Determination of the Rotational Barrier in Ethane by Vibrational Spectroscopy and Statistical Thermodynamics

ERIC Educational Resources Information Center

Ercolani, Gianfranco

2005-01-01

The finite-difference boundary-value method is a numerical method suited for the solution of the one-dimensional Schrodinger equation encountered in problems of hindered rotation. Further, the application of the method, in combination with experimental results for the evaluation of the rotational energy barrier in ethane is presented.

Statistical mechanics of a single particle in a multiscale random potential: Parisi landscapes in finite-dimensional Euclidean spaces

NASA Astrophysics Data System (ADS)

Fyodorov, Yan V.; Bouchaud, Jean-Philippe

2008-08-01

We construct an N-dimensional Gaussian landscape with multiscale, translation invariant, logarithmic correlations and investigate the statistical mechanics of a single particle in this environment. In the limit of high dimension N → ∞ the free energy of the system and overlap function are calculated exactly using the replica trick and Parisi's hierarchical ansatz. In the thermodynamic limit, we recover the most general version of the Derrida's generalized random energy model (GREM). The low-temperature behaviour depends essentially on the spectrum of length scales involved in the construction of the landscape. If the latter consists of K discrete values, the system is characterized by a K-step replica symmetry breaking solution. We argue that our construction is in fact valid in any finite spatial dimensions N >= 1. We discuss the implications of our results for the singularity spectrum describing multifractality of the associated Boltzmann-Gibbs measure. Finally we discuss several generalizations and open problems, such as the dynamics in such a landscape and the construction of a generalized multifractal random walk.

Feature Screening for Ultrahigh Dimensional Categorical Data with Applications.

PubMed

Huang, Danyang; Li, Runze; Wang, Hansheng

2014-01-01

Ultrahigh dimensional data with both categorical responses and categorical covariates are frequently encountered in the analysis of big data, for which feature screening has become an indispensable statistical tool. We propose a Pearson chi-square based feature screening procedure for categorical response with ultrahigh dimensional categorical covariates. The proposed procedure can be directly applied for detection of important interaction effects. We further show that the proposed procedure possesses screening consistency property in the terminology of Fan and Lv (2008). We investigate the finite sample performance of the proposed procedure by Monte Carlo simulation studies, and illustrate the proposed method by two empirical datasets.

Conformal anomaly of some 2-d Z (n) models

NASA Astrophysics Data System (ADS)

William, Peter

1991-01-01

We describe a numerical calculation of the conformal anomaly in the case of some two-dimensional statistical models undergoing a second-order phase transition, utilizing a recently developed method to compute the partition function exactly. This computation is carried out on a massively parallel CM2 machine, using the finite size scaling behaviour of the free energy.

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

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Adamian, A.

1988-01-01

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

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

PubMed

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

2015-04-07

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

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

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

Quantum statistical mechanics of nonrelativistic membranes: crumpling transition at finite temperature

NASA Astrophysics Data System (ADS)

Borelli, M. E. S.; Kleinert, H.; Schakel, Adriaan M. J.

2000-03-01

The effect of quantum fluctuations on a nearly flat, nonrelativistic two-dimensional membrane with extrinsic curvature stiffness and tension is investigated. The renormalization group analysis is carried out in first-order perturbative theory. In contrast to thermal fluctuations, which soften the membrane at large scales and turn it into a crumpled surface, quantum fluctuations are found to stiffen the membrane, so that it exhibits a Hausdorff dimension equal to two. The large-scale behavior of the membrane is further studied at finite temperature, where a nontrivial fixed point is found, signaling a crumpling transition.

On the statistical mechanics of the 2D stochastic Euler equation

NASA Astrophysics Data System (ADS)

Bouchet, Freddy; Laurie, Jason; Zaboronski, Oleg

2011-12-01

The dynamics of vortices and large scale structures is qualitatively very different in two dimensional flows compared to its three dimensional counterparts, due to the presence of multiple integrals of motion. These are believed to be responsible for a variety of phenomena observed in Euler flow such as the formation of large scale coherent structures, the existence of meta-stable states and random abrupt changes in the topology of the flow. In this paper we study stochastic dynamics of the finite dimensional approximation of the 2D Euler flow based on Lie algebra su(N) which preserves all integrals of motion. In particular, we exploit rich algebraic structure responsible for the existence of Euler's conservation laws to calculate the invariant measures and explore their properties and also study the approach to equilibrium. Unexpectedly, we find deep connections between equilibrium measures of finite dimensional su(N) truncations of the stochastic Euler equations and random matrix models. Our work can be regarded as a preparation for addressing the questions of large scale structures, meta-stability and the dynamics of random transitions between different flow topologies in stochastic 2D Euler flows.

Topology of Large-Scale Structures of Galaxies in two Dimensions—Systematic Effects

NASA Astrophysics Data System (ADS)

Appleby, Stephen; Park, Changbom; Hong, Sungwook E.; Kim, Juhan

2017-02-01

We study the two-dimensional topology of galactic distribution when projected onto two-dimensional spherical shells. Using the latest Horizon Run 4 simulation data, we construct the genus of the two-dimensional field and consider how this statistic is affected by late-time nonlinear effects—principally gravitational collapse and redshift space distortion (RSD). We also consider systematic and numerical artifacts, such as shot noise, galaxy bias, and finite pixel effects. We model the systematics using a Hermite polynomial expansion and perform a comprehensive analysis of known effects on the two-dimensional genus, with a view toward using the statistic for cosmological parameter estimation. We find that the finite pixel effect is dominated by an amplitude drop and can be made less than 1% by adopting pixels smaller than 1/3 of the angular smoothing length. Nonlinear gravitational evolution introduces time-dependent coefficients of the zeroth, first, and second Hermite polynomials, but the genus amplitude changes by less than 1% between z = 1 and z = 0 for smoothing scales {R}{{G}}> 9 {Mpc}/{{h}}. Non-zero terms are measured up to third order in the Hermite polynomial expansion when studying RSD. Differences in the shapes of the genus curves in real and redshift space are small when we adopt thick redshift shells, but the amplitude change remains a significant ˜ { O }(10 % ) effect. The combined effects of galaxy biasing and shot noise produce systematic effects up to the second Hermite polynomial. It is shown that, when sampling, the use of galaxy mass cuts significantly reduces the effect of shot noise relative to random sampling.

Two-dimensional evolution equation of finite-amplitude internal gravity waves in a uniformly stratified fluid

PubMed

Kataoka; Tsutahara; Akuzawa

2000-02-14

We derive a fully nonlinear evolution equation that can describe the two-dimensional motion of finite-amplitude long internal waves in a uniformly stratified three-dimensional fluid of finite depth. The derived equation is the two-dimensional counterpart of the evolution equation obtained by Grimshaw and Yi [J. Fluid Mech. 229, 603 (1991)]. In the small-amplitude limit, our equation is reduced to the celebrated Kadomtsev-Petviashvili equation.

Shearlet-based measures of entropy and complexity for two-dimensional patterns

NASA Astrophysics Data System (ADS)

Brazhe, Alexey

2018-06-01

New spatial entropy and complexity measures for two-dimensional patterns are proposed. The approach is based on the notion of disequilibrium and is built on statistics of directional multiscale coefficients of the fast finite shearlet transform. Shannon entropy and Jensen-Shannon divergence measures are employed. Both local and global spatial complexity and entropy estimates can be obtained, thus allowing for spatial mapping of complexity in inhomogeneous patterns. The algorithm is validated in numerical experiments with a gradually decaying periodic pattern and Ising surfaces near critical state. It is concluded that the proposed algorithm can be instrumental in describing a wide range of two-dimensional imaging data, textures, or surfaces, where an understanding of the level of order or randomness is desired.

Classification of real Lie superalgebras based on a simple Lie algebra, giving rise to interesting examples involving {mathfrak {su}}(2,2)

NASA Astrophysics Data System (ADS)

Guzzo, H.; Hernández, I.; Sánchez-Valenzuela, O. A.

2014-09-01

Finite dimensional semisimple real Lie superalgebras are described via finite dimensional semisimple complex Lie superalgebras. As an application of these results, finite dimensional real Lie superalgebras mathfrak {m}=mathfrak {m}_0 oplus mathfrak {m}_1 for which mathfrak {m}_0 is a simple Lie algebra are classified up to isomorphism.

Finite-dimensional integrable systems: A collection of research problems

NASA Astrophysics Data System (ADS)

Bolsinov, A. V.; Izosimov, A. M.; Tsonev, D. M.

2017-05-01

This article suggests a series of problems related to various algebraic and geometric aspects of integrability. They reflect some recent developments in the theory of finite-dimensional integrable systems such as bi-Poisson linear algebra, Jordan-Kronecker invariants of finite dimensional Lie algebras, the interplay between singularities of Lagrangian fibrations and compatible Poisson brackets, and new techniques in projective geometry.

A Thin Codimension-One Decomposition of the Hilbert Cube

ERIC Educational Resources Information Center

Phon-On, Aniruth

2010-01-01

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

[Construction of platform on the three-dimensional finite element model of the dentulous mandibular body of a normal person].

PubMed

Gong, Lu-Lu; Zhu, Jing; Ding, Zu-Quan; Li, Guo-Qiang; Wang, Li-Ming; Yan, Bo-Yong

2008-04-01

To develop a method to construct a three-dimensional finite element model of the dentulous mandibular body of a normal person. A series of pictures with the interval of 0.1 mm were taken by CT scanning. After extracting the coordinates of key points of some pictures by the procedure, we used a C program to process the useful data, and constructed a platform of the three-dimensional finite element model of the dentulous mandibular body with the Ansys software for finite element analysis. The experimental results showed that the platform of the three-dimensional finite element model of the dentulous mandibular body was more accurate and applicable. The exact three-dimensional shape of model was well constructed, and each part of this model, such as one single tooth, can be deleted, which can be used to emulate various tooth-loss clinical cases. The three-dimensional finite element model is constructed with life-like shapes of dental cusps. Each part of this model can be easily removed. In conclusion, this experiment provides a good platform of biomechanical analysis on various tooth-loss clinical cases.

Improved finite element methodology for integrated thermal structural analysis

NASA Technical Reports Server (NTRS)

Dechaumphai, P.; Thornton, E. A.

1982-01-01

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

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

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

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

2013-07-01

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

Continuous family of finite-dimensional representations of a solvable Lie algebra arising from singularities

PubMed Central

Yau, Stephen S.-T.

1983-01-01

A natural mapping from the set of complex analytic isolated hypersurface singularities to the set of finite dimensional Lie algebras is first defined. It is proven that the image under this natural mapping is contained in the set of solvable Lie algebras. This approach gives rise to a continuous inequivalent family of finite dimensional representations of a solvable Lie algebra. PMID:16593401

Applications of an exponential finite difference technique

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

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

1988-07-01

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

Nonlinear damping model for flexible structures. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Zang, Weijian

1990-01-01

The study of nonlinear damping problem of flexible structures is addressed. Both passive and active damping, both finite dimensional and infinite dimensional models are studied. In the first part, the spectral density and the correlation function of a single DOF nonlinear damping model is investigated. A formula for the spectral density is established with O(Gamma(sub 2)) accuracy based upon Fokker-Planck technique and perturbation. The spectral density depends upon certain first order statistics which could be obtained if the stationary density is known. A method is proposed to find the approximate stationary density explicitly. In the second part, the spectral density of a multi-DOF nonlinear damping model is investigated. In the third part, energy type nonlinear damping model in an infinite dimensional setting is studied.

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

PubMed

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

2013-04-01

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

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

USGS Publications Warehouse

Lee, Jonathan K.; Froehlich, David C.

1987-01-01

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

Nonlinear Conservation Laws and Finite Volume Methods

NASA Astrophysics Data System (ADS)

Leveque, Randall J.

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

Orthogonality preserving infinite dimensional quadratic stochastic operators

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

Akın, Hasan; Mukhamedov, Farrukh

In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.

Limit theorems for Lévy walks in d dimensions: rare and bulk fluctuations

NASA Astrophysics Data System (ADS)

Fouxon, Itzhak; Denisov, Sergey; Zaburdaev, Vasily; Barkai, Eli

2017-04-01

We consider super-diffusive Lévy walks in d≥slant 2 dimensions when the duration of a single step, i.e. a ballistic motion performed by a walker, is governed by a power-law tailed distribution of infinite variance and finite mean. We demonstrate that the probability density function (PDF) of the coordinate of the random walker has two different scaling limits at large times. One limit describes the bulk of the PDF. It is the d-dimensional generalization of the one-dimensional Lévy distribution and is the counterpart of the central limit theorem (CLT) for random walks with finite dispersion. In contrast with the one-dimensional Lévy distribution and the CLT this distribution does not have a universal shape. The PDF reflects anisotropy of the single-step statistics however large the time is. The other scaling limit, the so-called ‘infinite density’, describes the tail of the PDF which determines second (dispersion) and higher moments of the PDF. This limit repeats the angular structure of the PDF of velocity in one step. A typical realization of the walk consists of anomalous diffusive motion (described by anisotropic d-dimensional Lévy distribution) interspersed with long ballistic flights (described by infinite density). The long flights are rare but due to them the coordinate increases so much that their contribution determines the dispersion. We illustrate the concept by considering two types of Lévy walks, with isotropic and anisotropic distributions of velocities. Furthermore, we show that for isotropic but otherwise arbitrary velocity distributions the d-dimensional process can be reduced to a one-dimensional Lévy walk. We briefly discuss the consequences of non-universality for the d  >  1 dimensional fractional diffusion equation, in particular the non-uniqueness of the fractional Laplacian.

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

NASA Astrophysics Data System (ADS)

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

2011-11-01

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

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

NASA Technical Reports Server (NTRS)

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

1975-01-01

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

Adaptive finite element methods for two-dimensional problems in computational fracture mechanics

NASA Technical Reports Server (NTRS)

Min, J. B.; Bass, J. M.; Spradley, L. W.

1994-01-01

Some recent results obtained using solution-adaptive finite element methods in two-dimensional problems in linear elastic fracture mechanics are presented. The focus is on the basic issue of adaptive finite element methods for validating the new methodology by computing demonstration problems and comparing the stress intensity factors to analytical results.

Application of laser ranging and VLBI data to a study of plate tectonic driving forces. [finite element method

NASA Technical Reports Server (NTRS)

Solomon, S. C.

1980-01-01

The measurability of changes in plate driving or resistive forces associated with plate boundary earthquakes by laser rangefinding or VLBI is considered with emphasis on those aspects of plate forces that can be characterized by such measurements. Topics covered include: (1) analytic solutions for two dimensional stress diffusion in a plate following earthquake faulting on a finite fault; (2) two dimensional finite-element solutions for the global state of stress at the Earth's surface for possible plate driving forces; and (3) finite-element solutions for three dimensional stress diffusion in a viscoelastic Earth following earthquake faulting.

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

NASA Technical Reports Server (NTRS)

Burns, John A.; Marrekchi, Hamadi

1993-01-01

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

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.

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.

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

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.

1987-01-01

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

exponential finite difference technique for solving partial differential equations

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

Handschuh, R.F.

1987-01-01

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

Sign phase transition in the problem of interfering directed paths

NASA Astrophysics Data System (ADS)

Baldwin, C. L.; Laumann, C. R.; Spivak, B.

2018-01-01

We investigate the statistical properties of interfering directed paths in disordered media. At long distance, the average sign of the sum over paths may tend to zero (sign disordered) or remain finite (sign ordered) depending on dimensionality and the concentration of negative scattering sites x . We show that in two dimensions the sign-ordered phase is unstable even for arbitrarily small x by identifying rare destabilizing events. In three dimensions, we present strong evidence that there is a sign phase transition at a finite xc>0 . These results have consequences for several different physical systems. In two-dimensional insulators at low temperature, the variable-range-hopping magnetoresistance is always negative, while in three dimensions, it changes sign at the point of the sign phase transition. We also show that in the sign-disordered regime a small magnetic field may enhance superconductivity in a random system of D -wave superconducting grains embedded in a metallic matrix. Finally, the existence of the sign phase transition in three dimensions implies new features in the spin-glass phase diagram at high temperature.

Approximate Approaches to the One-Dimensional Finite Potential Well

ERIC Educational Resources Information Center

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

2011-01-01

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

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

NASA Astrophysics Data System (ADS)

Yi, Tae-Hyeong; Park, Ja-Rin

2017-06-01

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

Statistics of Advective Stretching in Three-dimensional Incompressible Flows

NASA Astrophysics Data System (ADS)

Subramanian, Natarajan; Kellogg, Louise H.; Turcotte, Donald L.

2009-09-01

We present a method to quantify kinematic stretching in incompressible, unsteady, isoviscous, three-dimensional flows. We extend the method of Kellogg and Turcotte (J. Geophys. Res. 95:421-432, 1990) to compute the axial stretching/thinning experienced by infinitesimal ellipsoidal strain markers in arbitrary three-dimensional incompressible flows and discuss the differences between our method and the computation of Finite Time Lyapunov Exponent (FTLE). We use the cellular flow model developed in Solomon and Mezic (Nature 425:376-380, 2003) to study the statistics of stretching in a three-dimensional unsteady cellular flow. We find that the probability density function of the logarithm of normalised cumulative stretching (log S) for a globally chaotic flow, with spatially heterogeneous stretching behavior, is not Gaussian and that the coefficient of variation of the Gaussian distribution does not decrease with time as t^{-1/2} . However, it is observed that stretching becomes exponential log S˜ t and the probability density function of log S becomes Gaussian when the time dependence of the flow and its three-dimensionality are increased to make the stretching behaviour of the flow more spatially uniform. We term these behaviors weak and strong chaotic mixing respectively. We find that for strongly chaotic mixing, the coefficient of variation of the Gaussian distribution decreases with time as t^{-1/2} . This behavior is consistent with a random multiplicative stretching process.

