Finite-volume effects and the electromagnetic contributions to kaon and pion masses

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

Basak, Subhasish; Bazavov, Alexei; Bernard, Claude

2014-09-25

We report on the MILC Collaboration calculation of electromagnetic effects on light pseudoscalar mesons. The simulations employ asqtad staggered dynamical quarks in QCD plus quenched photons, with lattice spacings varying from 0.12 to 0.06 fm. Finite volume corrections for the MILC realization of lattice electrodynamics have been calculated in chiral perturbation theory and applied to the lattice data. These corrections differ from those calculated by Hayakawa and Uno because our treatment of zero modes differs from theirs. Updated results for the corrections to "Dashen's theorem" are presented.

Static and dynamic structural-sensitivity derivative calculations in the finite-element-based Engineering Analysis Language (EAL) system

NASA Technical Reports Server (NTRS)

Camarda, C. J.; Adelman, H. M.

1984-01-01

The implementation of static and dynamic structural-sensitivity derivative calculations in a general purpose, finite-element computer program denoted the Engineering Analysis Language (EAL) System is described. Derivatives are calculated with respect to structural parameters, specifically, member sectional properties including thicknesses, cross-sectional areas, and moments of inertia. Derivatives are obtained for displacements, stresses, vibration frequencies and mode shapes, and buckling loads and mode shapes. Three methods for calculating derivatives are implemented (analytical, semianalytical, and finite differences), and comparisons of computer time and accuracy are made. Results are presented for four examples: a swept wing, a box beam, a stiffened cylinder with a cutout, and a space radiometer-antenna truss.

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

DTIC Science & Technology

1979-09-01

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

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.

Application of finite element approach to transonic flow problems

NASA Technical Reports Server (NTRS)

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

1976-01-01

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

Finite Difference Schemes as Algebraic Correspondences between Layers

NASA Astrophysics Data System (ADS)

Malykh, Mikhail; Sevastianov, Leonid

2018-02-01

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

A time dependent difference theory for sound propagation in ducts with flow. [characteristic of inlet and exhaust ducts of turbofan engines

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1979-01-01

A time dependent numerical solution of the linearized continuity and momentum equation was developed for sound propagation in a two dimensional straight hard or soft wall duct with a sheared mean flow. The time dependent governing acoustic difference equations and boundary conditions were developed along with a numerical determination of the maximum stable time increments. A harmonic noise source radiating into a quiescent duct was analyzed. This explicit iteration method then calculated stepwise in real time to obtain the transient as well as the steady state solution of the acoustic field. Example calculations were presented for sound propagation in hard and soft wall ducts, with no flow and plug flow. Although the problem with sheared flow was formulated and programmed, sample calculations were not examined. The time dependent finite difference analysis was found to be superior to the steady state finite difference and finite element techniques because of shorter solution times and the elimination of large matrix storage requirements.

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

DTIC Science & Technology

1980-01-01

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

FINITE-DIFFERENCE ELECTROMAGNETIC DEPOSITION/THERMOREGULATORY MODEL: COMPARISON BETWEEN THEORY AND MEASUREMENTS (JOURNAL VERSION)

EPA Science Inventory

The rate of the electromagnetic energy deposition and the resultant thermoregulatory response of a block model of a squirrel monkey exposed to plane-wave fields at 350 MHz were calculated using a finite-difference procedure. Noninvasive temperature measurements in live squirrel m...

A finite difference Davidson procedure to sidestep full ab initio hessian calculation: Application to characterization of stationary points and transition state searches

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

Sharada, Shaama Mallikarjun; Bell, Alexis T., E-mail: mhg@bastille.cchem.berkeley.edu, E-mail: bell@cchem.berkeley.edu; Head-Gordon, Martin, E-mail: mhg@bastille.cchem.berkeley.edu, E-mail: bell@cchem.berkeley.edu

2014-04-28

The cost of calculating nuclear hessians, either analytically or by finite difference methods, during the course of quantum chemical analyses can be prohibitive for systems containing hundreds of atoms. In many applications, though, only a few eigenvalues and eigenvectors, and not the full hessian, are required. For instance, the lowest one or two eigenvalues of the full hessian are sufficient to characterize a stationary point as a minimum or a transition state (TS), respectively. We describe here a method that can eliminate the need for hessian calculations for both the characterization of stationary points as well as searches for saddlemore » points. A finite differences implementation of the Davidson method that uses only first derivatives of the energy to calculate the lowest eigenvalues and eigenvectors of the hessian is discussed. This method can be implemented in conjunction with geometry optimization methods such as partitioned-rational function optimization (P-RFO) to characterize stationary points on the potential energy surface. With equal ease, it can be combined with interpolation methods that determine TS guess structures, such as the freezing string method, to generate approximate hessian matrices in lieu of full hessians as input to P-RFO for TS optimization. This approach is shown to achieve significant cost savings relative to exact hessian calculation when applied to both stationary point characterization as well as TS optimization. The basic reason is that the present approach scales one power of system size lower since the rate of convergence is approximately independent of the size of the system. Therefore, the finite-difference Davidson method is a viable alternative to full hessian calculation for stationary point characterization and TS search particularly when analytical hessians are not available or require substantial computational effort.« less

Finite Element Analysis of New Crankshaft Automatic Adjustment Mechanism of Pumping Unit

NASA Astrophysics Data System (ADS)

Wu, Jufei; Wang, Qian

2017-12-01

In this paper, the crankshaft automatic adjustment mechanism designed on CYJY10-4.2-53HF pumping unit is used as the research object. The simulation of the friction and bending moment of the crank is carried out by ANSYS Workbench, and the finite element simulation results are compared with the theoretical calculation results to verify the theoretical calculation. The final result is that the finite element analysis of the friction of the crank is basically consistent with the theoretical calculation; The analysis and calculation of the stress and deformation about the two kinds of ultimate conditions of the guide platform are carried out too; The dynamic state analysis of the mechanism is carried out to obtain the vibration modes and natural frequencies of the vibration of the different parts of the counterweight under the condition of no preload force so that the frequency of the array can avoid the natural frequency, and can effectively avoid the resonance phenomenon, and for different modes we can improve the stiffness of the structure.

Gradient corrections to the exchange-correlation free energy

DOE PAGES

Sjostrom, Travis; Daligault, Jerome

2014-10-07

We develop the first-order gradient correction to the exchange-correlation free energy of the homogeneous electron gas for use in finite-temperature density functional calculations. Based on this, we propose and implement a simple temperature-dependent extension for functionals beyond the local density approximation. These finite-temperature functionals show improvement over zero-temperature functionals, as compared to path-integral Monte Carlo calculations for deuterium equations of state, and perform without computational cost increase compared to zero-temperature functionals and so should be used for finite-temperature calculations. Furthermore, while the present functionals are valid at all temperatures including zero, non-negligible difference with zero-temperature functionals begins at temperatures abovemore » 10 000 K.« less

Calculating the Malliavin derivative of some stochastic mechanics problems

PubMed Central

Hauseux, Paul; Hale, Jack S.

2017-01-01

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

Finite-difference solution for turbulent swirling compressible flow in axisymmetric ducts with struts

NASA Technical Reports Server (NTRS)

Anderson, O. L.

1974-01-01

A finite-difference procedure for computing the turbulent, swirling, compressible flow in axisymmetric ducts is described. Arbitrary distributions of heat and mass transfer at the boundaries can be treated, and the effects of struts, inlet guide vanes, and flow straightening vanes can be calculated. The calculation procedure is programmed in FORTRAN 4 and has operated successfully on the UNIVAC 1108, IBM 360, and CDC 6600 computers. The analysis which forms the basis of the procedure, a detailed description of the computer program, and the input/output formats are presented. The results of sample calculations performed with the computer program are compared with experimental data.

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.

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 volume for three-flavour Partially Quenched Chiral Perturbation Theory through NNLO in the meson sector

NASA Astrophysics Data System (ADS)

Bijnens, Johan; Rössler, Thomas

2015-11-01

We present a calculation of the finite volume corrections to meson masses and decay constants in three flavour Partially Quenched Chiral Perturbation Theory (PQChPT) through two-loop order in the chiral expansion for the flavour-charged (or off-diagonal) pseudoscalar mesons. The analytical results are obtained for three sea quark flavours with one, two or three different masses. We reproduce the known infinite volume results and the finite volume results in the unquenched case. The calculation has been performed using the supersymmetric formulation of PQChPT as well as with a quark flow technique.

Quantum Monte Carlo calculations of two neutrons in finite volume

DOE PAGES

Klos, P.; Lynn, J. E.; Tews, I.; ...

2016-11-18

Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliary-field diffusion Monte Carlo calculations of the ground state and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effective field theory interactions. We compare the results against exact diagonalizations and present a detailed analysis of the finite-volume effects, whose understanding is crucial formore » determining observables from the calculated energies. Finally, using the Lüscher formula, we extract the low-energy S-wave scattering parameters from ground- and excited-state energies for different box sizes.« less

Improved Regional Seismic Event Locations Using 3-D Velocity Models

DTIC Science & Technology

1999-12-15

regional velocity model to estimate event hypocenters. Travel times for the regional phases are calculated using a sophisticated eikonal finite...can greatly improve estimates of event locations. Our algorithm calculates travel times using a finite difference approximation of the eikonal ...such as IASP91 or J-B. 3-D velocity models require more sophisticated travel time modeling routines; thus, we use a 3-D eikonal equation solver

Estimating finite-population reproductive numbers in heterogeneous populations.

PubMed

Keegan, Lindsay T; Dushoff, Jonathan

2016-05-21

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

Vector two-point functions in finite volume using partially quenched chiral perturbation theory at two loops

NASA Astrophysics Data System (ADS)

Bijnens, Johan; Relefors, Johan

2017-12-01

We calculate vector-vector correlation functions at two loops using partially quenched chiral perturbation theory including finite volume effects and twisted boundary conditions. We present expressions for the flavor neutral cases and the flavor charged case with equal masses. Using these expressions we give an estimate for the ratio of disconnected to connected contributions for the strange part of the electromagnetic current. We give numerical examples for the effects of partial quenching, finite volume and twisting and suggest the use of different twists to check the size of finite volume effects. The main use of this work is expected to be for lattice QCD calculations of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment.

Benchmark model correction of monitoring system based on Dynamic Load Test of Bridge

NASA Astrophysics Data System (ADS)

Shi, Jing-xian; Fan, Jiang

2018-03-01

Structural health monitoring (SHM) is a field of research in the area, and it’s designed to achieve bridge safety and reliability assessment, which needs to be carried out on the basis of the accurate simulation of the finite element model. Bridge finite element model is simplified of the structural section form, support conditions, material properties and boundary condition, which is based on the design and construction drawings, and it gets the calculation models and the results.But according to the design and specification requirements established finite element model due to its cannot fully reflect the true state of the bridge, so need to modify the finite element model to obtain the more accurate finite element model. Based on Da-guan river crossing of Ma - Zhao highway in Yunnan province as the background to do the dynamic load test test, we find that the impact coefficient of the theoretical model of the bridge is very different from the coefficient of the actual test, and the change is different; according to the actual situation, the calculation model is adjusted to get the correct frequency of the bridge, the revised impact coefficient found that the modified finite element model is closer to the real state, and provides the basis for the correction of the finite model.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao

1994-01-01

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

A one-dimensional model to describe flow localization in viscoplastic slender bars subjected to super critical impact velocities

NASA Astrophysics Data System (ADS)

Vaz-Romero, A.; Rodríguez-Martínez, J. A.

2018-01-01

In this paper we investigate flow localization in viscoplastic slender bars subjected to dynamic tension. We explore loading rates above the critical impact velocity: the wave initiated in the impacted end by the applied velocity is the trigger for the localization of plastic deformation. The problem has been addressed using two kinds of numerical simulations: (1) one-dimensional finite difference calculations and (2) axisymmetric finite element computations. The latter calculations have been used to validate the capacity of the finite difference model to describe plastic flow localization at high impact velocities. The finite difference model, which highlights due to its simplicity, allows to obtain insights into the role played by the strain rate and temperature sensitivities of the material in the process of dynamic flow localization. Specifically, we have shown that viscosity can stabilize the material behavior to the point of preventing the appearance of the critical impact velocity. This is a key outcome of our investigation, which, to the best of the authors' knowledge, has not been previously reported in the literature.

A superlinear iteration method for calculation of finite length journal bearing's static equilibrium position.

PubMed

Zhou, Wenjie; Wei, Xuesong; Wang, Leqin; Wu, Guangkuan

2017-05-01

Solving the static equilibrium position is one of the most important parts of dynamic coefficients calculation and further coupled calculation of rotor system. The main contribution of this study is testing the superlinear iteration convergence method-twofold secant method, for the determination of the static equilibrium position of journal bearing with finite length. Essentially, the Reynolds equation for stable motion is solved by the finite difference method and the inner pressure is obtained by the successive over-relaxation iterative method reinforced by the compound Simpson quadrature formula. The accuracy and efficiency of the twofold secant method are higher in comparison with the secant method and dichotomy. The total number of iterative steps required for the twofold secant method are about one-third of the secant method and less than one-eighth of dichotomy for the same equilibrium position. The calculations for equilibrium position and pressure distribution for different bearing length, clearance and rotating speed were done. In the results, the eccentricity presents linear inverse proportional relationship to the attitude angle. The influence of the bearing length, clearance and bearing radius on the load-carrying capacity was also investigated. The results illustrate that larger bearing length, larger radius and smaller clearance are good for the load-carrying capacity of journal bearing. The application of the twofold secant method can greatly reduce the computational time for calculation of the dynamic coefficients and dynamic characteristics of rotor-bearing system with a journal bearing of finite length.

A superlinear iteration method for calculation of finite length journal bearing's static equilibrium position

PubMed Central

Zhou, Wenjie; Wei, Xuesong; Wang, Leqin

2017-01-01

Solving the static equilibrium position is one of the most important parts of dynamic coefficients calculation and further coupled calculation of rotor system. The main contribution of this study is testing the superlinear iteration convergence method—twofold secant method, for the determination of the static equilibrium position of journal bearing with finite length. Essentially, the Reynolds equation for stable motion is solved by the finite difference method and the inner pressure is obtained by the successive over-relaxation iterative method reinforced by the compound Simpson quadrature formula. The accuracy and efficiency of the twofold secant method are higher in comparison with the secant method and dichotomy. The total number of iterative steps required for the twofold secant method are about one-third of the secant method and less than one-eighth of dichotomy for the same equilibrium position. The calculations for equilibrium position and pressure distribution for different bearing length, clearance and rotating speed were done. In the results, the eccentricity presents linear inverse proportional relationship to the attitude angle. The influence of the bearing length, clearance and bearing radius on the load-carrying capacity was also investigated. The results illustrate that larger bearing length, larger radius and smaller clearance are good for the load-carrying capacity of journal bearing. The application of the twofold secant method can greatly reduce the computational time for calculation of the dynamic coefficients and dynamic characteristics of rotor-bearing system with a journal bearing of finite length. PMID:28572997

A program for calculating photonic band structures, Green's functions and transmission/reflection coefficients using a non-orthogonal FDTD method

NASA Astrophysics Data System (ADS)

Ward, A. J.; Pendry, J. B.

2000-06-01

In this paper we present an updated version of our ONYX program for calculating photonic band structures using a non-orthogonal finite difference time domain method. This new version employs the same transparent formalism as the first version with the same capabilities for calculating photonic band structures or causal Green's functions but also includes extra subroutines for the calculation of transmission and reflection coefficients. Both the electric and magnetic fields are placed onto a discrete lattice by approximating the spacial and temporal derivatives with finite differences. This results in discrete versions of Maxwell's equations which can be used to integrate the fields forwards in time. The time required for a calculation using this method scales linearly with the number of real space points used in the discretization so the technique is ideally suited to handling systems with large and complicated unit cells.

A Kirchhoff approach to seismic modeling and prestack depth migration

NASA Astrophysics Data System (ADS)

Liu, Zhen-Yue

1993-05-01

The Kirchhoff integral provides a robust method for implementing seismic modeling and prestack depth migration, which can handle lateral velocity variation and turning waves. With a little extra computation cost, the Kirchoff-type migration can obtain multiple outputs that have the same phase but different amplitudes, compared with that of other migration methods. The ratio of these amplitudes is helpful in computing some quantities such as reflection angle. I develop a seismic modeling and prestack depth migration method based on the Kirchhoff integral, that handles both laterally variant velocity and a dip beyond 90 degrees. The method uses a finite-difference algorithm to calculate travel times and WKBJ amplitudes for the Kirchhoff integral. Compared to ray-tracing algorithms, the finite-difference algorithm gives an efficient implementation and single-valued quantities (first arrivals) on output. In my finite difference algorithm, the upwind scheme is used to calculate travel times, and the Crank-Nicolson scheme is used to calculate amplitudes. Moreover, interpolation is applied to save computation cost. The modeling and migration algorithms require a smooth velocity function. I develop a velocity-smoothing technique based on damped least-squares to aid in obtaining a successful migration.

Finite-difference simulation of transonic separated flow using a full potential boundary layer interaction approach

NASA Technical Reports Server (NTRS)

Van Dalsem, W. R.; Steger, J. L.

1983-01-01

A new, fast, direct-inverse, finite-difference boundary-layer code has been developed and coupled with a full-potential transonic airfoil analysis code via new inviscid-viscous interaction algorithms. The resulting code has been used to calculate transonic separated flows. The results are in good agreement with Navier-Stokes calculations and experimental data. Solutions are obtained in considerably less computer time than Navier-Stokes solutions of equal resolution. Because efficient inviscid and viscous algorithms are used, it is expected this code will also compare favorably with other codes of its type as they become available.

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

PubMed Central

Calzolari, Arrigo; Nardelli, Marco Buongiorno

2013-01-01

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

Finite difference methods for the solution of unsteady potential flows

NASA Technical Reports Server (NTRS)

Caradonna, F. X.

1982-01-01

Various problems which are confronted in the development of an unsteady finite difference potential code are reviewed mainly in the context of what is done for a typical small disturbance and full potential method. The issues discussed include choice of equations, linearization and conservation, differencing schemes, and algorithm development. A number of applications, including unsteady three dimensional rotor calculations, are demonstrated.

Seismic wavefield modeling based on time-domain symplectic and Fourier finite-difference method

NASA Astrophysics Data System (ADS)

Fang, Gang; Ba, Jing; Liu, Xin-xin; Zhu, Kun; Liu, Guo-Chang

2017-06-01

Seismic wavefield modeling is important for improving seismic data processing and interpretation. Calculations of wavefield propagation are sometimes not stable when forward modeling of seismic wave uses large time steps for long times. Based on the Hamiltonian expression of the acoustic wave equation, we propose a structure-preserving method for seismic wavefield modeling by applying the symplectic finite-difference method on time grids and the Fourier finite-difference method on space grids to solve the acoustic wave equation. The proposed method is called the symplectic Fourier finite-difference (symplectic FFD) method, and offers high computational accuracy and improves the computational stability. Using acoustic approximation, we extend the method to anisotropic media. We discuss the calculations in the symplectic FFD method for seismic wavefield modeling of isotropic and anisotropic media, and use the BP salt model and BP TTI model to test the proposed method. The numerical examples suggest that the proposed method can be used in seismic modeling of strongly variable velocities, offering high computational accuracy and low numerical dispersion. The symplectic FFD method overcomes the residual qSV wave of seismic modeling in anisotropic media and maintains the stability of the wavefield propagation for large time steps.

Finite-difference modeling of the electroseismic logging in a fluid-saturated porous formation

NASA Astrophysics Data System (ADS)

Guan, Wei; Hu, Hengshan

2008-05-01

In a fluid-saturated porous medium, an electromagnetic (EM) wavefield induces an acoustic wavefield due to the electrokinetic effect. A potential geophysical application of this effect is electroseismic (ES) logging, in which the converted acoustic wavefield is received in a fluid-filled borehole to evaluate the parameters of the porous formation around the borehole. In this paper, a finite-difference scheme is proposed to model the ES logging responses to a vertical low frequency electric dipole along the borehole axis. The EM field excited by the electric dipole is calculated separately by finite-difference first, and is considered as a distributed exciting source term in a set of extended Biot's equations for the converted acoustic wavefield in the formation. This set of equations is solved by a modified finite-difference time-domain (FDTD) algorithm that allows for the calculation of dynamic permeability so that it is not restricted to low-frequency poroelastic wave problems. The perfectly matched layer (PML) technique without splitting the fields is applied to truncate the computational region. The simulated ES logging waveforms approximately agree with those obtained by the analytical method. The FDTD algorithm applies also to acoustic logging simulation in porous formations.

Finite difference time domain calculation of transients in antennas with nonlinear loads

NASA Technical Reports Server (NTRS)

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

1991-01-01

In this paper transient fields for antennas with more general geometries are calculated directly using Finite Difference Time Domain methods. In each FDTD cell which contains a nonlinear load, a nonlinear equation is solved at each time step. As a test case the transient current in a long dipole antenna with a nonlinear load excited by a pulsed plane wave is computed using this approach. The results agree well with both calculated and measured results previously published. The approach given here extends the applicability of the FDTD method to problems involving scattering from targets including nonlinear loads and materials, and to coupling between antennas containing nonlinear loads. It may also be extended to propagation through nonlinear materials.

Quantum Monte Carlo calculations of van der Waals interactions between aromatic benzene rings

NASA Astrophysics Data System (ADS)

Azadi, Sam; Kühne, T. D.

2018-05-01

The magnitude of finite-size effects and Coulomb interactions in quantum Monte Carlo simulations of van der Waals interactions between weakly bonded benzene molecules are investigated. To that extent, two trial wave functions of the Slater-Jastrow and Backflow-Slater-Jastrow types are employed to calculate the energy-volume equation of state. We assess the impact of the backflow coordinate transformation on the nonlocal correlation energy. We found that the effect of finite-size errors in quantum Monte Carlo calculations on energy differences is particularly large and may even be more important than the employed trial wave function. In addition to the cohesive energy, the singlet excitonic energy gap and the energy gap renormalization of crystalline benzene at different densities are computed.

Pathloss Calculation Using the Transmission Line Matrix and Finite Difference Time Domain Methods With Coarse Grids

DOE PAGES

Nutaro, James; Kuruganti, Teja

2017-02-24

Numerical simulations of the wave equation that are intended to provide accurate time domain solutions require a computational mesh with grid points separated by a distance less than the wavelength of the source term and initial data. However, calculations of radio signal pathloss generally do not require accurate time domain solutions. This paper describes an approach for calculating pathloss by using the finite difference time domain and transmission line matrix models of wave propagation on a grid with points separated by distances much greater than the signal wavelength. The calculated pathloss can be kept close to the true value formore » freespace propagation with an appropriate selection of initial conditions. This method can also simulate diffraction with an error governed by the ratio of the signal wavelength to the grid spacing.« less

Higher-order finite-difference formulation of periodic Orbital-free Density Functional Theory

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

Ghosh, Swarnava; Suryanarayana, Phanish, E-mail: phanish.suryanarayana@ce.gatech.edu

2016-02-15

We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we develop a generalized framework for performing OF-DFT simulations with different variants of the electronic kinetic energy. In particular, we propose a self-consistent field (SCF) type fixed-point method for calculations involving linear-response kinetic energy functionals. In this framework, evaluation of both the electronic ground-state and forces on the nuclei are amenable to computations that scale linearly with the number of atoms. We develop a parallel implementation of this formulation using the finite-difference discretization.more » We demonstrate that higher-order finite-differences can achieve relatively large convergence rates with respect to mesh-size in both the energies and forces. Additionally, we establish that the fixed-point iteration converges rapidly, and that it can be further accelerated using extrapolation techniques like Anderson's mixing. We validate the accuracy of the results by comparing the energies and forces with plane-wave methods for selected examples, including the vacancy formation energy in Aluminum. Overall, the suitability of the proposed formulation for scalable high performance computing makes it an attractive choice for large-scale OF-DFT calculations consisting of thousands of atoms.« less

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

Implementation of structural response sensitivity calculations in a large-scale finite-element analysis system

NASA Technical Reports Server (NTRS)

Giles, G. L.; Rogers, J. L., Jr.

1982-01-01

The implementation includes a generalized method for specifying element cross-sectional dimensions as design variables that can be used in analytically calculating derivatives of output quantities from static stress, vibration, and buckling analyses for both membrane and bending elements. Limited sample results for static displacements and stresses are presented to indicate the advantages of analytically calclating response derivatives compared to finite difference methods. Continuing developments to implement these procedures into an enhanced version of the system are also discussed.

Pion properties at finite isospin chemical potential with isospin symmetry breaking

NASA Astrophysics Data System (ADS)

Wu, Zuqing; Ping, Jialun; Zong, Hongshi

2017-12-01

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

Linear and nonlinear susceptibilities from diffusion quantum Monte Carlo: application to periodic hydrogen chains.

PubMed

Umari, P; Marzari, Nicola

2009-09-07

We calculate the linear and nonlinear susceptibilities of periodic longitudinal chains of hydrogen dimers with different bond-length alternations using a diffusion quantum Monte Carlo approach. These quantities are derived from the changes in electronic polarization as a function of applied finite electric field--an approach we recently introduced and made possible by the use of a Berry-phase, many-body electric-enthalpy functional. Calculated susceptibilities and hypersusceptibilities are found to be in excellent agreement with the best estimates available from quantum chemistry--usually extrapolations to the infinite-chain limit of calculations for chains of finite length. It is found that while exchange effects dominate the proper description of the susceptibilities, second hypersusceptibilities are greatly affected by electronic correlations. We also assess how different approximations to the nodal surface of the many-body wave function affect the accuracy of the calculated susceptibilities.

Simple way to calculate a UV-finite one-loop quantum energy in the Randall-Sundrum model

NASA Astrophysics Data System (ADS)

Altshuler, Boris L.

2017-04-01

The surprising simplicity of Barvinsky-Nesterov or equivalently Gelfand-Yaglom methods of calculation of quantum determinants permits us to obtain compact expressions for a UV-finite difference of one-loop quantum energies for two arbitrary values of the parameter of the double-trace asymptotic boundary conditions. This result generalizes the Gubser and Mitra calculation for the particular case of difference of "regular" and "irregular" one-loop energies in the one-brane Randall-Sundrum model. The approach developed in the paper also allows us to get "in one line" the one-loop quantum energies in the two-brane Randall-Sundrum model. The relationship between "one-loop" expressions corresponding to the mixed Robin and to double-trace asymptotic boundary conditions is traced.

Calculation methods study on hot spot stress of new girder structure detail

NASA Astrophysics Data System (ADS)

Liao, Ping; Zhao, Renda; Jia, Yi; Wei, Xing

2017-10-01

To study modeling calculation methods of new girder structure detail's hot spot stress, based on surface extrapolation method among hot spot stress method, a few finite element analysis models of this welded detail were established by finite element software ANSYS. The influence of element type, mesh density, different local modeling methods of the weld toe and extrapolation methods was analyzed on hot spot stress calculation results at the toe of welds. The results show that the difference of the normal stress in the thickness direction and the surface direction among different models is larger when the distance from the weld toe is smaller. When the distance from the toe is greater than 0.5t, the normal stress of solid models, shell models with welds and non-weld shell models tends to be consistent along the surface direction. Therefore, it is recommended that the extrapolated point should be selected outside the 0.5t for new girder welded detail. According to the results of the calculation and analysis, shell models have good grid stability, and extrapolated hot spot stress of solid models is smaller than that of shell models. So it is suggested that formula 2 and solid45 should be carried out during the hot spot stress extrapolation calculation of this welded detail. For each finite element model under different shell modeling methods, the results calculated by formula 2 are smaller than those of the other two methods, and the results of shell models with welds are the largest. Under the same local mesh density, the extrapolated hot spot stress decreases gradually with the increase of the number of layers in the thickness direction of the main plate, and the variation range is within 7.5%.

Statistical properties and condensate fluctuation of attractive Bose gas with finite number of particles

NASA Astrophysics Data System (ADS)

Bera, Sangita; Lekala, Mantile Leslie; Chakrabarti, Barnali; Bhattacharyya, Satadal; Rampho, Gaotsiwe Joel

2017-09-01

'We study the condensate fluctuation and several statistics of weakly interacting attractive Bose gas of 7 Li atoms in harmonic trap. Using exact recursion relation we calculate canonical ensemble partition function and study the thermal evolution of the condensate. As 7 Li condensate is associated with collapse, the number of condensate atom is truly finite and it facilitates to study the condensate in mesoscopic region. Being highly correlated, we utilize the two-body correlated basis function to get the many-body effective potential which is further used to calculate the energy levels. Taking van der Waals interaction as interatomic interaction we calculate several quantities like condensate fraction N, root-mean-square fluctuation δn0 and different orders of central moments. We observe the effect of finite size on the calculation of condensate fluctuations and the effect of attractive interaction over the noninteracting limit. We observe the depletion of the condensate with increase in temperature. The calculated moments nicely exhibit the mesoscopic effect. The sharp fall in the root-mean-square fluctuation near the critical point signifies the possibility of phase transition.

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

On-the-fly Numerical Surface Integration for Finite-Difference Poisson-Boltzmann Methods.

PubMed

Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

2011-11-01

Most implicit solvation models require the definition of a molecular surface as the interface that separates the solute in atomic detail from the solvent approximated as a continuous medium. Commonly used surface definitions include the solvent accessible surface (SAS), the solvent excluded surface (SES), and the van der Waals surface. In this study, we present an efficient numerical algorithm to compute the SES and SAS areas to facilitate the applications of finite-difference Poisson-Boltzmann methods in biomolecular simulations. Different from previous numerical approaches, our algorithm is physics-inspired and intimately coupled to the finite-difference Poisson-Boltzmann methods to fully take advantage of its existing data structures. Our analysis shows that the algorithm can achieve very good agreement with the analytical method in the calculation of the SES and SAS areas. Specifically, in our comprehensive test of 1,555 molecules, the average unsigned relative error is 0.27% in the SES area calculations and 1.05% in the SAS area calculations at the grid spacing of 1/2Å. In addition, a systematic correction analysis can be used to improve the accuracy for the coarse-grid SES area calculations, with the average unsigned relative error in the SES areas reduced to 0.13%. These validation studies indicate that the proposed algorithm can be applied to biomolecules over a broad range of sizes and structures. Finally, the numerical algorithm can also be adapted to evaluate the surface integral of either a vector field or a scalar field defined on the molecular surface for additional solvation energetics and force calculations.

Pasta phases in core-collapse supernova matter

NASA Astrophysics Data System (ADS)

Pais, Helena; Chiacchiera, Silvia; Providência, Constança

2016-04-01

The pasta phase in core-collapse supernova matter (finite temperatures and fixed proton fractions) is studied within relativistic mean field models. Three different calculations are used for comparison, the Thomas-Fermi (TF), the Coexisting Phases (CP) and the Compressible Liquid Drop (CLD) approximations. The effects of including light clusters in nuclear matter and the densities at which the transitions between pasta configurations and to uniform matter occur are also investigated. The free energy and pressure, in the space of particle number densities and temperatures expected to cover the pasta region, are calculated. Finally, a comparison with a finite temperature Skyrme-Hartree-Fock calculation is drawn.

Finite difference methods for the solution of unsteady potential flows

NASA Technical Reports Server (NTRS)

Caradonna, F. X.

1985-01-01

A brief review is presented of various problems which are confronted in the development of an unsteady finite difference potential code. This review is conducted mainly in the context of what is done for a typical small disturbance and full potential methods. The issues discussed include choice of equation, linearization and conservation, differencing schemes, and algorithm development. A number of applications including unsteady three-dimensional rotor calculation, are demonstrated.

HEMP 3D: A finite difference program for calculating elastic-plastic flow, appendix B

NASA Astrophysics Data System (ADS)

Wilkins, Mark L.

1993-05-01

The HEMP 3D program can be used to solve problems in solid mechanics involving dynamic plasticity and time dependent material behavior and problems in gas dynamics. The equations of motion, the conservation equations, and the constitutive relations listed below are solved by finite difference methods following the format of the HEMP computer simulation program formulated in two space dimensions and time.

An investigation of several numerical procedures for time-asymptotic compressible Navier-Stokes solutions

NASA Technical Reports Server (NTRS)

Rudy, D. H.; Morris, D. J.; Blanchard, D. K.; Cooke, C. H.; Rubin, S. G.

1975-01-01

The status of an investigation of four numerical techniques for the time-dependent compressible Navier-Stokes equations is presented. Results for free shear layer calculations in the Reynolds number range from 1000 to 81000 indicate that a sequential alternating-direction implicit (ADI) finite-difference procedure requires longer computing times to reach steady state than a low-storage hopscotch finite-difference procedure. A finite-element method with cubic approximating functions was found to require excessive computer storage and computation times. A fourth method, an alternating-direction cubic spline technique which is still being tested, is also described.

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

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

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

NASA Technical Reports Server (NTRS)

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

2003-01-01

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

Noise Reduction Design of the Volute for a Centrifugal Compressor

NASA Astrophysics Data System (ADS)

Song, Zhen; Wen, Huabing; Hong, Liangxing; Jin, Yudong

2017-08-01

In order to effectively control the aerodynamic noise of a compressor, this paper takes into consideration a marine exhaust turbocharger compressor as a research object. According to the different design concept of volute section, tongue and exit cone, six different volute models were established. The finite volume method is used to calculate the flow field, whiles the finite element method is used for the acoustic calculation. Comparison and analysis of different structure designs from three aspects: noise level, isentropic efficiency and Static pressure recovery coefficient. The results showed that under the concept of volute section model 1 yielded the best result, under the concept of tongue analysis model 3 yielded the best result and finally under exit cone analysis model 6 yielded the best results.

Simulation of 2D rarefied gas flows based on the numerical solution of the Boltzmann equation

NASA Astrophysics Data System (ADS)

Poleshkin, Sergey O.; Malkov, Ewgenij A.; Kudryavtsev, Alexey N.; Shershnev, Anton A.; Bondar, Yevgeniy A.; Kohanchik, A. A.

2017-10-01

There are various methods for calculating rarefied gas flows, in particular, statistical methods and deterministic methods based on the finite-difference solutions of the Boltzmann nonlinear kinetic equation and on the solutions of model kinetic equations. There is no universal method; each has its disadvantages in terms of efficiency or accuracy. The choice of the method depends on the problem to be solved and on parameters of calculated flows. Qualitative theoretical arguments help to determine the range of parameters of effectively solved problems for each method; however, it is advisable to perform comparative tests of calculations of the classical problems performed by different methods and with different parameters to have quantitative confirmation of this reasoning. The paper provides the results of the calculations performed by the authors with the help of the Direct Simulation Monte Carlo method and finite-difference methods of solving the Boltzmann equation and model kinetic equations. Based on this comparison, conclusions are made on selecting a particular method for flow simulations in various ranges of flow parameters.

Pretest 3-D finite element modeling of the wedge pillar portion of the WIPP (Waste Isolation Pilot Plant) Geomechanical Evaluation (Room G) in situ experiment. [Waste Isolation Pilot Plant

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

Preece, D.S.

Pretest 3-D finite element calculations have been performed on the wedge pillar portion of the WIPP Geomechanical Evaluation Experiment. The wedge pillar separates two drifts that intersect at an angle of 7.5/sup 0/. Purpose of the experiment is to provide data on the creep behavior of the wedge and progressive failure at the tip. The first set of calculations utilized a symmetry plane on the center-line of the wedge which allowed treatment of the entire configuration by modeling half of the geometry. Two 3-D calculations in this first set were performed with different drift widths to study the influence ofmore » drift size on closure and maximum stress. A cross-section perpendicular to the wedge was also analyzed with 2-D finite element models and the results compared to the 3-D results. In another set of 3-D calculations both drifts were modeled but with less distance between the drifts and the outer boundaries. Results of these calculations are compared with results from the other calculations to better understand the influence of boundary conditions.« less

Hybrid transfer-matrix FDTD method for layered periodic structures.

PubMed

Deinega, Alexei; Belousov, Sergei; Valuev, Ilya

2009-03-15

A hybrid transfer-matrix finite-difference time-domain (FDTD) method is proposed for modeling the optical properties of finite-width planar periodic structures. This method can also be applied for calculation of the photonic bands in infinite photonic crystals. We describe the procedure of evaluating the transfer-matrix elements by a special numerical FDTD simulation. The accuracy of the new method is tested by comparing computed transmission spectra of a 32-layered photonic crystal composed of spherical or ellipsoidal scatterers with the results of direct FDTD and layer-multiple-scattering calculations.

Time-dependent density functional theory with twist-averaged boundary conditions

NASA Astrophysics Data System (ADS)

Schuetrumpf, B.; Nazarewicz, W.; Reinhard, P.-G.

2016-05-01

Background: Time-dependent density functional theory is widely used to describe excitations of many-fermion systems. In its many applications, three-dimensional (3D) coordinate-space representation is used, and infinite-domain calculations are limited to a finite volume represented by a spatial box. For finite quantum systems (atoms, molecules, nuclei, hadrons), the commonly used periodic or reflecting boundary conditions introduce spurious quantization of the continuum states and artificial reflections from boundary; hence, an incorrect treatment of evaporated particles. Purpose: The finite-volume artifacts for finite systems can be practically cured by invoking an absorbing potential in a certain boundary region sufficiently far from the described system. However, such absorption cannot be applied in the calculations of infinite matter (crystal electrons, quantum fluids, neutron star crust), which suffer from unphysical effects stemming from a finite computational box used. Here, twist-averaged boundary conditions (TABC) have been used successfully to diminish the finite-volume effects. In this work, we extend TABC to time-dependent modes. Method: We use the 3D time-dependent density functional framework with the Skyrme energy density functional. The practical calculations are carried out for small- and large-amplitude electric dipole and quadrupole oscillations of 16O. We apply and compare three kinds of boundary conditions: periodic, absorbing, and twist-averaged. Results: Calculations employing absorbing boundary conditions (ABC) and TABC are superior to those based on periodic boundary conditions. For low-energy excitations, TABC and ABC variants yield very similar results. With only four twist phases per spatial direction in TABC, one obtains an excellent reduction of spurious fluctuations. In the nonlinear regime, one has to deal with evaporated particles. In TABC, the floating nucleon gas remains in the box; the amount of nucleons in the gas is found to be roughly the same as the number of absorbed particles in ABC. Conclusion: We demonstrate that by using TABC, one can reduce finite-volume effects drastically without adding any additional parameters associated with absorption at large distances. Moreover, TABC are an obvious choice for time-dependent calculations for infinite systems. Since TABC calculations for different twists can be performed independently, the method is trivially adapted to parallel computing.

A user's guide for V174, a program using a finite difference method to analyze transonic flow over oscillating wings

NASA Technical Reports Server (NTRS)

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

1977-01-01

The design and usage of a pilot program using a finite difference method for calculating the pressure distributions over harmonically oscillating wings in transonic flow are discussed. The procedure used is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The steady velocity potential which must be obtained from some other program, is required for input. The unsteady differential equation is linear, complex in form with spatially varying coefficients. Because sinusoidal motion is assumed, time is not a variable. The numerical solution is obtained through a finite difference formulation and a line relaxation solution method.

Sensitivity calculations for iteratively solved problems

NASA Technical Reports Server (NTRS)

Haftka, R. T.

1985-01-01

The calculation of sensitivity derivatives of solutions of iteratively solved systems of algebraic equations is investigated. A modified finite difference procedure is presented which improves the accuracy of the calculated derivatives. The procedure is demonstrated for a simple algebraic example as well as an element-by-element preconditioned conjugate gradient iterative solution technique applied to truss examples.

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

PubMed

Wang, Pei; Xianlong, Gao; Li, Haibin

2013-08-01

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

Optimization Based Efficiencies in First Order Reliability Analysis

NASA Technical Reports Server (NTRS)

Peck, Jeffrey A.; Mahadevan, Sankaran

2003-01-01

This paper develops a method for updating the gradient vector of the limit state function in reliability analysis using Broyden's rank one updating technique. In problems that use commercial code as a black box, the gradient calculations are usually done using a finite difference approach, which becomes very expensive for large system models. The proposed method replaces the finite difference gradient calculations in a standard first order reliability method (FORM) with Broyden's Quasi-Newton technique. The resulting algorithm of Broyden updates within a FORM framework (BFORM) is used to run several example problems, and the results compared to standard FORM results. It is found that BFORM typically requires fewer functional evaluations that FORM to converge to the same answer.

Finite-Difference Solution for Laminar or Turbulent Boundary Layer Flow over Axisymmetric Bodies with Ideal Gas, CF4, or Equilibrium Air Chemistry

NASA Technical Reports Server (NTRS)

Hamilton, H. Harris, II; Millman, Daniel R.; Greendyke, Robert B.

1992-01-01

A computer code was developed that uses an implicit finite-difference technique to solve nonsimilar, axisymmetric boundary layer equations for both laminar and turbulent flow. The code can treat ideal gases, air in chemical equilibrium, and carbon tetrafluoride (CF4), which is a useful gas for hypersonic blunt-body simulations. This is the only known boundary layer code that can treat CF4. Comparisons with experimental data have demonstrated that accurate solutions are obtained. The method should prove useful as an analysis tool for comparing calculations with wind tunnel experiments and for making calculations about flight vehicles where equilibrium air chemistry assumptions are valid.

Finite-difference solution for laminar or turbulent boundary layer flow over axisymmetric bodies with ideal gas, CF4, or equilibrium air chemistry

NASA Astrophysics Data System (ADS)

Hamilton, H. Harris, II; Millman, Daniel R.; Greendyke, Robert B.

1992-12-01

A computer code was developed that uses an implicit finite-difference technique to solve nonsimilar, axisymmetric boundary layer equations for both laminar and turbulent flow. The code can treat ideal gases, air in chemical equilibrium, and carbon tetrafluoride (CF4), which is a useful gas for hypersonic blunt-body simulations. This is the only known boundary layer code that can treat CF4. Comparisons with experimental data have demonstrated that accurate solutions are obtained. The method should prove useful as an analysis tool for comparing calculations with wind tunnel experiments and for making calculations about flight vehicles where equilibrium air chemistry assumptions are valid.

Semi-analytic valuation of stock loans with finite maturity

NASA Astrophysics Data System (ADS)

Lu, Xiaoping; Putri, Endah R. M.

2015-10-01

In this paper we study stock loans of finite maturity with different dividend distributions semi-analytically using the analytical approximation method in Zhu (2006). Stock loan partial differential equations (PDEs) are established under Black-Scholes framework. Laplace transform method is used to solve the PDEs. Optimal exit price and stock loan value are obtained in Laplace space. Values in the original time space are recovered by numerical Laplace inversion. To demonstrate the efficiency and accuracy of our semi-analytic method several examples are presented, the results are compared with those calculated using existing methods. We also present a calculation of fair service fee charged by the lender for different loan parameters.

The Laguerre finite difference one-way equation solver

NASA Astrophysics Data System (ADS)

Terekhov, Andrew V.

2017-05-01

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

Unmitigated numerical solution to the diffraction term in the parabolic nonlinear ultrasound wave equation.

PubMed

Hasani, Mojtaba H; Gharibzadeh, Shahriar; Farjami, Yaghoub; Tavakkoli, Jahan

2013-09-01

Various numerical algorithms have been developed to solve the Khokhlov-Kuznetsov-Zabolotskaya (KZK) parabolic nonlinear wave equation. In this work, a generalized time-domain numerical algorithm is proposed to solve the diffraction term of the KZK equation. This algorithm solves the transverse Laplacian operator of the KZK equation in three-dimensional (3D) Cartesian coordinates using a finite-difference method based on the five-point implicit backward finite difference and the five-point Crank-Nicolson finite difference discretization techniques. This leads to a more uniform discretization of the Laplacian operator which in turn results in fewer calculation gridding nodes without compromising accuracy in the diffraction term. In addition, a new empirical algorithm based on the LU decomposition technique is proposed to solve the system of linear equations obtained from this discretization. The proposed empirical algorithm improves the calculation speed and memory usage, while the order of computational complexity remains linear in calculation of the diffraction term in the KZK equation. For evaluating the accuracy of the proposed algorithm, two previously published algorithms are used as comparison references: the conventional 2D Texas code and its generalization for 3D geometries. The results show that the accuracy/efficiency performance of the proposed algorithm is comparable with the established time-domain methods.

Prediction of local proximal tibial subchondral bone structural stiffness using subject-specific finite element modeling: Effect of selected density-modulus relationship.

PubMed

Nazemi, S Majid; Amini, Morteza; Kontulainen, Saija A; Milner, Jaques S; Holdsworth, David W; Masri, Bassam A; Wilson, David R; Johnston, James D

2015-08-01

Quantitative computed tomography based subject-specific finite element modeling has potential to clarify the role of subchondral bone alterations in knee osteoarthritis initiation, progression, and pain initiation. Calculation of bone elastic moduli from image data is a basic step when constructing finite element models. However, different relationships between elastic moduli and imaged density (known as density-modulus relationships) have been reported in the literature. The objective of this study was to apply seven different trabecular-specific and two cortical-specific density-modulus relationships from the literature to finite element models of proximal tibia subchondral bone, and identify the relationship(s) that best predicted experimentally measured local subchondral structural stiffness with highest explained variance and least error. Thirteen proximal tibial compartments were imaged via quantitative computed tomography. Imaged bone mineral density was converted to elastic moduli using published density-modulus relationships and mapped to corresponding finite element models. Proximal tibial structural stiffness values were compared to experimentally measured stiffness values from in-situ macro-indentation testing directly on the subchondral bone surface (47 indentation points). Regression lines between experimentally measured and finite element calculated stiffness had R(2) values ranging from 0.56 to 0.77. Normalized root mean squared error varied from 16.6% to 337.6%. Of the 21 evaluated density-modulus relationships in this study, Goulet combined with Snyder and Schneider or Rho appeared most appropriate for finite element modeling of local subchondral bone structural stiffness. Though, further studies are needed to optimize density-modulus relationships and improve finite element estimates of local subchondral bone structural stiffness. Copyright © 2015 Elsevier Ltd. All rights reserved.

