynamics for Everyone: Robust Finite-Difference Heat Transfer Models using MS Excel 2007 Spreadsheets

NASA Astrophysics Data System (ADS)

Grose, C. J.

2008-05-01

Numerical geodynamics models of heat transfer are typically thought of as specialized topics of research requiring knowledge of specialized modelling software, linux platforms, and state-of-the-art finite-element codes. I have implemented analytical and numerical finite-difference techniques with Microsoft Excel 2007 spreadsheets to solve for complex solid-earth heat transfer problems for use by students, teachers, and practicing scientists without specialty in geodynamics modelling techniques and applications. While implementation of equations for use in Excel spreadsheets is occasionally cumbersome, once case boundary structure and node equations are developed, spreadsheet manipulation becomes routine. Model experimentation by modifying parameter values, geometry, and grid resolution makes Excel a useful tool whether in the classroom at the undergraduate or graduate level or for more engaging student projects. Furthermore, the ability to incorporate complex geometries and heat-transfer characteristics makes it ideal for first and occasionally higher order geodynamics simulations to better understand and constrain the results of professional field research in a setting that does not require the constraints of state-of-the-art modelling codes. The straightforward expression and manipulation of model equations in excel can also serve as a medium to better understand the confusing notations of advanced mathematical problems. To illustrate the power and robustness of computation and visualization in spreadsheet models I focus primarily on one-dimensional analytical and two-dimensional numerical solutions to two case problems: (i) the cooling of oceanic lithosphere and (ii) temperatures within subducting slabs. Excel source documents will be made available.

Nonlinear dynamics, chaos and complex cardiac arrhythmias

NASA Technical Reports Server (NTRS)

Glass, L.; Courtemanche, M.; Shrier, A.; Goldberger, A. L.

1987-01-01

Periodic stimulation of a nonlinear cardiac oscillator in vitro gives rise to complex dynamics that is well described by one-dimensional finite difference equations. As stimulation parameters are varied, a large number of different phase-locked and chaotic rhythms is observed. Similar rhythms can be observed in the intact human heart when there is interaction between two pacemaker sites. Simplified models are analyzed, which show some correspondence to clinical observations.

A thermal analysis of a spirally wound battery using a simple mathematical model

NASA Technical Reports Server (NTRS)

Evans, T. I.; White, R. E.

1989-01-01

A two-dimensional thermal model for spirally wound batteries has been developed. The governing equation of the model is the energy balance. Convective and insulated boundary conditions are used, and the equations are solved using a finite element code called TOPAZ2D. The finite element mesh is generated using a preprocessor to TOPAZ2D called MAZE. The model is used to estimate temperature profiles within a spirally wound D-size cell. The model is applied to the lithium/thionyl chloride cell because of the thermal management problems that this cell exhibits. Simplified one-dimensional models are presented that can be used to predict best and worst temperature profiles. The two-dimensional model is used to predict the regions of maximum temperature within the spirally wound cell. Normal discharge as well as thermal runaway conditions are investigated.

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

NASA Astrophysics Data System (ADS)

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

1986-12-01

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

Adaptive mixed finite element methods for Darcy flow in fractured porous media

NASA Astrophysics Data System (ADS)

Chen, Huangxin; Salama, Amgad; Sun, Shuyu

2016-10-01

In this paper, we propose adaptive mixed finite element methods for simulating the single-phase Darcy flow in two-dimensional fractured porous media. The reduced model that we use for the simulation is a discrete fracture model coupling Darcy flows in the matrix and the fractures, and the fractures are modeled by one-dimensional entities. The Raviart-Thomas mixed finite element methods are utilized for the solution of the coupled Darcy flows in the matrix and the fractures. In order to improve the efficiency of the simulation, we use adaptive mixed finite element methods based on novel residual-based a posteriori error estimators. In addition, we develop an efficient upscaling algorithm to compute the effective permeability of the fractured porous media. Several interesting examples of Darcy flow in the fractured porous media are presented to demonstrate the robustness of the algorithm.

A three-dimensional, time-dependent model of Mobile Bay

NASA Technical Reports Server (NTRS)

Pitts, F. H.; Farmer, R. C.

1976-01-01

A three-dimensional, time-variant mathematical model for momentum and mass transport in estuaries was developed and its solution implemented on a digital computer. The mathematical model is based on state and conservation equations applied to turbulent flow of a two-component, incompressible fluid having a free surface. Thus, bouyancy effects caused by density differences between the fresh and salt water, inertia from thare river and tidal currents, and differences in hydrostatic head are taken into account. The conservation equations, which are partial differential equations, are solved numerically by an explicit, one-step finite difference scheme and the solutions displayed numerically and graphically. To test the validity of the model, a specific estuary for which scaled model and experimental field data are available, Mobile Bay, was simulated. Comparisons of velocity, salinity and water level data show that the model is valid and a viable means of simulating the hydrodynamics and mass transport in non-idealized estuaries.

Finite element analysis of true and pseudo surface acoustic waves in one-dimensional phononic crystals

NASA Astrophysics Data System (ADS)

Graczykowski, B.; Alzina, F.; Gomis-Bresco, J.; Sotomayor Torres, C. M.

2016-01-01

In this paper, we report a theoretical investigation of surface acoustic waves propagating in one-dimensional phononic crystal. Using finite element method eigenfrequency and frequency response studies, we develop two model geometries suitable to distinguish true and pseudo (or leaky) surface acoustic waves and determine their propagation through finite size phononic crystals, respectively. The novelty of the first model comes from the application of a surface-like criterion and, additionally, functional damping domain. Exemplary calculated band diagrams show sorted branches of true and pseudo surface acoustic waves and their quantified surface confinement. The second model gives a complementary study of transmission, reflection, and surface-to-bulk losses of Rayleigh surface waves in the case of a phononic crystal with a finite number of periods. Here, we demonstrate that a non-zero transmission within non-radiative band gaps can be carried via leaky modes originating from the coupling of local resonances with propagating waves in the substrate. Finally, we show that the transmission, reflection, and surface-to-bulk losses can be effectively optimised by tuning the geometrical properties of a stripe.

On infinite-dimensional state spaces

NASA Astrophysics Data System (ADS)

Fritz, Tobias

2013-05-01

It is well known that the canonical commutation relation [x, p] = i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p] = i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context from which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V-1U2V = U3, then finite-dimensionality entails the relation UV-1UV = V-1UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V-1U2V = U3 holds only up to ɛ and then yields a lower bound on the dimension.

Calculation of three-dimensional compressible laminar and turbulent boundary layers. An implicit finite-difference procedure for solving the three-dimensional compressible laminar, transitional, and turbulent boundary-layer equations

NASA Technical Reports Server (NTRS)

Harris, J. E.

1975-01-01

An implicit finite-difference procedure is presented for solving the compressible three-dimensional boundary-layer equations. The method is second-order accurate, unconditionally stable (conditional stability for reverse cross flow), and efficient from the viewpoint of computer storage and processing time. The Reynolds stress terms are modeled by (1) a single-layer mixing length model and (2) a two-layer eddy viscosity model. These models, although simple in concept, accurately predicted the equilibrium turbulent flow for the conditions considered. Numerical results are compared with experimental wall and profile data for a cone at an angle of attack larger than the cone semiapex angle. These comparisons clearly indicate that the numerical procedure and turbulence models accurately predict the experimental data with as few as 21 nodal points in the plane normal to the wall boundary.

Numerical simulation using vorticity-vector potential formulation

NASA Technical Reports Server (NTRS)

Tokunaga, Hiroshi

1993-01-01

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

User-Defined Material Model for Progressive Failure Analysis

NASA Technical Reports Server (NTRS)

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

2006-01-01

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

Finite-element three-dimensional ground-water (FE3DGW) flow model - formulation, program listings and users' manual

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

Gupta, S.K.; Cole, C.R.; Bond, F.W.

1979-12-01

The Assessment of Effectiveness of Geologic Isolation Systems (AEGIS) Program is developing and applying the methodology for assessing the far-field, long-term post-closure safety of deep geologic nuclear waste repositories. AEGIS is being performed by Pacific Northwest Laboratory (PNL) under contract with the Office of Nuclear Waste Isolation (OWNI) for the Department of Energy (DOE). One task within AEGIS is the development of methodology for analysis of the consequences (water pathway) from loss of repository containment as defined by various release scenarios. Analysis of the long-term, far-field consequences of release scenarios requires the application of numerical codes which simulate the hydrologicmore » systems, model the transport of released radionuclides through the hydrologic systems to the biosphere, and, where applicable, assess the radiological dose to humans. Hydrologic and transport models are available at several levels of complexity or sophistication. Model selection and use are determined by the quantity and quality of input data. Model development under AEGIS and related programs provides three levels of hydrologic models, two levels of transport models, and one level of dose models (with several separate models). This document consists of the description of the FE3DGW (Finite Element, Three-Dimensional Groundwater) Hydrologic model third level (high complexity) three-dimensional, finite element approach (Galerkin formulation) for saturated groundwater flow.« less

Single-cone finite-difference schemes for the (2+1)-dimensional Dirac equation in general electromagnetic textures

NASA Astrophysics Data System (ADS)

Pötz, Walter

2017-11-01

A single-cone finite-difference lattice scheme is developed for the (2+1)-dimensional Dirac equation in presence of general electromagnetic textures. The latter is represented on a (2+1)-dimensional staggered grid using a second-order-accurate finite difference scheme. A Peierls-Schwinger substitution to the wave function is used to introduce the electromagnetic (vector) potential into the Dirac equation. Thereby, the single-cone energy dispersion and gauge invariance are carried over from the continuum to the lattice formulation. Conservation laws and stability properties of the formal scheme are identified by comparison with the scheme for zero vector potential. The placement of magnetization terms is inferred from consistency with the one for the vector potential. Based on this formal scheme, several numerical schemes are proposed and tested. Elementary examples for single-fermion transport in the presence of in-plane magnetization are given, using material parameters typical for topological insulator surfaces.

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.

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.

Revisiting of Multiscale Static Analysis of Notched Laminates Using the Generalized Method of Cells

NASA Technical Reports Server (NTRS)

Naghipour Ghezeljeh, Paria; Arnold, Steven M.; Pineda, Evan J.

2016-01-01

Composite material systems generally exhibit a range of behavior on different length scales (from constituent level to macro); therefore, a multiscale framework is beneficial for the design and engineering of these material systems. The complex nature of the observed composite failure during experiments suggests the need for a three-dimensional (3D) multiscale model to attain a reliable prediction. However, the size of a multiscale three-dimensional finite element model can become prohibitively large and computationally costly. Two-dimensional (2D) models are preferred due to computational efficiency, especially if many different configurations have to be analyzed for an in-depth damage tolerance and durability design study. In this study, various 2D and 3D multiscale analyses will be employed to conduct a detailed investigation into the tensile failure of a given multidirectional, notched carbon fiber reinforced polymer laminate. Threedimensional finite element analysis is typically considered more accurate than a 2D finite element model, as compared with experiments. Nevertheless, in the absence of adequate mesh refinement, large differences may be observed between a 2D and 3D analysis, especially for a shear-dominated layup. This observed difference has not been widely addressed in previous literature and is the main focus of this paper.

Exact Lyapunov exponent of the harmonic magnon modes of one-dimensional Heisenberg-Mattis spin glasses

NASA Astrophysics Data System (ADS)

Sepehrinia, Reza; Niry, M. D.; Bozorg, B.; Tabar, M. Reza Rahimi; Sahimi, Muhammad

2008-03-01

A mapping is developed between the linearized equation of motion for the dynamics of the transverse modes at T=0 of the Heisenberg-Mattis model of one-dimensional (1D) spin glasses and the (discretized) random wave equation. The mapping is used to derive an exact expression for the Lyapunov exponent (LE) of the magnon modes of spin glasses and to show that it follows anomalous scaling at low magnon frequencies. In addition, through numerical simulations, the differences between the LE and the density of states of the wave equation in a discrete 1D model of randomly disordered media (those with a finite correlation length) and that of continuous media (with a zero correlation length) are demonstrated and emphasized.

Stress analysis in platform-switching implants: a 3-dimensional finite element study.

PubMed

Pellizzer, Eduardo Piza; Verri, Fellippo Ramos; Falcón-Antenucci, Rosse Mary; Júnior, Joel Ferreira Santiago; de Carvalho, Paulo Sérgio Perri; de Moraes, Sandra Lúcia Dantas; Noritomi, Pedro Yoshito

2012-10-01

The aim of this study was to evaluate the influence of the platform-switching technique on stress distribution in implant, abutment, and peri-implant tissues, through a 3-dimensional finite element study. Three 3-dimensional mandibular models were fabricated using the SolidWorks 2006 and InVesalius software. Each model was composed of a bone block with one implant 10 mm long and of different diameters (3.75 and 5.00 mm). The UCLA abutments also ranged in diameter from 5.00 mm to 4.1 mm. After obtaining the geometries, the models were transferred to the software FEMAP 10.0 for pre- and postprocessing of finite elements to generate the mesh, loading, and boundary conditions. A total load of 200 N was applied in axial (0°), oblique (45°), and lateral (90°) directions. The models were solved by the software NeiNastran 9.0 and transferred to the software FEMAP 10.0 to obtain the results that were visualized through von Mises and maximum principal stress maps. Model A (implants with 3.75 mm/abutment with 4.1 mm) exhibited the highest area of stress concentration with all loadings (axial, oblique, and lateral) for the implant and the abutment. All models presented the stress areas at the abutment level and at the implant/abutment interface. Models B (implant with 5.0 mm/abutment with 5.0 mm) and C (implant with 5.0 mm/abutment with 4.1 mm) presented minor areas of stress concentration and similar distribution pattern. For the cortical bone, low stress concentration was observed in the peri-implant region for models B and C in comparison to model A. The trabecular bone exhibited low stress that was well distributed in models B and C. Model A presented the highest stress concentration. Model B exhibited better stress distribution. There was no significant difference between the large-diameter implants (models B and C).

An introduction to three-dimensional climate modeling

NASA Technical Reports Server (NTRS)

Washington, W. M.; Parkinson, C. L.

1986-01-01

The development and use of three-dimensional computer models of the earth's climate are discussed. The processes and interactions of the atmosphere, oceans, and sea ice are examined. The basic theory of climate simulation which includes the fundamental equations, models, and numerical techniques for simulating the atmosphere, oceans, and sea ice is described. Simulated wind, temperature, precipitation, ocean current, and sea ice distribution data are presented and compared to observational data. The responses of the climate to various environmental changes, such as variations in solar output or increases in atmospheric carbon dioxide, are modeled. Future developments in climate modeling are considered. Information is also provided on the derivation of the energy equation, the finite difference barotropic forecast model, the spectral transform technique, and the finite difference shallow water waved equation model.

A finite element evaluation of mechanical function for 3 distal extension partial dental prosthesis designs with a 3-dimensional nonlinear method for modeling soft tissue.

PubMed

Nakamura, Yoshinori; Kanbara, Ryo; Ochiai, Kent T; Tanaka, Yoshinobu

2014-10-01

The mechanical evaluation of the function of partial removable dental prostheses with 3-dimensional finite element modeling requires the accurate assessment and incorporation of soft tissue behavior. The differential behaviors of the residual ridge mucosa and periodontal ligament tissues have been shown to exhibit nonlinear displacement. The mathematic incorporation of known values simulating nonlinear soft tissue behavior has not been investigated previously via 3-dimensional finite element modeling evaluation to demonstrate the effect of prosthesis design on the supporting tissues. The purpose of this comparative study was to evaluate the functional differences of 3 different partial removable dental prosthesis designs with 3-dimensional finite element analysis modeling and a simulated patient model incorporating known viscoelastic, nonlinear soft tissue properties. Three different designs of distal extension removable partial dental prostheses were analyzed. The stress distributions to the supporting abutments and soft tissue displacements of the designs tested were calculated and mechanically compared. Among the 3 dental designs evaluated, the RPI prosthesis demonstrated the lowest stress concentrations on the tissue supporting the tooth abutment and also provided wide mucosa-borne areas of support, thereby demonstrating a mechanical advantage and efficacy over the other designs evaluated. The data and results obtained from this study confirmed that the functional behavior of partial dental prostheses with supporting abutments and soft tissues are consistent with the conventional theories of design and clinical experience. The validity and usefulness of this testing method for future applications and testing protocols are shown. Copyright © 2014 Editorial Council for the Journal of Prosthetic Dentistry. Published by Elsevier Inc. All rights reserved.

Development of a Finite-Difference Time Domain (FDTD) Model for Propagation of Transient Sounds in Very Shallow Water.

PubMed

Sprague, Mark W; Luczkovich, Joseph J

2016-01-01

This finite-difference time domain (FDTD) model for sound propagation in very shallow water uses pressure and velocity grids with both 3-dimensional Cartesian and 2-dimensional cylindrical implementations. Parameters, including water and sediment properties, can vary in each dimension. Steady-state and transient signals from discrete and distributed sources, such as the surface of a vibrating pile, can be used. The cylindrical implementation uses less computation but requires axial symmetry. The Cartesian implementation allows asymmetry. FDTD calculations compare well with those of a split-step parabolic equation. Applications include modeling the propagation of individual fish sounds, fish aggregation sounds, and distributed sources.

Density-matrix renormalization group method for the conductance of one-dimensional correlated systems using the Kubo formula

NASA Astrophysics Data System (ADS)

Bischoff, Jan-Moritz; Jeckelmann, Eric

2017-11-01

We improve the density-matrix renormalization group (DMRG) evaluation of the Kubo formula for the zero-temperature linear conductance of one-dimensional correlated systems. The dynamical DMRG is used to compute the linear response of a finite system to an applied ac source-drain voltage; then the low-frequency finite-system response is extrapolated to the thermodynamic limit to obtain the dc conductance of an infinite system. The method is demonstrated on the one-dimensional spinless fermion model at half filling. Our method is able to replicate several predictions of the Luttinger liquid theory such as the renormalization of the conductance in a homogeneous conductor, the universal effects of a single barrier, and the resonant tunneling through a double barrier.

Conversion and comparison of the mathematical, three-dimensional, finite-difference, ground-water flow model to the modular, three-dimensional, finite-difference, ground-water flow model for the Tesuque aquifer system in northern New Mexico

USGS Publications Warehouse

Umari, A.M.; Szeliga, T.L.

1989-01-01

The three-dimensional finite-difference groundwater model (using a mathematical groundwater flow code) of the Tesuque aquifer system in northern New Mexico was converted to run using the U.S. Geological Survey 's modular groundwater flow code. Results from the final versions of the predevelopment and 1947 to 2080 transient simulations of the two models are compared. A correlation coefficient of 0.9905 was obtained for the match in block-by-block head-dependent fluxes for predevelopment conditions. There are, however, significant differences in at least two specific cases. In the first case, a difference is associated with the net loss from the Pojoaque River and its tributaries to the aquifer. The net loss by the river is given as 1.134 cu ft/sec using the original groundwater model, which is 38.1% less than the net loss by the river of 1.8319 cu ft/sec computed in this study. In the second case, the large difference is computed for the transient decline in the hydraulic head of a model block near Tesuque Pueblo. The hydraulic-head decline by 2080 is, using the original model, 249 ft, which is 14.7% less than the hydraulic head of 292 ft computed by this study. In general, the differences between the two sets of results are not large enough to lead to different conclusions regarding the behavior of the system at steady state or when pumped. (USGS)

Thermal Pollution Mathematical Model. Volume 3: User's Manual for One-Dimensional Numerical Model for the Seasonal Thermocline. [environment impact of thermal discharges from power plants

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.; Nwadike, E. V.

1980-01-01

A user's manual for a one dimensional thermal model to predict the temperature profiles of a deep body of water for any number of annual cycles is presented. The model is essentially a set of partial differential equations which are solved by finite difference methods using a high speed digital computer. The model features the effects of area change with depth, nonlinear interaction of wind generated turbulence and buoyancy, adsorption of radiative heat flux below the surface, thermal discharges, and the effects of vertical convection caused by discharge. The main assumption in the formulation is horizontal homogeneity. The environmental impact of thermal discharges from power plants is emphasized. Although the model is applicable to most lakes, a specific site (Lake Keowee, S.C.) application is described in detail. The programs are written in FORTRAN 5.

A probabilistic model of a porous heat exchanger

NASA Technical Reports Server (NTRS)

Agrawal, O. P.; Lin, X. A.

1995-01-01

This paper presents a probabilistic one-dimensional finite element model for heat transfer processes in porous heat exchangers. The Galerkin approach is used to develop the finite element matrices. Some of the submatrices are asymmetric due to the presence of the flow term. The Neumann expansion is used to write the temperature distribution as a series of random variables, and the expectation operator is applied to obtain the mean and deviation statistics. To demonstrate the feasibility of the formulation, a one-dimensional model of heat transfer phenomenon in superfluid flow through a porous media is considered. Results of this formulation agree well with the Monte-Carlo simulations and the analytical solutions. Although the numerical experiments are confined to parametric random variables, a formulation is presented to account for the random spatial variations.

Sensitivities Kernels of Seismic Traveltimes and Amplitudes for Quality Factor and Boundary Topography

NASA Astrophysics Data System (ADS)

Hsieh, M.; Zhao, L.; Ma, K.

2010-12-01

Finite-frequency approach enables seismic tomography to fully utilize the spatial and temporal distributions of the seismic wavefield to improve resolution. In achieving this goal, one of the most important tasks is to compute efficiently and accurately the (Fréchet) sensitivity kernels of finite-frequency seismic observables such as traveltime and amplitude to the perturbations of model parameters. In scattering-integral approach, the Fréchet kernels are expressed in terms of the strain Green tensors (SGTs), and a pre-established SGT database is necessary to achieve practical efficiency for a three-dimensional reference model in which the SGTs must be calculated numerically. Methods for computing Fréchet kernels for seismic velocities have long been established. In this study, we develop algorithms based on the finite-difference method for calculating Fréchet kernels for the quality factor Qμ and seismic boundary topography. Kernels for the quality factor can be obtained in a way similar to those for seismic velocities with the help of the Hilbert transform. The effects of seismic velocities and quality factor on either traveltime or amplitude are coupled. Kernels for boundary topography involve spatial gradient of the SGTs and they also exhibit interesting finite-frequency characteristics. Examples of quality factor and boundary topography kernels will be shown for a realistic model for the Taiwan region with three-dimensional velocity variation as well as surface and Moho discontinuity topography.

Numerical Analysis of the Trailblazer Inlet Flowfield for Hypersonic Mach Numbers

NASA Technical Reports Server (NTRS)

Steffen, C. J., Jr.; DeBonis, J. R.

1999-01-01

A study of the Trailblazer vehicle inlet was conducted using the Global Air Sampling Program (GASP) code for flight Mach numbers ranging from 4-12. Both perfect gas and finite rate chemical analysis were performed with the intention of making detailed comparisons between the two results. Inlet performance was assessed using total pressure recovery and kinetic energy efficiency. These assessments were based upon a one-dimensional stream-thrust-average of the axisymmetric flowfield. Flow visualization utilized to examine the detailed shock structures internal to this mixed-compression inlet. Kinetic energy efficiency appeared to be the least sensitive to differences between the perfect gas and finite rate chemistry results. Total pressure recovery appeared to be the most sensitive discriminator between the perfect gas and finite rate chemistry results for flight Mach numbers above Mach 6. Adiabatic wall temperature was consistently overpredicted by the perfect gas model for flight Mach numbers above Mach 4. The predicted shock structures were noticeably different for Mach numbers from 6-12. At Mach 4, the perfect gas and finite rate chemistry models collapse to the same result.

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1984-01-01

Various analytical and numerical methods used to evaluate the stress intensity factors for cracks in three-dimensional (3-D) solids are reviewed. Classical exact solutions and many of the approximate methods used in 3-D analyses of cracks are reviewed. The exact solutions for embedded elliptic cracks in infinite solids are discussed. The approximate methods reviewed are the finite element methods, the boundary integral equation (BIE) method, the mixed methods (superposition of analytical and finite element method, stress difference method, discretization-error method, alternating method, finite element-alternating method), and the line-spring model. The finite element method with singularity elements is the most widely used method. The BIE method only needs modeling of the surfaces of the solid and so is gaining popularity. The line-spring model appears to be the quickest way to obtain good estimates of the stress intensity factors. The finite element-alternating method appears to yield the most accurate solution at the minimum cost.

TWO-DIMENSIONAL MODELING OF CURRENT CIRCULATION AND CONTAMINANT TRANSPORT IN SURFACE WATERS

EPA Science Inventory

The main objectives of this paper are to briefly describe and evaluate three different applications of two-dimensional, depth-averaged, finite-element models for hydrodynamics (RMA2) and transport (RMA4) ([1] and [2], respectively), which were run using the FastTABS user interfac...

Modeling and control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Mingori, D. L.

1988-01-01

This monograph presents integrated modeling and controller design methods for flexible structures. The controllers, or compensators, developed are optimal in the linear-quadratic-Gaussian sense. The performance objectives, sensor and actuator locations and external disturbances influence both the construction of the model and the design of the finite dimensional compensator. The modeling and controller design procedures are carried out in parallel to ensure compatibility of these two aspects of the design problem. Model reduction techniques are introduced to keep both the model order and the controller order as small as possible. A linear distributed, or infinite dimensional, model is the theoretical basis for most of the text, but finite dimensional models arising from both lumped-mass and finite element approximations also play an important role. A central purpose of the approach here is to approximate an optimal infinite dimensional controller with an implementable finite dimensional compensator. Both convergence theory and numerical approximation methods are given. Simple examples are used to illustrate the theory.

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)

[Three-dimensional finite element modeling and biomechanical simulation for evaluating and improving postoperative internal instrumentation of neck-thoracic vertebral tumor en bloc resection].

PubMed

Qinghua, Zhao; Jipeng, Li; Yongxing, Zhang; He, Liang; Xuepeng, Wang; Peng, Yan; Xiaofeng, Wu

2015-04-07

To employ three-dimensional finite element modeling and biomechanical simulation for evaluating the stability and stress conduction of two postoperative internal fixed modeling-multilevel posterior instrumentation ( MPI) and MPI with anterior instrumentation (MPAI) with neck-thoracic vertebral tumor en bloc resection. Mimics software and computed tomography (CT) images were used to establish the three-dimensional (3D) model of vertebrae C5-T2 and simulated the C7 en bloc vertebral resection for MPI and MPAI modeling. Then the statistics and images were transmitted into the ANSYS finite element system and 20N distribution load (simulating body weight) and applied 1 N · m torque on neutral point for simulating vertebral displacement and stress conduction and distribution of motion mode, i. e. flexion, extension, bending and rotating. With a better stability, the displacement of two adjacent vertebral bodies of MPI and MPAI modeling was less than that of complete vertebral modeling. No significant differences existed between each other. But as for stress shielding effect reduction, MPI was slightly better than MPAI. From biomechanical point of view, two internal instrumentations with neck-thoracic tumor en bloc resection may achieve an excellent stability with no significant differences. But with better stress conduction, MPI is more advantageous in postoperative reconstruction.

A finite difference solution for the propagation of sound in near sonic flows

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Lester, H. C.

1983-01-01

An explicit time/space finite difference procedure is used to model the propagation of sound in a quasi one-dimensional duct containing high Mach number subsonic flow. Nonlinear acoustic equations are derived by perturbing the time-dependent Euler equations about a steady, compressible mean flow. The governing difference relations are based on a fourth-order, two-step (predictor-corrector) MacCormack scheme. The solution algorithm functions by switching on a time harmonic source and allowing the difference equations to iterate to a steady state. The principal effect of the non-linearities was to shift acoustical energy to higher harmonics. With increased source strengths, wave steepening was observed. This phenomenon suggests that the acoustical response may approach a shock behavior at at higher sound pressure level as the throat Mach number aproaches unity. On a peak level basis, good agreement between the nonlinear finite difference and linear finite element solutions was observed, even through a peak sound pressure level of about 150 dB occurred in the throat region. Nonlinear steady state waveform solutions are shown to be in excellent agreement with a nonlinear asymptotic theory.

A 3-D turbulent flow analysis using finite elements with k-ɛ model

NASA Astrophysics Data System (ADS)

Okuda, H.; Yagawa, G.; Eguchi, Y.

1989-03-01

This paper describes the finite element turbulent flow analysis, which is suitable for three-dimensional large scale problems. The k-ɛ turbulence model as well as the conservation equations of mass and momentum are discretized in space using rather low order elements. Resulting coefficient matrices are evaluated by one-point quadrature in order to reduce the computational storage and the CPU cost. The time integration scheme based on the velocity correction method is employed to obtain steady state solutions. For the verification of this FEM program, two-dimensional plenum flow is simulated and compared with experiment. As the application to three-dimensional practical problems, the turbulent flows in the upper plenum of the fast breeder reactor are calculated for various boundary conditions.

[Three-dimensional finite element study on the change of glossopharyngeum in patient with obstructive sleep apnea hypopnea syndrome during titrated mandible advancement].

PubMed

Yang, Suixing; Feng, Jing; Zhang, Zuo; Qu, Aili; Gong, Miao; Tang, Jie; Fan, Junheng; Li, Songqing; Zhao, Yanling

2013-04-01

To construct a three-dimensional finite element model of the upper airway and adjacent structure of an obstructive sleep apnea hypopnea syndrome (OSAHS) patient for biomechanical analysis. And to study the influence of glossopharyngeum of an OSAHS patient with three-dimensional finite element model during titrated mandible advancement. DICOM format image information of an OSAHS patient's upper airway was obtained by thin-section CT scanning and digital image processing were utilized to construct a three-dimensional finite element model by Mimics 10.0, Imageware 10.0 and Ansys software. The changes and the law of glossopharyngeum were observed by biomechanics and morphology after loading with titrated mandible advancement. A three-dimensional finite element model of the adjacent upper airway structure of OSAHS was established successfully. After loading, the transverse diameter of epiglottis tip of glossopharyngeum increased significantly, although the sagittal diameter decreased correspondingly. The principal stress was mainly distributed in anterior wall of the upper airway. The location of principal stress concentration did not change significantly with the increasing of distance. The stress of glossopharyngeum increased during titrated mandible advancement. A more precise three-dimensional finite model of upper airway and adjacent structure of an OSAHS patient is established and improved efficiency by Mimics, Imageware and Ansys software. The glossopharyngeum of finite element model of OSAHS is analyzed by titrated mandible advancement and can effectively show the relationship between mandible advancement and the glossopharyngeum.

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.

Review of literature on the finite-element solution of the equations of two-dimensional surface-water flow in the horizontal plane

USGS Publications Warehouse

Lee, Jonathan K.; Froehlich, David C.

1987-01-01

Published literature on the application of the finite-element method to solving the equations of two-dimensional surface-water flow in the horizontal plane is reviewed in this report. The finite-element method is ideally suited to modeling two-dimensional flow over complex topography with spatially variable resistance. A two-dimensional finite-element surface-water flow model with depth and vertically averaged velocity components as dependent variables allows the user great flexibility in defining geometric features such as the boundaries of a water body, channels, islands, dikes, and embankments. The following topics are reviewed in this report: alternative formulations of the equations of two-dimensional surface-water flow in the horizontal plane; basic concepts of the finite-element method; discretization of the flow domain and representation of the dependent flow variables; treatment of boundary conditions; discretization of the time domain; methods for modeling bottom, surface, and lateral stresses; approaches to solving systems of nonlinear equations; techniques for solving systems of linear equations; finite-element alternatives to Galerkin's method of weighted residuals; techniques of model validation; and preparation of model input data. References are listed in the final chapter.

Comparisons of Particle Tracking Techniques and Galerkin Finite Element Methods in Flow Simulations on Watershed Scales

NASA Astrophysics Data System (ADS)

Shih, D.; Yeh, G.

2009-12-01

This paper applies two numerical approximations, the particle tracking technique and Galerkin finite element method, to solve the diffusive wave equation in both one-dimensional and two-dimensional flow simulations. The finite element method is one of most commonly approaches in numerical problems. It can obtain accurate solutions, but calculation times may be rather extensive. The particle tracking technique, using either single-velocity or average-velocity tracks to efficiently perform advective transport, could use larger time-step sizes than the finite element method to significantly save computational time. Comparisons of the alternative approximations are examined in this poster. We adapt the model WASH123D to examine the work. WASH123D is an integrated multimedia, multi-processes, physics-based computational model suitable for various spatial-temporal scales, was first developed by Yeh et al., at 1998. The model has evolved in design capability and flexibility, and has been used for model calibrations and validations over the course of many years. In order to deliver a locally hydrological model in Taiwan, the Taiwan Typhoon and Flood Research Institute (TTFRI) is working with Prof. Yeh to develop next version of WASH123D. So, the work of our preliminary cooperationx is also sketched in this poster.

On infinite-dimensional state spaces

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

Fritz, Tobias

It is well known that the canonical commutation relation [x, p]=i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p]=i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context frommore » which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V{sup -1}U{sup 2}V=U{sup 3}, then finite-dimensionality entails the relation UV{sup -1}UV=V{sup -1}UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V{sup -1}U{sup 2}V=U{sup 3} holds only up to {epsilon} and then yields a lower bound on the dimension.« less

A three-dimensional finite element model of near-field scanning microwave microscopy

NASA Astrophysics Data System (ADS)

Balusek, Curtis; Friedman, Barry; Luna, Darwin; Oetiker, Brian; Babajanyan, Arsen; Lee, Kiejin

2012-10-01

A three-dimensional finite element model of an experimental near-field scanning microwave microscope (NSMM) has been developed and compared to experiment on non conducting samples. The microwave reflection coefficient S11 is calculated as a function of frequency with no adjustable parameters. There is qualitative agreement with experiment in that the resonant frequency can show a sizable increase with sample dielectric constant; a result that is not obtained with a two-dimensional model. The most realistic model shows a semi-quantitative agreement with experiment. The effect of different sample thicknesses and varying tip sample distances is investigated numerically and shown to effect NSMM performance in a way consistent with experiment. Visualization of the electric field indicates that the field is primarily determined by the shape of the coupling hooks.

FeynArts model file for MSSM transition counterterms from DREG to DRED

NASA Astrophysics Data System (ADS)

Stöckinger, Dominik; Varšo, Philipp

2012-02-01

The FeynArts model file MSSMdreg2dred implements MSSM transition counterterms which can convert one-loop Green functions from dimensional regularization to dimensional reduction. They correspond to a slight extension of the well-known Martin/Vaughn counterterms, specialized to the MSSM, and can serve also as supersymmetry-restoring counterterms. The paper provides full analytic results for the counterterms and gives one- and two-loop usage examples. The model file can simplify combining MS¯-parton distribution functions with supersymmetric renormalization or avoiding the renormalization of ɛ-scalars in dimensional reduction. Program summaryProgram title:MSSMdreg2dred.mod Catalogue identifier: AEKR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKR_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: LGPL-License [1] No. of lines in distributed program, including test data, etc.: 7600 No. of bytes in distributed program, including test data, etc.: 197 629 Distribution format: tar.gz Programming language: Mathematica, FeynArts Computer: Any, capable of running Mathematica and FeynArts Operating system: Any, with running Mathematica, FeynArts installation Classification: 4.4, 5, 11.1 Subprograms used: Cat Id Title Reference ADOW_v1_0 FeynArts CPC 140 (2001) 418 Nature of problem: The computation of one-loop Feynman diagrams in the minimal supersymmetric standard model (MSSM) requires regularization. Two schemes, dimensional regularization and dimensional reduction are both common but have different pros and cons. In order to combine the advantages of both schemes one would like to easily convert existing results from one scheme into the other. Solution method: Finite counterterms are constructed which correspond precisely to the one-loop scheme differences for the MSSM. They are provided as a FeynArts [2] model file. Using this model file together with FeynArts, the (ultra-violet) regularization of any MSSM one-loop Green function is switched automatically from dimensional regularization to dimensional reduction. In particular the counterterms serve as supersymmetry-restoring counterterms for dimensional regularization. Restrictions: The counterterms are restricted to the one-loop level and the MSSM. Running time: A few seconds to generate typical Feynman graphs with FeynArts.

Dynamical Quasicondensation of Hard-Core Bosons at Finite Momenta: A Non-equilibrium Condensation Effect

NASA Astrophysics Data System (ADS)

Heidrich-Meisner, Fabian; Vidmar, L.; Ronzheimer, J. P.; Hodgman, S.; Schreiber, M.; Braun, S.; Langer, S.; Bloch, I.; Schneider, U.

2016-05-01

Long-range order in quantum many-body systems is usually associated with equilibrium situations. Here, we experimentally investigate the quasicondensation of strongly interacting bosons at finite momenta in a far-from-equilibrium case. We prepare an inhomogeneous initial state consisting of one-dimensional Mott insulators in the center of otherwise empty one-dimensional chains in an optical lattice with a lattice constant d. After suddenly quenching the trapping potential to zero, we observe the onset of coherence in spontaneously forming quasicondensates in the lattice. Remarkably, the emerging phase order differs from the ground-state order and is characterized by peaks at finite momenta +/-(π / 2)(ℏ / d) in the momentum distribution function. Supported by the DFG via FOR 801.

Factors Influencing Progressive Failure Analysis Predictions for Laminated Composite Structure

NASA Technical Reports Server (NTRS)

Knight, Norman F., Jr.

2008-01-01

Progressive failure material modeling methods used for structural analysis including failure initiation and material degradation are presented. Different failure initiation criteria and material degradation models are described that define progressive failure formulations. These progressive failure formulations are implemented in a user-defined material model for use with a nonlinear finite element analysis tool. The failure initiation criteria include the maximum stress criteria, maximum strain criteria, the Tsai-Wu failure polynomial, and the Hashin criteria. The material degradation model is based on the ply-discounting approach where the local material constitutive coefficients are degraded. Applications and extensions of the progressive failure analysis material model address two-dimensional plate and shell finite elements and three-dimensional solid finite elements. Implementation details are described in the present paper. Parametric studies for laminated composite structures are discussed to illustrate the features of the progressive failure modeling methods that have been implemented and to demonstrate their influence on progressive failure analysis predictions.

Finite element analysis of true and pseudo surface acoustic waves in one-dimensional phononic crystals

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

Graczykowski, B., E-mail: bartlomiej.graczykowski@icn.cat; Alzina, F.; Gomis-Bresco, J.

In this paper, we report a theoretical investigation of surface acoustic waves propagating in one-dimensional phononic crystal. Using finite element method eigenfrequency and frequency response studies, we develop two model geometries suitable to distinguish true and pseudo (or leaky) surface acoustic waves and determine their propagation through finite size phononic crystals, respectively. The novelty of the first model comes from the application of a surface-like criterion and, additionally, functional damping domain. Exemplary calculated band diagrams show sorted branches of true and pseudo surface acoustic waves and their quantified surface confinement. The second model gives a complementary study of transmission, reflection,more » and surface-to-bulk losses of Rayleigh surface waves in the case of a phononic crystal with a finite number of periods. Here, we demonstrate that a non-zero transmission within non-radiative band gaps can be carried via leaky modes originating from the coupling of local resonances with propagating waves in the substrate. Finally, we show that the transmission, reflection, and surface-to-bulk losses can be effectively optimised by tuning the geometrical properties of a stripe.« less

THREE-DIMENSIONAL MODELING OF COHESIVE SEDIMENT TRANSPORT IN A PARTIALLY STRATIFIED MICRO-TIDAL ESTUARY TO ASSESS EFFECTIVENESS OF SEDIMENT TRAPS

EPA Science Inventory

The three-dimensional (3D) finite difference model Environmental Fluid Dynamics Code (EFDC) was used to simulate the hydrodynamics and sediment transport in a partially stratified micro-tidal estuary. The estuary modeled consisted of a 16-km reach of the St. Johns River, Florida,...

Application of FDM and FEM in solving the simultaneous heat and moisture transfer inside bread during baking

NASA Astrophysics Data System (ADS)

Zhou, Weibiao

2005-01-01

Heat and mass transfer inside bread during baking can be taken as a multiphase flow problem, involving heat, liquid water and water vapour. Among the various developed models, the one based on an evaporation-condensation mechanism well explains several unique phenomenal observations during baking, and is most promising. This paper presents the results of numerically solving the one-dimensional case of this simultaneous transfer model by applying finite difference methods (FDM) and finite element methods (FEM). In particular, various FDM and FEM schemes are applied and the sensitivity of the results to the changes within the parameters are studied. Changes in bread temperature and moisture are characterised by some critical values such as peak water level and dry-out time. Comparison between the results by FDM and FEM is made.

Numerical Simulation of a Solar Domestic Hot Water System

NASA Astrophysics Data System (ADS)

Mongibello, L.; Bianco, N.; Di Somma, M.; Graditi, G.; Naso, V.

2014-11-01

An innovative transient numerical model is presented for the simulation of a solar Domestic Hot Water (DHW) system. The solar collectors have been simulated by using a zerodimensional analytical model. The temperature distributions in the heat transfer fluid and in the water inside the tank have been evaluated by one-dimensional models. The reversion elimination algorithm has been used to include the effects of natural convection among the water layers at different heights in the tank on the thermal stratification. A finite difference implicit scheme has been implemented to solve the energy conservation equation in the coil heat exchanger, and the energy conservation equation in the tank has been solved by using the finite difference Euler implicit scheme. Energy conservation equations for the solar DHW components models have been coupled by means of a home-made implicit algorithm. Results of the simulation performed using as input data the experimental values of the ambient temperature and the solar irradiance in a summer day are presented and discussed.

COSIM: A Finite-Difference Computer Model to Predict Ternary Concentration Profiles Associated With Oxidation and Interdiffusion of Overlay-Coated Substrates

NASA Technical Reports Server (NTRS)

Nesbitt, James A.

2001-01-01

A finite-difference computer program (COSIM) has been written which models the one-dimensional, diffusional transport associated with high-temperature oxidation and interdiffusion of overlay-coated substrates. The program predicts concentration profiles for up to three elements in the coating and substrate after various oxidation exposures. Surface recession due to solute loss is also predicted. Ternary cross terms and concentration-dependent diffusion coefficients are taken into account. The program also incorporates a previously-developed oxide growth and spalling model to simulate either isothermal or cyclic oxidation exposures. In addition to predicting concentration profiles after various oxidation exposures, the program can also be used to predict coating life based on a concentration dependent failure criterion (e.g., surface solute content drops to 2%). The computer code is written in FORTRAN and employs numerous subroutines to make the program flexible and easily modifiable to other coating oxidation problems.

Uncovering low dimensional macroscopic chaotic dynamics of large finite size complex systems

NASA Astrophysics Data System (ADS)

Skardal, Per Sebastian; Restrepo, Juan G.; Ott, Edward

2017-08-01

In the last decade, it has been shown that a large class of phase oscillator models admit low dimensional descriptions for the macroscopic system dynamics in the limit of an infinite number N of oscillators. The question of whether the macroscopic dynamics of other similar systems also have a low dimensional description in the infinite N limit has, however, remained elusive. In this paper, we show how techniques originally designed to analyze noisy experimental chaotic time series can be used to identify effective low dimensional macroscopic descriptions from simulations with a finite number of elements. We illustrate and verify the effectiveness of our approach by applying it to the dynamics of an ensemble of globally coupled Landau-Stuart oscillators for which we demonstrate low dimensional macroscopic chaotic behavior with an effective 4-dimensional description. By using this description, we show that one can calculate dynamical invariants such as Lyapunov exponents and attractor dimensions. One could also use the reconstruction to generate short-term predictions of the macroscopic dynamics.

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.

Modifications to the modular three-dimensional finite-difference ground-water flow model used for the Columbia Plateau Regional Aquifer-System Analysis, Washington, Oregon, and Idaho

USGS Publications Warehouse

Hansen, A.J.