Nonlinear micromechanics-based finite element analysis of the interfacial behaviour of FRP-strengthened reinforced concrete beams

NASA Astrophysics Data System (ADS)

Abd El Baky, Hussien

This research work is devoted to theoretical and numerical studies on the flexural behaviour of FRP-strengthened concrete beams. The objectives of this research are to extend and generalize the results of simple experiments, to recommend new design guidelines based on accurate numerical tools, and to enhance our comprehension of the bond performance of such beams. These numerical tools can be exploited to bridge the existing gaps in the development of analysis and modelling approaches that can predict the behaviour of FRP-strengthened concrete beams. The research effort here begins with the formulation of a concrete model and development of FRP/concrete interface constitutive laws, followed by finite element simulations for beams strengthened in flexure. Finally, a statistical analysis is carried out taking the advantage of the aforesaid numerical tools to propose design guidelines. In this dissertation, an alternative incremental formulation of the M4 microplane model is proposed to overcome the computational complexities associated with the original formulation. Through a number of numerical applications, this incremental formulation is shown to be equivalent to the original M4 model. To assess the computational efficiency of the incremental formulation, the "arc-length" numerical technique is also considered and implemented in the original Bazant et al. [2000] M4 formulation. Finally, the M4 microplane concrete model is coded in FORTRAN and implemented as a user-defined subroutine into the commercial software package ADINA, Version 8.4. Then this subroutine is used with the finite element package to analyze various applications involving FRP strengthening. In the first application a nonlinear micromechanics-based finite element analysis is performed to investigate the interfacial behaviour of FRP/concrete joints subjected to direct shear loadings. The intention of this part is to develop a reliable bond--slip model for the FRP/concrete interface. The bond--slip relation is developed considering the interaction between the interfacial normal and shear stress components along the bonded length. A new approach is proposed to describe the entire tau-s relationship based on three separate models. The first model captures the shear response of an orthotropic FRP laminate. The second model simulates the shear characteristics of an adhesive layer, while the third model represents the shear nonlinearity of a thin layer inside the concrete, referred to as the interfacial layer. The proposed bond--slip model reflects the geometrical and material characteristics of the FRP, concrete, and adhesive layers. Two-dimensional and three-dimensional nonlinear displacement-controlled finite element (FE) models are then developed to investigate the flexural and FRP/concrete interfacial responses of FRP-strengthened reinforced concrete beams. The three-dimensional finite element model is created to accommodate cases of beams having FRP anchorage systems. Discrete interface elements are proposed and used to simulate the FRP/concrete interfacial behaviour before and after cracking. The FE models are capable of simulating the various failure modes, including debonding of the FRP either at the plate end or at intermediate cracks. Particular attention is focused on the effect of crack initiation and propagation on the interfacial behaviour. This study leads to an accurate and refined interpretation of the plate-end and intermediate crack debonding failure mechanisms for FRP-strengthened beams with and without FRP anchorage systems. Finally, the FE models are used to conduct a parametric study to generalize the findings of the FE analysis. The variables under investigation include two material characteristics; namely, the concrete compressive strength and axial stiffness of the FRP laminates as well as three geometric properties; namely, the steel reinforcement ratio, the beam span length and the beam depth. The parametric study is followed by a statistical analysis for 43 strengthened beams involving the five aforementioned variables. The response surface methodology (RSM) technique is employed to optimize the accuracy of the statistical models while minimizing the numbers of finite element runs. In particular, a face-centred design (FCD) is applied to evaluate the influence of the critical variables on the debonding load and debonding strain limits in the FRP laminates. Based on these statistical models, a nonlinear statistical regression analysis is used to propose design guidelines for the FRP flexural strengthening of reinforced concrete beams. (Abstract shortened by UMI.)

Tomograms for open quantum systems: In(finite) dimensional optical and spin systems

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

Thapliyal, Kishore, E-mail: tkishore36@yahoo.com; Banerjee, Subhashish, E-mail: subhashish@iitj.ac.in; Pathak, Anirban, E-mail: anirban.pathak@gmail.com

Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained frommore » experimentally generated tomograms and nonclassicality observed from them. -- Highlights: •Tomograms are constructed for open quantum systems. •Finite and infinite dimensional quantum systems are studied. •Finite dimensional systems (phase states, single & two qubit spin states) are studied. •A dissipative harmonic oscillator is considered as an infinite dimensional system. •Both pure dephasing as well as dissipation effects are studied.« less

Modeling and control of flexible structures

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

Compressing random microstructures via stochastic Wang tilings.

PubMed

Novák, Jan; Kučerová, Anna; Zeman, Jan

2012-10-01

This Rapid Communication presents a stochastic Wang tiling-based technique to compress or reconstruct disordered microstructures on the basis of given spatial statistics. Unlike the existing approaches based on a single unit cell, it utilizes a finite set of tiles assembled by a stochastic tiling algorithm, thereby allowing to accurately reproduce long-range orientation orders in a computationally efficient manner. Although the basic features of the method are demonstrated for a two-dimensional particulate suspension, the present framework is fully extensible to generic multidimensional media.

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

PubMed

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

2015-11-01

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

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

DTIC Science & Technology

1984-12-30

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

Finite-Dimensional Representations for Controlled Diffusions with Delay

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

Federico, Salvatore, E-mail: salvatore.federico@unimi.it; Tankov, Peter, E-mail: tankov@math.univ-paris-diderot.fr

2015-02-15

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which the solution of the SDDE and a linear path functional of it admit a finite-dimensional Markovian representation. As a second contribution, we show how approximate finite-dimensional Markovian representations may be constructed when these conditions are not satisfied, and provide an estimate of the error corresponding to these approximations. These results are applied to optimal control and optimal stopping problems for stochastic systems with delay.

Finite-dimensional linear approximations of solutions to general irregular nonlinear operator equations and equations with quadratic operators

NASA Astrophysics Data System (ADS)

Kokurin, M. Yu.

2010-11-01

A general scheme for improving approximate solutions to irregular nonlinear operator equations in Hilbert spaces is proposed and analyzed in the presence of errors. A modification of this scheme designed for equations with quadratic operators is also examined. The technique of universal linear approximations of irregular equations is combined with the projection onto finite-dimensional subspaces of a special form. It is shown that, for finite-dimensional quadratic problems, the proposed scheme provides information about the global geometric properties of the intersections of quadrics.

Inferring Markov chains: Bayesian estimation, model comparison, entropy rate, and out-of-class modeling.

PubMed

Strelioff, Christopher C; Crutchfield, James P; Hübler, Alfred W

2007-07-01

Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer kth order Markov chains, for arbitrary k , from finite data by applying Bayesian methods to both parameter estimation and model-order selection. Extending existing results for multinomial models of discrete data, we connect inference to statistical mechanics through information-theoretic (type theory) techniques. We establish a direct relationship between Bayesian evidence and the partition function which allows for straightforward calculation of the expectation and variance of the conditional relative entropy and the source entropy rate. Finally, we introduce a method that uses finite data-size scaling with model-order comparison to infer the structure of out-of-class processes.

Nonlinear Control Systems

DTIC Science & Technology

2007-03-01

Finite -dimensional regulators for a class of infinite dimensional systems ,” Systems and Control Letters, 3 (1983), 7-12. [11] B...semiglobal stabilizability by encoded state feedback,” to appear in Systems and Control Letters. 22 29. C. De Persis, A. Isidori, “Global stabilization of...nonequilibrium setting, for both finite and infinite dimensional control systems . Our objectives for distributed parameter systems included

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

Giunta, G.; Belouettar, S.

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

Level statistics of a noncompact cosmological billiard

NASA Astrophysics Data System (ADS)

Csordas, Andras; Graham, Robert; Szepfalusy, Peter

1991-08-01

A noncompact chaotic billiard on a two-dimensional space of constant negative curvature, the infinite equilateral triangle describing anisotropy oscillations in the very early universe, is studied quantum-mechanically. A Weyl formula with a logarithmic correction term is derived for the smoothed number of states function. For one symmetry class of the eigenfunctions, the level spacing distribution, the spectral rigidity Delta3, and the Sigma2 statistics are determined numerically using the finite matrix approximation. Systematic deviations are found both from the Gaussian orthogonal ensemble (GOE) and the Poissonian ensemble. However, good agreement with the GOE is found if the fundamental triangle is deformed in such a way that it no longer tiles the space.

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

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

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

NASA Astrophysics Data System (ADS)

Lechleiter, A.

2015-09-01

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

Quantum approach to classical statistical mechanics.

PubMed

Somma, R D; Batista, C D; Ortiz, G

2007-07-20

We present a new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This classical-to-quantum mapping allows us to extend the scope of standard optimization methods by unifying them under a general framework. The quantum annealing method is naturally extended to simulate classical systems at finite temperatures. We derive the rates to assure convergence to the optimal thermodynamic state using the adiabatic theorem of quantum mechanics. For simulated and quantum annealing, we obtain the asymptotic rates of T(t) approximately (pN)/(k(B)logt) and gamma(t) approximately (Nt)(-c/N), for the temperature and magnetic field, respectively. Other annealing strategies are also discussed.

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

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

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

1997-03-01

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

Estimating the proportion of true null hypotheses when the statistics are discrete.

PubMed

Dialsingh, Isaac; Austin, Stefanie R; Altman, Naomi S

2015-07-15

In high-dimensional testing problems π0, the proportion of null hypotheses that are true is an important parameter. For discrete test statistics, the P values come from a discrete distribution with finite support and the null distribution may depend on an ancillary statistic such as a table margin that varies among the test statistics. Methods for estimating π0 developed for continuous test statistics, which depend on a uniform or identical null distribution of P values, may not perform well when applied to discrete testing problems. This article introduces a number of π0 estimators, the regression and 'T' methods that perform well with discrete test statistics and also assesses how well methods developed for or adapted from continuous tests perform with discrete tests. We demonstrate the usefulness of these estimators in the analysis of high-throughput biological RNA-seq and single-nucleotide polymorphism data. implemented in R. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

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

NASA Astrophysics Data System (ADS)

Rauter, Matthias

2017-04-01

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

The intermediates take it all: asymptotics of higher criticism statistics and a powerful alternative based on equal local levels.

PubMed

Gontscharuk, Veronika; Landwehr, Sandra; Finner, Helmut

2015-01-01

The higher criticism (HC) statistic, which can be seen as a normalized version of the famous Kolmogorov-Smirnov statistic, has a long history, dating back to the mid seventies. Originally, HC statistics were used in connection with goodness of fit (GOF) tests but they recently gained some attention in the context of testing the global null hypothesis in high dimensional data. The continuing interest for HC seems to be inspired by a series of nice asymptotic properties related to this statistic. For example, unlike Kolmogorov-Smirnov tests, GOF tests based on the HC statistic are known to be asymptotically sensitive in the moderate tails, hence it is favorably applied for detecting the presence of signals in sparse mixture models. However, some questions around the asymptotic behavior of the HC statistic are still open. We focus on two of them, namely, why a specific intermediate range is crucial for GOF tests based on the HC statistic and why the convergence of the HC distribution to the limiting one is extremely slow. Moreover, the inconsistency in the asymptotic and finite behavior of the HC statistic prompts us to provide a new HC test that has better finite properties than the original HC test while showing the same asymptotics. This test is motivated by the asymptotic behavior of the so-called local levels related to the original HC test. By means of numerical calculations and simulations we show that the new HC test is typically more powerful than the original HC test in normal mixture models. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

An Interactive Preprocessor Program with Graphics for a Three-Dimensional Finite Element Code.

ERIC Educational Resources Information Center

Hamilton, Claude Hayden, III

The development and capabilities of an interactive preprocessor program with graphics for an existing three-dimensional finite element code is presented. This preprocessor program, EDGAP3D, is designed to be used in conjunction with the Texas Three Dimensional Grain Analysis Program (TXCAP3D). The code presented in this research is capable of the…

Rough surface reconstruction for ultrasonic NDE simulation

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

Choi, Wonjae; Shi, Fan; Lowe, Michael J. S.

2014-02-18

The reflection of ultrasound from rough surfaces is an important topic for the NDE of safety-critical components, such as pressure-containing components in power stations. The specular reflection from a rough surface of a defect is normally lower than it would be from a flat surface, so it is typical to apply a safety factor in order that justification cases for inspection planning are conservative. The study of the statistics of the rough surfaces that might be expected in candidate defects according to materials and loading, and the reflections from them, can be useful to develop arguments for realistic safety factors.more » This paper presents a study of real rough crack surfaces that are representative of the potential defects in pressure-containing power plant. Two-dimensional (area) values of the height of the roughness have been measured and their statistics analysed. Then a means to reconstruct model cases with similar statistics, so as to enable the creation of multiple realistic realizations of the surfaces, has been investigated, using random field theory. Rough surfaces are reconstructed, based on a real surface, and results for these two-dimensional descriptions of the original surface have been compared with those from the conventional model based on a one-dimensional correlation coefficient function. In addition, ultrasonic reflections from them are simulated using a finite element method.« less

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

NASA Technical Reports Server (NTRS)

Cwik, Tom; Zuffada, Cinzia; Jamnejad, Vahraz

1996-01-01

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

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Simulation of wave propagation in three-dimensional random media

NASA Astrophysics Data System (ADS)

Coles, Wm. A.; Filice, J. P.; Frehlich, R. G.; Yadlowsky, M.

1995-04-01

Quantitative error analyses for the simulation of wave propagation in three-dimensional random media, when narrow angular scattering is assumed, are presented for plane-wave and spherical-wave geometry. This includes the errors that result from finite grid size, finite simulation dimensions, and the separation of the two-dimensional screens along the propagation direction. Simple error scalings are determined for power-law spectra of the random refractive indices of the media. The effects of a finite inner scale are also considered. The spatial spectra of the intensity errors are calculated and compared with the spatial spectra of

Scaling in biomechanical experimentation: a finite similitude approach.

PubMed

Ochoa-Cabrero, Raul; Alonso-Rasgado, Teresa; Davey, Keith

2018-06-01

Biological experimentation has many obstacles: resource limitations, unavailability of materials, manufacturing complexities and ethical compliance issues; any approach that resolves all or some of these is of some interest. The aim of this study is applying the recently discovered concept of finite similitude as a novel approach for the design of scaled biomechanical experiments supported with analysis using a commercial finite-element package and validated by means of image correlation software. The study of isotropic scaling of synthetic bones leads to the selection of three-dimensional (3D) printed materials for the trial-space materials. These materials conforming to the theory are analysed in finite-element models of a cylinder and femur geometries undergoing compression, tension, torsion and bending tests to assess the efficacy of the approach using reverse scaling of the approach. The finite-element results show similar strain patterns in the surface for the cylinder with a maximum difference of less than 10% and for the femur with a maximum difference of less than 4% across all tests. Finally, the trial-space, physical-trial experimentation using 3D printed materials for compression and bending testing provides a good agreement in a Bland-Altman statistical analysis, providing good supporting evidence for the practicality of the approach. © 2018 The Author(s).

A semi-implicit finite difference model for three-dimensional tidal circulation,

USGS Publications Warehouse

Casulli, V.; Cheng, R.T.

1992-01-01

A semi-implicit finite difference formulation for the numerical solution of three-dimensional tidal circulation is presented. The governing equations are the three-dimensional Reynolds equations in which the pressure is assumed to be hydrostatic. A minimal degree of implicitness has been introduced in the finite difference formula so that in the absence of horizontal viscosity the resulting algorithm is unconditionally stable at a minimal computational cost. When only one vertical layer is specified this method reduces, as a particular case, to a semi-implicit scheme for the solutions of the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm is fast, accurate and mass conservative. This formulation includes the simulation of flooding and drying of tidal flats, and is fully vectorizable for an efficient implementation on modern vector computers.

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.

Ablative Thermal Response Analysis Using the Finite Element Method

NASA Technical Reports Server (NTRS)

Dec John A.; Braun, Robert D.

2009-01-01

A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the finite element and finite difference methods are described. As a first step in developing a three dimensional finite element based ablative thermal response capability, a one dimensional computer tool has been developed. The finite element method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the element equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed.

[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.

Finite-dimensional Liouville integrable Hamiltonian systems generated from Lax pairs of a bi-Hamiltonian soliton hierarchy by symmetry constraints

NASA Astrophysics Data System (ADS)

Manukure, Solomon

2018-04-01

We construct finite-dimensional Hamiltonian systems by means of symmetry constraints from the Lax pairs and adjoint Lax pairs of a bi-Hamiltonian hierarchy of soliton equations associated with the 3-dimensional special linear Lie algebra, and discuss the Liouville integrability of these systems based on the existence of sufficiently many integrals of motion.