Comparison of measured and calculated temperatures for a Mach 8 hypersonic wing test structure

NASA Technical Reports Server (NTRS)

Quinn, R. D.; Fields, R. A.

1986-01-01

Structural temperatures were measured on a hypersonic wing test structure during a heating test that simulated a Mach 8 thermal environment. Measured data are compared to design calculations and temperature predictions obtained from a finite-difference thermal analysis.

Spallation studies in Estane

NASA Astrophysics Data System (ADS)

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

2000-04-01

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

Hybrid multicore/vectorisation technique applied to the elastic wave equation on a staggered grid

NASA Astrophysics Data System (ADS)

Titarenko, Sofya; Hildyard, Mark

2017-07-01

In modern physics it has become common to find the solution of a problem by solving numerically a set of PDEs. Whether solving them on a finite difference grid or by a finite element approach, the main calculations are often applied to a stencil structure. In the last decade it has become usual to work with so called big data problems where calculations are very heavy and accelerators and modern architectures are widely used. Although CPU and GPU clusters are often used to solve such problems, parallelisation of any calculation ideally starts from a single processor optimisation. Unfortunately, it is impossible to vectorise a stencil structured loop with high level instructions. In this paper we suggest a new approach to rearranging the data structure which makes it possible to apply high level vectorisation instructions to a stencil loop and which results in significant acceleration. The suggested method allows further acceleration if shared memory APIs are used. We show the effectiveness of the method by applying it to an elastic wave propagation problem on a finite difference grid. We have chosen Intel architecture for the test problem and OpenMP (Open Multi-Processing) since they are extensively used in many applications.

Dynamic analysis of suspension cable based on vector form intrinsic finite element method

NASA Astrophysics Data System (ADS)

Qin, Jian; Qiao, Liang; Wan, Jiancheng; Jiang, Ming; Xia, Yongjun

2017-10-01

A vector finite element method is presented for the dynamic analysis of cable structures based on the vector form intrinsic finite element (VFIFE) and mechanical properties of suspension cable. Firstly, the suspension cable is discretized into different elements by space points, the mass and external forces of suspension cable are transformed into space points. The structural form of cable is described by the space points at different time. The equations of motion for the space points are established according to the Newton’s second law. Then, the element internal forces between the space points are derived from the flexible truss structure. Finally, the motion equations of space points are solved by the central difference method with reasonable time integration step. The tangential tension of the bearing rope in a test ropeway with the moving concentrated loads is calculated and compared with the experimental data. The results show that the tangential tension of suspension cable with moving loads is consistent with the experimental data. This method has high calculated precision and meets the requirements of engineering application.

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

Wight, L.; Zaslawsky, M.

Two approaches for calculating soil structure interaction (SSI) are compared: finite element and lumped mass. Results indicate that the calculations with the lumped mass method are generally conservative compared to those obtained by the finite element method. They also suggest that a closer agreement between the two sets of calculations is possible, depending on the use of frequency-dependent soil springs and dashpots in the lumped mass calculations. There is a total lack of suitable guidelines for implementing the lumped mass method of calculating SSI, which leads to the conclusion that the finite element method is generally superior for calculative purposes.

Lightning Threat Analysis for the Space Shuttle Launch Pad and the Payload Changeout Room Using Finite Difference Methods

NASA Technical Reports Server (NTRS)

Collier, Richard S.

1997-01-01

This report describes finite difference computer calculations for the Space Shuttle Launch Pad which predict lightning induced electric currents and electric and magnetic fields caused by a lightning strike to the Lightning Protection System caternary wire. Description of possible lightning threats to Shuttle Payload components together with specifications for protection of these components, result from the calculation of lightning induced electric and magnetic fields inside and outside the during a lightning event. These fields also induce currents and voltages on cables and circuits which may be connected to, or a part of, shuttle payload components. These currents and voltages are also calculated. These threat levels are intended as a guide for designers of payload equipment to specify any shielding and/or lightning protection mitigation which may be required for payload components which are in the process of preparation or being transferred into the Shuttle Orbiter.

Computational methods for vortex dominated compressible flows

NASA Technical Reports Server (NTRS)

Murman, Earll M.

1987-01-01

The principal objectives were to: understand the mechanisms by which Euler equation computations model leading edge vortex flows; understand the vortical and shock wave structures that may exist for different wing shapes, angles of incidence, and Mach numbers; and compare calculations with experiments in order to ascertain the limitations and advantages of Euler equation models. The initial approach utilized the cell centered finite volume Jameson scheme. The final calculation utilized a cell vertex finite volume method on an unstructured grid. Both methods used Runge-Kutta four stage schemes for integrating the equations. The principal findings are briefly summarized.

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

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

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

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

Finite-element reentry heat-transfer analysis of space shuttle Orbiter

NASA Technical Reports Server (NTRS)

Ko, William L.; Quinn, Robert D.; Gong, Leslie

1986-01-01

A structural performance and resizing (SPAR) finite-element thermal analysis computer program was used in the heat-transfer analysis of the space shuttle orbiter subjected to reentry aerodynamic heating. Three wing cross sections and one midfuselage cross section were selected for the thermal analysis. The predicted thermal protection system temperatures were found to agree well with flight-measured temperatures. The calculated aluminum structural temperatures also agreed reasonably well with the flight data from reentry to touchdown. The effects of internal radiation and of internal convection were found to be significant. The SPAR finite-element solutions agreed reasonably well with those obtained from the conventional finite-difference method.

Stress-intensity factors for small surface and corner cracks in plates

NASA Technical Reports Server (NTRS)

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

1988-01-01

Three-dimensional finite-element and finite-alternating methods were used to obtain the stress-intensity factors for small surface and corner cracked plates subjected to remote tension and bending loads. The crack-depth-to-crack-length ratios (a/c) ranged from 0.2 to 1 and the crack-depth-to-plate-thickness ratios (a/t) ranged from 0.05 to 0.2. The performance of the finite-element alternating method was studied on these crack configurations. A study of the computational effort involved in the finite-element alternating method showed that several crack configurations could be analyzed with a single rectangular mesh idealization, whereas the conventional finite-element method requires a different mesh for each configuration. The stress-intensity factors obtained with the finite-element-alternating method agreed well (within 5 percent) with those calculated from the finite-element method with singularity elements.

The use of spectral methods in bidomain studies.

PubMed

Trayanova, N; Pilkington, T

1992-01-01

A Fourier transform method is developed for solving the bidomain coupled differential equations governing the intracellular and extracellular potentials on a finite sheet of cardiac cells undergoing stimulation. The spectral formulation converts the system of differential equations into a "diagonal" system of algebraic equations. Solving the algebraic equations directly and taking the inverse transform of the potentials proved numerically less expensive than solving the coupled differential equations by means of traditional numerical techniques, such as finite differences; the comparison between the computer execution times showed that the Fourier transform method was about 40 times faster than the finite difference method. By application of the Fourier transform method, transmembrane potential distributions in the two-dimensional myocardial slice were calculated. For a tissue characterized by a ratio of the intra- to extracellular conductivities that is different in all principal directions, the transmembrane potential distribution exhibits a rather complicated geometrical pattern. The influence of the different anisotropy ratios, the finite tissue size, and the stimuli configuration on the pattern of membrane polarization is investigated.

Strain-energy-release rate analysis of the end-notched flexure specimen using the finite-element method

NASA Technical Reports Server (NTRS)

Salpekar, S. A.; Raju, I. S.; Obrien, T. K.

1987-01-01

Two-dimensional finite-element analysis of the end-notched flexure specimen was performed using 8-node isoparametric, parabolic elements to evaluate compliance and mode II strain energy release rates, G sub II. The G sub II values were computed using two different techniques: the virtural crack-closure technique (VCCT) and the rate of change of compliance with crack length (compliance derivative method). The analysis was performed for various crack-length-to-semi-span (a/L) ratios ranging from 0.2 to 0.9. Three material systems representing a wide range of material properties were analyzed. The compliance and strain energy release rates of the specimen calculated with the present finite-element analysis agree very well with beam theory equations including transverse shear. The G sub II values calculated using the compliance derivative method compared extremely well with those calculated using the VCCT. The G sub II values obtained by the compliance derivative method using the top or bottom beam deflections agreed closely with each other. The strain energy release rates from a plane-stress analysis were higher than the plane-strain values by only a small percentage, indicating that either assumption may be used in the analysis. The G sub II values for one material system calculated from the finite-element analysis agreed with one solution in the literature and disagreed with the other solution in the literature.

Energy Efficiency of Induction Motors Running Off Frequency Converters with Pulse-Width Voltage Modulation{sup 1}

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

Shvetsov, N. K., E-mail: elmash@em.ispu.ru

2016-11-15

The results of calculations of the increase in losses in an induction motor with frequency control and different forms of the supply voltage are presented. The calculations were performed by an analytic method based on harmonic analysis of the supply voltage as well as numerical calculation of the electromagnetic processes by the finite-element method.

International Conference on Numerical Methods in Fluid Dynamics, 7th, Stanford University, Stanford and Moffett Field, CA, June 23-27, 1980, Proceedings

NASA Technical Reports Server (NTRS)

Reynolds, W. C. (Editor); Maccormack, R. W.

1981-01-01

Topics discussed include polygon transformations in fluid mechanics, computation of three-dimensional horseshoe vortex flow using the Navier-Stokes equations, an improved surface velocity method for transonic finite-volume solutions, transonic flow calculations with higher order finite elements, the numerical calculation of transonic axial turbomachinery flows, and the simultaneous solutions of inviscid flow and boundary layer at transonic speeds. Also considered are analytical solutions for the reflection of unsteady shock waves and relevant numerical tests, reformulation of the method of characteristics for multidimensional flows, direct numerical simulations of turbulent shear flows, the stability and separation of freely interacting boundary layers, computational models of convective motions at fluid interfaces, viscous transonic flow over airfoils, and mixed spectral/finite difference approximations for slightly viscous flows.

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

NASA Astrophysics Data System (ADS)

Ying, Jinyong; Xie, Dexuan

2015-10-01

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

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.

On the wavelet optimized finite difference method

NASA Technical Reports Server (NTRS)

Jameson, Leland

1994-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

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

NASA Astrophysics Data System (ADS)

Fuchs, Lukas; Schmeling, Harro; Koyi, Hemin

2013-04-01

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

Finite-Temperature Entanglement Dynamics in an Anisotropic Two-Qubit Heisenberg Spin Chain

NASA Astrophysics Data System (ADS)

Chen, Tao; Shan, Chuanjia; Li, Jinxing; Liu, Tangkun; Huang, Yanxia; Li, Hong

2010-07-01

This paper investigates the entanglement dynamics of an anisotropic two-qubit Heisenberg spin chain in the presence of decoherence at finite temperature. The time evolution of the concurrence is studied for different initial Werner states. The influences of initial purity, finite temperature, spontaneous decay and Hamiltonian on the entanglement evolution are analyzed in detail. Our calculations show that the finite temperature restricts the evolution of the entanglement all the time when the Hamiltonian improves it and the spontaneous decay to the reservoirs can produce quantum entanglement with the anisotropy of spin-spin interaction. Finally, the steady-state concurrence which may remain non-zero for low temperature is also given.

Recent Developments in the Formability of Aluminum Alloys

NASA Astrophysics Data System (ADS)

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

2005-08-01

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

Recent Developments in the Formability of Aluminum Alloys

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

Banabic, Dorel; Paraianu, Liana; Jurco, Paul

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

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

NASA Technical Reports Server (NTRS)

Stremel, P. M.

1984-01-01

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

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.

Weak form implementation of the semi-analytical finite element (SAFE) method for a variety of elastodynamic waveguides

NASA Astrophysics Data System (ADS)

Hakoda, Christopher; Lissenden, Clifford; Rose, Joseph L.

2018-04-01

Dispersion curves are essential to any guided wave NDE project. The Semi-Analytical Finite Element (SAFE) method has significantly increased the ease by which these curves can be calculated. However, due to misconceptions regarding theory and fragmentation based on different finite-element software, the theory has stagnated, and adoption by researchers who are new to the field has been slow. This paper focuses on the relationship between the SAFE formulation and finite element theory, and the implementation of the SAFE method in a weak form for plates, pipes, layered waveguides/composites, curved waveguides, and arbitrary cross-sections is shown. The benefits of the weak form are briefly described, as is implementation in open-source and commercial finite element software.

Finite difference time domain calculation of transients in antennas with nonlinear loads

NASA Technical Reports Server (NTRS)

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

1991-01-01

Determining transient electromagnetic fields in antennas with nonlinear loads is a challenging problem. Typical methods used involve calculating frequency domain parameters at a large number of different frequencies, then applying Fourier transform methods plus nonlinear equation solution techniques. If the antenna is simple enough so that the open circuit time domain voltage can be determined independently of the effects of the nonlinear load on the antennas current, time stepping methods can be applied in a straightforward way. Here, transient fields for antennas with more general geometries are calculated directly using Finite Difference Time Domain (FDTD) methods. In each FDTD cell which contains a nonlinear load, a nonlinear equation is solved at each time step. As a test case, the transient current in a long dipole antenna with a nonlinear load excited by a pulsed plane wave is computed using this approach. The results agree well with both calculated and measured results previously published. The approach given here extends the applicability of the FDTD method to problems involving scattering from targets, including nonlinear loads and materials, and to coupling between antennas containing nonlinear loads. It may also be extended to propagation through nonlinear materials.

Towards a systematic assessment of errors in diffusion Monte Carlo calculations of semiconductors: Case study of zinc selenide and zinc oxide

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

Yu, Jaehyung; Wagner, Lucas K.; Ertekin, Elif, E-mail: ertekin@illinois.edu

2015-12-14

The fixed node diffusion Monte Carlo (DMC) method has attracted interest in recent years as a way to calculate properties of solid materials with high accuracy. However, the framework for the calculation of properties such as total energies, atomization energies, and excited state energies is not yet fully established. Several outstanding questions remain as to the effect of pseudopotentials, the magnitude of the fixed node error, and the size of supercell finite size effects. Here, we consider in detail the semiconductors ZnSe and ZnO and carry out systematic studies to assess the magnitude of the energy differences arising from controlledmore » and uncontrolled approximations in DMC. The former include time step errors and supercell finite size effects for ground and optically excited states, and the latter include pseudopotentials, the pseudopotential localization approximation, and the fixed node approximation. We find that for these compounds, the errors can be controlled to good precision using modern computational resources and that quantum Monte Carlo calculations using Dirac-Fock pseudopotentials can offer good estimates of both cohesive energy and the gap of these systems. We do however observe differences in calculated optical gaps that arise when different pseudopotentials are used.« less

Development of models of the magnetorheological fluid damper

NASA Astrophysics Data System (ADS)

Kazakov, Yu. B.; Morozov, N. A.; Nesterov, S. A.

2017-06-01

The algorithm for analytical calculation of a power characteristic of magnetorheological (MR) dampers taking into account the rheological properties of MR fluid is considered. The nonlinear magnetorheological characteristics are represented by piecewise linear approximation to MR fluid areas with different viscosities. The extended calculated power characteristics of a MR damper are received and they coincide with actual results. The finite element model of a MR damper is developed; it allows carrying out the analysis of a MR damper taking into account the mutual influence of electromagnetic, hydrodynamic and thermal fields. The results of finite element simulation coincide with analytical solutions that allows using them for design development of a MR damper.

Lattice dynamics calculations based on density-functional perturbation theory in real space

NASA Astrophysics Data System (ADS)

Shang, Honghui; Carbogno, Christian; Rinke, Patrick; Scheffler, Matthias

2017-06-01

A real-space formalism for density-functional perturbation theory (DFPT) is derived and applied for the computation of harmonic vibrational properties in molecules and solids. The practical implementation using numeric atom-centered orbitals as basis functions is demonstrated exemplarily for the all-electron Fritz Haber Institute ab initio molecular simulations (FHI-aims) package. The convergence of the calculations with respect to numerical parameters is carefully investigated and a systematic comparison with finite-difference approaches is performed both for finite (molecules) and extended (periodic) systems. Finally, the scaling tests and scalability tests on massively parallel computer systems demonstrate the computational efficiency.

Influence of gap states on the nonresonant second hyperpolarizabilities of conjugated organic polymers

NASA Technical Reports Server (NTRS)

Beratan, David N.

1989-01-01

The presence of conjugation and substitution defects introduces gap states in finite polyenes that are shown to influence the size and sign of the second molecular hyperpolarizability (SMH). Using a one-electron tight-binding model, the dependence of SMH on the defect-state occupancy and energy in finite polyenes is calculated. Defects can cause a significant decrease or enhancement of SMH by impeding charge delocalization or by creating partly filled bands (mimicking the one-band limit), respectively. Concomitant sign changes in SMH are predicted. Calculation results suggest strategies for designing molecules that can be either photochemically or electrochemically switched between states with considerably different SMHs.

Numerical modeling on carbon fiber composite material in Gaussian beam laser based on ANSYS

NASA Astrophysics Data System (ADS)

Luo, Ji-jun; Hou, Su-xia; Xu, Jun; Yang, Wei-jun; Zhao, Yun-fang

2014-02-01

Based on the heat transfer theory and finite element method, the macroscopic ablation model of Gaussian beam laser irradiated surface is built and the value of temperature field and thermal ablation development is calculated and analyzed rationally by using finite element software of ANSYS. Calculation results show that the ablating form of the materials in different irritation is of diversity. The laser irradiated surface is a camber surface rather than a flat surface, which is on the lowest point and owns the highest power density. Research shows that the higher laser power density absorbed by material surface, the faster the irritation surface regressed.

Finite element modeling as a tool for predicting the fracture behavior of robocast scaffolds.

PubMed

Miranda, Pedro; Pajares, Antonia; Guiberteau, Fernando

2008-11-01

The use of finite element modeling to calculate the stress fields in complex scaffold structures and thus predict their mechanical behavior during service (e.g., as load-bearing bone implants) is evaluated. The method is applied to identifying the fracture modes and estimating the strength of robocast hydroxyapatite and beta-tricalcium phosphate scaffolds, consisting of a three-dimensional lattice of interpenetrating rods. The calculations are performed for three testing configurations: compression, tension and shear. Different testing orientations relative to the calcium phosphate rods are considered for each configuration. The predictions for the compressive configurations are compared to experimental data from uniaxial compression tests.

Modeling aluminum-lithium alloy welding characteristics

NASA Technical Reports Server (NTRS)

Bernstein, Edward L.

1996-01-01

The purpose of this project was to develop a finite element model of the heat-affected zone in the vicinity of a weld line on a plate in order to determine an accurate plastic strain history. The resulting plastic strain increments calculated by the finite element program were then to be used to calculate the measure of damage D. It was hoped to determine the effects of varying welding parameters, such as beam power, efficiency, and weld speed, and the effect of different material properties on the occurrence of microfissuring. The results were to be compared first to the previous analysis of Inconel 718, and then extended to aluminum 2195.

Third harmonic ac susceptibility of superconductors with finite thickness

NASA Astrophysics Data System (ADS)

Qin, M. J.; Ong, C. K.

Third harmonic ac susceptibility of superconducting strips with finite thickness in perpendicularly applied magnetic field Ha = H0 sin(ω t) have been calculated. The flux creep effect is taken into account by using a power-law electric field E( j) = Ec( j/ jc) n. Results for different thicknesses and creep exponents n have been derived and compared to the results derived from the Bean critical state model.

Solution of electromagnetic scattering problems using time domain techniques

NASA Technical Reports Server (NTRS)

Britt, Charles L.

1989-01-01

New methods are developed to calculate the electromagnetic diffraction or scattering characteristics of objects of arbitrary material and shape. The methods extend the efforts of previous researchers in the use of finite-difference and pulse response techniques. Examples are given of the scattering from infinite conducting and nonconducting cylinders, open channel, sphere, cone, cone sphere, coated disk, open boxes, and open and closed finite cylinders with axially incident waves.

Dynamic simulation and preliminary finite element analysis of gunshot wounds to the human mandible.

PubMed

Tang, Zhen; Tu, Wenbing; Zhang, Gang; Chen, Yubin; Lei, Tao; Tan, Yinghui

2012-05-01

Due to the complications arising from gunshot wounds to the maxillofacial region, traditional models of gunshot wounds cannot meet our research needs. In this study, we established a finite element model and conducted preliminary simulation and analysis to determine the injury mechanism and degree of damage for gunshot wounds to the human mandible. Based on a previously developed modelling method that used animal experiments and internal parameters, digital computed tomography data for the human mandible were used to establish a three-dimensional finite element model of the human mandible. The mechanism by which a gunshot injures the mandible was dynamically simulated under different shot conditions. First, the residual velocities of the shootings using different projectiles at varying entry angles and impact velocities were calculated. Second, the energy losses of the projectiles and the rates of energy loss after exiting the mandible were calculated. Finally, the data were compared and analysed. The dynamic processes involved in gunshot wounds to the human mandible were successfully simulated using two projectiles, three impact velocities, and three entry angles. The stress distributions in different parts of mandible after injury were also simulated. Based on the computation and analysis of the modelling data, we found that the injury severity of the mandible and the injury efficiency of the projectiles differ under different injury conditions. The finite element model has many advantages for the analysis of ballistic wounds, and is expected to become an improved model for studying maxillofacial gunshot wounds. Copyright © 2011 Elsevier Ltd. All rights reserved.

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

PubMed

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

2010-06-21

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

Numerical modeling of Harmonic Imaging and Pulse Inversion fields

NASA Astrophysics Data System (ADS)

Humphrey, Victor F.; Duncan, Tracy M.; Duck, Francis

2003-10-01

Tissue Harmonic Imaging (THI) and Pulse Inversion (PI) Harmonic Imaging exploit the harmonics generated as a result of nonlinear propagation through tissue to improve the performance of imaging systems. A 3D finite difference model, that solves the KZK equation in the frequency domain, is used to investigate the finite amplitude fields produced by rectangular transducers driven with short pulses and their inverses, in water and homogeneous tissue. This enables the characteristic of the fields and the effective PI field to be calculated. The suppression of the fundamental field in PI is monitored, and the suppression of side lobes and a reduction in the effective beamwidth for each field are calculated. In addition, the differences between the pulse and inverse pulse spectra resulting from the use of very short pulses are noted, and the differences in the location of the fundamental and second harmonic spectral peaks observed.

A mimetic finite difference method for the Stokes problem with elected edge bubbles

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

Lipnikov, K; Berirao, L

2009-01-01

A new mimetic finite difference method for the Stokes problem is proposed and analyzed. The unstable P{sub 1}-P{sub 0} discretization is stabilized by adding a small number of bubble functions to selected mesh edges. A simple strategy for selecting such edges is proposed and verified with numerical experiments. The discretizations schemes for Stokes and Navier-Stokes equations must satisfy the celebrated inf-sup (or the LBB) stability condition. The stability condition implies a balance between discrete spaces for velocity and pressure. In finite elements, this balance is frequently achieved by adding bubble functions to the velocity space. The goal of this articlemore » is to show that the stabilizing edge bubble functions can be added only to a small set of mesh edges. This results in a smaller algebraic system and potentially in a faster calculations. We employ the mimetic finite difference (MFD) discretization technique that works for general polyhedral meshes and can accomodate non-uniform distribution of stabilizing bubbles.« less

Fulde–Ferrell superfluids in spinless ultracold Fermi gases

NASA Astrophysics Data System (ADS)

Zheng, Zhen-Fei; Guo, Guang-Can; Zheng, Zhen; Zou, Xu-Bo

2018-06-01

The Fulde–Ferrell (FF) superfluid phase, in which fermions form finite momentum Cooper pairings, is well studied in spin-singlet superfluids in past decades. Different from previous works that engineer the FF state in spinful cold atoms, we show that the FF state can emerge in spinless Fermi gases confined in optical lattice associated with nearest-neighbor interactions. The mechanism of the spinless FF state relies on the split Fermi surfaces by tuning the chemistry potential, which naturally gives rise to finite momentum Cooper pairings. The phase transition is accompanied by changed Chern numbers, in which, different from the conventional picture, the band gap does not close. By beyond-mean-field calculations, we find the finite momentum pairing is more robust, yielding the system promising for maintaining the FF state at finite temperature. Finally we present the possible realization and detection scheme of the spinless FF state.

Microscopic and macroscopic instabilities in finitely strained porous elastomers

NASA Astrophysics Data System (ADS)

Michel, J. C.; Lopez-Pamies, O.; Ponte Castañeda, P.; Triantafyllidis, N.

2007-05-01

The present work is an in-depth study of the connections between microstructural instabilities and their macroscopic manifestations—as captured through the effective properties—in finitely strained porous elastomers. The powerful second-order homogenization (SOH) technique initially developed for random media, is used for the first time here to study the onset of failure in periodic porous elastomers and the results are compared to more accurate finite element method (FEM) calculations. The influence of different microgeometries (random and periodic), initial porosity, matrix constitutive law and macroscopic load orientation on the microscopic buckling (for periodic microgeometries) and macroscopic loss of ellipticity (for all microgeometries) is investigated in detail. In addition to the above-described stability-based onset-of-failure mechanisms, constraints on the principal solution are also addressed, thus giving a complete picture of the different possible failure mechanisms present in finitely strained porous elastomers.

Fast calculation of the sensitivity matrix in magnetic induction tomography by tetrahedral edge finite elements and the reciprocity theorem.

PubMed

Hollaus, K; Magele, C; Merwa, R; Scharfetter, H

2004-02-01

Magnetic induction tomography of biological tissue is used to reconstruct the changes in the complex conductivity distribution by measuring the perturbation of an alternating primary magnetic field. To facilitate the sensitivity analysis and the solution of the inverse problem a fast calculation of the sensitivity matrix, i.e. the Jacobian matrix, which maps the changes of the conductivity distribution onto the changes of the voltage induced in a receiver coil, is needed. The use of finite differences to determine the entries of the sensitivity matrix does not represent a feasible solution because of the high computational costs of the basic eddy current problem. Therefore, the reciprocity theorem was exploited. The basic eddy current problem was simulated by the finite element method using symmetric tetrahedral edge elements of second order. To test the method various simulations were carried out and discussed.

Integrated analyses in plastics forming

NASA Astrophysics Data System (ADS)

Bo, Wang

This is the thesis which explains the progress made in the analysis, simulation and testing of plastics forming. This progress can be applied to injection and compression mould design. Three activities of plastics forming have been investigated, namely filling analysis, cooling analysis and ejecting analysis. The filling section of plastics forming has been analysed and calculated by using MOLDFLOW and FILLCALC V. software. A comparing of high speed compression moulding and injection moulding has been made. The cooling section of plastics forming has been analysed by using MOLDFLOW software and a finite difference computer program. The latter program can be used as a sample program to calculate the feasibility of cooling different materials to required target temperatures under controlled cooling conditions. The application of thermal imaging has been also introduced to determine the actual process temperatures. Thermal imaging can be used as a powerful tool to analyse mould surface temperatures and to verify the mathematical model. A buckling problem for ejecting section has been modelled and calculated by PATRAN/ABAQUS finite element analysis software and tested. These calculations and analysis are applied to the special case but can be use as an example for general analysis and calculation in the ejection section of plastics forming.

Varieties of operator manipulation. [for solving differential equations and calculating finite differences

NASA Technical Reports Server (NTRS)

Doohovskoy, A.

1977-01-01

A change in MACSYMA syntax is proposed to accommodate the operator manipulators necessary to implement direct and indirect methods for the solution of differential equations, calculus of finite differences, and the fractional calculus, as well as their modern counterparts. To illustrate the benefits and convenience of this syntax extension, an example is given to show how MACSYMA's pattern-matching capability can be used to implement a particular set of operator identities which can then be used to obtain exact solutions to nonlinear differential equations.

A convergent 2D finite-difference scheme for the Dirac–Poisson system and the simulation of graphene

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

Brinkman, D., E-mail: Daniel.Brinkman@asu.edu; School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287; Heitzinger, C., E-mail: Clemens.Heitzinger@asu.edu

2014-01-15

We present a convergent finite-difference scheme of second order in both space and time for the 2D electromagnetic Dirac equation. We apply this method in the self-consistent Dirac–Poisson system to the simulation of graphene. The model is justified for low energies, where the particles have wave vectors sufficiently close to the Dirac points. In particular, we demonstrate that our method can be used to calculate solutions of the Dirac–Poisson system where potentials act as beam splitters or Veselago lenses.

Tools for Designing and Analyzing Structures

NASA Technical Reports Server (NTRS)

Luz, Paul L.

2005-01-01

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

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.

Numerical solution of nonlinear partial differential equations of mixed type. [finite difference approximation

NASA Technical Reports Server (NTRS)

Jameson, A.

1976-01-01

A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.

Finite Element Analysis of Walking Beam of a New Compound Adjustment Balance Pumping Unit

NASA Astrophysics Data System (ADS)

Wu, Jufei; Wang, Qian; Han, Yunfei

2017-12-01

In this paper, taking the designer of the new compound balance pumping unit beam as our research target, the three-dimensional model is established by Solid Works, the load and the constraint are determined. ANSYS Workbench is used to analyze the tail and the whole of the beam, the stress and deformation are obtained to meet the strength requirements. The finite element simulation and theoretical calculation of the moment of the center axis beam are carried out. The finite element simulation results are compared with the calculated results of the theoretical mechanics model to verify the correctness of the theoretical calculation. Finally, the finite element analysis is consistent with the theoretical calculation results. The theoretical calculation results are preferable, and the bending moment value provides the theoretical reference for the follow-up optimization and research design.

Shape sensitivity analysis of flutter response of a laminated wing

NASA Technical Reports Server (NTRS)

Bergen, Fred D.; Kapania, Rakesh K.

1988-01-01

A method is presented for calculating the shape sensitivity of a wing aeroelastic response with respect to changes in geometric shape. Yates' modified strip method is used in conjunction with Giles' equivalent plate analysis to predict the flutter speed, frequency, and reduced frequency of the wing. Three methods are used to calculate the sensitivity of the eigenvalue. The first method is purely a finite difference calculation of the eigenvalue derivative directly from the solution of the flutter problem corresponding to the two different values of the shape parameters. The second method uses an analytic expression for the eigenvalue sensitivities of a general complex matrix, where the derivatives of the aerodynamic, mass, and stiffness matrices are computed using a finite difference approximation. The third method also uses an analytic expression for the eigenvalue sensitivities, but the aerodynamic matrix is computed analytically. All three methods are found to be in good agreement with each other. The sensitivities of the eigenvalues were used to predict the flutter speed, frequency, and reduced frequency. These approximations were found to be in good agreement with those obtained using a complete reanalysis.

Introducing a new methodology for the calculation of local philicity and multiphilic descriptor: an alternative to the finite difference approximation

NASA Astrophysics Data System (ADS)

Sánchez-Márquez, Jesús; Zorrilla, David; García, Víctor; Fernández, Manuel

2018-07-01

This work presents a new development based on the condensation scheme proposed by Chamorro and Pérez, in which new terms to correct the frozen molecular orbital approximation have been introduced (improved frontier molecular orbital approximation). The changes performed on the original development allow taking into account the orbital relaxation effects, providing equivalent results to those achieved by the finite difference approximation and leading also to a methodology with great advantages. Local reactivity indices based on this new development have been obtained for a sample set of molecules and they have been compared with those indices based on the frontier molecular orbital and finite difference approximations. A new definition based on the improved frontier molecular orbital methodology for the dual descriptor index is also shown. In addition, taking advantage of the characteristics of the definitions obtained with the new condensation scheme, the descriptor local philicity is analysed by separating the components corresponding to the frontier molecular orbital approximation and orbital relaxation effects, analysing also the local parameter multiphilic descriptor in the same way. Finally, the effect of using the basis set is studied and calculations using DFT, CI and Möller-Plesset methodologies are performed to analyse the consequence of different electronic-correlation levels.

Friedberg-Lee model at finite temperature and density

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

Mao Hong; CCAST; Yao Minjie

2008-06-15

The Friedberg-Lee model is studied at finite temperature and density. By using the finite temperature field theory, the effective potential of the Friedberg-Lee model and the bag constant B(T) and B(T,{mu}) have been calculated at different temperatures and densities. It is shown that there is a critical temperature T{sub C}{approx_equal}106.6 MeV when {mu}=0 MeV and a critical chemical potential {mu}{approx_equal}223.1 MeV for fixing the temperature at T=50 MeV. We also calculate the soliton solutions of the Friedberg-Lee model at finite temperature and density. It turns out that when T{<=}T{sub C} (or {mu}{<=}{mu}{sub C}), there is a bag constant B(T) [ormore » B(T,{mu})] and the soliton solutions are stable. However, when T>T{sub C} (or {mu}>{mu}{sub C}) the bag constant B(T)=0 MeV [or B(T,{mu})=0 MeV] and there is no soliton solution anymore, therefore, the confinement of quarks disappears quickly.« less

Fluctuations and correlations of conserved charges in QCD at finite temperature with effective models

NASA Astrophysics Data System (ADS)

Fu, Wei-Jie; Liu, Yu-Xin; Wu, Yue-Liang

2010-01-01

We study fluctuations of conserved charges including baryon number, electric charge, and strangeness as well as the correlations among these conserved charges in the 2+1 flavor Polyakov-Nambu-Jona-Lasinio model at finite temperature. The calculated results are compared with those obtained from recent lattice calculations performed with an improved staggered fermion action at two values of the lattice cutoff with almost physical up and down quark masses and a physical value for the strange quark mass. We find that our calculated results are well consistent with those obtained in lattice calculations except for some quantitative differences for fluctuations related with strange quarks. Our calculations indicate that there is a pronounced cusp in the ratio of the quartic to quadratic fluctuations of baryon number, i.e. χ4B/χ2B, at the critical temperature during the phase transition, which confirms that χ4B/χ2B is a useful probe of the deconfinement and chiral phase transition.

Equation of state and QCD transition at finite temperature

NASA Astrophysics Data System (ADS)

Bazavov, A.; Bhattacharya, T.; Cheng, M.; Christ, N. H.; Detar, C.; Ejiri, S.; Gottlieb, Steven; Gupta, R.; Heller, U. M.; Huebner, K.; Jung, C.; Karsch, F.; Laermann, E.; Levkova, L.; Miao, C.; Mawhinney, R. D.; Petreczky, P.; Schmidt, C.; Soltz, R. A.; Soeldner, W.; Sugar, R.; Toussaint, D.; Vranas, P.

2009-07-01

We calculate the equation of state in 2+1 flavor QCD at finite temperature with physical strange quark mass and almost physical light quark masses using lattices with temporal extent Nτ=8. Calculations have been performed with two different improved staggered fermion actions, the asqtad and p4 actions. Overall, we find good agreement between results obtained with these two O(a2) improved staggered fermion discretization schemes. A comparison with earlier calculations on coarser lattices is performed to quantify systematic errors in current studies of the equation of state. We also present results for observables that are sensitive to deconfining and chiral aspects of the QCD transition on Nτ=6 and 8 lattices. We find that deconfinement and chiral symmetry restoration happen in the same narrow temperature interval. In an appendix we present a simple parametrization of the equation of state that can easily be used in hydrodynamic model calculations. In this parametrization we include an estimate of current uncertainties in the lattice calculations which arise from cutoff and quark mass effects.

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.

Design sensitivity analysis with Applicon IFAD using the adjoint variable method

NASA Technical Reports Server (NTRS)

Frederick, Marjorie C.; Choi, Kyung K.

1984-01-01

A numerical method is presented to implement structural design sensitivity analysis using the versatility and convenience of existing finite element structural analysis program and the theoretical foundation in structural design sensitivity analysis. Conventional design variables, such as thickness and cross-sectional areas, are considered. Structural performance functionals considered include compliance, displacement, and stress. It is shown that calculations can be carried out outside existing finite element codes, using postprocessing data only. That is, design sensitivity analysis software does not have to be imbedded in an existing finite element code. The finite element structural analysis program used in the implementation presented is IFAD. Feasibility of the method is shown through analysis of several problems, including built-up structures. Accurate design sensitivity results are obtained without the uncertainty of numerical accuracy associated with selection of a finite difference perturbation.

Post-1906 stress recovery of the San Andreas fault system calculated from three-dimensional finite element analysis

USGS Publications Warehouse

Parsons, T.

2002-01-01

The M = 7.8 1906 San Francisco earthquake cast a stress shadow across the San Andreas fault system, inhibiting other large earthquakes for at least 75 years. The duration of the stress shadow is a key question in San Francisco Bay area seismic hazard assessment. This study presents a three-dimensional (3-D) finite element simulation of post-1906 stress recovery. The model reproduces observed geologic slip rates on major strike-slip faults and produces surface velocity vectors comparable to geodetic measurements. Fault stressing rates calculated with the finite element model are evaluated against numbers calculated using deep dislocation slip. In the finite element model, tectonic stressing is distributed throughout the crust and upper mantle, whereas tectonic stressing calculated with dislocations is focused mostly on faults. In addition, the finite element model incorporates postseismic effects such as deep afterslip and viscoelastic relaxation in the upper mantle. More distributed stressing and postseismic effects in the finite element model lead to lower calculated tectonic stressing rates and longer stress shadow durations (17-74 years compared with 7-54 years). All models considered indicate that the 1906 stress shadow was completely erased by tectonic loading no later than 1980. However, the stress shadow still affects present-day earthquake probability. Use of stressing rate parameters calculated with the finite element model yields a 7-12% reduction in 30-year probability caused by the 1906 stress shadow as compared with calculations not incorporating interactions. The aggregate interaction-based probability on selected segments (not including the ruptured San Andreas fault) is 53-70% versus the noninteraction range of 65-77%.

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

A FORTRAN program for calculating nonlinear seismic ground response

USGS Publications Warehouse

Joyner, William B.

1977-01-01

The program described here was designed for calculating the nonlinear seismic response of a system of horizontal soil layers underlain by a semi-infinite elastic medium representing bedrock. Excitation is a vertically incident shear wave in the underlying medium. The nonlinear hysteretic behavior of the soil is represented by a model consisting of simple linear springs and Coulomb friction elements arranged as shown. A boundary condition is used which takes account of finite rigidity in the elastic substratum. The computations are performed by an explicit finite-difference scheme that proceeds step by step in space and time. A brief program description is provided here with instructions for preparing the input and a source listing. A more detailed discussion of the method is presented elsewhere as is the description of a different program employing implicit integration.

Flame trench analysis of NLS vehicles

NASA Technical Reports Server (NTRS)

Zeytinoglu, Nuri

1993-01-01

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

Comparison of the Young-Laplace law and finite element based calculation of ventricular wall stress: implications for postinfarct and surgical ventricular remodeling.

PubMed

Zhang, Zhihong; Tendulkar, Amod; Sun, Kay; Saloner, David A; Wallace, Arthur W; Ge, Liang; Guccione, Julius M; Ratcliffe, Mark B

2011-01-01

Both the Young-Laplace law and finite element (FE) based methods have been used to calculate left ventricular wall stress. We tested the hypothesis that the Young-Laplace law is able to reproduce results obtained with the FE method. Magnetic resonance imaging scans with noninvasive tags were used to calculate three-dimensional myocardial strain in 5 sheep 16 weeks after anteroapical myocardial infarction, and in 1 of those sheep 6 weeks after a Dor procedure. Animal-specific FE models were created from the remaining 5 animals using magnetic resonance images obtained at early diastolic filling. The FE-based stress in the fiber, cross-fiber, and circumferential directions was calculated and compared to stress calculated with the assumption that wall thickness is very much less than the radius of curvature (Young-Laplace law), and without that assumption (modified Laplace). First, circumferential stress calculated with the modified Laplace law is closer to results obtained with the FE method than stress calculated with the Young-Laplace law. However, there are pronounced regional differences, with the largest difference between modified Laplace and FE occurring in the inner and outer layers of the infarct borderzone. Also, stress calculated with the modified Laplace is very different than stress in the fiber and cross-fiber direction calculated with FE. As a consequence, the modified Laplace law is inaccurate when used to calculate the effect of the Dor procedure on regional ventricular stress. The FE method is necessary to determine stress in the left ventricle with postinfarct and surgical ventricular remodeling. Copyright © 2011 The Society of Thoracic Surgeons. Published by Elsevier Inc. All rights reserved.

Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: An accurate correction scheme for electrostatic finite-size effects

PubMed Central

Rocklin, Gabriel J.; Mobley, David L.; Dill, Ken A.; Hünenberger, Philippe H.

2013-01-01

The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges −5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol−1) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB calculations for a given system, its dependence on the box size being analytical. The latter scheme also provides insight into the physical origin of the finite-size effects. These two schemes also encompass a correction for discrete solvent effects that persists even in the limit of infinite box sizes. Application of either scheme essentially eliminates the size dependence of the corrected charging free energies (maximal deviation of 1.5 kJ mol−1). Because it is simple to apply, the analytical correction scheme offers a general solution to the problem of finite-size effects in free-energy calculations involving charged solutes, as encountered in calculations concerning, e.g., protein-ligand binding, biomolecular association, residue mutation, pKa and redox potential estimation, substrate transformation, solvation, and solvent-solvent partitioning. PMID:24320250

Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: an accurate correction scheme for electrostatic finite-size effects.

PubMed

Rocklin, Gabriel J; Mobley, David L; Dill, Ken A; Hünenberger, Philippe H

2013-11-14

The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges -5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol(-1)) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB calculations for a given system, its dependence on the box size being analytical. The latter scheme also provides insight into the physical origin of the finite-size effects. These two schemes also encompass a correction for discrete solvent effects that persists even in the limit of infinite box sizes. Application of either scheme essentially eliminates the size dependence of the corrected charging free energies (maximal deviation of 1.5 kJ mol(-1)). Because it is simple to apply, the analytical correction scheme offers a general solution to the problem of finite-size effects in free-energy calculations involving charged solutes, as encountered in calculations concerning, e.g., protein-ligand binding, biomolecular association, residue mutation, pKa and redox potential estimation, substrate transformation, solvation, and solvent-solvent partitioning.

Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: An accurate correction scheme for electrostatic finite-size effects

NASA Astrophysics Data System (ADS)

Rocklin, Gabriel J.; Mobley, David L.; Dill, Ken A.; Hünenberger, Philippe H.

2013-11-01

The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges -5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol-1) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB calculations for a given system, its dependence on the box size being analytical. The latter scheme also provides insight into the physical origin of the finite-size effects. These two schemes also encompass a correction for discrete solvent effects that persists even in the limit of infinite box sizes. Application of either scheme essentially eliminates the size dependence of the corrected charging free energies (maximal deviation of 1.5 kJ mol-1). Because it is simple to apply, the analytical correction scheme offers a general solution to the problem of finite-size effects in free-energy calculations involving charged solutes, as encountered in calculations concerning, e.g., protein-ligand binding, biomolecular association, residue mutation, pKa and redox potential estimation, substrate transformation, solvation, and solvent-solvent partitioning.

Determination of stress intensity factors for interface cracks under mixed-mode loading

NASA Technical Reports Server (NTRS)

Naik, Rajiv A.; Crews, John H., Jr.

1992-01-01

A simple technique was developed using conventional finite element analysis to determine stress intensity factors, K1 and K2, for interface cracks under mixed-mode loading. This technique involves the calculation of crack tip stresses using non-singular finite elements. These stresses are then combined and used in a linear regression procedure to calculate K1 and K2. The technique was demonstrated by calculating three different bimaterial combinations. For the normal loading case, the K's were within 2.6 percent of an exact solution. The normalized K's under shear loading were shown to be related to the normalized K's under normal loading. Based on these relations, a simple equation was derived for calculating K1 and K2 for mixed-mode loading from knowledge of the K's under normal loading. The equation was verified by computing the K's for a mixed-mode case with equal and normal shear loading. The correlation between exact and finite element solutions is within 3.7 percent. This study provides a simple procedure to compute K2/K1 ratio which has been used to characterize the stress state at the crack tip for various combinations of materials and loadings. Tests conducted over a range of K2/K1 ratios could be used to fully characterize interface fracture toughness.

Two-point correlation function for Dirichlet L-functions

NASA Astrophysics Data System (ADS)

Bogomolny, E.; Keating, J. P.

2013-03-01

The two-point correlation function for the zeros of Dirichlet L-functions at a height E on the critical line is calculated heuristically using a generalization of the Hardy-Littlewood conjecture for pairs of primes in arithmetic progression. The result matches the conjectured random-matrix form in the limit as E → ∞ and, importantly, includes finite-E corrections. These finite-E corrections differ from those in the case of the Riemann zeta-function, obtained in Bogomolny and Keating (1996 Phys. Rev. Lett. 77 1472), by certain finite products of primes which divide the modulus of the primitive character used to construct the L-function in question.

Algorithm development for Maxwell's equations for computational electromagnetism

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.