1993-01-01

The report documents modifications to the U.S. Geological Survey's modular three-dimensional finite-difference ground-water flow model used for a regional aquifer-system analysis of the Columbia Plateau. The report, which describes the concepts and mathematical basis for the modifications, is intended for potential users who are familiar with the original modular model. The modifications permit flow from a layer to any adjacent layer, allow the model to retain a cell of a layer that has been cut completely through by a canyon, and allow placing ground-water flow barriers on only specified branch conductances; a special version of the modified model uses a convergent grid. The report describes the data-input items that this modified model must read.

Biomechanical 3-Dimensional Finite Element Analysis of Obturator Protheses Retained with Zygomatic and Dental Implants in Maxillary Defects

PubMed Central

Akay, Canan; Yaluğ, Suat

2015-01-01

Background The objective of this study was to investigate the stress distribution in the bone around zygomatic and dental implants for 3 different implant-retained obturator prostheses designs in a Aramany class IV maxillary defect using 3-dimensional finite element analysis (FEA). Material\\Methods A 3-dimensional finite element model of an Aramany class IV defect was created. Three different implant-retained obturator prostheses were modeled: model 1 with 1 zygomatic implant and 1 dental implant, model 2 with 1 zygomatic implant and 2 dental implants, and model 3 with 2 zygomatic implants. Locator attachments were used as a superstructure. A 150-N load was applied 3 different ways. Qualitative analysis was based on the scale of maximum principal stress; values obtained through quantitative analysis are expressed in MPa. Results In all loading conditions, model 3 (when compared models 1 and 2) showed the lowest maximum principal stress value. Model 3 is the most appropirate reconstruction in Aramany class IV maxillary defects. Two zygomatic implants can reduce the stresses in model 3. The distribution of stresses on prostheses were more rational with the help of zygoma implants, which can distribute the stresses on each part of the maxilla. Conclusions Aramany class IV obturator prosthesis placement of 2 zygomatic implants in each side of the maxilla is more advantageous than placement of dental implants. In the non-defective side, increasing the number of dental implants is not as suitable as zygomatic implants. PMID:25714086

A two-dimensional, finite-difference model of the high plains aquifer in southern South Dakota

USGS Publications Warehouse

Kolm, K.E.; Case, H. L.

1983-01-01

The High Plains aquifer is the principal source of water for irrigation, industry, municipalities, and domestic use in south-central South Dakota. The aquifer, composed of upper sandstone units of the Arikaree Formation, and the overlying Ogallala and Sand Hills Formations, was simulated using a two-dimensional, finite-difference computer model. The maximum difference between simulated and measured potentiometric heads was less than 60 feet (1- to 4-percent error). Two-thirds of the simulated potentiometric heads were within 26 feet of the measured values (3-percent error). The estimated saturated thickness, computed from simulated potentiometric heads, was within 25-percent error of the known saturated thickness for 95 percent of the study area. (USGS)

Human vocal tract resonances and the corresponding mode shapes investigated by three-dimensional finite-element modelling based on CT measurement.

PubMed

Vampola, Tomáš; Horáček, Jaromír; Laukkanen, Anne-Maria; Švec, Jan G

2015-04-01

Resonance frequencies of the vocal tract have traditionally been modelled using one-dimensional models. These cannot accurately represent the events in the frequency region of the formant cluster around 2.5-4.5 kHz, however. Here, the vocal tract resonance frequencies and their mode shapes are studied using a three-dimensional finite element model obtained from computed tomography measurements of a subject phonating on vowel [a:]. Instead of the traditional five, up to eight resonance frequencies of the vocal tract were found below the prominent antiresonance around 4.7 kHz. The three extra resonances were found to correspond to modes which were axially asymmetric and involved the piriform sinuses, valleculae, and transverse vibrations in the oral cavity. The results therefore suggest that the phenomenon of speaker's and singer's formant clustering may be more complex than originally thought.

Stress distribution in fixed-partial prosthesis and peri-implant bone tissue with different framework materials and vertical misfit levels: a three-dimensional finite element analysis.

PubMed

Bacchi, Ataís; Consani, Rafael L X; Mesquita, Marcelo F; dos Santos, Mateus B F

2013-09-01

The purpose of this study was to evaluate the influence of superstructure material and vertical misfits on the stresses created in an implant-supported partial prosthesis. A three-dimensional (3-D) finite element model was prepared based on common clinical data. The posterior part of a severely resorbed jaw with two osseointegrated implants at the second premolar and second molar regions was modeled using specific modeling software (SolidWorks 2010). Finite element models were created by importing the solid model into mechanical simulation software (ANSYS Workbench 11). The models were divided into groups according to the prosthesis framework material (type IV gold alloy, silver-palladium alloy, commercially pure titanium, cobalt-chromium alloy, or zirconia) and vertical misfit level (10 µm, 50 µm, and 100 µm) created at one implant-prosthesis interface. The gap of the vertical misfit was set to be closed and the stress values were measured in the framework, porcelain veneer, retention screw, and bone tissue. Stiffer materials led to higher stress concentration in the framework and increased stress values in the retention screw, while in the same circumstances, the porcelain veneer showed lower stress values, and there was no significant difference in stress in the peri-implant bone tissue. A considerable increase in stress concentration was observed in all the structures evaluated within the misfit amplification. The framework material influenced the stress concentration in the prosthetic structures and retention screw, but not that in bone tissue. All the structures were significantly influenced by the increase in the misfit levels.

[Three-dimensional finite element analysis on cell culture membrane under mechanical load].

PubMed

Guo, Xin; Fan, Yubo; Song, Jinlin; Chen, Junkai

2002-01-01

A three-dimensional finite element model of the cell culture membrane was developed in the culture device under tension state made by us. The magnitude of tension and the displacement distribution in the membrane made of silicon rubber under different hydrostatic load were obtained by use of FEM analysis. A comparative study was made between the numerical and the experimental results. These results can serve as guides to the related cellular mechanical research.

TRIM—3D: a three-dimensional model for accurate simulation of shallow water flow

USGS Publications Warehouse

Casulli, Vincenzo; Bertolazzi, Enrico; Cheng, Ralph T.

1993-01-01

A semi-implicit finite difference formulation for the numerical solution of three-dimensional tidal circulation is discussed. The governing equations are the three-dimensional Reynolds equations in which the pressure is assumed to be hydrostatic. A minimal degree of implicitness has been introduced in the finite difference formula so that the resulting algorithm permits the use of large time steps at a minimal computational cost. This formulation includes the simulation of flooding and drying of tidal flats, and is fully vectorizable for an efficient implementation on modern vector computers. The high computational efficiency of this method has made it possible to provide the fine details of circulation structure in complex regions that previous studies were unable to obtain. For proper interpretation of the model results suitable interactive graphics is also an essential tool.

A comparison of 1D analytical model and 3D finite element analysis with experiments for a rosen-type piezoelectric transformer.

PubMed

Boukazouha, F; Poulin-Vittrant, G; Tran-Huu-Hue, L P; Bavencoffe, M; Boubenider, F; Rguiti, M; Lethiecq, M

2015-07-01

This article is dedicated to the study of Piezoelectric Transformers (PTs), which offer promising solutions to the increasing need for integrated power electronics modules within autonomous systems. The advantages offered by such transformers include: immunity to electromagnetic disturbances; ease of miniaturisation for example, using conventional micro fabrication processes; and enhanced performance in terms of voltage gain and power efficiency. Central to the adequate description of such transformers is the need for complex analytical modeling tools, especially if one is attempting to include combined contributions due to (i) mechanical phenomena owing to the different propagation modes which differ at the primary and secondary sides of the PT; and (ii) electrical phenomena such as the voltage gain and power efficiency, which depend on the electrical load. The present work demonstrates an original one-dimensional (1D) analytical model, dedicated to a Rosen-type PT and simulation results are successively compared against that of a three-dimensional (3D) Finite Element Analysis (COMSOL Multiphysics software) and experimental results. The Rosen-type PT studied here is based on a single layer soft PZT (P191) with corresponding dimensions 18 mm × 3 mm × 1.5 mm, which operated at the second harmonic of 176 kHz. Detailed simulational and experimental results show that the presented 1D model predicts experimental measurements to within less than 10% error of the voltage gain at the second and third resonance frequency modes. Adjustment of the analytical model parameters is found to decrease errors relative to experimental voltage gain to within 1%, whilst a 2.5% error on the output admittance magnitude at the second resonance mode were obtained. Relying on the unique assumption of one-dimensionality, the present analytical model appears as a useful tool for Rosen-type PT design and behavior understanding. Copyright © 2015 Elsevier B.V. All rights reserved.

Investigating cerebral oedema using poroelasticity.

PubMed

Vardakis, John C; Chou, Dean; Tully, Brett J; Hung, Chang C; Lee, Tsong H; Tsui, Po-Hsiang; Ventikos, Yiannis

2016-01-01

Cerebral oedema can be classified as the tangible swelling produced by expansion of the interstitial fluid volume. Hydrocephalus can be succinctly described as the abnormal accumulation of cerebrospinal fluid (CSF) within the brain which ultimately leads to oedema within specific sites of parenchymal tissue. Using hydrocephalus as a test bed, one is able to account for the necessary mechanisms involved in the interaction between oedema formation and cerebral fluid production, transport and drainage. The current state of knowledge about integrative cerebral dynamics and transport phenomena indicates that poroelastic theory may provide a suitable framework to better understand various diseases. In this work, Multiple-Network Poroelastic Theory (MPET) is used to develop a novel spatio-temporal model of fluid regulation and tissue displacement within the various scales of the cerebral environment. The model is applied through two formats, a one-dimensional finite difference - Computational Fluid Dynamics (CFD) coupling framework, as well as a two-dimensional Finite Element Method (FEM) formulation. These are used to investigate the role of endoscopic fourth ventriculostomy in alleviating oedema formation due to fourth ventricle outlet obstruction (1D coupled model) in addition to observing the capability of the FEM template in capturing important characteristics allied to oedema formation, like for instance in the periventricular region (2D model). Copyright © 2015 The Authors. Published by Elsevier Ltd.. All rights reserved.

Three-dimensional finite element analysis of implant-assisted removable partial dentures.

PubMed

Eom, Ju-Won; Lim, Young-Jun; Kim, Myung-Joo; Kwon, Ho-Beom

2017-06-01

Whether the implant abutment in implant-assisted removable partial dentures (IARPDs) functions as a natural removable partial denture (RPD) tooth abutment is unknown. The purpose of this 3-dimensional finite element study was to analyze the biomechanical behavior of implant crown, bone, RPD, and IARPD. Finite element models of the partial maxilla, teeth, and prostheses were generated on the basis of a patient's computed tomographic data. The teeth, surveyed crowns, and RPDs were created in the model. With the generated components, four 3-dimensional finite element models of the partial maxilla were constructed: tooth-supported RPD (TB), implant-supported RPD (IB), tooth-tissue-supported RPD (TT), and implant-tissue-supported RPD (IT) models. Oblique loading of 300 N was applied on the crowns and denture teeth. The von Mises stress and displacement of the denture abutment tooth and implant system were identified. The highest von Mises stress values of both IARPDs occurred on the implants, while those of both natural tooth RPDs occurred on the frameworks of the RPDs. The highest von Mises stress of model IT was about twice that of model IB, while the value of model TT was similar to that of model TB. The maximum displacement was greater in models TB and TT than in models IB and IT. Among the 4 models, the highest maximum displacement value was observed in the model TT and the lowest value was in the model IB. Finite element analysis revealed that the stress distribution pattern of the IARPDs was different from that of the natural tooth RPDs and the stress distribution of implant-supported RPD was different from that of implant-tissue-supported RPD. When implants are used for RPD abutments, more consideration concerning the RPD design and the number or location of the implant is necessary. Copyright © 2016 Editorial Council for the Journal of Prosthetic Dentistry. Published by Elsevier Inc. All rights reserved.

Thermal modeling of phase change solidification in thermal control devices including natural convection effects

NASA Technical Reports Server (NTRS)

Ukanwa, A. O.; Stermole, F. J.; Golden, J. O.

1972-01-01

Natural convection effects in phase change thermal control devices were studied. A mathematical model was developed to evaluate natural convection effects in a phase change test cell undergoing solidification. Although natural convection effects are minimized in flight spacecraft, all phase change devices are ground tested. The mathematical approach to the problem was to first develop a transient two-dimensional conduction heat transfer model for the solidification of a normal paraffin of finite geometry. Next, a transient two-dimensional model was developed for the solidification of the same paraffin by a combined conduction-natural-convection heat transfer model. Throughout the study, n-hexadecane (n-C16H34) was used as the phase-change material in both the theoretical and the experimental work. The models were based on the transient two-dimensional finite difference solutions of the energy, continuity, and momentum equations.

Streamer discharges as advancing imperfect conductors: inhomogeneities in long ionized channels

NASA Astrophysics Data System (ADS)

Luque, A.; González, M.; Gordillo-Vázquez, F. J.

2017-12-01

A major obstacle for the understanding of long electrical discharges is the complex dynamics of streamer coronas, formed by many thin conducting filaments. Building macroscopic models for these filaments is one approach to attain a deeper knowledge of the discharge corona. Here, we present a one-dimensional, macroscopic model of a propagating streamer channel with a finite and evolving internal conductivity. We represent the streamer as an advancing finite-conductivity channel with a surface charge density at its boundary. This charge evolves self-consistently due to the electric current that flows through the streamer body and within a thin layer at its surface. We couple this electrodynamic evolution with a field-dependent set of chemical reactions that determine the internal channel conductivity. With this one-dimensional model, we investigate the formation of persisting structures in the wake of a streamer head. In accordance with experimental observations, our model shows that a within a streamer channel some regions are driven towards high fields that can be maintaned for tens of nanoseconds.

Mechanics of the foot Part 2: A coupled solid-fluid model to investigate blood transport in the pathologic foot.

PubMed

Mithraratne, K; Ho, H; Hunter, P J; Fernandez, J W

2012-10-01

A coupled computational model of the foot consisting of a three-dimensional soft tissue continuum and a one-dimensional (1D) transient blood flow network is presented in this article. The primary aim of the model is to investigate the blood flow in major arteries of the pathologic foot where the soft tissue stiffening occurs. It has been reported in the literature that there could be up to about five-fold increase in the mechanical stiffness of the plantar soft tissues in pathologic (e.g. diabetic) feet compared with healthy ones. The increased stiffness results in higher tissue hydrostatic pressure within the plantar area of the foot when loaded. The hydrostatic pressure acts on the external surface of blood vessels and tend to reduce the flow cross-section area and hence the blood supply. The soft tissue continuum model of the foot was modelled as a tricubic Hermite finite element mesh representing all the muscles, skin and fat of the foot and treated as incompressible with transversely isotropic properties. The details of the mechanical model of soft tissue are presented in the companion paper, Part 1. The deformed state of the soft tissue continuum because of the applied ground reaction force at three foot positions (heel-strike, midstance and toe-off) was obtained by solving the Cauchy equations based on the theory of finite elasticity using the Galerkin finite element method. The geometry of the main arterial network in the foot was represented using a 1D Hermite cubic finite element mesh. The flow model consists of 1D Navier-Stokes equations and a nonlinear constitutive equation to describe vessel radius-transmural pressure relation. The latter was defined as the difference between the fluid and soft tissue hydrostatic pressure. Transient flow governing equations were numerically solved using the two-step Lax-Wendroff finite difference method. The geometry of both the soft tissue continuum and arterial network is anatomically-based and was developed using the data derived from visible human images and magnetic resonance images of a healthy male volunteer. Simulation results reveal that a two-fold increase in tissue stiffness leads to about 28% reduction in blood flow to the affected region. Copyright © 2012 John Wiley & Sons, Ltd.

Accuracy of three-dimensional seismic ground response analysis in time domain using nonlinear numerical simulations

NASA Astrophysics Data System (ADS)

Liang, Fayun; Chen, Haibing; Huang, Maosong

2017-07-01

To provide appropriate uses of nonlinear ground response analysis for engineering practice, a three-dimensional soil column with a distributed mass system and a time domain numerical analysis were implemented on the OpenSees simulation platform. The standard mesh of a three-dimensional soil column was suggested to be satisfied with the specified maximum frequency. The layered soil column was divided into multiple sub-soils with a different viscous damping matrix according to the shear velocities as the soil properties were significantly different. It was necessary to use a combination of other one-dimensional or three-dimensional nonlinear seismic ground analysis programs to confirm the applicability of nonlinear seismic ground motion response analysis procedures in soft soil or for strong earthquakes. The accuracy of the three-dimensional soil column finite element method was verified by dynamic centrifuge model testing under different peak accelerations of the earthquake. As a result, nonlinear seismic ground motion response analysis procedures were improved in this study. The accuracy and efficiency of the three-dimensional seismic ground response analysis can be adapted to the requirements of engineering practice.

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

NASA Technical Reports Server (NTRS)

Burns, John A.; Marrekchi, Hamadi

1993-01-01

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

Approximate Approaches to the One-Dimensional Finite Potential Well

ERIC Educational Resources Information Center

Singh, Shilpi; Pathak, Praveen; Singh, Vijay A.

2011-01-01

The one-dimensional finite well is a textbook problem. We propose approximate approaches to obtain the energy levels of the well. The finite well is also encountered in semiconductor heterostructures where the carrier mass inside the well (m[subscript i]) is taken to be distinct from mass outside (m[subscript o]). A relevant parameter is the mass…

Simulating Fatigue Crack Growth in Spiral Bevel Pinion

NASA Technical Reports Server (NTRS)

Ural, Ani; Wawrzynek, Paul A.; Ingraffe, Anthony R.

2003-01-01

This project investigates computational modeling of fatigue crack growth in spiral bevel gears. Current work is a continuation of the previous efforts made to use the Boundary Element Method (BEM) to simulate tooth-bending fatigue failure in spiral bevel gears. This report summarizes new results predicting crack trajectory and fatigue life for a spiral bevel pinion using the Finite Element Method (FEM). Predicting crack trajectories is important in determining the failure mode of a gear. Cracks propagating through the rim may result in catastrophic failure, whereas the gear may remain intact if one tooth fails and this may allow for early detection of failure. Being able to predict crack trajectories is insightful for the designer. However, predicting growth of three-dimensional arbitrary cracks is complicated due to the difficulty of creating three-dimensional models, the computing power required, and absence of closed- form solutions of the problem. Another focus of this project was performing three-dimensional contact analysis of a spiral bevel gear set incorporating cracks. These analyses were significant in determining the influence of change of tooth flexibility due to crack growth on the magnitude and location of contact loads. This is an important concern since change in contact loads might lead to differences in SIFs and therefore result in alteration of the crack trajectory. Contact analyses performed in this report showed the expected trend of decreasing tooth loads carried by the cracked tooth with increasing crack length. Decrease in tooth loads lead to differences between SIFs extracted from finite element contact analysis and finite element analysis with Hertz contact loads. This effect became more pronounced as the crack grew.

Summary Report of Working Group 2: Computation

NASA Astrophysics Data System (ADS)

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

2009-01-01

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

Summary Report of Working Group 2: Computation

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

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

2009-01-22

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

1-D DC Resistivity Modeling and Interpretation in Anisotropic Media Using Particle Swarm Optimization

NASA Astrophysics Data System (ADS)

Pekşen, Ertan; Yas, Türker; Kıyak, Alper

2014-09-01

We examine the one-dimensional direct current method in anisotropic earth formation. We derive an analytic expression of a simple, two-layered anisotropic earth model. Further, we also consider a horizontally layered anisotropic earth response with respect to the digital filter method, which yields a quasi-analytic solution over anisotropic media. These analytic and quasi-analytic solutions are useful tests for numerical codes. A two-dimensional finite difference earth model in anisotropic media is presented in order to generate a synthetic data set for a simple one-dimensional earth. Further, we propose a particle swarm optimization method for estimating the model parameters of a layered anisotropic earth model such as horizontal and vertical resistivities, and thickness. The particle swarm optimization is a naturally inspired meta-heuristic algorithm. The proposed method finds model parameters quite successfully based on synthetic and field data. However, adding 5 % Gaussian noise to the synthetic data increases the ambiguity of the value of the model parameters. For this reason, the results should be controlled by a number of statistical tests. In this study, we use probability density function within 95 % confidence interval, parameter variation of each iteration and frequency distribution of the model parameters to reduce the ambiguity. The result is promising and the proposed method can be used for evaluating one-dimensional direct current data in anisotropic media.

A four-dimensional primitive equation model for coupled coastal-deep ocean studies

NASA Technical Reports Server (NTRS)

Haidvogel, D. B.

1981-01-01

A prototype four dimensional continental shelf/deep ocean model is described. In its present form, the model incorporates the effects of finite amplitude topography, advective nonlinearities, and variable stratification and rotation. The model can be forced either directly by imposed atmospheric windstress and surface pressure distributions, and energetic mean currents imposed by the exterior oceanic circulation; or indirectly by initial distributions of shoreward propagation mesoscale waves and eddies. To avoid concerns over the appropriate specification of 'open' boundary conditions on the cross-shelf and seaward model boundaries, a periodic channel geometry (oriented along-coast) is used. The model employs a traditional finite difference expansion in the cross-shelf direction, and a Fourier (periodic) representation in the long-shelf coordinate.

Solving the forward problem of magnetoacoustic tomography with magnetic induction by means of the finite element method

NASA Astrophysics Data System (ADS)

Li, Xun; Li, Xu; Zhu, Shanan; He, Bin

2009-05-01

Magnetoacoustic tomography with magnetic induction (MAT-MI) is a recently proposed imaging modality to image the electrical impedance of biological tissue. It combines the good contrast of electrical impedance tomography with the high spatial resolution of sonography. In this paper, a three-dimensional MAT-MI forward problem was investigated using the finite element method (FEM). The corresponding FEM formulae describing the forward problem are introduced. In the finite element analysis, magnetic induction in an object with conductivity values close to biological tissues was first carried out. The stimulating magnetic field was simulated as that generated from a three-dimensional coil. The corresponding acoustic source and field were then simulated. Computer simulation studies were conducted using both concentric and eccentric spherical conductivity models with different geometric specifications. In addition, the grid size for finite element analysis was evaluated for the model calibration and evaluation of the corresponding acoustic field.

Solving the Forward Problem of Magnetoacoustic Tomography with Magnetic Induction by Means of the Finite Element Method

PubMed Central

Li, Xun; Li, Xu; Zhu, Shanan; He, Bin

2010-01-01

Magnetoacoustic Tomography with Magnetic Induction (MAT-MI) is a recently proposed imaging modality to image the electrical impedance of biological tissue. It combines the good contrast of electrical impedance tomography with the high spatial resolution of sonography. In this paper, three-dimensional MAT-MI forward problem was investigated using the finite element method (FEM). The corresponding FEM formulas describing the forward problem are introduced. In the finite element analysis, magnetic induction in an object with conductivity values close to biological tissues was first carried out. The stimulating magnetic field was simulated as that generated from a three-dimensional coil. The corresponding acoustic source and field were then simulated. Computer simulation studies were conducted using both concentric and eccentric spherical conductivity models with different geometric specifications. In addition, the grid size for finite element analysis was evaluated for model calibration and evaluation of the corresponding acoustic field. PMID:19351978

Improved finite element methodology for integrated thermal structural analysis

NASA Technical Reports Server (NTRS)

Dechaumphai, P.; Thornton, E. A.

1982-01-01

An integrated thermal-structural finite element approach for efficient coupling of thermal and structural analysis is presented. New thermal finite elements which yield exact nodal and element temperatures for one dimensional linear steady state heat transfer problems are developed. A nodeless variable formulation is used to establish improved thermal finite elements for one dimensional nonlinear transient and two dimensional linear transient heat transfer problems. The thermal finite elements provide detailed temperature distributions without using additional element nodes and permit a common discretization with lower order congruent structural finite elements. The accuracy of the integrated approach is evaluated by comparisons with analytical solutions and conventional finite element thermal structural analyses for a number of academic and more realistic problems. Results indicate that the approach provides a significant improvement in the accuracy and efficiency of thermal stress analysis for structures with complex temperature distributions.

Diffusion in different models of active Brownian motion

NASA Astrophysics Data System (ADS)

Lindner, B.; Nicola, E. M.

2008-04-01

Active Brownian particles (ABP) have served as phenomenological models of self-propelled motion in biology. We study the effective diffusion coefficient of two one-dimensional ABP models (simplified depot model and Rayleigh-Helmholtz model) differing in their nonlinear friction functions. Depending on the choice of the friction function the diffusion coefficient does or does not attain a minimum as a function of noise intensity. We furthermore discuss the case of an additional bias breaking the left-right symmetry of the system. We show that this bias induces a drift and that it generally reduces the diffusion coefficient. For a finite range of values of the bias, both models can exhibit a maximum in the diffusion coefficient vs. noise intensity.

Thermal Pollution Mathematical Model. Volume 2; Verification of One-Dimensional Numerical Model at Lake Keowee

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.; Nwadike, E. V.

1980-01-01

A one dimensional model for studying the thermal dynamics of cooling lakes was developed and verified. The model is essentially a set of partial differential equations which are solved by finite difference methods. The model includes the effects of variation of area with depth, surface heating due to solar radiation absorbed at the upper layer, and internal heating due to the transmission of solar radiation to the sub-surface layers. The exchange of mechanical energy between the lake and the atmosphere is included through the coupling of thermal diffusivity and wind speed. The effects of discharge and intake by power plants are also included. The numerical model was calibrated by applying it to Cayuga Lake. The model was then verified through a long term simulation using Lake Keowee data base. The comparison between measured and predicted vertical temperature profiles for the nine years is good. The physical limnology of Lake Keowee is presented through a set of graphical representations of the measured data base.

Development of finite element model for customized prostheses design for patient with pelvic bone tumor.

PubMed

Iqbal, Taimoor; Shi, Lei; Wang, Ling; Liu, Yaxiong; Li, Dichen; Qin, Mian; Jin, Zhongmin

2017-06-01

The aim of this study was to design a hemi-pelvic prosthesis for a patient affected by pelvic sarcoma. To investigate the biomechanical functionality of the pelvis reconstructed with designed custom-made prosthesis, a patient-specific finite element model of whole pelvis with primary ligaments inclusive was constructed based on the computed tomography images of the patient. Then, a finite element analysis was performed to calculate and compare the stress distribution between the normal and implanted pelvis models when undergoing three different static conditions-both-leg standing, single-leg standing for the healthy and the affected one. No significant differences were observed in the stresses between the normal and reconstructed pelvis for both-leg standing, but 20%-40% larger stresses were predicted for the peak stress of the single-leg standing (affected side). Moreover, two- to threefold of peak stresses were predicted within the prostheses compared to that of the normal pelvis especially for single-leg standing case, however, still below the allowable fatigue limitation. The study on the load transmission functionality of prosthesis indicated that it is crucial to carry out finite element analysis for functional evaluation of the designed customized prostheses before three-dimensional printing manufacturing, allowing better understanding of the possible peak stresses within the bone as well as the implants for safety precaution. The finite element model can be equally applicable to other bone tumor model for biomechanical studying.

[Establishment and validation of normal human L1-L5 lumbar three-dimensional finite element model].

PubMed

Zhu, Zhenqi; Liu, Chenjun; Wang, Jiefu; Wang, Kaifeng; Huang, Zhixin; Wang, Weida; Liu, Haiying

2014-10-14

To create and validate a L1-L5 lumbar three-dimensional finite element model. The L1-L5 lumbar spines of a male healthy volunteer were scanned with computed tomography (CT). And a L1-L5 lumbar three-dimensional finite element model was created with the aid of software packages of Mimics, Geomagic and Ansys. Then border conditions were set, unit type was determined, finite element mesh was divided and a model was established for loading and calculating. Average model stiffness under the conditions of flexion, extension, lateral bending and axial rotation was calculated and compared with the outcomes of former articles for validation. A normal human L1-L5 lumbar three-dimensional finite element model was established to include 459 340 elements and 661 938 nodes. After constraining the inferior endplate of L5 vertebral body, 500 kg × m × s⁻² compressive loading was imposed averagely on the superior endplate of L1 vertebral body. Then 10 kg × m² × s⁻² moment simulating flexion, extension, lateral bending and axial rotation were imposed on the superior endplate of L1 vertebral body. Eventually the average stiffness of all directions was calculated and it was similar to the outcomes of former articles. The L1-L5 lumbar three-dimensional finite element model is validated so that it may used with biomechanical simulation and analysis of normal or surgical models.

A superconducting nanowire can be modeled by using SPICE

NASA Astrophysics Data System (ADS)

Berggren, Karl K.; Zhao, Qing-Yuan; Abebe, Nathnael; Chen, Minjie; Ravindran, Prasana; McCaughan, Adam; Bardin, Joseph C.

2018-05-01

Modeling of superconducting nanowire single-photon detectors typically requires custom simulations or finite-element analysis in one or two dimensions. Here, we demonstrate two simplified one-dimensional SPICE models of a superconducting nanowire that can quickly and efficiently describe the electrical characteristics of a superconducting nanowire. These models may be of particular use in understanding alternative architectures for nanowire detectors and readouts.

BIOPLUME III

EPA Pesticide Factsheets

BIOPLUME III is a two-dimensional finite difference model for simulating the natural attenuation of organic contaminants in groundwater due to the processes of advection, dispersion, sorption, and biodegradation.

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.

Three-Dimensional Temperature Field Simulation for the Rotor of an Asynchronous Motor

ERIC Educational Resources Information Center

Wang, Yanwu; Fan, Chunli; Yang, Li; Sun, Fengrui

2010-01-01

A three-dimensional heat transfer model is built according to the rotor structure of an asynchronous motor, and three-dimensional temperature fields of the rotor under different working conditions, such as the unloaded, rated loaded and that with broken rotor bars, are studied based on the finite element numerical method and experiments. The…

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1984-01-01

Analytical and numerical methods evaluating the stress-intensity factors for three-dimensional cracks in solids are presented, with reference to fatigue failure in aerospace structures. The exact solutions for embedded elliptical and circular cracks in infinite solids, and the approximate methods, including the finite-element, the boundary-integral equation, the line-spring models, and the mixed methods are discussed. Among the mixed methods, the superposition of analytical and finite element methods, the stress-difference, the discretization-error, the alternating, and the finite element-alternating methods are reviewed. Comparison of the stress-intensity factor solutions for some three-dimensional crack configurations showed good agreement. Thus, the choice of a particular method in evaluating the stress-intensity factor is limited only to the availability of resources and computer programs.

Semi-implicit finite difference methods for three-dimensional shallow water flow

USGS Publications Warehouse

Casulli, Vincenzo; Cheng, Ralph T.

1992-01-01

A semi-implicit finite difference method for the numerical solution of three-dimensional shallow water flows is presented and discussed. The governing equations are the primitive three-dimensional turbulent mean flow equations where the pressure distribution in the vertical has been assumed to be hydrostatic. In the method of solution a minimal degree of implicitness has been adopted in such a fashion that the resulting algorithm is stable and gives a maximal computational efficiency at a minimal computational cost. At each time step the numerical method requires the solution of one large linear system which can be formally decomposed into a set of small three-diagonal systems coupled with one five-diagonal system. All these linear systems are symmetric and positive definite. Thus the existence and uniquencess of the numerical solution are assured. When only one vertical layer is specified, this method reduces as a special case to a semi-implicit scheme for solving the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm has been shown to be fast, accurate and mass-conservative and can also be applied to simulate flooding and drying of tidal mud-flats in conjunction with three-dimensional flows. Furthermore, the resulting algorithm is fully vectorizable for an efficient implementation on modern vector computers.

On applications of chimera grid schemes to store separation

NASA Technical Reports Server (NTRS)

Cougherty, F. C.; Benek, J. A.; Steger, J. L.

1985-01-01

A finite difference scheme which uses multiple overset meshes to simulate the aerodynamics of aircraft/store interaction and store separation is described. In this chimera, or multiple mesh, scheme, a complex configuration is mapped using a major grid about the main component of the configuration, and minor overset meshes are used to map each additional component such as a store. As a first step in modeling the aerodynamics of store separation, two dimensional inviscid flow calculations were carried out in which one of the minor meshes is allowed to move with respect to the major grid. Solutions of calibrated two dimensional problems indicate that allowing one mesh to move with respect to another does not adversely affect the time accuracy of an unsteady solution. Steady, inviscid three dimensional computations demonstrate the capability to simulate complex configurations, including closely packed multiple bodies.

Quasi-phases and pseudo-transitions in one-dimensional models with nearest neighbor interactions

NASA Astrophysics Data System (ADS)

de Souza, S. M.; Rojas, Onofre

2018-01-01

There are some particular one-dimensional models, such as the Ising-Heisenberg spin models with a variety of chain structures, which exhibit unexpected behaviors quite similar to the first and second order phase transition, which could be confused naively with an authentic phase transition. Through the analysis of the first derivative of free energy, such as entropy, magnetization, and internal energy, a "sudden" jump that closely resembles a first-order phase transition at finite temperature occurs. However, by analyzing the second derivative of free energy, such as specific heat and magnetic susceptibility at finite temperature, it behaves quite similarly to a second-order phase transition exhibiting an astonishingly sharp and fine peak. The correlation length also confirms the evidence of this pseudo-transition temperature, where a sharp peak occurs at the pseudo-critical temperature. We also present the necessary conditions for the emergence of these quasi-phases and pseudo-transitions.

3-d finite element model development for biomechanics: a software demonstration

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

Hollerbach, K.; Hollister, A.M.; Ashby, E.

1997-03-01

Finite element analysis is becoming an increasingly important part of biomechanics and orthopedic research, as computational resources become more powerful, and data handling algorithms become more sophisticated. Until recently, tools with sufficient power did not exist or were not accessible to adequately model complicated, three-dimensional, nonlinear biomechanical systems. In the past, finite element analyses in biomechanics have often been limited to two-dimensional approaches, linear analyses, or simulations of single tissue types. Today, we have the resources to model fully three-dimensional, nonlinear, multi-tissue, and even multi-joint systems. The authors will present the process of developing these kinds of finite element models,more » using human hand and knee examples, and will demonstrate their software tools.« less

Finite-momentum Bose-Einstein condensates in shaken two-dimensional square optical lattices

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

Di Liberto, M.; Scuola Superiore di Catania, Universita di Catania, Via Valdisavoia 9, I-95123 Catania; Tieleman, O.

2011-07-15

We consider ultracold bosons in a two-dimensional square optical lattice described by the Bose-Hubbard model. In addition, an external time-dependent sinusoidal force is applied to the system, which shakes the lattice along one of the diagonals. The effect of the shaking is to renormalize the nearest-neighbor-hopping coefficients, which can be arbitrarily reduced, can vanish, or can even change sign, depending on the shaking parameter. Therefore, it is necessary to account for higher-order-hopping terms, which are renormalized differently by the shaking, and to introduce anisotropy into the problem. We show that the competition between these different hopping terms leads to finite-momentummore » condensates with a momentum that may be tuned via the strength of the shaking. We calculate the boundaries between the Mott insulator and the different superfluid phases and present the time-of-flight images expected to be observed experimentally. Our results open up possibilities for the realization of bosonic analogs of the Fulde, Ferrel, Larkin, and Ovchinnikov phase describing inhomogeneous superconductivity.« less

A Two-Dimensional Linear Bicharacteristic Scheme for Electromagnetics

NASA Technical Reports Server (NTRS)

Beggs, John H.

2002-01-01

The upwind leapfrog or Linear Bicharacteristic Scheme (LBS) has previously been implemented and demonstrated on one-dimensional electromagnetic wave propagation problems. This memorandum extends the Linear Bicharacteristic Scheme for computational electromagnetics to model lossy dielectric and magnetic materials and perfect electrical conductors in two dimensions. This is accomplished by proper implementation of the LBS for homogeneous lossy dielectric and magnetic media and for perfect electrical conductors. Both the Transverse Electric and Transverse Magnetic polarizations are considered. Computational requirements and a Fourier analysis are also discussed. Heterogeneous media are modeled through implementation of surface boundary conditions and no special extrapolations or interpolations at dielectric material boundaries are required. Results are presented for two-dimensional model problems on uniform grids, and the Finite Difference Time Domain (FDTD) algorithm is chosen as a convenient reference algorithm for comparison. The results demonstrate that the two-dimensional explicit LBS is a dissipation-free, second-order accurate algorithm which uses a smaller stencil than the FDTD algorithm, yet it has less phase velocity error.

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.

Buckling Analysis of Single and Multi Delamination In Composite Beam Using Finite Element Method

NASA Astrophysics Data System (ADS)

Simanjorang, Hans Charles; Syamsudin, Hendri; Giri Suada, Muhammad

2018-04-01

Delamination is one type of imperfection in structure which found usually in the composite structure. Delamination may exist due to some factors namely in-service condition where the foreign objects hit the composite structure and creates inner defect and poor manufacturing that causes the initial imperfections. Composite structure is susceptible to the compressive loading. Compressive loading leads the instability phenomenon in the composite structure called buckling. The existence of delamination inside of the structure will cause reduction in buckling strength. This paper will explain the effect of delamination location to the buckling strength. The analysis will use the one-dimensional modelling approach using two- dimensional finite element method.

A Thin Codimension-One Decomposition of the Hilbert Cube

ERIC Educational Resources Information Center

Phon-On, Aniruth

2010-01-01

For cell-like upper semicontinuous (usc) decompositions "G" of finite dimensional manifolds "M", the decomposition space "M/G" turns out to be an ANR provided "M/G" is finite dimensional ([Dav07], page 129). Furthermore, if "M/G" is finite dimensional and has the Disjoint Disks Property (DDP), then "M/G" is homeomorphic to "M" ([Dav07], page 181).…

Three-Dimensional Sensitivity Kernels of Z/H Amplitude Ratios of Surface and Body Waves

NASA Astrophysics Data System (ADS)

Bao, X.; Shen, Y.

2017-12-01

The ellipticity of Rayleigh wave particle motion, or Z/H amplitude ratio, has received increasing attention in inversion for shallow Earth structures. Previous studies of the Z/H ratio assumed one-dimensional (1D) velocity structures beneath the receiver, ignoring the effects of three-dimensional (3D) heterogeneities on wave amplitudes. This simplification may introduce bias in the resulting models. Here we present 3D sensitivity kernels of the Z/H ratio to Vs, Vp, and density perturbations, based on finite-difference modeling of wave propagation in 3D structures and the scattering-integral method. Our full-wave approach overcomes two main issues in previous studies of Rayleigh wave ellipticity: (1) the finite-frequency effects of wave propagation in 3D Earth structures, and (2) isolation of the fundamental mode Rayleigh waves from Rayleigh wave overtones and converted Love waves. In contrast to the 1D depth sensitivity kernels in previous studies, our 3D sensitivity kernels exhibit patterns that vary with azimuths and distances to the receiver. The laterally-summed 3D sensitivity kernels and 1D depth sensitivity kernels, based on the same homogeneous reference model, are nearly identical with small differences that are attributable to the single period of the 1D kernels and a finite period range of the 3D kernels. We further verify the 3D sensitivity kernels by comparing the predictions from the kernels with the measurements from numerical simulations of wave propagation for models with various small-scale perturbations. We also calculate and verify the amplitude kernels for P waves. This study shows that both Rayleigh and body wave Z/H ratios provide vertical and lateral constraints on the structure near the receiver. With seismic arrays, the 3D kernels afford a powerful tool to use the Z/H ratios to obtain accurate and high-resolution Earth models.

A two dimensional finite difference time domain analysis of the quiet zone fields of an anechoic chamber

NASA Technical Reports Server (NTRS)

Ryan, Deirdre A.; Luebbers, Raymond J.; Nguyen, Truong X.; Kunz, Karl S.; Steich, David J.

1992-01-01

Prediction of anechoic chamber performance is a difficult problem. Electromagnetic anechoic chambers exist for a wide range of frequencies but are typically very large when measured in wavelengths. Three dimensional finite difference time domain (FDTD) modeling of anechoic chambers is possible with current computers but at frequencies lower than most chamber design frequencies. However, two dimensional FDTD (2D-FTD) modeling enables much greater detail at higher frequencies and offers significant insight into compact anechoic chamber design and performance. A major subsystem of an anechoic chamber for which computational electromagnetic analyses exist is the reflector. First, an analysis of the quiet zone fields of a low frequency anechoic chamber produced by a uniform source and a reflector in two dimensions using the FDTD method is presented. The 2D-FDTD results are compared with results from a three dimensional corrected physical optics calculation and show good agreement. Next, a directional source is substituted for the uniform radiator. Finally, a two dimensional anechoic chamber geometry, including absorbing materials, is considered, and the 2D-FDTD results for these geometries appear reasonable.

Neuronal models in infinite-dimensional spaces and their finite-dimensional projections: Part II.

PubMed

Brzychczy, S; Leszczyński, H; Poznanski, R R

2012-09-01

Application of comparison theorem is used to examine the validitiy of the "lumped parameter assumption" in describing the behavior of solutions of the continuous cable equation U(t) = DU(xx)+f(U) with the discrete cable equation dV(n)/dt = d*(V(n+1) - 2V(n) + V(n-1)) + f(V(n)), where f is a nonlinear functional describing the internal diffusion of electrical potential in single neurons. While the discrete cable equation looks like a finite difference approximation of the continuous cable equation, solutions of the two reveal significantly different behavior which imply that the compartmental models (spiking neurons) are poor quantifiers of neurons, contrary to what is commonly accepted in computational neuroscience.

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

A Unique Finite Element Modeling of the Periodic Wave Transformation over Sloping and Barred Beaches by Beji and Nadaoka's Extended Boussinesq Equations

PubMed Central

Jabbari, Mohammad Hadi; Sayehbani, Mesbah; Reisinezhad, Arsham

2013-01-01

This paper presents a numerical model based on one-dimensional Beji and Nadaoka's Extended Boussinesq equations for simulation of periodic wave shoaling and its decomposition over morphological beaches. A unique Galerkin finite element and Adams-Bashforth-Moulton predictor-corrector methods are employed for spatial and temporal discretization, respectively. For direct application of linear finite element method in spatial discretization, an auxiliary variable is hereby introduced, and a particular numerical scheme is offered to rewrite the equations in lower-order form. Stability of the suggested numerical method is also analyzed. Subsequently, in order to display the ability of the presented model, four different test cases are considered. In these test cases, dispersive and nonlinearity effects of the periodic waves over sloping beaches and barred beaches, which are the common coastal profiles, are investigated. Outputs are compared with other existing numerical and experimental data. Finally, it is concluded that the current model can be further developed to model any morphological development of coastal profiles. PMID:23853534

Numerical simulation of rarefied gas flow through a slit

NASA Technical Reports Server (NTRS)

Keith, Theo G., Jr.; Jeng, Duen-Ren; De Witt, Kenneth J.; Chung, Chan-Hong

1990-01-01

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas from one reservoir to another through a two-dimensional slit. The cases considered are for hard vacuum downstream pressure, finite pressure ratios, and isobaric pressure with thermal diffusion, which are not well established in spite of the simplicity of the flow field. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, three kinds of collision sampling techniques, the time counter (TC) method, the null collision (NC) method, and the no time counter (NTC) method, are used.

Bak-Tang-Wiesenfeld model in the upper critical dimension: Induced criticality in lower-dimensional subsystems

NASA Astrophysics Data System (ADS)

Dashti-Naserabadi, H.; Najafi, M. N.