ANALYTICAL SOLUTION TO SATURATED FLOW IN A FINITE STRATIFIED AQUIFER

EPA Science Inventory

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

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

NASA Astrophysics Data System (ADS)

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

2004-07-01

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

Advances in three-dimensional field analysis and evaluation of performance parameters of electrical machines

NASA Astrophysics Data System (ADS)

Sivasubramaniam, Kiruba

This thesis makes advances in three dimensional finite element analysis of electrical machines and the quantification of their parameters and performance. The principal objectives of the thesis are: (1)the development of a stable and accurate method of nonlinear three-dimensional field computation and application to electrical machinery and devices; and (2)improvement in the accuracy of determination of performance parameters, particularly forces and torque computed from finite elements. Contributions are made in two general areas: a more efficient formulation for three dimensional finite element analysis which saves time and improves accuracy, and new post-processing techniques to calculate flux density values from a given finite element solution. A novel three-dimensional magnetostatic solution based on a modified scalar potential method is implemented. This method has significant advantages over the traditional total scalar, reduced scalar or vector potential methods. The new method is applied to a 3D geometry of an iron core inductor and a permanent magnet motor. The results obtained are compared with those obtained from traditional methods, in terms of accuracy and speed of computation. A technique which has been observed to improve force computation in two dimensional analysis using a local solution of Laplace's equation in the airgap of machines is investigated and a similar method is implemented in the three dimensional analysis of electromagnetic devices. A new integral formulation to improve force calculation from a smoother flux-density profile is also explored and implemented. Comparisons are made and conclusions drawn as to how much improvement is obtained and at what cost. This thesis also demonstrates the use of finite element analysis to analyze torque ripples due to rotor eccentricity in permanent magnet BLDC motors. A new method for analyzing torque harmonics based on data obtained from a time stepping finite element analysis of the machine is explored and implemented.

Comparison of one-dimensional probabilistic finite element method with direct numerical simulation of dynamically loaded heterogeneous materials

NASA Astrophysics Data System (ADS)

Robbins, Joshua; Voth, Thomas

2011-06-01

Material response to dynamic loading is often dominated by microstructure such as grain topology, porosity, inclusions, and defects; however, many models rely on assumptions of homogeneity. We use the probabilistic finite element method (WK Liu, IJNME, 1986) to introduce local uncertainty to account for material heterogeneity. The PFEM uses statistical information about the local material response (i.e., its expectation, coefficient of variation, and autocorrelation) drawn from knowledge of the microstructure, single crystal behavior, and direct numerical simulation (DNS) to determine the expectation and covariance of the system response (velocity, strain, stress, etc). This approach is compared to resolved grain-scale simulations of the equivalent system. The microstructures used for the DNS are produced using Monte Carlo simulations of grain growth, and a sufficient number of realizations are computed to ensure a meaningful comparison. Finally, comments are made regarding the suitability of one-dimensional PFEM for modeling material heterogeneity. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Designing Two-Dimensional Dirac Heterointerfaces of Few-Layer Graphene and Tetradymite-Type Sb2Te3 for Thermoelectric Applications.

PubMed

Jang, Woosun; Lee, Jiwoo; In, Chihun; Choi, Hyunyong; Soon, Aloysius

2017-12-06

Despite the ubiquitous nature of the Peltier effect in low-dimensional thermoelectric devices, the influence of finite temperature on the electronic structure and transport in the Dirac heterointerfaces of the few-layer graphene and layered tetradymite, Sb 2 Te 3 (which coincidently have excellent thermoelectric properties) are not well understood. In this work, using the first-principles density-functional theory calculations, we investigate the detailed atomic and electronic structure of these Dirac heterointerfaces of graphene and Sb 2 Te 3 and further re-examine the effect of finite temperature on the electronic band structures using a phenomenological temperature-broadening model based on Fermi-Dirac statistics. We then proceed to understand the underlying charge redistribution process in this Dirac heterointerfaces and through solving the Boltzmann transport equation, we present the theoretical evidence of electron-hole asymmetry in its electrical conductivity as a consequence of this charge redistribution mechanism. We finally propose that the hexagonal-stacked Dirac heterointerfaces are useful as efficient p-n junction building blocks in the next-generation thermoelectric devices where the electron-hole asymmetry promotes the thermoelectric transport by "hot" excited charge carriers.

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

NASA Technical Reports Server (NTRS)

Verbestel, John; Smith, Howard W.

1993-01-01

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

Quantum mean-field approximation for lattice quantum models: Truncating quantum correlations and retaining classical ones

NASA Astrophysics Data System (ADS)

Malpetti, Daniele; Roscilde, Tommaso

2017-02-01

The mean-field approximation is at the heart of our understanding of complex systems, despite its fundamental limitation of completely neglecting correlations between the elementary constituents. In a recent work [Phys. Rev. Lett. 117, 130401 (2016), 10.1103/PhysRevLett.117.130401], we have shown that in quantum many-body systems at finite temperature, two-point correlations can be formally separated into a thermal part and a quantum part and that quantum correlations are generically found to decay exponentially at finite temperature, with a characteristic, temperature-dependent quantum coherence length. The existence of these two different forms of correlation in quantum many-body systems suggests the possibility of formulating an approximation, which affects quantum correlations only, without preventing the correct description of classical fluctuations at all length scales. Focusing on lattice boson and quantum Ising models, we make use of the path-integral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum mean-field (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster mean-field theory at T =0 , while at any finite temperature it produces a family of systematically improved, semi-classical approximations to the quantum statistical mechanics of the lattice theory at hand. Contrary to standard MF approximations, the correct nature of thermal critical phenomena is captured by any cluster size. In the two exemplary cases of the two-dimensional quantum Ising model and of two-dimensional quantum rotors, we study systematically the convergence of the cQMF approximation towards the exact result, and show that the convergence is typically linear or sublinear in the boundary-to-bulk ratio of the clusters as T →0 , while it becomes faster than linear as T grows. These results pave the way towards the development of semiclassical numerical approaches based on an approximate, yet systematically improved account of quantum correlations.

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

NASA Technical Reports Server (NTRS)

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

2003-01-01

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

Stable Direct Adaptive Control of Linear Infinite-dimensional Systems Using a Command Generator Tracker Approach

NASA Technical Reports Server (NTRS)

Balas, M. J.; Kaufman, H.; Wen, J.

1985-01-01

A command generator tracker approach to model following contol of linear distributed parameter systems (DPS) whose dynamics are described on infinite dimensional Hilbert spaces is presented. This method generates finite dimensional controllers capable of exponentially stable tracking of the reference trajectories when certain ideal trajectories are known to exist for the open loop DPS; we present conditions for the existence of these ideal trajectories. An adaptive version of this type of controller is also presented and shown to achieve (in some cases, asymptotically) stable finite dimensional control of the infinite dimensional DPS.

Bayesian estimation of Karhunen–Loève expansions; A random subspace approach

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

Chowdhary, Kenny; Najm, Habib N.

One of the most widely-used statistical procedures for dimensionality reduction of high dimensional random fields is Principal Component Analysis (PCA), which is based on the Karhunen-Lo eve expansion (KLE) of a stochastic process with finite variance. The KLE is analogous to a Fourier series expansion for a random process, where the goal is to find an orthogonal transformation for the data such that the projection of the data onto this orthogonal subspace is optimal in the L 2 sense, i.e, which minimizes the mean square error. In practice, this orthogonal transformation is determined by performing an SVD (Singular Value Decomposition)more » on the sample covariance matrix or on the data matrix itself. Sampling error is typically ignored when quantifying the principal components, or, equivalently, basis functions of the KLE. Furthermore, it is exacerbated when the sample size is much smaller than the dimension of the random field. In this paper, we introduce a Bayesian KLE procedure, allowing one to obtain a probabilistic model on the principal components, which can account for inaccuracies due to limited sample size. The probabilistic model is built via Bayesian inference, from which the posterior becomes the matrix Bingham density over the space of orthonormal matrices. We use a modified Gibbs sampling procedure to sample on this space and then build a probabilistic Karhunen-Lo eve expansions over random subspaces to obtain a set of low-dimensional surrogates of the stochastic process. We illustrate this probabilistic procedure with a finite dimensional stochastic process inspired by Brownian motion.« less

Bayesian estimation of Karhunen–Loève expansions; A random subspace approach

DOE PAGES

Chowdhary, Kenny; Najm, Habib N.

2016-04-13

One of the most widely-used statistical procedures for dimensionality reduction of high dimensional random fields is Principal Component Analysis (PCA), which is based on the Karhunen-Lo eve expansion (KLE) of a stochastic process with finite variance. The KLE is analogous to a Fourier series expansion for a random process, where the goal is to find an orthogonal transformation for the data such that the projection of the data onto this orthogonal subspace is optimal in the L 2 sense, i.e, which minimizes the mean square error. In practice, this orthogonal transformation is determined by performing an SVD (Singular Value Decomposition)more » on the sample covariance matrix or on the data matrix itself. Sampling error is typically ignored when quantifying the principal components, or, equivalently, basis functions of the KLE. Furthermore, it is exacerbated when the sample size is much smaller than the dimension of the random field. In this paper, we introduce a Bayesian KLE procedure, allowing one to obtain a probabilistic model on the principal components, which can account for inaccuracies due to limited sample size. The probabilistic model is built via Bayesian inference, from which the posterior becomes the matrix Bingham density over the space of orthonormal matrices. We use a modified Gibbs sampling procedure to sample on this space and then build a probabilistic Karhunen-Lo eve expansions over random subspaces to obtain a set of low-dimensional surrogates of the stochastic process. We illustrate this probabilistic procedure with a finite dimensional stochastic process inspired by Brownian motion.« less

Lp harmonic 1-forms on minimal hypersurfaces with finite index

NASA Astrophysics Data System (ADS)

Choi, Hagyun; Seo, Keomkyo

2018-07-01

Let N be a complete simply connected Riemannian manifold with sectional curvature KN satisfying -k2 ≤KN ≤ 0 for a nonzero constant k. In this paper we prove that if M is an n(≥ 3) -dimensional complete minimal hypersurface with finite index in N, then the space of Lp harmonic 1-forms on M must be finite dimensional for certain p > 0 provided the bottom of the spectrum of the Laplace operator is sufficiently large. In particular, M has finitely many ends. These results can be regarded as an extension of Li-Wang (2002).

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

NASA Astrophysics Data System (ADS)

Song, Huimin

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

[Finite element analysis on the effect of lateral wedge insole intervention on the contact characteristics of the subtalar joint].

PubMed

Zhou, En-Chang; Tang, Ping; Zhu, Chuan-Ying; Liu, Shi-Ming

2017-01-25

To establish a three-dimensional finite element model of the lower limb bones, and investigate the changes of the contact characteristics of the subtalar joint after using laterally wedge insole intervention. Using the reverse modeling technology, the lower limb bones of normal adult volunteers was scanned by CT. Mimics 10.0 and Geomagic Studio 6.0 software were used to reconstruct the 3D morphology of bones and external soft tissue of the feet. The laterally wedge insole was designed in ProE 5.0. And then all the models were imported into Hyperwork 10.0 and meshed, and given the material properties. The finite element analysis was carried out in ABAQUS 6.9. A three-dimensional finite element model of the lower extremity was established, which was consisted of 95 365 nodes and 246 238 elements. The contact area of the standing state of the lower joint was larger than that of the anterior middle joint surface. The peak stress was concentrated in the anterior lateral part of the posterior articular surface, and the average stress value was(3.85±1.03) MPa. Compared with the model of 0°, the contact area of the subtalar joint was reduced accordingly. There was a significant correlation between anterior middle joint | r |=0.964, P =0.008, and posterior articular | r |=0.978, P =0.002. The equivalent stress of 0° model distributed from(3.07±1.14) MPa to(3.85± 1.03) MPa, which had no statistically difference. Compared with the 0° model, the equivalent stress of the anterior and middle joint surfaces of the 8° model was significantly reduced( P <0.05), but the peak stress of the posterior articular surface was significantly increased( P <0.05). In the 12° model, the peak stress was sharply increased to(10.51±3.53) MPa. Compared with 8° model, there was no statistically difference( P <0.05). Although the peak stress was slightly increased in 16° model, but compared with 12° model, there was no statistically differences( P >0.05). Although a certain valgus can be obtained in subtalar by wearing LWI, the result comes at the cost of the stress concentration on posterior surface. Through this study, we can find that LWI with 8° tilt angle could provide appropriate valgus moment without causing excessive concentration. Therefore, in order to avoid secondary ankle complications, we should not increase the tilt angle blindly.

Nonlinear initial-boundary value solutions by the finite element method. [for Navier-Stokes equations of two dimensional flow

NASA Technical Reports Server (NTRS)

Baker, A. J.

1974-01-01

The finite-element method is used to establish a numerical solution algorithm for the Navier-Stokes equations for two-dimensional flows of a viscous compressible fluid. Numerical experiments confirm the advection property for the finite-element equivalent of the nonlinear convection term for both unidirectional and recirculating flowfields. For linear functionals, the algorithm demonstrates good accuracy using coarse discretizations and h squared convergence with discretization refinement.

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

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

2014-01-01

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

Electromagnetic density of modes for a finite-size three-dimensional structure.

PubMed

D'Aguanno, Giuseppe; Mattiucci, Nadia; Centini, Marco; Scalora, Michael; Bloemer, Mark J

2004-05-01

The concept of the density of modes has been lacking a precise mathematical definition for a finite-size structure. With the explosive growth in the fabrication of photonic crystals and nanostructures, which are inherently finite in size, a workable definition is imperative. We give a simple and physically intuitive definition of the electromagnetic density of modes based on the Green's function for a generic three-dimensional open cavity filled with a linear, isotropic, dielectric material.

MOFAT: A TWO-DIMENSIONAL FINITE ELEMENT PROGRAM FOR MULTIPHASE FLOW AND MULTICOMPONENT TRANSPORT - PROGRAM DOCUMENTATION AND USER'S GUIDE

EPA Science Inventory

This manual describes a two-dimensional, finite element model for coupled multiphase flow and multicomponent transport in planar or radially symmetric vertical sections. low and transport of three fluid phases, including water, nonaqueous phase liquid (NAPL), and gas are consider...

Diffusion with finite-helicity field tensor: A mechanism of generating heterogeneity

NASA Astrophysics Data System (ADS)

Sato, N.; Yoshida, Z.

2018-02-01

Topological constraints on a dynamical system often manifest themselves as breaking of the Hamiltonian structure; well-known examples are nonholonomic constraints on Lagrangian mechanics. The statistical mechanics under such topological constraints is the subject of this study. Conventional arguments based on phase spaces, Jacobi identity, invariant measure, or the H theorem are no longer applicable since all these notions stem from the symplectic geometry underlying canonical Hamiltonian systems. Remembering that Hamiltonian systems are endowed with field tensors (canonical 2-forms) that have zero helicity, our mission is to extend the scope toward the class of systems governed by finite-helicity field tensors. Here, we introduce a class of field tensors that are characterized by Beltrami vectors. We prove an H theorem for this Beltrami class. The most general class of energy-conserving systems are non-Beltrami, for which we identify the "field charge" that prevents the entropy to maximize, resulting in creation of heterogeneous distributions. The essence of the theory can be delineated by classifying three-dimensional dynamics. We then generalize to arbitrary (finite) dimensions.

Phase Transitions in Finite Systems

NASA Astrophysics Data System (ADS)

Chomaz, Philippe; Gulminelli, Francesca

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

Optimal least-squares finite element method for elliptic problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Povinelli, Louis A.

1991-01-01

An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.

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

NASA Astrophysics Data System (ADS)

Lonsdale, R. D.; Webster, R.

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

On mechanics and material length scales of failure in heterogeneous interfaces using a finite strain high performance solver

NASA Astrophysics Data System (ADS)

Mosby, Matthew; Matouš, Karel

2015-12-01

Three-dimensional simulations capable of resolving the large range of spatial scales, from the failure-zone thickness up to the size of the representative unit cell, in damage mechanics problems of particle reinforced adhesives are presented. We show that resolving this wide range of scales in complex three-dimensional heterogeneous morphologies is essential in order to apprehend fracture characteristics, such as strength, fracture toughness and shape of the softening profile. Moreover, we show that computations that resolve essential physical length scales capture the particle size-effect in fracture toughness, for example. In the vein of image-based computational materials science, we construct statistically optimal unit cells containing hundreds to thousands of particles. We show that these statistically representative unit cells are capable of capturing the first- and second-order probability functions of a given data-source with better accuracy than traditional inclusion packing techniques. In order to accomplish these large computations, we use a parallel multiscale cohesive formulation and extend it to finite strains including damage mechanics. The high-performance parallel computational framework is executed on up to 1024 processing cores. A mesh convergence and a representative unit cell study are performed. Quantifying the complex damage patterns in simulations consisting of tens of millions of computational cells and millions of highly nonlinear equations requires data-mining the parallel simulations, and we propose two damage metrics to quantify the damage patterns. A detailed study of volume fraction and filler size on the macroscopic traction-separation response of heterogeneous adhesives is presented.

On the correct implementation of Fermi-Dirac statistics and electron trapping in nonlinear electrostatic plane wave propagation in collisionless plasmas

NASA Astrophysics Data System (ADS)

Schamel, Hans; Eliasson, Bengt

2016-05-01

Quantum statistics and electron trapping have a decisive influence on the propagation characteristics of coherent stationary electrostatic waves. The description of these strictly nonlinear structures, which are of electron hole type and violate linear Vlasov theory due to the particle trapping at any excitation amplitude, is obtained by a correct reduction of the three-dimensional Fermi-Dirac distribution function to one dimension and by a proper incorporation of trapping. For small but finite amplitudes, the holes become of cnoidal wave type and the electron density is shown to be described by a ϕ ( x ) 1 / 2 rather than a ϕ ( x ) expansion, where ϕ ( x ) is the electrostatic potential. The general coefficients are presented for a degenerate plasma as well as the quantum statistical analogue to these steady state coherent structures, including the shape of ϕ ( x ) and the nonlinear dispersion relation, which describes their phase velocity.

Bearing-Load Modeling and Analysis Study for Mechanically Connected Structures

NASA Technical Reports Server (NTRS)

Knight, Norman F., Jr.