1990-01-01

A new algorithm has been developed for solving Maxwell's equations for the electromagnetic field. It solves the equations in the time domain with central, finite differences. The time advancement is performed implicitly, using an alternating direction implicit procedure. The space discretization is performed with finite volumes, using curvilinear coordinates with electromagnetic components along those directions. Sample calculations are presented of scattering from a metal pin, a square and a circle to demonstrate the capabilities of the new algorithm.

Wave multiple scattering by a finite number of unclosed circular cylinders

NASA Technical Reports Server (NTRS)

Veliyev, E. I.; Veremey, V. V.

1984-01-01

The boundary value problem of plane H-polarized electromagnetic wave multiple scattering by a finite number of unclosed circular cylinders is solved. The solution is obtained by two different methods: the method of successive scattering and the method of partial matrix inversion for simultaneous dual equations. The advantages of the successive scattering method are shown. Computer calculations of the suface currents and the total cross section are presented for the structure of two screens.

Rotordynamic coefficients for labyrinth seals calculated by means of a finite difference technique

NASA Technical Reports Server (NTRS)

Nordmann, R.; Weiser, P.

1989-01-01

The compressible, turbulent, time dependent and three dimensional flow in a labyrinth seal can be described by the Navier-Stokes equations in conjunction with a turbulence model. Additionally, equations for mass and energy conservation and an equation of state are required. To solve these equations, a perturbation analysis is performed yielding zeroth order equations for centric shaft position and first order equations describing the flow field for small motions around the seal center. For numerical solution a finite difference method is applied to the zeroth and first order equations resulting in leakage and dynamic seal coefficients respectively.

Determination of stresses in gas-turbine disks subjected to plastic flow and creep

NASA Technical Reports Server (NTRS)

Millenson, M B; Manson, S S

1948-01-01

A finite-difference method previously presented for computing elastic stresses in rotating disks is extended to include the computation of the disk stresses when plastic flow and creep are considered. A finite-difference method is employed to eliminate numerical integration and to permit nontechnical personnel to make the calculations with a minimum of engineering supervision. Illustrative examples are included to facilitate explanation of the procedure by carrying out the computations on a typical gas-turbine disk through a complete running cycle. The results of the numerical examples presented indicate that plastic flow markedly alters the elastic-stress distribution.

Three-loop hard-thermal-loop perturbation theory thermodynamics at finite temperature and finite baryonic and isospin chemical potential

NASA Astrophysics Data System (ADS)

Andersen, Jens O.; Haque, Najmul; Mustafa, Munshi G.; Strickland, Michael

2016-03-01

In a previous paper [N. Haque et al., J. High Energy Phys. 05 (2014) 27], we calculated the three-loop thermodynamic potential of QCD at finite temperature T and quark chemical potentials μq using the hard-thermal-loop perturbation theory (HTLpt) reorganization of finite temperature and density QCD. The result allows us to study the thermodynamics of QCD at finite temperature and finite baryon, strangeness, and isospin chemical potentials μB, μS, and μI. We calculate the pressure at nonzero μB and μI with μS=0 , and the energy density, the entropy density, the trace anomaly, and the speed of sound at nonzero μI with μB=μS=0 . The second- and fourth-order isospin susceptibilities are calculated at μB=μS=μI=0 . Our results can be directly compared to lattice QCD without Taylor expansions around μq=0 since QCD has no sign problem at μB=μS=0 and finite isospin chemical potential μI.

76 FR 53497 - Florida Power and Light Company; St. Lucie Plant, Units 1 and 2; Environmental Assessment and...

Federal Register 2010, 2011, 2012, 2013, 2014

2011-08-26

... Appendix G to the Code for calculating K IM factors, and instead applies FEM [finite element modeling..., Units 1 and 2 are calculated using the CE NSSS finite element modeling methods. The Need for the... Society of Mechanical Engineers (ASME) Code, Section XI, Appendix G) or determined by applying finite...

A FORTRAN program for calculating three dimensional, inviscid and rotational flows with shock waves in axial compressor blade rows: User's manual

NASA Technical Reports Server (NTRS)

Thompkins, W. T., Jr.

1982-01-01

A FORTRAN-IV computer program was developed for the calculation of the inviscid transonic/supersonic flow field in a fully three dimensional blade passage of an axial compressor rotor or stator. Rotors may have dampers (part span shrouds). MacCormack's explicit time marching method is used to solve the unsteady Euler equations on a finite difference mesh. This technique captures shocks and smears them over several grid points. Input quantities are blade row geometry, operating conditions and thermodynamic quanities. Output quantities are three velocity components, density and internal energy at each mesh point. Other flow quanities are calculated from these variables. A short graphics package is included with the code, and may be used to display the finite difference grid, blade geometry and static pressure contour plots on blade to blade calculation surfaces or blade suction and pressure surfaces. The flow in a low aspect ratio transonic compressor was analyzed and compared with high response total pressure probe measurements and gas fluorescence static density measurements made in the MIT blowdown wind tunnel. These comparisons show that the computed flow fields accurately model the measured shock wave locations and overall aerodynamic performance.

Calculation of Sensitivity Derivatives in an MDAO Framework

NASA Technical Reports Server (NTRS)

Moore, Kenneth T.

2012-01-01

During gradient-based optimization of a system, it is necessary to generate the derivatives of each objective and constraint with respect to each design parameter. If the system is multidisciplinary, it may consist of a set of smaller "components" with some arbitrary data interconnection and process work ow. Analytical derivatives in these components can be used to improve the speed and accuracy of the derivative calculation over a purely numerical calculation; however, a multidisciplinary system may include both components for which derivatives are available and components for which they are not. Three methods to calculate the sensitivity of a mixed multidisciplinary system are presented: the finite difference method, where the derivatives are calculated numerically; the chain rule method, where the derivatives are successively cascaded along the system's network graph; and the analytic method, where the derivatives come from the solution of a linear system of equations. Some improvements to these methods, to accommodate mixed multidisciplinary systems, are also presented; in particular, a new method is introduced to allow existing derivatives to be used inside of finite difference. All three methods are implemented and demonstrated in the open-source MDAO framework OpenMDAO. It was found that there are advantages to each of them depending on the system being solved.

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.

Large Eddy simulation of compressible flows with a low-numerical dissipation patch-based adaptive mesh refinement method

NASA Astrophysics Data System (ADS)

Pantano, Carlos

2005-11-01

We describe a hybrid finite difference method for large-eddy simulation (LES) of compressible flows with a low-numerical dissipation scheme and structured adaptive mesh refinement (SAMR). Numerical experiments and validation calculations are presented including a turbulent jet and the strongly shock-driven mixing of a Richtmyer-Meshkov instability. The approach is a conservative flux-based SAMR formulation and as such, it utilizes refinement to computational advantage. The numerical method for the resolved scale terms encompasses the cases of scheme alternation and internal mesh interfaces resulting from SAMR. An explicit centered scheme that is consistent with a skew-symmetric finite difference formulation is used in turbulent flow regions while a weighted essentially non-oscillatory (WENO) scheme is employed to capture shocks. The subgrid stresses and transports are calculated by means of the streched-vortex model, Misra & Pullin (1997)

Algorithm for quantum-mechanical finite-nuclear-mass variational calculations of atoms with two p electrons using all-electron explicitly correlated Gaussian basis functions

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

Sharkey, Keeper L.; Pavanello, Michele; Bubin, Sergiy

2009-12-15

A new algorithm for calculating the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for quantum-mechanical calculations of atoms with two p electrons or a single d electron have been derived and implemented. The Hamiltonian used in the approach was obtained by rigorously separating the center-of-mass motion and it explicitly depends on the finite mass of the nucleus. The approach was employed to perform test calculations on the isotopes of the carbon atom in their ground electronic states and to determine the finite-nuclear-mass corrections for these states.

Communication: Finite size correction in periodic coupled cluster theory calculations of solids.

PubMed

Liao, Ke; Grüneis, Andreas

2016-10-14

We present a method to correct for finite size errors in coupled cluster theory calculations of solids. The outlined technique shares similarities with electronic structure factor interpolation methods used in quantum Monte Carlo calculations. However, our approach does not require the calculation of density matrices. Furthermore we show that the proposed finite size corrections achieve chemical accuracy in the convergence of second-order Møller-Plesset perturbation and coupled cluster singles and doubles correlation energies per atom for insulating solids with two atomic unit cells using 2 × 2 × 2 and 3 × 3 × 3 k-point meshes only.

[Application of finite element method in spinal biomechanics].

PubMed

Liu, Qiang; Zhang, Jun; Sun, Shu-Chun; Wang, Fei

2017-02-25

The finite element model is one of the most important methods in study of modern spinal biomechanics, according to the needs to simulate the various states of the spine, calculate the stress force and strain distribution of the different groups in the state, and explore its principle of mechanics, mechanism of injury, and treatment effectiveness. In addition, in the study of the pathological state of the spine, the finite element is mainly used in the understanding the mechanism of lesion location, evaluating the effects of different therapeutic tool, assisting and completing the selection and improvement of therapeutic tool, in order to provide a theoretical basis for the rehabilitation of spinal lesions. Finite element method can be more provide the service for the patients suffering from spinal correction, operation and individual implant design. Among the design and performance evaluation of the implant need to pay attention to the individual difference and perfect the evaluation system. At present, how to establish a model which is more close to the real situation has been the focus and difficulty of the study of human body's finite element.Although finite element method can better simulate complex working condition, it is necessary to improve the authenticity of the model and the sharing of the group by using many kinds of methods, such as image science, statistics, kinematics and so on. Copyright© 2017 by the China Journal of Orthopaedics and Traumatology Press.

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

NASA Technical Reports Server (NTRS)

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

2006-01-01

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

Nonvariational calculation of the relativistic, finite-size, and QED corrections for the 2 1S excited state of the helium atom

NASA Astrophysics Data System (ADS)

Haftel, M. I.; Mandelzweig, V. B.

1994-05-01

Relativistic and QED corrections are calculated by using a direct solution of the Schrödinger equation for the 2 1S excited state of the helium atom obtained with the correlation-function hyperspherical-harmonic method. Our extremely accurate nonvariational results for relativistic, QED, and finite-size corrections coincide exactly (up to 0.000 03 cm-1) with the values obtained in precision variational calculations of Drake [Nucl. Instrum. Methods Phys. Res. B 5, 2207 (1988)] and Baker, Hill, and Morgan [in Relativistic, Quantum Electrodynamic and Weak Interaction Effects in Atoms, edited by Walter Johnson, Peter Mohr, and Joseph Sucher, AIP Conf. Proc. No. 189 (AIP, New York, 1989), p. 123] for both infinite and finite nuclear masses. This confirms that a discrepancy of 0.0033 cm-1 between theory and experiment is not a result of an inaccuracy of variational wave functions, but is rooted in our inadequate knowledge of the QED operators. A better understanding of the different QED contributions to the operators (such as, for example, a more precise estimate of the Bethe logarithm) is therefore needed to explain the discrepancy.

Nucleon resonance structure in the finite volume of lattice QCD

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

Wu, Jia -Jun; Kamano, H.; Lee, T. -S. H.

An approach for relating the nucleon resonances extracted from πN reaction data to lattice QCD calculations has been developed by using the finite-volume Hamiltonian method. Within models of πN reactions, bare states are introduced to parametrize the intrinsic excitations of the nucleon. We show that the resonance can be related to the probability P N*(E) of finding the bare state, N*, in the πN scattering states in infinite volume. We further demonstrate that the probability P V N*(E) of finding the same bare states in the eigenfunctions of the underlying Hamiltonian in finite volume approaches P N*(E) as the volumemore » increases. Our findings suggest that the comparison of P N*(E) and P V N*(E) can be used to examine whether the nucleon resonances extracted from the πN reaction data within the dynamical models are consistent with lattice QCD calculation. We also discuss the measurement of P V N*(E) directly from lattice QCD. Furthermore, the practical differences between our approach and the approach using the Lüscher formalism to relate LQCD calculations to the nucleon resonance poles embedded in the data are also discussed.« less

Nucleon resonance structure in the finite volume of lattice QCD

DOE PAGES

Wu, Jia -Jun; Kamano, H.; Lee, T. -S. H.; ...

2017-06-19

An approach for relating the nucleon resonances extracted from πN reaction data to lattice QCD calculations has been developed by using the finite-volume Hamiltonian method. Within models of πN reactions, bare states are introduced to parametrize the intrinsic excitations of the nucleon. We show that the resonance can be related to the probability P N*(E) of finding the bare state, N*, in the πN scattering states in infinite volume. We further demonstrate that the probability P V N*(E) of finding the same bare states in the eigenfunctions of the underlying Hamiltonian in finite volume approaches P N*(E) as the volumemore » increases. Our findings suggest that the comparison of P N*(E) and P V N*(E) can be used to examine whether the nucleon resonances extracted from the πN reaction data within the dynamical models are consistent with lattice QCD calculation. We also discuss the measurement of P V N*(E) directly from lattice QCD. Furthermore, the practical differences between our approach and the approach using the Lüscher formalism to relate LQCD calculations to the nucleon resonance poles embedded in the data are also discussed.« less

Effect of conduction band non-parabolicity on the optical gain of quantum cascade lasers based on the effective two-band finite difference method

NASA Astrophysics Data System (ADS)

Cho, Gookbin; Kim, Jungho

2017-09-01

We theoretically investigate the effect of conduction band non-parabolicity (NPB) on the optical gain spectrum of quantum cascade lasers (QCLs) using the effective two-band finite difference method. Based on the effective two-band model to consider the NPB effect in the multiple quantum wells (QWs), the wave functions and confined energies of electron states are calculated in two different active-region structures, which correspond to three-QW single-phonon and four-QW double-phonon resonance designs. In addition, intersubband optical dipole moments and polar-optical-phonon scattering times are calculated and compared without and with the conduction band NPB effect. Finally, the calculation results of optical gain spectra are compared in the two QCL structures having the same peak gain wavelength of 8.55 μm. The gain peaks are greatly shifted to longer wavelengths and the overall gain magnitudes are slightly reduced when the NPB effect is considered. Compared with the three-QW active-region design, the redshift of the peak gain is more prominent in the four-QW active-region design, which makes use of higher electronic states for the lasing transition.

Equivalent Circuit Parameter Calculation of Interior Permanent Magnet Motor Involving Iron Loss Resistance Using Finite Element Method

NASA Astrophysics Data System (ADS)

Yamazaki, Katsumi

In this paper, we propose a method to calculate the equivalent circuit parameters of interior permanent magnet motors including iron loss resistance using the finite element method. First, the finite element analysis considering harmonics and magnetic saturation is carried out to obtain time variations of magnetic fields in the stator and the rotor core. Second, the iron losses of the stator and the rotor are calculated from the results of the finite element analysis with the considerations of harmonic eddy current losses and the minor hysteresis losses of the core. As a result, we obtain the equivalent circuit parameters i.e. the d-q axis inductance and the iron loss resistance as functions of operating condition of the motor. The proposed method is applied to an interior permanent magnet motor to calculate the characteristics based on the equivalent circuit obtained by the proposed method. The calculated results are compared with the experimental results to verify the accuracy.

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

PubMed

Röhrle, Oliver; Pullan, Andrew J

2007-01-01

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

Mass Efficiency Considerations for Thermally Insulated Structural Skin of an Aerospace Vehicle

NASA Technical Reports Server (NTRS)

Blosser, Max L.

2012-01-01

An approximate equation was derived to predict the mass of insulation required to limit the maximum temperature reached by an insulated structure subjected to a transient heating pulse. In the course of the derivation two figures of merit were identified. One figure of merit correlates to the effectiveness of the heat capacity of the underlying structural material in reducing the amount of required insulation. The second figure of merit provides an indicator of the mass efficiency of the insulator material. An iterative, one dimensional finite element analysis was used to size the external insulation required to protect the structure at a single location on the Space Shuttle Orbiter and a reusable launch vehicle. Required insulation masses were calculated for a range of different materials for both structure and insulator. The required insulation masses calculated using the approximate equation were shown to typically agree with finite element results within 10 to 20 percent over the range of parameters studied. Finite element results closely followed the trends indicated by both figures of merit.

A comparison of matrix methods for calculating eigenvalues in acoustically lined ducts

NASA Technical Reports Server (NTRS)

Watson, W.; Lansing, D. L.

1976-01-01

Three approximate methods - finite differences, weighted residuals, and finite elements - were used to solve the eigenvalue problem which arises in finding the acoustic modes and propagation constants in an absorptively lined two-dimensional duct without airflow. The matrix equations derived for each of these methods were solved for the eigenvalues corresponding to various values of wall impedance. Two matrix orders, 20 x 20 and 40 x 40, were used. The cases considered included values of wall admittance for which exact eigenvalues were known and for which several nearly equal roots were present. Ten of the lower order eigenvalues obtained from the three approximate methods were compared with solutions calculated from the exact characteristic equation in order to make an assessment of the relative accuracy and reliability of the three methods. The best results were given by the finite element method using a cubic polynomial. Excellent accuracy was consistently obtained, even for nearly equal eigenvalues, by using a 20 x 20 order matrix.

Calculation of transonic flows using an extended integral equation method

NASA Technical Reports Server (NTRS)

Nixon, D.

1976-01-01

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

Experimental analysis and simulation calculation of the inductances of loosely coupled transformer

NASA Astrophysics Data System (ADS)

Kerui, Chen; Yang, Han; Yan, Zhang; Nannan, Gao; Ying, Pei; Hongbo, Li; Pei, Li; Liangfeng, Guo

2017-11-01

The experimental design of iron-core wireless power transmission system is designed, and an experimental model of loosely coupled transformer is built. Measuring the air gap on both sides of the transformer 15mm inductor under the parameters. The feasibility and feasibility of using the finite element method to calculate the coil inductance parameters of the loosely coupled transformer are analyzed. The system was modeled by ANSYS, and the magnetic field was calculated by finite element method, and the inductance parameters were calculated. The finite element method is used to calculate the inductive parameters of the loosely coupled transformer, and the basis for the accurate compensation of the capacitance of the wireless power transmission system is established.

Efficient calculation of higher-order optical waveguide dispersion.

PubMed

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

2010-09-13

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

Magnetic Chern bands and triplon Hall effect in an extended Shastry-Sutherland model

NASA Astrophysics Data System (ADS)

Malki, M.; Schmidt, K. P.

2017-05-01

We study topological properties of one-triplon bands in an extended Shastry-Sutherland model relevant for the frustrated quantum magnet SrCu2(BO3)2 . To this end perturbative continuous unitary transformations are applied about the isolated dimer limit allowing us to calculate the one-triplon dispersion up to high order in various couplings including intra- and interdimer Dzyaloshinskii-Moriya interactions and a general uniform magnetic field. We determine the Berry curvature and the Chern number of the different one-triplon bands. We demonstrate the occurrence of Chern numbers ±1 and ±2 for the case that two components of the magnetic field are finite. Finally, we also calculate the triplon Hall effect arising at finite temperatures.

Electrodynamic multiple-scattering method for the simulation of optical trapping atop periodic metamaterials

NASA Astrophysics Data System (ADS)

Yannopapas, Vassilios; Paspalakis, Emmanuel

2018-07-01

We present a new theoretical tool for simulating optical trapping of nanoparticles in the presence of an arbitrary metamaterial design. The method is based on rigorously solving Maxwell's equations for the metamaterial via a hybrid discrete-dipole approximation/multiple-scattering technique and direct calculation of the optical force exerted on the nanoparticle by means of the Maxwell stress tensor. We apply the method to the case of a spherical polystyrene probe trapped within the optical landscape created by illuminating of a plasmonic metamaterial consisting of periodically arranged tapered metallic nanopyramids. The developed technique is ideally suited for general optomechanical calculations involving metamaterial designs and can compete with purely numerical methods such as finite-difference or finite-element schemes.

Finite Element Based HWB Centerbody Structural Optimization and Weight Prediction

NASA Technical Reports Server (NTRS)

Gern, Frank H.

2012-01-01

This paper describes a scalable structural model suitable for Hybrid Wing Body (HWB) centerbody analysis and optimization. The geometry of the centerbody and primary wing structure is based on a Vehicle Sketch Pad (VSP) surface model of the aircraft and a FLOPS compatible parameterization of the centerbody. Structural analysis, optimization, and weight calculation are based on a Nastran finite element model of the primary HWB structural components, featuring centerbody, mid section, and outboard wing. Different centerbody designs like single bay or multi-bay options are analyzed and weight calculations are compared to current FLOPS results. For proper structural sizing and weight estimation, internal pressure and maneuver flight loads are applied. Results are presented for aerodynamic loads, deformations, and centerbody weight.

Polymer photonic crystal slab waveguides

NASA Astrophysics Data System (ADS)

Liguda, C.; Böttger, G.; Kuligk, A.; Blum, R.; Eich, M.; Roth, H.; Kunert, J.; Morgenroth, W.; Elsner, H.; Meyer, H. G.

2001-04-01

We present details of the fabrication, calculations, and transmission measurements for finite two-dimensional (2D) polymer photonic crystal (PC) slab waveguides, which were fabricated from a benzocyclobutene polymer on a low refractive index substrate from Teflon. A square air hole lattice (500 nm lattice constant, 300 nm hole diameter) was realized by electron beam lithography and reactive ion etching. Polarization and wavelength dependent transmission results show TE-like and TM-like stop gaps at 1.3 μm excitation wavelengths and are in good agreement with the calculated data obtained by 2D and three-dimensional finite difference time domain methods. Transmission was suppressed by 15 dB in the center of the TE-like stop gap for a PC length of ten lattice constants.

Seebeck coefficient of one electron

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

Durrani, Zahid A. K., E-mail: z.durrani@imperial.ac.uk

2014-03-07

The Seebeck coefficient of one electron, driven thermally into a semiconductor single-electron box, is investigated theoretically. With a finite temperature difference ΔT between the source and charging island, a single electron can charge the island in equilibrium, directly generating a Seebeck effect. Seebeck coefficients for small and finite ΔT are calculated and a thermally driven Coulomb staircase is predicted. Single-electron Seebeck oscillations occur with increasing ΔT, as one electron at a time charges the box. A method is proposed for experimental verification of these effects.

Finite-temperature Gutzwiller approximation from the time-dependent variational principle

NASA Astrophysics Data System (ADS)

Lanatà, Nicola; Deng, Xiaoyu; Kotliar, Gabriel

2015-08-01

We develop an extension of the Gutzwiller approximation to finite temperatures based on the Dirac-Frenkel variational principle. Our method does not rely on any entropy inequality, and is substantially more accurate than the approaches proposed in previous works. We apply our theory to the single-band Hubbard model at different fillings, and show that our results compare quantitatively well with dynamical mean field theory in the metallic phase. We discuss potential applications of our technique within the framework of first-principle calculations.

Numerical investigation of electron localization in polymer chains

NASA Astrophysics Data System (ADS)

Paulsson, Magnus; Stafström, Sven

1998-01-01

Using finite-size scaling, we have calculated the localization-delocalization phase diagrams for electronic wave functions in different disordered polymeric systems. The disorder considered here simulates finite polymer chain lengths, breaks in the conjugation, and disorder in an external potential. It is shown that a system of interacting chains, even at rather weak interchain interactions, allows for enough flexibility for the scattered waves to avoid dephasing and localization. Localization and the metal-insulator transition in highly conducting polymers are discussed in view of these results.

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.

Internal and external 2-d boundary layer flows

NASA Technical Reports Server (NTRS)

Crawford, M. E.; Kays, W. M.

1978-01-01

Computer program computes general two dimensional turbulent boundary-layer flow using finite-difference techniques. Structure allows for user modification to accommodate unique problems. Program should prove useful in many applications where accurate boundary-layer flow calculations are required.

Application of finite difference techniques to noise propagation in jet engine ducts

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1973-01-01

A finite difference formulation is presented for wave propagation in a rectangular two-dimensional duct without steady flow. The difference technique, which should be used in the study of acoustically treated inlet and exhausts ducts used in turbofan engines, can readily handle acoustical flow field complications such as axial variations in wall impedance and cross-section area. In the numerical analysis, the continuous acoustic field is lumped into a series of grid points in which the pressure and velocity at each grid point are separated into real and imaginary terms. An example calculation is also presented for the sound attenuation in a two-dimensional straight soft-walled suppressor.

Application of finite difference techniques to noise propagation in jet engine ducts

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1973-01-01

A finite difference formulation is presented for wave propagation in a rectangular two-dimensional duct without steady flow. The difference technique, which should be useful in the study of acoustically treated inlet and exhausts ducts used in turbofan engines, can readily handle acoustical flow field complications such as axial variations in wall impedance and cross section area. In the numerical analysis, the continuous acoustic field is lumped into a series of grid points in which the pressure and velocity at each grid point are separated into real and imaginary terms. An example calculation is also presented for the sound attenuation in a two-dimensional straight soft-walled suppressor.

Partition of unity finite element method for quantum mechanical materials calculations

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

Pask, J. E.; Sukumar, N.

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

Partition of unity finite element method for quantum mechanical materials calculations

DOE PAGES

Pask, J. E.; Sukumar, N.

2016-11-09

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

Simulation of hot spots formation and evolution in HMX

NASA Astrophysics Data System (ADS)

Wang, Cheng; Yang, Tonghui

2017-06-01

In order to study the formation and evolution of hot spots under shock loading, HMX explosives were selected as the object of study for the two-dimensional finite difference numerical simulation. A fifth order finite difference weighted essentially non-oscillatory (WENO) scheme and a third order TVD Runge-Kutta method are utilized for the spatial discretization and the time advance, respectively. The governing equations are based on the fluid elasto-plastic control equations. The Mie-Gruneisen equation of state and the ideal gas equation of state are selected to use in the state equation of the solid explosives and gas material. In order to simplify the calculation of the model, the reaction can be considered to complete in one step. The calculated area is [ 3.0 ×10-5 m ] × [ 3.0 ×10-5 m ] . The radius is 0.6 ×10-5 m, and the internal gas is not involved in the reaction. The calculation area is divided into 300×300 grids and 10 grids are selected from the bottom of each column to give the particle velocity u as the initial condition. In the selected grid, different initial velocity 100m/s and 200m/s are loaded respectively to study the influence of hot spot formation and evolution in different impact intensity.

Lattice Boltzmann model for the compressible Navier-Stokes equations with flexible specific-heat ratio.

PubMed

Kataoka, Takeshi; Tsutahara, Michihisa

2004-03-01

We have developed a lattice Boltzmann model for the compressible Navier-Stokes equations with a flexible specific-heat ratio. Several numerical results are presented, and they agree well with the corresponding solutions of the Navier-Stokes equations. In addition, an explicit finite-difference scheme is proposed for the numerical calculation that can make a stable calculation with a large Courant number.

The electronic and optical properties of quantum nano-structures

NASA Astrophysics Data System (ADS)

Ham, Heon

In semiconducting quantum nano-structures, the excitonic effects play an important role when we fabricate opto-electronic devices, such as lasers, diodes, detectors, etc. To gain a better understanding of the excitonic effects in quantum nano-structures, we investigated the exciton binding energy, oscillator strength, and linewidth in quantum nano-structures using both the infinite and finite well models. We investigated also the hydrogenic impurity binding energy and the photoionization cross section of the hydrogenic impurity in a spherical quantum dot. In our work, the variational approach is used in all calculations, because the Hamiltonian of the system is not separable, due to the different symmetries of the Coulomb and confining potentials. In the infinite well model of the semiconducting quantum nanostructures, the binding energy of the exciton increases with decreasing width of the potential barriers due to the increase in the effective strength of the Coulomb interaction between the electron and hole. In the finite well model, the exciton binding energy reaches a peak value, and the binding energy decreases with further decrease in the width of the potential barriers. The exciton linewidth in the infinite well model increases with decreasing wire radius, because the scattering rate of the exciton increases with decreasing wire radius. In the finite well model, the exciton linewidth in a cylindrical quantum wire reaches a peak value and the exciton linewidth decreases with further decrease in the wire radius, because the exciton is not well confined at very smaller wire radii. The binding energy of the hydrogenic impurity in a spherical quantum dot has also calculated using both the infinite and the finite well models. The binding energy of the hydrogenic impurity was calculated for on center and off center impurities in the spherical quantum dots. With decreasing radii of the dots, the binding energy of the hydrogenic impurity increases in the infinite well model. The binding energy of the hydrogenic impurity in the finite well model reaches a peak value and decreases with further decrease in the dot radii for both on center and off center impurities. We have calculated the photoionization cross section as a function of the radius and the frequency using both the infinite and finite well models. The photoionizaton cross section has a peak value at a frequency where the photon energy equals the difference between the final and initial state energies of the impurity. The behavior of the cross section with dot radius depends upon the location of the impurity and the polarization of the electromagnetic field.

Broadband ground motion simulation using a paralleled hybrid approach of Frequency Wavenumber and Finite Difference method

NASA Astrophysics Data System (ADS)

Chen, M.; Wei, S.

2016-12-01

The serious damage of Mexico City caused by the 1985 Michoacan earthquake 400 km away indicates that urban areas may be affected by remote earthquakes. To asses earthquake risk of urban areas imposed by distant earthquakes, we developed a hybrid Frequency Wavenumber (FK) and Finite Difference (FD) code implemented with MPI, since the computation of seismic wave propagation from a distant earthquake using a single numerical method (e.g. Finite Difference, Finite Element or Spectral Element) is very expensive. In our approach, we compute the incident wave field (ud) at the boundaries of the excitation box, which surrounding the local structure, using a paralleled FK method (Zhu and Rivera, 2002), and compute the total wave field (u) within the excitation box using a parallelled 2D FD method. We apply perfectly matched layer (PML) absorbing condition to the diffracted wave field (u-ud). Compared to previous Generalized Ray Theory and Finite Difference (Wen and Helmberger, 1998), Frequency Wavenumber and Spectral Element (Tong et al., 2014), and Direct Solution Method and Spectral Element hybrid method (Monteiller et al., 2013), our absorbing boundary condition dramatically suppress the numerical noise. The MPI implementation of our method can greatly speed up the calculation. Besides, our hybrid method also has a potential use in high resolution array imaging similar to Tong et al. (2014).

Applications of algebraic topology to compatible spatial discretizations.

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

Bochev, Pavel Blagoveston; Hyman, James M.

We provide a common framework for compatible discretizations using algebraic topology to guide our analysis. The main concept is the natural inner product on cochains, which induces a combinatorial Hodge theory. The framework comprises of mutually consistent operations of differentiation and integration, has a discrete Stokes theorem, and preserves the invariants of the DeRham cohomology groups. The latter allows for an elementary calculation of the kernel of the discrete Laplacian. Our framework provides an abstraction that includes examples of compatible finite element, finite volume and finite difference methods. We describe how these methods result from the choice of a reconstructionmore » operator and when they are equivalent.« less

Predictions of thermal buckling strengths of hypersonic aircraft sandwich panels using minimum potential energy and finite element methods

NASA Technical Reports Server (NTRS)

Ko, William L.

1995-01-01

Thermal buckling characteristics of hypersonic aircraft sandwich panels of various aspect ratios were investigated. The panel is fastened at its four edges to the substructures under four different edge conditions and is subjected to uniform temperature loading. Minimum potential energy theory and finite element methods were used to calculate the panel buckling temperatures. The two methods gave fairly close buckling temperatures. However, the finite element method gave slightly lower buckling temperatures than those given by the minimum potential energy theory. The reasons for this slight discrepancy in eigensolutions are discussed in detail. In addition, the effect of eigenshifting on the eigenvalue convergence rate is discussed.

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.

Accurate solutions for transonic viscous flow over finite wings

NASA Technical Reports Server (NTRS)

Vatsa, V. N.

1986-01-01

An explicit multistage Runge-Kutta type time-stepping scheme is used for solving the three-dimensional, compressible, thin-layer Navier-Stokes equations. A finite-volume formulation is employed to facilitate treatment of complex grid topologies encountered in three-dimensional calculations. Convergence to steady state is expedited through usage of acceleration techniques. Further numerical efficiency is achieved through vectorization of the computer code. The accuracy of the overall scheme is evaluated by comparing the computed solutions with the experimental data for a finite wing under different test conditions in the transonic regime. A grid refinement study ir conducted to estimate the grid requirements for adequate resolution of salient features of such flows.

Strain energy release rate analysis of the end-notched flexure specimen using the finite-element method

NASA Technical Reports Server (NTRS)

Salpekar, S. A.; Raju, I. S.; O'Brien, T. K.

1988-01-01

Two-dimensional finite-element analysis of the end-notched flexure specimen was performed using 8-node isoparametric, parabolic elements to evaluate compliance and mode II strain energy release rates, G sub II. The G sub II values were computed using two different techniques: the virtual crack-closure technique (VCCT) and the rate of change of compliance with crack length (compliance derivative method). The analysis was performed for various crack-length-to-semi-span (a/L) ratios ranging from 0.2 to 0.9. Three material systems representing a wide range of material properties were analyzed. The compliance and strain energy release rates of the specimen calculated with the present finite-element analysis agree very well with beam theory equations including transverse shear. The G sub II values calculated using the compliance derivative method compared extremely well with those calculated using the VCCT. The G sub II values obtained by the compliance derivative method using the top or bottom beam deflections agreed closely with each other. The strain energy release rates from a plane-stress analysis were higher than the plane-strain values by only a small percentage, indicating that either assumption may be used in the analysis. The G sub II values for one material system calculated from the finte-element analysis agreed with one solution in the literature and disagreed with the other solution in the literature.

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

NASA Astrophysics Data System (ADS)

Watrous, Mitchell James

1997-12-01

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

Revision of the documentation for a model for calculating effects of liquid waste disposal in deep saline aquifers

USGS Publications Warehouse

INTERA Environmental Consultants, Inc.

1979-01-01

The major limitation of the model arises using second-order correct (central-difference) finite-difference approximation in space. To avoid numerical oscillations in the solution, the user must restrict grid block and time step sizes depending upon the magnitude of the dispersivity.

Computational fluid dynamics: An engineering tool?

NASA Astrophysics Data System (ADS)

Anderson, J. D., Jr.

1982-06-01

Computational fluid dynamics in general, and time dependent finite difference techniques in particular, are examined from the point of view of direct engineering applications. Examples are given of the supersonic blunt body problem and gasdynamic laser calculations, where such techniques are clearly engineering tools. In addition, Navier-Stokes calculations of chemical laser flows are discussed as an example of a near engineering tool. Finally, calculations of the flowfield in a reciprocating internal combustion engine are offered as a promising future engineering application of computational fluid dynamics.

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

NASA Technical Reports Server (NTRS)

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

1982-01-01

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

A new sensitivity analysis for structural optimization of composite rotor blades

NASA Technical Reports Server (NTRS)

Venkatesan, C.; Friedmann, P. P.; Yuan, Kuo-An

1993-01-01

This paper presents a detailed mathematical derivation of the sensitivity derivatives for the structural dynamic, aeroelastic stability and response characteristics of a rotor blade in hover and forward flight. The formulation is denoted by the term semianalytical approach, because certain derivatives have to be evaluated by a finite difference scheme. Using the present formulation, sensitivity derivatives for the structural dynamic and aeroelastic stability characteristics, were evaluated for both isotropic and composite rotor blades. Based on the results, useful conclusions are obtained regarding the relative merits of the semi-analytical approach, for calculating sensitivity derivatives, when compared to a pure finite difference approach.

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

Decomposition of the Seismic Source Using Numerical Simulations and Observations of Nuclear Explosions

DTIC Science & Technology

2017-05-31

SUBJECT TERMS nonlinear finite element calculations, nuclear explosion monitoring, topography 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18...3D North Korea calculations........ Figure 6. The CRAM 3D finite element outer grid (left) is rectangular......................... Figure 7. Stress...Figure 6. The CRAM 3D finite element outer grid (left) is rectangular. The inner grid (center) is shaped to match the shape of the explosion shock wave

Higher-order adaptive finite-element methods for Kohn–Sham density functional theory

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

Motamarri, P.; Nowak, M.R.; Leiter, K.

2013-11-15

We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn–Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss–Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100–200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposedmore » solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn–Sham DFT problem. Our studies suggest that staggering computational savings—of the order of 1000-fold—relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn–Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688 atoms using modest computational resources, and good scalability of the present implementation up to 192 processors.« less

Dielectric Response and Born Dynamic Charge of BN Nanotubes from Ab Initio Finite Electric Field Calculations

NASA Astrophysics Data System (ADS)

Guo, Guang-Yu; Ishibashi, Shoji; Tamura, Tomoyuki; Terakura, Kiyoyuki

2007-03-01

Since the discovery of carbon nanotubes (CNTs) in 1991 by Iijima, carbon and other nanotubes have attracted considerable interest worldwide because of their unusual properties and also great potentials for technological applications. Though CNTs continue to attract great interest, other nanotubes such as BN nanotubes (BN-NTs) may offer different opportunities that CNTs cannot provide. In this contribution, we present the results of our recent systematic ab initio calculations of the static dielectric constant, electric polarizability, Born dynamical charge, electrostriction coefficient and piezoelectric constant of BN-NTs using the latest crystalline finite electric field theory [1]. [1] I. Souza, J. Iniguez, and D. Vanderbilt, Phys. Rev. Lett. 89, 117602 (2002); P. Umari and A. Pasquarello, Phys. Rev. Lett. 89, 157602 (2002).

A study of the diffusional behavior of a two-phase metal matrix composite exposed to a high temperature environment

NASA Technical Reports Server (NTRS)

Tenney, D. R.

1974-01-01

The progress of diffusion-controlled filament-matrix interaction in a metal matrix composite where the filaments and matrix comprise a two-phase binary alloy system was studied by mathematically modeling compositional changes resulting from prolonged elevated temperature exposure. The analysis treats a finite, diffusion-controlled, two-phase moving-interface problem by means of a variable-grid finite-difference technique. The Ni-W system was selected as an example system. Modeling was carried out for the 1000 to 1200 C temperature range for unidirectional composites containing from 6 to 40 volume percent tungsten filaments in a Ni matrix. The results are displayed to show both the change in filament diameter and matrix composition as a function of exposure time. Compositional profiles produced between first and second nearest neighbor filaments were calculated by superposition of finite-difference solutions of the diffusion equations.

Numerical simulation of aerothermal loads in hypersonic engine inlets due to shock impingement

NASA Technical Reports Server (NTRS)

Ramakrishnan, R.

1992-01-01

The effect of shock impingement on an axial corner simulating the inlet of a hypersonic vehicle engine is modeled using a finite-difference procedure. A three-dimensional dynamic grid adaptation procedure is utilized to move the grids to regions with strong flow gradients. The adaptation procedure uses a grid relocation stencil that is valid at both the interior and boundary points of the finite-difference grid. A linear combination of spatial derivatives of specific flow variables, calculated with finite-element interpolation functions, are used as adaptation measures. This computational procedure is used to study laminar and turbulent Mach 6 flows in the axial corner. The description of flow physics and qualitative measures of heat transfer distributions on cowl and strut surfaces obtained from the analysis are compared with experimental observations. Conclusions are drawn regarding the capability of the numerical scheme for enhanced modeling of high-speed compressible flows.

The quantum Ising chain with a generalized defect

NASA Astrophysics Data System (ADS)

Grimm, Uwe

1990-08-01

The finite-size scaling properties of the quantum Ising chain with different types of generalized defects are studied. This not only means an alteration of the coupling constant as previously examined, but also an additional arbitrary transformation in the algebra of observables at one site of the chain. One can distinguish between two classes of generalized defects: on the one hand those which do not affect the finite-size integrability of the Ising chain, and on the other hand those that destroy this property. In this context, finite-size integrability is always understood as a synonym for the possibility to write the hamiltonian of the finite chain as a bilinear expression in fermionic operators by means of a Jordan-Wigner transformation. Concerning the first type of defect, an exact solution for the scaling spectrum is obtained for the most universal defect that preserves the global Z2 symmetry of the chain. It is shown that in the continuum limit this yields the same result as for one properly chosen ordinary defect, that is changing the coupling constant only, and thus the finite-size scaling spectra can be described by irreps of a shifted u(1) Kac-Moody algebra. The other type of defect is examined by means of numerical finite-size calculations. In contrast to the first case, these calculations suggest a non-continuous dependence of the scaling dimensions on the defect parameters. A conjecture for the operator content involving only one primary field of a Virasoro algebra with central charge c= {1}/{2} is given.

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.

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

NASA Technical Reports Server (NTRS)

Walton, William C., Jr.

1960-01-01

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

Accuracy Improvement in Magnetic Field Modeling for an Axisymmetric Electromagnet

NASA Technical Reports Server (NTRS)

Ilin, Andrew V.; Chang-Diaz, Franklin R.; Gurieva, Yana L.; Il,in, Valery P.

2000-01-01

This paper examines the accuracy and calculation speed for the magnetic field computation in an axisymmetric electromagnet. Different numerical techniques, based on an adaptive nonuniform grid, high order finite difference approximations, and semi-analitical calculation of boundary conditions are considered. These techniques are being applied to the modeling of the Variable Specific Impulse Magnetoplasma Rocket. For high-accuracy calculations, a fourth-order scheme offers dramatic advantages over a second order scheme. For complex physical configurations of interest in plasma propulsion, a second-order scheme with nonuniform mesh gives the best results. Also, the relative advantages of various methods are described when the speed of computation is an important consideration.

A robust method of computing finite difference coefficients based on Vandermonde matrix

NASA Astrophysics Data System (ADS)

Zhang, Yijie; Gao, Jinghuai; Peng, Jigen; Han, Weimin

2018-05-01

When the finite difference (FD) method is employed to simulate the wave propagation, high-order FD method is preferred in order to achieve better accuracy. However, if the order of FD scheme is high enough, the coefficient matrix of the formula for calculating finite difference coefficients is close to be singular. In this case, when the FD coefficients are computed by matrix inverse operator of MATLAB, inaccuracy can be produced. In order to overcome this problem, we have suggested an algorithm based on Vandermonde matrix in this paper. After specified mathematical transformation, the coefficient matrix is transformed into a Vandermonde matrix. Then the FD coefficients of high-order FD method can be computed by the algorithm of Vandermonde matrix, which prevents the inverse of the singular matrix. The dispersion analysis and numerical results of a homogeneous elastic model and a geophysical model of oil and gas reservoir demonstrate that the algorithm based on Vandermonde matrix has better accuracy compared with matrix inverse operator of MATLAB.

Bolt clampup relaxation in a graphite/epoxy laminate

NASA Technical Reports Server (NTRS)

Shivakumar, K. N.; Crews, J. H., Jr.

1982-01-01

A simple bolted joint was analyzed to calculate bolt clampup relaxation for a graphite/epoxy (T300/5208) laminate. A viscoelastic finite element analysis of a double-lap joint with a steel bolt was conducted. Clampup forces were calculated for various steady-state temperature-moisture conditions using a 20-year exposure duration. The finite element analysis predicted that clampup forces relax even for the room-temperature-dry condition. The relaxations were 8, 13, 20, and 30 percent for exposure durations of 1 day, 1 month, 1 year, and 20 years, respectively. As expected, higher temperatures and moisture levels each increased the relaxation rate. The combined viscoelastic effects of steady-state temperature and moisture appeared to be additive. From the finite-element analysis, a simple equation was developed for clampup force relaxation. This generalized equation was used to calculate clampup forces for the same temperature-moisture conditions as used in the finite-element analysis. The two sets of calculated results agreed well.

Benchmark measurements and calculations of a 3-dimensional neutron streaming experiment

NASA Astrophysics Data System (ADS)

Barnett, D. A., Jr.

1991-02-01

An experimental assembly known as the Dog-Legged Void assembly was constructed to measure the effect of neutron streaming in iron and void regions. The primary purpose of the measurements was to provide benchmark data against which various neutron transport calculation tools could be compared. The measurements included neutron flux spectra at four places and integral measurements at two places in the iron streaming path as well as integral measurements along several axial traverses. These data have been used in the verification of Oak Ridge National Laboratory's three-dimensional discrete ordinates code, TORT. For a base case calculation using one-half inch mesh spacing, finite difference spatial differencing, an S(sub 16) quadrature and P(sub 1) cross sections in the MUFT multigroup structure, the calculated solution agreed to within 18 percent with the spectral measurements and to within 24 percent of the integral measurements. Variations on the base case using a fewgroup energy structure and P(sub 1) and P(sub 3) cross sections showed similar agreement. Calculations using a linear nodal spatial differencing scheme and fewgroup cross sections also showed similar agreement. For the same mesh size, the nodal method was seen to require 2.2 times as much CPU time as the finite difference method. A nodal calculation using a typical mesh spacing of 2 inches, which had approximately 32 times fewer mesh cells than the base case, agreed with the measurements to within 34 percent and yet required on 8 percent of the CPU time.

Computationally efficient finite-difference modal method for the solution of Maxwell's equations.

PubMed

Semenikhin, Igor; Zanuccoli, Mauro

2013-12-01

In this work, a new implementation of the finite-difference (FD) modal method (FDMM) based on an iterative approach to calculate the eigenvalues and corresponding eigenfunctions of the Helmholtz equation is presented. Two relevant enhancements that significantly increase the speed and accuracy of the method are introduced. First of all, the solution of the complete eigenvalue problem is avoided in favor of finding only the meaningful part of eigenmodes by using iterative methods. Second, a multigrid algorithm and Richardson extrapolation are implemented. Simultaneous use of these techniques leads to an enhancement in terms of accuracy, which allows a simple method such as the FDMM with a typical three-point difference scheme to be significantly competitive with an analytical modal method.

An overlapped grid method for multigrid, finite volume/difference flow solvers: MaGGiE

NASA Technical Reports Server (NTRS)

Baysal, Oktay; Lessard, Victor R.