2017-10-01

We present extensive numerical simulations of Bak-Tang-Wiesenfeld (BTW) sandpile model on the hypercubic lattice in the upper critical dimension Du=4 . After re-extracting the critical exponents of avalanches, we concentrate on the three- and two-dimensional (2D) cross sections seeking for the induced criticality which are reflected in the geometrical and local exponents. Various features of finite-size scaling (FSS) theory have been tested and confirmed for all dimensions. The hyperscaling relations between the exponents of the distribution functions and the fractal dimensions are shown to be valid for all dimensions. We found that the exponent of the distribution function of avalanche mass is the same for the d -dimensional cross sections and the d -dimensional BTW model for d =2 and 3. The geometrical quantities, however, have completely different behaviors with respect to the same-dimensional BTW model. By analyzing the FSS theory for the geometrical exponents of the two-dimensional cross sections, we propose that the 2D induced models have degrees of similarity with the Gaussian free field (GFF). Although some local exponents are slightly different, this similarity is excellent for the fractal dimensions. The most important one showing this feature is the fractal dimension of loops df, which is found to be 1.50 ±0.02 ≈3/2 =dfGFF .

Bak-Tang-Wiesenfeld model in the upper critical dimension: Induced criticality in lower-dimensional subsystems.

PubMed

Dashti-Naserabadi, H; Najafi, M N

2017-10-01

We present extensive numerical simulations of Bak-Tang-Wiesenfeld (BTW) sandpile model on the hypercubic lattice in the upper critical dimension D_{u}=4. After re-extracting the critical exponents of avalanches, we concentrate on the three- and two-dimensional (2D) cross sections seeking for the induced criticality which are reflected in the geometrical and local exponents. Various features of finite-size scaling (FSS) theory have been tested and confirmed for all dimensions. The hyperscaling relations between the exponents of the distribution functions and the fractal dimensions are shown to be valid for all dimensions. We found that the exponent of the distribution function of avalanche mass is the same for the d-dimensional cross sections and the d-dimensional BTW model for d=2 and 3. The geometrical quantities, however, have completely different behaviors with respect to the same-dimensional BTW model. By analyzing the FSS theory for the geometrical exponents of the two-dimensional cross sections, we propose that the 2D induced models have degrees of similarity with the Gaussian free field (GFF). Although some local exponents are slightly different, this similarity is excellent for the fractal dimensions. The most important one showing this feature is the fractal dimension of loops d_{f}, which is found to be 1.50±0.02≈3/2=d_{f}^{GFF}.

Bicylindrical model of Herschel-Quincke tube-duct system: theory and comparison with experiment and finite element method.

PubMed

Poirier, B; Ville, J M; Maury, C; Kateb, D

2009-09-01

An analytical three dimensional bicylindrical model is developed in order to take into account the effects of the saddle-shaped area for the interface of a n-Herschel-Quincke tube system with the main duct. Results for the scattering matrix of this system deduced from this model are compared, in the plane wave frequency domain, versus experimental and numerical data and a one dimensional model with and without tube length correction. The results are performed with a two-Herschel-Quincke tube configuration having the same diameter as the main duct. In spite of strong assumptions on the acoustic continuity conditions at the interfaces, this model is shown to improve the nonperiodic amplitude variations and the frequency localization of the minima of the transmission and reflection coefficients with respect to one dimensional model with length correction and a three dimensional model.

Constructing space difference schemes which satisfy a cell entropy inequality

NASA Technical Reports Server (NTRS)

Merriam, Marshal L.

1989-01-01

A numerical methodology for solving convection problems is presented, using finite difference schemes which satisfy the second law of thermodynamics on a cell-by-cell basis in addition to the usual conservation laws. It is shown that satisfaction of a cell entropy inequality is sufficient, in some cases, to guarantee nonlinear stability. Some details are given for several one-dimensional problems, including the quasi-one-dimensional Euler equations applied to flow in a nozzle.

Thermal Modeling and Analysis of a Cryogenic Tank Design Exposed to Extreme Heating Profiles

NASA Technical Reports Server (NTRS)

Stephens, Craig A.; Hanna, Gregory J.

1991-01-01

A cryogenic test article, the Generic Research Cryogenic Tank, was designed to qualitatively simulate the thermal response of transatmospheric vehicle fuel tanks exposed to the environment of hypersonic flight. One-dimensional and two-dimensional finite-difference thermal models were developed to simulate the thermal response and assist in the design of the Generic Research Cryogenic Tank. The one-dimensional thermal analysis determined the required insulation thickness to meet the thermal design criteria and located the purge jacket to eliminate the liquefaction of air. The two-dimensional thermal analysis predicted the temperature gradients developed within the pressure-vessel wall, estimated the cryogen boiloff, and showed the effects the ullage condition has on pressure-vessel temperatures. The degree of ullage mixing, location of the applied high-temperature profile, and the purge gas influence on insulation thermal conductivity had significant effects on the thermal behavior of the Generic Research Cryogenic Tank. In addition to analysis results, a description of the Generic Research Cryogenic Tank and the role it will play in future thermal structures and transatmospheric vehicle research at the NASA Dryden Flight Research Facility is presented.

Grid-size dependence of Cauchy boundary conditions used to simulate stream-aquifer interactions

USGS Publications Warehouse

Mehl, S.; Hill, M.C.

2010-01-01

This work examines the simulation of stream–aquifer interactions as grids are refined vertically and horizontally and suggests that traditional methods for calculating conductance can produce inappropriate values when the grid size is changed. Instead, different grid resolutions require different estimated values. Grid refinement strategies considered include global refinement of the entire model and local refinement of part of the stream. Three methods of calculating the conductance of the Cauchy boundary conditions are investigated. Single- and multi-layer models with narrow and wide streams produced stream leakages that differ by as much as 122% as the grid is refined. Similar results occur for globally and locally refined grids, but the latter required as little as one-quarter the computer execution time and memory and thus are useful for addressing some scale issues of stream–aquifer interactions. Results suggest that existing grid-size criteria for simulating stream–aquifer interactions are useful for one-layer models, but inadequate for three-dimensional models. The grid dependence of the conductance terms suggests that values for refined models using, for example, finite difference or finite-element methods, cannot be determined from previous coarse-grid models or field measurements. Our examples demonstrate the need for a method of obtaining conductances that can be translated to different grid resolutions and provide definitive test cases for investigating alternative conductance formulations.

Phase-space finite elements in a least-squares solution of the transport equation

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

Drumm, C.; Fan, W.; Pautz, S.

2013-07-01

The linear Boltzmann transport equation is solved using a least-squares finite element approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular finite elements approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular finite elements: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshingmore » tool to generate a mesh. In this manner, much of the spatial finite-elements machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam elements, also building upon the spatial finite elements capabilities. The methods described here can make use of either continuous or discontinuous finite elements in space, angle and/or energy, with the use of continuous finite elements resulting in a smaller problem size and the use of discontinuous finite elements resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous finite elements, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space finite elements capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field. (authors)« less

Time-domain simulation of constitutive relations for nonlinear acoustics including relaxation for frequency power law attenuation media modeling

NASA Astrophysics Data System (ADS)

Jiménez, Noé; Camarena, Francisco; Redondo, Javier; Sánchez-Morcillo, Víctor; Konofagou, Elisa E.

2015-10-01

We report a numerical method for solving the constitutive relations of nonlinear acoustics, where multiple relaxation processes are included in a generalized formulation that allows the time-domain numerical solution by an explicit finite differences scheme. Thus, the proposed physical model overcomes the limitations of the one-way Khokhlov-Zabolotskaya-Kuznetsov (KZK) type models and, due to the Lagrangian density is implicitly included in the calculation, the proposed method also overcomes the limitations of Westervelt equation in complex configurations for medical ultrasound. In order to model frequency power law attenuation and dispersion, such as observed in biological media, the relaxation parameters are fitted to both exact frequency power law attenuation/dispersion media and also empirically measured attenuation of a variety of tissues that does not fit an exact power law. Finally, a computational technique based on artificial relaxation is included to correct the non-negligible numerical dispersion of the finite difference scheme, and, on the other hand, improve stability trough artificial attenuation when shock waves are present. This technique avoids the use of high-order finite-differences schemes leading to fast calculations. The present algorithm is especially suited for practical configuration where spatial discontinuities are present in the domain (e.g. axisymmetric domains or zero normal velocity boundary conditions in general). The accuracy of the method is discussed by comparing the proposed simulation solutions to one dimensional analytical and k-space numerical solutions.

Analysis of high-rise constructions with the using of three-dimensional models of rods in the finite element program PRINS

NASA Astrophysics Data System (ADS)

Agapov, Vladimir

2018-03-01

The necessity of new approaches to the modeling of rods in the analysis of high-rise constructions is justified. The possibility of the application of the three-dimensional superelements of rods with rectangular cross section for the static and dynamic calculation of the bar and combined structures is considered. The results of the eighteen-story spatial frame free vibrations analysis using both one-dimensional and three-dimensional models of rods are presented. A comparative analysis of the obtained results is carried out and the conclusions on the possibility of three-dimensional superelements application in static and dynamic analysis of high-rise constructions are given on its basis.

Three-dimensional local grid refinement for block-centered finite-difference groundwater models using iteratively coupled shared nodes: A new method of interpolation and analysis of errors

USGS Publications Warehouse

Mehl, S.; Hill, M.C.

2004-01-01

This paper describes work that extends to three dimensions the two-dimensional local-grid refinement method for block-centered finite-difference groundwater models of Mehl and Hill [Development and evaluation of a local grid refinement method for block-centered finite-difference groundwater models using shared nodes. Adv Water Resour 2002;25(5):497-511]. In this approach, the (parent) finite-difference grid is discretized more finely within a (child) sub-region. The grid refinement method sequentially solves each grid and uses specified flux (parent) and specified head (child) boundary conditions to couple the grids. Iteration achieves convergence between heads and fluxes of both grids. Of most concern is how to interpolate heads onto the boundary of the child grid such that the physics of the parent-grid flow is retained in three dimensions. We develop a new two-step, "cage-shell" interpolation method based on the solution of the flow equation on the boundary of the child between nodes shared with the parent grid. Error analysis using a test case indicates that the shared-node local grid refinement method with cage-shell boundary head interpolation is accurate and robust, and the resulting code is used to investigate three-dimensional local grid refinement of stream-aquifer interactions. Results reveal that (1) the parent and child grids interact to shift the true head and flux solution to a different solution where the heads and fluxes of both grids are in equilibrium, (2) the locally refined model provided a solution for both heads and fluxes in the region of the refinement that was more accurate than a model without refinement only if iterations are performed so that both heads and fluxes are in equilibrium, and (3) the accuracy of the coupling is limited by the parent-grid size - A coarse parent grid limits correct representation of the hydraulics in the feedback from the child grid.

Realization of discrete quantum billiards in a two-dimensional optical lattice

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

Krimer, Dmitry O.; Max-Planck Institute for the Physics of Complex Systems, Noethnitzer Strasse 38, D-01187 Dresden; Khomeriki, Ramaz

2011-10-15

We propose a method for optical visualization of the Bose-Hubbard model with two interacting bosons in the form of two-dimensional (2D) optical lattices consisting of optical waveguides, where the waveguides at the diagonal are characterized by different refractive indices than others elsewhere, modeling the boson-boson interaction. We study the light intensity distribution function averaged over the direction of propagation for both ordered and disordered cases, exploring the sensitivity of the averaged picture with respect to the beam injection position. For our finite systems, the resulting patterns are reminiscent the ones set in billiards, and therefore we introduce a definition ofmore » discrete quantum billiards and discuss the possible relevance to its well-established continuous counterpart.« less

The Coupling of Finite Element and Integral Equation Representations for Efficient Three-Dimensional Modeling of Electromagnetic Scattering and Radiation

NASA Technical Reports Server (NTRS)

Cwik, Tom; Zuffada, Cinzia; Jamnejad, Vahraz

1996-01-01

Finite element modeling has proven useful for accurtely simulating scattered or radiated fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of a wavelength.

User's manual for three dimensional FDTD version B code for scattering from frequency-dependent dielectric materials

NASA Technical Reports Server (NTRS)

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

1992-01-01

The Penn State Finite Difference Time Domain Electromagnetic Code Version B is a three dimensional numerical electromagnetic scattering code based upon the Finite Difference Time Domain Technique (FDTD). The supplied version of the code is one version of our current three dimensional FDTD code set. This manual provides a description of the code and corresponding results for several scattering problems. The manual is organized into 14 sections: introduction, description of the FDTD method, operation, resource requirements, Version B code capabilities, a brief description of the default scattering geometry, a brief description of each subroutine, a description of the include file, a discussion of radar cross section computations, a discussion of some scattering results, a sample problem setup section, a new problem checklist, references and figure titles.

Lattice vibrations in the Frenkel-Kontorova model. I. Phonon dispersion, number density, and energy

NASA Astrophysics Data System (ADS)

Meng, Qingping; Wu, Lijun; Welch, David O.; Zhu, Yimei

2015-06-01

We studied the lattice vibrations of two interpenetrating atomic sublattices via the Frenkel-Kontorova (FK) model of a linear chain of harmonically interacting atoms subjected to an on-site potential using the technique of thermodynamic Green's functions based on quantum field-theoretical methods. General expressions were deduced for the phonon frequency-wave-vector dispersion relations, number density, and energy of the FK model system. As the application of the theory, we investigated in detail cases of linear chains with various periods of the on-site potential of the FK model. Some unusual but interesting features for different amplitudes of the on-site potential of the FK model are discussed. In the commensurate structure, the phonon spectrum always starts at a finite frequency, and the gaps of the spectrum are true ones with a zero density of modes. In the incommensurate structure, the phonon spectrum starts from zero frequency, but at a nonzero wave vector; there are some modes inside these gap regions, but their density is very low. In our approximation, the energy of a higher-order commensurate state of the one-dimensional system at a finite temperature may become indefinitely close to the energy of an incommensurate state. This finding implies that the higher-order incommensurate-commensurate transitions are continuous ones and that the phase transition may exhibit a "devil's staircase" behavior at a finite temperature.

Modeling bistable behaviors in morphing structures through finite element simulations.

PubMed

Guo, Qiaohang; Zheng, Huang; Chen, Wenzhe; Chen, Zi

2014-01-01

Bistable structures, exemplified by the Venus flytrap and slap bracelets, can transit between different configurations upon certain external stimulation. Here we study, through three-dimensional finite element simulations, the bistable behaviors in elastic plates in the absence of terminate loads, but with pre-strains in one (or both) of the two composite layers. Both the scenarios with and without a given geometric mis-orientation angle are investigated, the results of which are consistent with recent theoretical and experimental studies. This work can open ample venues for programmable designs of plant/shell structures with large deformations, with applications in designing bio-inspired robotics for biomedical research and morphing/deployable structures in aerospace engineering.

Limitations to the use of two-dimensional thermal modeling of a nuclear waste repository

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

Davis, B.W.

1979-01-04

Thermal modeling of a nuclear waste repository is basic to most waste management predictive models. It is important that the modeling techniques accurately determine the time-dependent temperature distribution of the waste emplacement media. Recent modeling studies show that the time-dependent temperature distribution can be accurately modeled in the far-field using a 2-dimensional (2-D) planar numerical model; however, the near-field cannot be modeled accurately enough by either 2-D axisymmetric or 2-D planar numerical models for repositories in salt. The accuracy limits of 2-D modeling were defined by comparing results from 3-dimensional (3-D) TRUMP modeling with results from both 2-D axisymmetric andmore » 2-D planar. Both TRUMP and ADINAT were employed as modeling tools. Two-dimensional results from the finite element code, ADINAT were compared with 2-D results from the finite difference code, TRUMP; they showed almost perfect correspondence in the far-field. This result adds substantially to confidence in future use of ADINAT and its companion stress code ADINA for thermal stress analysis. ADINAT was found to be somewhat sensitive to time step and mesh aspect ratio. 13 figures, 4 tables.« less

Stability analysis of Eulerian-Lagrangian methods for the one-dimensional shallow-water equations

USGS Publications Warehouse

Casulli, V.; Cheng, R.T.

1990-01-01

In this paper stability and error analyses are discussed for some finite difference methods when applied to the one-dimensional shallow-water equations. Two finite difference formulations, which are based on a combined Eulerian-Lagrangian approach, are discussed. In the first part of this paper the results of numerical analyses for an explicit Eulerian-Lagrangian method (ELM) have shown that the method is unconditionally stable. This method, which is a generalized fixed grid method of characteristics, covers the Courant-Isaacson-Rees method as a special case. Some artificial viscosity is introduced by this scheme. However, because the method is unconditionally stable, the artificial viscosity can be brought under control either by reducing the spatial increment or by increasing the size of time step. The second part of the paper discusses a class of semi-implicit finite difference methods for the one-dimensional shallow-water equations. This method, when the Eulerian-Lagrangian approach is used for the convective terms, is also unconditionally stable and highly accurate for small space increments or large time steps. The semi-implicit methods seem to be more computationally efficient than the explicit ELM; at each time step a single tridiagonal system of linear equations is solved. The combined explicit and implicit ELM is best used in formulating a solution strategy for solving a network of interconnected channels. The explicit ELM is used at channel junctions for each time step. The semi-implicit method is then applied to the interior points in each channel segment. Following this solution strategy, the channel network problem can be reduced to a set of independent one-dimensional open-channel flow problems. Numerical results support properties given by the stability and error analyses. ?? 1990.

A Finite Difference Method for Modeling Migration of Impurities in Multilayer Systems

NASA Astrophysics Data System (ADS)

Tosa, V.; Kovacs, Katalin; Mercea, P.; Piringer, O.

2008-09-01

A finite difference method to solve the one-dimensional diffusion of impurities in a multilayer system was developed for the special case in which a partition coefficient K impose a ratio of the concentrations at the interface between two adiacent layers. The fictitious point method was applied to derive the algebraic equations for the mesh points at the interface, while for the non-uniform mesh points within the layers a combined method was used. The method was tested and then applied to calculate migration of impurities from multilayer systems into liquids or solids samples, in migration experiments performed for quality testing purposes. An application was developed in the field of impurities migrations from multilayer plastic packagings into food, a problem of increasing importance in food industry.

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.

MODFLOW-LGR-Modifications to the streamflow-routing package (SFR2) to route streamflow through locally refined grids

USGS Publications Warehouse

Mehl, Steffen W.; Hill, Mary C.

2011-01-01

This report documents modifications to the Streamflow-Routing Package (SFR2) to route streamflow through grids constructed using the multiple-refined-areas capability of shared node Local Grid Refinement (LGR) of MODFLOW-2005. MODFLOW-2005 is the U.S. Geological Survey modular, three-dimensional, finite-difference groundwater-flow model. LGR provides the capability to simulate groundwater flow by using one or more block-shaped, higher resolution local grids (child model) within a coarser grid (parent model). LGR accomplishes this by iteratively coupling separate MODFLOW-2005 models such that heads and fluxes are balanced across the shared interfacing boundaries. Compatibility with SFR2 allows for streamflow routing across grids. LGR can be used in two- and three-dimensional, steady-state and transient simulations and for simulations of confined and unconfined groundwater systems.

Existence of global weak solution for a reduced gravity two and a half layer model

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

Guo, Zhenhua, E-mail: zhenhua.guo.math@gmail.com; Li, Zilai, E-mail: lizilai0917@163.com; Yao, Lei, E-mail: yaolei1056@hotmail.com

2013-12-15

We investigate the existence of global weak solution to a reduced gravity two and a half layer model in one-dimensional bounded spatial domain or periodic domain. Also, we show that any possible vacuum state has to vanish within finite time, then the weak solution becomes a unique strong one.

Three-Dimensional Finite Element Analysis on Stress Distribution of Internal Implant-Abutment Engagement Features.

PubMed

Cho, Sung-Yong; Huh, Yun-Hyuk; Park, Chan-Jin; Cho, Lee-Ra

To investigate the stress distribution in an implant-abutment complex with a preloaded abutment screw by comparing implant-abutment engagement features using three-dimensional finite element analysis (FEA). For FEA modeling, two implants-one with a single (S) engagement system and the other with a double (D) engagement system-were placed in the human mandibular molar region. Two types of abutments (hexagonal, conical) were connected to the implants. Different implant models (a single implant, two parallel implants, and mesial and tilted distal implants with 1-mm bone loss) were assumed. A static axial force and a 45-degree oblique force of 200 N were applied as the sum of vectors to the top of the prosthetic occlusal surface with a preload of 30 Ncm in the abutment screw. The von Mises stresses at the implant-abutment and abutment-screw interfaces were measured. In the single implant model, the S-conical abutment type exhibited broader stress distribution than the S-hexagonal abutment. In the double engagement system, the stress concentration was high in the lower contact area of the implant-abutment engagement. In the tilted implant model, the stress concentration point was different from that in the parallel implant model because of the difference in the bone level. The double engagement system demonstrated a high stress concentration at the lower contact area of the implant-abutment interface. To decrease the stress concentration, the type of engagement features of the implant-abutment connection should be carefully considered.

Exact edge, bulk, and bound states of finite topological systems

NASA Astrophysics Data System (ADS)

Duncan, Callum W.; Öhberg, Patrik; Valiente, Manuel

2018-05-01

Finite topologically nontrivial systems are characterized, among many other unique properties, by the presence of bound states at their physical edges. These topological edge modes can be distinguished from usual Shockley waves energetically, as their energies remain finite and in gap even when the boundaries of the system represent an effectively infinite and sharp energetic barrier. Theoretically, the existence of topological edge modes can be shown by means of the bulk-edge correspondence and topological invariants. On a clean one-dimensional lattice and reducible two-dimensional models, in either the commensurate or semi-infinite case, the edge modes can be essentially obtained analytically, as shown previously [Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993), 10.1103/PhysRevLett.71.3697; D. Hügel and B. Paredes, Phys. Rev. A 89, 023619 (2014), 10.1103/PhysRevA.89.023619]. In this work, we put forward a method for obtaining the spectrum and wave functions of topological edge modes for arbitrary finite lattices, including the incommensurate case. A small number of parameters are easily determined numerically, with the form of the eigenstates remaining fully analytical. We also obtain the bulk modes in the finite system analytically and their associated eigenenergies, which lie within the infinite-size limit continuum. Our method is general and can be easily applied to obtain the properties of nontopological models and/or extended to include impurities. As an example, we consider a relevant case of an impurity located next to one edge of a one-dimensional system, equivalent to a softened boundary in a separable two-dimensional model. We show that a localized impurity can have a drastic effect on the original topological edge modes of the system. Using the periodic Harper and Hofstadter models to illustrate our method, we find that, on increasing the impurity strength, edge states can enter or exit the continuum, and a trivial Shockley state bound to the impurity may appear. The fate of the topological edge modes in the presence of impurities can be addressed by quenching the impurity strength. We find that at certain critical impurity strengths, the transition probability for a particle initially prepared in an edge mode to decay into the bulk exhibits discontinuities that mark the entry and exit points of edge modes from and into the bulk spectrum.

Estimation in a semi-Markov transformation model

PubMed Central

Dabrowska, Dorota M.

2012-01-01

Multi-state models provide a common tool for analysis of longitudinal failure time data. In biomedical applications, models of this kind are often used to describe evolution of a disease and assume that patient may move among a finite number of states representing different phases in the disease progression. Several authors developed extensions of the proportional hazard model for analysis of multi-state models in the presence of covariates. In this paper, we consider a general class of censored semi-Markov and modulated renewal processes and propose the use of transformation models for their analysis. Special cases include modulated renewal processes with interarrival times specified using transformation models, and semi-Markov processes with with one-step transition probabilities defined using copula-transformation models. We discuss estimation of finite and infinite dimensional parameters of the model, and develop an extension of the Gaussian multiplier method for setting confidence bands for transition probabilities. A transplant outcome data set from the Center for International Blood and Marrow Transplant Research is used for illustrative purposes. PMID:22740583

Numerical approach for finite volume three-body interaction

NASA Astrophysics Data System (ADS)

Guo, Peng; Gasparian, Vladimir

2018-01-01

In the present work, we study a numerical approach to one dimensional finite volume three-body interaction, the method is demonstrated by considering a toy model of three spinless particles interacting with pair-wise δ -function potentials. The numerical results are compared with the exact solutions of three spinless bosons interaction when the strength of short-range interactions are set equal for all pairs.

Effect of heat transfer of melt/solid interface shape and solute segregation in Edge-Defined Film-Fed growth - Finite element analysis

NASA Technical Reports Server (NTRS)

Ettouney, H. M.; Brown, R. A.

1982-01-01

The effects of the heat transfer environment in Edge-Defined Film-Fed Growth on melt-solid interface shape and lateral dopant segregation are studied by finite-element analysis of two-dimensional models for heat and mass transfer. Heat transfer configurations are studied that correspond to the uniform surroundings assumed in previous models and to lowand high-speed growth systems. The maximum growth rate for a silicon sheet is calculated and the range of validity of one-dimensional heat transfer models is established. The lateral segregation that results from curvature of the solidification interface is calculated for two solutes, boron and aluminum. In this way, heat transfer is linked directly to the uniformity of the product crystal.

Comparison between results of solution of Burgers' equation and Laplace's equation by Galerkin and least-square finite element methods

NASA Astrophysics Data System (ADS)

Adib, Arash; Poorveis, Davood; Mehraban, Farid

2018-03-01

In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.

COSIM: A Finite-Difference Computer Model to Predict Ternary Concentration Profiles Associated with Oxidation and Interdiffusion of Overlay-Coated Substrates

NASA Technical Reports Server (NTRS)

Nesbitt, James A.

2000-01-01

A finite-difference computer program (COSIM) has been written which models the one-dimensional, diffusional transport associated with high-temperature oxidation and interdiffusion of overlay-coated substrates. The program predicts concentration profiles for up to three elements in the coating and substrate after various oxidation exposures. Surface recession due to solute loss is also predicted. Ternary cross terms and concentration-dependent diffusion coefficients are taken into account. The program also incorporates a previously-developed oxide growth and spalling model to simulate either isothermal or cyclic oxidation exposures. In addition to predicting concentration profiles after various oxidation exposures, the program can also be used to predict coating fife based on a concentration dependent failure criterion (e.g., surface solute content drops to two percent). The computer code, written in an extension of FORTRAN 77, employs numerous subroutines to make the program flexible and easily modifiable to other coating oxidation problems.

Numerical Modeling of Three-Dimensional Confined Flows

NASA Technical Reports Server (NTRS)

Greywall, M. S.

1981-01-01

A three dimensional confined flow model is presented. The flow field is computed by calculating velocity and enthalpy along a set of streamlines. The finite difference equations are obtained by applying conservation principles to streamtubes constructed around the chosen streamlines. With appropriate substitutions for the body force terms, the approach computes three dimensional magnetohydrodynamic channel flows. A listing of a computer code, based on this approach is presented in FORTRAN IV language. The code computes three dimensional compressible viscous flow through a rectangular duct, with the duct cross section specified along the axis.

A one-dimensional nonlinear problem of thermoelasticity in extended thermodynamics

NASA Astrophysics Data System (ADS)

Rawy, E. K.

2018-06-01

We solve a nonlinear, one-dimensional initial boundary-value problem of thermoelasticity in generalized thermodynamics. A Cattaneo-type evolution equation for the heat flux is used, which differs from the one used extensively in the literature. The hyperbolic nature of the associated linear system is clarified through a study of the characteristic curves. Progressive wave solutions with two finite speeds are noted. A numerical treatment is presented for the nonlinear system using a three-step, quasi-linearization, iterative finite-difference scheme for which the linear system of equations is the initial step in the iteration. The obtained results are discussed in detail. They clearly show the hyperbolic nature of the system, and may be of interest in investigating thermoelastic materials, not only at low temperatures, but also during high temperature processes involving rapid changes in temperature as in laser treatment of surfaces.

Development and application of a three dimensional numerical model for predicting pollutant and sediment transport using an Eulerian-Lagrangian marker particle technique

NASA Technical Reports Server (NTRS)

Pavish, D. L.; Spaulding, M. L.

1977-01-01

A computer coded Lagrangian marker particle in Eulerian finite difference cell solution to the three dimensional incompressible mass transport equation, Water Advective Particle in Cell Technique, WAPIC, was developed, verified against analytic solutions, and subsequently applied in the prediction of long term transport of a suspended sediment cloud resulting from an instantaneous dredge spoil release. Numerical results from WAPIC were verified against analytic solutions to the three dimensional incompressible mass transport equation for turbulent diffusion and advection of Gaussian dye releases in unbounded uniform and uniformly sheared uni-directional flow, and for steady-uniform plug channel flow. WAPIC was utilized to simulate an analytic solution for non-equilibrium sediment dropout from an initially vertically uniform particle distribution in one dimensional turbulent channel flow.

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

NASA Technical Reports Server (NTRS)

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

1999-01-01

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

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.

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.

Stability Test for Transient-Temperature Calculations

NASA Technical Reports Server (NTRS)

Campbell, W.

1984-01-01

Graphical test helps assure numerical stability of calculations of transient temperature or diffusion in composite medium. Rectangular grid forms basis of two-dimensional finite-difference model for heat conduction or other diffusion like phenomena. Model enables calculation of transient heat transfer among up to four different materials that meet at grid point.

Comparison between Modelled and Measured Magnetic Field Scans of Different Planar Coil Topologies for Stress Sensor Applications.

PubMed

Gibbs, Robert; Moreton, Gregory; Meydan, Turgut; Williams, Paul

2018-03-21

The investigation of planar coils of differing topologies, when combined with a magnetostrictive amorphous ribbon to form a stress-sensitive self-inductor, is an active research area for applications as stress or pressure sensors. Four topologies of planar coil (Circular, Mesh, Meander, and Square) have been constructed using copper track on 30 mm wide PCB substrate. The coils are energized to draw 0.4 A and the resulting magnetic field distribution is observed with a newly developed three-dimensional magnetic field scanner. The system is based on a variably angled Micromagnetics ® STJ-020 tunneling magneto-resistance sensor with a spatial resolution of 5-10 µm and sensitivity to fields of less than 10 A/m. These experimental results are compared with the fields computed by ANSYS Maxwell ® finite element modelling of the same topologies. Measured field shape and strength correspond well with the results of modelling, including direct observation of corner and edge effects. Three-dimensional analysis of the field shape produced by the square coil, isolating the components H ( x ) and H ( z ) , is compared with the three-dimensional field solutions from modelling. The finite element modelling is validated and the accuracy and utility of the new system for three-dimensional scanning of general stray fields is confirmed.

Comparison between Modelled and Measured Magnetic Field Scans of Different Planar Coil Topologies for Stress Sensor Applications

PubMed Central

Moreton, Gregory

2018-01-01

The investigation of planar coils of differing topologies, when combined with a magnetostrictive amorphous ribbon to form a stress-sensitive self-inductor, is an active research area for applications as stress or pressure sensors. Four topologies of planar coil (Circular, Mesh, Meander, and Square) have been constructed using copper track on 30 mm wide PCB substrate. The coils are energized to draw 0.4 A and the resulting magnetic field distribution is observed with a newly developed three-dimensional magnetic field scanner. The system is based on a variably angled Micromagnetics® STJ-020 tunneling magneto-resistance sensor with a spatial resolution of 5–10 µm and sensitivity to fields of less than 10 A/m. These experimental results are compared with the fields computed by ANSYS Maxwell® finite element modelling of the same topologies. Measured field shape and strength correspond well with the results of modelling, including direct observation of corner and edge effects. Three-dimensional analysis of the field shape produced by the square coil, isolating the components H(x) and H(z), is compared with the three-dimensional field solutions from modelling. The finite element modelling is validated and the accuracy and utility of the new system for three-dimensional scanning of general stray fields is confirmed. PMID:29561809

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Exact solution of two interacting run-and-tumble random walkers with finite tumble duration

NASA Astrophysics Data System (ADS)

Slowman, A. B.; Evans, M. R.; Blythe, R. A.

2017-09-01

We study a model of interacting run-and-tumble random walkers operating under mutual hardcore exclusion on a one-dimensional lattice with periodic boundary conditions. We incorporate a finite, poisson-distributed, tumble duration so that a particle remains stationary whilst tumbling, thus generalising the persistent random walker model. We present the exact solution for the nonequilibrium stationary state of this system in the case of two random walkers. We find this to be characterised by two lengthscales, one arising from the jamming of approaching particles, and the other from one particle moving when the other is tumbling. The first of these lengthscales vanishes in a scaling limit where the continuous-space dynamics is recovered whilst the second remains finite. Thus the nonequilibrium stationary state reveals a rich structure of attractive, jammed and extended pieces.

Comprehensive Numerical Analysis of Finite Difference Time Domain Methods for Improving Optical Waveguide Sensor Accuracy

PubMed Central

Samak, M. Mosleh E. Abu; Bakar, A. Ashrif A.; Kashif, Muhammad; Zan, Mohd Saiful Dzulkifly

2016-01-01

This paper discusses numerical analysis methods for different geometrical features that have limited interval values for typically used sensor wavelengths. Compared with existing Finite Difference Time Domain (FDTD) methods, the alternating direction implicit (ADI)-FDTD method reduces the number of sub-steps by a factor of two to three, which represents a 33% time savings in each single run. The local one-dimensional (LOD)-FDTD method has similar numerical equation properties, which should be calculated as in the previous method. Generally, a small number of arithmetic processes, which result in a shorter simulation time, are desired. The alternating direction implicit technique can be considered a significant step forward for improving the efficiency of unconditionally stable FDTD schemes. This comparative study shows that the local one-dimensional method had minimum relative error ranges of less than 40% for analytical frequencies above 42.85 GHz, and the same accuracy was generated by both methods.

Improved finite-difference computation of the van der Waals force: One-dimensional case

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

Pinto, Fabrizio

2009-10-15

We present an improved demonstration of the calculation of Casimir forces in one-dimensional systems based on the recently proposed numerical imaginary frequency Green's function computation approach. The dispersion force on two thick lossy dielectric slabs separated by an empty gap and placed within a perfectly conducting cavity is obtained from the Green's function of the modified Helmholtz equation by means of an ordinary finite-difference method. In order to demonstrate the possibility to develop algorithms to explore complex geometries in two and three dimensions to higher order in the mesh spacing, we generalize existing classical electromagnetism algebraic methods to generate themore » difference equations for dielectric boundaries not coinciding with any grid points. Diagnostic tests are presented to monitor the accuracy of our implementation of the method and follow-up applications in higher dimensions are introduced.« less

Transport of volatile organic compounds across the capillary fringe

USGS Publications Warehouse

McCarthy, Kathleen A.; Johnson, Richard L.

1993-01-01

Physical experiments were conducted to investigate the transport of a dissolved volatile organic compound (trichloroethylene, TCE) from shallow groundwater to the unsaturated zone under a variety of conditions including changes in the soil moisture profile and water table position. Experimental data indicated that at moderate groundwater velocities (0.1 m/d), vertical mechanical dispersion was negligible and molecular diffusion was the dominant vertical transport mechanism. Under these conditions, TCE concentrations decreased nearly 3 orders of magnitude across the capillary fringe and soil gas concentrations remained low relative to those of underlying groundwater. Data collected during a water table drop showed a short-term increase in concentrations throughout most of the unsaturated zone, but these concentrations quickly declined and approached initial values after the water table was returned to its original level. In the deep part of the unsaturated zone, the water table drop resulted in a long-term decrease in concentrations, illustrating the effects of hysteresis in the soil moisture profile. A two-dimensional random walk advection-diffusion model was developed to simulate the experimental conditions, and numerical simulations agreed well with experimental data. A simpler, one-dimensional finite-difference diffusion-dispersion model was also developed. One-dimensional simulations based on molecular diffusion also agreed well with experimental data. Simulations which incorporated mechanical dispersion tended to overestimate flux across the capillary fringe. Good agreement between the one- and two-dimensional models suggested that a simple, one-dimensional approximation of vertical transport across the capillary fringe can be useful when conditions are appropriate.

Two Dimensional Finite Element Model to Study Calcium Distribution in Oocytes

NASA Astrophysics Data System (ADS)

Naik, Parvaiz Ahmad; Pardasani, Kamal Raj

2015-06-01

Cytosolic free calcium concentration is a key regulatory factor and perhaps the most widely used means of controlling cellular function. Calcium can enter cells through different pathways which are activated by specific stimuli including membrane depolarization, chemical signals and calcium depletion of intracellular stores. One of the important components of oocyte maturation is differentiation of the Ca2+ signaling machinery which is essential for egg activation after fertilization. Eggs acquire the ability to produce the fertilization-specific calcium signal during oocyte maturation. The calcium concentration patterns required during different stages of oocyte maturation are still not completely known. Also the mechanisms involved in calcium dynamics in oocyte cell are still not well understood. In view of above a two dimensional FEM model has been proposed to study calcium distribution in an oocyte cell. The parameters such as buffers, ryanodine receptor, SERCA pump and voltage gated calcium channel are incorporated in the model. Based on the biophysical conditions the initial and boundary conditions have been framed. The model is transformed into variational form and Ritz finite element method has been employed to obtain the solution. A program has been developed in MATLAB 7.10 for the entire problem and executed to obtain numerical results. The numerical results have been used to study the effect of buffers, RyR, SERCA pump and VGCC on calcium distribution in an oocyte cell.

A finite area scheme for shallow granular flows on three-dimensional surfaces

NASA Astrophysics Data System (ADS)

Rauter, Matthias

2017-04-01

Shallow granular flow models have become a popular tool for the estimation of natural hazards, such as landslides, debris flows and avalanches. The shallowness of the flow allows to reduce the three-dimensional governing equations to a quasi two-dimensional system. Three-dimensional flow fields are replaced by their depth-integrated two-dimensional counterparts, which yields a robust and fast method [1]. A solution for a simple shallow granular flow model, based on the so-called finite area method [3] is presented. The finite area method is an adaption of the finite volume method [4] to two-dimensional curved surfaces in three-dimensional space. This method handles the three dimensional basal topography in a simple way, making the model suitable for arbitrary (but mildly curved) topography, such as natural terrain. Furthermore, the implementation into the open source software OpenFOAM [4] is shown. OpenFOAM is a popular computational fluid dynamics application, designed so that the top-level code mimics the mathematical governing equations. This makes the code easy to read and extendable to more sophisticated models. Finally, some hints on how to get started with the code and how to extend the basic model will be given. I gratefully acknowledge the financial support by the OEAW project "beyond dense flow avalanches". Savage, S. B. & Hutter, K. 1989 The motion of a finite mass of granular material down a rough incline. Journal of Fluid Mechanics 199, 177-215. Ferziger, J. & Peric, M. 2002 Computational methods for fluid dynamics, 3rd edn. Springer. Tukovic, Z. & Jasak, H. 2012 A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow. Computers & fluids 55, 70-84. Weller, H. G., Tabor, G., Jasak, H. & Fureby, C. 1998 A tensorial approach to computational continuum mechanics using object-oriented techniques. Computers in physics 12(6), 620-631.

[Finite element stress analysis of all-ceramic continuous crowns of the lower anterior teeth in differential shoulder thickness].

PubMed

Ouyang, Shao-bo; Wang, Jun; Zhang, Hong-bin; Liao, Lan; Zhu, Hong-shui

2014-04-01

To investigate the stress distributions under load in 3 types of all-ceramic continuous crowns of the lower anterior teeth with differential shoulder thickness. Cone-beam CT (CBCT) was used to scan the in vitro mandibular central incisors, and achieve three-dimensional finite element model of all-ceramic continuous crowns with different shoulder width by using Mimics, Abaqus software. Different load conditions were simulated based on this model to study the effect of shoulder width variation on finite element analysis of 3 kinds of different all-ceramic materials of incisors fixed continuous crowns of the mandibular. Using CBCT, Mimics10.01 software and Abaqus 6.11 software, three-dimensional finite element model of all-ceramic continuous crowns of the mandibular incisor, abutment, periodontal ligament and alveolar bone was established. Different ceramic materials and various shoulder width had minor no impact on the equivalent stress peak of periodontal membrane, as well as alveolar bone. With the same shoulder width and large area of vertical loading of 120 N, the tensile stress was the largest in In-Ceram Alumina, followed by In-Ceram Zirconia and the minimum was IPS.Empress II. Under large area loading of 120 N 45° labially, when the material was IPS.Empress II, with the shoulder width increased, the porcelain plate edge of the maximum tensile stress value increased, while the other 2 materials had no obvious change. Finite element model has good geometric similarity. In the setting range of this study, when the elastic modulus of ceramic materials is bigger, the tensile stress of the continuous crown is larger. Supported by Research Project of Department of Education, Jiangxi Province (GJJ09130).

A two-dimensional, finite-difference model of the oxidation of a uranium carbide fuel pellet

NASA Astrophysics Data System (ADS)

Shepherd, James; Fairweather, Michael; Hanson, Bruce C.; Heggs, Peter J.

2015-12-01

The oxidation of spent uranium carbide fuel, a candidate fuel for Generation IV nuclear reactors, is an important process in its potential reprocessing cycle. However, the oxidation of uranium carbide in air is highly exothermic. A model has therefore been developed to predict the temperature rise, as well as other useful information such as reaction completion times, under different reaction conditions in order to help in deriving safe oxidation conditions. Finite difference-methods are used to model the heat and mass transfer processes occurring during the reaction in two dimensions and are coupled to kinetics found in the literature.

Hydrogeology of well-field areas near Tampa, Florida; Phase I, development and documentation of a two-dimensional finite-difference model for simulation of steady-state ground-water flow

USGS Publications Warehouse

Hutchinson, C.B.; Johnson, Dale M.; Gerhart, James M.

1981-01-01

A two-dimensional finite-difference model was developed for simulation of steady-state ground-water flow in the Floridan aquifer throughout a 932-square-mile area, which contains nine municipal well fields. The overlying surficial aquifer contains a constant-head water table and is coupled to the Floridan aquifer by a leakage term that represents flow through a confining layer separating the two aquifers. Under the steady-state condition, all storage terms are set to zero. Utilization of the head-controlled flux condition allows head and flow to vary at the model-grid boundaries. Procedures are described to calibrate the model, test its sensitivity to input-parameter errors, and verify its accuracy for predictive purposes. Also included are attachments that describe setting up and running the model. An example model-interrogation run shows anticipated drawdowns that should result from pumping at the newly constructed Cross Bar Ranch and Morris Bridge well fields. (USGS)

User's manual for three dimensional FDTD version C code for scattering from frequency-independent dielectric and magnetic materials

NASA Technical Reports Server (NTRS)

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

1991-01-01

The Penn State Finite Difference Time Domain Electromagnetic Scattering Code Version C is a three dimensional numerical electromagnetic scattering code based upon the Finite Difference Time Domain Technique (FDTD). The supplied version of the code is one version of our current three dimensional FDTD code set. This manual provides a description of the code and corresponding results for several scattering problems. The manual is organized into fourteen sections: introduction, description of the FDTD method, operation, resource requirements, Version C code capabilities, a brief description of the default scattering geometry, a brief description of each subroutine, a description of the include file (COMMONC.FOR), a section briefly discussing Radar Cross Section (RCS) computations, a section discussing some scattering results, a sample problem setup section, a new problem checklist, references and figure titles.

User's manual for three dimensional FDTD version D code for scattering from frequency-dependent dielectric and magnetic materials

NASA Technical Reports Server (NTRS)

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

1991-01-01

The Penn State Finite Difference Time Domain Electromagnetic Scattering Code Version D is a three dimensional numerical electromagnetic scattering code based upon the Finite Difference Time Domain Technique (FDTD). The supplied version of the code is one version of our current three dimensional FDTD code set. This manual provides a description of the code and corresponding results for several scattering problems. The manual is organized into fourteen sections: introduction, description of the FDTD method, operation, resource requirements, Version D code capabilities, a brief description of the default scattering geometry, a brief description of each subroutine, a description of the include file (COMMOND.FOR), a section briefly discussing Radar Cross Section (RCS) computations, a section discussing some scattering results, a sample problem setup section, a new problem checklist, references and figure titles.