2006-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

A finite element-boundary integral method for scattering and radiation by two- and three-dimensional structures

NASA Technical Reports Server (NTRS)

Jin, Jian-Ming; Volakis, John L.; Collins, Jeffery D.

1991-01-01

A review of a hybrid finite element-boundary integral formulation for scattering and radiation by two- and three-dimensional composite structures is presented. In contrast to other hybrid techniques involving the finite element method, the proposed one is in principle exact and can be implemented using a low O(N) storage. This is of particular importance for large scale applications and is a characteristic of the boundary chosen to terminate the finite element mesh, usually as close to the structure as possible. A certain class of these boundaries lead to convolutional boundary integrals which can be evaluated via the fast Fourier transform (FFT) without a need to generate a matrix; thus, retaining the O(N) storage requirement. The paper begins with a general description of the method. A number of two- and three-dimensional applications are then given, including numerical computations which demonstrate the method's accuracy, efficiency, and capability.

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.

Some Classes of Imperfect Information Finite State-Space Stochastic Games with Finite-Dimensional Solutions

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

McEneaney, William M.

2004-08-15

Stochastic games under imperfect information are typically computationally intractable even in the discrete-time/discrete-state case considered here. We consider a problem where one player has perfect information.A function of a conditional probability distribution is proposed as an information state.In the problem form here, the payoff is only a function of the terminal state of the system,and the initial information state is either linear ora sum of max-plus delta functions.When the initial information state belongs to these classes, its propagation is finite-dimensional.The state feedback value function is also finite-dimensional,and obtained via dynamic programming,but has a nonstandard form due to the necessity ofmore » an expanded state variable.Under a saddle point assumption,Certainty Equivalence is obtained and the proposed function is indeed an information state.« less

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

NASA Technical Reports Server (NTRS)

Ransom, Jonathan B.

2002-01-01

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

Mapping of the Bak, Tang, and Wiesenfeld sandpile model on a two-dimensional Ising-correlated percolation lattice to the two-dimensional self-avoiding random walk

NASA Astrophysics Data System (ADS)

Cheraghalizadeh, J.; Najafi, M. N.; Dashti-Naserabadi, H.; Mohammadzadeh, H.

2017-11-01

The self-organized criticality on the random fractal networks has many motivations, like the movement pattern of fluid in the porous media. In addition to the randomness, introducing correlation between the neighboring portions of the porous media has some nontrivial effects. In this paper, we consider the Ising-like interactions between the active sites as the simplest method to bring correlations in the porous media, and we investigate the statistics of the BTW model in it. These correlations are controlled by the artificial "temperature" T and the sign of the Ising coupling. Based on our numerical results, we propose that at the Ising critical temperature Tc the model is compatible with the universality class of two-dimensional (2D) self-avoiding walk (SAW). Especially the fractal dimension of the loops, which are defined as the external frontier of the avalanches, is very close to DfSAW=4/3 . Also, the corresponding open curves has conformal invariance with the root-mean-square distance Rrms˜t3 /4 (t being the parametrization of the curve) in accordance with the 2D SAW. In the finite-size study, we observe that at T =Tc the model has some aspects compatible with the 2D BTW model (e.g., the 1 /log(L ) -dependence of the exponents of the distribution functions) and some in accordance with the Ising model (e.g., the 1 /L -dependence of the fractal dimensions). The finite-size scaling theory is tested and shown to be fulfilled for all statistical observables in T =Tc . In the off-critical temperatures in the close vicinity of Tc the exponents show some additional power-law behaviors in terms of T -Tc with some exponents that are reported in the text. The spanning cluster probability at the critical temperature also scales with L1/2, which is different from the regular 2D BTW model.

Finite Element in Angle Unit Sphere Meshing for Charged Particle Transport.

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

Ortega, Mario Ivan; Drumm, Clifton R.

Finite element in angle formulations of the charged particle transport equation require the discretization of the unit sphere. In Sceptre, a three-dimensional surface mesh of a sphere is transformed into a two-dimensional mesh. Projection of a sphere onto a two-dimensional surface is well studied with map makers spending the last few centuries attempting to create maps that preserve proportion and area. Using these techniques, various meshing schemes for the unit sphere were investigated.

Three-dimensional compact explicit-finite difference time domain scheme with density variation

NASA Astrophysics Data System (ADS)

Tsuchiya, Takao; Maruta, Naoki

2018-07-01

In this paper, the density variation is implemented in the three-dimensional compact-explicit finite-difference time-domain (CE-FDTD) method. The formulation is first developed based on the continuity equation and the equation of motion, which include the density. Some numerical demonstrations are performed for the three-dimensional sound wave propagation in a two density layered medium. The numerical results are compared with the theoretical results to verify the proposed formulation.

A Statistical Approach for the Concurrent Coupling of Molecular Dynamics and Finite Element Methods

NASA Technical Reports Server (NTRS)

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

2007-01-01

Molecular dynamics (MD) methods are opening new opportunities for simulating the fundamental processes of material behavior at the atomistic level. However, increasing the size of the MD domain quickly presents intractable computational demands. A robust approach to surmount this computational limitation has been to unite continuum modeling procedures such as the finite element method (FEM) with MD analyses thereby reducing the region of atomic scale refinement. The challenging problem is to seamlessly connect the two inherently different simulation techniques at their interface. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the typical boundary value problem used to define a coupled domain. The method uses statistical averaging of the atomistic MD domain to provide displacement interface boundary conditions to the surrounding continuum FEM region, which, in return, generates interface reaction forces applied as piecewise constant traction boundary conditions to the MD domain. The two systems are computationally disconnected and communicate only through a continuous update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM) as opposed to a direct coupling method where interface atoms and FEM nodes are individually related. The methodology is inherently applicable to three-dimensional domains, avoids discretization of the continuum model down to atomic scales, and permits arbitrary temperatures to be applied.

[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.

A finite element conjugate gradient FFT method for scattering

NASA Technical Reports Server (NTRS)

Collins, Jeffery D.; Zapp, John; Hsa, Chang-Yu; Volakis, John L.

1990-01-01

An extension of a two dimensional formulation is presented for a three dimensional body of revolution. With the introduction of a Fourier expansion of the vector electric and magnetic fields, a coupled two dimensional system is generated and solved via the finite element method. An exact boundary condition is employed to terminate the mesh and the fast fourier transformation (FFT) is used to evaluate the boundary integrals for low O(n) memory demand when an iterative solution algorithm is used. By virtue of the finite element method, the algorithm is applicable to structures of arbitrary material composition. Several improvements to the two dimensional algorithm are also described. These include: (1) modifications for terminating the mesh at circular boundaries without distorting the convolutionality of the boundary integrals; (2) the development of nonproprietary mesh generation routines for two dimensional applications; (3) the development of preprocessors for interfacing SDRC IDEAS with the main algorithm; and (4) the development of post-processing algorithms based on the public domain package GRAFIC to generate two and three dimensional gray level and color field maps.

Explorations in fuzzy physics and non-commutative geometry

NASA Astrophysics Data System (ADS)

Kurkcuoglu, Seckin

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

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.

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

PubMed

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

2013-02-01

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

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

NASA Technical Reports Server (NTRS)

Liu, Jiwen; Tiwari, Surendra N.

1994-01-01

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

Extension of vibrational power flow techniques to two-dimensional structures

NASA Technical Reports Server (NTRS)

Cuschieri, J. M.

1987-01-01

In the analysis of the vibration response and structure-borne vibration transmission between elements of a complex structure, statistical energy analysis (SEA) or Finite Element Analysis (FEA) are generally used. However, an alternative method is using vibrational power flow techniques which can be especially useful in the mid- frequencies between the optimum frequency regimes for FEA and SEA. Power flow analysis has in general been used on one-dimensional beam-like structures or between structures with point joints. In this paper, the power flow technique is extended to two-dimensional plate like structures joined along a common edge without frequency or spatial averaging the results, such that the resonant response of the structure is determined. The power flow results are compared to results obtained using FEA at low frequencies and SEA at high frequencies. The agreement with FEA results is good but the power flow technique has an improved computational efficiency. Compared to the SEA results the power flow results show a closer representation of the actual response of the structure.

Pauli structures arising from confined particles interacting via a statistical potential

NASA Astrophysics Data System (ADS)

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

2017-09-01

There have been suggestions that the Pauli exclusion principle alone can lead a non-interacting (free) system of identical fermions to form crystalline structures dubbed Pauli crystals. Single-shot imaging experiments for the case of ultra-cold systems of free spin-polarized fermionic atoms in a two-dimensional harmonic trap appear to show geometric arrangements that cannot be characterized as Wigner crystals. This work explores this idea and considers a well-known approach that enables one to treat a quantum system of free fermions as a system of classical particles interacting with a statistical interaction potential. The model under consideration, though classical in nature, incorporates the quantum statistics by endowing the classical particles with an effective interaction potential. The reasonable expectation is that possible Pauli crystal features seen in experiments may manifest in this model that captures the correct quantum statistics as a first order correction. We use the Monte Carlo simulated annealing method to obtain the most stable configurations of finite two-dimensional systems of confined particles that interact with an appropriate statistical repulsion potential. We consider both an isotropic harmonic and a hard-wall confinement potential. Despite minor differences, the most stable configurations observed in our model correspond to the reported Pauli crystals in single-shot imaging experiments of free spin-polarized fermions in a harmonic trap. The crystalline configurations observed appear to be different from the expected classical Wigner crystal structures that would emerge should the confined classical particles had interacted with a pair-wise Coulomb repulsion.

On infinite-dimensional state spaces

NASA Astrophysics Data System (ADS)

Fritz, Tobias

2013-05-01

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

A multiscale coupled finite-element and phase-field framework to modeling stressed grain growth in polycrystalline thin films

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

Jamshidian, M., E-mail: jamshidian@cc.iut.ac.ir; Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstrasse 15, 99423 Weimar; Thamburaja, P., E-mail: prakash.thamburaja@gmail.com

A previously-developed finite-deformation- and crystal-elasticity-based constitutive theory for stressed grain growth in cubic polycrystalline bodies has been augmented to include a description of excess surface energy and grain-growth stagnation mechanisms through the use of surface effect state variables in a thermodynamically-consistent manner. The constitutive theory was also implemented into a multiscale coupled finite-element and phase-field computational framework. With the material parameters in the constitutive theory suitably calibrated, our three-dimensional numerical simulations show that the constitutive model is able to accurately predict the experimentally-determined evolution of crystallographic texture and grain size statistics in polycrystalline copper thin films deposited on polyimide substratemore » and annealed at high-homologous temperatures. In particular, our numerical analyses show that the broad texture transition observed in the annealing experiments of polycrystalline thin films is caused by grain growth stagnation mechanisms. - Graphical abstract: - Highlights: • Developing a theory for stressed grain growth in polycrystalline thin films. • Implementation into a multiscale coupled finite-element and phase-field framework. • Quantitative reproduction of the experimental grain growth data by simulations. • Revealing the cause of texture transition to be due to the stagnation mechanisms.« less

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

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

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

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

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

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

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at; Tuffaha, Amjad, E-mail: atufaha@aus.edu

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solutionmore » of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.« less

Cluster properties of the one-dimensional lattice gas: the microscopic meaning of grand potential.

PubMed

Fronczak, Agata

2013-02-01

Using a concrete example, we demonstrate how the combinatorial approach to a general system of particles, which was introduced in detail in an earlier paper [Fronczak, Phys. Rev. E 86, 041139 (2012)], works and where this approach provides a genuine extension of results obtained through more traditional methods of statistical mechanics. We study the cluster properties of a one-dimensional lattice gas with nearest-neighbor interactions. Three cases (the infinite temperature limit, the range of finite temperatures, and the zero temperature limit) are discussed separately, yielding interesting results and providing alternative proof of known results. In particular, the closed-form expression for the grand partition function in the zero temperature limit is obtained, which results in the nonanalytic behavior of the grand potential, in accordance with the Yang-Lee theory.

Lack of a thermodynamic finite-temperature spin-glass phase in the two-dimensional randomly coupled ferromagnet

NASA Astrophysics Data System (ADS)

Zhu, Zheng; Ochoa, Andrew J.; Katzgraber, Helmut G.

2018-05-01

The search for problems where quantum adiabatic optimization might excel over classical optimization techniques has sparked a recent interest in inducing a finite-temperature spin-glass transition in quasiplanar topologies. We have performed large-scale finite-temperature Monte Carlo simulations of a two-dimensional square-lattice bimodal spin glass with next-nearest ferromagnetic interactions claimed to exhibit a finite-temperature spin-glass state for a particular relative strength of the next-nearest to nearest interactions [Phys. Rev. Lett. 76, 4616 (1996), 10.1103/PhysRevLett.76.4616]. Our results show that the system is in a paramagnetic state in the thermodynamic limit, despite zero-temperature simulations [Phys. Rev. B 63, 094423 (2001), 10.1103/PhysRevB.63.094423] suggesting the existence of a finite-temperature spin-glass transition. Therefore, deducing the finite-temperature behavior from zero-temperature simulations can be dangerous when corrections to scaling are large.

On the effects of grid ill-conditioning in three dimensional finite element vector potential magnetostatic field computations

NASA Technical Reports Server (NTRS)

Wang, R.; Demerdash, N. A.

1990-01-01

The effects of finite element grid geometries and associated ill-conditioning were studied in single medium and multi-media (air-iron) three dimensional magnetostatic field computation problems. The sensitivities of these 3D field computations to finite element grid geometries were investigated. It was found that in single medium applications the unconstrained magnetic vector potential curl-curl formulation in conjunction with first order finite elements produce global results which are almost totally insensitive to grid geometries. However, it was found that in multi-media (air-iron) applications first order finite element results are sensitive to grid geometries and consequent elemental shape ill-conditioning. These sensitivities were almost totally eliminated by means of the use of second order finite elements in the field computation algorithms. Practical examples are given in this paper to demonstrate these aspects mentioned above.

BOPACE 3-D (the Boeing Plastic Analysis Capability for 3-dimensional Solids Using Isoparametric Finite Elements)

NASA Technical Reports Server (NTRS)

Vos, R. G.; Straayer, J. W.

1975-01-01

The BOPACE 3-D is a finite element computer program, which provides a general family of three-dimensional isoparametric solid elements, and includes a new algorithm for improving the efficiency of the elastic-plastic-creep solution procedure. Theoretical, user, and programmer oriented sections are presented to describe the program.

Calculation methods for compressible turbulent boundary layers, 1976

NASA Technical Reports Server (NTRS)

Bushnell, D. M.; Cary, A. M., Jr.; Harris, J. E.

1977-01-01

Equations and closure methods for compressible turbulent boundary layers are discussed. Flow phenomena peculiar to calculation of these boundary layers were considered, along with calculations of three dimensional compressible turbulent boundary layers. Procedures for ascertaining nonsimilar two and three dimensional compressible turbulent boundary layers were appended, including finite difference, finite element, and mass-weighted residual methods.

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

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

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

Finite state modeling of aeroelastic systems

NASA Technical Reports Server (NTRS)

Vepa, R.

1977-01-01

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

Simulation of wave propagation in three-dimensional random media

NASA Technical Reports Server (NTRS)

Coles, William A.; Filice, J. P.; Frehlich, R. G.; Yadlowsky, M.

1993-01-01

Quantitative error analysis for simulation of wave propagation in three dimensional random media assuming narrow angular scattering are presented for the plane wave and spherical wave geometry. This includes the errors resulting from finite grid size, finite simulation dimensions, and the separation of the two-dimensional screens along the propagation direction. Simple error scalings are determined for power-law spectra of the random refractive index of the media. The effects of a finite inner scale are also considered. The spatial spectra of the intensity errors are calculated and compared to the spatial spectra of intensity. The numerical requirements for a simulation of given accuracy are determined for realizations of the field. The numerical requirements for accurate estimation of higher moments of the field are less stringent.

Least-squares finite element solutions for three-dimensional backward-facing step flow

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Hou, Lin-Jun; Lin, Tsung-Liang

1993-01-01

Comprehensive numerical solutions of the steady state incompressible viscous flow over a three-dimensional backward-facing step up to Re equals 800 are presented. The results are obtained by the least-squares finite element method (LSFEM) which is based on the velocity-pressure-vorticity formulation. The computed model is of the same size as that of Armaly's experiment. Three-dimensional phenomena are observed even at low Reynolds number. The calculated values of the primary reattachment length are in good agreement with experimental results.

Signatures of chaos in the Brillouin zone.

PubMed

Barr, Aaron; Barr, Ariel; Porter, Max D; Reichl, Linda E

2017-10-01

When the classical dynamics of a particle in a finite two-dimensional billiard undergoes a transition to chaos, the quantum dynamics of the particle also shows manifestations of chaos in the form of scarring of wave functions and changes in energy level spacing distributions. If we "tile" an infinite plane with such billiards, we find that the Bloch states on the lattice undergo avoided crossings, energy level spacing statistics change from Poisson-like to Wigner-like, and energy sheets of the Brillouin zone begin to "mix" as the classical dynamics of the billiard changes from regular to chaotic behavior.

Subgrid or Reynolds stress-modeling for three-dimensional turbulence computations

NASA Technical Reports Server (NTRS)

Rubesin, M. W.

1975-01-01

A review is given of recent advances in two distinct computational methods for evaluating turbulence fields, namely, statistical Reynolds stress modeling and turbulence simulation, where large eddies are followed in time. It is shown that evaluation of the mean Reynolds stresses, rather than use of a scalar eddy viscosity, permits an explanation of streamline curvature effects found in several experiments. Turbulence simulation, with a new volume averaging technique and third-order accurate finite-difference computing is shown to predict the decay of isotropic turbulence in incompressible flow with rather modest computer storage requirements, even at Reynolds numbers of aerodynamic interest.