1990-01-01

The objective is to develop a domain decomposition method via overlapping/embedding the component grids, which is to be used by upwind, multi-grid, finite volume solution algorithms. A computer code, given the name MaGGiE (Multi-Geometry Grid Embedder) is developed to meet this objective. MaGGiE takes independently generated component grids as input, and automatically constructs the composite mesh and interpolation data, which can be used by the finite volume solution methods with or without multigrid convergence acceleration. Six demonstrative examples showing various aspects of the overlap technique are presented and discussed. These cases are used for developing the procedure for overlapping grids of different topologies, and to evaluate the grid connection and interpolation data for finite volume calculations on a composite mesh. Time fluxes are transferred between mesh interfaces using a trilinear interpolation procedure. Conservation losses are minimal at the interfaces using this method. The multi-grid solution algorithm, using the coaser grid connections, improves the convergence time history as compared to the solution on composite mesh without multi-gridding.

A finite-step method for estimating the spanwise lift distribution of wings in symmetric, yawed, and rotary flight at low speeds

NASA Technical Reports Server (NTRS)

Krenkel, A. R.

1978-01-01

The finite-step method was programmed for computing the span loading and stability derivatives of trapezoidal shaped wings in symmetric, yawed, and rotary flight. Calculations were made for a series of different wing planforms and the results compared with several available methods for estimating these derivatives in the linear angle of attack range. The agreement shown was generally good except in a few cases. An attempt was made to estimate the nonlinear variation of lift with angle of attack in the high alpha range by introducing the measured airfoil section data into the finite-step method. The numerical procedure was found to be stable only at low angles of attack.

Frequency response function (FRF) based updating of a laser spot welded structure

NASA Astrophysics Data System (ADS)

Zin, M. S. Mohd; Rani, M. N. Abdul; Yunus, M. A.; Sani, M. S. M.; Wan Iskandar Mirza, W. I. I.; Mat Isa, A. A.

2018-04-01

The objective of this paper is to present frequency response function (FRF) based updating as a method for matching the finite element (FE) model of a laser spot welded structure with a physical test structure. The FE model of the welded structure was developed using CQUAD4 and CWELD element connectors, and NASTRAN was used to calculate the natural frequencies, mode shapes and FRF. Minimization of the discrepancies between the finite element and experimental FRFs was carried out using the exceptional numerical capability of NASTRAN Sol 200. The experimental work was performed under free-free boundary conditions using LMS SCADAS. Avast improvement in the finite element FRF was achieved using the frequency response function (FRF) based updating with two different objective functions proposed.

Finite key analysis for symmetric attacks in quantum key distribution

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

Meyer, Tim; Kampermann, Hermann; Kleinmann, Matthias

2006-10-15

We introduce a constructive method to calculate the achievable secret key rate for a generic class of quantum key distribution protocols, when only a finite number n of signals is given. Our approach is applicable to all scenarios in which the quantum state shared by Alice and Bob is known. In particular, we consider the six state protocol with symmetric eavesdropping attacks, and show that for a small number of signals, i.e., below n{approx}10{sup 4}, the finite key rate differs significantly from the asymptotic value for n{yields}{infinity}. However, for larger n, a good approximation of the asymptotic value is found.more » We also study secret key rates for protocols using higher-dimensional quantum systems.« less

A Mixed Finite Volume Element Method for Flow Calculations in Porous Media

NASA Technical Reports Server (NTRS)

Jones, Jim E.

1996-01-01

A key ingredient in the simulation of flow in porous media is the accurate determination of the velocities that drive the flow. The large scale irregularities of the geology, such as faults, fractures, and layers suggest the use of irregular grids in the simulation. Work has been done in applying the finite volume element (FVE) methodology as developed by McCormick in conjunction with mixed methods which were developed by Raviart and Thomas. The resulting mixed finite volume element discretization scheme has the potential to generate more accurate solutions than standard approaches. The focus of this paper is on a multilevel algorithm for solving the discrete mixed FVE equations. The algorithm uses a standard cell centered finite difference scheme as the 'coarse' level and the more accurate mixed FVE scheme as the 'fine' level. The algorithm appears to have potential as a fast solver for large size simulations of flow in porous media.

Least-squares finite element methods for compressible Euler equations

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Carey, G. F.

1990-01-01

A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.

Analysis of the cylinder’s movement characteristics after entering water based on CFD

NASA Astrophysics Data System (ADS)

Liu, Xianlong

2017-10-01

It’s a variable speed motion after the cylinder vertical entry the water. Using dynamic mesh is mostly unstructured grid, and the calculation results are not ideal and consume huge computing resources. CFD method is used to calculate the resistance of the cylinder at different velocities. Cubic spline interpolation method is used to obtain the resistance at fixed speeds. The finite difference method is used to solve the motion equation, and the acceleration, velocity, displacement and other physical quantities are obtained after the cylinder enters the water.

Large scale phononic metamaterials for seismic isolation

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

Aravantinos-Zafiris, N.; Sigalas, M. M.

In this work, we numerically examine structures that could be characterized as large scale phononic metamaterials. These novel structures could have band gaps in the frequency spectrum of seismic waves when their dimensions are chosen appropriately, thus raising the belief that they could be serious candidates for seismic isolation structures. Different and easy to fabricate structures were examined made from construction materials such as concrete and steel. The well-known finite difference time domain method is used in our calculations in order to calculate the band structures of the proposed metamaterials.

Heat capacity of the neutron star inner crust within an extended nuclear statistical equilibrium model

NASA Astrophysics Data System (ADS)

Burrello, S.; Gulminelli, F.; Aymard, F.; Colonna, M.; Raduta, Ad. R.

2015-11-01

Background: Superfluidity in the crust is a key ingredient for the cooling properties of proto-neutron stars. Present theoretical calculations employ the quasiparticle mean-field Hartree-Fock-Bogoliubov theory with temperature-dependent occupation numbers for the quasiparticle states. Purpose: Finite temperature stellar matter is characterized by a whole distribution of different nuclear species. We want to assess the importance of this distribution on the calculation of heat capacity in the inner crust. Method: Following a recent work, the Wigner-Seitz cell is mapped into a model with cluster degrees of freedom. The finite temperature distribution is then given by a statistical collection of Wigner-Seitz cells. We additionally introduce pairing correlations in the local density BCS approximation both in the homogeneous unbound neutron component, and in the interface region between clusters and neutrons. Results: The heat capacity is calculated in the different baryonic density conditions corresponding to the inner crust, and in a temperature range varying from 100 KeV to 2 MeV. We show that accounting for the cluster distribution has a small effect at intermediate densities, but it considerably affects the heat capacity both close to the outer crust and close to the core. We additionally show that it is very important to consider the temperature evolution of the proton fraction for a quantitatively reliable estimation of the heat capacity. Conclusions: We present the first modelization of stellar matter containing at the same time a statistical distribution of clusters at finite temperature, and pairing correlations in the unbound neutron component. The effect of the nuclear distribution on the superfluid properties can be easily added in future calculations of the neutron star cooling curves. A strong influence of resonance population on the heat capacity at high temperature is observed, which deserves to be further studied within more microscopic calculations.

FDTD modeling of thin impedance sheets

NASA Technical Reports Server (NTRS)

Luebbers, Raymond J.; Kunz, Karl S.

1991-01-01

Thin sheets of resistive or dielectric material are commonly encountered in radar cross section calculations. Analysis of such sheets is simplified by using sheet impedances. In this paper it is shown that sheet impedances can be modeled easily and accurately using Finite Difference Time Domain (FDTD) methods.

Calculated shape dependence of electromagnetic field in tip-enhanced Raman scattering by using a monopole antenna model

NASA Astrophysics Data System (ADS)

Kitahama, Yasutaka; Itoh, Tamitake; Suzuki, Toshiaki

2018-05-01

To evaluate the shape of an Ag tip with regard to tip-enhanced Raman scattering (TERS) signal, the enhanced electromagnetic (EM) field and scattering spectrum, arising from surface plasmon resonance at the apex of the tip, were calculated using a finite-difference time domain (FDTD) method. In the calculated forward scattering spectra from the smooth Ag tip, the band appeared within the visible region, similar to the experimental results and calculation for a corrugated Ag cone. In the FDTD calculation of TERS, the Ag tip acting as a monopole antenna was adopted by insertion of a perfect electric conductor between the root of the tip and a top boundary surface of the calculation space. As a result, the EM field was only enhanced at the apex. The shape dependence i.e. the EM field calculated at the apex with various curvatures on the different tapered tips, obtained using the monopole antenna model, was different from that simulated using a conventional dipole antenna model.

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

NASA Technical Reports Server (NTRS)

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

1979-01-01

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

Nuclear relaxation and vibrational contributions to the static electrical properties of polyatomic molecules: beyond the Hartree-Fock approximation

NASA Astrophysics Data System (ADS)

Luis, Josep M.; Martí, Josep; Duran, Miquel; Andrés, JoséL.

1997-04-01

Electronic and nuclear contributions to the static molecular electrical properties, along with the Stark tuning rate ( δνE ) and the infrared cross section changes ( δSE) have been calculated at the SCF level and at different correlated levels of theory, using a TZ2P basis set and finite field techniques. Nuclear contributions to these molecular properties have also been calculated using a recent analytical approach that allow both to check the accuracy of the finite field values, and to evaluate the importance of higher-order derivatives. The HF, CO, H 2O, H 2CO, and CH 4 molecules have been studied and the results compared to experimental date when available. The paper shows that nuclear relaxation and vibrational contributions must be included in order to obtain accurate values of the static electrical properties. Two different, combined approaches are proposed to predict experimental values of the electrical properties to an error smaller than 5%.

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

NASA Technical Reports Server (NTRS)

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

1982-01-01

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

Technical Note: Adjoint formulation of the TOMCAT atmospheric transport scheme in the Eulerian backtracking framework (RETRO-TOM)

NASA Astrophysics Data System (ADS)

Haines, P. E.; Esler, J. G.; Carver, G. D.

2014-06-01

A new methodology for the formulation of an adjoint to the transport component of the chemistry transport model TOMCAT is described and implemented in a new model, RETRO-TOM. The Eulerian backtracking method is used, allowing the forward advection scheme (Prather's second-order moments) to be efficiently exploited in the backward adjoint calculations. Prather's scheme is shown to be time symmetric, suggesting the possibility of high accuracy. To attain this accuracy, however, it is necessary to make a careful treatment of the "density inconsistency" problem inherent to offline transport models. The results are verified using a series of test experiments. These demonstrate the high accuracy of RETRO-TOM when compared with direct forward sensitivity calculations, at least for problems in which flux limiters in the advection scheme are not required. RETRO-TOM therefore combines the flexibility and stability of a "finite difference of adjoint" formulation with the accuracy of an "adjoint of finite difference" formulation.

Technical Note: Adjoint formulation of the TOMCAT atmospheric transport scheme in the Eulerian backtracking framework (RETRO-TOM)

NASA Astrophysics Data System (ADS)

Haines, P. E.; Esler, J. G.; Carver, G. D.

2014-01-01

A new methodology for the formulation of an adjoint to the transport component of the chemistry transport model TOMCAT is described and implemented in a new model RETRO-TOM. The Eulerian backtracking method is used, allowing the forward advection scheme (Prather's second-order moments), to be efficiently exploited in the backward adjoint calculations. Prather's scheme is shown to be time-symmetric suggesting the possibility of high accuracy. To attain this accuracy, however, it is necessary to make a careful treatment of the "density inconsistency" problem inherent to offline transport models. The results are verified using a series of test experiments. These demonstrate the high accuracy of RETRO-TOM when compared with direct forward sensitivity calculations, at least for problems in which flux-limiters in the advection scheme are not required. RETRO-TOM therefore combines the flexibility and stability of a "finite difference of adjoint" formulation with the accuracy of an "adjoint of finite difference" formulation.

Sensitivity Analysis of Flutter Response of a Wing Incorporating Finite-Span Corrections

NASA Technical Reports Server (NTRS)

Issac, Jason Cherian; Kapania, Rakesh K.; Barthelemy, Jean-Francois M.

1994-01-01

Flutter analysis of a wing is performed in compressible flow using state-space representation of the unsteady aerodynamic behavior. Three different expressions are used to incorporate corrections due to the finite-span effects of the wing in estimating the lift-curve slope. The structural formulation is based on a Rayleigh-Pitz technique with Chebyshev polynomials used for the wing deflections. The aeroelastic equations are solved as an eigen-value problem to determine the flutter speed of the wing. The flutter speeds are found to be higher in these cases, when compared to that obtained without accounting for the finite-span effects. The derivatives of the flutter speed with respect to the shape parameters, namely: aspect ratio, area, taper ratio and sweep angle, are calculated analytically. The shape sensitivity derivatives give a linear approximation to the flutter speed curves over a range of values of the shape parameter which is perturbed. Flutter and sensitivity calculations are performed on a wing using a lifting-surface unsteady aerodynamic theory using modules from a system of programs called FAST.

On the ab initio calculation of vibrational formation entropy of point defect: the case of the silicon vacancy

NASA Astrophysics Data System (ADS)

Seeberger, Pia; Vidal, Julien

2017-08-01

Formation entropy of point defects is one of the last crucial elements required to fully describe the temperature dependence of point defect formation. However, while many attempts have been made to compute them for very complicated systems, very few works have been carried out such as to assess the different effects of finite size effects and precision on such quantity. Large discrepancies can be found in the literature for a system as primitive as the silicon vacancy. In this work, we have proposed a systematic study of formation entropy for silicon vacancy in its 3 stable charge states: neutral, +2 and -2 for supercells with size not below 432 atoms. Rationalization of the formation entropy is presented, highlighting importance of finite size error and the difficulty to compute such quantities due to high numerical requirement. It is proposed that the direct calculation of formation entropy of VSi using first principles methods will be plagued by very high computational workload (or large numerical errors) and finite size dependent results.

Simulation of Thermographic Responses of Delaminations in Composites with Quadrupole Method

NASA Technical Reports Server (NTRS)

Winfree, William P.; Zalameda, Joseph N.; Howell, Patricia A.; Cramer, K. Elliott

2016-01-01

The application of the quadrupole method for simulating thermal responses of delaminations in carbon fiber reinforced epoxy composites materials is presented. The method solves for the flux at the interface containing the delamination. From the interface flux, the temperature at the surface is calculated. While the results presented are for single sided measurements, with ash heating, expansion of the technique to arbitrary temporal flux heating or through transmission measurements is simple. The quadrupole method is shown to have two distinct advantages relative to finite element or finite difference techniques. First, it is straight forward to incorporate arbitrary shaped delaminations into the simulation. Second, the quadrupole method enables calculation of the thermal response at only the times of interest. This, combined with a significant reduction in the number of degrees of freedom for the same simulation quality, results in a reduction of the computation time by at least an order of magnitude. Therefore, it is a more viable technique for model based inversion of thermographic data. Results for simulations of delaminations in composites are presented and compared to measurements and finite element method results.

Improved finite difference schemes for transonic potential calculations

NASA Technical Reports Server (NTRS)

Hafez, M.; Osher, S.; Whitlow, W., Jr.

1984-01-01

Engquist and Osher (1980) have introduced a finite difference scheme for solving the transonic small disturbance equation, taking into account cases in which only compression shocks are admitted. Osher et al. (1983) studied a class of schemes for the full potential equation. It is proved that these schemes satisfy a new discrete 'entropy inequality' which rules out expansion shocks. However, the conducted analysis is restricted to steady two-dimensional flows. The present investigation is concerned with the adoption of a heuristic approach. The full potential equation in conservation form is solved with the aid of a modified artificial density method, based on flux biasing. It is shown that, with the current scheme, expansion shocks are not possible.

A users guide for A344: A program using a finite difference method to analyze transonic flow over oscillating airfoils

NASA Technical Reports Server (NTRS)

Weatherill, W. H.; Ehlers, F. E.

1979-01-01

The design and usage of a pilot program for calculating the pressure distributions over harmonically oscillating airfoils in transonic flow are described. The procedure used is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equations for small disturbances. The steady velocity potential which must be obtained from some other program, was required for input. The unsteady equation, as solved, is linear with spatially varying coefficients. Since sinusoidal motion was assumed, time was not a variable. The numerical solution was obtained through a finite difference formulation and either a line relaxation or an out of core direct solution method.

Analysis of multi lobe journal bearings with surface roughness using finite difference method

NASA Astrophysics Data System (ADS)

PhaniRaja Kumar, K.; Bhaskar, SUdaya; Manzoor Hussain, M.

2018-04-01

Multi lobe journal bearings are used for high operating speeds and high loads in machines. In this paper symmetrical multi lobe journal bearings are analyzed to find out the effect of surface roughnessduring non linear loading. Using the fourth order RungeKutta method, time transient analysis was performed to calculate and plot the journal centre trajectories. Flow factor method is used to evaluate the roughness and the finite difference method (FDM) is used to predict the pressure distribution over the bearing surface. The Transient analysis is done on the multi lobe journal bearings for threedifferent surface roughness orientations. Longitudinal surface roughness is more effective when compared with isotopic and traverse surface roughness.

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.

A singular finite element technique for calculating continuum damping of Alfvén eigenmodes

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

Bowden, G. W.; Hole, M. J.

2015-02-15

Damping due to continuum resonances can be calculated using dissipation-less ideal magnetohydrodynamics provided that the poles due to these resonances are properly treated. We describe a singular finite element technique for calculating the continuum damping of Alfvén waves. A Frobenius expansion is used to determine appropriate finite element basis functions on an inner region surrounding a pole due to the continuum resonance. The location of the pole due to the continuum resonance and mode frequency is calculated iteratively using a Galerkin method. This method is used to find the complex frequency and mode structure of a toroidicity-induced Alfvén eigenmode inmore » a large aspect ratio circular tokamak and is shown to agree closely with a complex contour technique.« less

The Kπ Interaction in Finite Volume

NASA Astrophysics Data System (ADS)

Zhou, Dan; Cui, Er-Liang; Chen, Hua-Xing; Geng, Li-Sheng; Zhu, Li-Hua

We calculate energy levels of the Kπ scattering in the K∗ channel in finite volume using chiral unitary theory. We use these energy levels to obtain the Kπ phase shifts and the K∗ meson properties. We also investigate their dependence on the pion mass and compare this with Lattice QCD calculations.

Regional teleseismic body-wave tomography with component-differential finite-frequency sensitivity kernels

NASA Astrophysics Data System (ADS)

Yu, Y.; Shen, Y.; Chen, Y. J.

2015-12-01

By using ray theory in conjunction with the Born approximation, Dahlen et al. [2000] computed 3-D sensitivity kernels for finite-frequency seismic traveltimes. A series of studies have been conducted based on this theory to model the mantle velocity structure [e.g., Hung et al., 2004; Montelli et al., 2004; Ren and Shen, 2008; Yang et al., 2009; Liang et al., 2011; Tang et al., 2014]. One of the simplifications in the calculation of the kernels is the paraxial assumption, which may not be strictly valid near the receiver, the region of interest in regional teleseismic tomography. In this study, we improve the accuracy of traveltime sensitivity kernels of the first P arrival by eliminating the paraxial approximation. For calculation efficiency, the traveltime table built by the Fast Marching Method (FMM) is used to calculate both the wave vector and the geometrical spreading at every grid in the whole volume. The improved kernels maintain the sign, but with different amplitudes at different locations. We also find that when the directivity of the scattered wave is being taken into consideration, the differential sensitivity kernel of traveltimes measured at the vertical and radial component of the same receiver concentrates beneath the receiver, which can be used to invert for the structure inside the Earth. Compared with conventional teleseismic tomography, which uses the differential traveltimes between two stations in an array, this method is not affected by instrument response and timing errors, and reduces the uncertainty caused by the finite dimension of the model in regional tomography. In addition, the cross-dependence of P traveltimes to S-wave velocity anomaly is significant and sensitive to the structure beneath the receiver. So with the component-differential finite-frequency sensitivity kernel, the anomaly of both P-wave and S-wave velocity and Vp/Vs ratio can be achieved at the same time.

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

NASA Astrophysics Data System (ADS)

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

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

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

NASA Astrophysics Data System (ADS)

Duda, Piotr

2016-04-01

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

The effect of nonlinear propagation on heating of tissue: A numerical model of diagnostic ultrasound beams

NASA Astrophysics Data System (ADS)

Cahill, Mark D.; Humphrey, Victor F.; Doody, Claire

2000-07-01

Thermal safety indices for diagnostic ultrasound beams are calculated under the assumption that the sound propagates under linear conditions. A non-axisymmetric finite difference model is used to solve the KZK equation, and so to model the beam of a diagnostic scanner in pulsed Doppler mode. Beams from both a uniform focused rectangular source and a linear array are considered. Calculations are performed in water, and in attenuating media with tissue-like characteristics. Attenuating media are found to exhibit significant nonlinear effects for finite-amplitude beams. The resulting loss of intensity by the beam is then used as the source term in a model of tissue heating to estimate the maximum temperature rises. These are compared with the thermal indices, derived from the properties of the water-propagated beams.

Numerical study of supersonic combustion using a finite rate chemistry model

NASA Technical Reports Server (NTRS)

Chitsomboon, T.; Tiwari, S. N.; Kumar, A.; Drummond, J. P.

1986-01-01

The governing equations of two-dimensional chemically reacting flows are presented together with a global two-step chemistry model for H2-air combustion. The explicit unsplit MacCormack finite difference algorithm is used to advance the discrete system of the governing equations in time until convergence is attained. The source terms in the species equations are evaluated implicitly to alleviate stiffness associated with fast reactions. With implicit source terms, the species equations give rise to a block-diagonal system which can be solved very efficiently on vector-processing computers. A supersonic reacting flow in an inlet-combustor configuration is calculated for the case where H2 is injected into the flow from the side walls and the strut. Results of the calculation are compared against the results obtained by using a complete reaction model.

Methods for the calculation of axial wave numbers in lined ducts with mean flow

NASA Technical Reports Server (NTRS)

Eversman, W.

1981-01-01

A survey is made of the methods available for the calculation of axial wave numbers in lined ducts. Rectangular and circular ducts with both uniform and non-uniform flow are considered as are ducts with peripherally varying liners. A historical perspective is provided by a discussion of the classical methods for computing attenuation when no mean flow is present. When flow is present these techniques become either impractical or impossible. A number of direct eigenvalue determination schemes which have been used when flow is present are discussed. Methods described are extensions of the classical no-flow technique, perturbation methods based on the no-flow technique, direct integration methods for solution of the eigenvalue equation, an integration-iteration method based on the governing differential equation for acoustic transmission, Galerkin methods, finite difference methods, and finite element methods.

Development of the software tool for generation and visualization of the finite element head model with bone conduction sounds

NASA Astrophysics Data System (ADS)

Nikolić, Dalibor; Milošević, Žarko; Saveljić, Igor; Filipović, Nenad

2015-12-01

Vibration of the skull causes a hearing sensation. We call it Bone Conduction (BC) sound. There are several investigations about transmission properties of bone conducted sound. The aim of this study was to develop a software tool for easy generation of the finite element (FE) model of the human head with different materials based on human head anatomy and to calculate sound conduction through the head. Developed software tool generates a model in a few steps. The first step is to do segmentation of CT medical images (DICOM) and to generate a surface mesh files (STL). Each STL file presents a different layer of human head with different material properties (brain, CSF, different layers of the skull bone, skin, etc.). The next steps are to make tetrahedral mesh from obtained STL files, to define FE model boundary conditions and to solve FE equations. This tool uses PAK solver, which is the open source software implemented in SIFEM FP7 project, for calculations of the head vibration. Purpose of this tool is to show impact of the bone conduction sound of the head on the hearing system and to estimate matching of obtained results with experimental measurements.

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.

Finite element method for calculating spectral and optical characteristics of axially symmetric quantum dots

NASA Astrophysics Data System (ADS)

Gusev, A. A.; Chuluunbaatar, O.; Vinitsky, S. I.; Derbov, V. L.; Hai, L. L.; Kazaryan, E. M.; Sarkisyan, H. A.

2018-04-01

We present new calculation schemes using high-order finite element method implemented on unstructured grids with triangle elements for solving boundary-value problems that describe axially symmetric quantum dots. The efficiency of the algorithms and software is demonstrated by benchmark calculations of the energy spectrum, the envelope eigenfunctions of electron, hole and exciton states, and the direct interband light absorption in conical and spheroidal impenetrable quantum dots.

Calculation of Derivative Thermodynamic Hydration and Aqueous Partial Molar Properties of Ions Based on Atomistic Simulations.

PubMed

Dahlgren, Björn; Reif, Maria M; Hünenberger, Philippe H; Hansen, Niels

2012-10-09

The raw ionic solvation free energies calculated on the basis of atomistic (explicit-solvent) simulations are extremely sensitive to the boundary conditions and treatment of electrostatic interactions used during these simulations. However, as shown recently [Kastenholz, M. A.; Hünenberger, P. H. J. Chem. Phys.2006, 124, 224501 and Reif, M. M.; Hünenberger, P. H. J. Chem. Phys.2011, 134, 144104], the application of an appropriate correction scheme allows for a conversion of the methodology-dependent raw data into methodology-independent results. In this work, methodology-independent derivative thermodynamic hydration and aqueous partial molar properties are calculated for the Na(+) and Cl(-) ions at P° = 1 bar and T(-) = 298.15 K, based on the SPC water model and on ion-solvent Lennard-Jones interaction coefficients previously reoptimized against experimental hydration free energies. The hydration parameters considered are the hydration free energy and enthalpy. The aqueous partial molar parameters considered are the partial molar entropy, volume, heat capacity, volume-compressibility, and volume-expansivity. Two alternative calculation methods are employed to access these properties. Method I relies on the difference in average volume and energy between two aqueous systems involving the same number of water molecules, either in the absence or in the presence of the ion, along with variations of these differences corresponding to finite pressure or/and temperature changes. Method II relies on the calculation of the hydration free energy of the ion, along with variations of this free energy corresponding to finite pressure or/and temperature changes. Both methods are used considering two distinct variants in the application of the correction scheme. In variant A, the raw values from the simulations are corrected after the application of finite difference in pressure or/and temperature, based on correction terms specifically designed for derivative parameters at P° and T(-). In variant B, these raw values are corrected prior to differentiation, based on corresponding correction terms appropriate for the different simulation pressures P and temperatures T. The results corresponding to the different calculation schemes show that, except for the hydration free energy itself, accurate methodological independence and quantitative agreement with even the most reliable experimental parameters (ion-pair properties) are not yet reached. Nevertheless, approximate internal consistency and qualitative agreement with experimental results can be achieved, but only when an appropriate correction scheme is applied, along with a careful consideration of standard-state issues. In this sense, the main merit of the present study is to set a clear framework for these types of calculations and to point toward directions for future improvements, with the ultimate goal of reaching a consistent and quantitative description of single-ion hydration thermodynamics in molecular dynamics simulations.

Mechanistic interpretation of nondestructive pavement testing deflections

NASA Astrophysics Data System (ADS)

Hoffman, M. S.; Thompson, M. R.

1981-06-01

A method for the back calculation of material properties in flexible pavements based on the interpretation of surface deflection measurements is proposed. The ILLI-PAVE, a stress-dependent finite element pavement model, was used to generate data for developing algorithms and nomographs for deflection basin interpretation. Twenty four different flexible pavement sections throughout the State of Illinois were studied. Deflections were measured and loading mode effects on pavement response were investigated. The factors controlling the pavement response to different loading modes are identified and explained. Correlations between different devices are developed. The back calculated parameters derived from the proposed evaluation procedure can be used as inputs for asphalt concrete overlay design.

Finite difference methods for reducing numerical diffusion in TEACH-type calculations. [Teaching Elliptic Axisymmetric Characteristics Heuristically

NASA Technical Reports Server (NTRS)

Syed, S. A.; Chiappetta, L. M.

1985-01-01

A methodological evaluation for two-finite differencing schemes for computer-aided gas turbine design is presented. The two computational schemes include; a Bounded Skewed Finite Differencing Scheme (BSUDS); and a Quadratic Upwind Differencing Scheme (QSDS). In the evaluation, the derivations of the schemes were incorporated into two-dimensional and three-dimensional versions of the Teaching Axisymmetric Characteristics Heuristically (TEACH) computer code. Assessments were made according to performance criteria for the solution of problems of turbulent, laminar, and coannular turbulent flow. The specific performance criteria used in the evaluation were simplicity, accuracy, and computational economy. It is found that the BSUDS scheme performed better with respect to the criteria than the QUDS. Some of the reasons for the more successful performance BSUDS are discussed.

Radon transport model into a porous ground layer of finite capacity

NASA Astrophysics Data System (ADS)

Parovik, Roman

2017-10-01

The model of radon transfer is considered in a porous ground layer of finite power. With the help of the Laplace integral transformation, a numerical solution of this model is obtained which is based on the construction of a generalized quadrature formula of the highest degree of accuracy for the transition to the original - the function of solving this problem. The calculated curves are constructed and investigated depending on the diffusion and advection coefficients.The work was a mathematical model that describes the effect of the sliding attachment (stick-slip), taking into account hereditarity. This model can be regarded as a mechanical model of earthquake preparation. For such a model was proposed explicit finite- difference scheme, on which were built the waveform and phase trajectories hereditarity effect of stick-slip.

Electrostatic Estimation of Intercalant Jump-Diffusion Barriers Using Finite-Size Ion Models.

PubMed

Zimmermann, Nils E R; Hannah, Daniel C; Rong, Ziqin; Liu, Miao; Ceder, Gerbrand; Haranczyk, Maciej; Persson, Kristin A

2018-02-01

We report on a scheme for estimating intercalant jump-diffusion barriers that are typically obtained from demanding density functional theory-nudged elastic band calculations. The key idea is to relax a chain of states in the field of the electrostatic potential that is averaged over a spherical volume using different finite-size ion models. For magnesium migrating in typical intercalation materials such as transition-metal oxides, we find that the optimal model is a relatively large shell. This data-driven result parallels typical assumptions made in models based on Onsager's reaction field theory to quantitatively estimate electrostatic solvent effects. Because of its efficiency, our potential of electrostatics-finite ion size (PfEFIS) barrier estimation scheme will enable rapid identification of materials with good ionic mobility.

FDTD Modeling and Counteraction to Scintillation Effects in the lonosphere

DTIC Science & Technology

2014-04-05

collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT...for vectorial diffraction calculations and its numerical implementation,” J. Opt. Soc. Am. A, 23 (3), pp. 713-722, 2006. [21] Coe, R. L. and E. J...Seibel, “Improved near-field calculations using vectorial diffraction integrals in the finite-difference time-domain method,” J. Opt. Soc. Am. A, 28

Polarization effects on spectra of spherical core/shell nanostructures: Perturbation theory against finite difference approach

NASA Astrophysics Data System (ADS)

Ibral, Asmaa; Zouitine, Asmaa; Assaid, El Mahdi; El Achouby, Hicham; Feddi, El Mustapha; Dujardin, Francis

2015-02-01

Poisson equation is solved analytically in the case of a point charge placed anywhere in a spherical core/shell nanostructure, immersed in aqueous or organic solution or embedded in semiconducting or insulating matrix. Conduction and valence band-edge alignments between core and shell are described by finite height barriers. Influence of polarization charges induced at the surfaces where two adjacent materials meet is taken into account. Original expressions of electrostatic potential created everywhere in the space by a source point charge are derived. Expressions of self-polarization potential describing the interaction of a point charge with its own image-charge are deduced. Contributions of double dielectric constant mismatch to electron and hole ground state energies as well as nanostructure effective gap are calculated via first order perturbation theory and also by finite difference approach. Dependencies of electron, hole and gap energies against core to shell radii ratio are determined in the case of ZnS/CdSe core/shell nanostructure immersed in water or in toluene. It appears that finite difference approach is more efficient than first order perturbation method and that the effect of polarization charge may in no case be neglected as its contribution can reach a significant proportion of the value of nanostructure gap.

Calculation of three-dimensional compressible laminar and turbulent boundary layers. Calculation of three-dimensional compressible boundary layers on arbitrary wings

NASA Technical Reports Server (NTRS)

Cebeci, T.; Kaups, K.; Ramsey, J.; Moser, A.

1975-01-01

A very general method for calculating compressible three-dimensional laminar and turbulent boundary layers on arbitrary wings is described. The method utilizes a nonorthogonal coordinate system for the boundary-layer calculations and includes a geometry package that represents the wing analytically. In the calculations all the geometric parameters of the coordinate system are accounted for. The Reynolds shear-stress terms are modeled by an eddy-viscosity formulation developed by Cebeci. The governing equations are solved by a very efficient two-point finite-difference method used earlier by Keller and Cebeci for two-dimensional flows and later by Cebeci for three-dimensional flows.

Implementation of a finite-amplitude method in a relativistic meson-exchange model

NASA Astrophysics Data System (ADS)

Sun, Xuwei; Lu, Dinghui

2017-08-01

The finite-amplitude method is a feasible numerical approach to large scale random phase approximation calculations. It avoids the storage and calculation of residual interaction elements as well as the diagonalization of the RPA matrix, which will be prohibitive when the configuration space is huge. In this work we finished the implementation of a finite-amplitude method in a relativistic meson exchange mean field model with axial symmetry. The direct variation approach makes our FAM scheme capable of being extended to the multipole excitation case.

Three friendly walkers

NASA Astrophysics Data System (ADS)

Jensen, Iwan

2017-01-01

More than 15 years ago Guttmann and Vöge (2002 J. Stat. Plan. Inference 101 107), introduced a model of friendly walkers. Since then it has remained unsolved. In this paper we provide the exact solution to a closely allied model which essentially only differs in the boundary conditions. The exact solution is expressed in terms of the reciprocal of the generating function for vicious walkers which is a D-finite function. However, ratios of D-finite functions are inherently not D-finite and in this case we prove that the friendly walkers generating function is the solution to a non-linear differential equation with polynomial coefficients, it is in other words D-algebraic. We find using numerically exact calculations a conjectured expression for the generating function of the original model as a ratio of a D-finite function and the generating function for vicious walkers. We obtain an expression for this D-finite function in terms of a {{}2}{{F}1} hypergeometric function with a rational pullback and its first and second derivatives. Dedicated to Tony Guttmann on the occasion of his 70th birthday.

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.

Thermodynamic evaluation of transonic compressor rotors using the finite volume approach

NASA Technical Reports Server (NTRS)

Nicholson, S.; Moore, J.

1986-01-01

A method was developed which calculates two-dimensional, transonic, viscous flow in ducts. The finite volume, time marching formulation is used to obtain steady flow solutions of the Reynolds-averaged form of the Navier Stokes equations. The entire calculation is performed in the physical domain. The method is currently limited to the calculation of attached flows. The features of the current method can be summarized as follows. Control volumes are chosen so that smoothing of flow properties, typically required for stability, is now needed. Different time steps are used in the different governing equations to improve the convergence speed of the viscous calculations. A new pressure interpolation scheme is introduced which improves the shock capturing ability of the method. A multi-volume method for pressure changes in the boundary layer allows calculations which use very long and thin control volumes. A special discretization technique is also used to stabilize these calculations. A special formulation of the energy equation is used to provide improved transient behavior of solutions which use the full energy equation. The method is then compared with a wide variety of test cases. The freestream Mach numbers range from 0.075 to 2.8 in the calculations. Transonic viscous flow in a converging diverging nozzle is calculated with the method; the Mach number upstream of the shock is approximately 1.25. The agreement between the calculated and measured shock strength and total pressure losses is good. Essentially incompressible turbulent boundary layer flow in a adverse pressure gradient is calculated and the computed distribution of mean velocity and shear stress are in good agreement with the measurements. At the other end of the Mach number range, a flat plate turbulent boundary layer with a freestream Mach number of 2.8 is calculated using the full energy equation; the computed total temperature distribution and recovery factor agree well with the measurements when a variable Prandtl number is used through the boundary layer.

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

NASA Astrophysics Data System (ADS)

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

2015-05-01

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

Implementation of different turbulence model to find proper model to estimate aerodynamic properties of airfoils

NASA Astrophysics Data System (ADS)

Sogukpinar, Haci; Bozkurt, Ismail

2018-02-01

In this paper, aerodynamic calculations of NACA 4 series airfoil of 0012 are performed by using Finite-Volume Method and obtained results are compared with experimental data to correlate the numerical accuracy of CFD approximation. Then other airfoils are simulated with k-ɛ, k-w Spalart-Allmaras and SST model. The governing equations are the Reynolds-Averaged-Navier-Stokes (RANS) equations. The performance of different airfoils (NACA 0008, 0009, 0010, 0012, 0015, 0018, 0021, 0024) at different angle of attack are investigated and compared with most used turbulence models for industrial applications. According to the results of the comparison of numerical calculations and experimental data, k-w and SST models are considered to be closest to experimental results for the calculation of the lift coefficient.

Radiation pattern of a borehole radar antenna

USGS Publications Warehouse

Ellefsen, K.J.; Wright, D.L.

2002-01-01

To understand better how a borehole antenna radiates radar waves into a formation, this phenomenon is simulated numerically using the finite-difference, time-domain method. The simulations are of two different antenna models that include features like a driving point fed by a coaxial cable, resistive loading of the antenna, and a water-filled borehole. For each model, traces are calculated in the far-field region, and then, from these traces, radiation patterns are calculated. The radiation patterns show that the amplitude of the radar wave is strongly affected by its frequency, its propagation direction, and the resistive loading of the antenna.

Accuracy of iron loss estimation in induction motors by using different iron loss models

NASA Astrophysics Data System (ADS)

Štumberger, B.; Hamler, A.; Goričan, V.; Jesenik, M.; Trlep, M.

2004-05-01

The paper presents iron loss estimation in a three-phase induction motor by using different iron loss models for the posterior iron loss calculation. The iron losses were determined by using modeled properties of used electrical steel and calculated distribution of magnetic induction B(t) in all parts of the motor by using 2D finite element software for a complete cycle of field variation. The comparison between estimated and measured core losses for a 4kW induction motor at no-load in dependency on supply voltage is given.

Thermal management of batteries

NASA Astrophysics Data System (ADS)

Gibbard, H. F.; Chen, C.-C.

Control of the internal temperature during high rate discharge or charge can be a major design problem for large, high energy density battery systems. A systematic approach to the thermal management of such systems is described for different load profiles based on: thermodynamic calculations of internal heat generation; calorimetric measurements of heat flux; analytical and finite difference calculations of the internal temperature distribution; appropriate system designs for heat removal and temperature control. Examples are presented of thermal studies on large lead-acid batteries for electrical utility load levelling and nickel-zinc and lithium-iron sulphide batteries for electric vehicle propulsion.

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.

A finite element model for tides and resonance along the north coast of British Columbia

NASA Astrophysics Data System (ADS)

Foreman, M. G. G.; Henry, R. F.; Walters, R. A.; Ballantyne, V. A.

1993-02-01

A finite element, barotropic, tidal model is developed for the north coast of British Columbia. The model is run with eight tidal constituents and the results are compared with the Flather (1987) finite difference model, and with extensive tide gauge and current meter observations. Although the tidal potential, Earth tide, and loading tide are included in the forcing, their inclusion is shown to change the largest M2 amplitudes by only 2.5% and the largest K1 amplitudes by less than 1%. Root mean square differences between observed and calculated sea level amplitudes and phases are within 1.9 cm and 2.9° for all but one constituent, but the model currents do not in general, compare as favourably. The barotropic currents observed in Hecate Strait are reproduced well, but elsewhere evidence is shown that model inaccuracies are due to baroclinic effects. Tidal residual currents calculated by the model suggest the existence of eddies off the tip of Cape St. James, Cape Chacon, and around Goose Island and Learmonth Banks. The shallow water constituents in Hecate Strait are shown to have significant contributions from the constructive interference of signals propagating into Dixon Entrance and Queen Charlotte Sound. Using the model, the longest resonant period of the system is estimated to be 7.6 hours with an energy dissipation parameter, Q, of 9.5.

Comparison of variational real-space representations of the kinetic energy operator

NASA Astrophysics Data System (ADS)

Skylaris, Chris-Kriton; Diéguez, Oswaldo; Haynes, Peter D.; Payne, Mike C.

2002-08-01

We present a comparison of real-space methods based on regular grids for electronic structure calculations that are designed to have basis set variational properties, using as a reference the conventional method of finite differences (a real-space method that is not variational) and the reciprocal-space plane-wave method which is fully variational. We find that a definition of the finite-difference method [P. Maragakis, J. Soler, and E. Kaxiras, Phys. Rev. B 64, 193101 (2001)] satisfies one of the two properties of variational behavior at the cost of larger errors than the conventional finite-difference method. On the other hand, a technique which represents functions in a number of plane waves which is independent of system size closely follows the plane-wave method and therefore also the criteria for variational behavior. Its application is only limited by the requirement of having functions strictly localized in regions of real space, but this is a characteristic of an increasing number of modern real-space methods, as they are designed to have a computational cost that scales linearly with system size.

CALCULATION OF GAMMA SPECTRA IN A PLASTIC SCINTILLATOR FOR ENERGY CALIBRATIONAND DOSE COMPUTATION.

PubMed

Kim, Chankyu; Yoo, Hyunjun; Kim, Yewon; Moon, Myungkook; Kim, Jong Yul; Kang, Dong Uk; Lee, Daehee; Kim, Myung Soo; Cho, Minsik; Lee, Eunjoong; Cho, Gyuseong

2016-09-01

Plastic scintillation detectors have practical advantages in the field of dosimetry. Energy calibration of measured gamma spectra is important for dose computation, but it is not simple in the plastic scintillators because of their different characteristics and a finite resolution. In this study, the gamma spectra in a polystyrene scintillator were calculated for the energy calibration and dose computation. Based on the relationship between the energy resolution and estimated energy broadening effect in the calculated spectra, the gamma spectra were simply calculated without many iterations. The calculated spectra were in agreement with the calculation by an existing method and measurements. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

ChPT loops for the lattice: pion mass and decay constant, HVP at finite volume and nn̅-oscillations

NASA Astrophysics Data System (ADS)

Bijnens, Johan

2018-03-01

I present higher loop order results for several calculations in Chiral perturbation Theory. 1) Two-loop results at finite volume for hadronic vacuum polarization. 2) A three-loop calculation of the pion mass and decay constant in two-flavour ChPT. For the pion mass all needed auxiliary parameters can be determined from lattice calculations of ππ-scattering. 3) Chiral corrections to neutron-anti-neutron oscillations.

A combined registration and finite element analysis method for fast estimation of intraoperative brain shift; phantom and animal model study.

PubMed

Mohammadi, Amrollah; Ahmadian, Alireza; Rabbani, Shahram; Fattahi, Ehsan; Shirani, Shapour

2017-12-01

Finite element models for estimation of intraoperative brain shift suffer from huge computational cost. In these models, image registration and finite element analysis are two time-consuming processes. The proposed method is an improved version of our previously developed Finite Element Drift (FED) registration algorithm. In this work the registration process is combined with the finite element analysis. In the Combined FED (CFED), the deformation of whole brain mesh is iteratively calculated by geometrical extension of a local load vector which is computed by FED. While the processing time of the FED-based method including registration and finite element analysis was about 70 s, the computation time of the CFED was about 3.2 s. The computational cost of CFED is almost 50% less than similar state of the art brain shift estimators based on finite element models. The proposed combination of registration and structural analysis can make the calculation of brain deformation much faster. Copyright © 2016 John Wiley & Sons, Ltd.

Finite-difference solution of the compressible stability eigenvalue problem

NASA Technical Reports Server (NTRS)

Malik, M. R.

1982-01-01

A compressible stability analysis computer code is developed. The code uses a matrix finite difference method for local eigenvalue solution when a good guess for the eigenvalue is available and is significantly more computationally efficient than the commonly used initial value approach. The local eigenvalue search procedure also results in eigenfunctions and, at little extra work, group velocities. A globally convergent eigenvalue procedure is also developed which may be used when no guess for the eigenvalue is available. The global problem is formulated in such a way that no unstable spurious modes appear so that the method is suitable for use in a black box stability code. Sample stability calculations are presented for the boundary layer profiles of a Laminar Flow Control (LFC) swept wing.

Moving magnets in a micromagnetic finite-difference framework

NASA Astrophysics Data System (ADS)

Rissanen, Ilari; Laurson, Lasse

2018-05-01

We present a method and an implementation for smooth linear motion in a finite-difference-based micromagnetic simulation code, to be used in simulating magnetic friction and other phenomena involving moving microscale magnets. Our aim is to accurately simulate the magnetization dynamics and relative motion of magnets while retaining high computational speed. To this end, we combine techniques for fast scalar potential calculation and cubic b-spline interpolation, parallelizing them on a graphics processing unit (GPU). The implementation also includes the possibility of explicitly simulating eddy currents in the case of conducting magnets. We test our implementation by providing numerical examples of stick-slip motion of thin films pulled by a spring and the effect of eddy currents on the switching time of magnetic nanocubes.

Thermokinetic Modeling of Phase Transformation in the Laser Powder Deposition Process

NASA Astrophysics Data System (ADS)

Foroozmehr, Ehsan; Kovacevic, Radovan

2009-08-01

A finite element model coupled with a thermokinetic model is developed to predict the phase transformation of the laser deposition of AISI 4140 on a substrate with the same material. Four different deposition patterns, long-bead, short-bead, spiral-in, and spiral-out, are used to cover a similar area. Using a finite element model, the temperature history of the laser powder deposition (LPD) process is determined. The martensite transformation as well as martensite tempering is considered to calculate the final fraction of martensite, ferrite, cementite, ɛ-carbide, and retained austenite. Comparing the surface hardness topography of different patterns reveals that path planning is a critical parameter in laser surface modification. The predicted results are in a close agreement with the experimental results.