User's manual for three dimensional FDTD version A code for scattering from frequency-independent dielectric materials

NASA Technical Reports Server (NTRS)

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

1992-01-01

The Penn State Finite Difference Time Domain (FDTD) Electromagnetic Scattering Code Version A is a three dimensional numerical electromagnetic scattering code based on the Finite Difference Time Domain technique. The supplied version of the code is one version of our current three dimensional FDTD code set. The manual provides a description of the code and the corresponding results for the default scattering problem. The manual is organized into 14 sections: introduction, description of the FDTD method, operation, resource requirements, Version A code capabilities, a brief description of the default scattering geometry, a brief description of each subroutine, a description of the include file (COMMONA.FOR), a section briefly discussing radar cross section (RCS) computations, a section discussing the scattering results, a sample problem setup section, a new problem checklist, references, and figure titles.

User's manual for three dimensional FDTD version C code for scattering from frequency-independent dielectric and magnetic materials

NASA Technical Reports Server (NTRS)

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

1992-01-01

The Penn State Finite Difference Time Domain Electromagnetic Scattering Code Version C is a three-dimensional numerical electromagnetic scattering code based on the Finite Difference Time Domain (FDTD) technique. The supplied version of the code is one version of our current three-dimensional FDTD code set. The manual given here provides a description of the code and corresponding results for several scattering problems. The manual is organized into 14 sections: introduction, description of the FDTD method, operation, resource requirements, Version C code capabilities, a brief description of the default scattering geometry, a brief description of each subroutine, a description of the include file (COMMONC.FOR), a section briefly discussing radar cross section computations, a section discussing some scattering results, a new problem checklist, references, and figure titles.

User's manual for three dimensional FDTD version B code for scattering from frequency-dependent dielectric materials

NASA Technical Reports Server (NTRS)

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

1991-01-01

The Penn State Finite Difference Time Domain Electromagnetic Scattering Code Version B is a three dimensional numerical electromagnetic scattering code based upon the Finite Difference Time Domain Technique (FDTD). The supplied version of the code is one version of our current three dimensional FDTD code set. This manual provides a description of the code and corresponding results for several scattering problems. The manual is organized into fourteen sections: introduction, description of the FDTD method, operation, resource requirements, Version B code capabilities, a brief description of the default scattering geometry, a brief description of each subroutine, a description of the include file (COMMONB.FOR), a section briefly discussing Radar Cross Section (RCS) computations, a section discussing some scattering results, a sample problem setup section, a new problem checklist, references and figure titles.

Cochlear pharmacokinetics with local inner ear drug delivery using a three-dimensional finite-element computer model.

PubMed

Plontke, Stefan K; Siedow, Norbert; Wegener, Raimund; Zenner, Hans-Peter; Salt, Alec N

2007-01-01

Cochlear fluid pharmacokinetics can be better represented by three-dimensional (3D) finite-element simulations of drug dispersal. Local drug deliveries to the round window membrane are increasingly being used to treat inner ear disorders. Crucial to the development of safe therapies is knowledge of drug distribution in the inner ear with different delivery methods. Computer simulations allow application protocols and drug delivery systems to be evaluated, and may permit animal studies to be extrapolated to the larger cochlea of the human. A finite-element 3D model of the cochlea was constructed based on geometric dimensions of the guinea pig cochlea. Drug propagation along and between compartments was described by passive diffusion. To demonstrate the potential value of the model, methylprednisolone distribution in the cochlea was calculated for two clinically relevant application protocols using pharmacokinetic parameters derived from a prior one-dimensional (1D) model. In addition, a simplified geometry was used to compare results from 3D with 1D simulations. For the simplified geometry, calculated concentration profiles with distance were in excellent agreement between the 1D and the 3D models. Different drug delivery strategies produce very different concentration time courses, peak concentrations and basal-apical concentration gradients of drug. In addition, 3D computations demonstrate the existence of substantial gradients across the scalae in the basal turn. The 3D model clearly shows the presence of drug gradients across the basal scalae of guinea pigs, demonstrating the necessity of a 3D approach to predict drug movements across and between scalae with larger cross-sectional areas, such as the human, with accuracy. This is the first model to incorporate the volume of the spiral ligament and to calculate diffusion through this structure. Further development of the 3D model will have to incorporate a more accurate geometry of the entire inner ear and incorporate more of the specific processes that contribute to drug removal from the inner ear fluids. Appropriate computer models may assist in both drug and drug delivery system design and can thus accelerate the development of a rationale-based local drug delivery to the inner ear and its successful establishment in clinical practice. Copyright 2007 S. Karger AG, Basel.

Cochlear Pharmacokinetics with Local Inner Ear Drug Delivery Using a Three-Dimensional Finite-Element Computer Model

PubMed Central

Plontke, Stefan K.; Siedow, Norbert; Wegener, Raimund; Zenner, Hans-Peter; Salt, Alec N.

2006-01-01

Hypothesis: Cochlear fluid pharmacokinetics can be better represented by three-dimensional (3D) finite-element simulations of drug dispersal. Background: Local drug deliveries to the round window membrane are increasingly being used to treat inner ear disorders. Crucial to the development of safe therapies is knowledge of drug distribution in the inner ear with different delivery methods. Computer simulations allow application protocols and drug delivery systems to be evaluated, and may permit animal studies to be extrapolated to the larger cochlea of the human. Methods: A finite-element 3D model of the cochlea was constructed based on geometric dimensions of the guinea pig cochlea. Drug propagation along and between compartments was described by passive diffusion. To demonstrate the potential value of the model, methylprednisolone distribution in the cochlea was calculated for two clinically relevant application protocols using pharmacokinetic parameters derived from a prior one-dimensional (1D) model. In addition, a simplified geometry was used to compare results from 3D with 1D simulations. Results: For the simplified geometry, calculated concentration profiles with distance were in excellent agreement between the 1D and the 3D models. Different drug delivery strategies produce very different concentration time courses, peak concentrations and basal-apical concentration gradients of drug. In addition, 3D computations demonstrate the existence of substantial gradients across the scalae in the basal turn. Conclusion: The 3D model clearly shows the presence of drug gradients across the basal scalae of guinea pigs, demonstrating the necessity of a 3D approach to predict drug movements across and between scalae with larger cross-sectional areas, such as the human, with accuracy. This is the first model to incorporate the volume of the spiral ligament and to calculate diffusion through this structure. Further development of the 3D model will have to incorporate a more accurate geometry of the entire inner ear and incorporate more of the specific processes that contribute to drug removal from the inner ear fluids. Appropriate computer models may assist in both drug and drug delivery system design and can thus accelerate the development of a rationale-based local drug delivery to the inner ear and its successful establishment in clinical practice. PMID:17119332

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.

Cavity master equation for the continuous time dynamics of discrete-spin models.

PubMed

Aurell, E; Del Ferraro, G; Domínguez, E; Mulet, R

2017-05-01

We present an alternate method to close the master equation representing the continuous time dynamics of interacting Ising spins. The method makes use of the theory of random point processes to derive a master equation for local conditional probabilities. We analytically test our solution studying two known cases, the dynamics of the mean-field ferromagnet and the dynamics of the one-dimensional Ising system. We present numerical results comparing our predictions with Monte Carlo simulations in three different models on random graphs with finite connectivity: the Ising ferromagnet, the random field Ising model, and the Viana-Bray spin-glass model.

Cavity master equation for the continuous time dynamics of discrete-spin models

NASA Astrophysics Data System (ADS)

Aurell, E.; Del Ferraro, G.; Domínguez, E.; Mulet, R.

2017-05-01

We present an alternate method to close the master equation representing the continuous time dynamics of interacting Ising spins. The method makes use of the theory of random point processes to derive a master equation for local conditional probabilities. We analytically test our solution studying two known cases, the dynamics of the mean-field ferromagnet and the dynamics of the one-dimensional Ising system. We present numerical results comparing our predictions with Monte Carlo simulations in three different models on random graphs with finite connectivity: the Ising ferromagnet, the random field Ising model, and the Viana-Bray spin-glass model.

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.

Finite-temperature spin dynamics in a perturbed quantum critical Ising chain with an E₈ symmetry.

PubMed

Wu, Jianda; Kormos, Márton; Si, Qimiao

2014-12-12

A spectrum exhibiting E₈ symmetry is expected to arise when a small longitudinal field is introduced in the transverse-field Ising chain at its quantum critical point. Evidence for this spectrum has recently come from neutron scattering measurements in cobalt niobate, a quasi-one-dimensional Ising ferromagnet. Unlike its zero-temperature counterpart, the finite-temperature dynamics of the model has not yet been determined. We study the dynamical spin structure factor of the model at low frequencies and nonzero temperatures, using the form factor method. Its frequency dependence is singular, but differs from the diffusion form. The temperature dependence of the nuclear magnetic resonance (NMR) relaxation rate has an activated form, whose prefactor we also determine. We propose NMR experiments as a means to further test the applicability of the E₈ description for CoNb₂O₆.

Comparison of SOM point densities based on different criteria.

PubMed

Kohonen, T

1999-11-15

Point densities of model (codebook) vectors in self-organizing maps (SOMs) are evaluated in this article. For a few one-dimensional SOMs with finite grid lengths and a given probability density function of the input, the numerically exact point densities have been computed. The point density derived from the SOM algorithm turned out to be different from that minimizing the SOM distortion measure, showing that the model vectors produced by the basic SOM algorithm in general do not exactly coincide with the optimum of the distortion measure. A new computing technique based on the calculus of variations has been introduced. It was applied to the computation of point densities derived from the distortion measure for both the classical vector quantization and the SOM with general but equal dimensionality of the input vectors and the grid, respectively. The power laws in the continuum limit obtained in these cases were found to be identical.

Decay of Bogoliubov excitations in one-dimensional Bose gases

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

Ristivojevic, Zoran; Matveev, K. A.

For this research, we study the decay of Bogoliubov quasiparticles in one-dimensional Bose gases. Starting from the hydrodynamic Hamiltonian, we develop a microscopic theory that enables one to systematically study both the excitations and their decay. At zero temperature, the leading mechanism of decay of a quasiparticle is disintegration into three others. We find that low-energy quasiparticles (phonons) decay with the rate that scales with the seventh power of momentum, whereas the rate of decay of the high-energy quasiparticles does not depend on momentum. In addition, our approach allows us to study analytically the quasiparticle decay in the whole crossovermore » region between the two limiting cases. When applied to integrable models, including the Lieb-Liniger model of bosons with contact repulsion, our theory confirms the absence of the decay of quasiparticle excitations. Finally, we account for two types of integrability-breaking perturbations that enable finite decay: three-body interaction between the bosons and two-body interaction of finite range.« less

Decay of Bogoliubov excitations in one-dimensional Bose gases

DOE PAGES

Ristivojevic, Zoran; Matveev, K. A.

2016-07-11

For this research, we study the decay of Bogoliubov quasiparticles in one-dimensional Bose gases. Starting from the hydrodynamic Hamiltonian, we develop a microscopic theory that enables one to systematically study both the excitations and their decay. At zero temperature, the leading mechanism of decay of a quasiparticle is disintegration into three others. We find that low-energy quasiparticles (phonons) decay with the rate that scales with the seventh power of momentum, whereas the rate of decay of the high-energy quasiparticles does not depend on momentum. In addition, our approach allows us to study analytically the quasiparticle decay in the whole crossovermore » region between the two limiting cases. When applied to integrable models, including the Lieb-Liniger model of bosons with contact repulsion, our theory confirms the absence of the decay of quasiparticle excitations. Finally, we account for two types of integrability-breaking perturbations that enable finite decay: three-body interaction between the bosons and two-body interaction of finite range.« less

Computational Modeling of Electrochemical-Poroelastic Bending Behaviors of Conducting Polymer (PPy) Membranes

NASA Astrophysics Data System (ADS)

Toi, Yutaka; Jung, Woosang

The electrochemical-poroelastic bending behavior of conducting polymer actuators has an attractive feature, considering their potential applications such as artificial muscles or MEMS. In the present study, a computational modeling is presented for the bending behavior of polypyrrole-based actuators. The one-dimensional governing equation for the ionic transportation in electrolytes given by Tadokoro et al. is combined with the finite element modeling for the poroelastic behavior of polypyrroles considering the effect of finite deformation. The validity of the proposed model has been illustrated by comparing the computed results with the experimental results in the literatures.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 2: Derivation of finite-element equations and comparisons with analytical solutions

USGS Publications Warehouse

Cooley, Richard L.

1992-01-01

MODFE, a modular finite-element model for simulating steady- or unsteady-state, area1 or axisymmetric flow of ground water in a heterogeneous anisotropic aquifer is documented in a three-part series of reports. In this report, part 2, the finite-element equations are derived by minimizing a functional of the difference between the true and approximate hydraulic head, which produces equations that are equivalent to those obtained by either classical variational or Galerkin techniques. Spatial finite elements are triangular with linear basis functions, and temporal finite elements are one dimensional with linear basis functions. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining units; (3) specified recharge or discharge at points, along lines, or areally; (4) flow across specified-flow, specified-head, or head-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining units combined with aquifer dewatering, and evapotranspiration. The matrix equations produced by the finite-element method are solved by the direct symmetric-Doolittle method or the iterative modified incomplete-Cholesky conjugate-gradient method. The direct method can be efficient for small- to medium-sized problems (less than about 500 nodes), and the iterative method is generally more efficient for larger-sized problems. Comparison of finite-element solutions with analytical solutions for five example problems demonstrates that the finite-element model can yield accurate solutions to ground-water flow problems.

Creating physically-based three-dimensional microstructures: Bridging phase-field and crystal plasticity models.

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

Lim, Hojun; Owen, Steven J.; Abdeljawad, Fadi F.

In order to better incorporate microstructures in continuum scale models, we use a novel finite element (FE) meshing technique to generate three-dimensional polycrystalline aggregates from a phase field grain growth model of grain microstructures. The proposed meshing technique creates hexahedral FE meshes that capture smooth interfaces between adjacent grains. Three dimensional realizations of grain microstructures from the phase field model are used in crystal plasticity-finite element (CP-FE) simulations of polycrystalline a -iron. We show that the interface conformal meshes significantly reduce artificial stress localizations in voxelated meshes that exhibit the so-called "wedding cake" interfaces. This framework provides a direct linkmore » between two mesoscale models - phase field and crystal plasticity - and for the first time allows mechanics simulations of polycrystalline materials using three-dimensional hexahedral finite element meshes with realistic topological features.« less

Large Eddy Simulation ... Where Do We Stand? International Workshop Held in St. Petersburg Beach, Florida on 19-21 December 1990.

DTIC Science & Technology

1990-01-01

S. Orszag, Chairman 1. P. Moin Some Issues in Computation of Turbulent Flows. 2. M. Lesieur, P. Comte, X. Normand, 0. Metais and A. Silveira Spectral...Richtmeyer’s computational experience with one-dimensional shock waves (1950) indicated the value of a non-linear artificial viscosity. Charney and... computer architecture and the advantages of semi-Lagrangian advective schemes may lure large-scale atmospheric modelers back to finite-difference

Analysis of combustion instability in liquid fuel rocket motors. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Wong, K. W.

1979-01-01

The development of an analytical technique used in the solution of nonlinear velocity-sensitive combustion instability problems is presented. The Galerkin method was used and proved successful. The pressure wave forms exhibit a strong second harmonic distortion and a variety of behaviors are possible depending on the nature of the combustion process and the parametric values involved. A one dimensional model provides insight into the problem by allowing a comparison of Galerkin solutions with more exact finite difference computations.

Two-Dimensional Grids About Airfoils and Other Shapes

NASA Technical Reports Server (NTRS)

Sorenson, R.

1982-01-01

GRAPE computer program generates two-dimensional finite-difference grids about airfoils and other shapes by use of Poisson differential equation. GRAPE can be used with any boundary shape, even one specified by tabulated points and including limited number of sharp corners. Numerically stable and computationally fast, GRAPE provides aerodynamic analyst with efficient and consistant means of grid generation.

A finite volume model simulation for the Broughton Archipelago, Canada

NASA Astrophysics Data System (ADS)

Foreman, M. G. G.; Czajko, P.; Stucchi, D. J.; Guo, M.

A finite volume circulation model is applied to the Broughton Archipelago region of British Columbia, Canada and used to simulate the three-dimensional velocity, temperature, and salinity fields that are required by a companion model for sea lice behaviour, development, and transport. The absence of a high resolution atmospheric model necessitated the installation of nine weather stations throughout the region and the development of a simple data assimilation technique that accounts for topographic steering in interpolating/extrapolating the measured winds to the entire model domain. The circulation model is run for the period of March 13-April 3, 2008 and correlation coefficients between observed and model currents, comparisons between model and observed tidal harmonics, and root mean square differences between observed and model temperatures and salinities all showed generally good agreement. The importance of wind forcing in the near-surface circulation, differences between this simulation and one computed with another model, the effects of bathymetric smoothing on channel velocities, further improvements necessary for this model to accurately simulate conditions in May and June, and the implication of near-surface current patterns at a critical location in the 'migration corridor' of wild juvenile salmon, are also discussed.

Analysis and test for space shuttle propellant dynamics

NASA Technical Reports Server (NTRS)

Berry, R. L.; Demchak, L. J.; Tegart, J. R.

1983-01-01

This report presents the results of a study to develop an analytical model capable of predicting the dynamic interaction forces on the Shuttle External Tank, due to large amplitude propellant slosh during RTLS separation. The report details low-g drop tower and KC-135 test programs that were conducted to investigate propellant reorientation during RTLS. In addition, the development of a nonlinear finite element slosh model (LAMPS2, two dimensional, and one LAMPS3, three dimensional) is presented. Correlation between the model and test data is presented as a verification of the modeling approach.

Study on Damage Evaluation and Machinability of UD-CFRP for the Orthogonal Cutting Operation Using Scanning Acoustic Microscopy and the Finite Element Method.

PubMed

Wang, Dongyao; He, Xiaodong; Xu, Zhonghai; Jiao, Weicheng; Yang, Fan; Jiang, Long; Li, Linlin; Liu, Wenbo; Wang, Rongguo

2017-02-20

Owing to high specific strength and designability, unidirectional carbon fiber reinforced polymer (UD-CFRP) has been utilized in numerous fields to replace conventional metal materials. Post machining processes are always required for UD-CFRP to achieve dimensional tolerance and assembly specifications. Due to inhomogeneity and anisotropy, UD-CFRP differs greatly from metal materials in machining and failure mechanism. To improve the efficiency and avoid machining-induced damage, this paper undertook to study the correlations between cutting parameters, fiber orientation angle, cutting forces, and cutting-induced damage for UD-CFRP laminate. Scanning acoustic microscopy (SAM) was employed and one-/two-dimensional damage factors were then created to quantitatively characterize the damage of the laminate workpieces. According to the 3D Hashin's criteria a numerical model was further proposed in terms of the finite element method (FEM). A good agreement between simulation and experimental results was validated for the prediction and structural optimization of the UD-CFRP.

Study on Damage Evaluation and Machinability of UD-CFRP for the Orthogonal Cutting Operation Using Scanning Acoustic Microscopy and the Finite Element Method

PubMed Central

Wang, Dongyao; He, Xiaodong; Xu, Zhonghai; Jiao, Weicheng; Yang, Fan; Jiang, Long; Li, Linlin; Liu, Wenbo; Wang, Rongguo

2017-01-01

Owing to high specific strength and designability, unidirectional carbon fiber reinforced polymer (UD-CFRP) has been utilized in numerous fields to replace conventional metal materials. Post machining processes are always required for UD-CFRP to achieve dimensional tolerance and assembly specifications. Due to inhomogeneity and anisotropy, UD-CFRP differs greatly from metal materials in machining and failure mechanism. To improve the efficiency and avoid machining-induced damage, this paper undertook to study the correlations between cutting parameters, fiber orientation angle, cutting forces, and cutting-induced damage for UD-CFRP laminate. Scanning acoustic microscopy (SAM) was employed and one-/two-dimensional damage factors were then created to quantitatively characterize the damage of the laminate workpieces. According to the 3D Hashin’s criteria a numerical model was further proposed in terms of the finite element method (FEM). A good agreement between simulation and experimental results was validated for the prediction and structural optimization of the UD-CFRP. PMID:28772565

Bearing-Load Modeling and Analysis Study for Mechanically Connected Structures

NASA Technical Reports Server (NTRS)

Knight, Norman F., Jr.

2006-01-01

Bearing-load response for a pin-loaded hole is studied within the context of two-dimensional finite element analyses. Pin-loaded-hole configurations are representative of mechanically connected structures, such as a stiffener fastened to a rib of an isogrid panel, that are idealized as part of a larger structural component. Within this context, the larger structural component may be idealized as a two-dimensional shell finite element model to identify load paths and high stress regions. Finite element modeling and analysis aspects of a pin-loaded hole are considered in the present paper including the use of linear and nonlinear springs to simulate the pin-bearing contact condition. Simulating pin-connected structures within a two-dimensional finite element analysis model using nonlinear spring or gap elements provides an effective way for accurate prediction of the local effective stress state and peak forces.

Parallel numerical modeling of hybrid-dimensional compositional non-isothermal Darcy flows in fractured porous media

NASA Astrophysics Data System (ADS)

Xing, F.; Masson, R.; Lopez, S.

2017-09-01

This paper introduces a new discrete fracture model accounting for non-isothermal compositional multiphase Darcy flows and complex networks of fractures with intersecting, immersed and non-immersed fractures. The so called hybrid-dimensional model using a 2D model in the fractures coupled with a 3D model in the matrix is first derived rigorously starting from the equi-dimensional matrix fracture model. Then, it is discretized using a fully implicit time integration combined with the Vertex Approximate Gradient (VAG) finite volume scheme which is adapted to polyhedral meshes and anisotropic heterogeneous media. The fully coupled systems are assembled and solved in parallel using the Single Program Multiple Data (SPMD) paradigm with one layer of ghost cells. This strategy allows for a local assembly of the discrete systems. An efficient preconditioner is implemented to solve the linear systems at each time step and each Newton type iteration of the simulation. The numerical efficiency of our approach is assessed on different meshes, fracture networks, and physical settings in terms of parallel scalability, nonlinear convergence and linear convergence.

A generalized volumetric dispersion model for a class of two-phase separation/reaction: finite difference solutions

NASA Astrophysics Data System (ADS)

Siripatana, Chairat; Thongpan, Hathaikarn; Promraksa, Arwut

2017-03-01

This article explores a volumetric approach in formulating differential equations for a class of engineering flow problems involving component transfer within or between two phases. In contrast to conventional formulation which is based on linear velocities, this work proposed a slightly different approach based on volumetric flow-rate which is essentially constant in many industrial processes. In effect, many multi-dimensional flow problems found industrially can be simplified into multi-component or multi-phase but one-dimensional flow problems. The formulation is largely generic, covering counter-current, concurrent or batch, fixed and fluidized bed arrangement. It was also intended to use for start-up, shut-down, control and steady state simulation. Since many realistic and industrial operation are dynamic with variable velocity and porosity in relation to position, analytical solutions are rare and limited to only very simple cases. Thus we also provide a numerical solution using Crank-Nicolson finite difference scheme. This solution is inherently stable as tested against a few cases published in the literature. However, it is anticipated that, for unconfined flow or non-constant flow-rate, traditional formulation should be applied.

[Three-dimensional finite element stress distribution and displacement analysis of alveolar ridge retained by conical telescope].

PubMed

Lin, Ying-he; Man, Yi; Liang, Xing; Qu, Yi-li; Lu, Xuan

2004-11-01

To study the stress distribution and displacement of edentulous alveolar ridge of removable partial denture which is retained by using conical telescope. An ideal three dimensional finite element model was constructed by using SCT image reconstruction technique, self-programming and ANSYS software. The static load was applied. The stress and displacement characteristics of these different types of materials which form the metal part of the conical telescope were compared and analyzed. Generally, the four materials produced almost the same stress and displacement at the site of the edentulous alveolar ridge. From the viewpoint of dynamics, the application of different materials in making the metal part of conical telescope is feasible.

Explorations in fuzzy physics and non-commutative geometry

NASA Astrophysics Data System (ADS)

Kurkcuoglu, Seckin

Fuzzy spaces arise as discrete approximations to continuum manifolds. They are usually obtained through quantizing coadjoint orbits of compact Lie groups and they can be described in terms of finite-dimensional matrix algebras, which for large matrix sizes approximate the algebra of functions of the limiting continuum manifold. Their ability to exactly preserve the symmetries of their parent manifolds is especially appealing for physical applications. Quantum Field Theories are built over them as finite-dimensional matrix models preserving almost all the symmetries of their respective continuum models. In this dissertation, we first focus our attention to the study of fuzzy supersymmetric spaces. In this regard, we obtain the fuzzy supersphere S2,2F through quantizing the supersphere, and demonstrate that it has exact supersymmetry. We derive a finite series formula for the *-product of functions over S2,2F and analyze the differential geometric information encoded in this formula. Subsequently, we show that quantum field theories on S2,2F are realized as finite-dimensional supermatrix models, and in particular we obtain the non-linear sigma model over the fuzzy supersphere by constructing the fuzzy supersymmetric extensions of a certain class of projectors. We show that this model too, is realized as a finite-dimensional supermatrix model with exact supersymmetry. Next, we show that fuzzy spaces have a generalized Hopf algebra structure. By focusing on the fuzzy sphere, we establish that there is a *-homomorphism from the group algebra SU(2)* of SU(2) to the fuzzy sphere. Using this and the canonical Hopf algebra structure of SU(2)* we show that both the fuzzy sphere and their direct sum are Hopf algebras. Using these results, we discuss processes in which a fuzzy sphere with angular momenta J splits into fuzzy spheres with angular momenta K and L. Finally, we study the formulation of Chern-Simons (CS) theory on an infinite strip of the non-commutative plane. We develop a finite-dimensional matrix model, whose large size limit approximates the CS theory on the infinite strip, and show that there are edge observables in this model obeying a finite-dimensional Lie algebra, that resembles the Kac-Moody algebra.

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.

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.

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.

Construction and validation of a three-dimensional finite element model of degenerative scoliosis.

PubMed

Zheng, Jie; Yang, Yonghong; Lou, Shuliang; Zhang, Dongsheng; Liao, Shenghui

2015-12-24

With the aging of the population, degenerative scoliosis (DS) incidence rate is increasing. In recent years, increasing research on this topic has been carried out, yet biomechanical research on the subject is seldom seen and in vitro biomechanical model of DS nearly cannot be available. The objective of this study was to develop and validate a complete three-dimensional finite element model of DS in order to build the digital platform for further biomechanical study. A 55-year-old female DS patient (Suer Pan, ID number was P141986) was selected for this study. This study was performed in accordance with the ethical standards of Declaration of Helsinki and its amendments and was approved by the local ethics committee (117 hospital of PLA ethics committee). Spiral computed tomography (CT) scanning was conducted on the patient's lumbar spine from the T12 to S1. CT images were then imported into a finite element modeling system. A three-dimensional solid model was then formed from segmentation of the CT scan. The three-dimensional model of each vertebra was then meshed, and material properties were assigned to each element according to the pathological characteristics of DS. Loads and boundary conditions were then applied in such a manner as to simulate in vitro biomechanical experiments conducted on lumbar segments. The results of the model were then compared with experimental results in order to validate the model. An integral three-dimensional finite element model of DS was built successfully, consisting of 113,682 solid elements, 686 cable elements, 33,329 shell elements, 4968 target elements, 4968 contact elements, totaling 157,635 elements, and 197,374 nodes. The model accurately described the physical features of DS and was geometrically similar to the object of study. The results of analysis with the finite element model agreed closely with in vitro experiments, validating the accuracy of the model. The three-dimensional finite element model of DS built in this study is clear, reliable, and effective for further biomechanical simulation study of DS.

An adaptive mesh-moving and refinement procedure for one-dimensional conservation laws

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Flaherty, Joseph E.; Arney, David C.

1993-01-01

We examine the performance of an adaptive mesh-moving and /or local mesh refinement procedure for the finite difference solution of one-dimensional hyperbolic systems of conservation laws. Adaptive motion of a base mesh is designed to isolate spatially distinct phenomena, and recursive local refinement of the time step and cells of the stationary or moving base mesh is performed in regions where a refinement indicator exceeds a prescribed tolerance. These adaptive procedures are incorporated into a computer code that includes a MacCormack finite difference scheme wih Davis' artificial viscosity model and a discretization error estimate based on Richardson's extrapolation. Experiments are conducted on three problems in order to qualify the advantages of adaptive techniques relative to uniform mesh computations and the relative benefits of mesh moving and refinement. Key results indicate that local mesh refinement, with and without mesh moving, can provide reliable solutions at much lower computational cost than possible on uniform meshes; that mesh motion can be used to improve the results of uniform mesh solutions for a modest computational effort; that the cost of managing the tree data structure associated with refinement is small; and that a combination of mesh motion and refinement reliably produces solutions for the least cost per unit accuracy.

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.

Random isotropic one-dimensional XY-model

NASA Astrophysics Data System (ADS)

Gonçalves, L. L.; Vieira, A. P.

1998-01-01

The 1D isotropic s = ½XY-model ( N sites), with random exchange interaction in a transverse random field is considered. The random variables satisfy bimodal quenched distributions. The solution is obtained by using the Jordan-Wigner fermionization and a canonical transformation, reducing the problem to diagonalizing an N × N matrix, corresponding to a system of N noninteracting fermions. The calculations are performed numerically for N = 1000, and the field-induced magnetization at T = 0 is obtained by averaging the results for the different samples. For the dilute case, in the uniform field limit, the magnetization exhibits various discontinuities, which are the consequence of the existence of disconnected finite clusters distributed along the chain. Also in this limit, for finite exchange constants J A and J B, as the probability of J A varies from one to zero, the saturation field is seen to vary from Γ A to Γ B, where Γ A(Γ B) is the value of the saturation field for the pure case with exchange constant equal to J A(J B) .

BIOPLUME III: NATURAL ATTENTUATION DECISION SUPPORT SYSTEM USER'S MANUAL - VERSION 1.0

EPA Science Inventory

The BIOPLUME III program is a two-dimensional, finite difference model for simulating the natural attenuation of organic contaminants in ground water due to the processes of advection, dispersion, sorption, and biodegradation. The model simulates the biodegradation of organic...

Progress in multi-dimensional upwind differencing

NASA Technical Reports Server (NTRS)

Vanleer, Bram

1992-01-01

Multi-dimensional upwind-differencing schemes for the Euler equations are reviewed. On the basis of the first-order upwind scheme for a one-dimensional convection equation, the two approaches to upwind differencing are discussed: the fluctuation approach and the finite-volume approach. The usual extension of the finite-volume method to the multi-dimensional Euler equations is not entirely satisfactory, because the direction of wave propagation is always assumed to be normal to the cell faces. This leads to smearing of shock and shear waves when these are not grid-aligned. Multi-directional methods, in which upwind-biased fluxes are computed in a frame aligned with a dominant wave, overcome this problem, but at the expense of robustness. The same is true for the schemes incorporating a multi-dimensional wave model not based on multi-dimensional data but on an 'educated guess' of what they could be. The fluctuation approach offers the best possibilities for the development of genuinely multi-dimensional upwind schemes. Three building blocks are needed for such schemes: a wave model, a way to achieve conservation, and a compact convection scheme. Recent advances in each of these components are discussed; putting them all together is the present focus of a worldwide research effort. Some numerical results are presented, illustrating the potential of the new multi-dimensional schemes.

Cellular interface morphologies in directional solidification. III - The effects of heat transfer and solid diffusivity

NASA Technical Reports Server (NTRS)

Ungar, Lyle H.; Bennett, Mark J.; Brown, Robert A.

1985-01-01

The shape and stability of two-dimensional finite-amplitude cellular interfaces arising during directional solidification are compared for several solidification models that account differently for latent heat released at the interface, unequal thermal conductivities of melt and solid, and solute diffusivity in the solid. Finite-element analysis and computer-implemented perturbation methods are used to analyze the families of steadily growing cellular forms that evolve from the planar state. In all models a secondary bifurcation between different families of finite-amplitude cells exists that halves the spatial wavelength of the stable interface. The quantitative location of this transition is very dependent on the details of the model. Large amounts of solute diffusion in the solid retard the growth of large-amplitude cells.

Lattice vibrations in the Frenkel-Kontorova model. I. Phonon dispersion, number density, and energy

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

Meng, Qingping; Wu, Lijun; Welch, David O.

2015-06-17

We studied the lattice vibrations of two inter-penetrating atomic sublattices via the Frenkel-Kontorova (FK) model of a linear chain of harmonically interacting atoms subjected to an on-site potential, using the technique of thermodynamic Green's functions based on quantum field-theoretical methods. General expressions were deduced for the phonon frequency-wave-vector dispersion relations, number density, and energy of the FK model system. In addition, as the application of the theory, we investigated in detail cases of linear chains with various periods of the on-site potential of the FK model. Some unusual but interesting features for different amplitudes of the on-site potential of themore » FK model are discussed. In the commensurate structure, the phonon spectrum always starts at a finite frequency, and the gaps of the spectrum are true ones with a zero density of modes. In the incommensurate structure, the phonon spectrum starts from zero frequency, but at a non-zero wave vector; there are some modes inside these gap regions, but their density is very low. In our approximation, the energy of a higher-order commensurate state of the one-dimensional system at a finite temperature may become indefinitely close to the energy of an incommensurate state. This finding implies that the higher-order incommensurate-commensurate transitions are continuous ones and that the phase transition may exhibit a “devil's staircase” behavior at a finite temperature.« less

A discontinuous Galerkin method for two-dimensional PDE models of Asian options

NASA Astrophysics Data System (ADS)

Hozman, J.; Tichý, T.; Cvejnová, D.

2016-06-01

In our previous research we have focused on the problem of plain vanilla option valuation using discontinuous Galerkin method for numerical PDE solution. Here we extend a simple one-dimensional problem into two-dimensional one and design a scheme for valuation of Asian options, i.e. options with payoff depending on the average of prices collected over prespecified horizon. The algorithm is based on the approach combining the advantages of the finite element methods together with the piecewise polynomial generally discontinuous approximations. Finally, an illustrative example using DAX option market data is provided.

Rarefied gas flow through two-dimensional nozzles

NASA Technical Reports Server (NTRS)

De Witt, Kenneth J.; Jeng, Duen-Ren; Keith, Theo G., Jr.; Chung, Chan-Hong

1989-01-01

A kinetic theory analysis is made of the flow of a rarefied gas from one reservoir to another through two-dimensional nozzles with arbitrary curvature. The Boltzmann equation simplified by a model collision integral is solved by means of finite-difference approximations with the discrete ordinate method. The physical space is transformed by a general grid generation technique and the velocity space is transformed to a polar coordinate system. A numerical code is developed which can be applied to any two-dimensional passage of complicated geometry for the flow regimes from free-molecular to slip. Numerical values of flow quantities can be calculated for the entire physical space including both inside the nozzle and in the outside plume. Predictions are made for the case of parallel slots and compared with existing literature data. Also, results for the cases of convergent or divergent slots and two-dimensional nozzles with arbitrary curvature at arbitrary knudsen number are presented.

Quantum Monte Carlo study of spin correlations in the one-dimensional Hubbard model

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

Sandvik, A.W.; Scalapino, D.J.; Singh, C.

1993-07-15

The one-dimensional Hubbard model is studied at and close to half-filling using a generalization of Handscomb's quantum Monte Carlo method. Results for spin-correlation functions and susceptibilities are presented for systems of up to 128 sites. The spin-correlation function at low temperature is well described by a recently introduced formula relating the correlation function of a finite periodic system to the corresponding [ital T]=0 correlation function of the infinite system. For the [ital T][r arrow]0 divergence of the [ital q]=2[ital k][sub [ital F

The effect of screw tunnels on the biomechanical stability of vertebral body after pedicle screws removal: a finite element analysis.

PubMed

Liu, Jia-Ming; Zhang, Yu; Zhou, Yang; Chen, Xuan-Yin; Huang, Shan-Hu; Hua, Zi-Kai; Liu, Zhi-Li

2017-06-01

Posterior reduction and pedicle screw fixation is a widely used procedure for thoracic and lumbar vertebrae fractures. Usually, the pedicle screws would be removed after the fracture healing and screw tunnels would be left. The aim of this study is to evaluate the effect of screw tunnels on the biomechanical stability of the lumbar vertebral body after pedicle screws removal by finite element analysis (FEA). First, the CT values of the screw tunnels wall in the fractured vertebral bodies were measured in patients whose pedicle screws were removed, and they were then compared with the values of vertebral cortical bone. Second, an adult patient was included and the CT images of the lumbar spine were harvested. Three dimensional finite element models of the L1 vertebra with unilateral or bilateral screw tunnels were created based on the CT images. Different compressive loads were vertically acted on the models. The maximum loads which the models sustained and the distribution of the force in the different parts of the models were recorded and compared with each other. The CT values of the tunnels wall and vertebral cortical bone were 387.126±62.342 and 399.204±53.612, which were not statistically different (P=0.149). The models of three dimensional tetrahedral mesh finite element of normal lumbar 1 vertebra were established with good geometric similarity and realistic appearance. After given the compressive loads, the cortical bone was the first one to reach its ultimate stress. The maximum loads which the bilateral screw tunnels model, unilateral screw tunnel model, and normal vertebral model can sustain were 3.97 Mpa, 3.83 Mpa, and 3.78 Mpa, respectively. For the diameter of the screw tunnels, the model with a diameter of 6.5 mm could sustain the largest load. In addition, the stress distributing on the outside of the cortical bone gradually decreased as the thickness of the tunnel wall increased. Based on the FEA, pedicle screw tunnels would not decrease the biomechanical stability and strength of the vertebral body. A large diameter of screw tunnel and thick tunnel wall were helpful for the biomechanical stability of the vertebral body.

Performance analysis of successive over relaxation method for solving glioma growth model

NASA Astrophysics Data System (ADS)

Hussain, Abida; Faye, Ibrahima; Muthuvalu, Mohana Sundaram

2016-11-01

Brain tumor is one of the prevalent cancers in the world that lead to death. In light of the present information of the properties of gliomas, mathematical models have been developed by scientists to quantify the proliferation and invasion dynamics of glioma. In this study, one-dimensional glioma growth model is considered, and finite difference method is used to discretize the problem. Then, two stationary methods, namely Gauss-Seidel (GS) and Successive Over Relaxation (SOR) are used to solve the governing algebraic system. The performance of the methods are evaluated in terms of number of iteration and computational time. On the basis of performance analysis, SOR method is shown to be more superior compared to GS method.

Photothermal modeling of thulium fibre laser-tissue interactions

NASA Astrophysics Data System (ADS)

Warnaby, Catherine E.; Coleman, Daniel J.; King, Terence A.

2003-10-01

A one-dimensional finite difference model has been used to investigate the temperature distribution within thulium fibre laser-irradiated tissue. Temperature-time and temperature-depth profiles are presented for various laser stimulus parameters in the 2 micron region. These current calculations are aimed at determining theoretical temperature distributions in the application of relatively low power fibre lasers for thermal stimulation of cutaneous nerves in human pain processing. Theoretical skin surface temperatures are compared with those from thermal camera measurements during thulium fibre laser irradiation. The effectiveness of the thulium fibre laser for thermally stimulating cutaneous nerves is confirmed.

Broadband Ground Motion Synthesis of the 1999 Turkey Earthquakes Based On: 3-D Velocity Inversion, Finite Difference Calculations and Emprical Greens Functions

NASA Astrophysics Data System (ADS)

Gok, R.; Kalafat, D.; Hutchings, L.

2003-12-01

We analyze over 3,500 aftershocks recorded by several seismic networks during the 1999 Marmara, Turkey earthquakes. The analysis provides source parameters of the aftershocks, a three-dimensional velocity structure from tomographic inversion, an input three-dimensional velocity model for a finite difference wave propagation code (E3D, Larsen 1998), and records available for use as empirical Green's functions. Ultimately our goal is to model the 1999 earthquakes from DC to 25 Hz and study fault rupture mechanics and kinematic rupture models. We performed the simultaneous inversion for hypocenter locations and three-dimensional P- and S- wave velocity structure of Marmara Region using SIMULPS14 along with 2,500 events with more than eight P- readings and an azimuthal gap of less than 180\\deg. The resolution of calculated velocity structure is better in the eastern Marmara than the western Marmara region due to the dense ray coverage. We used the obtained velocity structure as input into the finite difference algorithm and validated the model by using M < 4 earthquakes as point sources and matching long period waveforms (f < 0.5 Hz). We also obtained Mo, fc and individual station kappa values for over 500 events by performing a simultaneous inversion to fit these parameters with a Brune source model. We used the results of the source inversion to deconvolve out a Brune model from small to moderate size earthquakes (M < 4.0) to obtain empirical Green's function (EGF) for the higher frequency range of ground motion synthesis (0.5 < f > 25 Hz). We additionally obtained the source scaling relation (energy-moment) of these aftershocks. We have generated several scenarios constrained by a priori knowledge of the Izmit and Duzce rupture parameters to validate our prediction capability.

A three-dimensional inverse finite element analysis of the heel pad.

PubMed

Chokhandre, Snehal; Halloran, Jason P; van den Bogert, Antonie J; Erdemir, Ahmet

2012-03-01

Quantification of plantar tissue behavior of the heel pad is essential in developing computational models for predictive analysis of preventive treatment options such as footwear for patients with diabetes. Simulation based studies in the past have generally adopted heel pad properties from the literature, in return using heel-specific geometry with material properties of a different heel. In exceptional cases, patient-specific material characterization was performed with simplified two-dimensional models, without further evaluation of a heel-specific response under different loading conditions. The aim of this study was to conduct an inverse finite element analysis of the heel in order to calculate heel-specific material properties in situ. Multidimensional experimental data available from a previous cadaver study by Erdemir et al. ("An Elaborate Data Set Characterizing the Mechanical Response of the Foot," ASME J. Biomech. Eng., 131(9), pp. 094502) was used for model development, optimization, and evaluation of material properties. A specimen-specific three-dimensional finite element representation was developed. Heel pad material properties were determined using inverse finite element analysis by fitting the model behavior to the experimental data. Compression dominant loading, applied using a spherical indenter, was used for optimization of the material properties. The optimized material properties were evaluated through simulations representative of a combined loading scenario (compression and anterior-posterior shear) with a spherical indenter and also of a compression dominant loading applied using an elevated platform. Optimized heel pad material coefficients were 0.001084 MPa (μ), 9.780 (α) (with an effective Poisson's ratio (ν) of 0.475), for a first-order nearly incompressible Ogden material model. The model predicted structural response of the heel pad was in good agreement for both the optimization (<1.05% maximum tool force, 0.9% maximum tool displacement) and validation cases (6.5% maximum tool force, 15% maximum tool displacement). The inverse analysis successfully predicted the material properties for the given specimen-specific heel pad using the experimental data for the specimen. The modeling framework and results can be used for accurate predictions of the three-dimensional interaction of the heel pad with its surroundings.

Landau damping of Bogoliubov excitations in two- and three-dimensional optical lattices at finite temperatures

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

Tsuchiya, Shunji; Department of Physics, Waseda University, 3-4-1 Okubo, Tokyo 169-8555; Griffin, Allan

2005-11-15

We study the Landau damping of Bogoliubov excitations in two- and three-dimensional optical lattices at finite temperatures, extending our recent work on one-dimensional (1D) optical lattices. We use a Bose-Hubbard tight-binding model and the Popov approximation to calculate the temperature dependence of the number of condensate atoms n{sup c0}(T) in each lattice well. As with 1D optical lattices, damping only occurs if the Bogoliubov excitations exhibit anomalous dispersion (i.e., the excitation energy bends upward at low momentum), analogous to the case of phonons in superfluid {sup 4}He. This leads to the disappearance of all damping processes in a D-dimensional simplemore » cubic optical lattice when Un{sup c0}{>=}6DJ, where U is the on-site interaction, and J is the hopping matrix element.« less

Combined Uncertainty and A-Posteriori Error Bound Estimates for CFD Calculations: Theory and Implementation

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

2014-01-01

Simulation codes often utilize finite-dimensional approximation resulting in numerical error. Some examples include, numerical methods utilizing grids and finite-dimensional basis functions, particle methods using a finite number of particles. These same simulation codes also often contain sources of uncertainty, for example, uncertain parameters and fields associated with the imposition of initial and boundary data,uncertain physical model parameters such as chemical reaction rates, mixture model parameters, material property parameters, etc.