Condensation and critical exponents of an ideal non-Abelian gas

NASA Astrophysics Data System (ADS)

Talaei, Zahra; Mirza, Behrouz; Mohammadzadeh, Hosein

2017-11-01

We investigate an ideal gas obeying non-Abelian statistics and derive the expressions for some thermodynamic quantities. It is found that thermodynamic quantities are finite at the condensation point where their derivatives diverge and, near this point, they behave as \\vert T-Tc\\vert^{-ρ} in which Tc denotes the condensation temperature and ρ is a critical exponent. The critical exponents related to the heat capacity and compressibility are obtained by fitting numerical results and others are obtained using the scaling law hypothesis for a three-dimensional non-Abelian ideal gas. This set of critical exponents introduces a new universality class.

Stress-intensity factor equations for cracks in three-dimensional finite bodies

NASA Technical Reports Server (NTRS)

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

1981-01-01

Empirical stress intensity factor equations are presented for embedded elliptical cracks, semi-elliptical surface cracks, quarter-elliptical corner cracks, semi-elliptical surface cracks at a hole, and quarter-elliptical corner cracks at a hole in finite plates. The plates were subjected to remote tensile loading. Equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and where applicable, hole radius. The stress intensity factors used to develop the equations were obtained from three dimensional finite element analyses of these crack configurations.

Fourier analysis of finite element preconditioned collocation schemes

NASA Technical Reports Server (NTRS)

Deville, Michel O.; Mund, Ernest H.

1990-01-01

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

Hopping and the Stokes–Einstein relation breakdown in simple glass formers

PubMed Central

Charbonneau, Patrick; Jin, Yuliang; Parisi, Giorgio; Zamponi, Francesco

2014-01-01

One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition—like that of other statistical systems—is exact when the spatial dimension d→∞, the evolution of systems properties with d may not be smooth. Finite-dimensional effects could dramatically change what happens in physical dimensions, d=2,3. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes–Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step toward describing dynamic facilitation in the framework of the mean-field theory of glasses. PMID:25288722

Hopping and the Stokes-Einstein relation breakdown in simple glass formers.

PubMed

Charbonneau, Patrick; Jin, Yuliang; Parisi, Giorgio; Zamponi, Francesco

2014-10-21

One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition--like that of other statistical systems--is exact when the spatial dimension d → ∞, the evolution of systems properties with d may not be smooth. Finite-dimensional effects could dramatically change what happens in physical dimensions,d = 2, 3. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes-Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step toward describing dynamic facilitation in the framework of the mean-field theory of glasses.

The finite body triangulation: algorithms, subgraphs, homogeneity estimation and application.

PubMed

Carson, Cantwell G; Levine, Jonathan S

2016-09-01

The concept of a finite body Dirichlet tessellation has been extended to that of a finite body Delaunay 'triangulation' to provide a more meaningful description of the spatial distribution of nonspherical secondary phase bodies in 2- and 3-dimensional images. A finite body triangulation (FBT) consists of a network of minimum edge-to-edge distances between adjacent objects in a microstructure. From this is also obtained the characteristic object chords formed by the intersection of the object boundary with the finite body tessellation. These two sets of distances form the basis of a parsimonious homogeneity estimation. The characteristics of the spatial distribution are then evaluated with respect to the distances between objects and the distances within them. Quantitative analysis shows that more physically representative distributions can be obtained by selecting subgraphs, such as the relative neighbourhood graph and the minimum spanning tree, from the finite body tessellation. To demonstrate their potential, we apply these methods to 3-dimensional X-ray computed tomographic images of foamed cement and their 2-dimensional cross sections. The Python computer code used to estimate the FBT is made available. Other applications for the algorithm - such as porous media transport and crack-tip propagation - are also discussed. © 2016 The Authors Journal of Microscopy © 2016 Royal Microscopical Society.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

The finite-dimensional Freeman thesis.

PubMed

Rudolph, Lee

2008-06-01

I suggest a modification--and mathematization--of Freeman's thesis on the relations among "perception", "the finite brain", and "the world", based on my recent proposal that the theory of finite topological spaces is both an adequate and a natural mathematical foundation for human psychology.

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

NASA Technical Reports Server (NTRS)

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

2004-01-01

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

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

NASA Technical Reports Server (NTRS)

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

2002-01-01

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

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

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

1984-01-01

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

Analysis of Ninety Degree Flexure Tests for Characterization of Composite Transverse Tensile Strength

NASA Technical Reports Server (NTRS)

OBrien, T. Kevin; Krueger, Ronald

2001-01-01

Finite element (FE) analysis was performed on 3-point and 4-point bending test configurations of ninety degree oriented glass-epoxy and graphite-epoxy composite beams to identify deviations from beam theory predictions. Both linear and geometric non-linear analyses were performed using the ABAQUS finite element code. The 3-point and 4-point bending specimens were first modeled with two-dimensional elements. Three-dimensional finite element models were then performed for selected 4-point bending configurations to study the stress distribution across the width of the specimens and compare the results to the stresses computed from two-dimensional plane strain and plane stress analyses and the stresses from beam theory. Stresses for all configurations were analyzed at load levels corresponding to the measured transverse tensile strength of the material.

Three-Dimensional Finite Element Ablative Thermal Response and Thermostructural Design of Thermal Protection Systems

NASA Technical Reports Server (NTRS)

Dec, John A.; Braun, Robert D.

2011-01-01

A finite element ablation and thermal response program is presented for simulation of three-dimensional transient thermostructural analysis. The three-dimensional governing differential equations and finite element formulation are summarized. A novel probabilistic design methodology for thermal protection systems is presented. The design methodology is an eight step process beginning with a parameter sensitivity study and is followed by a deterministic analysis whereby an optimum design can determined. The design process concludes with a Monte Carlo simulation where the probabilities of exceeding design specifications are estimated. The design methodology is demonstrated by applying the methodology to the carbon phenolic compression pads of the Crew Exploration Vehicle. The maximum allowed values of bondline temperature and tensile stress are used as the design specifications in this study.

Gauged supergravities from M-theory reductions

NASA Astrophysics Data System (ADS)

Katmadas, Stefanos; Tomasiello, Alessandro

2018-04-01

In supergravity compactifications, there is in general no clear prescription on how to select a finite-dimensional family of metrics on the internal space, and a family of forms on which to expand the various potentials, such that the lower-dimensional effective theory is supersymmetric. We propose a finite-dimensional family of deformations for regular Sasaki-Einstein seven-manifolds M 7, relevant for M-theory compactifications down to four dimensions. It consists of integrable Cauchy-Riemann structures, corresponding to complex deformations of the Calabi-Yau cone M 8 over M 7. The non-harmonic forms we propose are the ones contained in one of the Kohn-Rossi cohomology groups, which is finite-dimensional and naturally controls the deformations of Cauchy-Riemann structures. The same family of deformations can be also described in terms of twisted cohomology of the base M 6, or in terms of Milnor cycles arising in deformations of M 8. Using existing results on SU(3) structure compactifications, we briefly discuss the reduction of M-theory on our class of deformed Sasaki-Einstein manifolds to four-dimensional gauged supergravity.

Stress concentration investigations using NASTRAN

NASA Technical Reports Server (NTRS)

Gillcrist, M. C.; Parnell, L. A.

1986-01-01

Parametic investigations are performed using several two dimensional finite element formulations to determine their suitability for use in predicting extremum stresses in marine propellers. Comparisons are made of two NASTRAN elements (CTRIM6 and CTRAIA2) wherein elasticity properties have been modified to yield plane strain results. The accuracy of the elements is investigated by comparing finite element stress predictions with experimentally determined stresses in two classical cases: (1) tension in a flat plate with a circular hole; and (2) a filleted flat bar subjected to in-plane bending. The CTRIA2 element is found to provide good results. The displacement field from a three dimensional finite element model of a representative marine propeller is used as the boundary condition for the two dimensional plane strain investigations of stresses in the propeller blade and fillet. Stress predictions from the three dimensional analysis are compared with those from the two dimensional models. The validity of the plane strain modifications to the NASTRAN element is checked by comparing the modified CTRIA2 element stress predictions with those of the ABAQUS plane strain element, CPE4.

On infinite-dimensional state spaces

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

Fritz, Tobias

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

Approximation of Optimal Infinite Dimensional Compensators for Flexible Structures

NASA Technical Reports Server (NTRS)

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

1985-01-01

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

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

NASA Astrophysics Data System (ADS)

Merdan, Ziya; Karakuş, Özlem

2016-11-01

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

Influence of two-dimensional hygrothermal gradients on interlaminar stresses near free edges

NASA Technical Reports Server (NTRS)

Farley, G. L.; Herakovich, C. T.

1977-01-01

Interlaminar stresses are determined for mechanical loading, uniform hygrothermal loading, and gradient moisture loading through implementation of a finite element computer code. Nonuniform two-dimensional hygroscopic gradients are obtained from a finite difference solution of the diffusion equation. It is shown that hygroscopic induced stresses can be larger than those resulting from mechanical and thermal loading, and that the distribution of the interlaminar normal stress may be changed significantly in the presence of a two-dimensional moisture gradient in the boundary layer of a composite laminate.

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

NASA Technical Reports Server (NTRS)

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

1979-01-01

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

Diffusion Characteristics of Upwind Schemes on Unstructured Triangulations

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1998-01-01

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and dimensionally-split finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the dimensionally-split finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2-3 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a 20-25 speedup over finite volume.

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

PubMed

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

2012-10-01

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

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.

Glassy phase in quenched disordered crystalline membranes

NASA Astrophysics Data System (ADS)

Coquand, O.; Essafi, K.; Kownacki, J.-P.; Mouhanna, D.

2018-03-01

We investigate the flat phase of D -dimensional crystalline membranes embedded in a d -dimensional space and submitted to both metric and curvature quenched disorders using a nonperturbative renormalization group approach. We identify a second-order phase transition controlled by a finite-temperature, finite-disorder fixed point unreachable within the leading order of ɛ =4 -D and 1 /d expansions. This critical point divides the flow diagram into two basins of attraction: that associated with the finite-temperature fixed point controlling the long-distance behavior of disorder-free membranes and that associated with the zero-temperature, finite-disorder fixed point. Our work thus strongly suggests the existence of a whole low-temperature glassy phase for quenched disordered crystalline membranes and, possibly, for graphene and graphene-like compounds.

Features of statistical dynamics in a finite system

NASA Astrophysics Data System (ADS)

Yan, Shiwei; Sakata, Fumihiko; Zhuo, Yizhong

2002-03-01

We study features of statistical dynamics in a finite Hamilton system composed of a relevant one degree of freedom coupled to an irrelevant multidegree of freedom system through a weak interaction. Special attention is paid on how the statistical dynamics changes depending on the number of degrees of freedom in the irrelevant system. It is found that the macrolevel statistical aspects are strongly related to an appearance of the microlevel chaotic motion, and a dissipation of the relevant motion is realized passing through three distinct stages: dephasing, statistical relaxation, and equilibrium regimes. It is clarified that the dynamical description and the conventional transport approach provide us with almost the same macrolevel and microlevel mechanisms only for the system with a very large number of irrelevant degrees of freedom. It is also shown that the statistical relaxation in the finite system is an anomalous diffusion and the fluctuation effects have a finite correlation time.

Features of statistical dynamics in a finite system.

PubMed

Yan, Shiwei; Sakata, Fumihiko; Zhuo, Yizhong

2002-03-01

We study features of statistical dynamics in a finite Hamilton system composed of a relevant one degree of freedom coupled to an irrelevant multidegree of freedom system through a weak interaction. Special attention is paid on how the statistical dynamics changes depending on the number of degrees of freedom in the irrelevant system. It is found that the macrolevel statistical aspects are strongly related to an appearance of the microlevel chaotic motion, and a dissipation of the relevant motion is realized passing through three distinct stages: dephasing, statistical relaxation, and equilibrium regimes. It is clarified that the dynamical description and the conventional transport approach provide us with almost the same macrolevel and microlevel mechanisms only for the system with a very large number of irrelevant degrees of freedom. It is also shown that the statistical relaxation in the finite system is an anomalous diffusion and the fluctuation effects have a finite correlation time.

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

Treesearch

Hongmei Gu; John F. Hunt

2006-01-01

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

A two-dimensional finite-difference solution for the temperature distribution in a radial gas turbine guide vane blade

NASA Technical Reports Server (NTRS)

Hosny, W. M.; Tabakoff, W.

1975-01-01

A two-dimensional finite difference numerical technique is presented to determine the temperature distribution in a solid blade of a radial guide vane. A computer program is written in Fortran IV for IBM 370/165 computer. The computer results obtained from these programs have a similar behavior and trend as those obtained by experimental results.

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

PubMed

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

2015-12-24

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

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

PubMed

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

2018-05-22

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

Three-dimensional supersonic flow around double compression ramp with finite span

NASA Astrophysics Data System (ADS)

Lee, H. S.; Lee, J. H.; Park, G.; Park, S. H.; Byun, Y. H.

2017-01-01

Three-dimensional flows of Mach number 3 around a double-compression ramp with finite span have been investigated numerically. Shadowgraph visualisation images obtained in a supersonic wind tunnel are used for comparison. A three-dimensional Reynolds-averaged Navier-Stokes solver was used to obtain steady numerical solutions. Two-dimensional numerical results are also compared. Four different cases were studied: two different second ramp angles of 30° and 45° in configurations with and without sidewalls, respectively. Results showed that there is a leakage of mass and momentum fluxes heading outwards in the spanwise direction for three-dimensional cases without sidewalls. The leakage changed the flow characteristics of the shock-induced boundary layer and resulted in the discrepancy between the experimental data and two-dimensional numerical results. It is found that suppressing the flow leakage by attaching the sidewalls enhances the two-dimensionality of the experimental data for the double-compression ramp flow.

Hybrid phase transition into an absorbing state: Percolation and avalanches

NASA Astrophysics Data System (ADS)

Lee, Deokjae; Choi, S.; Stippinger, M.; Kertész, J.; Kahng, B.

2016-04-01

Interdependent networks are more fragile under random attacks than simplex networks, because interlayer dependencies lead to cascading failures and finally to a sudden collapse. This is a hybrid phase transition (HPT), meaning that at the transition point the order parameter has a jump but there are also critical phenomena related to it. Here we study these phenomena on the Erdős-Rényi and the two-dimensional interdependent networks and show that the hybrid percolation transition exhibits two kinds of critical behaviors: divergence of the fluctuations of the order parameter and power-law size distribution of finite avalanches at a transition point. At the transition point global or "infinite" avalanches occur, while the finite ones have a power law size distribution; thus the avalanche statistics also has the nature of a HPT. The exponent βm of the order parameter is 1 /2 under general conditions, while the value of the exponent γm characterizing the fluctuations of the order parameter depends on the system. The critical behavior of the finite avalanches can be described by another set of exponents, βa and γa. These two critical behaviors are coupled by a scaling law: 1 -βm=γa .

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

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

Weatherby, J.R.

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

The direct field boundary impedance of two-dimensional periodic structures with application to high frequency vibration prediction.

PubMed

Langley, Robin S; Cotoni, Vincent

2010-04-01

Large sections of many types of engineering construction can be considered to constitute a two-dimensional periodic structure, with examples ranging from an orthogonally stiffened shell to a honeycomb sandwich panel. In this paper, a method is presented for computing the boundary (or edge) impedance of a semi-infinite two-dimensional periodic structure, a quantity which is referred to as the direct field boundary impedance matrix. This terminology arises from the fact that none of the waves generated at the boundary (the direct field) are reflected back to the boundary in a semi-infinite system. The direct field impedance matrix can be used to calculate elastic wave transmission coefficients, and also to calculate the coupling loss factors (CLFs), which are required by the statistical energy analysis (SEA) approach to predicting high frequency vibration levels in built-up systems. The calculation of the relevant CLFs enables a two-dimensional periodic region of a structure to be modeled very efficiently as a single subsystem within SEA, and also within related methods, such as a recently developed hybrid approach, which couples the finite element method with SEA. The analysis is illustrated by various numerical examples involving stiffened plate structures.

Computing the optimal path in stochastic dynamical systems

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

Bauver, Martha; Forgoston, Eric, E-mail: eric.forgoston@montclair.edu; Billings, Lora

2016-08-15

In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high-dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a two-dimensionalmore » system that describes a single population with internal noise. This model has an analytical solution for the optimal path. The numerical solution found using our computational method agrees well with the analytical result. The second example is a more complicated four-dimensional system where our numerical method must be used to find the optimal path. The third example, although a seemingly simple two-dimensional system, demonstrates the success of our method in finding the optimal path where other numerical methods are known to fail. In the fourth example, the optimal path lies in six-dimensional space and demonstrates the power of our method in computing paths in higher-dimensional spaces.« less

A Mechanical Power Flow Capability for the Finite Element Code NASTRAN

DTIC Science & Technology

1989-07-01

perimental methods. statistical energy analysis , the finite element method, and a finite element analog-,y using heat conduction equations. Experimental...weights and inertias of the transducers attached to an experimental structure may produce accuracy problems. Statistical energy analysis (SEA) is a...405-422 (1987). 8. Lyon, R.L., Statistical Energy Analysis of Dynamical Sistems, The M.I.T. Press, (1975). 9. Mickol, J.D., and R.J. Bernhard, "An

On the theory of oscillating airfoils of finite span in subsonic compressible flow

NASA Technical Reports Server (NTRS)

Reissner, Eric

1950-01-01

The problem of oscillating lifting surface of finite span in subsonic compressible flow is reduced to an integral equation. The kernel of the integral equation is approximated by a simpler expression, on the basis of the assumption of sufficiently large aspect ratio. With this approximation the double integral occurring in the formulation of the problem is reduced to two single integrals, one of which is taken over the chord and the other over the span of the lifting surface. On the basis of this reduction the three-dimensional problem appears separated into two two-dimensional problems, one of them being effectively the problem of two-dimensional flow and the other being the problem of spanwise circulation distribution. Earlier results concerning the oscillating lifting surface of finite span in incompressible flow are contained in the present more general results.