Predict the fatigue life of crack based on extended finite element method and SVR

NASA Astrophysics Data System (ADS)

Song, Weizhen; Jiang, Zhansi; Jiang, Hui

2018-05-01

Using extended finite element method (XFEM) and support vector regression (SVR) to predict the fatigue life of plate crack. Firstly, the XFEM is employed to calculate the stress intensity factors (SIFs) with given crack sizes. Then predicetion model can be built based on the function relationship of the SIFs with the fatigue life or crack length. Finally, according to the prediction model predict the SIFs at different crack sizes or different cycles. Because of the accuracy of the forward Euler method only ensured by the small step size, a new prediction method is presented to resolve the issue. The numerical examples were studied to demonstrate the proposed method allow a larger step size and have a high accuracy.

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.

Method for calculating the aerodynamic loading on an oscillating finite wing in subsonic and sonic flow

NASA Technical Reports Server (NTRS)

Runyan, Harry L; Woolston, Donald S

1957-01-01

A method is presented for calculating the loading on a finite wing oscillating in subsonic or sonic flow. The method is applicable to any plan form and may be used for determining the loading on deformed wings. The procedure is approximate and requires numerical integration over the wing surface.

Solution of the neutronics code dynamic benchmark by finite element method

NASA Astrophysics Data System (ADS)

Avvakumov, A. V.; Vabishchevich, P. N.; Vasilev, A. O.; Strizhov, V. F.

2016-10-01

The objective is to analyze the dynamic benchmark developed by Atomic Energy Research for the verification of best-estimate neutronics codes. The benchmark scenario includes asymmetrical ejection of a control rod in a water-type hexagonal reactor at hot zero power. A simple Doppler feedback mechanism assuming adiabatic fuel temperature heating is proposed. The finite element method on triangular calculation grids is used to solve the three-dimensional neutron kinetics problem. The software has been developed using the engineering and scientific calculation library FEniCS. The matrix spectral problem is solved using the scalable and flexible toolkit SLEPc. The solution accuracy of the dynamic benchmark is analyzed by condensing calculation grid and varying degree of finite elements.

Incompressible Navier-Stokes and parabolized Navier-Stokes solution procedures and computational techniques

NASA Technical Reports Server (NTRS)

Rubin, S. G.

1982-01-01

Recent developments with finite-difference techniques are emphasized. The quotation marks reflect the fact that any finite discretization procedure can be included in this category. Many so-called finite element collocation and galerkin methods can be reproduced by appropriate forms of the differential equations and discretization formulas. Many of the difficulties encountered in early Navier-Stokes calculations were inherent not only in the choice of the different equations (accuracy), but also in the method of solution or choice of algorithm (convergence and stability, in the manner in which the dependent variables or discretized equations are related (coupling), in the manner that boundary conditions are applied, in the manner that the coordinate mesh is specified (grid generation), and finally, in recognizing that for many high Reynolds number flows not all contributions to the Navier-Stokes equations are necessarily of equal importance (parabolization, preferred direction, pressure interaction, asymptotic and mathematical character). It is these elements that are reviewed. Several Navier-Stokes and parabolized Navier-Stokes formulations are also presented.

Stress analysis of the cracked-lap-shear specimen - An ASTM round-robin

NASA Technical Reports Server (NTRS)

Johnson, W. S.

1987-01-01

This ASTM Round Robin was conducted to evaluate the state of the art in stress analysis of adhesively bonded joint specimens. Specifically, the participants were asked to calculate the strain-energy-release rate for two different geometry cracked lap shear (CLS) specimens at four different debond lengths. The various analytical techniques consisted of 2- and 3-dimensional finite element analysis, beam theory, plate theory, and a combination of beam theory and finite element analysis. The results were examined in terms of the total strain-energy-release rate and the mode I to mode II ratio as a function of debond length for each specimen geometry. These results basically clustered into two groups: geometric linear or geometric nonlinear analysis. The geometric nonlinear analysis is required to properly analyze the CLS specimens. The 3-D finite element analysis gave indications of edge closure plus some mode III loading. Each participant described his analytical technique and results. Nine laboratories participated.

Stress analysis of the cracked lap shear specimens: An ASTM round robin

NASA Technical Reports Server (NTRS)

Johnson, W. S.

1986-01-01

This ASTM Round Robin was conducted to evaluate the state of the art in stress analysis of adhesively bonded joint specimens. Specifically, the participants were asked to calculate the strain-energy-release rate for two different geometry cracked lap shear (CLS) specimens at four different debond lengths. The various analytical techniques consisted of 2- and 3-dimensional finite element analysis, beam theory, plate theory, and a combination of beam theory and finite element analysis. The results were examined in terms of the total strain-energy-release rate and the mode I to mode II ratio as a function of debond length for each specimen geometry. These results basically clustered into two groups: geometric linear or geometric nonlinear analysis. The geometric nonlinear analysis is required to properly analyze the CLS specimens. The 3-D finite element analysis gave indications of edge closure plus some mode III loading. Each participant described his analytical technique and results. Nine laboratories participated.

An Integrated Finite Element-based Simulation Framework: From Hole Piercing to Hole Expansion

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

Hu, Xiaohua; Sun, Xin; Golovashchenko, Segey F.

An integrated finite element-based modeling framework is developed to predict the hole expansion ratio (HER) of AA6111-T4 sheet by considering the piercing-induced damages around the hole edge. Using damage models and parameters calibrated from previously reported tensile stretchability studies, the predicted HER correlates well with experimentally measured HER values for different hole piercing clearances. The hole piercing model shows burrs are not generated on the sheared surface for clearances less than 20%, which corresponds well with the experimental data on pierced holes cross-sections. Finite-element-calculated HER also is not especially sensitive to piercing clearances less than this value. However, as clearancesmore » increase to 30% and further to 40%, the HER values are predicted to be considerably smaller, also consistent with experimental measurements. Upon validation, the integrated modeling framework is used to examine the effects of different hole piercing and hole expansion conditions on the critical HERs for AA6111-T4.« less

Quality-assurance study of the special - purpose finite-element program - SPECTROM: I. Thermal, thermoelastic, and viscoelastic problems. [Comparison with MARC-CDC

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

Wagner, R.A.

1980-12-01

This comparison study involves a preliminary verification of finite element calculations. The methodology of the comparison study consists of solving four example problems with both the SPECTROM finite element program and the MARC-CDC general purpose finite element program. The results show close agreement for all example problems.

Structural Acoustic Physics Based Modeling of Curved Composite Shells

DTIC Science & Technology

2017-09-19

Results show that the finite element computational models accurately match analytical calculations, and that the composite material studied in this...products. 15. SUBJECT TERMS Finite Element Analysis, Structural Acoustics, Fiber-Reinforced Composites, Physics-Based Modeling 16. SECURITY...2 4 FINITE ELEMENT MODEL DESCRIPTION

Finite element analysis of thrust angle contact ball slewing bearing

NASA Astrophysics Data System (ADS)

Deng, Biao; Guo, Yuan; Zhang, An; Tang, Shengjin

2017-12-01

In view of the large heavy slewing bearing no longer follows the rigid ring hupothesis under the load condition, the entity finite element model of thrust angular contact ball bearing was established by using finite element analysis software ANSYS. The boundary conditions of the model were set according to the actual condition of slewing bearing, the internal stress state of the slewing bearing was obtained by solving and calculation, and the calculated results were compared with the numerical results based on the rigid ring assumption. The results show that more balls are loaded in the result of finite element method, and the maximum contact stresses between the ball and raceway have some reductions. This is because the finite element method considers the ferrule as an elastic body. The ring will produce structure deformation in the radial plane when the heavy load slewing bearings are subjected to external loads. The results of the finite element method are more in line with the actual situation of the slewing bearing in the engineering.

An inverse method to determine the mechanical properties of the iris in vivo

PubMed Central

2014-01-01

Background Understanding the mechanical properties of the iris can help to have an insight into the eye diseases with abnormalities of the iris morphology. Material parameters of the iris were simply calculated relying on the ex vivo experiment. However, the mechanical response of the iris in vivo is different from that ex vivo, therefore, a method was put forward to determine the material parameters of the iris using the optimization method in combination with the finite element method based on the in vivo experiment. Material and methods Ocular hypertension was induced by rapid perfusion to the anterior chamber, during perfusion intraocular pressures in the anterior and posterior chamber were record by sensors, images of the anterior segment were captured by the ultrasonic system. The displacement of the characteristic points on the surface of the iris was calculated. A finite element model of the anterior chamber was developed using the ultrasonic image before perfusion, the multi-island genetic algorithm was employed to determine the material parameters of the iris by minimizing the difference between the finite element simulation and the experimental measurements. Results Material parameters of the iris in vivo were identified as the iris was taken as a nearly incompressible second-order Ogden solid. Values of the parameters μ1, α1, μ2 and α2 were 0.0861 ± 0.0080 MPa, 54.2546 ± 12.7180, 0.0754 ± 0.0200 MPa, and 48.0716 ± 15.7796 respectively. The stability of the inverse finite element method was verified, the sensitivity of the model parameters was investigated. Conclusion Material properties of the iris in vivo could be determined using the multi-island genetic algorithm coupled with the finite element method based on the experiment. PMID:24886660

Heat transfer models for predicting Salmonella enteritidis in shell eggs through supply chain distribution.

PubMed

Almonacid, S; Simpson, R; Teixeira, A

2007-11-01

Egg and egg preparations are important vehicles for Salmonella enteritidis infections. The influence of time-temperature becomes important when the presence of this organism is found in commercial shell eggs. A computer-aided mathematical model was validated to estimate surface and interior temperature of shell eggs under variable ambient and refrigerated storage temperature. A risk assessment of S. enteritidis based on the use of this model, coupled with S. enteritidis kinetics, has already been reported in a companion paper published earlier in JFS. The model considered the actual geometry and composition of shell eggs and was solved by numerical techniques (finite differences and finite elements). Parameters of interest such as local (h) and global (U) heat transfer coefficient, thermal conductivity, and apparent volumetric specific heat were estimated by an inverse procedure from experimental temperature measurement. In order to assess the error in predicting microbial population growth, theoretical and experimental temperatures were applied to a S. enteritidis growth model taken from the literature. Errors between values of microbial population growth calculated from model predicted compared with experimentally measured temperatures were satisfactorily low: 1.1% and 0.8% for the finite difference and finite element model, respectively.

One-shot calculation of temperature-dependent optical spectra and phonon-induced band-gap renormalization

NASA Astrophysics Data System (ADS)

Zacharias, Marios; Giustino, Feliciano

Electron-phonon interactions are of fundamental importance in the study of the optical properties of solids at finite temperatures. Here we present a new first-principles computational technique based on the Williams-Lax theory for performing predictive calculations of the optical spectra, including quantum zero-point renormalization and indirect absorption. The calculation of the Williams-Lax optical spectra is computationally challenging, as it involves the sampling over all possible nuclear quantum states. We develop an efficient computational strategy for performing ''one-shot'' finite-temperature calculations. These require only a single optimal configuration of the atomic positions. We demonstrate our methodology for the case of Si, C, and GaAs, yielding absorption coefficients in good agreement with experiment. This work opens the way for systematic calculations of optical spectra at finite temperature. This work was supported by the UK EPSRC (EP/J009857/1 and EP/M020517/) and the Leverhulme Trust (RL-2012-001), and the Graphene Flagship (EU-FP7-604391).

Systematics of α-decay fine structure in odd-mass nuclei based on a finite-range nucleon-nucleon interaction

NASA Astrophysics Data System (ADS)

Adel, A.; Alharbi, T.

2018-07-01

A systematic study on α-decay fine structure is presented for odd-mass nuclei in the range 83 ≤ Z ≤ 92. The α-decay partial half-lives and branching ratios to the ground and excited states of daughter nuclei are calculated in the framework of the Wentzel-Kramers-Brillouin (WKB) approximation with the implementation of the Bohr-Sommerfeld quantization condition. The microscopic α-daughter potential is obtained using the double-folding model with a realistic M3Y-Paris nucleon-nucleon (NN) interaction. The exchange potential, which accounts for the knock-on exchange of nucleons between the interacting nuclei, is calculated using the finite-range exchange NN interaction which is essentially a much better approximation as compared to the zero-range pseudo-potential adopted in the usual double-folding calculations. Our calculations of α-decay fine structure have been improved by considering the preformation factor extracted from the recently proposed cluster formation model on basis of the binding energy difference. The computed partial half-lives and branching ratios are compared with the recent experimental data and they are in good agreement.

Correlation of predicted and measured thermal stresses on an advanced aircraft structure with dissimilar materials. [hypersonic heating simulation

NASA Technical Reports Server (NTRS)

Jenkins, J. M.

1979-01-01

Additional information was added to a growing data base from which estimates of finite element model complexities can be made with respect to thermal stress analysis. The manner in which temperatures were smeared to the finite element grid points was examined from the point of view of the impact on thermal stress calculations. The general comparison of calculated and measured thermal stresses is guite good and there is little doubt that the finite element approach provided by NASTRAN results in correct thermal stress calculations. Discrepancies did exist between measured and calculated values in the skin and the skin/frame junctures. The problems with predicting skin thermal stress were attributed to inadequate temperature inputs to the structural model rather than modeling insufficiencies. The discrepancies occurring at the skin/frame juncture were most likely due to insufficient modeling elements rather than temperature problems.

Large-Scale First-Principles Molecular Dynamics Simulations with Electrostatic Embedding: Application to Acetylcholinesterase Catalysis

DOE PAGES

Fattebert, Jean-Luc; Lau, Edmond Y.; Bennion, Brian J.; ...

2015-10-22

Enzymes are complicated solvated systems that typically require many atoms to simulate their function with any degree of accuracy. We have recently developed numerical techniques for large scale First-Principles molecular dynamics simulations and applied them to study the enzymatic reaction catalyzed by acetylcholinesterase. We carried out Density functional theory calculations for a quantum mechanical (QM) sub- system consisting of 612 atoms with an O(N) complexity finite-difference approach. The QM sub-system is embedded inside an external potential field representing the electrostatic effect due to the environment. We obtained finite temperature sampling by First-Principles molecular dynamics for the acylation reaction of acetylcholinemore » catalyzed by acetylcholinesterase. Our calculations shows two energies barriers along the reaction coordinate for the enzyme catalyzed acylation of acetylcholine. In conclusion, the second barrier (8.5 kcal/mole) is rate-limiting for the acylation reaction and in good agreement with experiment.« less

Quantum field-theoretical description of neutrino and neutral kaon oscillations

NASA Astrophysics Data System (ADS)

Volobuev, Igor P.

2018-05-01

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

Elastic-plastic finite-element analyses of thermally cycled double-edge wedge specimens

NASA Technical Reports Server (NTRS)

Kaufman, A.; Hunt, L. E.

1982-01-01

Elastic-plastic stress-strain analyses were performed for double-edge wedge specimens subjected to thermal cycling in fluidized beds at 316 and 1088 C. Four cases involving different nickel-base alloys (IN 100, Mar M-200, NASA TAZ-8A, and Rene 80) were analyzed by using the MARC nonlinear, finite element computer program. Elastic solutions from MARC showed good agreement with previously reported solutions obtained by using the NASTRAN and ISO3DQ computer programs. Equivalent total strain ranges at the critical locations calculated by elastic analyses agreed within 3 percent with those calculated from elastic-plastic analyses. The elastic analyses always resulted in compressive mean stresses at the critical locations. However, elastic-plastic analyses showed tensile mean stresses for two of the four alloys and an increase in the compressive mean stress for the highest plastic strain case.

Computer simulations of austenite decomposition of microalloyed 700 MPa steel during cooling

NASA Astrophysics Data System (ADS)

Pohjonen, Aarne; Paananen, Joni; Mourujärvi, Juho; Manninen, Timo; Larkiola, Jari; Porter, David

2018-05-01

We present computer simulations of austenite decomposition to ferrite and bainite during cooling. The phase transformation model is based on Johnson-Mehl-Avrami-Kolmogorov type equations. The model is parameterized by numerical fitting to continuous cooling data obtained with Gleeble thermo-mechanical simulator and it can be used for calculation of the transformation behavior occurring during cooling along any cooling path. The phase transformation model has been coupled with heat conduction simulations. The model includes separate parameters to account for the incubation stage and for the kinetics after the transformation has started. The incubation time is calculated with inversion of the CCT transformation start time. For heat conduction simulations we employed our own parallelized 2-dimensional finite difference code. In addition, the transformation model was also implemented as a subroutine in commercial finite-element software Abaqus which allows for the use of the model in various engineering applications.

Electrophoresis of fd-virus particles: experiments and an analysis of the effect of finite rod lengths.

PubMed

Buitenhuis, Johan

2012-09-18

The electrophoretic mobility of rodlike fd viruses is measured and compared to theory, with the theoretical calculations performed according to Stigter (Stigter, D. Charged Colloidal Cylinder with a Gouy Double-Layer. J. Colloid Interface Sci. 1975, 53, 296-306. Stigter, D. Electrophoresis of Highly Charged Colloidal Cylinders in Univalent Salt- Solutions. 1. Mobility in Transverse Field. J. Phys. Chem. 1978, 82, 1417-1423. Stigter, D. Electrophoresis of Highly Charged Colloidal Cylinders in Univalent Salt Solutions. 2. Random Orientation in External Field and Application to Polyelectrolytes. J. Phys. Chem. 1978, 82, 1424-1429. Stigter, D. Theory of Conductance of Colloidal Electrolytes in Univalent Salt Solutions. J. Phys. Chem. 1979, 83, 1663-1670), who describes the electrophoretic mobility of infinite cylinders including relaxation effects. Using the dissociation constants of the ionizable groups on the surfaces of the fd viruses, we can calculate the mobility without any adjustable parameter (apart from the possible Stern layer thickness). In addition, the approximation in the theoretical description of Stigter (and others) of using a model of infinitely long cylinders, which consequently is independent of the aspect ratio, is examined by performing more elaborate numerical calculations for finite cylinders. It is shown that, although the electrophoretic mobility of cylindrical particles in the limit of low ionic strength depends on the aspect ratio much more than "end effects", at moderate and high ionic strengths the finite and infinite cylinder models differ only to a degree that can be attributed to end effects. Furthermore, the range of validity of the Stokes regime is systematically calculated.

FELIX-2.0: New version of the finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

NASA Astrophysics Data System (ADS)

Regnier, D.; Dubray, N.; Verrière, M.; Schunck, N.

2018-04-01

The time-dependent generator coordinate method (TDGCM) is a powerful method to study the large amplitude collective motion of quantum many-body systems such as atomic nuclei. Under the Gaussian Overlap Approximation (GOA), the TDGCM leads to a local, time-dependent Schrödinger equation in a multi-dimensional collective space. In this paper, we present the version 2.0 of the code FELIX that solves the collective Schrödinger equation in a finite element basis. This new version features: (i) the ability to solve a generalized TDGCM+GOA equation with a metric term in the collective Hamiltonian, (ii) support for new kinds of finite elements and different types of quadrature to compute the discretized Hamiltonian and overlap matrices, (iii) the possibility to leverage the spectral element scheme, (iv) an explicit Krylov approximation of the time propagator for time integration instead of the implicit Crank-Nicolson method implemented in the first version, (v) an entirely redesigned workflow. We benchmark this release on an analytic problem as well as on realistic two-dimensional calculations of the low-energy fission of 240Pu and 256Fm. Low to moderate numerical precision calculations are most efficiently performed with simplex elements with a degree 2 polynomial basis. Higher precision calculations should instead use the spectral element method with a degree 4 polynomial basis. We emphasize that in a realistic calculation of fission mass distributions of 240Pu, FELIX-2.0 is about 20 times faster than its previous release (within a numerical precision of a few percents).

Second order tensor finite element

NASA Technical Reports Server (NTRS)

Oden, J. Tinsley; Fly, J.; Berry, C.; Tworzydlo, W.; Vadaketh, S.; Bass, J.

1990-01-01

The results of a research and software development effort are presented for the finite element modeling of the static and dynamic behavior of anisotropic materials, with emphasis on single crystal alloys. Various versions of two dimensional and three dimensional hybrid finite elements were implemented and compared with displacement-based elements. Both static and dynamic cases are considered. The hybrid elements developed in the project were incorporated into the SPAR finite element code. In an extension of the first phase of the project, optimization of experimental tests for anisotropic materials was addressed. In particular, the problem of calculating material properties from tensile tests and of calculating stresses from strain measurements were considered. For both cases, numerical procedures and software for the optimization of strain gauge and material axes orientation were developed.

SU-F-T-428: An Optimization-Based Commissioning Tool for Finite Size Pencil Beam Dose Calculations

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

Li, Y; Tian, Z; Song, T

Purpose: Finite size pencil beam (FSPB) algorithms are commonly used to pre-calculate the beamlet dose distribution for IMRT treatment planning. FSPB commissioning, which usually requires fine tuning of the FSPB kernel parameters, is crucial to the dose calculation accuracy and hence the plan quality. Yet due to the large number of beamlets, FSPB commissioning could be very tedious. This abstract reports an optimization-based FSPB commissioning tool we have developed in MatLab to facilitate the commissioning. Methods: A FSPB dose kernel generally contains two types of parameters: the profile parameters determining the dose kernel shape, and a 2D scaling factors accountingmore » for the longitudinal and off-axis corrections. The former were fitted using the penumbra of a reference broad beam’s dose profile with Levenberg-Marquardt algorithm. Since the dose distribution of a broad beam is simply a linear superposition of the dose kernel of each beamlet calculated with the fitted profile parameters and scaled using the scaling factors, these factors could be determined by solving an optimization problem which minimizes the discrepancies between the calculated dose of broad beams and the reference dose. Results: We have commissioned a FSPB algorithm for three linac photon beams (6MV, 15MV and 6MVFFF). Dose of four field sizes (6*6cm2, 10*10cm2, 15*15cm2 and 20*20cm2) were calculated and compared with the reference dose exported from Eclipse TPS system. For depth dose curves, the differences are less than 1% of maximum dose after maximum dose depth for most cases. For lateral dose profiles, the differences are less than 2% of central dose at inner-beam regions. The differences of the output factors are within 1% for all the three beams. Conclusion: We have developed an optimization-based commissioning tool for FSPB algorithms to facilitate the commissioning, providing sufficient accuracy of beamlet dose calculation for IMRT optimization.« less

Numerical calculation of Kossel diagrams of cholesteric blue phases

NASA Astrophysics Data System (ADS)

Fukuda, Jun-ichi; Okumura, Yasushi; Kikuchi, Hirotsugu

2018-02-01

Kossel diagrams visualize the directions of strong Bragg reflections from a specimen with periodic ordering. They have played a pivotal role in the determination of the symmetry of cholesteric blue phases, and in the investigation of their structural changes under an electric field. In this work, we present direct numerical calculations of the Kossel diagrams of cholesteric blue phases by solving the Maxwell equations for the transmission and reflection of light incident upon a finite-thickness blue phase cell. Calculated Kossel diagrams are in good agreement with what is expected as a result of Bragg reflections, although some differences are present.

An automated procedure for calculating system matrices from perturbation data generated by an EAI Pacer and 100 hybrid computer system

NASA Technical Reports Server (NTRS)

Milner, E. J.; Krosel, S. M.

1977-01-01

Techniques are presented for determining the elements of the A, B, C, and D state variable matrices for systems simulated on an EAI Pacer 100 hybrid computer. An automated procedure systematically generates disturbance data necessary to linearize the simulation model and stores these data on a floppy disk. A separate digital program verifies this data, calculates the elements of the system matrices, and prints these matrices appropriately labeled. The partial derivatives forming the elements of the state variable matrices are approximated by finite difference calculations.

Calculated shape dependence of electromagnetic field in tip-enhanced Raman scattering by using a monopole antenna model.

PubMed

Kitahama, Yasutaka; Itoh, Tamitake; Suzuki, Toshiaki

2018-05-15

To evaluate the shape of an Ag tip with regard to tip-enhanced Raman scattering (TERS) signal, the enhanced electromagnetic (EM) field and scattering spectrum, arising from surface plasmon resonance at the apex of the tip, were calculated using a finite-difference time domain (FDTD) method. In the calculated forward scattering spectra from the smooth Ag tip, the band appeared within the visible region, similar to the experimental results and calculation for a corrugated Ag cone. In the FDTD calculation of TERS, the Ag tip acting as a monopole antenna was adopted by insertion of a perfect electric conductor between the root of the tip and a top boundary surface of the calculation space. As a result, the EM field was only enhanced at the apex. The shape dependence i.e. the EM field calculated at the apex with various curvatures on the different tapered tips, obtained using the monopole antenna model, was different from that simulated using a conventional dipole antenna model. Copyright © 2018 Elsevier B.V. All rights reserved.

A Combined FEM/MoM/GTD Technique To Analyze Elliptically Polarized Cavity-Backed Antennas With Finite Ground Plane

NASA Technical Reports Server (NTRS)

Reddy, C. J.; Deshpande, M. D.; Fralick, D. T.; Cockrell, C. R.; Beck, F. B.

1996-01-01

Radiation pattern prediction analysis of elliptically polarized cavity-backed aperture antennas in a finite ground plane is performed using a combined Finite Element Method/Method of Moments/Geometrical Theory of Diffraction (FEM/MoM/GTD) technique. The magnetic current on the cavity-backed aperture in an infinite ground plane is calculated using the combined FEM/MoM analysis. GTD, including the slope diffraction contribution, is used to calculate the diffracted fields caused by both soft and hard polarizations at the edges of the finite ground plane. Explicit expressions for regular diffraction coefficients and slope diffraction coefficients are presented. The slope of the incident magnetic field at the diffraction points is derived and analytical expressions are presented. Numerical results for the radiation patterns of a cavity-backed circular spiral microstrip patch antenna excited by a coaxial probe in a finite rectangular ground plane are computed and compared with experimental results.

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

NASA Technical Reports Server (NTRS)

Carlson, Ann B.; Wilmoth, Richard G.

1992-01-01

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

The detection and stabilisation of limit cycle for deterministic finite automata

NASA Astrophysics Data System (ADS)

Han, Xiaoguang; Chen, Zengqiang; Liu, Zhongxin; Zhang, Qing

2018-04-01

In this paper, the topological structure properties of deterministic finite automata (DFA), under the framework of the semi-tensor product of matrices, are investigated. First, the dynamics of DFA are converted into a new algebraic form as a discrete-time linear system by means of Boolean algebra. Using this algebraic description, the approach of calculating the limit cycles of different lengths is given. Second, we present two fundamental concepts, namely, domain of attraction of limit cycle and prereachability set. Based on the prereachability set, an explicit solution of calculating domain of attraction of a limit cycle is completely characterised. Third, we define the globally attractive limit cycle, and then the necessary and sufficient condition for verifying whether all state trajectories of a DFA enter a given limit cycle in a finite number of transitions is given. Fourth, the problem of whether a DFA can be stabilised to a limit cycle by the state feedback controller is discussed. Criteria for limit cycle-stabilisation are established. All state feedback controllers which implement the minimal length trajectories from each state to the limit cycle are obtained by using the proposed algorithm. Finally, an illustrative example is presented to show the theoretical results.

Finite element analysis of the biaxial cyclic tensile loading of the elastoplastic plate with the central hole: asymptotic regimes

NASA Astrophysics Data System (ADS)

Turkova, Vera; Stepanova, Larisa

2018-03-01

For elastistoplastic structure elements under cyclic loading three types of asymptotic behavior are well known: shakedown, cyclic plasticity or ratcheting. In structure elements operating in real conditions ratcheting must always be excluded since it caused the incremental fracture of structure by means of the accumulation of plastic strains. In the present study results of finite-element (FEM) calculations of the asymptotical behavior of an elastoplastic plate with the central circular and elliptic holes under the biaxial cyclic loading for three different materials are presented. Incremental cyclic loading of the sample with stress concentrator (the central hole) is performed in the multifunctional finite-element package SIMULIA Abaqus. The ranges of loads found for shakedown, cyclic plasticity and ratcheting are presented. The results obtained are generalized and analyzed. Convenient normalization is suggested. The chosen normalization allows us to present all computed results, corresponding to separate materials, within one common curve with minimum scattering of the points. Convenience of the generalized diagram consists in a possibility to find an asymptotical behavior of an inelastic structure for materials for which computer calculations were not made.

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 open source software tool to assign the material properties of bone for ABAQUS finite element simulations.

PubMed

Pegg, Elise C; Gill, Harinderjit S

2016-09-06

A new software tool to assign the material properties of bone to an ABAQUS finite element mesh was created and compared with Bonemat, a similar tool originally designed to work with Ansys finite element models. Our software tool (py_bonemat_abaqus) was written in Python, which is the chosen scripting language for ABAQUS. The purpose of this study was to compare the software packages in terms of the material assignment calculation and processing speed. Three element types were compared (linear hexahedral (C3D8), linear tetrahedral (C3D4) and quadratic tetrahedral elements (C3D10)), both individually and as part of a mesh. Comparisons were made using a CT scan of a hemi-pelvis as a test case. A small difference, of -0.05kPa on average, was found between Bonemat version 3.1 (the current version) and our Python package. Errors were found in the previous release of Bonemat (version 3.0 downloaded from www.biomedtown.org) during calculation of the quadratic tetrahedron Jacobian, and conversion of the apparent density to modulus when integrating over the Young׳s modulus field. These issues caused up to 2GPa error in the modulus assignment. For these reasons, we recommend users upgrade to the most recent release of Bonemat. Processing speeds were assessed for the three different element types. Our Python package took significantly longer (110s on average) to perform the calculations compared with the Bonemat software (10s). Nevertheless, the workflow advantages of the package and added functionality makes 'py_bonemat_abaqus' a useful tool for ABAQUS users. Copyright © 2016 Elsevier Ltd. All rights reserved.

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.

An empirical relationship for homogenization in single-phase binary alloy systems

NASA Technical Reports Server (NTRS)

Unnam, J.; Tenney, D. R.; Stein, B. A.

1979-01-01

A semiempirical formula is developed for describing the extent of interaction between constituents in single-phase binary alloy systems with planar, cylindrical, or spherical interfaces. The formula contains two parameters that are functions of mean concentration and interface geometry of the couple. The empirical solution is simple, easy to use, and does not involve sequential calculations, thereby allowing quick estimation of the extent of interactions without lengthy calculations. Results obtained with this formula are in good agreement with those from a finite-difference analysis.

Calculation of transonic aileron buzz

NASA Technical Reports Server (NTRS)

Steger, J. L.; Bailey, H. E.

1979-01-01

An implicit finite-difference computer code that uses a two-layer algebraic eddy viscosity model and exact geometric specification of the airfoil has been used to simulate transonic aileron buzz. The calculated results, which were performed on both the Illiac IV parallel computer processor and the Control Data 7600 computer, are in essential agreement with the original expository wind-tunnel data taken in the Ames 16-Foot Wind Tunnel just after World War II. These results and a description of the pertinent numerical techniques are included.

Electron Energy-Loss Spectroscopy (EELS)Calculation in Finite-Difference Time-Domain (FDTD) Package: EELS-FDTD

NASA Astrophysics Data System (ADS)

Large, Nicolas; Cao, Yang; Manjavacas, Alejandro; Nordlander, Peter

2015-03-01

Electron energy-loss spectroscopy (EELS) is a unique tool that is extensively used to investigate the plasmonic response of metallic nanostructures since the early works in the '50s. To be able to interpret and theoretically investigate EELS results, a myriad of different numerical techniques have been developed for EELS simulations (BEM, DDA, FEM, GDTD, Green dyadic functions). Although these techniques are able to predict and reproduce experimental results, they possess significant drawbacks and are often limited to highly symmetrical geometries, non-penetrating trajectories, small nanostructures, and free standing nanostructures. We present here a novel approach for EELS calculations using the Finite-difference time-domain (FDTD) method: EELS-FDTD. We benchmark our approach by direct comparison with results from the well-established boundary element method (BEM) and published experimental results. In particular, we compute EELS spectra for spherical nanoparticles, nanoparticle dimers, nanodisks supported by various substrates, and gold bowtie antennas on a silicon nitride substrate. Our EELS-FDTD implementation can be easily extended to more complex geometries and configurations and can be directly implemented within other numerical methods. Work funded by the Welch Foundation (C-1222, L-C-004), and the NSF (CNS-0821727, OCI-0959097).

Time-Dependent Parabolic Finite Difference Formulation for Harmonic Sound Propagation in a Two-Dimensional Duct with Flow

NASA Technical Reports Server (NTRS)

Kreider, Kevin L.; Baumeister, Kenneth J.

1996-01-01

An explicit finite difference real time iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for future large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable for a harmonic monochromatic sound field, a parabolic (in time) approximation is introduced to reduce the order of the governing equation. The analysis begins with a harmonic sound source radiating into a quiescent duct. This fully explicit iteration method then calculates stepwise in time to obtain the 'steady state' harmonic solutions of the acoustic field. For stability, applications of conventional impedance boundary conditions requires coupling to explicit hyperbolic difference equations at the boundary. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Influence of electrodes on the 448 kHz electric currents created by radiofrequency: A finite element study.

PubMed

Spottorno, J; Gonzalez de Vega, C; Buenaventura, M; Hernando, A

2017-01-01

Radiofrequency is a technology used in physical rehabilitation by physicians and physiotherapists for more than fifteen years, although there exist doubts on how it works. Indiba is a particular method that applies a voltage difference of 448 KHz between two electrodes, creating an electric current between them. These electrodes are an active one that is placed on different areas of the body and a passive one that is left on the same position during the treatment. There are two different types of active electrodes: the capacitive one and the resistive one. In this paper, it has been studied how the different electrodes affect the current density inside the body and thus how they affect the efficacy of the treatment. It shows how finite element calculations should help physicians in order to better understand its behavior and improve the treatments.

Strength analysis of an aircraft turbo-compressor engine turbine disc

NASA Astrophysics Data System (ADS)

Klimko, Marek

2017-09-01

This article deals with a strength analysis of a gas turbine rotor disc of the concrete type of an aircraft turbo-compressor engine (ATCE). The introductory part is dedicated to a basic description of the given engine, including the main technical parameters entering the calculation. The calculation is carried out by the finite difference method. This method allows to determine the tension of a generally shaped disc, which is affected by centrifugal forces of its weight, external load and heat stress caused by the difference of thermal gradients along the disc radius. The result of calculations are dependencies of the most important parameters, such as the reduced stress, radial stress, or the safety coefficient along the disc radius.

Monotonic Derivative Correction for Calculation of Supersonic Flows

ERIC Educational Resources Information Center

Bulat, Pavel V.; Volkov, Konstantin N.

2016-01-01

Aim of the study: This study examines numerical methods for solving the problems in gas dynamics, which are based on an exact or approximate solution to the problem of breakdown of an arbitrary discontinuity (the Riemann problem). Results: Comparative analysis of finite difference schemes for the Euler equations integration is conducted on the…

Comparison of seismic waveform inversion results for the rupture history of a finite fault: application to the 1986 North Palm Springs, California, earthquake

USGS Publications Warehouse

Hartzell, S.

1989-01-01

The July 8, 1986, North Palm Strings earthquake is used as a basis for comparison of several different approaches to the solution for the rupture history of a finite fault. The inversion of different waveform data is considered; both teleseismic P waveforms and local strong ground motion records. Linear parametrizations for slip amplitude are compared with nonlinear parametrizations for both slip amplitude and rupture time. Inversions using both synthetic and empirical Green's functions are considered. In general, accurate Green's functions are more readily calculable for the teleseismic problem where simple ray theory and flat-layered velocity structures are usually sufficient. However, uncertainties in the variation in t* with frequency most limit the resolution of teleseismic inversions. A set of empirical Green's functions that are well recorded at teleseismic distances could avoid the uncertainties in attenuation. In the inversion of strong motion data, the accurate calculation of propagation path effects other than attenuation effects is the limiting factor in the resolution of source parameters. -from Author

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

NASA Astrophysics Data System (ADS)

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

2012-10-01

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

Solving three-body-breakup problems with outgoing-flux asymptotic conditions

NASA Astrophysics Data System (ADS)

Randazzo, J. M.; Buezas, F.; Frapiccini, A. L.; Colavecchia, F. D.; Gasaneo, G.

2011-11-01

An analytically solvable three-body collision system (s wave) model is used to test two different theoretical methods. The first one is a configuration interaction expansion of the scattering wave function using a basis set of Generalized Sturmian Functions (GSF) with purely outgoing flux (CISF), introduced recently in A. L. Frapicinni, J. M. Randazzo, G. Gasaneo, and F. D. Colavecchia [J. Phys. B: At. Mol. Opt. Phys.JPAPEH0953-407510.1088/0953-4075/43/10/101001 43, 101001 (2010)]. The second one is a finite element method (FEM) calculation performed with a commercial code. Both methods are employed to analyze different ways of modeling the asymptotic behavior of the wave function in finite computational domains. The asymptotes can be simulated very accurately by choosing hyperspherical or rectangular contours with the FEM software. In contrast, the CISF method can be defined both in an infinite domain or within a confined region in space. We found that the hyperspherical (rectangular) FEM calculation and the infinite domain (confined) CISF evaluation are equivalent. Finally, we apply these models to the Temkin-Poet approach of hydrogen ionization.

Transpiration and film cooling boundary layer computer program. Volume 1: Numerical solutions of the turbulent boundary layer equations with equilibrium chemistry

NASA Technical Reports Server (NTRS)

Levine, J. N.

1971-01-01

A finite difference turbulent boundary layer computer program has been developed. The program is primarily oriented towards the calculation of boundary layer performance losses in rocket engines; however, the solution is general, and has much broader applicability. The effects of transpiration and film cooling as well as the effect of equilibrium chemical reactions (currently restricted to the H2-O2 system) can be calculated. The turbulent transport terms are evaluated using the phenomenological mixing length - eddy viscosity concept. The equations of motion are solved using the Crank-Nicolson implicit finite difference technique. The analysis and computer program have been checked out by solving a series of both laminar and turbulent test cases and comparing the results to data or other solutions. These comparisons have shown that the program is capable of producing very satisfactory results for a wide range of flows. Further refinements to the analysis and program, especially as applied to film cooling solutions, would be aided by the acquisition of a firm data base.

A comparative evaluation of mandibular finite element models with different lengths and elements for implant biomechanics.

PubMed

Teixeira, E R; Sato, Y; Akagawa, Y; Shindoi, N

1998-04-01

Further validity of finite element analysis (FEA) in implant biomechanics requires an increase of modelled range and mesh refinement, and a consequent increase in element number and calculation time. To develop a new method that allows a decrease of the modelled range and element number (along with less calculation time and less computer memory), 10 FEA models of the mandible with different mesio-distal lengths and elements were constructed based on three-dimensional graphic data of the bone structure around an osseointegrated implant. Analysis of stress distribution followed by 100 N loading with the fixation of the most external planes of the models indicated that a minimal bone length of 4.2 mm of the mesial and distal sides was acceptable for FEA representation. Moreover, unification of elements located far away from the implant surface did not affect stress distribution. These results suggest that it may be possible to develop a replica FEA implant model of the mandible with less range and fewer elements without altering stress distribution.

Program Calculates Forces in Bolted Structural Joints

NASA Technical Reports Server (NTRS)

Buder, Daniel A.

2005-01-01

FORTRAN 77 computer program calculates forces in bolts in the joints of structures. This program is used in conjunction with the NASTRAN finite-element structural-analysis program. A mathematical model of a structure is first created by approximating its load-bearing members with representative finite elements, then NASTRAN calculates the forces and moments that each finite element contributes to grid points located throughout the structure. The user selects the finite elements that correspond to structural members that contribute loads to the joints of interest, and identifies the grid point nearest to each such joint. This program reads the pertinent NASTRAN output, combines the forces and moments from the contributing elements to determine the resultant force and moment acting at each proximate grid point, then transforms the forces and moments from these grid points to the centroids of the affected joints. Then the program uses these joint loads to obtain the axial and shear forces in the individual bolts. The program identifies which bolts bear the greatest axial and/or shear loads. The program also performs a fail-safe analysis in which the foregoing calculations are repeated for a sequence of cases in which each fastener, in turn, is assumed not to transmit an axial force.

SPIREs: A Finite-Difference Frequency-Domain electromagnetic solver for inhomogeneous magnetized plasma cylinders

NASA Astrophysics Data System (ADS)

Melazzi, D.; Curreli, D.; Manente, M.; Carlsson, J.; Pavarin, D.

2012-06-01

We present SPIREs (plaSma Padova Inhomogeneous Radial Electromagnetic solver), a Finite-Difference Frequency-Domain (FDFD) electromagnetic solver in one dimension for the rapid calculation of the electromagnetic fields and the deposited power of a large variety of cylindrical plasma problems. The two Maxwell wave equations have been discretized using a staggered Yee mesh along the radial direction of the cylinder, and Fourier transformed along the other two dimensions and in time. By means of this kind of discretization, we have found that mode-coupling of fast and slow branches can be fully resolved without singularity issues that flawed other well-established methods in the past. Fields are forced by an antenna placed at a given distance from the plasma. The plasma can be inhomogeneous, finite-temperature, collisional, magnetized and multi-species. Finite-temperature Maxwellian effects, comprising Landau and cyclotron damping, have been included by means of the plasma Z dispersion function. Finite Larmor radius effects have been neglected. Radial variations of the plasma parameters are taken into account, thus extending the range of applications to a large variety of inhomogeneous plasma systems. The method proved to be fast and reliable, with accuracy depending on the spatial grid size. Two physical examples are reported: fields in a forced vacuum waveguide with the antenna inside, and forced plasma oscillations in the helicon radiofrequency range.

Large-eddy simulation using the finite element method

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

McCallen, R.C.; Gresho, P.M.; Leone, J.M. Jr.

1993-10-01

In a large-eddy simulation (LES) of turbulent flows, the large-scale motion is calculated explicitly (i.e., approximated with semi-empirical relations). Typically, finite difference or spectral numerical schemes are used to generate an LES; the use of finite element methods (FEM) has been far less prominent. In this study, we demonstrate that FEM in combination with LES provides a viable tool for the study of turbulent, separating channel flows, specifically the flow over a two-dimensional backward-facing step. The combination of these methodologies brings together the advantages of each: LES provides a high degree of accuracy with a minimum of empiricism for turbulencemore » modeling and FEM provides a robust way to simulate flow in very complex domains of practical interest. Such a combination should prove very valuable to the engineering community.« less

Coupled Aerodynamic and Structural Sensitivity Analysis of a High-Speed Civil Transport

NASA Technical Reports Server (NTRS)

Mason, B. H.; Walsh, J. L.

2001-01-01

An objective of the High Performance Computing and Communication Program at the NASA Langley Research Center is to demonstrate multidisciplinary shape and sizing optimization of a complete aerospace vehicle configuration by using high-fidelity, finite-element structural analysis and computational fluid dynamics aerodynamic analysis. In a previous study, a multi-disciplinary analysis system for a high-speed civil transport was formulated to integrate a set of existing discipline analysis codes, some of them computationally intensive, This paper is an extension of the previous study, in which the sensitivity analysis for the coupled aerodynamic and structural analysis problem is formulated and implemented. Uncoupled stress sensitivities computed with a constant load vector in a commercial finite element analysis code are compared to coupled aeroelastic sensitivities computed by finite differences. The computational expense of these sensitivity calculation methods is discussed.

Continuum calculations of continental deformation in transcurrent environments

NASA Technical Reports Server (NTRS)

Sonder, L. J.; England, P. C.; Houseman, G. A.

1986-01-01

A thin viscous sheet approximation is used to investigate continental deformation near a strike-slip boundary. The vertically averaged velocity field is calculated for a medium characterized by a power law rheology with stress exponent n. Driving stresses include those applied along boundaries of the sheet and those arising from buoyancy forces related to lateral differences in crustal thickness. Exact and approximate analytic solutions for a region with a sinusoidal strike-slip boundary condition are compared with solutions for more geologically relevant boundary conditions obtained using a finite element technique. The across-strike length scale of the deformation is approximately 1/4pi x sq rt n times the dominant wavelength of the imposed strike-slip boundary condition for both the analytic and the numerical solutions; this result is consistent with length scales observed in continental regions of large-scale transcurrent faulting. An approximate, linear relationship between displacement and rotation is found that depends only on the deformation length scale and the rheology. Calculated displacements, finite rotations, and distribution of crustal thicknesses are consistent with those observed in the region of the Pacific-North America plate boundary in California.

Criteria for representing circular arc and sine wave spar webs by non-curved elements

NASA Technical Reports Server (NTRS)

Jenkins, J. M.

1979-01-01

The basic problem of how to simply represent a curved web of a spar in a finite element structural model was addressed. The ratio of flat web to curved web axial deformations and longitudinal rotations were calculated using NASTRAN models. Multiplying factors were developed from these calculations for various web thicknesses. These multiplying factors can be applied directly to the area and moment of inertia inputs of the finite element model. This allows the thermal stress relieving configurations of sine wave and circular arc webs to be simply accounted for in finite element structural models.