A three-dimensional finite element model of human atrial anatomy: New methods for cubic Hermite meshes with extraordinary vertices

PubMed Central

Gonzales, Matthew J.; Sturgeon, Gregory; Krishnamurthy, Adarsh; Hake, Johan; Jonas, René; Stark, Paul; Rappel, Wouter-Jan; Narayan, Sanjiv M.; Zhang, Yongjie; Segars, W. Paul; McCulloch, Andrew D.

2013-01-01

High-order cubic Hermite finite elements have been valuable in modeling cardiac geometry, fiber orientations, biomechanics, and electrophysiology, but their use in solving three-dimensional problems has been limited to ventricular models with simple topologies. Here, we utilized a subdivision surface scheme and derived a generalization of the “local-to-global” derivative mapping scheme of cubic Hermite finite elements to construct bicubic and tricubic Hermite models of the human atria with extraordinary vertices from computed tomography images of a patient with atrial fibrillation. To an accuracy of 0.6 millimeters, we were able to capture the left atrial geometry with only 142 bicubic Hermite finite elements, and the right atrial geometry with only 90. The left and right atrial bicubic Hermite meshes were G1 continuous everywhere except in the one-neighborhood of extraordinary vertices, where the mean dot products of normals at adjacent elements were 0.928 and 0.925. We also constructed two biatrial tricubic Hermite models and defined fiber orientation fields in agreement with diagrammatic data from the literature using only 42 angle parameters. The meshes all have good quality metrics, uniform element sizes, and elements with aspect ratios near unity, and are shared with the public. These new methods will allow for more compact and efficient patient-specific models of human atrial and whole heart physiology. PMID:23602918

Numerical algorithms for computations of feedback laws arising in control of flexible systems

NASA Technical Reports Server (NTRS)

Lasiecka, Irena

1989-01-01

Several continuous models will be examined, which describe flexible structures with boundary or point control/observation. Issues related to the computation of feedback laws are examined (particularly stabilizing feedbacks) with sensors and actuators located either on the boundary or at specific point locations of the structure. One of the main difficulties is due to the great sensitivity of the system (hyperbolic systems with unbounded control actions), with respect to perturbations caused either by uncertainty of the model or by the errors introduced in implementing numerical algorithms. Thus, special care must be taken in the choice of the appropriate numerical schemes which eventually lead to implementable finite dimensional solutions. Finite dimensional algorithms are constructed on a basis of a priority analysis of the properties of the original, continuous (infinite diversional) systems with the following criteria in mind: (1) convergence and stability of the algorithms and (2) robustness (reasonable insensitivity with respect to the unknown parameters of the systems). Examples with mixed finite element methods and spectral methods are provided.

Prediction of oxygen distribution in aortic valve leaflet considering diffusion and convection.

PubMed

Wang, Ling; Korossis, Sotirios; Fisher, John; Ingham, Eileen; Jin, Zhongmin

2011-07-01

Oxygen supply and transport is an important consideration in the development of tissue engineered constructs. Previous studies from our group have focused on the effect of tissue thickness on the oxygen diffusion within a three-dimensional aortic valve leaflet model, and highlighted the necessity for additional transport mechanisms such as oxygen convection. The aims of this study were to investigate the effect of interstitial fluid flow within the aortic valve leaflet, induced by the cyclic loading of the leaflet, on oxygen transport. Indentation testing and finite element modelings were employed to derive the biphasic properties of the leaflet tissue. The biphasic properties were subsequently used in the computational modeling of oxygen convection in the leaflet, which was based on the effective interstitial fluid velocity and the tissue deformation. Subsequently, the oxygen profile was predicted within the valve leaflet model by solving the diffusion and convection equation simultaneously utilizing the finite difference method. The compression modulus (E) and hydraulic permeability were determined by adapting a finite element model to the experimental indentation test on valvular tissue, E = 0.05MPa, and k =2.0 mm4/Ns. Finite element model of oxygen convection in valvular tissue incorporating the predicted biphasic properties was developed and the interstitial fluid flow rate was calculated falling in range of 0.025-0.25 mm/s depending on the tissue depth. Oxygen distribution within valvular tissue was predicted using one-dimensional oxygen diffusion model taking into consider the interstitial fluid effect. It was found that convection did enhance the oxygen transport in valvular tissue by up to 68% increase in the minimum oxygen tension within the tissue, depending on the strain level of the tissue as reaction of the magnitude and frequencies of the cardiac loading. The effective interstitial fluid velocity was found to play an important role in enhancing the oxygen transport within the valve leaflet. Such an understanding is important in the development of valvular tissue engineered constructs.

Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2006-01-01

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

Research in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Murman, Earll M.

1987-01-01

The numerical integration of quasi-one-dimensional unsteady flow problems which involve finite rate chemistry are discussed, and are expressed in terms of conservative form Euler and species conservation equations. Hypersonic viscous calculations for delta wing geometries is also examined. The conical Navier-Stokes equations model was selected in order to investigate the effects of viscous-inviscid interations. The more complete three-dimensional model is beyond the available computing resources. The flux vector splitting method with van Leer's MUSCL differencing is being used. Preliminary results were computed for several conditions.

Numerical simulation on hydromechanical coupling in porous media adopting three-dimensional pore-scale model.

PubMed

Liu, Jianjun; Song, Rui; Cui, Mengmeng

2014-01-01

A novel approach of simulating hydromechanical coupling in pore-scale models of porous media is presented in this paper. Parameters of the sandstone samples, such as the stress-strain curve, Poisson's ratio, and permeability under different pore pressure and confining pressure, are tested in laboratory scale. The micro-CT scanner is employed to scan the samples for three-dimensional images, as input to construct the model. Accordingly, four physical models possessing the same pore and rock matrix characteristics as the natural sandstones are developed. Based on the micro-CT images, the three-dimensional finite element models of both rock matrix and pore space are established by MIMICS and ICEM software platform. Navier-Stokes equation and elastic constitutive equation are used as the mathematical model for simulation. A hydromechanical coupling analysis in pore-scale finite element model of porous media is simulated by ANSYS and CFX software. Hereby, permeability of sandstone samples under different pore pressure and confining pressure has been predicted. The simulation results agree well with the benchmark data. Through reproducing its stress state underground, the prediction accuracy of the porous rock permeability in pore-scale simulation is promoted. Consequently, the effects of pore pressure and confining pressure on permeability are revealed from the microscopic view.

Numerical Simulation on Hydromechanical Coupling in Porous Media Adopting Three-Dimensional Pore-Scale Model

PubMed Central

Liu, Jianjun; Song, Rui; Cui, Mengmeng

2014-01-01

A novel approach of simulating hydromechanical coupling in pore-scale models of porous media is presented in this paper. Parameters of the sandstone samples, such as the stress-strain curve, Poisson's ratio, and permeability under different pore pressure and confining pressure, are tested in laboratory scale. The micro-CT scanner is employed to scan the samples for three-dimensional images, as input to construct the model. Accordingly, four physical models possessing the same pore and rock matrix characteristics as the natural sandstones are developed. Based on the micro-CT images, the three-dimensional finite element models of both rock matrix and pore space are established by MIMICS and ICEM software platform. Navier-Stokes equation and elastic constitutive equation are used as the mathematical model for simulation. A hydromechanical coupling analysis in pore-scale finite element model of porous media is simulated by ANSYS and CFX software. Hereby, permeability of sandstone samples under different pore pressure and confining pressure has been predicted. The simulation results agree well with the benchmark data. Through reproducing its stress state underground, the prediction accuracy of the porous rock permeability in pore-scale simulation is promoted. Consequently, the effects of pore pressure and confining pressure on permeability are revealed from the microscopic view. PMID:24955384

Finite difference numerical method for the superlattice Boltzmann transport equation and case comparison of CPU(C) and GPU(CUDA) implementations

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

Priimak, Dmitri

2014-12-01

We present a finite difference numerical algorithm for solving two dimensional spatially homogeneous Boltzmann transport equation which describes electron transport in a semiconductor superlattice subject to crossed time dependent electric and constant magnetic fields. The algorithm is implemented both in C language targeted to CPU and in CUDA C language targeted to commodity NVidia GPU. We compare performances and merits of one implementation versus another and discuss various software optimisation techniques.

Evaluating the effects of modeling errors for isolated finite three-dimensional targets

NASA Astrophysics Data System (ADS)

Henn, Mark-Alexander; Barnes, Bryan M.; Zhou, Hui

2017-10-01

Optical three-dimensional (3-D) nanostructure metrology utilizes a model-based metrology approach to determine critical dimensions (CDs) that are well below the inspection wavelength. Our project at the National Institute of Standards and Technology is evaluating how to attain key CD and shape parameters from engineered in-die capable metrology targets. More specifically, the quantities of interest are determined by varying the input parameters for a physical model until the simulations agree with the actual measurements within acceptable error bounds. As in most applications, establishing a reasonable balance between model accuracy and time efficiency is a complicated task. A well-established simplification is to model the intrinsically finite 3-D nanostructures as either periodic or infinite in one direction, reducing the computationally expensive 3-D simulations to usually less complex two-dimensional (2-D) problems. Systematic errors caused by this simplified model can directly influence the fitting of the model to the measurement data and are expected to become more apparent with decreasing lengths of the structures. We identify these effects using selected simulation results and present experimental setups, e.g., illumination numerical apertures and focal ranges, that can increase the validity of the 2-D approach.

Analysis of vegetation effect on waves using a vertical 2-D RANS model

USDA-ARS?s Scientific Manuscript database

A vertical two-dimensional (2-D) model has been applied in the simulation of wave propagation through vegetated water bodies. The model is based on an existing model SOLA-VOF which solves the Reynolds-Averaged Navier-Stokes (RANS) equations with the finite difference method on a staggered rectangula...

Moment Inversion of the DPRK Nuclear Tests Using Finite-Difference Three-dimensional Strain Green's Tensors

NASA Astrophysics Data System (ADS)

Bao, X.; Shen, Y.; Wang, N.

2017-12-01

Accurate estimation of the source moment is important for discriminating underground explosions from earthquakes and other seismic sources. In this study, we invert for the full moment tensors of the recent seismic events (since 2016) at the Democratic People's Republic of Korea (PRRK) Punggye-ri test site. We use waveform data from broadband seismic stations located in China, Korea, and Japan in the inversion. Using a non-staggered-grid, finite-difference algorithm, we calculate the strain Green's tensors (SGT) based on one-dimensional (1D) and three-dimensional (3D) Earth models. Taking advantage of the source-receiver reciprocity, a SGT database pre-calculated and stored for the Punggye-ri test site is used in inversion for the source mechanism of each event. With the source locations estimated from cross-correlation using regional Pn and Pn-coda waveforms, we obtain the optimal source mechanism that best fits synthetics to the observed waveforms of both body and surface waves. The moment solutions of the first three events (2016-01-06, 2016-09-09, and 2017-09-03) show dominant isotropic components, as expected from explosions, though there are also notable non-isotropic components. The last event ( 8 minutes after the mb6.3 explosion in 2017) contained mainly implosive component, suggesting a collapse following the explosion. The solutions from the 3D model can better fit observed waveforms than the corresponding solutions from the 1D model. The uncertainty in the resulting moment solution is influenced by heterogeneities not resolved by the Earth model according to the waveform misfit. Using the moment solutions, we predict the peak ground acceleration at the Punggye-ri test site and compare the prediction with corresponding InSAR and other satellite images.

Multi-Dimensional High Order Essentially Non-Oscillatory Finite Difference Methods in Generalized Coordinates

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

1998-01-01

This project is about the development of high order, non-oscillatory type schemes for computational fluid dynamics. Algorithm analysis, implementation, and applications are performed. Collaborations with NASA scientists have been carried out to ensure that the research is relevant to NASA objectives. The combination of ENO finite difference method with spectral method in two space dimension is considered, jointly with Cai [3]. The resulting scheme behaves nicely for the two dimensional test problems with or without shocks. Jointly with Cai and Gottlieb, we have also considered one-sided filters for spectral approximations to discontinuous functions [2]. We proved theoretically the existence of filters to recover spectral accuracy up to the discontinuity. We also constructed such filters for practical calculations.

[Three-dimensional Finite Element Analysis to T-shaped Fracture of Pelvis in Sitting Position].

PubMed

Fan, Yanping; Lei, Jianyin; Liu, Haibo; Li, Zhiqiang; Cai, Xianhua; Chen, Weiyi

2015-10-01

We developed a three-dimensional finite element model of the pelvis. According to Letournel methods, we established a pelvis model of T-shaped fracture with its three different fixation systems, i. e. double column reconstruction plates, anterior column plate combined with posterior column screws and anterior column plate combined with quadrilateral area screws. It was found that the pelvic model was effective and could be used to simulate the mechanical behavior of the pelvis. Three fixation systems had great therapeutic effect on the T-shaped fracture. All fixation systems could increase the stiffness of the model, decrease the stress concentration level and decrease the displacement difference along the fracture line. The quadrilateral area screws, which were drilled into cortical bone, could generate beneficial effect on the T-type fracture. Therefore, the third fixation system mentioned above (i. e. the anterior column plate combined with quadrilateral area screws) has the best biomechanical stability to the T-type fracture.

Development and verification of global/local analysis techniques for laminated composites

NASA Technical Reports Server (NTRS)

Thompson, Danniella Muheim; Griffin, O. Hayden, Jr.

1991-01-01

A two-dimensional to three-dimensional global/local finite element approach was developed, verified, and applied to a laminated composite plate of finite width and length containing a central circular hole. The resulting stress fields for axial compression loads were examined for several symmetric stacking sequences and hole sizes. Verification was based on comparison of the displacements and the stress fields with those accepted trends from previous free edge investigations and a complete three-dimensional finite element solution of the plate. The laminates in the compression study included symmetric cross-ply, angle-ply and quasi-isotropic stacking sequences. The entire plate was selected as the global model and analyzed with two-dimensional finite elements. Displacements along a region identified as the global/local interface were applied in a kinematically consistent fashion to independent three-dimensional local models. Local areas of interest in the plate included a portion of the straight free edge near the hole, and the immediate area around the hole. Interlaminar stress results obtained from the global/local analyses compares well with previously reported trends, and some new conclusions about interlaminar stress fields in plates with different laminate orientations and hole sizes are presented for compressive loading. The effectiveness of the global/local procedure in reducing the computational effort required to solve these problems is clearly demonstrated through examination of the computer time required to formulate and solve the linear, static system of equations which result for the global and local analyses to those required for a complete three-dimensional formulation for a cross-ply laminate. Specific processors used during the analyses are described in general terms. The application of this global/local technique is not limited software system, and was developed and described in as general a manner as possible.

BIOPLUME III

EPA Science Inventory

Bioplume II is a two-dimensional finite difference and Method of Characteristics (MOC) model for simulating the natural attenuation of organic contaminants in ground water due to the processes of advection, dispersion, sorption and biodegradation. The transport simulation in Biop...

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.

Finite element modeling of frictionally restrained composite interfaces

NASA Technical Reports Server (NTRS)

Ballarini, Roberto; Ahmed, Shamim

1989-01-01

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

Error and Uncertainty Quantification in the Numerical Simulation of Complex Fluid Flows

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

2010-01-01

The failure of numerical simulation to predict physical reality is often a direct consequence of the compounding effects of numerical error arising from finite-dimensional approximation and physical model uncertainty resulting from inexact knowledge and/or statistical representation. In this topical lecture, we briefly review systematic theories for quantifying numerical errors and restricted forms of model uncertainty occurring in simulations of fluid flow. A goal of this lecture is to elucidate both positive and negative aspects of applying these theories to practical fluid flow problems. Finite-element and finite-volume calculations of subsonic and hypersonic fluid flow are presented to contrast the differing roles of numerical error and model uncertainty. for these problems.

Interim report on nuclear waste depository thermal analysis

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

Altenbach, T.J.

1978-07-25

A thermal analysis of a deep geologic depository for spent nuclear fuel is being conducted. The TRUMP finite difference heat transfer code is used to analyze a 3-dimensional model of the depository. The model uses a unit cell consisting of one spent fuel canister buried in salt beneath a ventilated room in the depository. A base case was studied along with several parametric variations. It is concluded that this method is appropriate for analyzing the thermal response of the system, and that the most important parameter in determining the maximum temperatures is the canister heat generation rate. The effects ofmore » room ventilation and different depository media are secondary.« less

A three-dimensional finite element study on the stress distribution pattern of two prosthetic abutments for external hexagon implants.

PubMed

Moreira, Wagner; Hermann, Caio; Pereira, Jucélio Tomás; Balbinoti, Jean Anacleto; Tiossi, Rodrigo

2013-10-01

The purpose of this study was to evaluate the mechanical behavior of two different straight prosthetic abutments (one- and two-piece) for external hex butt-joint connection implants using three-dimensional finite element analysis (3D-FEA). Two 3D-FEA models were designed, one for the two-piece prosthetic abutment (2 mm in height, two-piece mini-conical abutment, Neodent) and another one for the one-piece abutment (2 mm in height, Slim Fit one-piece mini-conical abutment, Neodent), with their corresponding screws and implants (Titamax Ti, 3.75 diameter by 13 mm in length, Neodent). The model simulated the single restoration of a lower premolar using data from a computerized tomography of a mandible. The preload (20 N) after torque application for installation of the abutment and an occlusal loading were simulated. The occlusal load was simulated using average physiological bite force and direction (114.6 N in the axial direction, 17.1 N in the lingual direction and 23.4 N toward the mesial at an angle of 75° to the occlusal plan). The regions with the highest von Mises stress results were at the bottom of the initial two threads of both prosthetic abutments that were tested. The one-piece prosthetic abutment presented a more homogeneous behavior of stress distribution when compared with the two-piece abutment. Under the simulated chewing loads, the von Mises stresses for both tested prosthetic-abutments were within the tensile strength values of the materials analyzed which thus supports the clinical use of both prosthetic abutments.

A consistent hierarchy of generalized kinetic equation approximations to the master equation applied to surface catalysis.

PubMed

Herschlag, Gregory J; Mitran, Sorin; Lin, Guang

2015-06-21

We develop a hierarchy of approximations to the master equation for systems that exhibit translational invariance and finite-range spatial correlation. Each approximation within the hierarchy is a set of ordinary differential equations that considers spatial correlations of varying lattice distance; the assumption is that the full system will have finite spatial correlations and thus the behavior of the models within the hierarchy will approach that of the full system. We provide evidence of this convergence in the context of one- and two-dimensional numerical examples. Lower levels within the hierarchy that consider shorter spatial correlations are shown to be up to three orders of magnitude faster than traditional kinetic Monte Carlo methods (KMC) for one-dimensional systems, while predicting similar system dynamics and steady states as KMC methods. We then test the hierarchy on a two-dimensional model for the oxidation of CO on RuO2(110), showing that low-order truncations of the hierarchy efficiently capture the essential system dynamics. By considering sequences of models in the hierarchy that account for longer spatial correlations, successive model predictions may be used to establish empirical approximation of error estimates. The hierarchy may be thought of as a class of generalized phenomenological kinetic models since each element of the hierarchy approximates the master equation and the lowest level in the hierarchy is identical to a simple existing phenomenological kinetic models.

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.

Prethermalization and persistent order in the absence of a thermal phase transition

NASA Astrophysics Data System (ADS)

Halimeh, Jad C.; Zauner-Stauber, Valentin; McCulloch, Ian P.; de Vega, Inés; Schollwöck, Ulrich; Kastner, Michael

2017-01-01

We numerically study the dynamics after a parameter quench in the one-dimensional transverse-field Ising model with long-range interactions (∝1 /rα with distance r ), for finite chains and also directly in the thermodynamic limit. In nonequilibrium, i.e., before the system settles into a thermal state, we find a long-lived regime that is characterized by a prethermal value of the magnetization, which in general differs from its thermal value. We find that the ferromagnetic phase is stabilized dynamically: as a function of the quench parameter, the prethermal magnetization shows a transition between a symmetry-broken and a symmetric phase, even for those values of α for which no finite-temperature transition occurs in equilibrium. The dynamical critical point is shifted with respect to the equilibrium one, and the shift is found to depend on α as well as on the quench parameters.

Application of finite element substructuring to composite micromechanics. M.S. Thesis - Akron Univ., May 1984

NASA Technical Reports Server (NTRS)

Caruso, J. J.

1984-01-01

Finite element substructuring is used to predict unidirectional fiber composite hygral (moisture), thermal, and mechanical properties. COSMIC NASTRAN and MSC/NASTRAN are used to perform the finite element analysis. The results obtained from the finite element model are compared with those obtained from the simplified composite micromechanics equations. A unidirectional composite structure made of boron/HM-epoxy, S-glass/IMHS-epoxy and AS/IMHS-epoxy are studied. The finite element analysis is performed using three dimensional isoparametric brick elements and two distinct models. The first model consists of a single cell (one fiber surrounded by matrix) to form a square. The second model uses the single cell and substructuring to form a nine cell square array. To compare computer time and results with the nine cell superelement model, another nine cell model is constructed using conventional mesh generation techniques. An independent computer program consisting of the simplified micromechanics equation is developed to predict the hygral, thermal, and mechanical properties for this comparison. The results indicate that advanced techniques can be used advantageously for fiber composite micromechanics.

Influence of implant number on the biomechanical behaviour of mandibular implant-retained/supported overdentures: a three-dimensional finite element analysis.

PubMed

Liu, Jingyin; Pan, Shaoxia; Dong, Jing; Mo, Zhongjun; Fan, Yubo; Feng, Hailan

2013-03-01

The aim of this study was to evaluate strain distribution in peri-implant bone, stress in the abutments and denture stability of mandibular overdentures anchored by different numbers of implants under different loading conditions, through three-dimensional finite element analysis (3D FEA). Four 3D finite element models of mandibular overdentures were established, using between one and four Straumann implants with Locator attachments. Three types of load were applied to the overdenture in each model: 100N vertical and inclined loads on the left first molar and a 100N vertical load on the lower incisors. The biomechanical behaviours of peri-implant bone, implants, abutments and overdentures were recorded. Under vertical load on the lower incisors, the single-implant overdenture rotated over the implant from side to side, and no obvious increase of strain was found in peri-implant bone. Under the same loading conditions, the two-implant-retained overdenture showed more apparent rotation around the fulcrum line passing through the two implants, and the maximum equivalent stress in the abutments was higher than in the other models. In the three-implant-supported overdenture, no strain concentration was found in cortical bone around the middle implant under three loading conditions. Single-implant-retained mandibular overdentures do not show damaging strain concentration in the bone around the only implant and may be a cost-effective treatment option for edentulous patients. A third implant can be placed between the original two when patients rehabilitated by two-implant overdentures report constant and obvious denture rotation around the fulcrum line. Copyright © 2012 Elsevier Ltd. All rights reserved.

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.

Computer model of two-dimensional solute transport and dispersion in ground water

USGS Publications Warehouse

Konikow, Leonard F.; Bredehoeft, J.D.

1978-01-01

This report presents a model that simulates solute transport in flowing ground water. The model is both general and flexible in that it can be applied to a wide range of problem types. It is applicable to one- or two-dimensional problems involving steady-state or transient flow. The model computes changes in concentration over time caused by the processes of convective transport, hydrodynamic dispersion, and mixing (or dilution) from fluid sources. The model assumes that the solute is non-reactive and that gradients of fluid density, viscosity, and temperature do not affect the velocity distribution. However, the aquifer may be heterogeneous and (or) anisotropic. The model couples the ground-water flow equation with the solute-transport equation. The digital computer program uses an alternating-direction implicit procedure to solve a finite-difference approximation to the ground-water flow equation, and it uses the method of characteristics to solve the solute-transport equation. The latter uses a particle- tracking procedure to represent convective transport and a two-step explicit procedure to solve a finite-difference equation that describes the effects of hydrodynamic dispersion, fluid sources and sinks, and divergence of velocity. This explicit procedure has several stability criteria, but the consequent time-step limitations are automatically determined by the program. The report includes a listing of the computer program, which is written in FORTRAN IV and contains about 2,000 lines. The model is based on a rectangular, block-centered, finite difference grid. It allows the specification of any number of injection or withdrawal wells and of spatially varying diffuse recharge or discharge, saturated thickness, transmissivity, boundary conditions, and initial heads and concentrations. The program also permits the designation of up to five nodes as observation points, for which a summary table of head and concentration versus time is printed at the end of the calculations. The data input formats for the model require three data cards and from seven to nine data sets to describe the aquifer properties, boundaries, and stresses. The accuracy of the model was evaluated for two idealized problems for which analytical solutions could be obtained. In the case of one-dimensional flow the agreement was nearly exact, but in the case of plane radial flow a small amount of numerical dispersion occurred. An analysis of several test problems indicates that the error in the mass balance will be generally less than 10 percent. The test problems demonstrated that the accuracy and precision of the numerical solution is sensitive to the initial number of particles placed in each cell and to the size of the time increment, as determined by the stability criteria. Mass balance errors are commonly the greatest during the first several time increments, but tend to decrease and stabilize with time.

Two-dimensional finite element heat transfer model of softwood. Part II, Macrostructural effects

Treesearch

Hongmei Gu; John F. Hunt

2006-01-01

A two-dimensional finite element model was used to study the effects of structural features on transient heat transfer in softwood lumber with various orientations. Transient core temperature was modeled for lumber samples “cut” from various locations within a simulated log. The effects of ring orientation, earlywood to latewood (E/L) ratio, and ring density were...

Chiral spin liquids at finite temperature in a three-dimensional Kitaev model

NASA Astrophysics Data System (ADS)

Kato, Yasuyuki; Kamiya, Yoshitomo; Nasu, Joji; Motome, Yukitoshi

2017-11-01

Chiral spin liquids (CSLs) in three dimensions and thermal phase transitions to paramagnet are studied by unbiased Monte Carlo simulations. For an extension of the Kitaev model to a three-dimensional tricoordinate network dubbed the hypernonagon lattice, we derive low-energy effective models in two different anisotropic limits. We show that the effective interactions between the emergent Z2 degrees of freedom called fluxes are unfrustrated in one limit, while highly frustrated in the other. In both cases, we find a first-order phase transition to the CSL, where both time-reversal and parity symmetries are spontaneously broken. In the frustrated case, however, the CSL state is highly exotic—the flux configuration is subextensively degenerate while showing a directional order with broken C3 rotational symmetry. Our results provide two contrasting archetypes of CSLs in three dimensions, both of which allow approximation-free simulation for investigating the thermodynamics.

Experimental and Numerical Investigation of Adsorption/Desorption in Packed Sorption Beds Under Ideal and Non-Ideal Flows

NASA Technical Reports Server (NTRS)

Mohamadinejad, H.; Knox, J. C.; Smith, James E.

1999-01-01

The importance of the wall effect on packed beds in the adsorption and desorption of carbon dioxide, nitrogen, and water on molecular sieve 5A of 0.127 cm in radius is examined experimentally and with one-dimensional computer simulations. Experimental results are presented for a 22.5-cm long by 4.5-cm diameter cylindrical column with concentration measurements taken at various radial locations. The set of partial differential equations are solved using finite differences and Newman's method. Comparison of test data with the axial-dispersed, non-isothermal, linear driving force model suggests that a two-dimensional model (submitted to Separation Science and Technology) is required for accurate simulation of the average column breakthrough concentration. Additional comparisons of test data with the model provided information on the interactive effects of carrier gas coadsorption with CO2, as well as CO2-H2O interactions.

The application of finite volume methods for modelling three-dimensional incompressible flow on an unstructured mesh

NASA Astrophysics Data System (ADS)

Lonsdale, R. D.; Webster, R.

This paper demonstrates the application of a simple finite volume approach to a finite element mesh, combining the economy of the former with the geometrical flexibility of the latter. The procedure is used to model a three-dimensional flow on a mesh of linear eight-node brick (hexahedra). Simulations are performed for a wide range of flow problems, some in excess of 94,000 nodes. The resulting computer code ASTEC that incorporates these procedures is described.

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.

Finite state modeling of aeroelastic systems

NASA Technical Reports Server (NTRS)

Vepa, R.

1977-01-01

A general theory of finite state modeling of aerodynamic loads on thin airfoils and lifting surfaces performing completely arbitrary, small, time-dependent motions in an airstream is developed and presented. The nature of the behavior of the unsteady airloads in the frequency domain is explained, using as raw materials any of the unsteady linearized theories that have been mechanized for simple harmonic oscillations. Each desired aerodynamic transfer function is approximated by means of an appropriate Pade approximant, that is, a rational function of finite degree polynomials in the Laplace transform variable. The modeling technique is applied to several two dimensional and three dimensional airfoils. Circular, elliptic, rectangular and tapered planforms are considered as examples. Identical functions are also obtained for control surfaces for two and three dimensional airfoils.

Finite element simulation of crack depth measurements in concrete using diffuse ultrasound

NASA Astrophysics Data System (ADS)

Seher, Matthias; Kim, Jin-Yeon; Jacobs, Laurence J.

2012-05-01

This research simulates the measurements of crack depth in concrete using diffuse ultrasound. The finite element method is employed to simulate the ultrasonic diffusion process around cracks with different geometrical shapes, with the goal of gaining physical insight into the data obtained from experimental measurements. The commercial finite element software Ansys is used to implement the two-dimensional concrete model. The model is validated with an analytical solution and experimental results. It is found from the simulation results that preliminary knowledge of the crack geometry is required to interpret the energy evolution curves from measurements and to correctly determine the crack depth.

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.

Quantum Monte Carlo study of the transverse-field quantum Ising model on infinite-dimensional structures

NASA Astrophysics Data System (ADS)

Baek, Seung Ki; Um, Jaegon; Yi, Su Do; Kim, Beom Jun

2011-11-01

In a number of classical statistical-physical models, there exists a characteristic dimensionality called the upper critical dimension above which one observes the mean-field critical behavior. Instead of constructing high-dimensional lattices, however, one can also consider infinite-dimensional structures, and the question is whether this mean-field character extends to quantum-mechanical cases as well. We therefore investigate the transverse-field quantum Ising model on the globally coupled network and on the Watts-Strogatz small-world network by means of quantum Monte Carlo simulations and the finite-size scaling analysis. We confirm that both of the structures exhibit critical behavior consistent with the mean-field description. In particular, we show that the existing cumulant method has difficulty in estimating the correct dynamic critical exponent and suggest that an order parameter based on the quantum-mechanical expectation value can be a practically useful numerical observable to determine critical behavior when there is no well-defined dimensionality.

A comparison of analog and digital modeling techniques for simulating three-dimensional ground-water flow on Long Island, New York

USGS Publications Warehouse

Reilly, Thomas E.; Harbaugh, Arlen W.

1980-01-01

A three-dimensional electric-analog model of the Long Island, NY , groundwater system constructed by the U.S. Geological Survey in the early 1970 's was used as the basis for developing a digital, three-dimensional finite-difference model. The digital model was needed to provide faster modifications and more rapid solutions to water-management questions. Results generated by the two models are depicted as potentiometric-surface maps of the upper glacial and Magothy aquifers. Results compare favorably for all parts of Long Island except the northwestern part, where hydrologic discontinuities are most prevalent and which the two models represent somewhat differently. The mathematical and hydrologic principles used in development of ground-water models, and the procedures for calibration and acceptance, are presented in nontechnical terms. (USGS)

ANALYTICAL SOLUTION TO SATURATED FLOW IN A FINITE STRATIFIED AQUIFER

EPA Science Inventory

An analytical solution for the flow of water in a saturated-stratified aquitard-aquifer-aquitard system of finite length is presented. The analytical solution assumes one-dimensional horizontal flow in the aquifer and two-dimensional flow in the aquitards. Several examples are gi...

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.

Optimal Bandwidth for High Efficiency Thermoelectrics

NASA Astrophysics Data System (ADS)

Zhou, Jun; Yang, Ronggui; Chen, Gang; Dresselhaus, Mildred S.

2011-11-01

The thermoelectric figure of merit (ZT) in narrow conduction bands of different material dimensionalities is investigated for different carrier scattering models. When the bandwidth is zero, the transport distribution function (TDF) is finite, not infinite as previously speculated by Mahan and Sofo [Proc. Natl. Acad. Sci. U.S.A. 93, 7436 (1996)PNASA60027-842410.1073/pnas.93.15.7436], even though the carrier density of states goes to infinity. Such a finite TDF results in a zero electrical conductivity and thus a zero ZT. We point out that the optimal ZT cannot be found in an extremely narrow conduction band. The existence of an optimal bandwidth for a maximal ZT depends strongly on the scattering models and the dimensionality of the material. A nonzero optimal bandwidth for maximizing ZT also depends on the lattice thermal conductivity. A larger maximum ZT can be obtained for materials with a smaller lattice thermal conductivity.

Towards Humanlike Social Touch for Prosthetics and Sociable Robotics: Three-Dimensional Finite Element Simulations of Synthetic Finger Phalanges

NASA Astrophysics Data System (ADS)

Cabibihan, John-John; Ge, Shuzhi Sam

Synthetic skins with humanlike characteristic would make it possible to address some of the psychosocial requirements of prosthetic hands as well as the safety and acceptance issues in social robotics. This paper describes the development of three-dimensional finite element models of synthetic finger phalanges. With the aim of duplicating the skin compliance of human finger phalanges, the model was used to investigate the effects of (i) introducing open pockets in the internal structure and (ii) combining different materials as external and internal layers. The results show that having pockets in the internal structure of the design can increase the skin compliance of the synthetic phalanges and make it comparable with the human counterpart. Moreover, having different layers can be used to satisfy skin compliance and other design requirements such as wear and tear.

Measurement of the internal stress and electric field in a resonating piezoelectric transformer for high-voltage applications using the electro-optic and photoelastic effects

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

VanGordon, James A.; Kovaleski, Scott D., E-mail: kovaleskis@missouri.edu; Norgard, Peter

The high output voltages from piezoelectric transformers are currently being used to accelerate charged particle beams for x-ray and neutron production. Traditional methods of characterizing piezoelectric transformers (PTs) using electrical probes can decrease the voltage transformation ratio of the device due to the introduction of load impedances on the order of hundreds of kiloohms to hundreds of megaohms. Consequently, an optical diagnostic was developed that used the photoelastic and electro-optic effects present in piezoelectric materials that are transparent to a given optical wavelength to determine the internal stress and electric field. The combined effects of the piezoelectric, photoelastic, and electro-opticmore » effects result in a time-dependent change the refractive indices of the material and produce an artificially induced, time-dependent birefringence in the piezoelectric material. This induced time-dependent birefringence results in a change in the relative phase difference between the ordinary and extraordinary wave components of a helium-neon laser beam. The change in phase difference between the wave components was measured using a set of linear polarizers. The measured change in phase difference was used to calculate the stress and electric field based on the nonlinear optical properties, the piezoelectric constitutive equations, and the boundary conditions of the PT. Maximum stresses of approximately 10 MPa and electric fields of as high as 6 kV/cm were measured with the optical diagnostic. Measured results were compared to results from both a simple one-dimensional (1D) model of the piezoelectric transformer and a three-dimensional (3D) finite element model. Measured stresses and electric fields along the length of an operating length-extensional PT for two different electrical loads were within at least 50 % of 3D finite element simulated results. Additionally, the 3D finite element results were more accurate than the results from the 1D model for a wider range of electrical load impedances under test.« less

Measurement of the internal stress and electric field in a resonating piezoelectric transformer for high-voltage applications using the electro-optic and photoelastic effects.

PubMed

VanGordon, James A; Kovaleski, Scott D; Norgard, Peter; Gall, Brady B; Dale, Gregory E

2014-02-01

The high output voltages from piezoelectric transformers are currently being used to accelerate charged particle beams for x-ray and neutron production. Traditional methods of characterizing piezoelectric transformers (PTs) using electrical probes can decrease the voltage transformation ratio of the device due to the introduction of load impedances on the order of hundreds of kiloohms to hundreds of megaohms. Consequently, an optical diagnostic was developed that used the photoelastic and electro-optic effects present in piezoelectric materials that are transparent to a given optical wavelength to determine the internal stress and electric field. The combined effects of the piezoelectric, photoelastic, and electro-optic effects result in a time-dependent change the refractive indices of the material and produce an artificially induced, time-dependent birefringence in the piezoelectric material. This induced time-dependent birefringence results in a change in the relative phase difference between the ordinary and extraordinary wave components of a helium-neon laser beam. The change in phase difference between the wave components was measured using a set of linear polarizers. The measured change in phase difference was used to calculate the stress and electric field based on the nonlinear optical properties, the piezoelectric constitutive equations, and the boundary conditions of the PT. Maximum stresses of approximately 10 MPa and electric fields of as high as 6 kV/cm were measured with the optical diagnostic. Measured results were compared to results from both a simple one-dimensional (1D) model of the piezoelectric transformer and a three-dimensional (3D) finite element model. Measured stresses and electric fields along the length of an operating length-extensional PT for two different electrical loads were within at least 50 % of 3D finite element simulated results. Additionally, the 3D finite element results were more accurate than the results from the 1D model for a wider range of electrical load impedances under test.

A method for the computational modeling of the physics of heart murmurs

NASA Astrophysics Data System (ADS)

Seo, Jung Hee; Bakhshaee, Hani; Garreau, Guillaume; Zhu, Chi; Andreou, Andreas; Thompson, William R.; Mittal, Rajat

2017-05-01

A computational method for direct simulation of the generation and propagation of blood flow induced sounds is proposed. This computational hemoacoustic method is based on the immersed boundary approach and employs high-order finite difference methods to resolve wave propagation and scattering accurately. The current method employs a two-step, one-way coupled approach for the sound generation and its propagation through the tissue. The blood flow is simulated by solving the incompressible Navier-Stokes equations using the sharp-interface immersed boundary method, and the equations corresponding to the generation and propagation of the three-dimensional elastic wave corresponding to the murmur are resolved with a high-order, immersed boundary based, finite-difference methods in the time-domain. The proposed method is applied to a model problem of aortic stenosis murmur and the simulation results are verified and validated by comparing with known solutions as well as experimental measurements. The murmur propagation in a realistic model of a human thorax is also simulated by using the computational method. The roles of hemodynamics and elastic wave propagation on the murmur are discussed based on the simulation results.

The Finite-Size Scaling Relation for the Order-Parameter Probability Distribution of the Six-Dimensional Ising Model

NASA Astrophysics Data System (ADS)

Merdan, Ziya; Karakuş, Özlem

2016-11-01

The six dimensional Ising model with nearest-neighbor pair interactions has been simulated and verified numerically on the Creutz Cellular Automaton by using five bit demons near the infinite-lattice critical temperature with the linear dimensions L=4,6,8,10. The order parameter probability distribution for six dimensional Ising model has been calculated at the critical temperature. The constants of the analytical function have been estimated by fitting to probability function obtained numerically at the finite size critical point.

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

NASA Astrophysics Data System (ADS)

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

2014-07-01

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

Exact solution of a one-dimensional model of strained epitaxy on a periodically modulated substrate

NASA Astrophysics Data System (ADS)

Tokar, V. I.; Dreyssé, H.

2005-03-01

We consider a one-dimensional lattice gas model of strained epitaxy with the elastic strain accounted for through a finite number of cluster interactions comprising contiguous atomic chains. Interactions of this type arise in the models of strained epitaxy based on the Frenkel-Kontorova model. Furthermore, the deposited atoms interact with the substrate via an arbitrary periodic potential of period L . This model is solved exactly with the use of an appropriately adopted technique developed recently in the theory of protein folding. The advantage of the proposed approach over the standard transfer-matrix method is that it reduces the problem to finding the largest eigenvalue of a matrix of size L instead of 2L-1 , which is vital in the case of nanostructures where L may measure in hundreds of interatomic distances. Our major conclusion is that the substrate modulation always facilitates the size calibration of self-assembled nanoparticles in one- and two-dimensional systems.

Hydrogeology of well-field areas near Tampa, Florida; Phase 2, development and documentation of a quasi-three-dimensional finite-difference model for simulation of steady-state ground-water flow

USGS Publications Warehouse

Hutchinson, C.B.

1984-01-01

This report describes a quasi-three-dimensional finite-difference model for simulation of steady-state ground-water flow in the Floridan aquifer over a 932-square-mile area that contains 10 municipal well fields. The over-lying surficial aquifer contains a water table and is coupled to the Floridan aquifer by leakage term that represents flow through a confining layer separating the two aquifers. Under the steady-state condition, all storage terms are set to zero. Use of the head-controlled flux condition allows simulated head and flow changes to occur in the Floridan aquifer at the model boundaries. Procedures used to calibrate the model, test its sensitivity to input-parameter errors, and validate its accuracy for predictive purposes are described. Also included are attachments that describe setting up and running the model. Example model-interrogation runs show anticipated drawdowns under high, average, and low recharge conditions with 10 well fields pumping simultaneously at the maximum annual permitted rates totaling 186.9 million gallons per day. (USGS)

Functional Parallel Factor Analysis for Functions of One- and Two-dimensional Arguments.

PubMed

Choi, Ji Yeh; Hwang, Heungsun; Timmerman, Marieke E

2018-03-01

Parallel factor analysis (PARAFAC) is a useful multivariate method for decomposing three-way data that consist of three different types of entities simultaneously. This method estimates trilinear components, each of which is a low-dimensional representation of a set of entities, often called a mode, to explain the maximum variance of the data. Functional PARAFAC permits the entities in different modes to be smooth functions or curves, varying over a continuum, rather than a collection of unconnected responses. The existing functional PARAFAC methods handle functions of a one-dimensional argument (e.g., time) only. In this paper, we propose a new extension of functional PARAFAC for handling three-way data whose responses are sequenced along both a two-dimensional domain (e.g., a plane with x- and y-axis coordinates) and a one-dimensional argument. Technically, the proposed method combines PARAFAC with basis function expansion approximations, using a set of piecewise quadratic finite element basis functions for estimating two-dimensional smooth functions and a set of one-dimensional basis functions for estimating one-dimensional smooth functions. In a simulation study, the proposed method appeared to outperform the conventional PARAFAC. We apply the method to EEG data to demonstrate its empirical usefulness.

Biomechanical study of three kinds of internal fixation for the treatment of sacroiliac joint disruption using biomechanical test and finite element analysis.

PubMed

Wu, Tao; Ren, Xuejiao; Cui, Yunwei; Cheng, Xiaodong; Peng, Shuo; Hou, Zhiyong; Han, Yongtai

2018-06-19

To compare the stability of sacroiliac joint disruption fixed with three kinds of internal fixation using both biomechanical test and finite element analysis. Five embalmed specimens of an adult were used. The symphysis pubis rupture and left sacroiliac joint disruption were created. The symphysis pubis was stabilized with a five-hole plate. The sacroiliac joint disruption was fixed with three kinds of internal fixation in a randomized design. Displacements of the whole specimen and shifts in the gap were recorded. Three-dimensional finite element models of the pelvis, the pelvis with symphysis pubis rupture and left sacroiliac joint disruption, and three kinds of internal fixation techniques were created and analyzed. Under the vertical load, the displacements and shifts in the gap of the pelvis fixed with minimally invasive adjustable plate (MIAP) combined with one iliosacral (IS) screw were the smallest, and the average displacements of the pelvis fixed with an anterior plate were the largest one. The differences among them were significant. In finite element analysis and MIAP combined with one IS screw fixation showed relatively best fixation stability and lowest risks of implant failure than two IS screws fixation and anterior plate fixation. The stability of sacroiliac joint disruption fixed with MIAP combined with one IS screw is better than that fixed with two IS screws and anterior plate under vertical load.