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.

An efficient, explicit finite-rate algorithm to compute flows in chemical nonequilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

An explicit finite-rate code was developed to compute hypersonic viscous chemically reacting flows about three-dimensional bodies. Equations describing the finite-rate chemical reactions were fully coupled to the gas dynamic equations using a new coupling technique. The new technique maintains stability in the explicit finite-rate formulation while permitting relatively large global time steps.

Inverse finite-size scaling for high-dimensional significance analysis

NASA Astrophysics Data System (ADS)

Xu, Yingying; Puranen, Santeri; Corander, Jukka; Kabashima, Yoshiyuki

2018-06-01

We propose an efficient procedure for significance determination in high-dimensional dependence learning based on surrogate data testing, termed inverse finite-size scaling (IFSS). The IFSS method is based on our discovery of a universal scaling property of random matrices which enables inference about signal behavior from much smaller scale surrogate data than the dimensionality of the original data. As a motivating example, we demonstrate the procedure for ultra-high-dimensional Potts models with order of 1010 parameters. IFSS reduces the computational effort of the data-testing procedure by several orders of magnitude, making it very efficient for practical purposes. This approach thus holds considerable potential for generalization to other types of complex models.

Exact finite elements for conduction and convection

NASA Technical Reports Server (NTRS)

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

1981-01-01

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

Data-Adaptive Bias-Reduced Doubly Robust Estimation.

PubMed

Vermeulen, Karel; Vansteelandt, Stijn

2016-05-01

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

[Finite Element Modelling of the Eye for the Investigation of Accommodation].

PubMed

Martin, H; Stachs, O; Guthoff, R; Grabow, N

2016-12-01

Background: Accommodation research increasingly uses engineering methods. This article presents the use of the finite element method in accommodation research. Material and Methods: Geometry, material data and boundary conditions are prerequisites for the application of the finite element method. Published data on geometry and materials are reviewed. It is shown how boundary conditions are important and how they influence the results. Results: Two dimensional and three dimensional models of the anterior chamber of the eye are presented. With simple two dimensional models, it is shown that realistic results for the accommodation amplitude can always be achieved. More complex three dimensional models of the accommodation mechanism - including the ciliary muscle - require further investigations of the material data and of the morphology of the ciliary muscle, if they are to achieve realistic results for accommodation. Discussion and Conclusion: The efficiency and the limitations of the finite element method are especially clear for accommodation. Application of the method requires extensive preparation, including acquisition of geometric and material data and experimental validation. However, a validated model can be used as a basis for parametric studies, by systematically varying material data and geometric dimensions. This allows systematic investigation of how essential input parameters influence the results. Georg Thieme Verlag KG Stuttgart · New York.

Rotational Invariance of the 2d Spin - Spin Correlation Function

NASA Astrophysics Data System (ADS)

Pinson, Haru

2012-09-01

At the critical temperature in the 2d Ising model on the square lattice, we establish the rotational invariance of the spin-spin correlation function using the asymptotics of the spin-spin correlation function along special directions (McCoy and Wu in the two dimensional Ising model. Harvard University Press, Cambridge, 1973) and the finite difference Hirota equation for which the spin-spin correlation function is shown to satisfy (Perk in Phys Lett A 79:3-5, 1980; Perk in Proceedings of III international symposium on selected topics in statistical mechanics, Dubna, August 22-26, 1984, JINR, vol II, pp 138-151, 1985).

Chaotic Ising-like dynamics in traffic signals

PubMed Central

Suzuki, Hideyuki; Imura, Jun-ichi; Aihara, Kazuyuki

2013-01-01

The green and red lights of a traffic signal can be viewed as the up and down states of an Ising spin. Moreover, traffic signals in a city interact with each other, if they are controlled in a decentralised way. In this paper, a simple model of such interacting signals on a finite-size two-dimensional lattice is shown to have Ising-like dynamics that undergoes a ferromagnetic phase transition. Probabilistic behaviour of the model is realised by chaotic billiard dynamics that arises from coupled non-chaotic elements. This purely deterministic model is expected to serve as a starting point for considering statistical mechanics of traffic signals. PMID:23350034

Power calculation for overall hypothesis testing with high-dimensional commensurate outcomes.

PubMed

Chi, Yueh-Yun; Gribbin, Matthew J; Johnson, Jacqueline L; Muller, Keith E

2014-02-28

The complexity of system biology means that any metabolic, genetic, or proteomic pathway typically includes so many components (e.g., molecules) that statistical methods specialized for overall testing of high-dimensional and commensurate outcomes are required. While many overall tests have been proposed, very few have power and sample size methods. We develop accurate power and sample size methods and software to facilitate study planning for high-dimensional pathway analysis. With an account of any complex correlation structure between high-dimensional outcomes, the new methods allow power calculation even when the sample size is less than the number of variables. We derive the exact (finite-sample) and approximate non-null distributions of the 'univariate' approach to repeated measures test statistic, as well as power-equivalent scenarios useful to generalize our numerical evaluations. Extensive simulations of group comparisons support the accuracy of the approximations even when the ratio of number of variables to sample size is large. We derive a minimum set of constants and parameters sufficient and practical for power calculation. Using the new methods and specifying the minimum set to determine power for a study of metabolic consequences of vitamin B6 deficiency helps illustrate the practical value of the new results. Free software implementing the power and sample size methods applies to a wide range of designs, including one group pre-intervention and post-intervention comparisons, multiple parallel group comparisons with one-way or factorial designs, and the adjustment and evaluation of covariate effects. Copyright © 2013 John Wiley & Sons, Ltd.

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

NASA Technical Reports Server (NTRS)

Fahrenthold, Eric P.

2000-01-01

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

Predictive Rate-Distortion for Infinite-Order Markov Processes

NASA Astrophysics Data System (ADS)

Marzen, Sarah E.; Crutchfield, James P.

2016-06-01

Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on finite sequences cannot capture all of their past dependencies. Spectral arguments confirm a popular intuition: algorithms that cluster finite-length sequences fail dramatically when the underlying process has long-range temporal correlations and can fail even for processes generated by finite-memory hidden Markov models. We circumvent the curse of dimensionality in rate-distortion analysis of finite- and infinite-order processes by casting predictive rate-distortion objective functions in terms of the forward- and reverse-time causal states of computational mechanics. Examples demonstrate that the resulting algorithms yield substantial improvements.

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

PubMed Central

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

2015-01-01

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

Dental application of novel finite element analysis software for three-dimensional finite element modeling of a dentulous mandible from its computed tomography images.

PubMed

Nakamura, Keiko; Tajima, Kiyoshi; Chen, Ker-Kong; Nagamatsu, Yuki; Kakigawa, Hiroshi; Masumi, Shin-ich

2013-12-01

This study focused on the application of novel finite-element analysis software for constructing a finite-element model from the computed tomography data of a human dentulous mandible. The finite-element model is necessary for evaluating the mechanical response of the alveolar part of the mandible, resulting from occlusal force applied to the teeth during biting. Commercially available patient-specific general computed tomography-based finite-element analysis software was solely applied to the finite-element analysis for the extraction of computed tomography data. The mandibular bone with teeth was extracted from the original images. Both the enamel and the dentin were extracted after image processing, and the periodontal ligament was created from the segmented dentin. The constructed finite-element model was reasonably accurate using a total of 234,644 nodes and 1,268,784 tetrahedral and 40,665 shell elements. The elastic moduli of the heterogeneous mandibular bone were determined from the bone density data of the computed tomography images. The results suggested that the software applied in this study is both useful and powerful for creating a more accurate three-dimensional finite-element model of a dentulous mandible from the computed tomography data without the need for any other software.

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

NASA Astrophysics Data System (ADS)

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

1986-12-01

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

A two-dimensional statistical framework connecting thermodynamic profiles with filaments in the scrape off layer and application to experiments

NASA Astrophysics Data System (ADS)

Militello, F.; Farley, T.; Mukhi, K.; Walkden, N.; Omotani, J. T.

2018-05-01

A statistical framework was introduced in Militello and Omotani [Nucl. Fusion 56, 104004 (2016)] to correlate the dynamics and statistics of L-mode and inter-ELM plasma filaments with the radial profiles of thermodynamic quantities they generate in the Scrape Off Layer. This paper extends the framework to cases in which the filaments are emitted from the separatrix at different toroidal positions and with a finite toroidal velocity. It is found that the toroidal velocity does not affect the profiles, while the toroidal distribution of filament emission renormalises the waiting time between two events. Experimental data collected by visual camera imaging are used to evaluate the statistics of the fluctuations, to inform the choice of the probability distribution functions used in the application of the framework. It is found that the toroidal separation of the filaments is exponentially distributed, thus suggesting the lack of a toroidal modal structure. Finally, using these measurements, the framework is applied to an experimental case and good agreement is found.

Investigation of deformation of elements of three-dimensional reinforced concrete structures located in the soil, interacting with each other through rubber gaskets

NASA Astrophysics Data System (ADS)

Berezhnoi, D. V.; Balafendieva, I. S.; Sachenkov, A. A.; Sekaeva, L. R.

2017-06-01

In work the technique of calculation of elements of three-dimensional reinforced concrete substructures located in a soil, interacting with each other through rubber linings is realized. To describe the interaction of deformable structures with the ground, special “semi-infinite” finite elements are used. A technique has been implemented that allows one to describe the contact interaction of three-dimensional structures by means of a special contact finite element with specific properties. The obtained numerical results are compared with the experimental data, their good agreement is noted.

The smooth entropy formalism for von Neumann algebras

NASA Astrophysics Data System (ADS)

Berta, Mario; Furrer, Fabian; Scholz, Volkher B.

2016-01-01

We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the smooth conditional min- and max-entropy, we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-dimensional case. We generalize the entropic uncertainty relation with quantum side information of Tomamichel and Renner and discuss applications to quantum cryptography. In particular, we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra.

The smooth entropy formalism for von Neumann algebras

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

Berta, Mario, E-mail: berta@caltech.edu; Furrer, Fabian, E-mail: furrer@eve.phys.s.u-tokyo.ac.jp; Scholz, Volkher B., E-mail: scholz@phys.ethz.ch

2016-01-15

We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the smooth conditional min- and max-entropy, we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-dimensional case. We generalize the entropic uncertainty relation with quantum side information of Tomamichel and Renner and discuss applications to quantum cryptography. In particular, we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra.

MULTISCALE ADAPTIVE SMOOTHING MODELS FOR THE HEMODYNAMIC RESPONSE FUNCTION IN FMRI*

PubMed Central

Wang, Jiaping; Zhu, Hongtu; Fan, Jianqing; Giovanello, Kelly; Lin, Weili

2012-01-01

In the event-related functional magnetic resonance imaging (fMRI) data analysis, there is an extensive interest in accurately and robustly estimating the hemodynamic response function (HRF) and its associated statistics (e.g., the magnitude and duration of the activation). Most methods to date are developed in the time domain and they have utilized almost exclusively the temporal information of fMRI data without accounting for the spatial information. The aim of this paper is to develop a multiscale adaptive smoothing model (MASM) in the frequency domain by integrating the spatial and temporal information to adaptively and accurately estimate HRFs pertaining to each stimulus sequence across all voxels in a three-dimensional (3D) volume. We use two sets of simulation studies and a real data set to examine the finite sample performance of MASM in estimating HRFs. Our real and simulated data analyses confirm that MASM outperforms several other state-of-art methods, such as the smooth finite impulse response (sFIR) model. PMID:24533041

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

PubMed

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

2015-07-28

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

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

NASA Technical Reports Server (NTRS)

Hollis, Brian R.

1995-01-01

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

[Study on the effect of vertebrae semi-dislocation on the stress distribution in facet joint and interuertebral disc of patients with cervical syndrome based on the three dimensional finite element model].

PubMed

Zhang, Ming-cai; Lü, Si-zhe; Cheng, Ying-wu; Gu, Li-xu; Zhan, Hong-sheng; Shi, Yin-yu; Wang, Xiang; Huang, Shi-rong

2011-02-01

To study the effect of vertebrae semi-dislocation on the stress distribution in facet joint and interuertebral disc of patients with cervical syndrome using three dimensional finite element model. A patient with cervical spondylosis was randomly chosen, who was male, 28 years old, and diagnosed as cervical vertebra semidislocation by dynamic and static palpation and X-ray, and scanned from C(1) to C(7) by 0.75 mm slice thickness of CT. Based on the CT data, the software was used to construct the three dimensional finite element model of cervical vertebra semidislocation (C(4)-C(6)). Based on the model,virtual manipulation was used to correct the vertebra semidislocation by the software, and the stress distribution was analyzed. The result of finite element analysis showed that the stress distribution of C(5-6) facet joint and intervertebral disc changed after virtual manipulation. The vertebra semidislocation leads to the abnormal stress distribution of facet joint and intervertebral disc.

AutoCAD-To-GIFTS Translator Program

NASA Technical Reports Server (NTRS)

Jones, Andrew

1989-01-01

AutoCAD-to-GIFTS translator program, ACTOG, developed to facilitate quick generation of small finite-element models using CASA/GIFTS finite-element modeling program. Reads geometric data of drawing from Data Exchange File (DXF) used in AutoCAD and other PC-based drafting programs. Geometric entities recognized by ACTOG include points, lines, arcs, solids, three-dimensional lines, and three-dimensional faces. From this information, ACTOG creates GIFTS SRC file, which then reads into GIFTS preprocessor BULKM or modified and reads into EDITM to create finite-element model. SRC file used as is or edited for any number of uses. Written in Microsoft Quick-Basic (Version 2.0).

Mathematical Techniques for Nonlinear System Theory.

DTIC Science & Technology

1981-09-01

This report deals with research results obtained in the following areas: (1) Finite-dimensional linear system theory by algebraic methods--linear...Infinite-dimensional linear systems--realization theory of infinite-dimensional linear systems; (3) Nonlinear system theory --basic properties of

A low-dimensional analogue of holographic baryons

NASA Astrophysics Data System (ADS)

Bolognesi, Stefano; Sutcliffe, Paul

2014-04-01

Baryons in holographic QCD correspond to topological solitons in the bulk. The most prominent example is the Sakai-Sugimoto model, where the bulk soliton in the five-dimensional spacetime of AdS-type can be approximated by the flat space self-dual Yang-Mills instanton with a small size. Recently, the validity of this approximation has been verified by comparison with the numerical field theory solution. However, multi-solitons and solitons with finite density are currently beyond numerical field theory computations. Various approximations have been applied to investigate these important issues and have led to proposals for finite density configurations that include dyonic salt and baryonic popcorn. Here we introduce and investigate a low-dimensional analogue of the Sakai-Sugimoto model, in which the bulk soliton can be approximated by a flat space sigma model instanton. The bulk theory is a baby Skyrme model in a three-dimensional spacetime with negative curvature. The advantage of the lower-dimensional theory is that numerical simulations of multi-solitons and finite density solutions can be performed and compared with flat space instanton approximations. In particular, analogues of dyonic salt and baryonic popcorn configurations are found and analysed.

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.

The development of a three-dimensional partially elliptic flow computer program for combustor research

NASA Technical Reports Server (NTRS)

Pan, Y. S.

1978-01-01

A three dimensional, partially elliptic, computer program was developed. Without requiring three dimensional computer storage locations for all flow variables, the partially elliptic program is capable of predicting three dimensional combustor flow fields with large downstream effects. The program requires only slight increase of computer storage over the parabolic flow program from which it was developed. A finite difference formulation for a three dimensional, fully elliptic, turbulent, reacting, flow field was derived. Because of the negligible diffusion effects in the main flow direction in a supersonic combustor, the set of finite-difference equations can be reduced to a partially elliptic form. Only the pressure field was governed by an elliptic equation and requires three dimensional storage; all other dependent variables are governed by parabolic equations. A numerical procedure which combines a marching integration scheme with an iterative scheme for solving the elliptic pressure was adopted.

Finite Volume Algorithms for Heat Conduction

DTIC Science & Technology

2010-05-01

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

Integrated transient thermal-structural finite element analysis

NASA Technical Reports Server (NTRS)

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

1981-01-01

An integrated thermal structural finite element approach for efficient coupling of transient thermal and structural analysis is presented. Integrated thermal structural rod and one dimensional axisymmetric elements considering conduction and convection are developed and used in transient thermal structural applications. The improved accuracy of the integrated approach is illustrated by comparisons with exact transient heat conduction elasticity solutions and conventional finite element thermal finite element structural analyses.

Fractional representation theory - Robustness results with applications to finite dimensional control of a class of linear distributed systems

NASA Technical Reports Server (NTRS)

Nett, C. N.; Jacobson, C. A.; Balas, M. J.

1983-01-01

This paper reviews and extends the fractional representation theory. In particular, new and powerful robustness results are presented. This new theory is utilized to develop a preliminary design methodology for finite dimensional control of a class of linear evolution equations on a Banach space. The design is for stability in an input-output sense, but particular attention is paid to internal stability as well.