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

NASA Technical Reports Server (NTRS)

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

2006-01-01

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

Finite element analysis of notch behavior using a state variable constitutive equation

NASA Technical Reports Server (NTRS)

Dame, L. T.; Stouffer, D. C.; Abuelfoutouh, N.

1985-01-01

The state variable constitutive equation of Bodner and Partom was used to calculate the load-strain response of Inconel 718 at 649 C in the root of a notch. The constitutive equation was used with the Bodner-Partom evolution equation and with a second evolution equation that was derived from a potential function of the stress and state variable. Data used in determining constants for the constitutive models was from one-dimensional smooth bar tests. The response was calculated for a plane stress condition at the root of the notch with a finite element code using constant strain triangular elements. Results from both evolution equations compared favorably with the observed experimental response. The accuracy and efficiency of the finite element calculations also compared favorably to existing methods.

Human exposure assessment in the near field of GSM base-station antennas using a hybrid finite element/method of moments technique.

PubMed

Meyer, Frans J C; Davidson, David B; Jakobus, Ulrich; Stuchly, Maria A

2003-02-01

A hybrid finite-element method (FEM)/method of moments (MoM) technique is employed for specific absorption rate (SAR) calculations in a human phantom in the near field of a typical group special mobile (GSM) base-station antenna. The MoM is used to model the metallic surfaces and wires of the base-station antenna, and the FEM is used to model the heterogeneous human phantom. The advantages of each of these frequency domain techniques are, thus, exploited, leading to a highly efficient and robust numerical method for addressing this type of bioelectromagnetic problem. The basic mathematical formulation of the hybrid technique is presented. This is followed by a discussion of important implementation details-in particular, the linear algebra routines for sparse, complex FEM matrices combined with dense MoM matrices. The implementation is validated by comparing results to MoM (surface equivalence principle implementation) and finite-difference time-domain (FDTD) solutions of human exposure problems. A comparison of the computational efficiency of the different techniques is presented. The FEM/MoM implementation is then used for whole-body and critical-organ SAR calculations in a phantom at different positions in the near field of a base-station antenna. This problem cannot, in general, be solved using the MoM or FDTD due to computational limitations. This paper shows that the specific hybrid FEM/MoM implementation is an efficient numerical tool for accurate assessment of human exposure in the near field of base-station antennas.

Biomechanical characteristics of self-ligating brackets in a vertically displaced canine model: a finite element analysis.

PubMed

Kim, S-J; Kwon, Y-H; Hwang, C-J

2016-05-01

The objective of this study was to compare the biomechanical characteristics between two types of self-ligating brackets and conventional metal brackets using finite element analysis of a vertically displaced canine model focusing on the desired force on the canine and undesirable forces on adjacent teeth. Three-dimensional finite element models of the maxillary dentition with 1-mm, 2-mm, and 3-mm vertically displaced canines were constructed. Two different self-ligating brackets (In-Ovation C and Smart clip) and a conventional metal bracket (Micro-arch) were modeled. After a 0.016-inch NiTi (0.40 mm, round) wire was engaged, the displacement of each tooth was calculated using x-, y-, and z-coordinates, and the tensile and compressive stresses were calculated. The extrusion and maximal tensile stress of the canine differed little between the three brackets, but the intrusion and minimal compressive stress values of the adjacent teeth differed considerably and were highest in the Smart clip and least in the In-Ovation C. The extrusion and maximal tensile stress of the canine in the 3-mm displacement model was less than that in the 2-mm displacement model, and the intrusion and minimal compressive stress of the adjacent teeth increased with the degree of displacement. Self-ligating brackets were not superior to conventional brackets in leveling a vertically displaced canine. A continuous arch wire may not be recommended for leveling of severely displaced canines whether using self-ligating or conventional brackets. © 2016 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Finite Nilpotent BRST Transformations in Hamiltonian Formulation

NASA Astrophysics Data System (ADS)

Rai, Sumit Kumar; Mandal, Bhabani Prasad

2013-10-01

We consider the finite field dependent BRST (FFBRST) transformations in the context of Hamiltonian formulation using Batalin-Fradkin-Vilkovisky method. The non-trivial Jacobian of such transformations is calculated in extended phase space. The contribution from Jacobian can be written as exponential of some local functional of fields which can be added to the effective Hamiltonian of the system. Thus, FFBRST in Hamiltonian formulation with extended phase space also connects different effective theories. We establish this result with the help of two explicit examples. We also show that the FFBRST transformations is similar to the canonical transformations in the sector of Lagrange multiplier and its corresponding momenta.

Combining Thermal And Structural Analyses

NASA Technical Reports Server (NTRS)

Winegar, Steven R.

1990-01-01

Computer code makes programs compatible so stresses and deformations calculated. Paper describes computer code combining thermal analysis with structural analysis. Called SNIP (for SINDA-NASTRAN Interfacing Program), code provides interface between finite-difference thermal model of system and finite-element structural model when no node-to-element correlation between models. Eliminates much manual work in converting temperature results of SINDA (Systems Improved Numerical Differencing Analyzer) program into thermal loads for NASTRAN (NASA Structural Analysis) program. Used to analyze concentrating reflectors for solar generation of electric power. Large thermal and structural models needed to predict distortion of surface shapes, and SNIP saves considerable time and effort in combining models.

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

NASA Astrophysics Data System (ADS)

Porojan, Liliana; Topală, Florin

2017-08-01

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

Beyond Clausius-Mossotti - Wave propagation on a polarizable point lattice and the discrete dipole approximation. [electromagnetic scattering and absorption by interstellar grains

NASA Technical Reports Server (NTRS)

Draine, B. T.; Goodman, Jeremy

1993-01-01

We derive the dispersion relation for electromagnetic waves propagating on a lattice of polarizable points. From this dispersion relation we obtain a prescription for choosing dipole polarizabilities so that an infinite lattice with finite lattice spacing will mimic a continuum with dielectric constant. The discrete dipole approximation is used to calculate scattering and absorption by a finite target by replacing the target with an array of point dipoles. We compare different prescriptions for determining the dipole polarizabilities. We show that the most accurate results are obtained when the lattice dispersion relation is used to set the polarizabilities.

Simulation of ultrasonic and EMAT arrays using FEM and FDTD.

PubMed

Xie, Yuedong; Yin, Wuliang; Liu, Zenghua; Peyton, Anthony

2016-03-01

This paper presents a method which combines electromagnetic simulation and ultrasonic simulation to build EMAT array models. For a specific sensor configuration, Lorentz forces are calculated using the finite element method (FEM), which then can feed through to ultrasonic simulations. The propagation of ultrasound waves is numerically simulated using finite-difference time-domain (FDTD) method to describe their propagation within homogenous medium and their scattering phenomenon by cracks. Radiation pattern obtained with Hilbert transform on time domain waveforms is proposed to characterise the sensor in terms of its beam directivity and field distribution along the steering angle. Copyright © 2015 Elsevier B.V. All rights reserved.

K-theory of locally finite graph C∗-algebras

NASA Astrophysics Data System (ADS)

Iyudu, Natalia

2013-09-01

We calculate the K-theory of the Cuntz-Krieger algebra OE associated with an infinite, locally finite graph, via the Bass-Hashimoto operator. The formulae we get express the Grothendieck group and the Whitehead group in purely graph theoretic terms. We consider the category of finite (black-and-white, bi-directed) subgraphs with certain graph homomorphisms and construct a continuous functor to abelian groups. In this category K0 is an inductive limit of K-groups of finite graphs, which were calculated in Cornelissen et al. (2008) [3]. In the case of an infinite graph with the finite Betti number we obtain the formula for the Grothendieck group K0(OE)=Z, where β(E) is the first Betti number and γ(E) is the valency number of the graph E. We note that in the infinite case the torsion part of K0, which is present in the case of a finite graph, vanishes. The Whitehead group depends only on the first Betti number: K1(OE)=Z. These allow us to provide a counterexample to the fact, which holds for finite graphs, that K1(OE) is the torsion free part of K0(OE).

The Biomechanical Study of Extraforaminal Lumbar Interbody Fusion: A Three-Dimensional Finite-Element Analysis.

PubMed

Yang, Mingjie; Sun, Guixin; Guo, Song; Zeng, Cheng; Yan, Meijun; Han, Yingchao; Xia, Dongdong; Zhang, Jingjie; Li, Xinhua; Xiang, Yang; Pan, Jie; Li, Lijun; Tan, Jun

2017-01-01

Finite-element method was used to evaluate biomechanics stability of extraforaminal lumbar interbody fusion (ELIF) under different internal fixation. The L3-L5 level finite-element model was established to simulate decompression and internal fixation at L4-L5 segment. The intact finite model was treated in accordance with the different internal fixation. The treatment groups were exerted 400 N load and 6 N·m additional force from motion to calculate the angular displacement of L4-L5. The ROMs were smaller in all internal fixation groups than those in the intact model. Furthermore, the ROMs were smaller in ELIF + UPS group than in TLIF + UPS group under all operating conditions, especially left lateral flexion and right rotation. The ROMs were higher in ELIF + UPS group than in TLIF + BPS group. The ROMs of ELIF + UPS + TLFS group were much smaller than those in ELIF + UPS group, and as compared with TLIF + BPS group, there was no significant difference in the range of experimental loading. The biomechanical stability of ELIF with unilateral pedicle screw fixation is superior to that of TLIF with unilateral pedicle screw fixation but lower than that of TLIF with bilateral pedicle screws fixation. The stability of ELIF with unilateral fixation can be further improved by supplementing a translaminar facet screw.

Middle atmosphere project. A semi-spectral numerical model for the large-scale stratospheric circulation

NASA Technical Reports Server (NTRS)

Holton, J. R.; Wehrbein, W.

1979-01-01

The complete model is a semispectral model in which the longitudinal dependence is represented by expansion in zonal harmonics while the latitude and height dependencies are represented by a finite difference grid. The model is based on the primitive equations in the log pressure coordinate system. The lower boundary of the model domain is set at the 100 mb level (i.e., near the tropopause) and the effects of tropospheric forcing are included in the lower boundary condition. The upper boundary is at approximately 96 km, and the latitudinal extent is either global or hemispheric. The basic differential equations and boundary conditions are outlined. The finite difference equations are described. The initial conditions are discussed and a sample calculation is presented. The FORTRAN code is given in the appendix.

Finite difference method accelerated with sparse solvers for structural analysis of the metal-organic complexes

NASA Astrophysics Data System (ADS)

Guda, A. A.; Guda, S. A.; Soldatov, M. A.; Lomachenko, K. A.; Bugaev, A. L.; Lamberti, C.; Gawelda, W.; Bressler, C.; Smolentsev, G.; Soldatov, A. V.; Joly, Y.

2016-05-01

Finite difference method (FDM) implemented in the FDMNES software [Phys. Rev. B, 2001, 63, 125120] was revised. Thorough analysis shows, that the calculated diagonal in the FDM matrix consists of about 96% zero elements. Thus a sparse solver would be more suitable for the problem instead of traditional Gaussian elimination for the diagonal neighbourhood. We have tried several iterative sparse solvers and the direct one MUMPS solver with METIS ordering turned out to be the best. Compared to the Gaussian solver present method is up to 40 times faster and allows XANES simulations for complex systems already on personal computers. We show applicability of the software for metal-organic [Fe(bpy)3]2+ complex both for low spin and high spin states populated after laser excitation.

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.

Tomographic reconstruction of melanin structures of optical coherence tomography via the finite-difference time-domain simulation

NASA Astrophysics Data System (ADS)

Huang, Shi-Hao; Wang, Shiang-Jiu; Tseng, Snow H.

2015-03-01

Optical coherence tomography (OCT) provides high resolution, cross-sectional image of internal microstructure of biological tissue. We use the Finite-Difference Time-Domain method (FDTD) to analyze the data acquired by OCT, which can help us reconstruct the refractive index of the biological tissue. We calculate the refractive index tomography and try to match the simulation with the data acquired by OCT. Specifically, we try to reconstruct the structure of melanin, which has complex refractive indices and is the key component of human pigment system. The results indicate that better reconstruction can be achieved for homogenous sample, whereas the reconstruction is degraded for samples with fine structure or with complex interface. Simulation reconstruction shows structures of the Melanin that may be useful for biomedical optics applications.

Prediction of SA 349/2 GV blade loads in high speed flight using several rotor analyses

NASA Technical Reports Server (NTRS)

Gaubert, Michel; Yamauchi, Gloria K.

1987-01-01

The influence of blade dynamics, dynamic stall, and transonic aerodynamics on the predictions of rotor loads in high-speed flight are presented. Data were obtained from an Aerospatiale Gazelle SA 349/2 helicopter with three Grande Vitesse blades. Several analyses are used for this investigation. First, blade dynamics effects on the correlation are studied using three rotor analyses which differ mainly in the method of calculating the blade elastic response. Next, an ONERA dynamic stall model is used to predict retreating blade stall. Finally, advancing blade aerodynamic loads are calculated using a NASA-developed rotorcraft analysis coupled with two transonic finite-difference analyses.

Improved Algorithm For Finite-Field Normal-Basis Multipliers

NASA Technical Reports Server (NTRS)

Wang, C. C.

1989-01-01

Improved algorithm reduces complexity of calculations that must precede design of Massey-Omura finite-field normal-basis multipliers, used in error-correcting-code equipment and cryptographic devices. Algorithm represents an extension of development reported in "Algorithm To Design Finite-Field Normal-Basis Multipliers" (NPO-17109), NASA Tech Briefs, Vol. 12, No. 5, page 82.

Finite-size correction scheme for supercell calculations in Dirac-point two-dimensional materials.

PubMed

Rocha, C G; Rocha, A R; Venezuela, P; Garcia, J H; Ferreira, M S

2018-06-19

Modern electronic structure calculations are predominantly implemented within the super cell representation in which unit cells are periodically arranged in space. Even in the case of non-crystalline materials, defect-embedded unit cells are commonly used to describe doped structures. However, this type of computation becomes prohibitively demanding when convergence rates are sufficiently slow and may require calculations with very large unit cells. Here we show that a hitherto unexplored feature displayed by several 2D materials may be used to achieve convergence in formation- and adsorption-energy calculations with relatively small unit-cell sizes. The generality of our method is illustrated with Density Functional Theory calculations for different 2D hosts doped with different impurities, all of which providing accuracy levels that would otherwise require enormously large unit cells. This approach provides an efficient route to calculating the physical properties of 2D systems in general but is particularly suitable for Dirac-point materials doped with impurities that break their sublattice symmetry.

Relationship between sample volumes and modulus of human vertebral trabecular bone in micro-finite element analysis.

PubMed

Wen, Xin-Xin; Xu, Chao; Zong, Chun-Lin; Feng, Ya-Fei; Ma, Xiang-Yu; Wang, Fa-Qi; Yan, Ya-Bo; Lei, Wei

2016-07-01

Micro-finite element (μFE) models have been widely used to assess the biomechanical properties of trabecular bone. How to choose a proper sample volume of trabecular bone, which could predict the real bone biomechanical properties and reduce the calculation time, was an interesting problem. Therefore, the purpose of this study was to investigate the relationship between different sample volumes and apparent elastic modulus (E) calculated from μFE model. 5 Human lumbar vertebral bodies (L1-L5) were scanned by micro-CT. Cubic concentric samples of different lengths were constructed as the experimental groups and the largest possible volumes of interest (VOI) were constructed as the control group. A direct voxel-to-element approach was used to generate μFE models and steel layers were added to the superior and inferior surface to mimic axial compression tests. A 1% axial strain was prescribed to the top surface of the model to obtain the E values. ANOVA tests were performed to compare the E values from the different VOIs against that of the control group. Nonlinear function curve fitting was performed to study the relationship between volumes and E values. The larger cubic VOI included more nodes and elements, and more CPU times were needed for calculations. E values showed a descending tendency as the length of cubic VOI decreased. When the volume of VOI was smaller than (7.34mm(3)), E values were significantly different from the control group. The fit function showed that E values approached an asymptotic values with increasing length of VOI. Our study demonstrated that apparent elastic modulus calculated from μFE models were affected by the sample volumes. There was a descending tendency of E values as the length of cubic VOI decreased. Sample volume which was not smaller than (7.34mm(3)) was efficient enough and timesaving for the calculation of E. Copyright © 2016 Elsevier Ltd. All rights reserved.

Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result.

PubMed

Wu, Yang; Kelly, Damien P

2014-12-12

The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf's treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of [Formula: see text] and [Formula: see text] type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of [Formula: see text] and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by [Formula: see text], where [Formula: see text] is the replica order. These circular replicas are shown to be fundamentally different from the replicas that arise in a Cartesian coordinate system.

Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result

NASA Astrophysics Data System (ADS)

Wu, Yang; Kelly, Damien P.

2014-12-01

The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf's treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of ? and ? type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of ? and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by ?, where ? is the replica order. These circular replicas are shown to be fundamentally different from the replicas that arise in a Cartesian coordinate system.

An analytic solution for numerical modeling validation in electromagnetics: the resistive sphere

NASA Astrophysics Data System (ADS)

Swidinsky, Andrei; Liu, Lifei

2017-11-01

We derive the electromagnetic response of a resistive sphere to an electric dipole source buried in a conductive whole space. The solution consists of an infinite series of spherical Bessel functions and associated Legendre polynomials, and follows the well-studied problem of a conductive sphere buried in a resistive whole space in the presence of a magnetic dipole. Our result is particularly useful for controlled-source electromagnetic problems using a grounded electric dipole transmitter and can be used to check numerical methods of calculating the response of resistive targets (such as finite difference, finite volume, finite element and integral equation). While we elect to focus on the resistive sphere in our examples, the expressions in this paper are completely general and allow for arbitrary source frequency, sphere radius, transmitter position, receiver position and sphere/host conductivity contrast so that conductive target responses can also be checked. Commonly used mesh validation techniques consist of comparisons against other numerical codes, but such solutions may not always be reliable or readily available. Alternatively, the response of simple 1-D models can be tested against well-known whole space, half-space and layered earth solutions, but such an approach is inadequate for validating models with curved surfaces. We demonstrate that our theoretical results can be used as a complementary validation tool by comparing analytic electric fields to those calculated through a finite-element analysis; the software implementation of this infinite series solution is made available for direct and immediate application.

Calculation of reaction forces in the boiler supports using the method of equivalent stiffness of membrane wall.

PubMed

Sertić, Josip; Kozak, Dražan; Samardžić, Ivan

2014-01-01

The values of reaction forces in the boiler supports are the basis for the dimensioning of bearing steel structure of steam boiler. In this paper, the application of the method of equivalent stiffness of membrane wall is proposed for the calculation of reaction forces. The method of equalizing displacement, as the method of homogenization of membrane wall stiffness, was applied. On the example of "Milano" boiler, using the finite element method, the calculation of reactions in the supports for the real geometry discretized by the shell finite element was made. The second calculation was performed with the assumption of ideal stiffness of membrane walls and the third using the method of equivalent stiffness of membrane wall. In the third case, the membrane walls are approximated by the equivalent orthotropic plate. The approximation of membrane wall stiffness is achieved using the elasticity matrix of equivalent orthotropic plate at the level of finite element. The obtained results were compared, and the advantages of using the method of equivalent stiffness of membrane wall for the calculation of reactions in the boiler supports were emphasized.

Nonlinear susceptibilities of finite conjugated organic polymers

NASA Technical Reports Server (NTRS)

Beratan, David N.; Onuchic, Jose Nelson; Perry, Joseph W.

1987-01-01

Tight-binding calculations of the length dependence of the third-order molecular hyperpolarizability for polyenes and polyynes are reported. The pi-electron wave functions were determined by exploiting the limited translational symmetry of the molecules. Perturbation theory was used to calculate the longitudinal component of the electronic nonresonant hyperpolarizability. This is the first two-'band' calculation of third-order hyperpolarizabilities on finite pi-electron systems of varying length. In contrast to the results of the one-'band' models, the hyperpolarizability densities increase rapidly and then, after about 10-15 repeating units, approach an asymptotic value.

Finite geometry effects of field-aligned currents

NASA Technical Reports Server (NTRS)

Fung, Shing F.; Hoffman, R. A.

1992-01-01

Results are presented of model calculations of the magnetic field produced by finite current regions that would be measured by a spaceborne magnetometer. Conditions were examined under which the infinite current sheet approximation can be applied to the calculation of the field-aligned current (FAC) density, using satellite magnetometer data. The accuracy of the three methods used for calculating the current sheet normal direction with respect to the spacecraft trajectory was assessed. It is shown that the model can be used to obtain the position and the orientation of the spacecraft trajectory through the FAC region.

Pairing mechanism in Bi-O superconductors: A finite-size chain calculation

NASA Astrophysics Data System (ADS)

Aligia, A. A.; Nuez Regueiro, M. D.; Gagliano, E. R.

1989-09-01

We have studied the pairing mechanism in BiO3 systems by calculating the binding energy of a pair of holes in finite Bi-O chains, for parameters that simulate three-dimensional behavior. In agreement with previous results using perturbation theory in the hopping t, for covalent Bi-O binding and parameters for which the parent compound has a disproportionate ground state, pairing induced by the presence of biexcitons is obtained for sufficiently large interatomic Coulomb repulsion. The analysis of appropriate correlation functions shows a rapid metallization of the system as t and the number of holes increase. This fact shrinks the region of parameters for which the finite-size calculations can be trusted without further study. The same model for other parameters yields pairing in two other regimes: bipolaronic and magnetic excitonic.

Renyi Entropy of the Ideal Gas in Finite Momentum Intervals

NASA Astrophysics Data System (ADS)

Bialas, A.; Czyz, W.

2003-06-01

Coincidence probabilities of multiparticle events, as measured in finite momentum intervals for Bose and Fermi ideal gas, are calculated and compared with the exact expressions given in statistical physics.

A comparison of methods for computing the sigma-coordinate pressure gradient force for flow over sloped terrain in a hybrid theta-sigma model

NASA Technical Reports Server (NTRS)

Johnson, D. R.; Uccellini, L. W.

1983-01-01

In connection with the employment of the sigma coordinates introduced by Phillips (1957), problems can arise regarding an accurate finite-difference computation of the pressure gradient force. Over steeply sloped terrain, the calculation of the sigma-coordinate pressure gradient force involves computing the difference between two large terms of opposite sign which results in large truncation error. To reduce the truncation error, several finite-difference methods have been designed and implemented. The present investigation has the objective to provide another method of computing the sigma-coordinate pressure gradient force. Phillips' method is applied for the elimination of a hydrostatic component to a flux formulation. The new technique is compared with four other methods for computing the pressure gradient force. The work is motivated by the desire to use an isentropic and sigma-coordinate hybrid model for experiments designed to study flow near mountainous terrain.

Finite Element Analysis and Experimental Study on Elbow Vibration Transmission Characteristics

NASA Astrophysics Data System (ADS)

Qing-shan, Dai; Zhen-hai, Zhang; Shi-jian, Zhu

2017-11-01

Pipeline system vibration is one of the significant factors leading to the vibration and noise of vessel. Elbow is widely used in the pipeline system. However, the researches about vibration of elbow are little, and there is no systematic study. In this research, we firstly analysed the relationship between elbow vibration transmission characteristics and bending radius by ABAQUS finite element simulation. Then, we conducted the further vibration test to observe the vibration transmission characteristics of different elbows which have the same diameter and different bending radius under different flow velocity. The results of simulation calculation and experiment both showed that the vibration acceleration levels of the pipeline system decreased with the increase of bending radius of the elbow, which was beneficial to reduce the transmission of vibration in the pipeline system. The results could be used as reference for further studies and designs for the low noise installation of pipeline system.

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

FELIX-2.0: New version of the finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

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

Regnier, D.; Dubray, N.; Verriere, M.

The time-dependent generator coordinate method (TDGCM) is a powerful method to study the large amplitude collective motion of quantum many-body systems such as atomic nuclei. Under the Gaussian Overlap Approximation (GOA), the TDGCM leads to a local, time-dependent Schrödinger equation in a multi-dimensional collective space. In this study, we present the version 2.0 of the code FELIX that solves the collective Schrödinger equation in a finite element basis. This new version features: (i) the ability to solve a generalized TDGCM+GOA equation with a metric term in the collective Hamiltonian, (ii) support for new kinds of finite elements and different typesmore » of quadrature to compute the discretized Hamiltonian and overlap matrices, (iii) the possibility to leverage the spectral element scheme, (iv) an explicit Krylov approximation of the time propagator for time integration instead of the implicit Crank–Nicolson method implemented in the first version, (v) an entirely redesigned workflow. We benchmark this release on an analytic problem as well as on realistic two-dimensional calculations of the low-energy fission of 240Pu and 256Fm. Low to moderate numerical precision calculations are most efficiently performed with simplex elements with a degree 2 polynomial basis. Higher precision calculations should instead use the spectral element method with a degree 4 polynomial basis. Finally, we emphasize that in a realistic calculation of fission mass distributions of 240Pu, FELIX-2.0 is about 20 times faster than its previous release (within a numerical precision of a few percents).« less

On Calculation Methods and Results for Straight Cylindrical Roller Bearing Deflection, Stiffness, and Stress

NASA Technical Reports Server (NTRS)

Krantz, Timothy L.

2011-01-01

The purpose of this study was to assess some calculation methods for quantifying the relationships of bearing geometry, material properties, load, deflection, stiffness, and stress. The scope of the work was limited to two-dimensional modeling of straight cylindrical roller bearings. Preparations for studies of dynamic response of bearings with damaged surfaces motivated this work. Studies were selected to exercise and build confidence in the numerical tools. Three calculation methods were used in this work. Two of the methods were numerical solutions of the Hertz contact approach. The third method used was a combined finite element surface integral method. Example calculations were done for a single roller loaded between an inner and outer raceway for code verification. Next, a bearing with 13 rollers and all-steel construction was used as an example to do additional code verification, including an assessment of the leading order of accuracy of the finite element and surface integral method. Results from that study show that the method is at least first-order accurate. Those results also show that the contact grid refinement has a more significant influence on precision as compared to the finite element grid refinement. To explore the influence of material properties, the 13-roller bearing was modeled as made from Nitinol 60, a material with very different properties from steel and showing some potential for bearing applications. The codes were exercised to compare contact areas and stress levels for steel and Nitinol 60 bearings operating at equivalent power density. As a step toward modeling the dynamic response of bearings having surface damage, static analyses were completed to simulate a bearing with a spall or similar damage.

FELIX-2.0: New version of the finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

DOE PAGES

Regnier, D.; Dubray, N.; Verriere, M.; ...

2017-12-20

The time-dependent generator coordinate method (TDGCM) is a powerful method to study the large amplitude collective motion of quantum many-body systems such as atomic nuclei. Under the Gaussian Overlap Approximation (GOA), the TDGCM leads to a local, time-dependent Schrödinger equation in a multi-dimensional collective space. In this study, we present the version 2.0 of the code FELIX that solves the collective Schrödinger equation in a finite element basis. This new version features: (i) the ability to solve a generalized TDGCM+GOA equation with a metric term in the collective Hamiltonian, (ii) support for new kinds of finite elements and different typesmore » of quadrature to compute the discretized Hamiltonian and overlap matrices, (iii) the possibility to leverage the spectral element scheme, (iv) an explicit Krylov approximation of the time propagator for time integration instead of the implicit Crank–Nicolson method implemented in the first version, (v) an entirely redesigned workflow. We benchmark this release on an analytic problem as well as on realistic two-dimensional calculations of the low-energy fission of 240Pu and 256Fm. Low to moderate numerical precision calculations are most efficiently performed with simplex elements with a degree 2 polynomial basis. Higher precision calculations should instead use the spectral element method with a degree 4 polynomial basis. Finally, we emphasize that in a realistic calculation of fission mass distributions of 240Pu, FELIX-2.0 is about 20 times faster than its previous release (within a numerical precision of a few percents).« less

Stability of streamwise vortices

NASA Technical Reports Server (NTRS)

Khorrami, M. K.; Grosch, C. E.; Ash, R. L.

1987-01-01

A brief overview of some theoretical and computational studies of the stability of streamwise vortices is given. The local induction model and classical hydrodynamic vortex stability theories are discussed in some detail. The importance of the three-dimensionality of the mean velocity profile to the results of stability calculations is discussed briefly. The mean velocity profile is provided by employing the similarity solution of Donaldson and Sullivan. The global method of Bridges and Morris was chosen for the spatial stability calculations for the nonlinear eigenvalue problem. In order to test the numerical method, a second order accurate central difference scheme was used to obtain the coefficient matrices. It was shown that a second order finite difference method lacks the required accuracy for global eigenvalue calculations. Finally the problem was formulated using spectral methods and a truncated Chebyshev series.

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.

Finite-volume method with lattice Boltzmann flux scheme for incompressible porous media flow at the representative-elementary-volume scale.

PubMed

Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong

2016-02-01

Based on the Darcy-Brinkman-Forchheimer equation, a finite-volume computational model with lattice Boltzmann flux scheme is proposed for incompressible porous media flow in this paper. The fluxes across the cell interface are calculated by reconstructing the local solution of the generalized lattice Boltzmann equation for porous media flow. The time-scaled midpoint integration rule is adopted to discretize the governing equation, which makes the time step become limited by the Courant-Friedricks-Lewy condition. The force term which evaluates the effect of the porous medium is added to the discretized governing equation directly. The numerical simulations of the steady Poiseuille flow, the unsteady Womersley flow, the circular Couette flow, and the lid-driven flow are carried out to verify the present computational model. The obtained results show good agreement with the analytical, finite-difference, and/or previously published solutions.

Penalty-Based Finite Element Interface Technology for Analysis of Homogeneous and Composite Structures

NASA Technical Reports Server (NTRS)

Averill, Ronald C.

2002-01-01

An effective and robust interface element technology able to connect independently modeled finite element subdomains has been developed. This method is based on the use of penalty constraints and allows coupling of finite element models whose nodes do not coincide along their common interface. Additionally, the present formulation leads to a computational approach that is very efficient and completely compatible with existing commercial software. A significant effort has been directed toward identifying those model characteristics (element geometric properties, material properties, and loads) that most strongly affect the required penalty parameter, and subsequently to developing simple 'formulae' for automatically calculating the proper penalty parameter for each interface constraint. This task is especially critical in composite materials and structures, where adjacent sub-regions may be composed of significantly different materials or laminates. This approach has been validated by investigating a variety of two-dimensional problems, including composite laminates.

A 2D Daubechies finite wavelet domain method for transient wave response analysis in shear deformable laminated composite plates

NASA Astrophysics Data System (ADS)

Nastos, C. V.; Theodosiou, T. C.; Rekatsinas, C. S.; Saravanos, D. A.

2018-03-01

An efficient numerical method is developed for the simulation of dynamic response and the prediction of the wave propagation in composite plate structures. The method is termed finite wavelet domain method and takes advantage of the outstanding properties of compactly supported 2D Daubechies wavelet scaling functions for the spatial interpolation of displacements in a finite domain of a plate structure. The development of the 2D wavelet element, based on the first order shear deformation laminated plate theory is described and equivalent stiffness, mass matrices and force vectors are calculated and synthesized in the wavelet domain. The transient response is predicted using the explicit central difference time integration scheme. Numerical results for the simulation of wave propagation in isotropic, quasi-isotropic and cross-ply laminated plates are presented and demonstrate the high spatial convergence and problem size reduction obtained by the present method.

Magnetic Field Due to a Finite Length Current-Carrying Wire Using the Concept of Displacement Current

ERIC Educational Resources Information Center

Buschauer, Robert

2014-01-01

In undergraduate E&M courses the magnetic field due to a finite length, current-carrying wire can be calculated using the Biot-Savart law. However, to the author's knowledge, no textbook presents the calculation of this field using the Ampere-Maxwell law: ?B [multiplied by] dl = µ[subscript 0] (I + e[subscript 0] dF/dt) [multiplied by] 1

A study of unstable rock failures using finite difference and discrete element methods

NASA Astrophysics Data System (ADS)

Garvey, Ryan J.

Case histories in mining have long described pillars or faces of rock failing violently with an accompanying rapid ejection of debris and broken material into the working areas of the mine. These unstable failures have resulted in large losses of life and collapses of entire mine panels. Modern mining operations take significant steps to reduce the likelihood of unstable failure, however eliminating their occurrence is difficult in practice. Researchers over several decades have supplemented studies of unstable failures through the application of various numerical methods. The direction of the current research is to extend these methods and to develop improved numerical tools with which to study unstable failures in underground mining layouts. An extensive study is first conducted on the expression of unstable failure in discrete element and finite difference methods. Simulated uniaxial compressive strength tests are run on brittle rock specimens. Stable or unstable loading conditions are applied onto the brittle specimens by a pair of elastic platens with ranging stiffnesses. Determinations of instability are established through stress and strain histories taken for the specimen and the system. Additional numerical tools are then developed for the finite difference method to analyze unstable failure in larger mine models. Instability identifiers are established for assessing the locations and relative magnitudes of unstable failure through measures of rapid dynamic motion. An energy balance is developed which calculates the excess energy released as a result of unstable equilibria in rock systems. These tools are validated through uniaxial and triaxial compressive strength tests and are extended to models of coal pillars and a simplified mining layout. The results of the finite difference simulations reveal that the instability identifiers and excess energy calculations provide a generalized methodology for assessing unstable failures within potentially complex mine models. These combined numerical tools may be applied in future studies to design primary and secondary supports in bump-prone conditions, evaluate retreat mining cut sequences, asses pillar de-stressing techniques, or perform backanalyses on unstable failures in select mining layouts.

[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.

HCMM energy budget data as a model input for assessing regions of high potential groundwater pollution

NASA Technical Reports Server (NTRS)

Moore, D. G. (Principal Investigator); Tunheim, J. A.; Heilman, J.

1977-01-01

The author has identified the following significant results. The finite difference model was used to calculate the differences in surface temperature between two hypothetical sites which result from a temperature difference at 50 cm due to the presence of shallow ground water at one of the sites. Although qualitative results of the model seemed consistant with experimental results, further evaluation showed a need for taking account of differences in thermal conductivity due to different moisture profiles at the two sites considered.

Finite element analysis of helicopter structures

NASA Technical Reports Server (NTRS)

Rich, M. J.

1978-01-01

Application of the finite element analysis is now being expanded to three dimensional analysis of mechanical components. Examples are presented for airframe, mechanical components, and composite structure calculations. Data are detailed on the increase of model size, computer usage, and the effect on reducing stress analysis costs. Future applications for use of finite element analysis for helicopter structures are projected.

Aerodynamic interaction between vortical wakes and lifting two-dimensional bodies

NASA Technical Reports Server (NTRS)

Stremel, Paul M.

1989-01-01

Unsteady rotor wake interactions with the empennage, tail boom, and other aerodynamic surfaces of a helicopter have a significant influence on its aerodynamic performance, the ride quality, and vibration. A numerical method for computing the aerodynamic interaction between an interacting vortex wake and the viscous flow about arbitrary two-dimensional bodies was developed to address this helicopter problem. The method solves for the flow field velocities on a body-fitted computational mesh using finite-difference techniques. The interacting vortex wake is represented by an array of discrete vortices which, in turn, are represented by a finite-core model. The evolution of the interacting vortex wake is calculated by Lagrangian techniques. The viscous flow field of the two-dimensional body is calculated on an Eulerian grid. The flow around circular and elliptic cylinders in the absence of an interacting vortex wake was calculated. These results compare very well with other numerical results and with results obtained from experiment and thereby demonstrate the accuracy of the viscous solution. The interaction of a rotor wake with the flow about a 4 to 1 elliptic cylinder at 45 degree incidence was calculated for a Reynolds number of 3000. The results demonstrate the significant variations in the lift and drag on the elliptic cylinder in the presence of the interacting rotor wake.

The Relation of Finite Element and Finite Difference Methods

NASA Technical Reports Server (NTRS)

Vinokur, M.

1976-01-01

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

Treatment of late time instabilities in finite difference EMP scattering codes

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

Simpson, L.T.; Arman, S.; Holland, R.

1982-12-01

Time-domain solutions to the finite-differenced Maxwell's equations give rise to several well-known nonphysical propagation anomalies. In particular, when a radiative electric-field look back scheme is employed to terminate the calculation, a high-frequency, growing, numerical instability is introduced. This paper describes the constraints made on the mesh to minimize this instability, and a technique of applying an absorbing sheet to damp out this instability without altering the early time solution. Also described are techniques to extend the data record in the presence of high-frequency noise through application of a low-pass digital filter and the fitting of a damped sinusoid to themore » late-time tail of the data record. An application of these techniques is illustrated with numerical models of the FB-111 aircraft and the B-52 aircraft in the in-flight refueling configuration using the THREDE finite difference computer code. Comparisons are made with experimental scale model measurements with agreement typically on the order of 3 to 6 dB near the fundamental resonances.« less

Numerical investigation of finite-volume effects for the HVP

NASA Astrophysics Data System (ADS)

Boyle, Peter; Gülpers, Vera; Harrison, James; Jüttner, Andreas; Portelli, Antonin; Sachrajda, Christopher

2018-03-01

It is important to correct for finite-volume (FV) effects in the presence of QED, since these effects are typically large due to the long range of the electromagnetic interaction. We recently made the first lattice calculation of electromagnetic corrections to the hadronic vacuum polarisation (HVP). For the HVP, an analytical derivation of FV corrections involves a two-loop calculation which has not yet been carried out. We instead calculate the universal FV corrections numerically, using lattice scalar QED as an effective theory. We show that this method gives agreement with known analytical results for scalar mass FV effects, before applying it to calculate FV corrections for the HVP. This method for numerical calculation of FV effects is also widely applicable to quantities beyond the HVP.

Williams Element with Generalized Degrees of Freedom for Fracture Analysis of Multiple-Cracked Beam

NASA Astrophysics Data System (ADS)

Xu, Hua; Wei, Quyang; Yang, Lufeng

2017-10-01

In this paper, the method of finite element with generalized degrees of freedom (FEDOFs) is used to calculate the stress intensity factor (SIF) of multiple cracked beam and analysed the effect of minor cracks on the main crack SIF in different cases. Williams element is insensitive to the size of singular region. So that calculation efficiency is highly improved. Examples analysis validates that the SIF near the crack tip can be obtained directly though FEDOFs. And the result is well consistent with ANSYS solution and has a satisfied accuracy.

Calculation of wind-driven surface currents in the North Atlantic Ocean

NASA Technical Reports Server (NTRS)

Rees, T. H.; Turner, R. E.

1976-01-01

Calculations to simulate the wind driven near surface currents of the North Atlantic Ocean are described. The primitive equations were integrated on a finite difference grid with a horizontal resolution of 2.5 deg in longitude and latitude. The model ocean was homogeneous with a uniform depth of 100 m and with five levels in the vertical direction. A form of the rigid-lid approximation was applied. Generally, the computed surface current patterns agreed with observed currents. The development of a subsurface equatorial countercurrent was observed.

An implicit flux-split algorithm to calculate hypersonic flowfields in chemical equilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1987-01-01

An implicit, finite-difference, shock-capturing algorithm that calculates inviscid, hypersonic flows in chemical equilibrium is presented. The flux vectors and flux Jacobians are differenced using a first-order, flux-split technique. The equilibrium composition of the gas is determined by minimizing the Gibbs free energy at every node point. The code is validated by comparing results over an axisymmetric hemisphere against previously published results. The algorithm is also applied to more practical configurations. The accuracy, stability, and versatility of the algorithm have been promising.

Timelike pion form factor in lattice QCD

NASA Astrophysics Data System (ADS)

Feng, Xu; Aoki, Sinya; Hashimoto, Shoji; Kaneko, Takashi

2015-03-01

We perform a nonperturbative lattice calculation of the complex phase and modulus of the pion form factor in the timelike momentum region using the finite-volume technique. We use two ensembles of 2 +1 -flavor overlap fermions at pion masses mπ=380 and 290 MeV. By calculating the I =1 correlators in the center-of-mass and three moving frames, we obtain the form factor at ten different values of the timelike momentum transfer around the vector resonance. We compare the results with the phenomenological model of Gounaris-Sakurai and its variant.

Modeling the dynamic equilibrium between oligomers of (AlOCH3)n in methylaluminoxane (MAO). A theoretical study based on a combined quantum mechanical and statistical mechanical approach.

PubMed

Zurek, E; Woo, T K; Firman, T K; Ziegler, T

2001-01-15

Density functional theory (DFT) has been used to calculate the energies of 36 different methylaluminoxane (MAO) cage structures with the general formula (MeAlO)n, where n ranges from 4 to 16. A least-squares fit has been used to devise a formula which predicts the total energies of the MAO with different n's giving an rms deviation of 4.70 kcal/mol. These energies in conjunction with frequency calculations based on molecular mechanics have been used to estimate the finite temperature enthalpies, entropies, and free energies for these MAO structures. Furthermore, formulas have been devised which predict finite temperature enthalpies and entropies for MAO structures of any n for a temperature range of 198.15-598.15 K. Using these formulas, the free energies at different temperatures have been predicted for MAO structures where n ranges from 17 to 30. The free energy values were then used to predict the percentage of each n found at a given temperature. Our calculations give an average n value of 18.41, 17.23, 16.89, and 15.72 at 198.15, 298.15, 398.15, and 598.15 K, respectively. Topological arguments have also been used to show that the MAO cage structure contains a limited amount of square faces as compared to octagonal and hexagonal ones. It is also suggested that the limited number of square faces with their strained Al-O bonds explain the high molar Al:catalyst ratio required for activation. Moreover, in this study we outline a general methodology which may be used to calculate the percent abundance of an equilibrium mixture of oligomers with the general formula (X)n.

[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.

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.

Angle-resolved PED and AED calculations for different structures of the diamond C(111) surface

NASA Astrophysics Data System (ADS)

Niebergall, L.; Rennert, P.; Chassé, A.; Kucherenko, Yu

1998-05-01

Angle-resolved (AR) photoelectron diffraction (PED) spectra for electrons excited from the C 1s core state and angle-resolved KVV Auger electron diffraction (AED) spectra are calculated for the Pandey and the Tsai stucture models of diamond C(111) which extend previous investigations of the ideal structure. It is shown how to decide on the structure model by comparing PE spectra for different directions and by comparing PED and AED spectra. Calculations have been performed by evaluating the scattering path operator for a finite cluster in a curved-wave approximation. The different matrix elements for the photoelectron excitation and for the Auger process, respectively, are included. It is shown that the PED intensities are very sensitive to the surface reconstruction for polar angles in the range of 80°. In the AED intensities, polar scans in the plane perpendicular to the chain direction can be considered.

Reentry heat transfer analysis of the space shuttle orbiter

NASA Technical Reports Server (NTRS)

Ko, W. L.; Quinn, R. D.; Gong, L.

1982-01-01

A structural performance and resizing finite element thermal analysis computer program was used in the reentry heat transfer analysis of the space shuttle. Two typical wing cross sections and a midfuselage cross section were selected for the analysis. The surface heat inputs to the thermal models were obtained from aerodynamic heating analyses, which assumed a purely turbulent boundary layer, a purely laminar boundary layer, separated flow, and transition from laminar to turbulent flow. The effect of internal radiation was found to be quite significant. With the effect of the internal radiation considered, the wing lower skin temperature became about 39 C (70 F) lower. The results were compared with fight data for space transportation system, trajectory 1. The calculated and measured temperatures compared well for the wing if laminar flow was assumed for the lower surface and bay one upper surface and if separated flow was assumed for the upper surfaces of bays other than bay one. For the fuselage, good agreement between the calculated and measured data was obtained if laminar flow was assumed for the bottom surface. The structural temperatures were found to reach their peak values shortly before touchdown. In addition, the finite element solutions were compared with those obtained from the conventional finite difference solutions.

Simulations of surface stress effects in nanoscale single crystals

NASA Astrophysics Data System (ADS)

Zadin, V.; Veske, M.; Vigonski, S.; Jansson, V.; Muszinsky, J.; Parviainen, S.; Aabloo, A.; Djurabekova, F.

2018-04-01

Onset of vacuum arcing near a metal surface is often associated with nanoscale asperities, which may dynamically appear due to different processes ongoing in the surface and subsurface layers in the presence of high electric fields. Thermally activated processes, as well as plastic deformation caused by tensile stress due to an applied electric field, are usually not accessible by atomistic simulations because of the long time needed for these processes to occur. On the other hand, finite element methods, able to describe the process of plastic deformations in materials at realistic stresses, do not include surface properties. The latter are particularly important for the problems where the surface plays crucial role in the studied process, as for instance, in the case of plastic deformations at a nanovoid. In the current study by means of molecular dynamics (MD) and finite element simulations we analyse the stress distribution in single crystal copper containing a nanovoid buried deep under the surface. We have developed a methodology to incorporate the surface effects into the solid mechanics framework by utilizing elastic properties of crystals, pre-calculated using MD simulations. The method leads to computationally efficient stress calculations and can be easily implemented in commercially available finite element software, making it an attractive analysis tool.

Geometry reconstruction method for patient-specific finite element models for the assessment of tibia fracture risk in osteogenesis imperfecta.