Modeling and analysis of visual digital impact model for a Chinese human thorax.

PubMed

Zhu, Jin; Wang, Kai-Ming; Li, Shu; Liu, Hai-Yan; Jing, Xiao; Li, Xiao-Fang; Liu, Yi-He

2017-01-01

To establish a three-dimensional finite element model of the human chest for engineering research on individual protection. Computed tomography (CT) scanning data were used for three-dimensional reconstruction with the medical image reconstruction software Mimics. The finite element method (FEM) preprocessing software ANSYS ICEM CFD was used for cell mesh generation, and the relevant material behavior parameters of all of the model's parts were specified. The finite element model was constructed with the FEM software, and the model availability was verified based on previous cadaver experimental data. A finite element model approximating the anatomical structure of the human chest was established, and the model's simulation results conformed to the results of the cadaver experiment overall. Segment data of the human body and specialized software can be utilized for FEM model reconstruction to satisfy the need for numerical analysis of shocks to the human chest in engineering research on body mechanics.

Assessing waveform predictions of recent three-dimensional velocity models of the Tibetan Plateau

NASA Astrophysics Data System (ADS)

Bao, Xueyang; Shen, Yang

2016-04-01

Accurate velocity models are essential for both the determination of earthquake locations and source moments and the interpretation of Earth structures. With the increasing number of three-dimensional velocity models, it has become necessary to assess the models for accuracy in predicting seismic observations. Six models of the crustal and uppermost mantle structures in Tibet and surrounding regions are investigated in this study. Regional Rayleigh and Pn (or Pnl) waveforms from two ground truth events, including one nuclear explosion and one natural earthquake located in the study area, are simulated by using a three-dimensional finite-difference method. Synthetics are compared to observed waveforms in multiple period bands of 20-75 s for Rayleigh waves and 1-20 s for Pn/Pnl waves. The models are evaluated based on the phase delays and cross-correlation coefficients between synthetic and observed waveforms. A model generated from full-wave ambient noise tomography best predicts Rayleigh waves throughout the data set, as well as Pn/Pnl waves traveling from the Tarim Basin to the stations located in central Tibet. In general, the models constructed from P wave tomography are not well suited to predict Rayleigh waves, and vice versa. Possible causes of the differences between observed and synthetic waveforms, and frequency-dependent variations of the "best matching" models with the smallest prediction errors are discussed. This study suggests that simultaneous prediction for body and surface waves requires an integrated velocity model constructed with multiple seismic waveforms and consideration of other important properties, such as anisotropy.

Biomechanical three-dimensional finite element analysis of monolithic zirconia crown with different cement type

PubMed Central

2015-01-01

PURPOSE The objective of this study was to evaluate the influence of various cement types on the stress distribution in monolithic zirconia crowns under maximum bite force using the finite element analysis. MATERIALS AND METHODS The models of the prepared #46 crown (deep chamfer margin) were scanned and solid models composed of the monolithic zirconia crown, cement layer, and prepared tooth were produced using the computer-aided design technology and were subsequently translated into 3-dimensional finite element models. Four models were prepared according to different cement types (zinc phosphate, polycarboxylate, glass ionomer, and resin). A load of 700 N was applied vertically on the crowns (8 loading points). Maximum principal stress was determined. RESULTS Zinc phosphate cement had a greater stress concentration in the cement layer, while polycarboxylate cement had a greater stress concentration on the distal surface of the monolithic zirconia crown and abutment tooth. Resin cement and glass ionomer cement showed similar patterns, but resin cement showed a lower stress distribution on the lingual and mesial surface of the cement layer. CONCLUSION The test results indicate that the use of different luting agents that have various elastic moduli has an impact on the stress distribution of the monolithic zirconia crowns, cement layers, and abutment tooth. Resin cement is recommended for the luting agent of the monolithic zirconia crowns. PMID:26816578

Method for calculating internal radiation and ventilation with the ADINAT heat-flow code

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

Butkovich, T.R.; Montan, D.N.

1980-04-01

One objective of the spent fuel test in Climax Stock granite (SFTC) is to correctly model the thermal transport, and the changes in the stress field and accompanying displacements from the application of the thermal loads. We have chosen the ADINA and ADINAT finite element codes to do these calculations. ADINAT is a heat transfer code compatible to the ADINA displacement and stress analysis code. The heat flow problem encountered at SFTC requires a code with conduction, radiation, and ventilation capabilities, which the present version of ADINAT does not have. We have devised a method for calculating internal radiation andmore » ventilation with the ADINAT code. This method effectively reproduces the results from the TRUMP multi-dimensional finite difference code, which correctly models radiative heat transport between drift surfaces, conductive and convective thermal transport to and through air in the drifts, and mass flow of air in the drifts. The temperature histories for each node in the finite element mesh calculated with ADINAT using this method can be used directly in the ADINA thermal-mechanical calculation.« less

Analysis of Aerospike Plume Induced Base-Heating Environment

NASA Technical Reports Server (NTRS)

Wang, Ten-See

1998-01-01

Computational analysis is conducted to study the effect of an aerospike engine plume on X-33 base-heating environment during ascent flight. To properly account for the effect of forebody and aftbody flowfield such as shocks and to allow for potential plume-induced flow-separation, thermo-flowfield of trajectory points is computed. The computational methodology is based on a three-dimensional finite-difference, viscous flow, chemically reacting, pressure-base computational fluid dynamics formulation, and a three-dimensional, finite-volume, spectral-line based weighted-sum-of-gray-gases radiation absorption model computational heat transfer formulation. The predicted convective and radiative base-heat fluxes are presented.

Effect of Augmentation Material Stiffness on Adjacent Vertebrae after Osteoporotic Vertebroplasty Using Finite Element Analysis with Different Loading Methods.

PubMed

Cho, Ah-Reum; Cho, Sang-Bong; Lee, Jae-Ho; Kim, Kyung-Hoon

2015-11-01

Vertebroplasty is an effective treatment for osteoporotic vertebral fractures, which are one of the most common fractures associated with osteoporosis. However, clinical observation has shown that the risk of adjacent vertebral body fractures may increase after vertebroplasty. The mechanism underlying adjacent vertebral body fracture after vertebroplasty is not clear; excessive stiffness resulting from polymethyl methacrylate has been suspected as an important mechanism. The aim of our study was to compare the effects of bone cement stiffness on adjacent vertebrae after osteoporotic vertebroplasty under load-controlled versus displacement-controlled conditions. An experimental computer study using a finite element analysis. Medical research institute, university hospital, Korean. A three-dimensional digital anatomic model of L1/2 bone structure was reconstructed from human computed tomographic images. The reconstructed three-dimensional geometry was processed for finite element analysis such as meshing elements and applying material properties. Two boundary conditions, load-controlled and displacement-controlled methods, were applied to each of 5 deformation modes: compression, flexion, extension, lateral bending, and torsion. The adjacent L1 vertebra, irrespective of augmentation, revealed nearly similar maximum von Mises stresses under the load-controlled condition. However, for the displacement-controlled condition, the maximum von Mises stresses in the cortical bone and inferior endplate of the adjacent L1 vertebra increased significantly after cement augmentation. This increase was more significant than that with stiffer bone cement under all modes, except the torsion mode. The finite element model was simplified, excluding muscular forces and incorporating a large volume of bone cement, to more clearly demonstrate effects of bone cement stiffness on adjacent vertebrae after vertebroplasty. Excessive stiffness of augmented bone cement increases the risk of adjacent vertebral fractures after vertebroplasty in an osteoporotic finite element model. This result was most prominently observed using the displacement-controlled method.

Computer modeling of inversion layer MOS solar cells and arrays

NASA Technical Reports Server (NTRS)

Ho, Fat Duen

1991-01-01

A two dimensional numerical model of the inversion layer metal insulator semiconductor (IL/MIS) solar cell is proposed by using the finite element method. The two-dimensional current flow in the device is taken into account in this model. The electrostatic potential distribution, the electron concentration distribution, and the hole concentration distribution for different terminal voltages are simulated. The results of simple calculation are presented. The existing problems for this model are addressed. Future work is proposed. The MIS structures are studied and some of the results are reported.

Emergent behaviors of the Schrödinger-Lohe model on cooperative-competitive networks

NASA Astrophysics Data System (ADS)

Huh, Hyungjin; Ha, Seung-Yeal; Kim, Dohyun

2017-12-01

We present several sufficient frameworks leading to the emergent behaviors of the coupled Schrödinger-Lohe (S-L) model under the same one-body external potential on cooperative-competitive networks. The S-L model was first introduced as a possible phenomenological model exhibiting quantum synchronization and its emergent dynamics on all-to-all cooperative networks has been treated via two distinct approaches, Lyapunov functional approach and the finite-dimensional reduction based on pairwise correlations. In this paper, we further generalize the finite-dimensional dynamical systems approach for pairwise correlation functions on cooperative-competitive networks and provide several sufficient frameworks leading to the collective exponential synchronization. For small systems consisting of three and four quantum subsystem, we also show that the system for pairwise correlations can be reduced to the Lotka-Volterra model with cooperative and competitive interactions, in which lots of interesting dynamical patterns appear, e.g., existence of closed orbits and limit-cycles.

Analytic topologically nontrivial solutions of the (3 +1 )-dimensional U (1 ) gauged Skyrme model and extended duality

NASA Astrophysics Data System (ADS)

Avilés, L.; Canfora, F.; Dimakis, N.; Hidalgo, D.

2017-12-01

We construct the first analytic examples of topologically nontrivial solutions of the (3 +1 )-dimensional U (1 ) gauged Skyrme model within a finite box in (3 +1 )-dimensional flat space-time. There are two types of gauged solitons. The first type corresponds to gauged Skyrmions living within a finite volume. The second corresponds to gauged time crystals (smooth solutions of the U (1 ) gauged Skyrme model whose periodic time dependence is protected by a winding number). The notion of electromagnetic duality can be extended for these two types of configurations in the sense that the electric and one of the magnetic components can be interchanged. These analytic solutions show very explicitly the Callan-Witten mechanism (according to which magnetic monopoles may "swallow" part of the topological charge of the Skyrmion) since the electromagnetic field contributes directly to the conserved topological charge of the gauged Skyrmions. As it happens in superconductors, the magnetic field is suppressed in the core of the gauged Skyrmions. On the other hand, the electric field is strongly suppresed in the core of gauged time crystals.

Finite volume model for two-dimensional shallow environmental flow

USGS Publications Warehouse

Simoes, F.J.M.

2011-01-01

This paper presents the development of a two-dimensional, depth integrated, unsteady, free-surface model based on the shallow water equations. The development was motivated by the desire of balancing computational efficiency and accuracy by selective and conjunctive use of different numerical techniques. The base framework of the discrete model uses Godunov methods on unstructured triangular grids, but the solution technique emphasizes the use of a high-resolution Riemann solver where needed, switching to a simpler and computationally more efficient upwind finite volume technique in the smooth regions of the flow. Explicit time marching is accomplished with strong stability preserving Runge-Kutta methods, with additional acceleration techniques for steady-state computations. A simplified mass-preserving algorithm is used to deal with wet/dry fronts. Application of the model is made to several benchmark cases that show the interplay of the diverse solution techniques.

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

Sudiarta, I. Wayan; Angraini, Lily Maysari, E-mail: lilyangraini@unram.ac.id

We have applied the finite difference time domain (FDTD) method with the supersymmetric quantum mechanics (SUSY-QM) procedure to determine excited energies of one dimensional quantum systems. The theoretical basis of FDTD, SUSY-QM, a numerical algorithm and an illustrative example for a particle in a one dimensional square-well potential were given in this paper. It was shown that the numerical results were in excellent agreement with theoretical results. Numerical errors produced by the SUSY-QM procedure was due to errors in estimations of superpotentials and supersymmetric partner potentials.

Large perturbation flow field analysis and simulation for supersonic inlets

NASA Technical Reports Server (NTRS)

Varner, M. O.; Martindale, W. R.; Phares, W. J.; Kneile, K. R.; Adams, J. C., Jr.

1984-01-01

An analysis technique for simulation of supersonic mixed compression inlets with large flow field perturbations is presented. The approach is based upon a quasi-one-dimensional inviscid unsteady formulation which includes engineering models of unstart/restart, bleed, bypass, and geometry effects. Numerical solution of the governing time dependent equations of motion is accomplished through a shock capturing finite difference algorithm, of which five separate approaches are evaluated. Comparison with experimental supersonic wind tunnel data is presented to verify the present approach for a wide range of transient inlet flow conditions.

Multiple robustness in factorized likelihood models.

PubMed

Molina, J; Rotnitzky, A; Sued, M; Robins, J M

2017-09-01

We consider inference under a nonparametric or semiparametric model with likelihood that factorizes as the product of two or more variation-independent factors. We are interested in a finite-dimensional parameter that depends on only one of the likelihood factors and whose estimation requires the auxiliary estimation of one or several nuisance functions. We investigate general structures conducive to the construction of so-called multiply robust estimating functions, whose computation requires postulating several dimension-reducing models but which have mean zero at the true parameter value provided one of these models is correct.

Nonperturbative evaluation for anomalous dimension in 2-dimensional O (3 ) sigma model

NASA Astrophysics Data System (ADS)

Calle Jimenez, Sergio; Oka, Makoto; Sasaki, Kiyoshi

2018-06-01

We nonperturbatively calculate the wave-function renormalization in the two-dimensional O (3 ) sigma model. It is evaluated in a box with a finite spatial extent. We determine the anomalous dimension in the finite-volume scheme through an analysis of the step-scaling function. Results are compared with a perturbative evaluation, and reasonable behavior is observed.

Modeling and Validation of the Three Dimensional Deflection of an MRI-Compatible Magnetically-Actuated Steerable Catheter

PubMed Central

Liu, Taoming; Poirot, Nate Lombard; Franson, Dominique; Seiberlich, Nicole; Griswold, Mark A.; Çavuşoğlu, M. Cenk

2016-01-01

Objective This paper presents the three dimensional kinematic modeling of a novel steerable robotic ablation catheter system. The catheter, embedded with a set of current-carrying micro-coils, is actuated by the magnetic forces generated by the magnetic field of the magnetic resonance imaging (MRI) scanner. Methods This paper develops a 3D model of the MRI actuated steerable catheter system by using finite differences approach. For each finite segment, a quasi-static torque-deflection equilibrium equation is calculated using beam theory. By using the deflection displacements and torsion angles, the kinematic model of the catheter system is derived. Results The proposed models are validated by comparing the simulation results of the proposed model with the experimental results of a hardware prototype of the catheter design. The maximum tip deflection error is 4.70 mm and the maximum root-mean-square (RMS) error of the shape estimation is 3.48 mm. Conclusion The results demonstrate that the proposed model can successfully estimate the deflection motion of the catheter. Significance The presented three dimensional deflection model of the magnetically controlled catheter design paves the way to efficient control of the robotic catheter for treatment of atrial fibrillation. PMID:26731519

Three-dimensional electrical impedance tomography based on the complete electrode model.

PubMed

Vauhkonen, P J; Vauhkonen, M; Savolainen, T; Kaipio, J P

1999-09-01

In electrical impedance tomography an approximation for the internal resistivity distribution is computed based on the knowledge of the injected currents and measured voltages on the surface of the body. It is often assumed that the injected currents are confined to the two-dimensional (2-D) electrode plane and the reconstruction is based on 2-D assumptions. However, the currents spread out in three dimensions and, therefore, off-plane structures have significant effect on the reconstructed images. In this paper we propose a finite element-based method for the reconstruction of three-dimensional resistivity distributions. The proposed method is based on the so-called complete electrode model that takes into account the presence of the electrodes and the contact impedances. Both the forward and the inverse problems are discussed and results from static and dynamic (difference) reconstructions with real measurement data are given. It is shown that in phantom experiments with accurate finite element computations it is possible to obtain static images that are comparable with difference images that are reconstructed from the same object with the empty (saline filled) tank as a reference.

A method for reducing the order of nonlinear dynamic systems

NASA Astrophysics Data System (ADS)

Masri, S. F.; Miller, R. K.; Sassi, H.; Caughey, T. K.

1984-06-01

An approximate method that uses conventional condensation techniques for linear systems together with the nonparametric identification of the reduced-order model generalized nonlinear restoring forces is presented for reducing the order of discrete multidegree-of-freedom dynamic systems that possess arbitrary nonlinear characteristics. The utility of the proposed method is demonstrated by considering a redundant three-dimensional finite-element model half of whose elements incorporate hysteretic properties. A nonlinear reduced-order model, of one-third the order of the original model, is developed on the basis of wideband stationary random excitation and the validity of the reduced-order model is subsequently demonstrated by its ability to predict with adequate accuracy the transient response of the original nonlinear model under a different nonstationary random excitation.

Construction of a three-dimensional finite element model of maxillary first molar and it's supporting structures

PubMed Central

Begum, M. Sameena; Dinesh, M. R.; Tan, Kenneth F. H.; Jairaj, Vani; Md Khalid, K.; Singh, Varun Pratap

2015-01-01

The finite element method (FEM) is a powerful computational tool for solving stress-strain problems; its ability to handle material inhomogeneity and complex shapes makes the FEM, the most suitable method for the analysis of internal stress levels in the tooth, periodontium, and alveolar bone. This article intends to explain the steps involved in the generation of a three-dimensional finite element model of tooth, periodontal ligament (PDL) and alveolar bone, as the procedure of modeling is most important because the result is based on the nature of the modeling systems. Finite element analysis offers a means of determining strain-stress levels in the tooth, ligament, and bone structures for a broad range of orthodontic loading scenarios without producing tissue damage. PMID:26538895

User's manual of fd2: A software package for modeling seismological problems with 2-dimensional linear finite-difference method. Special report, 1 May-15 July 1993

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

Jih, R.S.

1993-07-15

Fd2 is a software package developed at Teledyne Geotech Alexandria Laboratories (TGAL) during the past several years for generating synthetic seismograms and displaying the wavefields. This package consists of primarily a 2-dimensional 2nd-order explicit linear finite-difference (LFD) code. LFD method has the advantage that the solution contains all conversions and all orders of multiple scattering. It permits examinations of fairly general models with arbitrary complex variations in material properties and free-surface geometry. Furthermore, it does not require many assumptions commonly invoked in other theoretical approaches. The basic limitations to the LFD method or the finite-element method are the computational costmore » and memory requirements. These constrain the size of the grid and the number of time steps that can be calculated over a reasonable time frame. Our LFD code has a distinguishable feature in that it allows the inclusion o topographical free surface. This is particularly useful in modeling nuclear explosions buried in mountains. In this topical report, sample scripts are presented to illustrate the usage of fd2 and several supporting routines for plotting out the synthetics, generating 2-dimensional media, as well as the graphic visualization of wavefields. The algorithms for handling the boundary conditions of polygonal topography are reviewed in detail. Thus this topical report serves as both a programmer's guide and the user's manual.« less

MODFLOW-2005, The U.S. Geological Survey Modular Ground-Water Model - Documentation of the Multiple-Refined-Areas Capability of Local Grid Refinement (LGR) and the Boundary Flow and Head (BFH) Package

USGS Publications Warehouse

Mehl, Steffen W.; Hill, Mary C.

2007-01-01

This report documents the addition of the multiple-refined-areas capability to shared node Local Grid Refinement (LGR) and Boundary Flow and Head (BFH) Package of MODFLOW-2005, the U.S. Geological Survey modular, three-dimensional, finite-difference ground-water flow model. LGR now provides the capability to simulate ground-water flow by using one or more block-shaped, higher resolution local grids (child model) within a coarser grid (parent model). LGR accomplishes this by iteratively coupling separate MODFLOW-2005 models such that heads and fluxes are balanced across the shared interfacing boundaries. The ability to have multiple, nonoverlapping areas of refinement is important in situations where there is more than one area of concern within a regional model. In this circumstance, LGR can be used to simulate these distinct areas with higher resolution grids. LGR can be used in two-and three-dimensional, steady-state and transient simulations and for simulations of confined and unconfined ground-water systems. The BFH Package can be used to simulate these situations by using either the parent or child models independently.

A new ghost-node method for linking different models and initial investigations of heterogeneity and nonmatching grids

USGS Publications Warehouse

Dickinson, J.E.; James, S.C.; Mehl, S.; Hill, M.C.; Leake, S.A.; Zyvoloski, G.A.; Faunt, C.C.; Eddebbarh, A.-A.

2007-01-01

A flexible, robust method for linking parent (regional-scale) and child (local-scale) grids of locally refined models that use different numerical methods is developed based on a new, iterative ghost-node method. Tests are presented for two-dimensional and three-dimensional pumped systems that are homogeneous or that have simple heterogeneity. The parent and child grids are simulated using the block-centered finite-difference MODFLOW and control-volume finite-element FEHM models, respectively. The models are solved iteratively through head-dependent (child model) and specified-flow (parent model) boundary conditions. Boundary conditions for models with nonmatching grids or zones of different hydraulic conductivity are derived and tested against heads and flows from analytical or globally-refined models. Results indicate that for homogeneous two- and three-dimensional models with matched grids (integer number of child cells per parent cell), the new method is nearly as accurate as the coupling of two MODFLOW models using the shared-node method and, surprisingly, errors are slightly lower for nonmatching grids (noninteger number of child cells per parent cell). For heterogeneous three-dimensional systems, this paper compares two methods for each of the two sets of boundary conditions: external heads at head-dependent boundary conditions for the child model are calculated using bilinear interpolation or a Darcy-weighted interpolation; specified-flow boundary conditions for the parent model are calculated using model-grid or hydrogeologic-unit hydraulic conductivities. Results suggest that significantly more accurate heads and flows are produced when both Darcy-weighted interpolation and hydrogeologic-unit hydraulic conductivities are used, while the other methods produce larger errors at the boundary between the regional and local models. The tests suggest that, if posed correctly, the ghost-node method performs well. Additional testing is needed for highly heterogeneous systems. ?? 2007 Elsevier Ltd. All rights reserved.

Influence of Trabecular Bone on Peri-Implant Stress and Strain Based on Micro-CT Finite Element Modeling of Beagle Dog

PubMed Central

Liao, Sheng-hui; Zhu, Xing-hao; Xie, Jing; Sohodeb, Vikesh Kumar; Ding, Xi

2016-01-01

The objective of this investigation is to analyze the influence of trabecular microstructure modeling on the biomechanical distribution of the implant-bone interface. Two three-dimensional finite element mandible models, one with trabecular microstructure (a refined model) and one with macrostructure (a simplified model), were built. The values of equivalent stress at the implant-bone interface in the refined model increased compared with those of the simplified model and strain on the contrary. The distributions of stress and strain were more uniform in the refined model of trabecular microstructure, in which stress and strain were mainly concentrated in trabecular bone. It was concluded that simulation of trabecular bone microstructure had a significant effect on the distribution of stress and strain at the implant-bone interface. These results suggest that trabecular structures could disperse stress and strain and serve as load buffers. PMID:27403424

Influence of Trabecular Bone on Peri-Implant Stress and Strain Based on Micro-CT Finite Element Modeling of Beagle Dog.

PubMed

Liao, Sheng-Hui; Zhu, Xing-Hao; Xie, Jing; Sohodeb, Vikesh Kumar; Ding, Xi

2016-01-01

The objective of this investigation is to analyze the influence of trabecular microstructure modeling on the biomechanical distribution of the implant-bone interface. Two three-dimensional finite element mandible models, one with trabecular microstructure (a refined model) and one with macrostructure (a simplified model), were built. The values of equivalent stress at the implant-bone interface in the refined model increased compared with those of the simplified model and strain on the contrary. The distributions of stress and strain were more uniform in the refined model of trabecular microstructure, in which stress and strain were mainly concentrated in trabecular bone. It was concluded that simulation of trabecular bone microstructure had a significant effect on the distribution of stress and strain at the implant-bone interface. These results suggest that trabecular structures could disperse stress and strain and serve as load buffers.

Mathematical and Numerical Analysis of Model Equations on Interactions of the HIV/AIDS Virus and the Immune System

NASA Astrophysics Data System (ADS)

Parumasur, N.; Willie, R.

2008-09-01

We consider a simple HIV/AIDs finite dimensional mathematical model on interactions of the blood cells, the HIV/AIDs virus and the immune system for consistence of the equations to the real biomedical situation that they model. A better understanding to a cure solution to the illness modeled by the finite dimensional equations is given. This is accomplished through rigorous mathematical analysis and is reinforced by numerical analysis of models developed for real life cases.

Slow-light-enhanced upconversion for photovoltaic applications in one-dimensional photonic crystals.

PubMed

Johnson, Craig M; Reece, Peter J; Conibeer, Gavin J

2011-10-15

We present an approach to realizing enhanced upconversion efficiency in erbium (Er)-doped photonic crystals. Slow-light-mode pumping of the first Er excited state transition can result in enhanced emission from higher-energy levels that may lead to finite subbandgap external quantum efficiency in crystalline silicon solar cells. Using a straightforward electromagnetic model, we calculate potential field enhancements of more than 18× within he slow-light mode of a one-dimensional photonic crystal and discuss design trade-offs and considerations for photovoltaics.

From Laser Scanning to Finite Element Analysis of Complex Buildings by Using a Semi-Automatic Procedure.

PubMed

Castellazzi, Giovanni; D'Altri, Antonio Maria; Bitelli, Gabriele; Selvaggi, Ilenia; Lambertini, Alessandro

2015-07-28

In this paper, a new semi-automatic procedure to transform three-dimensional point clouds of complex objects to three-dimensional finite element models is presented and validated. The procedure conceives of the point cloud as a stacking of point sections. The complexity of the clouds is arbitrary, since the procedure is designed for terrestrial laser scanner surveys applied to buildings with irregular geometry, such as historical buildings. The procedure aims at solving the problems connected to the generation of finite element models of these complex structures by constructing a fine discretized geometry with a reduced amount of time and ready to be used with structural analysis. If the starting clouds represent the inner and outer surfaces of the structure, the resulting finite element model will accurately capture the whole three-dimensional structure, producing a complex solid made by voxel elements. A comparison analysis with a CAD-based model is carried out on a historical building damaged by a seismic event. The results indicate that the proposed procedure is effective and obtains comparable models in a shorter time, with an increased level of automation.

Finite-size effects in Anderson localization of one-dimensional Bose-Einstein condensates

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

Cestari, J. C. C.; Foerster, A.; Gusmao, M. A.

We investigate the disorder-induced localization transition in Bose-Einstein condensates for the Anderson and Aubry-Andre models in the noninteracting limit using exact diagonalization. We show that, in addition to the standard superfluid fraction, other tools such as the entanglement and fidelity can provide clear signatures of the transition. Interestingly, the fidelity exhibits good sensitivity even for small lattices. Effects of the system size on these quantities are analyzed in detail, including the determination of a finite-size-scaling law for the critical disorder strength in the case of the Anderson model.

Unsteady streamflow simulation using a linear implicit finite-difference model

USGS Publications Warehouse

Land, Larry F.

1978-01-01

A computer program for simulating one-dimensional subcritical, gradually varied, unsteady flow in a stream has been developed and documented. Given upstream and downstream boundary conditions and channel geometry data, roughness coefficients, stage, and discharge can be calculated anywhere within the reach as a function of time. The program uses a linear implicit finite-difference technique that discritizes the partial differential equations. Then it arranges the coefficients of the continuity and momentum equations into a pentadiagonal matrix for solution. Because it is a reasonable compromise between computational accuracy, speed and ease of use,the technique is one of the most commonly used. The upstream boundary condition is a depth hydrograph. However, options also allow the boundary condition to be discharge or water-surface elevation. The downstream boundary condition is a depth which may be constant, self-setting, or unsteady. The reach may be divided into uneven increments and the cross sections may be nonprismatic and may vary from one to the other. Tributary and lateral inflow may enter the reach. The digital model will simulate such common problems as (1) flood waves, (2) releases from dams, and (3) channels where storage is a consideration. It may also supply the needed flow information for mass-transport simulation. (Woodard-USGS)

Electromigration of intergranular voids in metal films for microelectronic interconnects

NASA Astrophysics Data System (ADS)

Averbuch, Amir; Israeli, Moshe; Ravve, Igor

2003-04-01

Voids and cracks often occur in the interconnect lines of microelectronic devices. They increase the resistance of the circuits and may even lead to a fatal failure. Voids may occur inside a single grain, but often they appear on the boundary between two grains. In this work, we model and analyze numerically the migration and evolution of an intergranular void subjected to surface diffusion forces and external voltage applied to the interconnect. The grain-void interface is considered one-dimensional, and the physical formulation of the electromigration and diffusion model results in two coupled fourth-order one-dimensional time-dependent PDEs. The boundary conditions are specified at the triple points, which are common to both neighboring grains and the void. The solution of these equations uses a finite difference scheme in space and a Runge-Kutta integration scheme in time, and is also coupled to the solution of a static Laplace equation describing the voltage distribution throughout the grain. Since the voltage distribution is required only along the interface line, the two-dimensional discretization of the grain interior is not needed, and the static problem is solved by the boundary element method at each time step. The motion of the intergranular void was studied for different ratios between the diffusion and the electric field forces, and for different initial configurations of the void.

SUTRA (Saturated-Unsaturated Transport). A Finite-Element Simulation Model for Saturated-Unsaturated, Fluid-Density-Dependent Ground-Water Flow with Energy Transport or Chemically-Reactive Single-Species Solute Transport.

DTIC Science & Technology

1984-12-30

as three dimensional, when the assumption is made that all SUTRA parameters and coefficients have a constant value in the third space direction. A...finite element. The type of element employed by SUTRA for two-dimensional simulation is a quadrilateral which has a finite thickness in the third ... space dimension. This type of a quad- rilateral element and a typical two-dimensional mesh is shown in Figure 3.1. - All twelve edges of the two

Analytical Modeling of a Novel Transverse Flux Machine for Direct Drive Wind Turbine Applications: Preprint

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

Hasan, IIftekhar; Husain, Tausif; Uddin, Md Wasi

2015-08-24

This paper presents a nonlinear analytical model of a novel double-sided flux concentrating Transverse Flux Machine (TFM) based on the Magnetic Equivalent Circuit (MEC) model. The analytical model uses a series-parallel combination of flux tubes to predict the flux paths through different parts of the machine including air gaps, permanent magnets, stator, and rotor. The two-dimensional MEC model approximates the complex three-dimensional flux paths of the TFM and includes the effects of magnetic saturation. The model is capable of adapting to any geometry that makes it a good alternative for evaluating prospective designs of TFM compared to finite element solversmore » that are numerically intensive and require more computation time. A single-phase, 1-kW, 400-rpm machine is analytically modeled, and its resulting flux distribution, no-load EMF, and torque are verified with finite element analysis. The results are found to be in agreement, with less than 5% error, while reducing the computation time by 25 times.« less

Analytical Modeling of a Novel Transverse Flux Machine for Direct Drive Wind Turbine Applications

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

Hasan, IIftekhar; Husain, Tausif; Uddin, Md Wasi

2015-09-02

This paper presents a nonlinear analytical model of a novel double sided flux concentrating Transverse Flux Machine (TFM) based on the Magnetic Equivalent Circuit (MEC) model. The analytical model uses a series-parallel combination of flux tubes to predict the flux paths through different parts of the machine including air gaps, permanent magnets (PM), stator, and rotor. The two-dimensional MEC model approximates the complex three-dimensional flux paths of the TFM and includes the effects of magnetic saturation. The model is capable of adapting to any geometry which makes it a good alternative for evaluating prospective designs of TFM as compared tomore » finite element solvers which are numerically intensive and require more computation time. A single phase, 1 kW, 400 rpm machine is analytically modeled and its resulting flux distribution, no-load EMF and torque, verified with Finite Element Analysis (FEA). The results are found to be in agreement with less than 5% error, while reducing the computation time by 25 times.« less

Multipartite Entanglement in Topological Quantum Phases.

PubMed

Pezzè, Luca; Gabbrielli, Marco; Lepori, Luca; Smerzi, Augusto

2017-12-22

We witness multipartite entanglement in the ground state of the Kitaev chain-a benchmark model of a one dimensional topological superconductor-also with variable-range pairing, using the quantum Fisher information. Phases having a finite winding number, for both short- and long-range pairing, are characterized by a power-law diverging finite-size scaling of multipartite entanglement. Moreover, the occurring quantum phase transitions are sharply marked by the divergence of the derivative of the quantum Fisher information, even in the absence of a closing energy gap.

[Finite Element Modelling of the Eye for the Investigation of Accommodation].

PubMed

Martin, H; Stachs, O; Guthoff, R; Grabow, N

2016-12-01

Background: Accommodation research increasingly uses engineering methods. This article presents the use of the finite element method in accommodation research. Material and Methods: Geometry, material data and boundary conditions are prerequisites for the application of the finite element method. Published data on geometry and materials are reviewed. It is shown how boundary conditions are important and how they influence the results. Results: Two dimensional and three dimensional models of the anterior chamber of the eye are presented. With simple two dimensional models, it is shown that realistic results for the accommodation amplitude can always be achieved. More complex three dimensional models of the accommodation mechanism - including the ciliary muscle - require further investigations of the material data and of the morphology of the ciliary muscle, if they are to achieve realistic results for accommodation. Discussion and Conclusion: The efficiency and the limitations of the finite element method are especially clear for accommodation. Application of the method requires extensive preparation, including acquisition of geometric and material data and experimental validation. However, a validated model can be used as a basis for parametric studies, by systematically varying material data and geometric dimensions. This allows systematic investigation of how essential input parameters influence the results. Georg Thieme Verlag KG Stuttgart · New York.

Equation of state of the one- and three-dimensional Bose-Bose gases

NASA Astrophysics Data System (ADS)

Chiquillo, Emerson

2018-06-01

We calculate the equation of state of Bose-Bose gases in one and three dimensions in the framework of an effective quantum field theory. The beyond-mean-field approximation at zero temperature and the one-loop finite-temperature results are obtained performing functional integration on a local effective action. The ultraviolet divergent zero-point quantum fluctuations are removed by means of dimensional regularization. We derive the nonlinear Schrödinger equation to describe one- and three-dimensional Bose-Bose mixtures and solve it analytically in the one-dimensional scenario. This equation supports self-trapped brightlike solitonic droplets and self-trapped darklike solitons. At low temperature, we also find that the pressure and the number of particles of symmetric quantum droplets have a nontrivial dependence on the chemical potential and the difference between the intra- and the interspecies coupling constants.

Dental application of novel finite element analysis software for three-dimensional finite element modeling of a dentulous mandible from its computed tomography images.

PubMed

Nakamura, Keiko; Tajima, Kiyoshi; Chen, Ker-Kong; Nagamatsu, Yuki; Kakigawa, Hiroshi; Masumi, Shin-ich

2013-12-01

This study focused on the application of novel finite-element analysis software for constructing a finite-element model from the computed tomography data of a human dentulous mandible. The finite-element model is necessary for evaluating the mechanical response of the alveolar part of the mandible, resulting from occlusal force applied to the teeth during biting. Commercially available patient-specific general computed tomography-based finite-element analysis software was solely applied to the finite-element analysis for the extraction of computed tomography data. The mandibular bone with teeth was extracted from the original images. Both the enamel and the dentin were extracted after image processing, and the periodontal ligament was created from the segmented dentin. The constructed finite-element model was reasonably accurate using a total of 234,644 nodes and 1,268,784 tetrahedral and 40,665 shell elements. The elastic moduli of the heterogeneous mandibular bone were determined from the bone density data of the computed tomography images. The results suggested that the software applied in this study is both useful and powerful for creating a more accurate three-dimensional finite-element model of a dentulous mandible from the computed tomography data without the need for any other software.

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

NASA Technical Reports Server (NTRS)

Liu, Jiwen; Tiwari, Surendra N.

1994-01-01

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

A model of irreversible jam formation in dense traffic

NASA Astrophysics Data System (ADS)

Brankov, J. G.; Bunzarova, N. Zh.; Pesheva, N. C.; Priezzhev, V. B.

2018-03-01

We study an one-dimensional stochastic model of vehicular traffic on open segments of a single-lane road of finite size L. The vehicles obey a stochastic discrete-time dynamics which is a limiting case of the generalized Totally Asymmetric Simple Exclusion Process. This dynamics has been previously used by Bunzarova and Pesheva (2017) for an one-dimensional model of irreversible aggregation. The model was shown to have three stationary phases: a many-particle one, MP, a phase with completely filled configuration, CF, and a boundary perturbed MP+CF phase, depending on the values of the particle injection (α), ejection (β) and hopping (p) probabilities. Here we extend the results for the stationary properties of the MP+CF phase, by deriving exact expressions for the local density at the first site of the chain and the probability P(1) of a completely jammed configuration. The unusual phase transition, characterized by jumps in both the bulk density and the current (in the thermodynamic limit), as α crosses the boundary α = p from the MP to the CF phase, is explained by the finite-size behavior of P(1). By using a random walk theory, we find that, when α approaches from below the boundary α = p, three different regimes appear, as the size L → ∞: (i) the lifetime of the gap between the rightmost clusters is of the order O(L) in the MP phase; (ii) small jams, separated by gaps with lifetime O(1) , exist in the MP+CF phase close to the left chain boundary; and (iii) when β = p, the jams are divided by gaps with lifetime of the order O(L 1 / 2) . These results are supported by extensive Monte Carlo calculations.

Three-dimensional finite element analysis of vertical and angular misfit in implant-supported fixed prostheses.

PubMed

Assunção, Wirley Gonçalves; Gomes, Erica Alves; Rocha, Eduardo Passos; Delben, Juliana Aparecida

2011-01-01

Three-dimensional finite element analysis was used to evaluate the effect of vertical and angular misfit in three-piece implant-supported screw-retained fixed prostheses on the biomechanical response in the peri-implant bone, implants, and prosthetic components. Four three-dimensional models were fabricated to represent a right posterior mandibular section with one implant in the region of the second premolar (2PM) and another in the region of the second molar (2M). The implants were splinted by a three-piece implant-supported metal-ceramic prosthesis and differed according to the type of misfit, as represented by four different models: Control = prosthesis with complete fit to the implants; UAM (unilateral angular misfit) = prosthesis presenting unilateral angular misfit of 100 μm in the mesial region of the 2M; UVM (unilateral vertical misfit) = prosthesis presenting unilateral vertical misfit of 100 μm in the mesial region of the 2M; and TVM (total vertical misfit) = prosthesis presenting total vertical misfit of 100 μm in the platform of the framework in the 2M. A vertical load of 400 N was distributed and applied on 12 centric points by the software Ansys, ie, a vertical load of 150 N was applied to each molar in the prosthesis and a vertical load of 100 N was applied at the 2PM. The stress values and distribution in peri-implant bone tissue were similar for all groups. The models with misfit exhibited different distribution patterns and increased stress magnitude in comparison to the control. The highest stress values in group UAM were observed in the implant body and retention screw. The groups UVM and TVM exhibited high stress values in the platform of the framework and the implant hexagon, respectively. The three types of misfit influenced the magnitude and distribution of stresses. The influence of misfit on peri-implant bone tissue was modest. Each type of misfit increased the stress values in different regions of the system.

Displaying the results of three-dimensional analysis using GRAPE. Part one: vector graphics. [In FORTRAN for CDC 7600

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

Brown, B.E.

1979-10-01

GRAPE is a display program for three-dimensional polygon and polyhedral models. It can produce line-drawing and continuous-tone black and white or color images in still frame or movie mode. The code was written specifically to be a post-processor for finite element and finite difference analyses. It runs on the CDC 7600 computer, and is compiled with the LLL FTN system. The allocation of storage is dynamic. There are presently three data paths into the code. The first is the binary inerface from the analyses codes and this with the other databases is described. The second data path is the SAMPPmore » format, and the last is the MOVIE format. The code structure is described first; then the commands are discussed in general terms to try to give the user some feel for what they do. The next section deals with the exact format of the commands by overlay. Then examples are given and discussed. Next, the various output options are covered. 57 figures. (RWR)« less

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.

Influence of Micro Threads Alteration on Osseointegration and Primary Stability of Implants: An FEA and In Vivo Analysis in Rabbits.

PubMed

Chowdhary, Ramesh; Halldin, Anders; Jimbo, Ryo; Wennerberg, Ann

2015-06-01

To describe the early bone tissue response to implants with and without micro threads designed to the full length of an oxidized titanium implant. A pair of two-dimensional finite element models was designed using a computer aided three-dimensional interactive application files of an implant model with micro threads in between macro threads and one without micro threads. Oxidized titanium implants with (test implants n=20) and without (control implants n=20) micro thread were prepared. A total of 12 rabbits were used and each received four implants. Insertion torque while implant placement and removal torque analysis after 4 weeks was performed in nine rabbits, and histomorphometric analysis in three rabbits, respectively. Finite element analysis showed less stress accumulation in test implant models with 31Mpa when compared with 62.2 Mpa in control implant model. Insertion and removal torque analysis did not show any statistical significance between the two implant designs. At 4 weeks, there was a significant difference between the two groups in the percentage of new bone volume and bone-to-implant contact in the femur (p< .05); however, not in the tibia. The effect of micro threads was prominent in the femur suggesting that micro threads promote bone formation. The stress distribution supported by the micro threads was especially effective in the cancellous bone. © 2013 Wiley Periodicals, Inc.

Three-dimensional finite element models of the human pubic symphysis with viscohyperelastic soft tissues.

PubMed

Li, Zuoping; Alonso, Jorge E; Kim, Jong-Eun; Davidson, James S; Etheridge, Brandon S; Eberhardt, Alan W

2006-09-01

Three-dimensional finite element (FE) models of human pubic symphyses were constructed from computed tomography image data of one male and one female cadaver pelvis. The pubic bones, interpubic fibrocartilaginous disc and four pubic ligaments were segmented semi-automatically and meshed with hexahedral elements using automatic mesh generation schemes. A two-term viscoelastic Prony series, determined by curve fitting results of compressive creep experiments, was used to model the rate-dependent effects of the interpubic disc and the pubic ligaments. Three-parameter Mooney-Rivlin material coefficients were calculated for the discs using a heuristic FE approach based on average experimental joint compression data. Similarly, a transversely isotropic hyperelastic material model was applied to the ligaments to capture average tensile responses. Linear elastic isotropic properties were assigned to bone. The applicability of the resulting models was tested in bending simulations in four directions and in tensile tests of varying load rates. The model-predicted results correlated reasonably with the joint bending stiffnesses and rate-dependent tensile responses measured in experiments, supporting the validity of the estimated material coefficients and overall modeling approach. This study represents an important and necessary step in the eventual development of biofidelic pelvis models to investigate symphysis response under high-energy impact conditions, such as motor vehicle collisions.

Finite Difference Formulation for Prediction of Water Pollution

NASA Astrophysics Data System (ADS)

Johari, Hanani; Rusli, Nursalasawati; Yahya, Zainab

2018-03-01

Water is an important component of the earth. Human being and living organisms are demand for the quality of water. Human activity is one of the causes of the water pollution. The pollution happened give bad effect to the physical and characteristic of water contents. It is not practical to monitor all aspects of water flow and transport distribution. So, in order to help people to access to the polluted area, a prediction of water pollution concentration must be modelled. This study proposed a one-dimensional advection diffusion equation for predicting the water pollution concentration transport. The numerical modelling will be produced in order to predict the transportation of water pollution concentration. In order to approximate the advection diffusion equation, the implicit Crank Nicolson is used. For the purpose of the simulation, the boundary condition and initial condition, the spatial steps and time steps as well as the approximations of the advection diffusion equation have been encoded. The results of one dimensional advection diffusion equation have successfully been used to predict the transportation of water pollution concentration by manipulating the velocity and diffusion parameters.