Applications of FEM and BEM in two-dimensional fracture mechanics problems

NASA Technical Reports Server (NTRS)

Min, J. B.; Steeve, B. E.; Swanson, G. R.

1992-01-01

A comparison of the finite element method (FEM) and boundary element method (BEM) for the solution of two-dimensional plane strain problems in fracture mechanics is presented in this paper. Stress intensity factors (SIF's) were calculated using both methods for elastic plates with either a single-edge crack or an inclined-edge crack. In particular, two currently available programs, ANSYS for finite element analysis and BEASY for boundary element analysis, were used.

Evaluation of the parameters affecting bone temperature during drilling using a three-dimensional dynamic elastoplastic finite element model.

PubMed

Chen, Yung-Chuan; Tu, Yuan-Kun; Zhuang, Jun-Yan; Tsai, Yi-Jung; Yen, Cheng-Yo; Hsiao, Chih-Kun

2017-11-01

A three-dimensional dynamic elastoplastic finite element model was constructed and experimentally validated and was used to investigate the parameters which influence bone temperature during drilling, including the drill speed, feeding force, drill bit diameter, and bone density. Results showed the proposed three-dimensional dynamic elastoplastic finite element model can effectively simulate the temperature elevation during bone drilling. The bone temperature rise decreased with an increase in feeding force and drill speed, however, increased with the diameter of drill bit or bone density. The temperature distribution is significantly affected by the drilling duration; a lower drilling speed reduced the exposure duration, decreases the region of the thermally affected zone. The constructed model could be applied for analyzing the influence parameters during bone drilling to reduce the risk of thermal necrosis. It may provide important information for the design of drill bits and surgical drilling powers.

Entropy Stable Wall Boundary Conditions for the Three-Dimensional Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2015-01-01

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

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

NASA Astrophysics Data System (ADS)

Pötz, Walter

2017-11-01

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

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

NASA Technical Reports Server (NTRS)

Dewitt, K. J.; Baliga, G.

1982-01-01

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

Three dimensional finite element methods: Their role in the design of DC accelerator systems

NASA Astrophysics Data System (ADS)

Podaru, Nicolae C.; Gottdang, A.; Mous, D. J. W.

2013-04-01

High Voltage Engineering has designed, built and tested a 2 MV dual irradiation system that will be applied for radiation damage studies and ion beam material modification. The system consists of two independent accelerators which support simultaneous proton and electron irradiation (energy range 100 keV - 2 MeV) of target sizes of up to 300 × 300 mm2. Three dimensional finite element methods were used in the design of various parts of the system. The electrostatic solver was used to quantify essential parameters of the solid-state power supply generating the DC high voltage. The magnetostatic solver and ray tracing were used to optimize the electron/ion beam transport. Close agreement between design and measurements of the accelerator characteristics as well as beam performance indicate the usefulness of three dimensional finite element methods during accelerator system design.

Nature of self-diffusion in two-dimensional fluids

NASA Astrophysics Data System (ADS)

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho; Talkner, Peter; Kidera, Akinori; Lee, Eok Kyun

2017-12-01

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. We numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(t\\sqrt{{ln}t}), however with a rescaled time.

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

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

Influence of Micro Threads Alteration on Osseointegration and Primary Stability of Implants: An FEA and In Vivo Analysis in Rabbits.

PubMed

Chowdhary, Ramesh; Halldin, Anders; Jimbo, Ryo; Wennerberg, Ann

2015-06-01

To describe the early bone tissue response to implants with and without micro threads designed to the full length of an oxidized titanium implant. A pair of two-dimensional finite element models was designed using a computer aided three-dimensional interactive application files of an implant model with micro threads in between macro threads and one without micro threads. Oxidized titanium implants with (test implants n=20) and without (control implants n=20) micro thread were prepared. A total of 12 rabbits were used and each received four implants. Insertion torque while implant placement and removal torque analysis after 4 weeks was performed in nine rabbits, and histomorphometric analysis in three rabbits, respectively. Finite element analysis showed less stress accumulation in test implant models with 31Mpa when compared with 62.2 Mpa in control implant model. Insertion and removal torque analysis did not show any statistical significance between the two implant designs. At 4 weeks, there was a significant difference between the two groups in the percentage of new bone volume and bone-to-implant contact in the femur (p< .05); however, not in the tibia. The effect of micro threads was prominent in the femur suggesting that micro threads promote bone formation. The stress distribution supported by the micro threads was especially effective in the cancellous bone. © 2013 Wiley Periodicals, Inc.

[Three-dimensional finite analysis of the stress in first mandibular molar with composite class I restoration when various mixing ratios of bases were used].

PubMed

Zhou, Lan; Yang, Jin-Bo; Liu, Dan; Liu, Zhan; Chen, Ying; Gao, Bo

2008-06-01

To analyze the possible damage to the remaining tooth and composite restorations when various mixing ratios of bases were used. Testing elastic modulus and poission's ratio of glass-ionomer Vitrebond and self-cured calcium hydroxide Dycal with mixing ratios of 1:1, 3:4, 4:3. Micro-CT was used to scan the first mandibular molar, and the three-dimensional finite element model of the first permanent mandibular molar with class I cavity was established. Analyzing the stress of tooth structure, composite and base cement under physical load when different mixing ratios of base cement were used. The elastic modulus of base cement in various mixing ratios was different, which had the statistic significance. The magnitude and location of stress in restored tooth made no differences when the mixing ratios of Vitrebond and Dycal were changed. The peak stress and spreading area in the model with Dycal was more than that with Vitrebond. Changing the best mixing ratio of base cement can partially influence the mechanistic character, but make no differences on the magnitude and location of stress in restored tooth. During the treatment of deep caries, the base cement of the elastic modulus which is proximal to the dentin and restoration should be chosen to avoid the fracture of tooth or restoration.

Mapping of the Bak, Tang, and Wiesenfeld sandpile model on a two-dimensional Ising-correlated percolation lattice to the two-dimensional self-avoiding random walk.

PubMed

Cheraghalizadeh, J; Najafi, M N; Dashti-Naserabadi, H; Mohammadzadeh, H

2017-11-01

The self-organized criticality on the random fractal networks has many motivations, like the movement pattern of fluid in the porous media. In addition to the randomness, introducing correlation between the neighboring portions of the porous media has some nontrivial effects. In this paper, we consider the Ising-like interactions between the active sites as the simplest method to bring correlations in the porous media, and we investigate the statistics of the BTW model in it. These correlations are controlled by the artificial "temperature" T and the sign of the Ising coupling. Based on our numerical results, we propose that at the Ising critical temperature T_{c} the model is compatible with the universality class of two-dimensional (2D) self-avoiding walk (SAW). Especially the fractal dimension of the loops, which are defined as the external frontier of the avalanches, is very close to D_{f}^{SAW}=4/3. Also, the corresponding open curves has conformal invariance with the root-mean-square distance R_{rms}∼t^{3/4} (t being the parametrization of the curve) in accordance with the 2D SAW. In the finite-size study, we observe that at T=T_{c} the model has some aspects compatible with the 2D BTW model (e.g., the 1/log(L)-dependence of the exponents of the distribution functions) and some in accordance with the Ising model (e.g., the 1/L-dependence of the fractal dimensions). The finite-size scaling theory is tested and shown to be fulfilled for all statistical observables in T=T_{c}. In the off-critical temperatures in the close vicinity of T_{c} the exponents show some additional power-law behaviors in terms of T-T_{c} with some exponents that are reported in the text. The spanning cluster probability at the critical temperature also scales with L^{1/2}, which is different from the regular 2D BTW model.

An enriched finite element method to fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

Critical scaling of the mutual information in two-dimensional disordered Ising models

NASA Astrophysics Data System (ADS)

Sriluckshmy, P. V.; Mandal, Ipsita

2018-04-01

Rényi mutual information, computed from second Rényi entropies, can identify classical phase transitions from their finite-size scaling at critical points. We apply this technique to examine the presence or absence of finite temperature phase transitions in various two-dimensional models on a square lattice, which are extensions of the conventional Ising model by adding a quenched disorder. When the quenched disorder causes the nearest neighbor bonds to be both ferromagnetic and antiferromagnetic, (a) a spin glass phase exists only at zero temperature, and (b) a ferromagnetic phase exists at a finite temperature when the antiferromagnetic bond distributions are sufficiently dilute. Furthermore, finite temperature paramagnetic-ferromagnetic transitions can also occur when the disordered bonds involve only ferromagnetic couplings of random strengths. In our numerical simulations, the ‘zero temperature only’ phase transitions are identified when there is no consistent finite-size scaling of the Rényi mutual information curves, while for finite temperature critical points, the curves can identify the critical temperature T c by their crossings at T c and 2 Tc .

Finite-element simulation of blood perfusion in muscle tissue during compression and sustained contraction.

PubMed

Vankan, W J; Huyghe, J M; Slaaf, D W; van Donkelaar, C C; Drost, M R; Janssen, J D; Huson, A

1997-09-01

Mechanical interaction between tissue stress and blood perfusion in skeletal muscles plays an important role in blood flow impediment during sustained contraction. The exact mechanism of this interaction is not clear, and experimental investigation of this mechanism is difficult. We developed a finite-element model of the mechanical behavior of blood-perfused muscle tissue, which accounts for mechanical blood-tissue interaction in maximally vasodilated vasculature. Verification of the model was performed by comparing finite-element results of blood pressure and flow with experimental measurements in a muscle that is subject to well-controlled mechanical loading conditions. In addition, we performed simulations of blood perfusion during tetanic, isometric contraction and maximal vasodilation in a simplified, two-dimensional finite-element model of a rat calf muscle. A vascular waterfall in the venous compartment was identified as the main cause for blood flow impediment both in the experiment and in the finite-element simulations. The validated finite-element model offers possibilities for detailed analysis of blood perfusion in three-dimensional muscle models under complicated loading conditions.

Finite-size scaling and integer-spin Heisenberg chains

NASA Astrophysics Data System (ADS)

Bonner, Jill C.; Müller, Gerhard

1984-03-01

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

Three dimensional finite-element analysis of finite-thickness fracture specimens

NASA Technical Reports Server (NTRS)

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

1977-01-01

The stress-intensity factors for most of the commonly used fracture specimens (center-crack tension, single and double edge-crack tension, and compact), those that have a through-the-thickness crack, were calculated using a three dimensional finite-element elastic stress analysis. Three-dimensional singularity elements were used around the crack front. The stress intensity factors along the crack front were evaluated by using a force method, developed herein, that requires no prior assumption of either plane stress or plane strain. The calculated stress-intensity factors from the present analysis were compared with those from the literature whenever possible and were generally found to be in good agreement. The stress-intensity factors at the midplane for all specimens analyzed were within 3 percent of the two dimensional plane strain values. The stress intensity factors at the specimen surfaces were considerably lower than at the midplanes. For the center-crack tension specimens with large thickness to crack-length ratios, the stress-intensity factor reached a maximum near the surface of the specimen. In all other specimens considered the maximum stress intensity occurred at the midplane.

Three-dimensional elastic-plastic finite-element analyses of constraint variations in cracked bodies

NASA Technical Reports Server (NTRS)

Newman, J. C., Jr.; Bigelow, C. A.; Shivakumar, K. N.

1993-01-01

Three-dimensional elastic-plastic (small-strain) finite-element analyses were used to study the stresses, deformations, and constraint variations around a straight-through crack in finite-thickness plates for an elastic-perfectly plastic material under monotonic and cyclic loading. Middle-crack tension specimens were analyzed for thicknesses ranging from 1.25 to 20 mm with various crack lengths. Three local constraint parameters, related to the normal, tangential, and hydrostatic stresses, showed similar variations along the crack front for a given thickness and applied stress level. Numerical analyses indicated that cyclic stress history and crack growth reduced the local constraint parameters in the interior of a plate, especially at high applied stress levels. A global constraint factor alpha(sub g) was defined to simulate three-dimensional effects in two-dimensional crack analyses. The global constraint factor was calculated as an average through-the-thickness value over the crack-front plastic region. Values of alpha(sub g) were found to be nearly independent of crack length and were related to the stress-intensity factor for a given thickness.

A non-linear dimension reduction methodology for generating data-driven stochastic input models

NASA Astrophysics Data System (ADS)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

2008-06-01

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space Rn. An isometric mapping F from M to a low-dimensional, compact, connected set A⊂Rd(d≪n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology by constructing low-dimensional input stochastic models to represent thermal diffusivity in two-phase microstructures. This model is used in analyzing the effect of topological variations of two-phase microstructures on the evolution of temperature in heat conduction processes.

ANSYS duplicate finite-element checker routine

NASA Technical Reports Server (NTRS)

Ortega, R.

1995-01-01

An ANSYS finite-element code routine to check for duplicated elements within the volume of a three-dimensional (3D) finite-element mesh was developed. The routine developed is used for checking floating elements within a mesh, identically duplicated elements, and intersecting elements with a common face. A space shuttle main engine alternate turbopump development high pressure oxidizer turbopump finite-element model check using the developed subroutine is discussed. Finally, recommendations are provided for duplicate element checking of 3D finite-element models.

Identities of Finitely Generated Algebras Over AN Infinite Field

NASA Astrophysics Data System (ADS)

Kemer, A. R.

1991-02-01

It is proved that for each finitely generated associative PI-algebra U over an infinite field F, there is a finite-dimensional F-algebra C such that the ideals of identities of the algebras U and C coincide. This yields a positive solution to the local problem of Specht for algebras over an infinite field: A finitely generated free associative algebra satisfies the maximum condition for T-ideals.

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

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

1984-01-01

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

Evaluation of stress changes in the mandible with a fixed functional appliance: a finite element study.

PubMed

Chaudhry, Anshul; Sidhu, Maninder S; Chaudhary, Girish; Grover, Seema; Chaudhry, Nimisha; Kaushik, Ashutosh

2015-02-01

The aim of this study was to evaluate the effects of a fixed functional appliance (Forsus Fatigue Resistant Device; 3M Unitek, Monrovia, Calif) on the mandible with 3-dimensional finite element stress analysis. A 3-dimensional finite element model of the mandible was constructed from the images generated by cone-beam computed tomography of a patient undergoing fixed orthodontic treatment. The changes were studied with the finite element method, in the form of highest von Mises stress and maximum principal stress regions. More areas of stress were seen in the model of the mandible with the Forsus compared with the model of the mandible in the resting stage. This fixed functional appliance studied by finite element model analysis caused increases in the maximum principal stress and the von Mises stress in both the cortical bone and the condylar region of the mandible by more than 2 times. Copyright © 2015 American Association of Orthodontists. Published by Elsevier Inc. All rights reserved.

An ensemble Kalman filter for statistical estimation of physics constrained nonlinear regression models

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

Harlim, John, E-mail: jharlim@psu.edu; Mahdi, Adam, E-mail: amahdi@ncsu.edu; Majda, Andrew J., E-mail: jonjon@cims.nyu.edu

2014-01-15

A central issue in contemporary science is the development of nonlinear data driven statistical–dynamical models for time series of noisy partial observations from nature or a complex model. It has been established recently that ad-hoc quadratic multi-level regression models can have finite-time blow-up of statistical solutions and/or pathological behavior of their invariant measure. Recently, a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior. Here a new finite ensemble Kalman filtering algorithm is developed for estimating the state, the linear and nonlinear model coefficients, the model and the observation noise covariances from available partialmore » noisy observations of the state. Several stringent tests and applications of the method are developed here. In the most complex application, the perfect model has 57 degrees of freedom involving a zonal (east–west) jet, two topographic Rossby waves, and 54 nonlinearly interacting Rossby waves; the perfect model has significant non-Gaussian statistics in the zonal jet with blocked and unblocked regimes and a non-Gaussian skewed distribution due to interaction with the other 56 modes. We only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation. Numerically, we find that a three dimensional nonlinear stochastic model with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion, including the skew non-Gaussian distribution and autocorrelation decay. On the other hand, a similar stochastic model with zero memory levels fails to capture the crucial non-Gaussian behavior of the zonal jet from the perfect 57-mode model.« less

Exact finite elements for conduction and convection

NASA Technical Reports Server (NTRS)

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

1981-01-01

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

Supermultiplet of β-deformations from twistors

NASA Astrophysics Data System (ADS)

Milián, Segundo P.

2017-09-01

We consider the supermultiplet of linearized beta-deformation of 𝒩 = 4 super-Yang-Mills (SYM). It was previously studied on the gravitational side. We study the supermultiplet of beta-deformations on the field theory side and we compare two finite-dimensional representations of psl(4|4,R) algebra. We show that they are related by an intertwining operator. We develop a twistor-based approach which could be useful for studying other finite-dimensional and nonunitary representations in AdS/CFT correspondence.

Computational methods for the control of distributed parameter systems

NASA Technical Reports Server (NTRS)

Burns, J. A.; Cliff, E. M.; Powers, R. K.

1985-01-01

It is shown that care must be taken to ensure that finite dimensional approximations of distributed parameter systems preserve important system properties (i.e., controllability, observability, stabilizability, detectability, etc.). It is noted that, if the particular scheme used to construct the finite dimensional model does not take into account these system properties, the model may not be suitable for control design and analysis. These ideas are illustrated by a simple example, i.e., a cable-spring-mass system.

CELFE/NASTRAN Code for the Analysis of Structures Subjected to High Velocity Impact

NASA Technical Reports Server (NTRS)

Chamis, C. C.

1978-01-01

CELFE (Coupled Eulerian Lagrangian Finite Element)/NASTRAN Code three-dimensional finite element code has the capability for analyzing of structures subjected to high velocity impact. The local response is predicted by CELFE and, for large problems, the far-field impact response is predicted by NASTRAN. The coupling of the CELFE code with NASTRAN (CELFE/NASTRAN code) and the application of the code to selected three-dimensional high velocity impact problems are described.