PubMed

Caouette, Christiane; Ikin, Nicole; Villemure, Isabelle; Arnoux, Pierre-Jean; Rauch, Frank; Aubin, Carl-Éric

2017-04-01

Lower limb deformation in children with osteogenesis imperfecta (OI) impairs ambulation and may lead to fracture. Corrective surgery is based on empirical assessment criteria. The objective was to develop a reconstruction method of the tibia for OI patients that could be used as input of a comprehensive finite element model to assess fracture risks. Data were obtained from three children with OI and tibia deformities. Four pQCT scans were registered to biplanar radiographs, and a template mesh was deformed to fit the bone outline. Cortical bone thickness was computed. Sensitivity of the model to missing slices of pQCT was assessed by calculating maximal von Mises stress for a vertical hopping load case. Sensitivity of the model to ±5 % of cortical thickness measurements was assessed by calculating loads at fracture. Difference between the mesh contour and bone outline on the radiographs was below 1 mm. Removal of one pQCT slice increased maximal von Mises stress by up to 10 %. Simulated ±5 % variation of cortical bone thickness leads to variations of up to 4.1 % on predicted fracture loads. Using clinically available tibia imaging from children with OI, the developed reconstruction method allowed the building of patient-specific finite element models.

Finite-volume and partial quenching effects in the magnetic polarizability of the neutron

NASA Astrophysics Data System (ADS)

Hall, J. M. M.; Leinweber, D. B.; Young, R. D.

2014-03-01

There has been much progress in the experimental measurement of the electric and magnetic polarizabilities of the nucleon. Similarly, lattice QCD simulations have recently produced dynamical QCD results for the magnetic polarizability of the neutron approaching the chiral regime. In order to compare the lattice simulations with experiment, calculation of partial quenching and finite-volume effects is required prior to an extrapolation in quark mass to the physical point. These dependencies are described using chiral effective field theory. Corrections to the partial quenching effects associated with the sea-quark-loop electric charges are estimated by modeling corrections to the pion cloud. These are compared to the uncorrected lattice results. In addition, the behavior of the finite-volume corrections as a function of pion mass is explored. Box sizes of approximately 7 fm are required to achieve a result within 5% of the infinite-volume result at the physical pion mass. A variety of extrapolations are shown at different box sizes, providing a benchmark to guide future lattice QCD calculations of the magnetic polarizabilities. A relatively precise value for the physical magnetic polarizability of the neutron is presented, βn=1.93(11)stat(11)sys×10-4 fm3, which is in agreement with current experimental results.

Modeling the high-frequency complex modulus of silicone rubber using standing Lamb waves and an inverse finite element method.

PubMed

Jonsson, Ulf; Lindahl, Olof; Andersson, Britt

2014-12-01

To gain an understanding of the high-frequency elastic properties of silicone rubber, a finite element model of a cylindrical piezoelectric element, in contact with a silicone rubber disk, was constructed. The frequency-dependent elastic modulus of the silicone rubber was modeled by a fourparameter fractional derivative viscoelastic model in the 100 to 250 kHz frequency range. The calculations were carried out in the range of the first radial resonance frequency of the sensor. At the resonance, the hyperelastic effect of the silicone rubber was modeled by a hyperelastic compensating function. The calculated response was matched to the measured response by using the transitional peaks in the impedance spectrum that originates from the switching of standing Lamb wave modes in the silicone rubber. To validate the results, the impedance responses of three 5-mm-thick silicone rubber disks, with different radial lengths, were measured. The calculated and measured transitional frequencies have been compared in detail. The comparison showed very good agreement, with average relative differences of 0.7%, 0.6%, and 0.7% for the silicone rubber samples with radial lengths of 38.0, 21.4, and 11.0 mm, respectively. The average complex elastic moduli of the samples were (0.97 + 0.009i) GPa at 100 kHz and (0.97 + 0.005i) GPa at 250 kHz.

A modification of the finite-difference model for simulation of two dimensional ground-water flow to include surface-ground water relationships

USGS Publications Warehouse

Ozbilgin, M.M.; Dickerman, D.C.

1984-01-01

The two-dimensional finite-difference model for simulation of groundwater flow was modified to enable simulation of surface-water/groundwater interactions during periods of low streamflow. Changes were made to the program code in order to calculate surface-water heads for, and flow either to or from, contiguous surface-water bodies; and to allow for more convenient data input. Methods of data input and output were modified and entries (RSORT and HDRIVER) were added to the COEF and CHECKI subroutines to calculate surface-water heads. A new subroutine CALC was added to the program which initiates surface-water calculations. If CALC is not specified as a simulation option, the program runs the original version. The subroutines which solve the ground-water flow equations were not changed. Recharge, evapotranspiration, surface-water inflow, number of wells, pumping rate, and pumping duration can be varied for any time period. The Manning formula was used to relate stream depth and discharge in surface-water streams. Interactions between surface water and ground water are represented by the leakage term in the ground-water flow and surface-water mass balance equations. Documentation includes a flow chart, data deck instructions, input data, output summary, and program listing. Numerical results from the modified program are in good agreement with published analytical results. (USGS)

Real-space finite-difference approach for multi-body systems: path-integral renormalization group method and direct energy minimization method.

PubMed

Sasaki, Akira; Kojo, Masashi; Hirose, Kikuji; Goto, Hidekazu

2011-11-02

The path-integral renormalization group and direct energy minimization method of practical first-principles electronic structure calculations for multi-body systems within the framework of the real-space finite-difference scheme are introduced. These two methods can handle higher dimensional systems with consideration of the correlation effect. Furthermore, they can be easily extended to the multicomponent quantum systems which contain more than two kinds of quantum particles. The key to the present methods is employing linear combinations of nonorthogonal Slater determinants (SDs) as multi-body wavefunctions. As one of the noticeable results, the same accuracy as the variational Monte Carlo method is achieved with a few SDs. This enables us to study the entire ground state consisting of electrons and nuclei without the need to use the Born-Oppenheimer approximation. Recent activities on methodological developments aiming towards practical calculations such as the implementation of auxiliary field for Coulombic interaction, the treatment of the kinetic operator in imaginary-time evolutions, the time-saving double-grid technique for bare-Coulomb atomic potentials and the optimization scheme for minimizing the total-energy functional are also introduced. As test examples, the total energy of the hydrogen molecule, the atomic configuration of the methylene and the electronic structures of two-dimensional quantum dots are calculated, and the accuracy, availability and possibility of the present methods are demonstrated.

High-Accuracy Finite Element Method: Benchmark Calculations

NASA Astrophysics Data System (ADS)

Gusev, Alexander; Vinitsky, Sergue; Chuluunbaatar, Ochbadrakh; Chuluunbaatar, Galmandakh; Gerdt, Vladimir; Derbov, Vladimir; Góźdź, Andrzej; Krassovitskiy, Pavel

2018-02-01

We describe a new high-accuracy finite element scheme with simplex elements for solving the elliptic boundary-value problems and show its efficiency on benchmark solutions of the Helmholtz equation for the triangle membrane and hypercube.

An Unstructured Finite Volume Approach for Structural Dynamics in Response to Fluid Motions.

PubMed

Xia, Guohua; Lin, Ching-Long

2008-04-01

A new cell-vortex unstructured finite volume method for structural dynamics is assessed for simulations of structural dynamics in response to fluid motions. A robust implicit dual-time stepping method is employed to obtain time accurate solutions. The resulting system of algebraic equations is matrix-free and allows solid elements to include structure thickness, inertia, and structural stresses for accurate predictions of structural responses and stress distributions. The method is coupled with a fluid dynamics solver for fluid-structure interaction, providing a viable alternative to the finite element method for structural dynamics calculations. A mesh sensitivity test indicates that the finite volume method is at least of second-order accuracy. The method is validated by the problem of vortex-induced vibration of an elastic plate with different initial conditions and material properties. The results are in good agreement with existing numerical data and analytical solutions. The method is then applied to simulate a channel flow with an elastic wall. The effects of wall inertia and structural stresses on the fluid flow are investigated.

Numerical simulation of hypersonic inlet flows with equilibrium or finite rate chemistry

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao; Hsieh, Kwang-Chung; Shuen, Jian-Shun; Mcbride, Bonnie J.

1988-01-01

An efficient numerical program incorporated with comprehensive high temperature gas property models has been developed to simulate hypersonic inlet flows. The computer program employs an implicit lower-upper time marching scheme to solve the two-dimensional Navier-Stokes equations with variable thermodynamic and transport properties. Both finite-rate and local-equilibrium approaches are adopted in the chemical reaction model for dissociation and ionization of the inlet air. In the finite rate approach, eleven species equations coupled with fluid dynamic equations are solved simultaneously. In the local-equilibrium approach, instead of solving species equations, an efficient chemical equilibrium package has been developed and incorporated into the flow code to obtain chemical compositions directly. Gas properties for the reaction products species are calculated by methods of statistical mechanics and fit to a polynomial form for C(p). In the present study, since the chemical reaction time is comparable to the flow residence time, the local-equilibrium model underpredicts the temperature in the shock layer. Significant differences of predicted chemical compositions in shock layer between finite rate and local-equilibrium approaches have been observed.

A design tool for direct and non-stochastic calculations of near-field radiative transfer in complex structures: The NF-RT-FDTD algorithm

NASA Astrophysics Data System (ADS)

Didari, Azadeh; Pinar Mengüç, M.

2017-08-01

Advances in nanotechnology and nanophotonics are inextricably linked with the need for reliable computational algorithms to be adapted as design tools for the development of new concepts in energy harvesting, radiative cooling, nanolithography and nano-scale manufacturing, among others. In this paper, we provide an outline for such a computational tool, named NF-RT-FDTD, to determine the near-field radiative transfer between structured surfaces using Finite Difference Time Domain method. NF-RT-FDTD is a direct and non-stochastic algorithm, which accounts for the statistical nature of the thermal radiation and is easily applicable to any arbitrary geometry at thermal equilibrium. We present a review of the fundamental relations for far- and near-field radiative transfer between different geometries with nano-scale surface and volumetric features and gaps, and then we discuss the details of the NF-RT-FDTD formulation, its application to sample geometries and outline its future expansion to more complex geometries. In addition, we briefly discuss some of the recent numerical works for direct and indirect calculations of near-field thermal radiation transfer, including Scattering Matrix method, Finite Difference Time Domain method (FDTD), Wiener Chaos Expansion, Fluctuating Surface Current (FSC), Fluctuating Volume Current (FVC) and Thermal Discrete Dipole Approximations (TDDA).

Performance analysis for minimally nonlinear irreversible refrigerators at finite cooling power

NASA Astrophysics Data System (ADS)

Long, Rui; Liu, Zhichun; Liu, Wei

2018-04-01

The coefficient of performance (COP) for general refrigerators at finite cooling power have been systematically researched through the minimally nonlinear irreversible model, and its lower and upper bounds in different operating regions have been proposed. Under the tight coupling conditions, we have calculated the universal COP bounds under the χ figure of merit in different operating regions. When the refrigerator operates in the region with lower external flux, we obtained the general bounds (0 < ε <(√{ 9 + 8εC } - 3) / 2) under the χ figure of merit. We have also calculated the universal bounds for maximum gain in COP under different operating regions to give a further insight into the COP gain with the cooling power away from the maximum one. When the refrigerator operates in the region located between maximum cooling power and maximum COP with lower external flux, the upper bound for COP and the lower bound for relative gain in COP present large values, compared to a relative small loss from the maximum cooling power. If the cooling power is the main objective, it is desirable to operate the refrigerator at a slightly lower cooling power than at the maximum one, where a small loss in the cooling power induces a much larger COP enhancement.

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.

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.

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.

Long-term strength determination for cooled blades made of monocrystalline superalloys

NASA Astrophysics Data System (ADS)

Getsov, L. B.; Semenov, A. S.; Besschetnov, V. A.; Grishchenko, A. I.; Semenov, S. G.

2017-04-01

For the manufacture of blades for modern gas-turbine installations, monocrystalline alloys are used. Traditional methods for the calculation of stressed-deformed state and safety factors for these alloys developed and verified for polycrystalline materials need to be adjusted. This paper deals with methodological principles for an approach to the solving of the problem concerning a finite-element determination of the long-term static strength for cooled monocrystalline blades employed in gas-turbine installations based on the use of two different models (phenomenological and micromechanical) considering the inelastic deformation of monocrystalline superalloys. An analysis has been performed for the distribution of Schmid factors in the spherical triangle for primary and secondary octahedral and cubic slip systems. Calculations are performed using Larson-Miller's parametric dependences taking into account the crystallographic orientation of the material. A determination procedure for the anisotropy coefficients of long-term strength is described based on data for different orientations. A comparative analysis of the results of finite-element calculations made using phenomenological and micromechanical (crystallographic) creep models for the long-term static strength of cooled monocrystalline blades used in a gas-turbine engine has been performed. It is shown that the location of the most loaded sections of such a blade coincide with the results of calculations according to these models. It has been found that the micromechanical deformation model results in the obtaining of the most conservative estimate for the long-term strength of turbine blades made of monocrystalline alloys. It is shown that the calculations using models for materials with isotropic properties can produce considerable errors in determining the durability of the blades. The possibility is considered for using 1D-, 2D-, and 3D-models for turbine monocrystalline blades in the determination of their durability parameters.

Self-energy matrices for electron transport calculations within the real-space finite-difference formalism

NASA Astrophysics Data System (ADS)

Tsukamoto, Shigeru; Ono, Tomoya; Hirose, Kikuji; Blügel, Stefan

2017-03-01

The self-energy term used in transport calculations, which describes the coupling between electrode and transition regions, is able to be evaluated only from a limited number of the propagating and evanescent waves of a bulk electrode. This obviously contributes toward the reduction of the computational expenses in transport calculations. In this paper, we present a mathematical formula for reducing the computational expenses further without using any approximation and without losing accuracy. So far, the self-energy term has been handled as a matrix with the same dimension as the Hamiltonian submatrix representing the interaction between an electrode and a transition region. In this work, through the singular-value decomposition of the submatrix, the self-energy matrix is handled as a smaller matrix, whose dimension is the rank number of the Hamiltonian submatrix. This procedure is practical in the case of using the pseudopotentials in a separable form, and the computational expenses for determining the self-energy matrix are reduced by 90% when employing a code based on the real-space finite-difference formalism and projector-augmented wave method. In addition, this technique is applicable to the transport calculations using atomic or localized basis sets. Adopting the self-energy matrices obtained from this procedure, we present the calculation of the electron transport properties of C20 molecular junctions. The application demonstrates that the electron transmissions are sensitive to the orientation of the molecule with respect to the electrode surface. In addition, channel decomposition of the scattering wave functions reveals that some unoccupied C20 molecular orbitals mainly contribute to the electron conduction through the molecular junction.

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

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

Akhil Datta-Gupta

2006-12-31

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

Temperature field simulation and phantom validation of a Two-armed Spiral Antenna for microwave thermotherapy.

PubMed

Du, Yongxing; Zhang, Lingze; Sang, Lulu; Wu, Daocheng

2016-04-29

In this paper, an Archimedean planar spiral antenna for the application of thermotherapy was designed. This type of antenna was chosen for its compact structure, flexible application and wide heating area. The temperature field generated by the use of this Two-armed Spiral Antenna in a muscle-equivalent phantom was simulated and subsequently validated by experimentation. First, the specific absorption rate (SAR) of the field was calculated using the Finite Element Method (FEM) by Ansoft's High Frequency Structure Simulation (HFSS). Then, the temperature elevation in the phantom was simulated by an explicit finite difference approximation of the bioheat equation (BHE). The temperature distribution was then validated by a phantom heating experiment. The results showed that this antenna had a good heating ability and a wide heating area. A comparison between the calculation and the measurement showed a fair agreement in the temperature elevation. The validated model could be applied for the analysis of electromagnetic-temperature distribution in phantoms during the process of antenna design or thermotherapy experimentation.

A rocket engine design expert system

NASA Technical Reports Server (NTRS)

Davidian, Kenneth J.

1989-01-01

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

Fatigue Life Methodology for Tapered Hybrid Composite Flexbeams

NASA Technical Reports Server (NTRS)

urri, Gretchen B.; Schaff, Jeffery R.

2006-01-01

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

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.

A finite difference-time domain technique for modeling narrow apertures in conducting scatterers

NASA Technical Reports Server (NTRS)

Demarest, Kenneth R.

1987-01-01

The finite difference-time domain (FDTD) technique has proven to be a valuable tool for the calculation of the transient and steady state scattering characteristics of relatively complex scatterer and source configurations. In spite of its usefulness, it exhibits serious deficiencies when used to analyze geometries that contain fine detail. An FDTD technique is described that utilizes Babinet's principle to decouple the regions on both sides of the aperture. The result is an FDTD technique that is capable of modeling apertures that are much smaller than the spatial grid used in the analysis and yet is not perturbed by numerical noise when used in the 'scattered field' mode. Numerical results are presented that show the field penetration through cavity-backed apertures that are much smaller than the spatial grid used during the solution.

Green's function enriched Poisson solver for electrostatics in many-particle systems

NASA Astrophysics Data System (ADS)

Sutmann, Godehard

2016-06-01

A highly accurate method is presented for the construction of the charge density for the solution of the Poisson equation in particle simulations. The method is based on an operator adjusted source term which can be shown to produce exact results up to numerical precision in the case of a large support of the charge distribution, therefore compensating the discretization error of finite difference schemes. This is achieved by balancing an exact representation of the known Green's function of regularized electrostatic problem with a discretized representation of the Laplace operator. It is shown that the exact calculation of the potential is possible independent of the order of the finite difference scheme but the computational efficiency for higher order methods is found to be superior due to a faster convergence to the exact result as a function of the charge support.

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

PubMed

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

2009-06-22

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

An efficient finite element technique for sound propagation in axisymmetric hard wall ducts carrying high subsonic Mach number flows

NASA Technical Reports Server (NTRS)

Tag, I. A.; Lumsdaine, E.

1978-01-01

The general non-linear three-dimensional equation for acoustic potential is derived by using a perturbation technique. The linearized axisymmetric equation is then solved by using a finite element algorithm based on the Galerkin formulation for a harmonic time dependence. The solution is carried out in complex number notation for the acoustic velocity potential. Linear, isoparametric, quadrilateral elements with non-uniform distribution across the duct section are implemented. The resultant global matrix is stored in banded form and solved by using a modified Gauss elimination technique. Sound pressure levels and acoustic velocities are calculated from post element solutions. Different duct geometries are analyzed and compared with experimental results.

Free stream capturing in fluid conservation law for moving coordinates in three dimensions

NASA Technical Reports Server (NTRS)

Obayashi, Shigeru

1991-01-01

The free-stream capturing technique for both the finite-volume (FV) and finite-difference (FD) framework is summarized. For an arbitrary motion of the grid, the FV analysis shows that volumes swept by all six surfaces of the cell have to be computed correctly. This means that the free-stream capturing time-metric terms should be calculated not only from a surface vector of a cell at a single time level, but also from a volume swept by the cell surface in space and time. The FV free-stream capturing formulation is applicable to the FD formulation by proper translation from an FV cell to an FD mesh.

Computer program: Jet 3 to calculate the large elastic plastic dynamically induced deformations of free and restrained, partial and/or complete structural rings

NASA Technical Reports Server (NTRS)

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

1972-01-01

A user-oriented FORTRAN 4 computer program, called JET 3, is presented. The JET 3 program, which employs the spatial finite-element and timewise finite-difference method, can be used to predict the large two-dimensional elastic-plastic transient Kirchhoff-type deformations of a complete or partial structural ring, with various support conditions and restraints, subjected to a variety of initial velocity distributions and externally-applied transient forcing functions. The geometric shapes of the structural ring can be circular or arbitrarily curved and with variable thickness. Strain-hardening and strain-rate effects of the material are taken into account.

Finite elements for the calculation of turbulent flows in three-dimensional complex geometries

NASA Astrophysics Data System (ADS)

Ruprecht, A.

A finite element program for the calculation of incompressible turbulent flows is presented. In order to reduce the required storage an iterative algorithm is used which solves the necessary equations sequentially. The state of turbulence is defined by the k-epsilon model. In addition to the standard k-epsilon model, the modification of Bardina et al., taking into account the rotation of the mean flow, is investigated. With this program, the flow in the draft tube of a Kaplan turbine is examined. Calculations are carried out for swirling and nonswirling entrance flow. The results are compared with measurements.

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

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Trajectory Calculator for Finite-Radius Cutter on a Lathe

NASA Technical Reports Server (NTRS)

Savchenkov, Anatoliy; Strekalov, Dmitry; Yu, Nan

2009-01-01

A computer program calculates the two-dimensional trajectory (radial vs. axial position) of a finite-radius-of-curvature cutting tool on a lathe so as to cut a workpiece to a piecewise-continuous, analytically defined surface of revolution. (In the original intended application, the tool is a diamond cutter, and the workpiece is made of a crystalline material and is to be formed into an optical resonator disk.) The program also calculates an optimum cutting speed as F/L, where F is a material-dependent empirical factor and L is the effective instantaneous length of the cutting edge.

Probabilistic Based Modeling and Simulation Assessment

DTIC Science & Technology

2010-06-01

different crash and blast scenarios. With the integration of the high fidelity neck and head model, a methodology to calculate the probability of injury...variability, correlation, and multiple (often competing) failure metrics. Important scenarios include vehicular collisions, blast /fragment impact, and...first area of focus is to develop a methodology to integrate probabilistic analysis into finite element analysis of vehicle collisions and blast . The

Finite element calculation of residual stress in dental restorative material

NASA Astrophysics Data System (ADS)

Grassia, Luigi; D'Amore, Alberto

2012-07-01

A finite element methodology for residual stresses calculation in dental restorative materials is proposed. The material under concern is a multifunctional methacrylate-based composite for dental restorations, activated by visible light. Reaction kinetics, curing shrinkage, and viscoelastic relaxation functions were required as input data on a structural finite element solver. Post cure effects were considered in order to quantify the residual stresses coming out from natural contraction with respect to those debited to the chemical shrinkage. The analysis showed for a given test case that residual stresses frozen in the dental restoration at uniform temperature of 37°C are of the same order of magnitude of the strength of the dental composite material per se.

A method of selecting grid size to account for Hertz deformation in finite element analysis of spur gears

NASA Technical Reports Server (NTRS)

Coy, J. J.; Chao, C. H. C.

1981-01-01

A method of selecting grid size for the finite element analysis of gear tooth deflection is presented. The method is based on a finite element study of two cylinders in line contact, where the criterion for establishing element size was that there be agreement with the classical Hertzian solution for deflection. The results are applied to calculate deflection for the gear specimen used in the NASA spur gear test rig. Comparisons are made between the present results and the results of two other methods of calculation. The results have application in design of gear tooth profile modifications to reduce noise and dynamic loads.

Seismic gradiometry using ambient seismic noise in an anisotropic Earth

NASA Astrophysics Data System (ADS)

de Ridder, S. A. L.; Curtis, A.

2017-05-01

We introduce a wavefield gradiometry technique to estimate both isotropic and anisotropic local medium characteristics from short recordings of seismic signals by inverting a wave equation. The method exploits the information in the spatial gradients of a seismic wavefield that are calculated using dense deployments of seismic arrays. The application of the method uses the surface wave energy in the ambient seismic field. To estimate isotropic and anisotropic medium properties we invert an elliptically anisotropic wave equation. The spatial derivatives of the recorded wavefield are evaluated by calculating finite differences over nearby recordings, which introduces a systematic anisotropic error. A two-step approach corrects this error: finite difference stencils are first calibrated, then the output of the wave-equation inversion is corrected using the linearized impulse response to the inverted velocity anomaly. We test the procedure on ambient seismic noise recorded in a large and dense ocean bottom cable array installed over Ekofisk field. The estimated azimuthal anisotropy forms a circular geometry around the production-induced subsidence bowl. This conforms with results from studies employing controlled sources, and with interferometry correlating long records of seismic noise. Yet in this example, the results were obtained using only a few minutes of ambient seismic noise.

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

NASA Astrophysics Data System (ADS)

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

2009-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

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

USGS Publications Warehouse

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

2009-01-01

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

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

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

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

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

Momentum Advection on a Staggered Mesh

NASA Astrophysics Data System (ADS)

Benson, David J.

1992-05-01

Eulerian and ALE (arbitrary Lagrangian-Eulerian) hydrodynamics programs usually split a timestep into two parts. The first part is a Lagrangian step, which calculates the incremental motion of the material. The second part is referred to as the Eulerian step, the advection step, or the remap step, and it accounts for the transport of material between cells. In most finite difference and finite element formulations, all the solution variables except the velocities are cell-centered while the velocities are edge- or vertex-centered. As a result, the advection algorithm for the momentum is, by necessity, different than the algorithm used for the other variables. This paper reviews three momentum advection methods and proposes a new one. One method, pioneered in YAQUI, creates a new staggered mesh, while the other two, used in SALE and SHALE, are cell-centered. The new method is cell-centered and its relationship to the other methods is discussed. Both pure advection and strong shock calculations are presented to substantiate the mathematical analysis. From the standpoint of numerical accuracy, both the staggered mesh and the cell-centered algorithms can give good results, while the computational costs are highly dependent on the overall architecture of a code.

Calculation of flight vibration levels of the AH-1G helicopter and correlation with existing flight vibration measurements

NASA Technical Reports Server (NTRS)

Sopher, R.; Twomey, W. J.

1990-01-01

NASA-Langley is sponsoring a rotorcraft structural dynamics program with the objective to establish in the U.S. a superior capability to utilize finite element analysis models for calculations to support industrial design of helicopter airframe structures. In the initial phase of the program, teams from the major U.S. manufacturers of helicopter airframes will apply extant finite element analysis methods to calculate loads and vibrations of helicopter airframes, and perform correlations between analysis and measurements. The aforementioned rotorcraft structural dynamics program was given the acronym DAMVIBS (Design Analysis Method for Vibrations). Sikorsky's RDYNE Rotorcraft Dynamics Analysis used for the correlation study, the specifics of the application of RDYNE to the AH-1G, and comparisons of the predictions of the method with flight data for loads and vibrations on the AH-1G are described. RDYNE was able to predict trends of variations of loads and vibrations with airspeed, but in some instances magnitudes differed from measured results by factors of two or three to one. Sensitivities were studied of predictions to rotor inflow modeling, effects of torsional modes, number of blade bending modes, fuselage structural damping, and hub modal content.

Interpolation Hermite Polynomials For Finite Element Method

NASA Astrophysics Data System (ADS)

Gusev, Alexander; Vinitsky, Sergue; Chuluunbaatar, Ochbadrakh; Chuluunbaatar, Galmandakh; Gerdt, Vladimir; Derbov, Vladimir; Góźdź, Andrzej; Krassovitskiy, Pavel

2018-02-01

We describe a new algorithm for analytic calculation of high-order Hermite interpolation polynomials of the simplex and give their classification. A typical example of triangle element, to be built in high accuracy finite element schemes, is given.

The effects of finite rate chemical processes on high enthalpy nozzle performance - A comparison between SPARK and SEAGULL

NASA Technical Reports Server (NTRS)

Carpenter, M. H.

1988-01-01

The generalized chemistry version of the computer code SPARK is extended to include two higher-order numerical schemes, yielding fourth-order spatial accuracy for the inviscid terms. The new and old formulations are used to study the influences of finite rate chemical processes on nozzle performance. A determination is made of the computationally optimum reaction scheme for use in high-enthalpy nozzles. Finite rate calculations are compared with the frozen and equilibrium limits to assess the validity of each formulation. In addition, the finite rate SPARK results are compared with the constant ratio of specific heats (gamma) SEAGULL code, to determine its accuracy in variable gamma flow situations. Finally, the higher-order SPARK code is used to calculate nozzle flows having species stratification. Flame quenching occurs at low nozzle pressures, while for high pressures, significant burning continues in the nozzle.

Method and system employing finite state machine modeling to identify one of a plurality of different electric load types

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

Du, Liang; Yang, Yi; Harley, Ronald Gordon

A system is for a plurality of different electric load types. The system includes a plurality of sensors structured to sense a voltage signal and a current signal for each of the different electric loads; and a processor. The processor acquires a voltage and current waveform from the sensors for a corresponding one of the different electric load types; calculates a power or current RMS profile of the waveform; quantizes the power or current RMS profile into a set of quantized state-values; evaluates a state-duration for each of the quantized state-values; evaluates a plurality of state-types based on the powermore » or current RMS profile and the quantized state-values; generates a state-sequence that describes a corresponding finite state machine model of a generalized load start-up or transient profile for the corresponding electric load type; and identifies the corresponding electric load type.« less

[Three dimensional finite element analysis of maxillary anterior teeth retraction with micro-implant anchorage and sliding mechanics].

PubMed

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

2009-10-01

To investigate the biomechanical effects of micro-implant anchorage technique with sliding mechanics on maxillary anterior teeth retraction under different implant insertion heights and different retraction hook heights. The three dimensional finite element model of maxillary anterior teeth retraction force system was constructed with CT scanning and MIMICS software and the relationships between brackets, teeth, wire and micro-implant were simulating the clinical factions. Then the initial tooth displacement was calculated when the insertion heights were 4 mm and 8 mm and the retraction hook heights were 1, 4, 7, 10 mm respectively. With retraction hook height added, the anterior teeth movement changed from lingual crown tipping to labial crown tipping and the intrusion movement was more apparent when the micro-implant was inserted in a higher location. The ideal teeth movement control could be achieved by different insertion heights of micro-implant and different retraction hook heights in straight wire retraction force system.

[Biomechanical study of lumbar spine under different vibration conditions].

PubMed

Xiang, Pin; Du, Chengfei; Mo, Zhongjun; Gong, He; Wang, Lizhen; Fan, Yubo

2015-02-01

We observed the effect of vibration parameters on lumbar spine under different vibration conditions using finite element analysis method in our laboratory. In this study, the CT-images of L1-L5 segments were obtained. All images were used to develop 3D geometrical model using the Mimics10. 01 (Materialise, Belgium). Then it was modified using Geomagic Studio12. 0 (Raindrop Geomagic Inc. USA). Finite element (FE) mesh model was generated by Hypermesh11. 0 (Altair Engineering, Inc. USA) and Abaqus. Abaqus was used to calculate the stress distribution of L1-L5 under different vibration conditions. It was found that in a vibration cycle, tensile stress was occurred on lumbar vertebra mainly. Stress distributed evenly and stress concentration occurred on the left rear side of the upper endplate. The stress had no obvious changes under different frequencies, but the stress was higher when amplitude was greater. In conclusion, frequency and amplitude parameters have little effect on the stress distribution in vertebra. The stress magnitude is positively correlated with the amplitude.

Root-cause analysis of the better performance of the coarse-mesh finite-difference method for CANDU-type reactors

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

Shen, W.

2012-07-01

Recent assessment results indicate that the coarse-mesh finite-difference method (FDM) gives consistently smaller percent differences in channel powers than the fine-mesh FDM when compared to the reference MCNP solution for CANDU-type reactors. However, there is an impression that the fine-mesh FDM should always give more accurate results than the coarse-mesh FDM in theory. To answer the question if the better performance of the coarse-mesh FDM for CANDU-type reactors was just a coincidence (cancellation of errors) or caused by the use of heavy water or the use of lattice-homogenized cross sections for the cluster fuel geometry in the diffusion calculation, threemore » benchmark problems were set up with three different fuel lattices: CANDU, HWR and PWR. These benchmark problems were then used to analyze the root cause of the better performance of the coarse-mesh FDM for CANDU-type reactors. The analyses confirm that the better performance of the coarse-mesh FDM for CANDU-type reactors is mainly caused by the use of lattice-homogenized cross sections for the sub-meshes of the cluster fuel geometry in the diffusion calculation. Based on the analyses, it is recommended to use 2 x 2 coarse-mesh FDM to analyze CANDU-type reactors when lattice-homogenized cross sections are used in the core analysis. (authors)« less

The effect of loading time on flexible pavement dynamic response: a finite element analysis

NASA Astrophysics Data System (ADS)

Yin, Hao; Solaimanian, Mansour; Kumar, Tanmay; Stoffels, Shelley

2007-12-01

Dynamic response of asphalt concrete (AC) pavements under moving load is a key component for accurate prediction of flexible pavement performance. The time and temperature dependency of AC materials calls for utilizing advanced material characterization and mechanistic theories, such as viscoelasticity and stress/strain analysis. In layered elastic analysis, as implemented in the new Mechanistic-Empirical Pavement Design Guide (MEPDG), the time dependency is accounted for by calculating the loading times at different AC layer depths. In this study, the time effect on pavement response was evaluated by means of the concept of “pseudo temperature.” With the pavement temperature measured from instrumented thermocouples, the time and temperature dependency of AC materials was integrated into one single factor, termed “effective temperature.” Via this effective temperature, pavement responses under a transient load were predicted through finite element analysis. In the finite element model, viscoelastic behavior of AC materials was characterized through relaxation moduli, while the layers with unbound granular material were assumed to be in an elastic mode. The analysis was conducted for two different AC mixtures in a simplified flexible pavement structure at two different seasons. Finite element analysis results reveal that the loading time has a more pronounced impact on pavement response in the summer for both asphalt types. The results indicate that for reasonable prediction of dynamic response in flexible pavements, the effect of the depth-dependent loading time on pavement temperature should be considered.

The accuracy of the Gaussian-and-finite-element-Coulomb (GFC) method for the calculation of Coulomb integrals.

PubMed

Przybytek, Michal; Helgaker, Trygve

2013-08-07

We analyze the accuracy of the Coulomb energy calculated using the Gaussian-and-finite-element-Coulomb (GFC) method. In this approach, the electrostatic potential associated with the molecular electronic density is obtained by solving the Poisson equation and then used to calculate matrix elements of the Coulomb operator. The molecular electrostatic potential is expanded in a mixed Gaussian-finite-element (GF) basis set consisting of Gaussian functions of s symmetry centered on the nuclei (with exponents obtained from a full optimization of the atomic potentials generated by the atomic densities from symmetry-averaged restricted open-shell Hartree-Fock theory) and shape functions defined on uniform finite elements. The quality of the GF basis is controlled by means of a small set of parameters; for a given width of the finite elements d, the highest accuracy is achieved at smallest computational cost when tricubic (n = 3) elements are used in combination with two (γ(H) = 2) and eight (γ(1st) = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (αmin (G)=0.5). The error in the calculated Coulomb energy divided by the number of atoms in the system depends on the system type but is independent of the system size or the orbital basis set, vanishing approximately like d(4) with decreasing d. If the boundary conditions for the Poisson equation are calculated in an approximate way, the GFC method may lose its variational character when the finite elements are too small; with larger elements, it is less sensitive to inaccuracies in the boundary values. As it is possible to obtain accurate boundary conditions in linear time, the overall scaling of the GFC method for large systems is governed by another computational step-namely, the generation of the three-center overlap integrals with three Gaussian orbitals. The most unfavorable (nearly quadratic) scaling is observed for compact, truly three-dimensional systems; however, this scaling can be reduced to linear by introducing more effective techniques for recognizing significant three-center overlap distributions.

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.

Calculation of Reaction Forces in the Boiler Supports Using the Method of Equivalent Stiffness of Membrane Wall

PubMed Central

Sertić, Josip; Kozak, Dražan; Samardžić, Ivan

2014-01-01

The values of reaction forces in the boiler supports are the basis for the dimensioning of bearing steel structure of steam boiler. In this paper, the application of the method of equivalent stiffness of membrane wall is proposed for the calculation of reaction forces. The method of equalizing displacement, as the method of homogenization of membrane wall stiffness, was applied. On the example of “Milano” boiler, using the finite element method, the calculation of reactions in the supports for the real geometry discretized by the shell finite element was made. The second calculation was performed with the assumption of ideal stiffness of membrane walls and the third using the method of equivalent stiffness of membrane wall. In the third case, the membrane walls are approximated by the equivalent orthotropic plate. The approximation of membrane wall stiffness is achieved using the elasticity matrix of equivalent orthotropic plate at the level of finite element. The obtained results were compared, and the advantages of using the method of equivalent stiffness of membrane wall for the calculation of reactions in the boiler supports were emphasized. PMID:24959612

First principles calculation of finite temperature magnetism in Fe and Fe3C

NASA Astrophysics Data System (ADS)

Eisenbach, M.; Nicholson, D. M.; Rusanu, A.; Brown, G.

2011-04-01

Density functional calculations have proven to be a useful tool in the study of ground state properties of many materials. The investigation of finite temperature magnetism, on the other hand, has to rely usually on the usage of empirical models that allow the large number of evaluations of the systems Hamiltonian that are required to obtain the phase space sampling needed to obtain the free energy, specific heat, magnetization, susceptibility, and other quantities as function of temperature. We have demonstrated a solution to this problem that harnesses the computational power of today's large massively parallel computers by combining a classical Wang-Landau Monte-Carlo calculation [F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001)] with our first principles multiple scattering electronic structure code [Y. Wang et al., Phys. Rev. Lett. 75, 2867 (1995)] that allows the energy calculation of constrained magnetic states [M. Eisenbach et al., Proceedings of the Conference on High Performance Computing, Networking, Storage and Analysis (ACM, New York, 2009)]. We present our calculations of finite temperature properties of Fe and Fe3C using this approach and we find the Curie temperatures to be 980 and 425K, respectively.

Sensitivity of finite helical axis parameters to temporally varying realistic motion utilizing an idealized knee model.

PubMed

Johnson, T S; Andriacchi, T P; Erdman, A G

2004-01-01

Various uses of the screw or helical axis have previously been reported in the literature in an attempt to quantify the complex displacements and coupled rotations of in vivo human knee kinematics. Multiple methods have been used by previous authors to calculate the axis parameters, and it has been theorized that the mathematical stability and accuracy of the finite helical axis (FHA) is highly dependent on experimental variability and rotation increment spacing between axis calculations. Previous research has not addressed the sensitivity of the FHA for true in vivo data collection, as required for gait laboratory analysis. This research presents a controlled series of experiments simulating continuous data collection as utilized in gait analysis to investigate the sensitivity of the three-dimensional finite screw axis parameters of rotation, displacement, orientation and location with regard to time step increment spacing, utilizing two different methods for spatial location. Six-degree-of-freedom motion parameters are measured for an idealized rigid body knee model that is constrained to a planar motion profile for the purposes of error analysis. The kinematic data are collected using a multicamera optoelectronic system combined with an error minimization algorithm known as the point cluster method. Rotation about the screw axis is seen to be repeatable, accurate and time step increment insensitive. Displacement along the axis is highly dependent on time step increment sizing, with smaller rotation angles between calculations producing more accuracy. Orientation of the axis in space is accurate with only a slight filtering effect noticed during motion reversal. Locating the screw axis by a projected point onto the screw axis from the mid-point of the finite displacement is found to be less sensitive to motion reversal than finding the intersection of the axis with a reference plane. A filtering effect of the spatial location parameters was noted for larger time step increments during periods of little or no rotation.

Effect of different CT scanners and settings on femoral failure loads calculated by finite element models.

PubMed

Eggermont, Florieke; Derikx, Loes C; Free, Jeffrey; van Leeuwen, Ruud; van der Linden, Yvette M; Verdonschot, Nico; Tanck, Esther

2018-03-06

In a multi-center patient study, using different CT scanners, CT-based finite element (FE) models are utilized to calculate failure loads of femora with metastases. Previous studies showed that using different CT scanners can result in different outcomes. This study aims to quantify the effects of (i) different CT scanners; (ii) different CT protocols with variations in slice thickness, field of view (FOV), and reconstruction kernel; and (iii) air between calibration phantom and patient, on Hounsfield Units (HU), bone mineral density (BMD), and FE failure load. Six cadaveric femora were scanned on four CT scanners. Scans were made with multiple CT protocols and with or without an air gap between the body model and calibration phantom. HU and calibrated BMD were determined in cortical and trabecular regions of interest. Non-linear isotropic FE models were constructed to calculate failure load. Mean differences between CT scanners varied up to 7% in cortical HU, 6% in trabecular HU, 6% in cortical BMD, 12% in trabecular BMD, and 17% in failure load. Changes in slice thickness and FOV had little effect (≤4%), while reconstruction kernels had a larger effect on HU (16%), BMD (17%), and failure load (9%). Air between the body model and calibration phantom slightly decreased the HU, BMD, and failure loads (≤8%). In conclusion, this study showed that quantitative analysis of CT images acquired with different CT scanners, and particularly reconstruction kernels, can induce relatively large differences in HU, BMD, and failure loads. Additionally, if possible, air artifacts should be avoided. © 2018 Orthopaedic Research Society. © 2018 The Authors. Journal of Orthopaedic Research® Published by Wiley Periodicals, Inc. on behalf of the Orthopaedic Research Society. J Orthop Res. © 2018 The Authors. Journal of Orthopaedic Research® Published by Wiley Periodicals, Inc. on behalf of the Orthopaedic Research Society.

A re-evaluation of finite-element models and stress-intensity factors for surface cracks emanating from stress concentrations

NASA Technical Reports Server (NTRS)

Tan, P. W.; Raju, I. S.; Shivakumar, K. N.; Newman, J. C., Jr.

1988-01-01

A re-evaluation of the 3-D finite-element models and methods used to analyze surface crack at stress concentrations is presented. Previous finite-element models used by Raju and Newman for surface and corner cracks at holes were shown to have ill-shaped elements at the intersection of the hole and crack boundaries. These ill-shaped elements tended to make the model too stiff and, hence, gave lower stress-intensity factors near the hole-crack intersection than models without these elements. Improved models, without these ill-shaped elements, were developed for a surface crack at a circular hole and at a semi-circular edge notch. Stress-intensity factors were calculated by both the nodal-force and virtual-crack-closure methods. Both methods and different models gave essentially the same results. Comparisons made between the previously developed stress-intensity factor equations and the results from the improved models agreed well except for configurations with large notch-radii-to-plate-thickness ratios. Stress-intensity factors for a semi-elliptical surface crack located at the center of a semi-circular edge notch in a plate subjected to remote tensile loadings were calculated using the improved models. The ratio of crack depth to crack length ranged form 0.4 to 2; the ratio of crack depth to plate thickness ranged from 0.2 to 0.8; and the ratio of notch radius to the plate thickness ranged from 1 to 3. The models had about 15,000 degrees-of-freedom. Stress-intensity factors were calculated by using the nodal-force method.

The generator coordinate Dirac-Fock method for open-shell atomic systems

NASA Astrophysics Data System (ADS)

Malli, Gulzari L.; Ishikawa, Yasuyuki

1998-11-01

Recently we developed generator coordinate Dirac-Fock and Dirac-Fock-Breit methods for closed-shell systems assuming finite nucleus and have reported Dirac-Fock and Dirac-Fock-Breit energies for the atoms He through Nobelium (Z=102) [see Refs. Reference 10Reference 11Reference 12Reference 13]. In this paper, we generalize our earlier work on closed-shell systems and develop a generator coordinate Dirac-Fock method for open-shell systems. We present results for a number of representative open-shell heavy atoms (with nuclear charge Z>80) including the actinide and superheavy transactinide (with Z>103) atomic systems: Fr (Z=87), Ac (Z=89), and Lr (Z=103) to E113 (eka-thallium, Z=113). The high accuracy obtained in our open-shell Dirac-Fock calculations is similar to that of our closed-shell calculations, and we attribute it to the fact that the representation of the relativistic dynamics of an electron in a spherical ball finite nucleus near the origin in terms of our universal Gaussian basis set is as accurate as that provided by the numerical finite difference method. The DF SCF energies calculated by Desclaux [At. Data. Nucl. Data Tables 12, 311 (1973)] (apart from a typographic error for Fr pointed out here) are higher than those reported here for atoms of some of the superheavy transactinide elements by as much as 5 hartrees (136 eV). We believe that this is due to the use by Desclaux of much larger atomic masses than the currently accepted values for these elements.

Notch Sensitivity of Woven Ceramic Matrix Composites Under Tensile Loading: An Experimental, Analytical, and Finite Element Study

NASA Technical Reports Server (NTRS)

Haque, A.; Ahmed, L.; Ware, T.; Jeelani, S.; Verrilli, Michael J. (Technical Monitor)

2001-01-01

The stress concentrations associated with circular notches and subjected to uniform tensile loading in woven ceramic matrix composites (CMCs) have been investigated for high-efficient turbine engine applications. The CMC's were composed of Nicalon silicon carbide woven fabric in SiNC matrix manufactured through polymer impregnation process (PIP). Several combinations of hole diameter/plate width ratios and ply orientations were considered in this study. In the first part, the stress concentrations were calculated measuring strain distributions surrounding the hole using strain gages at different locations of the specimens during the initial portion of the stress-strain curve before any microdamage developed. The stress concentration was also calculated analytically using Lekhnitskii's solution for orthotropic plates. A finite-width correction factor for anisotropic and orthotropic composite plate was considered. The stress distributions surrounding the circular hole of a CMC's plate were further studied using finite element analysis. Both solid and shell elements were considered. The experimental results were compared with both the analytical and finite element solutions. Extensive optical and scanning electron microscopic examinations were carried out for identifying the fracture behavior and failure mechanisms of both the notched and notched specimens. The stress concentration factors (SCF) determined by analytical method overpredicted the experimental results. But the numerical solution underpredicted the experimental SCF. Stress concentration factors are shown to increase with enlarged hole size and the effects of ply orientations on stress concentration factors are observed to be negligible. In all the cases, the crack initiated at the notch edge and propagated along the width towards the edge of the specimens.