Multi-Material Closure Model for High-Order Finite Element Lagrangian Hydrodynamics

DOE PAGES

Dobrev, V. A.; Kolev, T. V.; Rieben, R. N.; ...

2016-04-27

We present a new closure model for single fluid, multi-material Lagrangian hydrodynamics and its application to high-order finite element discretizations of these equations [1]. The model is general with respect to the number of materials, dimension and space and time discretizations. Knowledge about exact material interfaces is not required. Material indicator functions are evolved by a closure computation at each quadrature point of mixed cells, which can be viewed as a high-order variational generalization of the method of Tipton [2]. This computation is defined by the notion of partial non-instantaneous pressure equilibration, while the full pressure equilibration is achieved bymore » both the closure model and the hydrodynamic motion. Exchange of internal energy between materials is derived through entropy considerations, that is, every material produces positive entropy, and the total entropy production is maximized in compression and minimized in expansion. Results are presented for standard one-dimensional two-material problems, followed by two-dimensional and three-dimensional multi-material high-velocity impact arbitrary Lagrangian–Eulerian calculations. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.« less

Multi-Material Closure Model for High-Order Finite Element Lagrangian Hydrodynamics

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

Dobrev, V. A.; Kolev, T. V.; Rieben, R. N.

We present a new closure model for single fluid, multi-material Lagrangian hydrodynamics and its application to high-order finite element discretizations of these equations [1]. The model is general with respect to the number of materials, dimension and space and time discretizations. Knowledge about exact material interfaces is not required. Material indicator functions are evolved by a closure computation at each quadrature point of mixed cells, which can be viewed as a high-order variational generalization of the method of Tipton [2]. This computation is defined by the notion of partial non-instantaneous pressure equilibration, while the full pressure equilibration is achieved bymore » both the closure model and the hydrodynamic motion. Exchange of internal energy between materials is derived through entropy considerations, that is, every material produces positive entropy, and the total entropy production is maximized in compression and minimized in expansion. Results are presented for standard one-dimensional two-material problems, followed by two-dimensional and three-dimensional multi-material high-velocity impact arbitrary Lagrangian–Eulerian calculations. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.« less

Finite-element simulation of blood perfusion in muscle tissue during compression and sustained contraction.

PubMed

Vankan, W J; Huyghe, J M; Slaaf, D W; van Donkelaar, C C; Drost, M R; Janssen, J D; Huson, A

1997-09-01

Mechanical interaction between tissue stress and blood perfusion in skeletal muscles plays an important role in blood flow impediment during sustained contraction. The exact mechanism of this interaction is not clear, and experimental investigation of this mechanism is difficult. We developed a finite-element model of the mechanical behavior of blood-perfused muscle tissue, which accounts for mechanical blood-tissue interaction in maximally vasodilated vasculature. Verification of the model was performed by comparing finite-element results of blood pressure and flow with experimental measurements in a muscle that is subject to well-controlled mechanical loading conditions. In addition, we performed simulations of blood perfusion during tetanic, isometric contraction and maximal vasodilation in a simplified, two-dimensional finite-element model of a rat calf muscle. A vascular waterfall in the venous compartment was identified as the main cause for blood flow impediment both in the experiment and in the finite-element simulations. The validated finite-element model offers possibilities for detailed analysis of blood perfusion in three-dimensional muscle models under complicated loading conditions.

Quantum mechanics over sets

NASA Astrophysics Data System (ADS)

Ellerman, David

2014-03-01

In models of QM over finite fields (e.g., Schumacher's ``modal quantum theory'' MQT), one finite field stands out, Z2, since Z2 vectors represent sets. QM (finite-dimensional) mathematics can be transported to sets resulting in quantum mechanics over sets or QM/sets. This gives a full probability calculus (unlike MQT with only zero-one modalities) that leads to a fulsome theory of QM/sets including ``logical'' models of the double-slit experiment, Bell's Theorem, QIT, and QC. In QC over Z2 (where gates are non-singular matrices as in MQT), a simple quantum algorithm (one gate plus one function evaluation) solves the Parity SAT problem (finding the parity of the sum of all values of an n-ary Boolean function). Classically, the Parity SAT problem requires 2n function evaluations in contrast to the one function evaluation required in the quantum algorithm. This is quantum speedup but with all the calculations over Z2 just like classical computing. This shows definitively that the source of quantum speedup is not in the greater power of computing over the complex numbers, and confirms the idea that the source is in superposition.

Stability of Blowup for a 1D Model of Axisymmetric 3D Euler Equation

NASA Astrophysics Data System (ADS)

Do, Tam; Kiselev, Alexander; Xu, Xiaoqian

2016-10-01

The question of the global regularity versus finite- time blowup in solutions of the 3D incompressible Euler equation is a major open problem of modern applied analysis. In this paper, we study a class of one-dimensional models of the axisymmetric hyperbolic boundary blow-up scenario for the 3D Euler equation proposed by Hou and Luo (Multiscale Model Simul 12:1722-1776, 2014) based on extensive numerical simulations. These models generalize the 1D Hou-Luo model suggested in Hou and Luo Luo and Hou (2014), for which finite-time blowup has been established in Choi et al. (arXiv preprint. arXiv:1407.4776, 2014). The main new aspects of this work are twofold. First, we establish finite-time blowup for a model that is a closer approximation of the three-dimensional case than the original Hou-Luo model, in the sense that it contains relevant lower-order terms in the Biot-Savart law that have been discarded in Hou and Luo Choi et al. (2014). Secondly, we show that the blow-up mechanism is quite robust, by considering a broader family of models with the same main term as in the Hou-Luo model. Such blow-up stability result may be useful in further work on understanding the 3D hyperbolic blow-up scenario.

Limiting similarity and functional diversity along environmental gradients

USGS Publications Warehouse

Schwilk, D.W.; Ackerly, D.D.

2005-01-01

Recent developments in community models emphasize the importance of incorporating stochastic processes (e.g. ecological drift) in models of niche-structured community assembly. We constructed a finite, spatially explicit, lottery model to simulate the distribution of species in a one-dimensional landscape with an underlying gradient in environmental conditions. Our framework combines the potential for ecological drift with environmentally-mediated competition for space in a heterogeneous environment. We examined the influence of niche breadth, dispersal distances, community size (total number of individuals) and the breadth of the environmental gradient on levels of species and functional trait diversity (i.e. differences in niche optima). Three novel results emerge from this model: (1) niche differences between adjacent species (e.g. limiting similarity) increase in smaller communities, because of the interaction of competitive effects and finite population sizes; (2) immigration from a regional species pool, stochasticity and niche-assembly generate a bimodal distribution of species residence times ('transient' and 'resident') under a heterogeneous environment; and (3) the magnitude of environmental heterogeneity has a U-shaped effect on diversity, because of shifts in species richness of resident vs. transient species. These predictions illustrate the potential importance of stochastic (although not necessarily neutral) processes in community assembly. ??2005 Blackwell Publishing Ltd/CNRS.

Global Culture: A Noise Induced Transition in Finite Systems

NASA Astrophysics Data System (ADS)

Klemm, Konstantin; Eguíluz, Victor M.; Toral, Raúl; San Miguel, Maxi

2003-04-01

We analyze Axelrod's model for the unbiased transmission of culture in the presence of noise. In a one-dimensional lattice, the dynamics is described in terms of a Lyapunov potential, where the disordered configurations are metastable states of the dynamics. In a two-dimensional lattice the dynamics is governed by the average relaxation time T for perturbations to the homogeneous configuration. If the noise rate is smaller than 1/T, the perturbations drive the system to a completely ordered configuration, whereas the system remains disordered for larger noise rates. Based on a mean-field approximation we obtain the average relaxation time T(N) = Nln(N) for system size N. Thus in the limit of infinite system size the system is disordered for any finite noise rate.

High order finite volume WENO schemes for the Euler equations under gravitational fields

NASA Astrophysics Data System (ADS)

Li, Gang; Xing, Yulong

2016-07-01

Euler equations with gravitational source terms are used to model many astrophysical and atmospheric phenomena. This system admits hydrostatic balance where the flux produced by the pressure is exactly canceled by the gravitational source term, and two commonly seen equilibria are the isothermal and polytropic hydrostatic solutions. Exact preservation of these equilibria is desirable as many practical problems are small perturbations of such balance. High order finite difference weighted essentially non-oscillatory (WENO) schemes have been proposed in [22], but only for the isothermal equilibrium state. In this paper, we design high order well-balanced finite volume WENO schemes, which can preserve not only the isothermal equilibrium but also the polytropic hydrostatic balance state exactly, and maintain genuine high order accuracy for general solutions. The well-balanced property is obtained by novel source term reformulation and discretization, combined with well-balanced numerical fluxes. Extensive one- and two-dimensional simulations are performed to verify well-balanced property, high order accuracy, as well as good resolution for smooth and discontinuous solutions.

Evaluation of the parameters affecting bone temperature during drilling using a three-dimensional dynamic elastoplastic finite element model.

PubMed

Chen, Yung-Chuan; Tu, Yuan-Kun; Zhuang, Jun-Yan; Tsai, Yi-Jung; Yen, Cheng-Yo; Hsiao, Chih-Kun

2017-11-01

A three-dimensional dynamic elastoplastic finite element model was constructed and experimentally validated and was used to investigate the parameters which influence bone temperature during drilling, including the drill speed, feeding force, drill bit diameter, and bone density. Results showed the proposed three-dimensional dynamic elastoplastic finite element model can effectively simulate the temperature elevation during bone drilling. The bone temperature rise decreased with an increase in feeding force and drill speed, however, increased with the diameter of drill bit or bone density. The temperature distribution is significantly affected by the drilling duration; a lower drilling speed reduced the exposure duration, decreases the region of the thermally affected zone. The constructed model could be applied for analyzing the influence parameters during bone drilling to reduce the risk of thermal necrosis. It may provide important information for the design of drill bits and surgical drilling powers.

MOFAT: A TWO-DIMENSIONAL FINITE ELEMENT PROGRAM FOR MULTIPHASE FLOW AND MULTICOMPONENT TRANSPORT - PROGRAM DOCUMENTATION AND USER'S GUIDE

EPA Science Inventory

This manual describes a two-dimensional, finite element model for coupled multiphase flow and multicomponent transport in planar or radially symmetric vertical sections. low and transport of three fluid phases, including water, nonaqueous phase liquid (NAPL), and gas are consider...

AutoCAD-To-GIFTS Translator Program

NASA Technical Reports Server (NTRS)

Jones, Andrew

1989-01-01

AutoCAD-to-GIFTS translator program, ACTOG, developed to facilitate quick generation of small finite-element models using CASA/GIFTS finite-element modeling program. Reads geometric data of drawing from Data Exchange File (DXF) used in AutoCAD and other PC-based drafting programs. Geometric entities recognized by ACTOG include points, lines, arcs, solids, three-dimensional lines, and three-dimensional faces. From this information, ACTOG creates GIFTS SRC file, which then reads into GIFTS preprocessor BULKM or modified and reads into EDITM to create finite-element model. SRC file used as is or edited for any number of uses. Written in Microsoft Quick-Basic (Version 2.0).

An optical flow-based state-space model of the vocal folds.

PubMed

Granados, Alba; Brunskog, Jonas

2017-06-01

High-speed movies of the vocal fold vibration are valuable data to reveal vocal fold features for voice pathology diagnosis. This work presents a suitable Bayesian model and a purely theoretical discussion for further development of a framework for continuum biomechanical features estimation. A linear and Gaussian nonstationary state-space model is proposed and thoroughly discussed. The evolution model is based on a self-sustained three-dimensional finite element model of the vocal folds, and the observation model involves a dense optical flow algorithm. The results show that the method is able to capture different deformation patterns between the computed optical flow and the finite element deformation, controlled by the choice of the model tissue parameters.

Fourier heat conduction as a strong kinetic effect in one-dimensional hard-core gases

NASA Astrophysics Data System (ADS)

Zhao, Hanqing; Wang, Wen-ge

2018-01-01

For a one-dimensional (1D) momentum conserving system, intensive studies have shown that generally its heat current autocorrelation function (HCAF) tends to decay in a power-law manner and results in the breakdown of the Fourier heat conduction law in the thermodynamic limit. This has been recognized to be a dominant hydrodynamic effect. Here we show that, instead, the kinetic effect can be dominant in some cases and leads to the Fourier law for finite-size systems. Usually the HCAF undergoes a fast decaying kinetic stage followed by a long slowly decaying hydrodynamic tail. In a finite range of the system size, we find that whether the system follows the Fourier law depends on whether the kinetic stage dominates. Our Rapid Communication is illustrated by the 1D hard-core gas models with which the HCAF is derived analytically and verified numerically by molecular dynamics simulations.

Effects of Thermal Resistance on One-Dimensional Thermal Analysis of the Epidermal Flexible Electronic Devices Integrated with Human Skin

NASA Astrophysics Data System (ADS)

Li, He; Cui, Yun

2017-12-01

Nowadays, flexible electronic devices are increasingly used in direct contact with human skin to monitor the real-time health of human body. Based on the Fourier heat conduction equation and Pennes bio-heat transfer equation, this paper deduces the analytical solutions of one - dimensional heat transfer for flexible electronic devices integrated with human skin under the condition of a constant power. The influence of contact thermal resistance between devices and skin is considered as well. The corresponding finite element model is established to verify the correctness of analytical solutions. The results show that the finite element analysis agrees well with the analytical solution. With bigger thermal resistance, temperature increase of skin surface will decrease. This result can provide guidance for the design of flexible electronic devices to reduce the negative impact that exceeding temperature leave on human skin.

A coupled modelling effort to study the fate of contaminated sediments downstream of the Coles Hill deposit, Virginia, USA

NASA Astrophysics Data System (ADS)

Castro-Bolinaga, C. F.; Zavaleta, E. R.; Diplas, P.

2015-03-01

This paper presents the preliminary results of a coupled modelling effort to study the fate of tailings (radioactive waste-by product) downstream of the Coles Hill uranium deposit located in Virginia, USA. The implementation of the overall modelling process includes a one-dimensional hydraulic model to qualitatively characterize the sediment transport process under severe flooding conditions downstream of the potential mining site, a two-dimensional ANSYS Fluent model to simulate the release of tailings from a containment cell located partially above the local ground surface into the nearby streams, and a one-dimensional finite-volume sediment transport model to examine the propagation of a tailings sediment pulse in the river network located downstream. The findings of this investigation aim to assist in estimating the potential impacts that tailings would have if they were transported into rivers and reservoirs located downstream of the Coles Hill deposit that serve as municipal drinking water supplies.

Evaluating BTEX concentration in soil using a simple one-dimensional vado zone model: application to a new fuel station in Valencia (Spain)

NASA Astrophysics Data System (ADS)

Rodrigo-Ilarri, Javier; Rodrigo-Clavero, María-Elena

2017-04-01

Specific studies of the impact of fuel spills on the vadose zone are currently required when trying to obtain the environmental permits for new fuel stations. The development of One-Dimensional mathematical models of fate and transport of BTEX on the vadose zone can therefore be used to understand the behavior of the pollutants under different scenarios. VLEACH - a simple One-Dimensional Finite Different Vadose Zone Leaching Model - uses an numerical approximation of the Millington Equation, a theoretical based model for gaseous diffusion in porous media. This equation has been widely used in the fields of soil physics and hydrology to calculate the gaseous or vapor diffusion in porous media. The model describes the movement of organic contaminants within and between three different phases: (1) as a solute dissolved in water, (2) as a gas in the vapor phase, and (3) as an absorbed compound in the soil phase. Initially, the equilibrium distribution of contaminant mass between liquid, gas and sorbed phases is calculated. Transport processes are then simulated. Liquid advective transport is calculated based on values defined by the user for infiltration and soil water content. The contaminant in the vapor phase migrates into or out of adjacent cells based on the calculated concentration gradients that exist between adjacent cells. After the mass is exchanged between the cells, the total mass in each cell is recalculated and re-equilibrated between the different phases. At the end of the simulation, (1) an overall area-weighted groundwater impact for the entire modeled area and (2) the concentration profile of BTEX on the vadose zone are calculated. This work shows the results obtained when applying VLEACH to analyze the contamination scenario caused by a BTEX spill coming from a set of future underground storage tanks located on a new fuel station in Aldaia (Valencia region - Spain).

[Finite element analysis of the stress distribution of two-piece post crown with different adhesives ].

PubMed

He, Lihui; Liu, Lijie; Gao, Bei; Gao, Shang; Chen, Yifu; Zhihui, Liu

2013-08-01

To establish three-dimensional finite element model of two-piece post crown to the mandibular first molar residual roots, and analyze the stress distribution characteristic to the residual roots with different adhesives, so as to get the best combination under different conditions. The complete mandibular first molar in vitro was selected, the crown was removed along the cemento-enamel junction, then the residual roots were scanned by CT. CT images were imported into a reverse engineering software, and the three-dimensional finite element model of the mandibular first molar residual roots was reconstructed. Titanium two-piece post crown of the mandibular first molar residual roots was produced, then was scanned by CT. The model was reconstructed and assembled by MIMICS. The stress distribution of the root canal and root section under the vertical load and lateral load with different bonding systems were analyzed. Three-dimensional finite element model of two-piece post crown to the mandibular first molar residual roots was established. With the increasing of elastic modulus of the adhesives, the maximum stress within the root canal was also increasing. Elastic modulus of zinc phosphate was the biggest, so the stress within the root canal was the biggest; elastic modulus of Superbond C&B was the smallest, so the stress within the root canal was the smallest. Lateral loading stress was much larger than the vertical load. Under vertical load, the load on the root section was even with different bonding systems. Under lateral load, the maximum stress was much larger than the vertical load. The stress on the root section was minimum using zinc phosphate binder, and the stress on the root section was maximum using Superbond C&B. In two-piece post crown restorations, there is significant difference between different adhesives on tooth protection. When the tooth structure of the root canal orifices is weak, in order to avoid the occurrence of splitting, the larger elastic modulus bonding system is the first choice, such as zinc phosphate binder. When the resistance form of the root canal orifices is good enough but the root is too weak, it is suggested that the smaller elastic modulus bonding system is the first choice, such as Superbond C&B.

[Study on the effect of vertebrae semi-dislocation on the stress distribution in facet joint and interuertebral disc of patients with cervical syndrome based on the three dimensional finite element model].

PubMed

Zhang, Ming-cai; Lü, Si-zhe; Cheng, Ying-wu; Gu, Li-xu; Zhan, Hong-sheng; Shi, Yin-yu; Wang, Xiang; Huang, Shi-rong

2011-02-01

To study the effect of vertebrae semi-dislocation on the stress distribution in facet joint and interuertebral disc of patients with cervical syndrome using three dimensional finite element model. A patient with cervical spondylosis was randomly chosen, who was male, 28 years old, and diagnosed as cervical vertebra semidislocation by dynamic and static palpation and X-ray, and scanned from C(1) to C(7) by 0.75 mm slice thickness of CT. Based on the CT data, the software was used to construct the three dimensional finite element model of cervical vertebra semidislocation (C(4)-C(6)). Based on the model,virtual manipulation was used to correct the vertebra semidislocation by the software, and the stress distribution was analyzed. The result of finite element analysis showed that the stress distribution of C(5-6) facet joint and intervertebral disc changed after virtual manipulation. The vertebra semidislocation leads to the abnormal stress distribution of facet joint and intervertebral disc.

Three-dimensional compact explicit-finite difference time domain scheme with density variation

NASA Astrophysics Data System (ADS)

Tsuchiya, Takao; Maruta, Naoki

2018-07-01

In this paper, the density variation is implemented in the three-dimensional compact-explicit finite-difference time-domain (CE-FDTD) method. The formulation is first developed based on the continuity equation and the equation of motion, which include the density. Some numerical demonstrations are performed for the three-dimensional sound wave propagation in a two density layered medium. The numerical results are compared with the theoretical results to verify the proposed formulation.

A comparison between numerically modelled and experimentally measured loss mechanisms in wave rotors

NASA Technical Reports Server (NTRS)

Paxson, Daniel E.

1993-01-01

A numerical model has been developed which is capable of predicting the performance of a wave rotor (pressure exchanger) of specified geometry over a wide range of operating conditions. The model can account for the major loss mechanisms of leakage from the tube ends, fluid viscosity, heat transfer to the tube wails, finite tube opening time, shock waves, and non-uniform port flows. It is a one dimensional flow model which follows a single tube as it rotates past the various stationary ports. Since the model is relatively simple (i.e., one dimensional) it uses little computer time. This makes it suitable for design as well as analytical purposes. This paper will present a brief description of the model then discuss a comparison between the model predictions and several wave rotor experiments.

A Comparison Between Numerically Modelled and Experimentally Measured Loss Mechanisms in Wave Rotors

NASA Technical Reports Server (NTRS)

Paxson, Daniel E.

1993-01-01

A numerical model has been developed which is capable of predicting the performance of a wave rotor (pressure exchanger) of specified geometry over a wide range of operating conditions. The model can account for the major loss mechanisms of leakage from the tube ends, fluid viscosity, heat transfer to the tube walls, finite tube opening time, shock waves, and non-uniform port flows. It is a one dimensional flow model which follows a single tube as it rotates past the various stationary ports. Since the model is relatively simple (i.e. one dimensional) it uses little computer time. This makes it suitable for design as well as analytical purposes. This paper will present a brief description of the model then discuss a comparison between the model predictions and several wave rotor experiments.

[Influence of trabecular microstructure modeling on finite element analysis of dental implant].

PubMed

Shen, M J; Wang, G G; Zhu, X H; Ding, X

2016-09-01

To analyze the influence of trabecular microstructure modeling on the biomechanical distribution of implant-bone interface with a three-dimensional finite element mandible model of trabecular structure. Dental implants were embeded in the mandibles of a beagle dog. After three months of the implant installation, the mandibles with dental implants were harvested and scaned by micro-CT and cone-beam CT. Two three-dimensional finite element mandible models, trabecular microstructure(precise model) and macrostructure(simplified model), were built. The values of stress and strain of implant-bone interface were calculated using the software of Ansys 14.0. Compared with the simplified model, the precise models' average values of the implant bone interface stress increased obviously and its maximum values did not change greatly. The maximum values of quivalent stress of the precise models were 80% and 110% of the simplified model and the average values were 170% and 290% of simplified model. The maximum and average values of equivalent strain of precise models were obviously decreased, and the maximum values of the equivalent effect strain were 17% and 26% of simplified model and the average ones were 21% and 16% of simplified model respectively. Stress and strain concentrations at implant-bone interface were obvious in the simplified model. However, the distributions of stress and strain were uniform in the precise model. The precise model has significant effect on the distribution of stress and strain at implant-bone interface.

Applications of finite-size scaling for atomic and non-equilibrium systems

NASA Astrophysics Data System (ADS)

Antillon, Edwin A.

We apply the theory of Finite-size scaling (FSS) to an atomic and a non-equilibrium system in order to extract critical parameters. In atomic systems, we look at the energy dependence on the binding charge near threshold between bound and free states, where we seek the critical nuclear charge for stability. We use different ab initio methods, such as Hartree-Fock, Density Functional Theory, and exact formulations implemented numerically with the finite-element method (FEM). Using Finite-size scaling formalism, where in this case the size of the system is related to the number of elements used in the basis expansion of the wavefunction, we predict critical parameters in the large basis limit. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that this combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems. In the second part we look at non-equilibrium one-dimensional model known as the raise and peel model describing a growing surface which grows locally and has non-local desorption. For a specific values of adsorption ( ua) and desorption (ud) the model shows interesting features. At ua = ud, the model is described by a conformal field theory (with conformal charge c = 0) and its stationary probability can be mapped to the ground state of a quantum chain and can also be related a two dimensional statistical model. For ua ≥ ud, the model shows a scale invariant phase in the avalanche distribution. In this work we study the surface dynamics by looking at avalanche distributions using FSS formalism and explore the effect of changing the boundary conditions of the model. The model shows the same universality for the cases with and with our the wall for an odd number of tiles removed, but we find a new exponent in the presence of a wall for an even number of avalanches released. We provide new conjecture for the probability distribution of avalanches with a wall obtained by using exact diagonalization of small lattices and Monte-Carlo simulations.

External Boundary Conditions for Three-Dimensional Problems of Computational Aerodynamics

NASA Technical Reports Server (NTRS)

Tsynkov, Semyon V.

1997-01-01

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

Comments on the Diffusive Behavior of Two Upwind Schemes

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1998-01-01

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and locally one-dimensional finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2.5 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a speedup of 29 over finite volume.

Finite element modeling of superelastic nickel-titanium orthodontic wires.

PubMed

Naceur, Ines Ben; Charfi, Amin; Bouraoui, Tarak; Elleuch, Khaled

2014-11-28

Thanks to its good corrosion resistance and biocompatibility, superelastic Ni–Ti wire alloys have been successfully used in orthodontic treatment. Therefore, it is important to quantify and evaluate the level of orthodontic force applied to the bracket and teeth in order to achieve tooth movement. In this study, three dimensional finite element models with a Gibbs-potential-based-formulation and thermodynamic principles were used. The aim was to evaluate the influence of possible intraoral temperature differences on the forces exerted by NiTi orthodontic arch wires with different cross sectional shapes and sizes. The prediction made by this phenomenological model, for superelastic tensile and bending tests, shows good agreement with the experimental data. A bending test is simulated to study the force variation of an orthodontic NiTi arch wire when it loaded up to the deflection of 3 mm, for this task one half of the arch wire and the 3 adjacent brackets were modeled. The results showed that the stress required for the martensite transformation increases with the increase of cross-sectional dimensions and temperature. Associated with this increase in stress, the plateau of this transformation becomes steeper. In addition, the area of the mechanical hysteresis, measured as the difference between the forces of the upper and lower plateau, increases.

[Three-dimensional stress analysis of periodontal ligament of mandible incisors fixed bridge abutments under dynamic loads by finite element method].

PubMed

Ma, Da; Tang, Liang; Pan, Yan-Huan

2007-12-01

Three-dimensional finite method was used to analyze stress and strain distributions of periodontal ligament of abutments under dynamic loads. Finite element analysis was performed on the model under dynamic loads with vertical and oblique directions. The stress and strain distributions and stress-time curves were analyzed to study the biomechanical behavior of periodontal ligament of abutments. The stress and strain distributions of periodontal ligament under dynamic load were same with the static load. But the maximum stress and strain decreased apparently. The rate of change was between 60%-75%. The periodontal ligament had time-dependent mechanical behaviors. Some level of residual stress in periodontal ligament was left after one mastication period. The stress-free time under oblique load was shorter than that of vertical load. The maximum stress and strain decrease apparently under dynamic loads. The periodontal ligament has time-dependent mechanical behaviors during one mastication. There is some level of residual stress left after one mastication period. The level of residual stress is related to the magnitude and the direction of loads. The direction of applied loads is one important factor that affected the stress distribution and accumulation and release of abutment periodontal ligament.

A low-dimensional analogue of holographic baryons

NASA Astrophysics Data System (ADS)

Bolognesi, Stefano; Sutcliffe, Paul

2014-04-01

Baryons in holographic QCD correspond to topological solitons in the bulk. The most prominent example is the Sakai-Sugimoto model, where the bulk soliton in the five-dimensional spacetime of AdS-type can be approximated by the flat space self-dual Yang-Mills instanton with a small size. Recently, the validity of this approximation has been verified by comparison with the numerical field theory solution. However, multi-solitons and solitons with finite density are currently beyond numerical field theory computations. Various approximations have been applied to investigate these important issues and have led to proposals for finite density configurations that include dyonic salt and baryonic popcorn. Here we introduce and investigate a low-dimensional analogue of the Sakai-Sugimoto model, in which the bulk soliton can be approximated by a flat space sigma model instanton. The bulk theory is a baby Skyrme model in a three-dimensional spacetime with negative curvature. The advantage of the lower-dimensional theory is that numerical simulations of multi-solitons and finite density solutions can be performed and compared with flat space instanton approximations. In particular, analogues of dyonic salt and baryonic popcorn configurations are found and analysed.

Unification of color postprocessing techniques for 3-dimensional computational mechanics

NASA Technical Reports Server (NTRS)

Bailey, Bruce Charles

1985-01-01

To facilitate the understanding of complex three-dimensional numerical models, advanced interactive color postprocessing techniques are introduced. These techniques are sufficiently flexible so that postprocessing difficulties arising from model size, geometric complexity, response variation, and analysis type can be adequately overcome. Finite element, finite difference, and boundary element models may be evaluated with the prototype postprocessor. Elements may be removed from parent models to be studied as independent subobjects. Discontinuous responses may be contoured including responses which become singular, and nonlinear color scales may be input by the user for the enhancement of the contouring operation. Hit testing can be performed to extract precise geometric, response, mesh, or material information from the database. In addition, stress intensity factors may be contoured along the crack front of a fracture model. Stepwise analyses can be studied, and the user can recontour responses repeatedly, as if he were paging through the response sets. As a system, these tools allow effective interpretation of complex analysis results.

The effectiveness of a new algorithm on a three-dimensional finite element model construction of bone trabeculae in implant biomechanics.

PubMed

Sato, Y; Teixeira, E R; Tsuga, K; Shindoi, N

1999-08-01

More validity of finite element analysis (FEA) in implant biomechanics requires element downsizing. However, excess downsizing needs computer memory and calculation time. To evaluate the effectiveness of a new algorithm established for more valid FEA model construction without downsizing, three-dimensional FEA bone trabeculae models with different element sizes (300, 150 and 75 micron) were constructed. Four algorithms of stepwise (1 to 4 ranks) assignment of Young's modulus accorded with bone volume in the individual cubic element was used and then stress distribution against vertical loading was analysed. The model with 300 micron element size, with 4 ranks of Young's moduli accorded with bone volume in each element presented similar stress distribution to the model with the 75 micron element size. These results show that the new algorithm was effective, and the use of the 300 micron element for bone trabeculae representation was proposed, without critical changes in stress values and for possible savings on computer memory and calculation time in the laboratory.

Numerical studies of interacting vortices

NASA Technical Reports Server (NTRS)

Liu, G. C.; Hsu, C. H.

1985-01-01

To get a basic understanding of the physics of flowfields modeled by vortex filaments with finite vortical cores, systematic numerical studies of the interactions of two dimensional vortices and pairs of coaxial axisymmetric circular vortex rings were made. Finite difference solutions of the unsteady incompressible Navier-Stokes equations were carried out using vorticity and stream function as primary variables. Special emphasis was placed on the formulation of appropriate boundary conditions necessary for the calculations in a finite computational domain. Numerical results illustrate the interaction of vortex filaments, demonstrate when and how they merge with each other, and establish the region of validity for an asymptotic analysis.

One-dimensional nonlinear instability study of a slightly viscoelastic, perfectly conducting liquid jet under a radial electric field

NASA Astrophysics Data System (ADS)

Li, Fang; Yin, Xie-Yuan; Yin, Xie-Zhen

2016-05-01

A one-dimensional electrified viscoelastic model is built to study the nonlinear behavior of a slightly viscoelastic, perfectly conducting liquid jet under a radial electric field. The equations are solved numerically using an implicit finite difference scheme together with a boundary element method. The electrified viscoelastic jet is found to evolve into a beads-on-string structure in the presence of the radial electric field. Although the radial electric field greatly enhances the linear instability of the jet, its influence on the decay of the filament thickness is limited during the nonlinear evolution of the jet. On the other hand, the radial electric field induces axial non-uniformity of the first normal stress difference within the filament. The first normal stress difference in the center region of the filament may be greatly decreased by the radial electric field. The regions with/without satellite droplets are illuminated on the χ (the electrical Bond number)-k (the dimensionless wave number) plane. Satellite droplets may be formed for larger wave numbers at larger radial electric fields.

A three-dimensional dual potential procedure with applications to wind tunnel inlets and interacting boundary layers

NASA Technical Reports Server (NTRS)

Rao, K. V.; Pletcher, R. H.; Steger, J. L.; Vandalsem, W. R.

1987-01-01

A dual potential decomposition of the velocity field into a scalar and a vector potential function is extended to three dimensions and used in the finite-difference simulation of steady three-dimensional inviscid rotational flows and viscous flow. The finite-difference procedure was used to simulate the flow through the 80 by 120 ft wind tunnel at NASA Ames Research Center. Rotational flow produced by the stagnation pressure drop across vanes and screens which are located at the entrance of the inlet is modeled using actuator disk theory. Results are presented for two different inlet vane and screen configurations. The numerical predictions are in good agreement with experimental data. The dual potential procedure was also applied to calculate the viscous flow along two and three dimensional troughs. Viscous effects are simulated by injecting vorticity which is computed from a boundary layer algorithm. For attached flow over a three dimensional trough, the present calculations are in good agreement with other numerical predictions. For separated flow, it is shown from a two dimensional analysis that the boundary layer approximation provides an accurate measure of the vorticity in regions close to the wall; whereas further away from the wall, caution has to be exercised in using the boundary-layer equations to supply vorticity to the dual potential formulation.

One-dimensional "atom" with zero-range potential perturbed by finite sequence of zero-duration laser pulses

NASA Astrophysics Data System (ADS)

Gusev, A. A.; Chuluunbaatar, O.; Popov, Yu. V.; Vinitsky, S. I.; Derbov, V. L.; Lovetskiy, K. P.

2018-04-01

The exactly soluble model of a train of zero-duration electromagnetic pulses interacting with a 1D atom with short-range interaction potential modelled by a δ-function is considered. The model is related to the up-to-date laser techniques providing the duration of pulses as short as a few attoseconds and the intensities higher than 1014 W/cm2.

Three-dimensional application of the Johnson-King turbulence model for a boundary-layer direct method

NASA Technical Reports Server (NTRS)

Kavsaoglu, Mehmet S.; Kaynak, Unver; Van Dalsem, William R.

1989-01-01

The Johnson-King turbulence model as extended to three-dimensional flows was evaluated using finite-difference boundary-layer direct method. Calculations were compared against the experimental data of the well-known Berg-Elsenaar incompressible flow over an infinite swept-wing. The Johnson-King model, which includes the nonequilibrium effects in a developing turbulent boundary-layer, was found to significantly improve the predictive quality of a direct boundary-layer method. The improvement was especially visible in the computations with increased three-dimensionality of the mean flow, larger integral parameters, and decreasing eddy-viscosity and shear stress magnitudes in the streamwise direction; all in better agreement with the experiment than simple mixing-length methods.

[Effect of zirconia abutment angulation on stress distribution in the abutment and the bone around implant: a finite element study].

PubMed

Yang, Yan-zhong; Tian, Xiao-hua; Zhou, Yan-min

2015-08-01

To investigate the effect of three different zirconia angular abutments on the stress distribution in bone and abutment using three-dimensional finite element analysis, and provide instruction for clinical application. Finite element analysis (FEA) was applied to analyze the stress distribution of three different zirconia/titanium angular abutments and bone around implant. The maximum Von Minses stress that existed in abutment, bolt and bone of the angular abutment model was significantly higher than that existed in the straight abutment model. The maximum Von Minses stress that existed in abutment, bolt and bone of the 20 ° angular abutment model was significantly higher than that existed in 15 ° angular abutment model. There was no significant difference between zirconia abutment model and titanium abutment model. The abutment angulation has a significant influence on the stress distribution in the abutment, bolt and bone, and exacerbates as the angulation increases, which suggest that we should take more attention to the implant orientation and use straight abutment or little angular abutment. The zirconia abutment can be used safely, and there is no noticeable difference between zirconia abutment and titanium abutment on stress distribution.

Evaluation of stress changes in the mandible with a fixed functional appliance: a finite element study.

PubMed

Chaudhry, Anshul; Sidhu, Maninder S; Chaudhary, Girish; Grover, Seema; Chaudhry, Nimisha; Kaushik, Ashutosh

2015-02-01

The aim of this study was to evaluate the effects of a fixed functional appliance (Forsus Fatigue Resistant Device; 3M Unitek, Monrovia, Calif) on the mandible with 3-dimensional finite element stress analysis. A 3-dimensional finite element model of the mandible was constructed from the images generated by cone-beam computed tomography of a patient undergoing fixed orthodontic treatment. The changes were studied with the finite element method, in the form of highest von Mises stress and maximum principal stress regions. More areas of stress were seen in the model of the mandible with the Forsus compared with the model of the mandible in the resting stage. This fixed functional appliance studied by finite element model analysis caused increases in the maximum principal stress and the von Mises stress in both the cortical bone and the condylar region of the mandible by more than 2 times. Copyright © 2015 American Association of Orthodontists. Published by Elsevier Inc. All rights reserved.

Fiber shape effects on metal matrix composite behavior

NASA Technical Reports Server (NTRS)

Brown, H. C.; Lee, H.-J.; Chamis, C. C.

1992-01-01

The effects of different fiber shapes on the behavior of a SiC/Ti-15 metal matrix composite is computationally simulated. A three-dimensional finite element model consisting of a group of nine unidirectional fibers is used in the analysis. The model is employed to represent five different fiber shapes: a circle, an ellipse, a kidney, and two different cross shapes. The distribution of microstresses and the composite material properties, such as moduli, coefficients of thermal expansion, and Poisson's ratios, are obtained from the finite element analysis for the various fiber shapes. Comparisons of these results are used to determine the sensitivity of the composite behavior to the different fiber shapes and assess their potential benefits. No clear benefits result from different fiber shapes though there are some increases/decreases in isolated properties.

Topological footprints of the Kitaev chain with long-range superconducting pairings at a finite temperature

NASA Astrophysics Data System (ADS)

Bhattacharya, Utso; Dutta, Amit

2018-06-01

We study the one-dimensional Kitaev chain with long-range superconductive pairing terms at a finite temperature where the system is prepared in a mixed state in equilibrium with a heat reservoir maintained at a constant temperature T . In order to probe the footprint of the ground-state topological behavior of the model at finite temperature, we look at two global quantities extracted out of two geometrical constructions: the Uhlmann and the interferometric phase. Interestingly, when the long-range effect dominates, the Uhlmann phase approach fails to reproduce the topological aspects of the model in the pure-state limit; on the other hand, the interferometric phase which has a proper pure state reduction, shows a behavior independent of the ambient temperature.

Limit theorems for Lévy walks in d dimensions: rare and bulk fluctuations

NASA Astrophysics Data System (ADS)

Fouxon, Itzhak; Denisov, Sergey; Zaburdaev, Vasily; Barkai, Eli

2017-04-01

We consider super-diffusive Lévy walks in d≥slant 2 dimensions when the duration of a single step, i.e. a ballistic motion performed by a walker, is governed by a power-law tailed distribution of infinite variance and finite mean. We demonstrate that the probability density function (PDF) of the coordinate of the random walker has two different scaling limits at large times. One limit describes the bulk of the PDF. It is the d-dimensional generalization of the one-dimensional Lévy distribution and is the counterpart of the central limit theorem (CLT) for random walks with finite dispersion. In contrast with the one-dimensional Lévy distribution and the CLT this distribution does not have a universal shape. The PDF reflects anisotropy of the single-step statistics however large the time is. The other scaling limit, the so-called ‘infinite density’, describes the tail of the PDF which determines second (dispersion) and higher moments of the PDF. This limit repeats the angular structure of the PDF of velocity in one step. A typical realization of the walk consists of anomalous diffusive motion (described by anisotropic d-dimensional Lévy distribution) interspersed with long ballistic flights (described by infinite density). The long flights are rare but due to them the coordinate increases so much that their contribution determines the dispersion. We illustrate the concept by considering two types of Lévy walks, with isotropic and anisotropic distributions of velocities. Furthermore, we show that for isotropic but otherwise arbitrary velocity distributions the d-dimensional process can be reduced to a one-dimensional Lévy walk. We briefly discuss the consequences of non-universality for the d  >  1 dimensional fractional diffusion equation, in particular the non-uniqueness of the fractional Laplacian.

Two-Layer Viscous Shallow-Water Equations and Conservation Laws

NASA Astrophysics Data System (ADS)

Kanayama, Hiroshi; Dan, Hiroshi

In our previous papers, the two-layer viscous shallow-water equations were derived from the three-dimensional Navier-Stokes equations under the hydrostatic assumption. Also, it was noted that the combination of upper and lower equations in the two-layer model produces the classical one-layer equations if the density of each layer is the same. Then, the two-layer equations were approximated by a finite element method which followed our numerical scheme established for the one-layer model in 1978. Also, it was numerically demonstrated that the interfacial instability generated when the densities are the same can be eliminated by providing a sufficient density difference. In this paper, we newly show that conservation laws are still valid in the two-layer model. Also, we show results of a new physical experiment for the interfacial instability.

Evaluation of an intact, an ACL-deficient, and a reconstructed human knee joint finite element model.

PubMed

Vairis, Achilles; Stefanoudakis, George; Petousis, Markos; Vidakis, Nectarios; Tsainis, Andreas-Marios; Kandyla, Betina

2016-02-01

The human knee joint has a three-dimensional geometry with multiple body articulations that produce complex mechanical responses under loads that occur in everyday life and sports activities. Understanding the complex mechanical interactions of these load-bearing structures is of use when the treatment of relevant diseases is evaluated and assisting devices are designed. The anterior cruciate ligament (ACL) in the knee is one of four main ligaments that connects the femur to the tibia and is often torn during sudden twisting motions, resulting in knee instability. The objective of this work is to study the mechanical behavior of the human knee joint and evaluate the differences in its response for three different states, i.e., intact, ACL-deficient, and surgically treated (reconstructed) knee. The finite element models corresponding to these states were developed. For the reconstructed model, a novel repair device was developed and patented by the author in previous work. Static load cases were applied, as have already been presented in a previous work, in order to compare the calculated results produced by the two models the ACL-deficient and the surgically reconstructed knee joint, under the exact same loading conditions. Displacements were calculated in different directions for the load cases studied and were found to be very close to those from previous modeling work and were in good agreement with experimental data presented in literature. The developed finite element model for both the intact and the ACL-deficient human knee joint is a reliable tool to study the kinematics of the human knee, as results of this study show. In addition, the reconstructed human knee joint model had kinematic behavior similar to the intact knee joint, showing that such reconstruction devices can restore human knee stability to an adequate extent.

Finite-Source Inversion for the 2004 Parkfield Earthquake using 3D Velocity Model Green's Functions

NASA Astrophysics Data System (ADS)

Kim, A.; Dreger, D.; Larsen, S.

2008-12-01

We determine finite fault models of the 2004 Parkfield earthquake using 3D Green's functions. Because of the dense station coverage and detailed 3D velocity structure model in this region, this earthquake provides an excellent opportunity to examine how the 3D velocity structure affects the finite fault inverse solutions. Various studies (e.g. Michaels and Eberhart-Phillips, 1991; Thurber et al., 2006) indicate that there is a pronounced velocity contrast across the San Andreas Fault along the Parkfield segment. Also the fault zone at Parkfield is wide as evidenced by mapped surface faults and where surface slip and creep occurred in the 1966 and the 2004 Parkfield earthquakes. For high resolution images of the rupture process"Ait is necessary to include the accurate 3D velocity structure for the finite source inversion. Liu and Aurchuleta (2004) performed finite fault inversions using both 1D and 3D Green's functions for 1989 Loma Prieta earthquake using the same source paramerization and data but different Green's functions and found that the models were quite different. This indicates that the choice of the velocity model significantly affects the waveform modeling at near-fault stations. In this study, we used the P-wave velocity model developed by Thurber et al (2006) to construct the 3D Green's functions. P-wave speeds are converted to S-wave speeds and density using by the empirical relationships of Brocher (2005). Using a finite difference method, E3D (Larsen and Schultz, 1995), we computed the 3D Green's functions numerically by inserting body forces at each station. Using reciprocity, these Green's functions are recombined to represent the ground motion at each station due to the slip on the fault plane. First we modeled the waveforms of small earthquakes to validate the 3D velocity model and the reciprocity of the Green"fs function. In the numerical tests we found that the 3D velocity model predicted the individual phases well at frequencies lower than 0.25 Hz but that the velocity model is fast at stations located very close to the fault. In this near-fault zone the model also underpredicts the amplitudes. This implies the need to include an additional low velocity zone in the fault zone to fit the data. For the finite fault modeling we use the same stations as in our previous study (Kim and Dreger 2008), and compare the results to investigate the effect of 3D Green's functions on kinematic source inversions. References: Brocher, T. M., (2005), Empirical relations between elastic wavespeeds and density in the Earth's crust, Bull. Seism. Soc. Am., 95, No. 6, 2081-2092. Eberhart-Phillips, D., and A.J. Michael, (1993), Three-dimensional velocity structure and seismicity in the Parkfield region, central California, J. Geophys. Res., 98, 15,737-15,758. Kim A., D. S. Dreger (2008), Rupture process of the 2004 Parkfield earthquake from near-fault seismic waveform and geodetic records, J. Geophys. Res., 113, B07308. Thurber, C., H. Zhang, F. Waldhauser, J. Hardebeck, A. Michaels, and D. Eberhart-Phillips (2006), Three- dimensional compressional wavespeed model, earthquake relocations, and focal mechanisms for the Parkfield, California, region, Bull. Seism. Soc. Am., 96, S38-S49. Larsen, S., and C. A. Schultz (1995), ELAS3D: 2D/3D elastic finite-difference wave propagation code, Technical Report No. UCRL-MA-121792, 19pp. Liu, P., and R. J. Archuleta (2004), A new nonlinear finite fault inversion with three-dimensional Green's functions: Application to the 1989 Loma Prieta, California, earthquake, J. Geophys. Res., 109, B02318.

From Laser Scanning to Finite Element Analysis of Complex Buildings by Using a Semi-Automatic Procedure

PubMed Central

Castellazzi, Giovanni; D’Altri, Antonio Maria; Bitelli, Gabriele; Selvaggi, Ilenia; Lambertini, Alessandro

2015-01-01

In this paper, a new semi-automatic procedure to transform three-dimensional point clouds of complex objects to three-dimensional finite element models is presented and validated. The procedure conceives of the point cloud as a stacking of point sections. The complexity of the clouds is arbitrary, since the procedure is designed for terrestrial laser scanner surveys applied to buildings with irregular geometry, such as historical buildings. The procedure aims at solving the problems connected to the generation of finite element models of these complex structures by constructing a fine discretized geometry with a reduced amount of time and ready to be used with structural analysis. If the starting clouds represent the inner and outer surfaces of the structure, the resulting finite element model will accurately capture the whole three-dimensional structure, producing a complex solid made by voxel elements. A comparison analysis with a CAD-based model is carried out on a historical building damaged by a seismic event. The results indicate that the proposed procedure is effective and obtains comparable models in a shorter time, with an increased level of automation. PMID:26225978

Analysis of wave motion in one-dimensional structures through fast-Fourier-transform-based wavelet finite element method

NASA Astrophysics Data System (ADS)

Shen, Wei; Li, Dongsheng; Zhang, Shuaifang; Ou, Jinping

2017-07-01

This paper presents a hybrid method that combines the B-spline wavelet on the interval (BSWI) finite element method and spectral analysis based on fast Fourier transform (FFT) to study wave propagation in One-Dimensional (1D) structures. BSWI scaling functions are utilized to approximate the theoretical wave solution in the spatial domain and construct a high-accuracy dynamic stiffness matrix. Dynamic reduction on element level is applied to eliminate the interior degrees of freedom of BSWI elements and substantially reduce the size of the system matrix. The dynamic equations of the system are then transformed and solved in the frequency domain through FFT-based spectral analysis which is especially suitable for parallel computation. A comparative analysis of four different finite element methods is conducted to demonstrate the validity and efficiency of the proposed method when utilized in high-frequency wave problems. Other numerical examples are utilized to simulate the influence of crack and delamination on wave propagation in 1D rods and beams. Finally, the errors caused by FFT and their corresponding solutions are presented.

Fast computation of the electrolyte-concentration transfer function of a lithium-ion cell model

NASA Astrophysics Data System (ADS)

Rodríguez, Albert; Plett, Gregory L.; Trimboli, M. Scott

2017-08-01

One approach to creating physics-based reduced-order models (ROMs) of battery-cell dynamics requires first generating linearized Laplace-domain transfer functions of all cell internal electrochemical variables of interest. Then, the resulting infinite-dimensional transfer functions can be reduced by various means in order to find an approximate low-dimensional model. These methods include Padé approximation or the Discrete-Time Realization algorithm. In a previous article, Lee and colleagues developed a transfer function of the electrolyte concentration for a porous-electrode pseudo-two-dimensional lithium-ion cell model. Their approach used separation of variables and Sturm-Liouville theory to compute an infinite-series solution to the transfer function, which they then truncated to a finite number of terms for reasons of practicality. Here, we instead use a variation-of-parameters approach to arrive at a different representation of the identical solution that does not require a series expansion. The primary benefits of the new approach are speed of computation of the transfer function and the removal of the requirement to approximate the transfer function by truncating the number of terms evaluated. Results show that the speedup of the new method can be more than 3800.

Indispensable finite time corrections for Fokker-Planck equations from time series data.

PubMed

Ragwitz, M; Kantz, H

2001-12-17

The reconstruction of Fokker-Planck equations from observed time series data suffers strongly from finite sampling rates. We show that previously published results are degraded considerably by such effects. We present correction terms which yield a robust estimation of the diffusion terms, together with a novel method for one-dimensional problems. We apply these methods to time series data of local surface wind velocities, where the dependence of the diffusion constant on the state variable shows a different behavior than previously suggested.

Finite Element Model for Failure Study of Two-Dimensional Triaxially Braided Composite

NASA Technical Reports Server (NTRS)

Li, Xuetao; Binienda, Wieslaw K.; Goldberg, Robert K.

2010-01-01

A new three-dimensional finite element model of two-dimensional triaxially braided composites is presented in this paper. This meso-scale modeling technique is used to examine and predict the deformation and damage observed in tests of straight sided specimens. A unit cell based approach is used to take into account the braiding architecture as well as the mechanical properties of the fiber tows, the matrix and the fiber tow-matrix interface. A 0 deg / plus or minus 60 deg. braiding configuration has been investigated by conducting static finite element analyses. Failure initiation and progressive degradation has been simulated in the fiber tows by use of the Hashin failure criteria and a damage evolution law. The fiber tow-matrix interface was modeled by using a cohesive zone approach to capture any fiber-matrix debonding. By comparing the analytical results to those obtained experimentally, the applicability of the developed model was assessed and the failure process was investigated.

A 2D nonlinear multiring model for blood flow in large elastic arteries

NASA Astrophysics Data System (ADS)

Ghigo, Arthur R.; Fullana, Jose-Maria; Lagrée, Pierre-Yves

2017-12-01

In this paper, we propose a two-dimensional nonlinear ;multiring; model to compute blood flow in axisymmetric elastic arteries. This model is designed to overcome the numerical difficulties of three-dimensional fluid-structure interaction simulations of blood flow without using the over-simplifications necessary to obtain one-dimensional blood flow models. This multiring model is derived by integrating over concentric rings of fluid the simplified long-wave Navier-Stokes equations coupled to an elastic model of the arterial wall. The resulting system of balance laws provides a unified framework in which both the motion of the fluid and the displacement of the wall are dealt with simultaneously. The mathematical structure of the multiring model allows us to use a finite volume method that guarantees the conservation of mass and the positivity of the numerical solution and can deal with nonlinear flows and large deformations of the arterial wall. We show that the finite volume numerical solution of the multiring model provides at a reasonable computational cost an asymptotically valid description of blood flow velocity profiles and other averaged quantities (wall shear stress, flow rate, ...) in large elastic and quasi-rigid arteries. In particular, we validate the multiring model against well-known solutions such as the Womersley or the Poiseuille solutions as well as against steady boundary layer solutions in quasi-rigid constricted and expanded tubes.

Vibration control of beams using stand-off layer damping: finite element modeling and experiments

NASA Astrophysics Data System (ADS)

Chaudry, A.; Baz, A.

2006-03-01

Damping treatments with stand-off layer (SOL) have been widely accepted as an attractive alternative to conventional constrained layer damping (CLD) treatments. Such an acceptance stems from the fact that the SOL, which is simply a slotted spacer layer sandwiched between the viscoelastic layer and the base structure, acts as a strain magnifier that considerably amplifies the shear strain and hence the energy dissipation characteristics of the viscoelastic layer. Accordingly, more effective vibration suppression can be achieved by using SOL as compared to employing CLD. In this paper, a comprehensive finite element model of the stand-off layer constrained damping treatment is developed. The model accounts for the geometrical and physical parameters of the slotted SOL, the viscoelastic, layer the constraining layer, and the base structure. The predictions of the model are validated against the predictions of a distributed transfer function model and a model built using a commercial finite element code (ANSYS). Furthermore, the theoretical predictions are validated experimentally for passive SOL treatments of different configurations. The obtained results indicate a close agreement between theory and experiments. Furthermore, the obtained results demonstrate the effectiveness of the CLD with SOL in enhancing the energy dissipation as compared to the conventional CLD. Extension of the proposed one-dimensional CLD with SOL to more complex structures is a natural extension to the present study.

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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.

A PML-FDTD ALGORITHM FOR SIMULATING PLASMA-COVERED CAVITY-BACKED SLOT ANTENNAS. (R825225)

EPA Science Inventory

A three-dimensional frequency-dependent finite-difference time-domain (FDTD) algorithm with perfectly matched layer (PML) absorbing boundary condition (ABC) and recursive convolution approaches is developed to model plasma-covered open-ended waveguide or cavity-backed slot antenn...

Revisiting 2D Lattice Based Spin Flip-Flop Ising Model: Magnetic Properties of a Thin Film and Its Temperature Dependence

ERIC Educational Resources Information Center

Singh, Satya Pal

2014-01-01

This paper presents a brief review of Ising's work done in 1925 for one dimensional spin chain with periodic boundary condition. Ising observed that no phase transition occurred at finite temperature in one dimension. He erroneously generalized his views in higher dimensions but that was not true. In 1941 Kramer and Wannier obtained…

a Bounded Finite-Difference Discretization of a Two-Dimensional Diffusion Equation with Logistic Nonlinear Reaction

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

In the present manuscript, we introduce a finite-difference scheme to approximate solutions of the two-dimensional version of Fisher's equation from population dynamics, which is a model for which the existence of traveling-wave fronts bounded within (0,1) is a well-known fact. The method presented here is a nonstandard technique which, in the linear regime, approximates the solutions of the original model with a consistency of second order in space and first order in time. The theory of M-matrices is employed here in order to elucidate conditions under which the method is able to preserve the positivity and the boundedness of solutions. In fact, our main result establishes relatively flexible conditions under which the preservation of the positivity and the boundedness of new approximations is guaranteed. Some simulations of the propagation of a traveling-wave solution confirm the analytical results derived in this work; moreover, the experiments evince a good agreement between the numerical result and the analytical solutions.

Linear and nonlinear interpretation of the direct strike lightning response of the NASA F106B thunderstorm research aircraft

NASA Technical Reports Server (NTRS)

Rudolph, T. H.; Perala, R. A.

1983-01-01

The objective of the work reported here is to develop a methodology by which electromagnetic measurements of inflight lightning strike data can be understood and extended to other aircraft. A linear and time invariant approach based on a combination of Fourier transform and three dimensional finite difference techniques is demonstrated. This approach can obtain the lightning channel current in the absence of the aircraft for given channel characteristic impedance and resistive loading. The model is applied to several measurements from the NASA F106B lightning research program. A non-linear three dimensional finite difference code has also been developed to study the response of the F106B to a lightning leader attachment. This model includes three species air chemistry and fluid continuity equations and can incorporate an experimentally based streamer formulation. Calculated responses are presented for various attachment locations and leader parameters. The results are compared qualitatively with measured inflight data.

Macroscopic traveling packet and soliton states of quasi-one-dimensional flocks.

PubMed

Guttenberg, Nicholas; Toner, John; Tu, Yuhai

2014-05-01

Using a continuum model for inhomogeneous flocks, we show that a finite but arbitrarily large moving "packet" of active particles (e.g., moving creatures) can form in a background of a lower density disordered phase of these particles, like a liquid drop surrounded by vapor. The "vapor density" of the disordered background can be made arbitrarily low. We find three basic types of quasi-one-dimensional states: "longitudinal", "transverse", and "oblique" states, with their internal velocity fields, respectively, parallel, perpendicular, and oblique to the interface. The transitions between these states are also studied.

Thermal analysis of fused deposition modeling process using infrared thermography imaging and finite element modeling

NASA Astrophysics Data System (ADS)

Zhou, Xunfei; Hsieh, Sheng-Jen

2017-05-01

After years of development, Fused Deposition Modeling (FDM) has become the most popular technique in commercial 3D printing due to its cost effectiveness and easy-to-operate fabrication process. Mechanical strength and dimensional accuracy are two of the most important factors for reliability of FDM products. However, the solid-liquid-solid state changes of material in the FDM process make it difficult to monitor and model. In this paper, an experimental model was developed to apply cost-effective infrared thermography imaging method to acquire temperature history of filaments at the interface and their corresponding cooling mechanism. A three-dimensional finite element model was constructed to simulate the same process using element "birth and death" feature and validated with the thermal response from the experimental model. In 6 of 9 experimental conditions, a maximum of 13% difference existed between the experimental and numerical models. This work suggests that numerical modeling of FDM process is reliable and can facilitate better understanding of bead spreading and road-to-road bonding mechanics during fabrication.

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.

Analysis of Ninety Degree Flexure Tests for Characterization of Composite Transverse Tensile Strength

NASA Technical Reports Server (NTRS)

OBrien, T. Kevin; Krueger, Ronald

2001-01-01

Finite element (FE) analysis was performed on 3-point and 4-point bending test configurations of ninety degree oriented glass-epoxy and graphite-epoxy composite beams to identify deviations from beam theory predictions. Both linear and geometric non-linear analyses were performed using the ABAQUS finite element code. The 3-point and 4-point bending specimens were first modeled with two-dimensional elements. Three-dimensional finite element models were then performed for selected 4-point bending configurations to study the stress distribution across the width of the specimens and compare the results to the stresses computed from two-dimensional plane strain and plane stress analyses and the stresses from beam theory. Stresses for all configurations were analyzed at load levels corresponding to the measured transverse tensile strength of the material.

[Three-dimensional finite element analysis of maxillary anterior teeth retraction force system in light wire technique].

PubMed

Zhang, Xiangfeng; Wang, Chao; Xia, Xi; Deng, Feng; Zhang, Yi

2015-06-01

This study aims to construct a three-dimensional finite element model of a maxillary anterior teeth retraction force system in light wire technique and to investigate the difference of hydrostatic pressure and initial displacement of upper anterior teeth under different torque values of tip back bend. A geometric three-dimensional model of the maxillary bone, including all the upper teeth, was achieved via CT scan. To construct the force model system, lingual brackets and wire were constructed by using the Solidworks. Brackets software, and wire were assembled to the teeth. ANASYS was used to calculate the hydrostatic pressure and the initial displacement of maxillary anterior teeth under different tip-back bend moments of 15, 30, 45, 60, and 75 Nmm when the class II elastic force was 0.556 N. Hydrostatic pressure was concentrated in the root apices and cervical margin of upper anterior teeth. Distal tipping and relative intrusive displacement were observed. The hydrostatic pressure and initial displacement of upper canine were greater than in the central and lateral incisors. This hydrostatic pressure and initial intrusive displacement increased with an increase in tip-back bend moment. Lingual retraction force system of maxillary anterior teeth in light wire technique can be applied safely and controllably. The type and quantity of teeth movement can be controlled by the alteration of tip-back bend moment.

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

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

Avilov, A A

2014-12-31

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

Two-dimensional finite element heat transfer model of softwood. Part I, Effective thermal conductivity

Treesearch

John F. Hunt; Hongmei Gu

2006-01-01

The anisotropy of wood complicates solution of heat and mass transfer problems that require analyses be based on fundamental material properties of the wood structure. Most heat transfer models use average thermal properties across either the radial or tangential direction and do not differentiate the effects of cellular alignment, earlywood/latewood differences, or...

A HIGHWAY MODEL FOR THE ADVECTION, DIFFUSION AND CHEMICAL REACTION OF POLLUTANTS RELEASED BY AUTOMOBILES: PART I. ADVECTION AND DIFFUSION OF SF6 TRACER GAS

EPA Science Inventory

A two-dimensional, finite-difference model simulating a highway has been developed which is able to handle linear and nonlinear chemical reactions. Transport of the pollutants is accomplished by use of an upstream-flux-corrected algorithm developed at the Naval Research Laborator...

Nonlinear 3D visco-resistive MHD modeling of fusion plasmas: a comparison between numerical codes

NASA Astrophysics Data System (ADS)

Bonfiglio, D.; Chacon, L.; Cappello, S.

2008-11-01

Fluid plasma models (and, in particular, the MHD model) are extensively used in the theoretical description of laboratory and astrophysical plasmas. We present here a successful benchmark between two nonlinear, three-dimensional, compressible visco-resistive MHD codes. One is the fully implicit, finite volume code PIXIE3D [1,2], which is characterized by many attractive features, notably the generalized curvilinear formulation (which makes the code applicable to different geometries) and the possibility to include in the computation the energy transport equation and the extended MHD version of Ohm's law. In addition, the parallel version of the code features excellent scalability properties. Results from this code, obtained in cylindrical geometry, are compared with those produced by the semi-implicit cylindrical code SpeCyl, which uses finite differences radially, and spectral formulation in the other coordinates [3]. Both single and multi-mode simulations are benchmarked, regarding both reversed field pinch (RFP) and ohmic tokamak magnetic configurations. [1] L. Chacon, Computer Physics Communications 163, 143 (2004). [2] L. Chacon, Phys. Plasmas 15, 056103 (2008). [3] S. Cappello, Plasma Phys. Control. Fusion 46, B313 (2004) & references therein.

Development of an Unstructured, Three-Dimensional Material Response Design Tool

NASA Technical Reports Server (NTRS)

Schulz, Joseph; Stern, Eric; Palmer, Grant; Muppidi, Suman; Schroeder, Olivia

2017-01-01

A preliminary verification and validation of a new material response model is presented. This model, Icarus, is intended to serve as a design tool for the thermal protection systems of re-entry vehicles. Currently, the capability of the model is limited to simulating the pyrolysis of a material as a result of the radiative and convective surface heating imposed on the material from the surrounding high enthalpy gas. Since the major focus behind the development of Icarus has been model extensibility, the hope is that additional physics can be quickly added. The extensibility is critical since thermal protection systems are becoming increasing complex, e.g. woven carbon polymers. Additionally, as a three-dimensional, unstructured, finite-volume model, Icarus is capable of modeling complex geometries as well as multi-dimensional physics, which have been shown to be important in some scenarios and are not captured by one-dimensional models. In this paper, the mathematical and numerical formulation is presented followed by a discussion of the software architecture and some preliminary verification and validation studies.

A study of the effect of space-dependent neutronics on stochastically-induced bifurcations in BWR dynamics

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

Analytis, G.T.

1995-09-01

A non-linear one-group space-dependent neutronic model for a finite one-dimensional core is coupled with a simple BWR feed-back model. In agreement with results obtained by the authors who originally developed the point-kinetics version of this model, we shall show numerically that stochastic reactivity excitations may result in limit-cycles and eventually in a chaotic behaviour, depending on the magnitude of the feed-back coefficient K. In the framework of this simple space-dependent model, the effect of the non-linearities on the different spatial harmonics is studied and the importance of the space-dependent effects is exemplified and assessed in terms of the importance ofmore » the higher harmonics. It is shown that under certain conditions, when the limit-cycle-type develop, the neutron spectra may exhibit strong space-dependent effects.« less

One-Dimensional Czedli-Type Islands

ERIC Educational Resources Information Center

Horvath, Eszter K.; Mader, Attila; Tepavcevic, Andreja

2011-01-01

The notion of an island has surfaced in recent algebra and coding theory research. Discrete versions provide interesting combinatorial problems. This paper presents the one-dimensional case with finitely many heights, a topic convenient for student research.

Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model

NASA Astrophysics Data System (ADS)

Nemoto, Takahiro; Jack, Robert L.; Lecomte, Vivien

2017-03-01

We analyze large deviations of the time-averaged activity in the one-dimensional Fredrickson-Andersen model, both numerically and analytically. The model exhibits a dynamical phase transition, which appears as a singularity in the large deviation function. We analyze the finite-size scaling of this phase transition numerically, by generalizing an existing cloning algorithm to include a multicanonical feedback control: this significantly improves the computational efficiency. Motivated by these numerical results, we formulate an effective theory for the model in the vicinity of the phase transition, which accounts quantitatively for the observed behavior. We discuss potential applications of the numerical method and the effective theory in a range of more general contexts.

A Block Iterative Finite Element Model for Nonlinear Leaky Aquifer Systems

NASA Astrophysics Data System (ADS)

Gambolati, Giuseppe; Teatini, Pietro

1996-01-01

A new quasi three-dimensional finite element model of groundwater flow is developed for highly compressible multiaquifer systems where aquitard permeability and elastic storage are dependent on hydraulic drawdown. The model is solved by a block iterative strategy, which is naturally suggested by the geological structure of the porous medium and can be shown to be mathematically equivalent to a block Gauss-Seidel procedure. As such it can be generalized into a block overrelaxation procedure and greatly accelerated by the use of the optimum overrelaxation factor. Results for both linear and nonlinear multiaquifer systems emphasize the excellent computational performance of the model and indicate that convergence in leaky systems can be improved up to as much as one order of magnitude.

A software platform for continuum modeling of ion channels based on unstructured mesh

NASA Astrophysics Data System (ADS)

Tu, B.; Bai, S. Y.; Chen, M. X.; Xie, Y.; Zhang, L. B.; Lu, B. Z.

2014-01-01

Most traditional continuum molecular modeling adopted finite difference or finite volume methods which were based on a structured mesh (grid). Unstructured meshes were only occasionally used, but an increased number of applications emerge in molecular simulations. To facilitate the continuum modeling of biomolecular systems based on unstructured meshes, we are developing a software platform with tools which are particularly beneficial to those approaches. This work describes the software system specifically for the simulation of a typical, complex molecular procedure: ion transport through a three-dimensional channel system that consists of a protein and a membrane. The platform contains three parts: a meshing tool chain for ion channel systems, a parallel finite element solver for the Poisson-Nernst-Planck equations describing the electrodiffusion process of ion transport, and a visualization program for continuum molecular modeling. The meshing tool chain in the platform, which consists of a set of mesh generation tools, is able to generate high-quality surface and volume meshes for ion channel systems. The parallel finite element solver in our platform is based on the parallel adaptive finite element package PHG which wass developed by one of the authors [1]. As a featured component of the platform, a new visualization program, VCMM, has specifically been developed for continuum molecular modeling with an emphasis on providing useful facilities for unstructured mesh-based methods and for their output analysis and visualization. VCMM provides a graphic user interface and consists of three modules: a molecular module, a meshing module and a numerical module. A demonstration of the platform is provided with a study of two real proteins, the connexin 26 and hemolysin ion channels.

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

NASA Technical Reports Server (NTRS)

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

1979-01-01

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

Spatiotemporal evolution in a (2+1)-dimensional chemotaxis model

NASA Astrophysics Data System (ADS)

Banerjee, Santo; Misra, Amar P.; Rondoni, L.

2012-01-01

Simulations are performed to investigate the nonlinear dynamics of a (2+1)-dimensional chemotaxis model of Keller-Segel (KS) type, with a logistic growth term. Because of its ability to display auto-aggregation, the KS model has been widely used to simulate self-organization in many biological systems. We show that the corresponding dynamics may lead to steady-states, to divergencies in a finite time as well as to the formation of spatiotemporal irregular patterns. The latter, in particular, appears to be chaotic in part of the range of bounded solutions, as demonstrated by the analysis of wavelet power spectra. Steady-states are achieved with sufficiently large values of the chemotactic coefficient (χ) and/or with growth rates r below a critical value rc. For r>rc, the solutions of the differential equations of the model diverge in a finite time. We also report on the pattern formation regime, for different values of χ, r and of the diffusion coefficient D.

Mechanical topological insulator in zero dimensions

NASA Astrophysics Data System (ADS)

Lera, Natalia; Alvarez, J. V.

2018-04-01

We study linear vibrational modes in finite isostatic Maxwell lattices, mechanical systems where the number of degrees of freedom matches the number of constraints. Recent progress in topological mechanics exploits the nontrivial topology of BDI class Hamiltonians in one dimenson and arising topological floppy modes at the edges. A finite frame, or zero-dimensional system, also exhibits a nonzero topological index according to the classification table. We construct mechanical insulating models in zero dimensions that complete the BDI classification in the available real space dimensions. We compute and interpret its nontrivial invariant Z2.

Personal computer study of finite-difference methods for the transonic small disturbance equation

NASA Technical Reports Server (NTRS)

Bland, Samuel R.

1989-01-01

Calculation of unsteady flow phenomena requires careful attention to the numerical treatment of the governing partial differential equations. The personal computer provides a convenient and useful tool for the development of meshes, algorithms, and boundary conditions needed to provide time accurate solution of these equations. The one-dimensional equation considered provides a suitable model for the study of wave propagation in the equations of transonic small disturbance potential flow. Numerical results for effects of mesh size, extent, and stretching, time step size, and choice of far-field boundary conditions are presented. Analysis of the discretized model problem supports these numerical results. Guidelines for suitable mesh and time step choices are given.

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

Mensah, P.F.; Stubblefield, M.A.; Pang, S.S.

Thermal characterization of a prepreg fabric used as the bonding material to join composite pipes has been modeled and solved using finite difference modeling (FDM) numerical analysis technique for one dimensional heat transfer through the material. Temperature distributions within the composite pipe joint are predicted. The prepreg material has temperature dependent thermal properties. Thus the resulting boundary value equations are non linear and analytical solutions cannot be obtained. This characterization is pertinent in determining the temperature profile in the prepreg layer during the manufacturing process for optimization purposes. In addition, in order to assess the effects of induced thermal stressmore » in the joint, the temperature profile is needed. The methodology employed in this analysis compares favorably with data from experimentation.« less

Sensitivity analysis of a wing aeroelastic response

NASA Technical Reports Server (NTRS)

Kapania, Rakesh K.; Eldred, Lloyd B.; Barthelemy, Jean-Francois M.

1991-01-01

A variation of Sobieski's Global Sensitivity Equations (GSE) approach is implemented to obtain the sensitivity of the static aeroelastic response of a three-dimensional wing model. The formulation is quite general and accepts any aerodynamics and structural analysis capability. An interface code is written to convert one analysis's output to the other's input, and visa versa. Local sensitivity derivatives are calculated by either analytic methods or finite difference techniques. A program to combine the local sensitivities, such as the sensitivity of the stiffness matrix or the aerodynamic kernel matrix, into global sensitivity derivatives is developed. The aerodynamic analysis package FAST, using a lifting surface theory, and a structural package, ELAPS, implementing Giles' equivalent plate model are used.

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.

Stress Distribution in Single Dental Implant System: Three-Dimensional Finite Element Analysis Based on an In Vitro Experimental Model.

PubMed

Rezende, Carlos Eduardo Edwards; Chase-Diaz, Melody; Costa, Max Doria; Albarracin, Max Laurent; Paschoeto, Gabriela; Sousa, Edson Antonio Capello; Rubo, José Henrique; Borges, Ana Flávia Sanches

2015-10-01

This study aimed to analyze the stress distribution in single implant system and to evaluate the compatibility of an in vitro model with finite element (FE) model. The in vitro model consisted of Brånemark implant; multiunit set abutment of 5 mm height; metal-ceramic screw-retained crown, and polyurethane simulating the bone. Deformations were recorded in the peri-implant region in the mesial and distal aspects, after an axial 300 N load application at the center of the occlusal aspect of the crown, using strain gauges. This in vitro model was scanned with micro CT to design a three-dimensional FE model and the strains in the peri-implant bone region were registered to check the compatibility between both models. The FE model was used to evaluate stress distribution in different parts of the system. The values obtained from the in vitro model (20-587 με) and the finite element analysis (81-588 με) showed agreement among them. The highest stresses because of axial and oblique load, respectively were 5.83 and 40 MPa for the cortical bone, 55 and 1200 MPa for the implant, and 80 and 470 MPa for the abutment screw. The FE method proved to be effective for evaluating the deformation around single implant. Oblique loads lead to higher stress concentrations.

A method for the direct numerical simulation of hypersonic boundary-layer instability with finite-rate chemistry

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

Marxen, Olaf, E-mail: olaf.marxen@vki.ac.be; Aeronautics and Aerospace Department, von Karman Institute for Fluid Dynamics, Chaussée de Waterloo, 72, 1640 Rhode-St-Genèse; Magin, Thierry E.

2013-12-15

A new numerical method is presented here that allows to consider chemically reacting gases during the direct numerical simulation of a hypersonic fluid flow. The method comprises the direct coupling of a solver for the fluid mechanical model and a library providing the physio-chemical model. The numerical method for the fluid mechanical model integrates the compressible Navier–Stokes equations using an explicit time advancement scheme and high-order finite differences. This Navier–Stokes code can be applied to the investigation of laminar-turbulent transition and boundary-layer instability. The numerical method for the physio-chemical model provides thermodynamic and transport properties for different gases as wellmore » as chemical production rates, while here we exclusively consider a five species air mixture. The new method is verified for a number of test cases at Mach 10, including the one-dimensional high-temperature flow downstream of a normal shock, a hypersonic chemical reacting boundary layer in local thermodynamic equilibrium and a hypersonic reacting boundary layer with finite-rate chemistry. We are able to confirm that the diffusion flux plays an important role for a high-temperature boundary layer in local thermodynamic equilibrium. Moreover, we demonstrate that the flow for a case previously considered as a benchmark for the investigation of non-equilibrium chemistry can be regarded as frozen. Finally, the new method is applied to investigate the effect of finite-rate chemistry on boundary layer instability by considering the downstream evolution of a small-amplitude wave and comparing results with those obtained for a frozen gas as well as a gas in local thermodynamic equilibrium.« less

On the theory of oscillating airfoils of finite span in subsonic compressible flow

NASA Technical Reports Server (NTRS)

Reissner, Eric

1950-01-01

The problem of oscillating lifting surface of finite span in subsonic compressible flow is reduced to an integral equation. The kernel of the integral equation is approximated by a simpler expression, on the basis of the assumption of sufficiently large aspect ratio. With this approximation the double integral occurring in the formulation of the problem is reduced to two single integrals, one of which is taken over the chord and the other over the span of the lifting surface. On the basis of this reduction the three-dimensional problem appears separated into two two-dimensional problems, one of them being effectively the problem of two-dimensional flow and the other being the problem of spanwise circulation distribution. Earlier results concerning the oscillating lifting surface of finite span in incompressible flow are contained in the present more general results.

BIOMECHANICAL ANALYSIS OF THE STRESSES GENERATED BY DIFFERENT DISOCCLUSION PATTERNS IN AN IMPLANT-SUPPORTED MANDIBULAR COMPLETE DENTURE

PubMed Central

Greco, Gustavo Diniz; Jansen, Wellington Corrêa; Landre, Janis; Seraidarian, Paulo Isaías

2009-01-01

Objectives: This study evaluated by three-dimensional finite element analysis the tensions generated by different disocclusion patterns (canine guide and bilateral balanced occlusion) in an implant-supported mandibular complete denture. Material and Methods: A three-dimensional model of implant-supported mandibular complete denture was fabricated according to the Brånemark protocol. A 5-element 3.75 x 13-mm screw-shape dental implant system was modeled for this study. The implants were located in the intermental foramen region with 3-mm-high prosthetic components joined by a nickel-chromium framework with 12-mm bilateral cantilever covered by acrylic resin and 12 acrylic denture teeth. SolidWorks® software was used before and after processing the simulations. The mechanical properties of the components were inserted in the model and a 15 N load was established in fixed points, in each one of the simulations. Data were collected in the entire nickel-chromium framework. The results were displayed three-dimensionally as color graphic scales. Results: The canine guide generated greater tensions in the region of the first implant, while the bilateral balanced occlusion generated great tensions in the entire metallic framework. The maximum tension found in the simulation of the bilateral balanced occlusion was 3.22 fold higher than the one found in the simulation of the disocclusion in canine guide. Conclusion: The pattern of disocclusion in canine guide is the ideal for implant-supported mandibular complete denture. PMID:19936535

Biomechanical analysis of the stresses generated by different disocclusion patterns in an implant-supported mandibular complete denture.

PubMed

Greco, Gustavo Diniz; Jansen, Wellington Corrêa; Landre Junior, Janis; Seraidarian, Paulo Isaías

2009-01-01

This study evaluated by three-dimensional finite element analysis the tensions generated by different disocclusion patterns (canine guide and bilateral balanced occlusion) in an implant-supported mandibular complete denture. A three-dimensional model of implant-supported mandibular complete denture was fabricated according to the Brånemark protocol. A 5-element 3.75 x 13-mm screw-shape dental implant system was modeled for this study. The implants were located in the inter-mental foramen region with 3-mm-high prosthetic components joined by a nickel-chromium framework with 12-mm bilateral cantilever covered by acrylic resin and 12 acrylic denture teeth. SolidWorks software was used before and after processing the simulations. The mechanical properties of the components were inserted in the model and a 15 N load was established in fixed points, in each one of the simulations. Data were collected in the entire nickel-chromium framework. The results were displayed three-dimensionally as color graphic scales. The canine guide generated greater tensions in the region of the first implant, while the bilateral balanced occlusion generated great tensions in the entire metallic framework. The maximum tension found in the simulation of the bilateral balanced occlusion was 3.22 fold higher than the one found in the simulation of the disocclusion in canine guide. The pattern of disocclusion in canine guide is the ideal for implant-supported mandibular complete denture.

Seismic wave propagation modeling

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

Jones, E.M.; Olsen, K.B.

1998-12-31

This is the final report of a one-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). A hybrid, finite-difference technique was developed for modeling nonlinear soil amplification from three-dimensional, finite-fault radiation patters for earthquakes in arbitrary earth models. The method was applied to the 17 January 1994 Northridge earthquake. Particle velocities were computed on a plane at 5-km depth, immediately above the causative fault. Time-series of the strike-perpendicular, lateral velocities then were propagated vertically in a soil column typical of the San Fernando Valley. Suitable material models were adapted from a suite used tomore » model ground motions at the US Nevada Test Site. The effects of nonlinearity reduced relative spectral amplitudes by about 40% at frequencies above 1.5 Hz but only by 10% at lower frequencies. Runs made with source-depth amplitudes increased by a factor of two showed relative amplitudes above 1.5 Hz reduced by a total of 70% above 1.5 Hz and 20% at lower frequencies. Runs made with elastic-plastic material models showed similar behavior to runs made with Masing-Rule models.« less

Two-dimensional thermal modeling of power monolithic microwave integrated circuits (MMIC's)

NASA Technical Reports Server (NTRS)

Fan, Mark S.; Christou, Aris; Pecht, Michael G.

1992-01-01

Numerical simulations of the two-dimensional temperature distributions for a typical GaAs MMIC circuit are conducted, aiming at understanding the heat conduction process of the circuit chip and providing temperature information for device reliability analysis. The method used is to solve the two-dimensional heat conduction equation with a control-volume-based finite difference scheme. In particular, the effects of the power dissipation and the ambient temperature are examined, and the criterion for the worst operating environment is discussed in terms of the allowed highest device junction temperature.

Flow of rarefied gases over two-dimensional bodies

NASA Technical Reports Server (NTRS)

Jeng, Duen-Ren; De Witt, Kenneth J.; Keith, Theo G., Jr.; Chung, Chan-Hong

1989-01-01

A kinetic-theory analysis is made of the flow of rarefied gases over two-dimensional bodies of arbitrary curvature. The Boltzmann equation simplified by a model collision integral is written in an arbitrary orthogonal curvilinear coordinate system, and solved by means of finite-difference approximation with the discrete ordinate method. A numerical code is developed which can be applied to any two-dimensional submerged body of arbitrary curvature for the flow regimes from free-molecular to slip at transonic Mach numbers. Predictions are made for the case of a right circular cylinder.

Inverse finite-size scaling for high-dimensional significance analysis

NASA Astrophysics Data System (ADS)

Xu, Yingying; Puranen, Santeri; Corander, Jukka; Kabashima, Yoshiyuki

2018-06-01

We propose an efficient procedure for significance determination in high-dimensional dependence learning based on surrogate data testing, termed inverse finite-size scaling (IFSS). The IFSS method is based on our discovery of a universal scaling property of random matrices which enables inference about signal behavior from much smaller scale surrogate data than the dimensionality of the original data. As a motivating example, we demonstrate the procedure for ultra-high-dimensional Potts models with order of 1010 parameters. IFSS reduces the computational effort of the data-testing procedure by several orders of magnitude, making it very efficient for practical purposes. This approach thus holds considerable potential for generalization to other types of complex models.

An explicit dissipation-preserving method for Riesz space-fractional nonlinear wave equations in multiple dimensions

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

2018-06-01

In this work, we investigate numerically a model governed by a multidimensional nonlinear wave equation with damping and fractional diffusion. The governing partial differential equation considers the presence of Riesz space-fractional derivatives of orders in (1, 2], and homogeneous Dirichlet boundary data are imposed on a closed and bounded spatial domain. The model under investigation possesses an energy function which is preserved in the undamped regime. In the damped case, we establish the property of energy dissipation of the model using arguments from functional analysis. Motivated by these results, we propose an explicit finite-difference discretization of our fractional model based on the use of fractional centered differences. Associated to our discrete model, we also propose discretizations of the energy quantities. We establish that the discrete energy is conserved in the undamped regime, and that it dissipates in the damped scenario. Among the most important numerical features of our scheme, we show that the method has a consistency of second order, that it is stable and that it has a quadratic order of convergence. Some one- and two-dimensional simulations are shown in this work to illustrate the fact that the technique is capable of preserving the discrete energy in the undamped regime. For the sake of convenience, we provide a Matlab implementation of our method for the one-dimensional scenario.

High-resolution two-dimensional and three-dimensional modeling of wire grid polarizers and micropolarizer arrays

NASA Astrophysics Data System (ADS)

Vorobiev, Dmitry; Ninkov, Zoran

2017-11-01

Recent advances in photolithography allowed the fabrication of high-quality wire grid polarizers for the visible and near-infrared regimes. In turn, micropolarizer arrays (MPAs) based on wire grid polarizers have been developed and used to construct compact, versatile imaging polarimeters. However, the contrast and throughput of these polarimeters are significantly worse than one might expect based on the performance of large area wire grid polarizers or MPAs, alone. We investigate the parameters that affect the performance of wire grid polarizers and MPAs, using high-resolution two-dimensional and three-dimensional (3-D) finite-difference time-domain simulations. We pay special attention to numerical errors and other challenges that arise in models of these and other subwavelength optical devices. Our tests show that simulations of these structures in the visible and near-IR begin to converge numerically when the mesh size is smaller than ˜4 nm. The performance of wire grid polarizers is very sensitive to the shape, spacing, and conductivity of the metal wires. Using 3-D simulations of micropolarizer "superpixels," we directly study the cross talk due to diffraction at the edges of each micropolarizer, which decreases the contrast of MPAs to ˜200∶1.

An experimental and analytical investigation on the response of GR/EP composite I-frames

NASA Technical Reports Server (NTRS)

Moas, E., Jr.; Boitnott, R. L.; Griffin, O. H., Jr.

1991-01-01

Six-foot diameter, semicircular graphite/epoxy specimens representative of generic aircraft frames were loaded quasi-statically to determine their load response and failure mechanisms for large deflections that occur in an airplane crash. These frame-skin specimens consisted of a cylindrical skin section cocured with a semicircular I-frame. Various frame laminate stacking sequences and geometries were evaluated by statically loading the specimen until multiple failures occurred. Two analytical methods were compared for modeling the frame-skin specimens: a two-dimensional branched-shell finite element analysis and a one-dimensional, closed-form, curved beam solution derived using an energy method. Excellent correlation was obtained between experimental results and the finite element predictions of the linear response of the frames prior to the initial failure. The beam solution was used for rapid parameter and design studies, and was found to be stiff in comparison with the finite element analysis. The specimens were found to be useful for evaluating composite frame designs.

Discontinuous finite element method for vector radiative transfer

NASA Astrophysics Data System (ADS)

Wang, Cun-Hai; Yi, Hong-Liang; Tan, He-Ping

2017-03-01

The discontinuous finite element method (DFEM) is applied to solve the vector radiative transfer in participating media. The derivation in a discrete form of the vector radiation governing equations is presented, in which the angular space is discretized by the discrete-ordinates approach with a local refined modification, and the spatial domain is discretized into finite non-overlapped discontinuous elements. The elements in the whole solution domain are connected by modelling the boundary numerical flux between adjacent elements, which makes the DFEM numerically stable for solving radiative transfer equations. Several various problems of vector radiative transfer are tested to verify the performance of the developed DFEM, including vector radiative transfer in a one-dimensional parallel slab containing a Mie/Rayleigh/strong forward scattering medium and a two-dimensional square medium. The fact that DFEM results agree very well with the benchmark solutions in published references shows that the developed DFEM in this paper is accurate and effective for solving vector radiative transfer problems.

Free Wake Analysis of Helicopter Rotor Blades in Hover Using a Finite Volume Technique

DTIC Science & Technology

1988-10-01

inboard, and root) which were replaced by a far wake model after four revolutions. Murman and Stremel 1121 calculated j two-dimensional unsteady wake...distributed to a fixed mesh, on which the velocities were calculated by a finite difference solution of Laplace’s equation. Stremel [131 applied this two...Analysis of a Hovering Rotor," Vertica, Vol. 6, No. 2, 1982. 12. Murman, E.M., and Stremel , P.M., "A Vortex Wake Capturing Method Po- tential Flow

A two-dimensional finite-difference solution for the temperature distribution in a radial gas turbine guide vane blade

NASA Technical Reports Server (NTRS)

Hosny, W. M.; Tabakoff, W.

1975-01-01

A two-dimensional finite difference numerical technique is presented to determine the temperature distribution in a solid blade of a radial guide vane. A computer program is written in Fortran IV for IBM 370/165 computer. The computer results obtained from these programs have a similar behavior and trend as those obtained by experimental results.

A finite-element model for simulation of two-dimensional steady-state ground-water flow in confined aquifers

USGS Publications Warehouse

Kuniansky, E.L.

1990-01-01

A computer program based on the Galerkin finite-element method was developed to simulate two-dimensional steady-state ground-water flow in either isotropic or anisotropic confined aquifers. The program may also be used for unconfined aquifers of constant saturated thickness. Constant head, constant flux, and head-dependent flux boundary conditions can be specified in order to approximate a variety of natural conditions, such as a river or lake boundary, and pumping well. The computer program was developed for the preliminary simulation of ground-water flow in the Edwards-Trinity Regional aquifer system as part of the Regional Aquifer-Systems Analysis Program. Results of the program compare well to analytical solutions and simulations .from published finite-difference models. A concise discussion of the Galerkin method is presented along with a description of the program. Provided in the Supplemental Data section are a listing of the computer program, definitions of selected program variables, and several examples of data input and output used in verifying the accuracy of the program.