Simulation-aided constitutive law development - Assessment of low triaxiality void nucleation models via extended finite element method

NASA Astrophysics Data System (ADS)

Zhao, Jifeng; Kontsevoi, Oleg Y.; Xiong, Wei; Smith, Jacob

2017-05-01

In this work, a multi-scale computational framework has been established in order to investigate, refine and validate constitutive behaviors in the context of the Gurson-Tvergaard-Needleman (GTN) void mechanics model. The eXtended Finite Element Method (XFEM) has been implemented in order to (1) develop statistical volume elements (SVE) of a matrix material with subscale inclusions and (2) to simulate the multi-void nucleation process due to interface debonding between the matrix and particle phases. Our analyses strongly suggest that under low stress triaxiality the nucleation rate of the voids f˙ can be well described by a normal distribution function with respect to the matrix equivalent stress (σe), as opposed to that proposed (σbar + 1 / 3σkk) in the original form of the single void GTN model. The modified form of the multi-void nucleation model has been validated based on a series of numerical experiments with different loading conditions, material properties, particle shape/size and spatial distributions. The utilization of XFEM allows for an invariant finite element mesh to represent varying microstructures, which implies suitability for drastically reducing complexity in generating the finite element discretizations for large stochastic arrays of microstructure configurations. The modified form of the multi-void nucleation model is further applied to study high strength steels by incorporating first principles calculations. The necessity of using a phenomenological interface separation law has been fully eliminated and replaced by the physics-based cohesive relationship obtained from Density Functional Theory (DFT) calculations in order to provide an accurate macroscopic material response.

Finite Element modelling of deformation induced by interacting volcanic sources

NASA Astrophysics Data System (ADS)

Pascal, Karen; Neuberg, Jürgen; Rivalta, Eleonora

2010-05-01

The displacement field due to magma movements in the subsurface is commonly modelled using the solutions for a point source (Mogi, 1958), a finite spherical source (McTigue, 1987), or a dislocation source (Okada, 1992) embedded in a homogeneous elastic half-space. When the magmatic system comprises more than one source, the assumption of homogeneity in the half-space is violated and several sources are combined, their respective deformation field being summed. We have investigated the effects of neglecting the interaction between sources on the surface deformation field. To do so, we calculated the vertical and horizontal displacements for models with adjacent sources and we tested them against the solutions of corresponding numerical 3D finite element models. We implemented several models combining spherical pressure sources and dislocation sources, varying their relative position. Furthermore we considered the impact of topography, loading, and magma compressibility. To quantify the discrepancies and compare the various models, we calculated the difference between analytical and numerical maximum horizontal or vertical surface displacements.We will demonstrate that for certain conditions combining analytical sources can cause an error of up to 20%. References: McTigue, D. F. (1987), Elastic Stress and Deformation Near a Finite Spherical Magma Body: Resolution of the Point Source Paradox, J. Geophys. Res. 92, 12931-12940. Mogi, K. (1958), Relations between the eruptions of various volcanoes and the deformations of the ground surfaces around them, Bull Earthquake Res Inst, Univ Tokyo 36, 99-134. Okada, Y. (1992), Internal Deformation Due to Shear and Tensile Faults in a Half-Space, Bulletin of the Seismological Society of America 82(2), 1018-1040.

Note on use of slope diffraction coefficients for aperture antennas on finite ground planes

NASA Technical Reports Server (NTRS)

Cockrell, C. R.; Beck, F. B.

1995-01-01

The use of slope diffraction coefficients along with regular diffraction coefficients for calculating the radiation patterns of aperture antennas in a finite ground plane is investigated. Explicit expressions for regular diffraction coefficients and slope diffraction coefficients are presented. The expressions for the incident magnetic field in terms of the magnetic current in the aperture are given. The slope of the incident magnetic field is calculated and closed form expressions are presented.

Thermal analysis and experimental study of end-pumped Nd: YLF laser at 1053 nm

NASA Astrophysics Data System (ADS)

El-Agmy, R. M.; Al-Hosiny, N.

2017-12-01

We have numerically analyzed the thermal effects in Nd: YLF laser rod. The calculations of temperature and stress distributions in the Nd: YLF laser rod was performed with finite element (FE) simulations. The calculations showed that the laser rod could be pumped up to a power of 40 W without fracture caused by thermal stress. The calculated thermal lens power of thermally induced lens in Nd: YLF ( σ-polarization) laser rod was analyzed and validated experimentally with two independent techniques. A Shack-Hartmann wavefront sensor and a Mach-Zehnder interferometer were used for direct measurements of focal thermal lens at different pump powers. The obtained measurements were coinciding with the FE simulations.

Calculation of unsteady aerodynamics for four AGARD standard aeroelastic configurations

NASA Technical Reports Server (NTRS)

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

1984-01-01

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

NUMERICAL ANALYSES FOR TREATING DIFFUSION IN SINGLE-, TWO-, AND THREE-PHASE BINARY ALLOY SYSTEMS

NASA Technical Reports Server (NTRS)

Tenney, D. R.

1994-01-01

This package consists of a series of three computer programs for treating one-dimensional transient diffusion problems in single and multiple phase binary alloy systems. An accurate understanding of the diffusion process is important in the development and production of binary alloys. Previous solutions of the diffusion equations were highly restricted in their scope and application. The finite-difference solutions developed for this package are applicable for planar, cylindrical, and spherical geometries with any diffusion-zone size and any continuous variation of the diffusion coefficient with concentration. Special techniques were included to account for differences in modal volumes, initiation and growth of an intermediate phase, disappearance of a phase, and the presence of an initial composition profile in the specimen. In each analysis, an effort was made to achieve good accuracy while minimizing computation time. The solutions to the diffusion equations for single-, two-, and threephase binary alloy systems are numerically calculated by the three programs NAD1, NAD2, and NAD3. NAD1 treats the diffusion between pure metals which belong to a single-phase system. Diffusion in this system is described by a one-dimensional Fick's second law and will result in a continuous composition variation. For computational purposes, Fick's second law is expressed as an explicit second-order finite difference equation. Finite difference calculations are made by choosing the grid spacing small enough to give convergent solutions of acceptable accuracy. NAD2 treats diffusion between pure metals which form a two-phase system. Diffusion in the twophase system is described by two partial differential equations (a Fick's second law for each phase) and an interface-flux-balance equation which describes the location of the interface. Actual interface motion is obtained by a mass conservation procedure. To account for changes in the thicknesses of the two phases as diffusion progresses, a variable grid technique developed by Murray and Landis is employed. These equations are expressed in finite difference form and solved numerically. Program NAD3 treats diffusion between pure metals which form a two-phase system with an intermediate third phase. Diffusion in the three-phase system is described by three partial differential expressions of Fick's second law and two interface-flux-balance equations. As with the two-phase case, a variable grid finite difference is used to numerically solve the diffusion equations. Computation time is minimized without sacrificing solution accuracy by treating the three-phase problem as a two-phase problem when the thickness of the intermediate phase is less than a preset value. Comparisons between these programs and other solutions have shown excellent agreement. The programs are written in FORTRAN IV for batch execution on the CDC 6600 with a central memory requirement of approximately 51K (octal) 60 bit words.

The decline of soil due to the pile of highway project Medan-Kualanamu (STA 35 + 901) with the finite element method

NASA Astrophysics Data System (ADS)

Hastuty, I. P.; Roesyanto; Sihite, A. B.

2018-02-01

Consolidation is the process of discharge of water from the ground through the pore cavity. Consolidation occurs in soft soil or unstable soil that allows an improvement in order to make the soil more stable. The method of using Prefabricated Vertical Drain (PVD) is one way to improve unstable soils. PVD works like a sand column that can drain water vertically. This study aims to determine the decrease, pore water pressure and soil consolidation rate with Prefabricated Vertical Drain (PVD) and without PVD analytically and using finite element method that affect the duration of soil decline to reach 90% consolidation or in other words soil does not decline anymore. Based on the analytical calculation, the decrease obtained is equal to 0.47 m meanwhile the result of calculation using finite element method is 0.45 m. The consolidation rate obtained from analytical calculation is 19 days with PVD and 115 days without PVD. The consolidation rate obtained from finite element method is 63 days with PVD and 110 days without PVD. And the pore water pressure is 0.92 KN/m2.

Power flows and Mechanical Intensities in structural finite element analysis

NASA Technical Reports Server (NTRS)

Hambric, Stephen A.

1989-01-01

The identification of power flow paths in dynamically loaded structures is an important, but currently unavailable, capability for the finite element analyst. For this reason, methods for calculating power flows and mechanical intensities in finite element models are developed here. Formulations for calculating input and output powers, power flows, mechanical intensities, and power dissipations for beam, plate, and solid element types are derived. NASTRAN is used to calculate the required velocity, force, and stress results of an analysis, which a post-processor then uses to calculate power flow quantities. The SDRC I-deas Supertab module is used to view the final results. Test models include a simple truss and a beam-stiffened cantilever plate. Both test cases showed reasonable power flow fields over low to medium frequencies, with accurate power balances. Future work will include testing with more complex models, developing an interactive graphics program to view easily and efficiently the analysis results, applying shape optimization methods to the problem with power flow variables as design constraints, and adding the power flow capability to NASTRAN.

Optimal Tikhonov Regularization in Finite-Frequency Tomography

NASA Astrophysics Data System (ADS)

Fang, Y.; Yao, Z.; Zhou, Y.

2017-12-01

The last decade has witnessed a progressive transition in seismic tomography from ray theory to finite-frequency theory which overcomes the resolution limit of the high-frequency approximation in ray theory. In addition to approximations in wave propagation physics, a main difference between ray-theoretical tomography and finite-frequency tomography is the sparseness of the associated sensitivity matrix. It is well known that seismic tomographic problems are ill-posed and regularizations such as damping and smoothing are often applied to analyze the tradeoff between data misfit and model uncertainty. The regularizations depend on the structure of the matrix as well as noise level of the data. Cross-validation has been used to constrain data uncertainties in body-wave finite-frequency inversions when measurements at multiple frequencies are available to invert for a common structure. In this study, we explore an optimal Tikhonov regularization in surface-wave phase-velocity tomography based on minimization of an empirical Bayes risk function using theoretical training datasets. We exploit the structure of the sensitivity matrix in the framework of singular value decomposition (SVD) which also allows for the calculation of complete resolution matrix. We compare the optimal Tikhonov regularization in finite-frequency tomography with traditional tradeo-off analysis using surface wave dispersion measurements from global as well as regional studies.

Assessment of the performance of rigid pavement back-calculation through finite element modeling

NASA Astrophysics Data System (ADS)

Shoukry, Samir N.; William, Gergis W.; Martinelli, David R.

1999-02-01

This study focuses on examining the behavior of rigid pavement layers during the Falling Weight Deflectometer (FWD) test. Factors affecting the design of a concrete slab, such as whether the joints are doweled or undoweled and the spacing between the transverse joints, were considered in this study. Explicit finite element analysis was employed to investigate pavement layers' responses to the action of the impulse of the FWD test. Models of various dimensions were developed to satisfy the factors under consideration. The accuracy of the finite element models developed in this investigation was verified by comparing the finite element- generated deflection basin with that experimentally measured during an actual test. The results showed that the measured deflection basin can be reproduced through finite element modeling of the pavement structure. The resulting deflection basins from the use FE modeling was processed in order to backcalculate pavement layer moduli. This approach provides a method for the evaluation of the performance of existing backcalculation programs which are based on static elastic layer analysis. Based upon the previous studies conducted for the selection of software, three different backcalculation programs were chosen for the evaluation: MODULUS5.0, EVERCALC4.0, and MODCOMP3. The results indicate that ignoring the dynamic nature of the load may lead to crude results, especially during backcalculation procedures.

Analytic calculation of finite-population reproductive numbers for direct- and vector-transmitted diseases with homogeneous mixing.

PubMed

Keegan, Lindsay; Dushoff, Jonathan

2014-05-01

The basic reproductive number, R0, provides a foundation for evaluating how various factors affect the incidence of infectious diseases. Recently, it has been suggested that, particularly for vector-transmitted diseases, R0 should be modified to account for the effects of finite host population within a single disease transmission generation. Here, we use a transmission factor approach to calculate such "finite-population reproductive numbers," under the assumption of homogeneous mixing, for both vector-borne and directly transmitted diseases. In the case of vector-borne diseases, we estimate finite-population reproductive numbers for both host-to-host and vector-to-vector generations, assuming that the vector population is effectively infinite. We find simple, interpretable formulas for all three of these quantities. In the direct case, we find that finite-population reproductive numbers diverge from R0 before R0 reaches half of the population size. In the vector-transmitted case, we find that the host-to-host number diverges at even lower values of R0, while the vector-to-vector number diverges very little over realistic parameter ranges.

Insights on finite size effects in ab initio study of CO adsorption and dissociation on Fe 110 surface

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

Chakrabarty, Aurab, E-mail: aurab.chakrabarty@qatar.tamu.edu; Bouhali, Othmane; Mousseau, Normand

Adsorption and dissociation of hydrocarbons on metallic surfaces represent crucial steps on the path to carburization, eventually leading to dusting corrosion. While adsorption of CO molecules on Fe surface is a barrier-less exothermic process, this is not the case for the dissociation of CO into C and O adatoms and the diffusion of C beneath the surface that are found to be associated with large energy barriers. In practice, these barriers can be affected by numerous factors that combine to favour the CO-Fe reaction such as the abundance of CO and other hydrocarbons as well as the presence of structuralmore » defects. From a numerical point of view, studying these factors is challenging and a step-by-step approach is necessary to assess, in particular, the influence of the finite box size on the reaction parameters for adsorption and dissociation of CO on metal surfaces. Here, we use density functional theory (DFT) total energy calculations with the climbing-image nudged elastic band method to estimate the adsorption energies and dissociation barriers for different CO coverages with surface supercells of different sizes. We further compute the effect of periodic boundary condition for DFT calculations and find that the contribution from van der Waals interaction in the computation of adsorption parameters is important as they contribute to correcting the finite-size error in small systems. The dissociation process involves carbon insertion into the Fe surface causing a lattice deformation that requires a larger surface system for unrestricted relaxation. We show that, in the larger surface systems associated with dilute CO-coverages, C-insertion is energetically more favourable, leading to a significant decrease in the dissociation barrier. This observation suggests that a large surface system with dilute coverage is necessary for all similar metal-hydrocarbon reactions in order to study their fundamental electronic mechanisms, as an isolated phenomenon, free from finite-size effects.« less

Insights on finite size effects in ab initio study of CO adsorption and dissociation on Fe 110 surface

NASA Astrophysics Data System (ADS)

Chakrabarty, Aurab; Bouhali, Othmane; Mousseau, Normand; Becquart, Charlotte S.; El-Mellouhi, Fedwa

2016-08-01

Adsorption and dissociation of hydrocarbons on metallic surfaces represent crucial steps on the path to carburization, eventually leading to dusting corrosion. While adsorption of CO molecules on Fe surface is a barrier-less exothermic process, this is not the case for the dissociation of CO into C and O adatoms and the diffusion of C beneath the surface that are found to be associated with large energy barriers. In practice, these barriers can be affected by numerous factors that combine to favour the CO-Fe reaction such as the abundance of CO and other hydrocarbons as well as the presence of structural defects. From a numerical point of view, studying these factors is challenging and a step-by-step approach is necessary to assess, in particular, the influence of the finite box size on the reaction parameters for adsorption and dissociation of CO on metal surfaces. Here, we use density functional theory (DFT) total energy calculations with the climbing-image nudged elastic band method to estimate the adsorption energies and dissociation barriers for different CO coverages with surface supercells of different sizes. We further compute the effect of periodic boundary condition for DFT calculations and find that the contribution from van der Waals interaction in the computation of adsorption parameters is important as they contribute to correcting the finite-size error in small systems. The dissociation process involves carbon insertion into the Fe surface causing a lattice deformation that requires a larger surface system for unrestricted relaxation. We show that, in the larger surface systems associated with dilute CO-coverages, C-insertion is energetically more favourable, leading to a significant decrease in the dissociation barrier. This observation suggests that a large surface system with dilute coverage is necessary for all similar metal-hydrocarbon reactions in order to study their fundamental electronic mechanisms, as an isolated phenomenon, free from finite-size effects.

Tension fatigue of glass/epoxy and graphite/epoxy tapered laminates

NASA Technical Reports Server (NTRS)

Murri, Gretchen B.; Obrien, T. Kevin; Salpekar, Satish A.

1990-01-01

Symmetric tapered laminates with internally dropped plies were tested with two different layups and two materials, S2/SP250 glass/epoxy and IM6/1827I graphite/epoxy. The specimens were loaded in cyclic tension until they delaminated unstably. Each combination of material and layup had a unique failure mode. Calculated values of strain energy release rate, G, from a finite element analysis model of delamination along the taper, and for delamination from a matrix ply crack, were used with mode I fatigue characterization data from tests of the tested materials to calculate expected delamination onset loads. Calculated values were compared to the experimental results. The comparison showed that when the calculated G was chosen according to the observed delamination failures, the agreement between the calculated and measured delamination onset loads was reasonable for each combination of layup and material.

Finite element methods for the biomechanics of soft hydrated tissues: nonlinear analysis and adaptive control of meshes.

PubMed

Spilker, R L; de Almeida, E S; Donzelli, P S

1992-01-01

This chapter addresses computationally demanding numerical formulations in the biomechanics of soft tissues. The theory of mixtures can be used to represent soft hydrated tissues in the human musculoskeletal system as a two-phase continuum consisting of an incompressible solid phase (collagen and proteoglycan) and an incompressible fluid phase (interstitial water). We first consider the finite deformation of soft hydrated tissues in which the solid phase is represented as hyperelastic. A finite element formulation of the governing nonlinear biphasic equations is presented based on a mixed-penalty approach and derived using the weighted residual method. Fluid and solid phase deformation, velocity, and pressure are interpolated within each element, and the pressure variables within each element are eliminated at the element level. A system of nonlinear, first-order differential equations in the fluid and solid phase deformation and velocity is obtained. In order to solve these equations, the contributions of the hyperelastic solid phase are incrementally linearized, a finite difference rule is introduced for temporal discretization, and an iterative scheme is adopted to achieve equilibrium at the end of each time increment. We demonstrate the accuracy and adequacy of the procedure using a six-node, isoparametric axisymmetric element, and we present an example problem for which independent numerical solution is available. Next, we present an automated, adaptive environment for the simulation of soft tissue continua in which the finite element analysis is coupled with automatic mesh generation, error indicators, and projection methods. Mesh generation and updating, including both refinement and coarsening, for the two-dimensional examples examined in this study are performed using the finite quadtree approach. The adaptive analysis is based on an error indicator which is the L2 norm of the difference between the finite element solution and a projected finite element solution. Total stress, calculated as the sum of the solid and fluid phase stresses, is used in the error indicator. To allow the finite difference algorithm to proceed in time using an updated mesh, solution values must be transferred to the new nodal locations. This rezoning is accomplished using a projected field for the primary variables. The accuracy and effectiveness of this adaptive finite element analysis is demonstrated using a linear, two-dimensional, axisymmetric problem corresponding to the indentation of a thin sheet of soft tissue. The method is shown to effectively capture the steep gradients and to produce solutions in good agreement with independent, converged, numerical solutions.

A 3D finite element model to investigate prosthetic interface stresses of different posterior tibial slope.

PubMed

Shen, Yi; Li, Xiaomiao; Fu, Xiaodong; Wang, Weili

2015-11-01

Posterior tibial slope that is created during proximal tibial resection in total knee arthroplasty has emerged as an important factor in the mechanics of the knee joint and the surgical outcome. But the ideal degree of posterior tibial slope for recovery of the knee joint function and preventions of complications remains controversial and should vary in different racial groups. The objective of this paper is to investigate the effects of posterior tibial slope on contact stresses in the tibial polyethylene component of total knee prostheses. Three-dimensional finite element analysis was used to calculate contact stresses in tibial polyethylene component of total knee prostheses subjected to a compressive load. The 3D finite element model of total knee prosthesis was constructed from the images produced by 3D scanning technology. Stresses in tibial polyethylene component were calculated with four different posterior tibial slopes (0°, 3°, 6° and 9°). The 3D finite element model of total knee prosthesis we presented was well validated. We found that the stress distribution in the polythene as evaluated by the distributions of the von Mises stress, the maximum principle stress, the minimum principle stress and the Cpress were more uniform with 3° and 6° posterior tibial slopes than with 0° and 9° posterior tibial slopes. Moreover, the peaks of the above stresses and trends of changes with increasing degree of knee flexion were more ideal with 3° and 6° posterior slopes. The results suggested that the tibial component inclination might be favourable to 7°-10° so far as the stress distribution is concerned. The range of the tibial component inclination also can decrease the wear of polyethylene. Chinese posterior tibial slope is bigger than in the West, and the current domestic use of prostheses is imported from the West, so their demands to tilt back bone cutting can lead to shorten the service life of prostheses; this experiment result is of important clinical significance, guiding orthopaedic surgeon after the best angle to cut bone.

76 FR 77563 - Florida Power & Light Company; St. Lucie Plant, Unit No. 1; Exemption

Federal Register 2010, 2011, 2012, 2013, 2014

2011-12-13

....2, because the P-T limits developed for St. Lucie, Unit 1, use a finite element method to determine... Code for calculating K Im factors, and instead applies FEM [finite element modeling] methods for...

Characterization of anisotropically shaped silver nanoparticle arrays via spectroscopic ellipsometry supported by numerical optical modeling

NASA Astrophysics Data System (ADS)

Gkogkou, Dimitra; Shaykhutdinov, Timur; Oates, Thomas W. H.; Gernert, Ulrich; Schreiber, Benjamin; Facsko, Stefan; Hildebrandt, Peter; Weidinger, Inez M.; Esser, Norbert; Hinrichs, Karsten

2017-11-01

The present investigation aims to study the optical response of anisotropic Ag nanoparticle arrays deposited on rippled silicon substrates by performing a qualitative comparison between experimental and theoretical results. Spectroscopic ellipsometry was used along with numerical calculations using finite-difference time-domain (FDTD) method and rigorous coupled wave analysis (RCWA) to reveal trends in the optical and geometrical properties of the nanoparticle array. Ellipsometric data show two resonances, in the orthogonal x and y directions, that originate from localized plasmon resonances as demonstrated by the calculated near-fields from FDTD calculations. The far-field calculations by RCWA point to decoupled resonances in x direction and possible coupling effects in y direction, corresponding to the short and long axis of the anisotropic nanoparticles, respectively.

A triangular thin shell finite element: Nonlinear analysis. [structural analysis

NASA Technical Reports Server (NTRS)

Thomas, G. R.; Gallagher, R. H.

1975-01-01

Aspects of the formulation of a triangular thin shell finite element which pertain to geometrically nonlinear (small strain, finite displacement) behavior are described. The procedure for solution of the resulting nonlinear algebraic equations combines a one-step incremental (tangent stiffness) approach with one iteration in the Newton-Raphson mode. A method is presented which permits a rational estimation of step size in this procedure. Limit points are calculated by means of a superposition scheme coupled to the incremental side of the solution procedure while bifurcation points are calculated through a process of interpolation of the determinants of the tangent-stiffness matrix. Numerical results are obtained for a flat plate and two curved shell problems and are compared with alternative solutions.

Mechanical properties investigation on single-wall ZrO2 nanotubes: A finite element method with equivalent Poisson's ratio for chemical bonds

NASA Astrophysics Data System (ADS)

Yang, Xiao; Li, Huijian; Hu, Minzheng; Liu, Zeliang; Wärnå, John; Cao, Yuying; Ahuja, Rajeev; Luo, Wei

2018-04-01

A method to obtain the equivalent Poisson's ratio in chemical bonds as classical beams with finite element method was proposed from experimental data. The UFF (Universal Force Field) method was employed to calculate the elastic force constants of Zrsbnd O bonds. By applying the equivalent Poisson's ratio, the mechanical properties of single-wall ZrNTs (ZrO2 nanotubes) were investigated by finite element analysis. The nanotubes' Young's modulus (Y), Poisson's ratio (ν) of ZrNTs as function of diameters, length and chirality have been discussed, respectively. We found that the Young's modulus of single-wall ZrNTs is calculated to be between 350 and 420 GPa.

Two-Nucleon Systems in a Finite Volume

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

Briceno, Raul

2014-11-01

I present the formalism and methodology for determining the nucleon-nucleon scattering parameters from the finite volume spectra obtained from lattice quantum chromodynamics calculations. Using the recently derived energy quantization conditions and the experimentally determined scattering parameters, the bound state spectra for finite volume systems with overlap with the 3S1-3D3 channel are predicted for a range of volumes. It is shown that the extractions of the infinite-volume deuteron binding energy and the low-energy scattering parameters, including the S-D mixing angle, are possible from Lattice QCD calculations of two-nucleon systems with boosts of |P| <= 2pi sqrt{3}/L in volumes with spatial extentsmore » L satisfying fm <~ L <~ 14 fm.« less

Nonlinear temperature dependent failure analysis of finite width composite laminates

NASA Technical Reports Server (NTRS)

Nagarkar, A. P.; Herakovich, C. T.

1979-01-01

A quasi-three dimensional, nonlinear elastic finite element stress analysis of finite width composite laminates including curing stresses is presented. Cross-ply, angle-ply, and two quasi-isotropic graphite/epoxy laminates are studied. Curing stresses are calculated using temperature dependent elastic properties that are input as percent retention curves, and stresses due to mechanical loading in the form of an axial strain are calculated using tangent modulii obtained by Ramberg-Osgood parameters. It is shown that curing stresses and stresses due to tensile loading are significant as edge effects in all types of laminate studies. The tensor polynomial failure criterion is used to predict the initiation of failure. The mode of failure is predicted by examining individual stress contributions to the tensor polynomial.

Modelling of Jupiter's Innermost Radiation Belt

NASA Technical Reports Server (NTRS)

Mihalov, J. D.; DeVincenzi, Donald (Technical Monitor)

1999-01-01

In order to understand better source and loss processes for energetic trapped protons near Jupiter, a modification of de Pater and Goertz' finite difference diffusion calculations for Jovian equatorial energetic electrons is made to apply to the case of protons inside the orbit of Metis. Explicit account is taken of energy loss in the Jovian ring. Comparison of the results is made with Galileo Probe measurements.

Comparison of RCS prediction techniques, computations and measurements

NASA Astrophysics Data System (ADS)

Brand, M. G. E.; Vanewijk, L. J.; Klinker, F.; Schippers, H.

1992-07-01

Three calculation methods to predict radar cross sections (RCS) of three dimensional objects are evaluated by computing the radar cross sections of a generic wing inlet configuration. The following methods are applied: a three dimensional high frequency method, a three dimensional boundary element method, and a two dimensional finite difference time domain method. The results of the computations are compared with the data of measurements.

An efficient numerical technique for calculating thermal spreading resistance

NASA Technical Reports Server (NTRS)

Gale, E. H., Jr.

1977-01-01

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

Two-dimensional heat flow analysis applied to heat sterilization of ponderosa pine and Douglas-fir square timbers

Treesearch

William T. Simpson

2004-01-01

Equations for a two-dimensional finite difference heat flow analysis were developed and applied to ponderosa pine and Douglas-fir square timbers to calculate the time required to heat the center of the squares to target temperature. The squares were solid piled, which made their surfaces inaccessible to the heating air, and thus surface temperatures failed to attain...

Tapered holey fibers for spot-size and numerical-aperture conversion.

PubMed

Town, G E; Lizier, J T

2001-07-15

Adiabatically tapered holey fibers are shown to be potentially useful for guided-wave spot-size and numerical-aperture conversion. Conditions for adiabaticity and design guidelines are provided in terms of the effective-index model. We also present finite-difference time-domain calculations of downtapered holey fiber, showing that large spot-size conversion factors are obtainable with minimal loss by use of short, optimally shaped tapers.

Experimental Quiet Sprocket Design and Noise Reduction in Tracked Vehicles

DTIC Science & Technology

1981-04-01

Track and Suspension Noise Reduction Statistical Energy Analysis Mechanical Impedance Measurement Finite Element Modal Analysis\\Noise Sources 2...shape and idler attachment are different. These differen- ces were investigated using the concepts of statistical energy analysis for hull generated noise...element r,’calculated from Statistical Energy Analysis . Such an approach will be valid within reasonable limits for frequencies of about 200 Hz and

On the stress calculation within phase-field approaches: a model for finite deformations

NASA Astrophysics Data System (ADS)

Schneider, Daniel; Schwab, Felix; Schoof, Ephraim; Reiter, Andreas; Herrmann, Christoph; Selzer, Michael; Böhlke, Thomas; Nestler, Britta

2017-08-01

Numerical simulations based on phase-field methods are indispensable in order to investigate interesting and important phenomena in the evolution of microstructures. Microscopic phase transitions are highly affected by mechanical driving forces and therefore the accurate calculation of the stresses in the transition region is essential. We present a method for stress calculations within the phase-field framework, which satisfies the mechanical jump conditions corresponding to sharp interfaces, although the sharp interface is represented as a volumetric region using the phase-field approach. This model is formulated for finite deformations, is independent of constitutive laws, and allows using any type of phase inherent inelastic strains.

Corrections of the finite relativistic contributions to the synodic month period Earth-Moon range oscillations: Agreement between the geocentric and the solar-system barycentric inertial-frame calculations

NASA Astrophysics Data System (ADS)

Nordtvedt, Ken

1993-04-01

We have corrected our calculation of the finite general relativistic contribution to the synodic month period Earth-Moon range oscillation by including previously overlooked terms in the Moon's post-Newtonian equation of motion: the corrected result x(t)~=(3gSr2/c2) cos(ω-Ω)t agrees with the Shahid-Saless calculation which was performed in the geocentric frame. It is also pointed out that at the level of a few millimeters synodic month period amplitude, the Moon's orbit is polarized by the solar radiation pressure force on the Moon.

Coupled NASTRAN/boundary element formulation for acoustic scattering

NASA Technical Reports Server (NTRS)

Everstine, Gordon C.; Henderson, Francis M.; Schuetz, Luise S.

1987-01-01

A coupled finite element/boundary element capability is described for calculating the sound pressure field scattered by an arbitrary submerged 3-D elastic structure. Structural and fluid impedances are calculated with no approximation other than discretization. The surface fluid pressures and normal velocities are first calculated by coupling a NASTRAN finite element model of the structure with a discretized form of the Helmholtz surface integral equation for the exterior field. Far field pressures are then evaluated from the surface solution using the Helmholtz exterior integral equation. The overall approach is illustrated and validated using a known analytic solution for scattering from submerged spherical shells.

Application of the Finite Element Method in Atomic and Molecular Physics

NASA Technical Reports Server (NTRS)

Shertzer, Janine

2007-01-01

The finite element method (FEM) is a numerical algorithm for solving second order differential equations. It has been successfully used to solve many problems in atomic and molecular physics, including bound state and scattering calculations. To illustrate the diversity of the method, we present here details of two applications. First, we calculate the non-adiabatic dipole polarizability of Hi by directly solving the first and second order equations of perturbation theory with FEM. In the second application, we calculate the scattering amplitude for e-H scattering (without partial wave analysis) by reducing the Schrodinger equation to set of integro-differential equations, which are then solved with FEM.

Effects of damping on mode shapes, volume 1

NASA Technical Reports Server (NTRS)

Gates, R. M.

1977-01-01

Displacement, velocity, and acceleration admittances were calculated for a realistic NASTRAN structural model of space shuttle for three conditions: liftoff, maximum dynamic pressure and end of solid rocket booster burn. The realistic model of the orbiter, external tank, and solid rocket motors included the representation of structural joint transmissibilities by finite stiffness and damping elements. Methods developed to incorporate structural joints and their damping characteristics into a finite element model of the space shuttle, to determine the point damping parameters required to produce realistic damping in the primary modes, and to calculate the effect of distributed damping on structural resonances through the calculation of admittances.

Finite area combustor theoretical rocket performance

NASA Technical Reports Server (NTRS)

Gordon, Sanford; Mcbride, Bonnie J.

1988-01-01

Previous to this report, the computer program of NASA SP-273 and NASA TM-86885 was capable of calculating theoretical rocket performance based only on the assumption of an infinite area combustion chamber (IAC). An option was added to this program which now also permits the calculation of rocket performance based on the assumption of a finite area combustion chamber (FAC). In the FAC model, the combustion process in the cylindrical chamber is assumed to be adiabatic, but nonisentropic. This results in a stagnation pressure drop from the injector face to the end of the chamber and a lower calculated performance for the FAC model than the IAC model.

A computational study of coherent structures in the wakes of two-dimensional bluff bodies

NASA Astrophysics Data System (ADS)

Pearce, Jeffrey Alan

1988-08-01

The periodic shedding of vortices from bluff bodies was first recognized in the late 1800's. Currently, there is great interest concerning the effect of vortex shedding on structures and on vehicle stability. In the design of bluff structures which will be exposed to a flow, knowledge of the shedding frequency and the amplitude of the aerodynamic forces is critical. The ability to computationally predict parameters associated with periodic vortex shedding is thus a valuable tool. In this study, the periodic shedding of vortices from several bluff body geometries is predicted. The study is conducted with a two-dimensional finite-difference code employed on various grid sizes. The effects of the grid size and time step on the accuracy of the solution are addressed. Strouhal numbers and aerodynamic force coefficients are computed for all of the bodies considered and compared with previous experimental results. Results indicate that the finite-difference code is capable of predicting periodic vortex shedding for all of the geometries tested. Refinement of the finite-difference grid was found to give little improvement in the prediction; however, the choice of time step size was shown to be critical. Predictions of Strouhal numbers were generally accurate, and the calculated aerodynamic forces generally exhibited behavior consistent with previous studies.

Theoretical and experimental investigation of the destruction of graphites in a flow of dissociated air

NASA Technical Reports Server (NTRS)

Bovina, T. A.; Zviagin, Y. V.; Markelov, N. V.; Chudetskiy, Y. V.

1986-01-01

A method is presented for calculating the heating and erosion of blunt bodies made of graphite in a high-enthalpy flow of dissociated air, assuming chemical equilibrium on the surface and taking account of the thermal effects of combustion and sublimation of graphite. The analysis involves the use of a finite difference scheme to solve an equation of unsteady heat conduction. Attention is given to the equilibrium vaporization of C, C2 and C3 molecules. The calculations agree well with experimental data for a wide range of temperatures and stagnation pressures.

Effects of thickness, insulation, and surface color on the net heat loss through an adobe wall

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

Herman, R.W.

1980-01-01

A finite difference computer program was written and run to study the net thermal losses through a large variety of adobe walls. Fifty-four different combinations of surface color, wall thickness, and insulation position and R value were modeled over a typical two week winter period for locations similar to Albuquerque, New Mexico. A transient analysis of the heat loss from the room to the interior wall surface was compared to both conventional U value and steady-state calculations.

Controllable light diffraction in woodpile photonic crystals filled with liquid crystal

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

Ho, Chih-Hua; Zeng, Hao; Wiersma, Diederik S.

2015-01-12

An approach to switching between different patterns of light beams transmitted through the woodpile photonic crystals filled with liquid crystals is proposed. The phase transition between the nematic and isotropic liquid crystal states leads to an observable variation of the spatial pattern transmitted through the photonic structure. The transmission profiles in the nematic phase also show polarization sensibility due to refractive index dependence on the field polarization. The experimental results are consistent with a numerical calculation by Finite Difference Time Domain method.

Implementation of a Pseudo-Bending Seismic Travel-Time Calculator in a Distributed Parallel Computing Environment

DTIC Science & Technology

2008-09-01

algorithms that have been proposed to accomplish it fall into three broad categories. Eikonal solvers (e.g., Vidale, 1988, 1990; Podvin and Lecomte, 1991...difference eikonal solvers, the FMM algorithm works by following a wavefront as it moves across a volume of grid points, updating the travel times in...the grid according to the eikonal differential equation, using a second-order finite-difference scheme. We chose to use FMM for our comparison because

Effects of mechanical properties of adhesive resin cements on stress distribution in fiber-reinforced composite adhesive fixed partial dentures.

PubMed

Yokoyama, Daiichiro; Shinya, Akikazu; Gomi, Harunori; Vallittu, Pekka K; Shinya, Akiyoshi

2012-01-01

Using finite element analysis (FEA), this study investigated the effects of the mechanical properties of adhesive resin cements on stress distributions in fiber-reinforced resin composite (FRC) adhesive fixed partial dentures (AFPDs). Two adhesive resin cements were compared: Super-Bond C&B and Panavia Fluoro Cement. The AFPD consisted of a pontic to replace a maxillary right lateral incisor and retainers on a maxillary central incisor and canine. FRC framework was made of isotropic, continuous, unidirectional E-glass fibers. Maximum principal stresses were calculated using finite element method (FEM). Test results revealed that differences in the mechanical properties of adhesive resin cements led to different stress distributions at the cement interfaces between AFPD and abutment teeth. Clinical implication of these findings suggested that the safety and longevity of an AFPD depended on choosing an adhesive resin cement with the appropriate mechanical properties.

Decay of Far-Flowfield in Trailing Vortices

NASA Technical Reports Server (NTRS)

Baldwin, B. S.; Chigier, N. A.; Sheaffer, Y. S.

1973-01-01

Methods for reduction of velocities in trailing vortices of large aircraft are of current interest for the purpose of shortening the waiting time between landings at central airports. We have made finite-difference calculations of the flow in turbulent wake vortices as an aid to interpretation of wind-tunnel and flight experiments directed toward that end. Finite-difference solutions are capable of adding flexibility to such investigations if they are based on an adequate model of turbulence. Interesting developments have been taking place in the knowledge of turbulence that may lead to a complete theory in the future. In the meantime, approximate methods that yield reasonable agreement with experiment are appropriate. The simplified turbulence model we have selected contains features that account for the major effects disclosed by more sophisticated models in which the parameters are not yet established. Several puzzles are thereby resolved that arose in previous theoretical investigations of wake vortices.

FORTRAN program for calculating velocities and streamlines on the hub-shroud mid-channel flow surface of an axial- or mixed-flow turbomachine. 1: User's manual

NASA Technical Reports Server (NTRS)

Katsanis, T.

1973-01-01

A FORTRAN 4 computer program has been developed that obtains a subsonic or shock-free transonic flow solution on the hub-shroud mid-channel flow surface of a turbomachine. The blade row may be fixed or rotating, and may be twisted and leaned. Flow may be axial or mixed, up to 45 deg from axial. Upstream and downstream flow variables may vary from hub to shroud, and provision is made to correct for loss of stagnation pressure. The results include velocities, streamlines, and flow angles on the flow surface; and approximate blade surface velocities. Subsonic solutions are obtained by a finite-difference stream-function solution. Transonic solutions are obtained by a velocity-gradient method, using information from a finite-difference stream-function solution at a reduced mass flow.

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.

Sensitivity Analysis for Coupled Aero-structural Systems

NASA Technical Reports Server (NTRS)

Giunta, Anthony A.

1999-01-01

A novel method has been developed for calculating gradients of aerodynamic force and moment coefficients for an aeroelastic aircraft model. This method uses the Global Sensitivity Equations (GSE) to account for the aero-structural coupling, and a reduced-order modal analysis approach to condense the coupling bandwidth between the aerodynamic and structural models. Parallel computing is applied to reduce the computational expense of the numerous high fidelity aerodynamic analyses needed for the coupled aero-structural system. Good agreement is obtained between aerodynamic force and moment gradients computed with the GSE/modal analysis approach and the same quantities computed using brute-force, computationally expensive, finite difference approximations. A comparison between the computational expense of the GSE/modal analysis method and a pure finite difference approach is presented. These results show that the GSE/modal analysis approach is the more computationally efficient technique if sensitivity analysis is to be performed for two or more aircraft design parameters.

Computation of the acoustic radiation force using the finite-difference time-domain method.

PubMed

Cai, Feiyan; Meng, Long; Jiang, Chunxiang; Pan, Yu; Zheng, Hairong

2010-10-01

The computational details related to calculating the acoustic radiation force on an object using a 2-D grid finite-difference time-domain method (FDTD) are presented. The method is based on propagating the stress and velocity fields through the grid and determining the energy flow with and without the object. The axial and radial acoustic radiation forces predicted by FDTD method are in excellent agreement with the results obtained by analytical evaluation of the scattering method. In particular, the results indicate that it is possible to trap the steel cylinder in the radial direction by optimizing the width of Gaussian source and the operation frequency. As the sizes of the relating objects are smaller than or comparable to wavelength, the algorithm presented here can be easily extended to 3-D and include torque computation algorithms, thus providing a highly flexible and universally usable computation engine.

FORTRAN program for calculating velocities and streamlines on the hub-shroud mid-channel flow surface of an axial-or mixed-flow turbomachine. 2: Programmer's manual

NASA Technical Reports Server (NTRS)

Katsanis, T.; Mcnally, W. D.

1974-01-01

A FORTRAN-IV computer program, MERIDL, has been developed that obtains a subsonic or shock-free transonic flow solution on the hub-shroud mid-channel flow surface of a turbomachine. The blade row may be fixed or rotating and may be twisted and leaned. Flow may be axial or mixed, up to 45 deg from axial. Upstream and downstream flow variables can vary from hub to shroud, and provision is made to correct for loss of stagnation pressure. The results include velocities, streamlines, and flow angles on the flow surface and approximate blade surface velocities. Subsonic solutions are obtained by a finite-difference stream-function solution. Transonic solutions are obtained by a velocity-gradient method, using information from a finite-difference stream-function solution at a reduced mass flow.

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

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

Effects of variable electrical conductivity and thermal conductivity on unsteady MHD free convection flow past an exponential accelerated inclined plate

NASA Astrophysics Data System (ADS)

Rana, B. M. Jewel; Ahmed, Rubel; Ahmmed, S. F.

2017-06-01

An analysis is carried out to investigate the effects of variable viscosity, thermal radiation, absorption of radiation and cross diffusion past an inclined exponential accelerated plate under the influence of variable heat and mass transfer. A set of suitable transformations has been used to obtain the non-dimensional coupled governing equations. Explicit finite difference technique has been used to solve the obtained numerical solutions of the present problem. Stability and convergence of the finite difference scheme have been carried out for this problem. Compaq Visual Fortran 6.6a has been used to calculate the numerical results. The effects of various physical parameters on the fluid velocity, temperature, concentration, coefficient of skin friction, rate of heat transfer, rate of mass transfer, streamlines and isotherms on the flow field have been presented graphically and discussed in details.

A novel equivalent definition of Caputo fractional derivative without singular kernel and superconvergent analysis

NASA Astrophysics Data System (ADS)

Liu, Zhengguang; Li, Xiaoli

2018-05-01

In this article, we present a new second-order finite difference discrete scheme for a fractal mobile/immobile transport model based on equivalent transformative Caputo formulation. The new transformative formulation takes the singular kernel away to make the integral calculation more efficient. Furthermore, this definition is also effective where α is a positive integer. Besides, the T-Caputo derivative also helps us to increase the convergence rate of the discretization of the α-order(0 < α < 1) Caputo derivative from O(τ2-α) to O(τ3-α), where τ is the time step. For numerical analysis, a Crank-Nicolson finite difference scheme to solve the fractal mobile/immobile transport model is introduced and analyzed. The unconditional stability and a priori estimates of the scheme are given rigorously. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.

Finite-difference time-domain (FDTD) analysis on the interaction between a metal block and a radially polarized focused beam.

PubMed

Kitamura, Kyoko; Sakai, Kyosuke; Noda, Susumu

2011-07-18

Radially polarized focused beams have attracted a great deal of attention because of their unique properties characterized by the longitudinal field. Although this longitudinal field is strongly confined to the beam axis, the energy flow, i.e., the Poynting vector, has null intensity on the axis. Hence, the interaction of the focused beam and matter has thus far been unclear. We analyzed the interactions between the focused beam and a subwavelength metal block placed at the center of the focus using three-dimensional finite-difference time-domain (FDTD) calculation. We found that most of the Poynting energy propagates through to the far-field, and that a strong enhancement of the electric field appeared on the metal surface. This enhancement is attributed to the constructive interference of the symmetric electric field and the coupling to the surface plasmon mode.

Probabilistic finite elements for fracture mechanics

NASA Technical Reports Server (NTRS)

Besterfield, Glen

1988-01-01

The probabilistic finite element method (PFEM) is developed for probabilistic fracture mechanics (PFM). A finite element which has the near crack-tip singular strain embedded in the element is used. Probabilistic distributions, such as expectation, covariance and correlation stress intensity factors, are calculated for random load, random material and random crack length. The method is computationally quite efficient and can be expected to determine the probability of fracture or reliability.

Finitized conformal spectrum of the Ising model on the cylinder and torus

NASA Astrophysics Data System (ADS)

O'Brien, David L.; Pearce, Paul A.; Ole Warnaar, S.

1996-02-01

The spectrum of the critical Ising model on a lattice with cylindrical and toroidal boundary conditions is calculated by commuting transfer matrix methods. Using a simple truncation procedure, we obtain the natural finitizations of the conformal spectra recently proposed by Melzer. These finitizations imply polynomial identities which in the large lattice limit give rise to the Rogers-Ramanujan identities for the c = {1}/{2} Virasoro characters.

Study on the adjustment capability of the excitation system located inside superconducting machine electromagnetic shield

NASA Astrophysics Data System (ADS)

Xia, D.; Xia, Z.

2017-12-01

The ability for the excitation system to adjust quickly plays a very important role in maintaining the normal operation of superconducting machines and power systems. However, the eddy currents in the electromagnetic shield of superconducting machines hinder the exciting magnetic field change and weaken the adjustment capability of the excitation system. To analyze this problem, a finite element calculation model for the transient electromagnetic field with moving parts is established. The effects of three different electromagnetic shields on the exciting magnetic field are analyzed using finite element method. The results show that the electromagnetic shield hinders the field changes significantly, the better its conductivity, the greater the effect on the superconducting machine excitation.