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

PubMed

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

2002-01-01

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

Measurement-based quantum teleportation on finite AKLT chains

NASA Astrophysics Data System (ADS)

Fujii, Akihiko; Feder, David

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

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.

Solution-adaptive finite element method in computational fracture mechanics

NASA Technical Reports Server (NTRS)

Min, J. B.; Bass, J. M.; Spradley, L. W.

1993-01-01

Some recent results obtained using solution-adaptive finite element method in linear elastic two-dimensional fracture mechanics problems are presented. The focus is on the basic issue of adaptive finite element method for validating the applications of new methodology to fracture mechanics problems by computing demonstration problems and comparing the stress intensity factors to analytical results.

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.

Two-Dimensional Finite Element Ablative Thermal Response Analysis of an Arcjet Stagnation Test

NASA Technical Reports Server (NTRS)

Dec, John A.; Laub, Bernard; Braun, Robert D.

2011-01-01

The finite element ablation and thermal response (FEAtR, hence forth called FEAR) design and analysis program simulates the one, two, or three-dimensional ablation, internal heat conduction, thermal decomposition, and pyrolysis gas flow of thermal protection system materials. As part of a code validation study, two-dimensional axisymmetric results from FEAR are compared to thermal response data obtained from an arc-jet stagnation test in this paper. The results from FEAR are also compared to the two-dimensional axisymmetric computations from the two-dimensional implicit thermal response and ablation program under the same arcjet conditions. The ablating material being used in this arcjet test is phenolic impregnated carbon ablator with an LI-2200 insulator as backup material. The test is performed at the NASA, Ames Research Center Interaction Heating Facility. Spatially distributed computational fluid dynamics solutions for the flow field around the test article are used for the surface boundary conditions.

2-D to 3-D global/local finite element analysis of cross-ply composite laminates

NASA Technical Reports Server (NTRS)

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

1990-01-01

An example of two-dimensional to three-dimensional global/local finite element analysis of a laminated composite plate with a hole is presented. The 'zoom' technique of global/local analysis is used, where displacements of the global/local interface from the two-dimensional global model are applied to the edges of the three-dimensional local model. Three different hole diameters, one, three, and six inches, are considered in order to compare the effect of hole size on the three-dimensional stress state around the hole. In addition, three different stacking sequences are analyzed for the six inch hole case in order to study the effect of stacking sequence. The existence of a 'critical' hole size, where the interlaminar stresses are maximum, is indicated. Dispersion of plies at the same angle, as opposed to clustering, is found to reduce the magnitude of some interlaminar stress components and increase others.

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

NASA Astrophysics Data System (ADS)

Mehta, Pravin K.

1990-10-01

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

Implementation of Finite Volume based Navier Stokes Algorithm Within General Purpose Flow Network Code

NASA Technical Reports Server (NTRS)

Schallhorn, Paul; Majumdar, Alok

2012-01-01

This paper describes a finite volume based numerical algorithm that allows multi-dimensional computation of fluid flow within a system level network flow analysis. There are several thermo-fluid engineering problems where higher fidelity solutions are needed that are not within the capacity of system level codes. The proposed algorithm will allow NASA's Generalized Fluid System Simulation Program (GFSSP) to perform multi-dimensional flow calculation within the framework of GFSSP s typical system level flow network consisting of fluid nodes and branches. The paper presents several classical two-dimensional fluid dynamics problems that have been solved by GFSSP's multi-dimensional flow solver. The numerical solutions are compared with the analytical and benchmark solution of Poiseulle, Couette and flow in a driven cavity.

Transition probabilities for non self-adjoint Hamiltonians in infinite dimensional Hilbert spaces

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

Bagarello, F., E-mail: fabio.bagarello@unipa.it

In a recent paper we have introduced several possible inequivalent descriptions of the dynamics and of the transition probabilities of a quantum system when its Hamiltonian is not self-adjoint. Our analysis was carried out in finite dimensional Hilbert spaces. This is useful, but quite restrictive since many physically relevant quantum systems live in infinite dimensional Hilbert spaces. In this paper we consider this situation, and we discuss some applications to well known models, introduced in the literature in recent years: the extended harmonic oscillator, the Swanson model and a generalized version of the Landau levels Hamiltonian. Not surprisingly we willmore » find new interesting features not previously found in finite dimensional Hilbert spaces, useful for a deeper comprehension of this kind of physical systems.« less

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

PubMed Central

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

2015-01-01

In this paper, a new semi-automatic procedure to transform three-dimensional point clouds of complex objects to three-dimensional finite element models is presented and validated. The procedure conceives of the point cloud as a stacking of point sections. The complexity of the clouds is arbitrary, since the procedure is designed for terrestrial laser scanner surveys applied to buildings with irregular geometry, such as historical buildings. The procedure aims at solving the problems connected to the generation of finite element models of these complex structures by constructing a fine discretized geometry with a reduced amount of time and ready to be used with structural analysis. If the starting clouds represent the inner and outer surfaces of the structure, the resulting finite element model will accurately capture the whole three-dimensional structure, producing a complex solid made by voxel elements. A comparison analysis with a CAD-based model is carried out on a historical building damaged by a seismic event. The results indicate that the proposed procedure is effective and obtains comparable models in a shorter time, with an increased level of automation. PMID:26225978

Finite-size scaling of clique percolation on two-dimensional Moore lattices

NASA Astrophysics Data System (ADS)

Dong, Jia-Qi; Shen, Zhou; Zhang, Yongwen; Huang, Zi-Gang; Huang, Liang; Chen, Xiaosong

2018-05-01

Clique percolation has attracted much attention due to its significance in understanding topological overlap among communities and dynamical instability of structured systems. Rich critical behavior has been observed in clique percolation on Erdős-Rényi (ER) random graphs, but few works have discussed clique percolation on finite dimensional systems. In this paper, we have defined a series of characteristic events, i.e., the historically largest size jumps of the clusters, in the percolating process of adding bonds and developed a new finite-size scaling scheme based on the interval of the characteristic events. Through the finite-size scaling analysis, we have found, interestingly, that, in contrast to the clique percolation on an ER graph where the critical exponents are parameter dependent, the two-dimensional (2D) clique percolation simply shares the same critical exponents with traditional site or bond percolation, independent of the clique percolation parameters. This has been corroborated by bridging two special types of clique percolation to site percolation on 2D lattices. Mechanisms for the difference of the critical behaviors between clique percolation on ER graphs and on 2D lattices are also discussed.

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

NASA Astrophysics Data System (ADS)

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

2013-06-01

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

A general algorithm using finite element method for aerodynamic configurations at low speeds

NASA Technical Reports Server (NTRS)

Balasubramanian, R.

1975-01-01

A finite element algorithm for numerical simulation of two-dimensional, incompressible, viscous flows was developed. The Navier-Stokes equations are suitably modelled to facilitate direct solution for the essential flow parameters. A leap-frog time differencing and Galerkin minimization of these model equations yields the finite element algorithm. The finite elements are triangular with bicubic shape functions approximating the solution space. The finite element matrices are unsymmetrically banded to facilitate savings in storage. An unsymmetric L-U decomposition is performed on the finite element matrices to obtain the solution for the boundary value problem.

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

PubMed

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

2017-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2009-05-01

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

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

NASA Astrophysics Data System (ADS)

Chen, Huangxin; Salama, Amgad; Sun, Shuyu

2016-10-01

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

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

PubMed Central

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

2010-01-01

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

Finite-amplitude strain waves in laser-excited plates.

PubMed

Mirzade, F Kh

2008-07-09

The governing equations for two-dimensional finite-amplitude longitudinal strain waves in isotropic laser-excited solid plates are derived. Geometric and weak material nonlinearities are included, and the interaction of longitudinal displacements with the field of concentration of non-equilibrium laser-generated atomic defects is taken into account. An asymptotic approach is used to show that the equations are reducible to the Kadomtsev-Petviashvili-Burgers nonlinear evolution equation for a longitudinal self-consistent strain field. It is shown that two-dimensional shock waves can propagate in plates.

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

NASA Astrophysics Data System (ADS)

Parumasur, N.; Willie, R.

2008-09-01

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

Three-dimensional elastic stress and displacement analysis of finite circular geometry solids containing cracks

NASA Technical Reports Server (NTRS)

Gyekenyesi, J. P.; Mendelson, A.; Kring, J.

1973-01-01

A seminumerical method is presented for solving a set of coupled partial differential equations subject to mixed and coupled boundary conditions. The use of this method is illustrated by obtaining solutions for two circular geometry and mixed boundary value problems in three-dimensional elasticity. Stress and displacement distributions are calculated in an axisymmetric, circular bar of finite dimensions containing a penny-shaped crack. Approximate results for an annular plate containing internal surface cracks are also presented.

A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank

NASA Astrophysics Data System (ADS)

Fu, Yuchen; Shelley-Abrahamson, Seth

2016-06-01

We give explicit constructions of some finite-dimensional representations of generalized double affine Hecke algebras (GDAHA) of higher rank using R-matrices for U_q(sl_N). Our construction is motivated by an analogous construction of Silvia Montarani in the rational case. Using the Drinfeld-Kohno theorem for Knizhnik-Zamolodchikov differential equations, we prove that the explicit representations we produce correspond to Montarani's representations under a monodromy functor introduced by Etingof, Gan, and Oblomkov.

Two-dimensional potential flow past a smooth wall with partly constant curvature

NASA Technical Reports Server (NTRS)

Koppenfels, Werner Von

1941-01-01

The speed of a two-dimensional flow potential flow past a smooth wall, which evinces a finite curvature jump at a certain point and approximates to two arcs in the surrounding area, has a vertical tangent of inflection in the critical point as a function of the arc length of the boundary curve. This report looks at a general theorem of the local character of the conformal function at the critical point as well as the case of the finite curvature jump.

Three dimensional flow computations in a turbine scroll

NASA Technical Reports Server (NTRS)

Hamed, A.; Ghantous, C. A.

1982-01-01

The compressible three dimensional inviscid flow in the scroll and vaneless nozzle of radial inflow turbines is analyzed. A FORTRAN computer program for the numerical solution of this complex flow field using the finite element method is presented. The program input consists of the mass flow rate and stagnation conditions at the scroll inlet and of the finite element discretization parameters and nodal coordinates. The output includes the pressure, Mach number and velocity magnitude and direction at all the nodal points.

Elasto-Plastic 3D Finite Element Contact Analysis of a Hole Containing a Circular Insert in a Fatigue Test Coupon

DTIC Science & Technology

2015-08-01

primarily concerned with the results of a three-dimensional elasto– plastic finite element contact analysis of a typical aluminium fatigue test coupon...determine the nonlinear three-dimensional elasto–plastic contact stress distributions around a circular hole in an aluminium plate that is fitted...Australian Air Force (RAAF) airframes. An aluminium -alloy fatigue test coupon (see Figure 1) has been designed and applied in support of the validation of

ALE3D: An Arbitrary Lagrangian-Eulerian Multi-Physics Code

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

Noble, Charles R.; Anderson, Andrew T.; Barton, Nathan R.

ALE3D is a multi-physics numerical simulation software tool utilizing arbitrary-Lagrangian- Eulerian (ALE) techniques. The code is written to address both two-dimensional (2D plane and axisymmetric) and three-dimensional (3D) physics and engineering problems using a hybrid finite element and finite volume formulation to model fluid and elastic-plastic response of materials on an unstructured grid. As shown in Figure 1, ALE3D is a single code that integrates many physical phenomena.

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

NASA Technical Reports Server (NTRS)

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

1991-01-01

The Finite Difference Time Domain Electromagnetic Scattering Code Version A is a three dimensional numerical electromagnetic scattering code based upon the Finite Difference Time Domain Technique (FDTD). This manual provides a description of the code and corresponding results for the default scattering problem. In addition to the description, the operation, resource requirements, version A code capabilities, a description of each subroutine, a brief discussion of the radar cross section computations, and a discussion of the scattering results.

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

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

Unsteady Performance of Finite-Span Pitching Propulsors in Mixtures of Side-by-Side and In-Line Arrangements

NASA Astrophysics Data System (ADS)

Kurt, Melike; Moored, Keith

2016-11-01

Birds, insects, and fish propel themselves by flapping their wings or oscillating their fins in unsteady motions. Many of these animals fly or swim in groups or collectives, typically described as flocks, swarms and schools. The three-dimensional steady flow interactions and the two dimensional unsteady flow interactions that occur in collectives are well characterized. However, the interactions that occur among three-dimensional unsteady propulsors remain relatively unexplored. The aim of the current study is to measure the forces acting on and the energetics of two finite-span pitching wings. The wings are arranged in mixtures of canonical in-line and side-by-side configurations while the phase delay between the pitching wings is varied. The thrust force, fluid-mediated interaction force between the wings and the propulsive efficiency are quantified. The three-dimensional interaction mechanisms are compared and contrasted with previously examined two-dimensional mechanisms. Stereoscopic particle image velocimetry is employed to characterize the three-dimensional flow structures along the span of the pitching wings.

Effects of anterior offsetting of humeral head component in posteriorly unstable total shoulder arthroplasty: Finite element modeling of cadaver specimens.

PubMed

Lewis, Gregory S; Conaway, William K; Wee, Hwabok; Kim, H Mike

2017-02-28

A novel technique of "anterior offsetting" of the humeral head component to address posterior instability in total shoulder arthroplasty has been proposed, and its biomechanical benefits have been previously demonstrated experimentally. The present study sought to characterize the changes in joint mechanics associated with anterior offsetting with various amounts of glenoid retroversion using cadaver specimen-specific 3-dimensional finite element models. Specimen-specific computational finite element models were developed through importing digitized locations of six musculotendinous units of the rotator cuff and deltoid muscles based off three cadaveric shoulder specimens implanted with total shoulder arthroplasty in either anatomic or anterior humeral head offset. Additional glenoid retroversion angles (0°, 10°, 20°, and 30°) other than each specimen׳s actual retroversion were modeled. Contact area, contact force, peak pressure, center of pressure, and humeral head displacement were calculated at each offset and retroversion for statistical analysis. Anterior offsetting was associated with significant anterior shift of center of pressure and humeral head displacement upon muscle loading (p<0.05). Although statistically insignificant, anterior offsetting was associated with increased contact area and decreased peak pressure (p > 0.05). All study variables showed significant differences when compared between the 4 different glenoid retroversion angles (p < 0.05) except for total force (p < 0.05). The study finding suggests that the anterior offsetting technique may contribute to joint stability in posteriorly unstable shoulder arthroplasty and may reduce eccentric loading on glenoid components although the long term clinical results are yet to be investigated in future. Copyright © 2017 Elsevier Ltd. All rights reserved.

Generalized Fourier analyses of the advection-diffusion equation - Part I: one-dimensional domains

NASA Astrophysics Data System (ADS)

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

2004-07-01

This paper presents a detailed multi-methods comparison of the spatial errors associated with finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. The errors are reported in terms of non-dimensional phase and group speed, discrete diffusivity, artificial diffusivity, and grid-induced anisotropy. It is demonstrated that Fourier analysis provides an automatic process for separating the discrete advective operator into its symmetric and skew-symmetric components and characterizing the spectral behaviour of each operator. For each of the numerical methods considered, asymptotic truncation error and resolution estimates are presented for the limiting cases of pure advection and pure diffusion. It is demonstrated that streamline upwind Petrov-Galerkin and its control-volume finite element analogue, the streamline upwind control-volume method, produce both an artificial diffusivity and a concomitant phase speed adjustment in addition to the usual semi-discrete artifacts observed in the phase speed, group speed and diffusivity. The Galerkin finite element method and its streamline upwind derivatives are shown to exhibit super-convergent behaviour in terms of phase and group speed when a consistent mass matrix is used in the formulation. In contrast, the CVFEM method and its streamline upwind derivatives yield strictly second-order behaviour. In Part II of this paper, we consider two-dimensional semi-discretizations of the advection-diffusion equation and also assess the affects of grid-induced anisotropy observed in the non-dimensional phase speed, and the discrete and artificial diffusivities. Although this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common analysis framework. Published in 2004 by John Wiley & Sons, Ltd.

Finite micro-tab system for load control on a wind turbine

NASA Astrophysics Data System (ADS)

Bach, A. B.; Lennie, M.; Pechlivanoglou, G.; Nayeri, C. N.; Paschereit, C. O.

2014-06-01

Finite micro-tabs have been investigated experimentally to evaluate the potential for load control on wind turbines. Two dimensional full span, as well as multiple finite tabs of various aspect ratios have been studied on an AH93W174 airfoil at different chord wise positions. A force balance was used to measure the aerodynamic loads. Furthermore, the wake vortex system consisting of the Karman vortex street as well as the tab tip vortices was analyzed with a 12-hole probe and hot wire anemometry. Finally, conventional oil paint as well as a quantitative digital flow analysis technique called SMARTviz were used to visualize the flow around the finite tab configurations. Results have shown that the devices are an effective solution to alleviate the airfoils overall load. The influence of the tab height, tab position as well as the finite tab aspect ratio on the lift and lift to drag ratio have been evaluated. It could be shown, that the lift difference can either be varied by changing the tab height as well as by altering the aspect ratio of the finite tabs. The drag of a two-dimensional flap is directly associated with the vortex street, while in the case of the finite tab, the solidity ratio of the tabs has the strongest effect on the drag. Therefore, the application of a finite tab system showed to improve the lift to drag ratio.

A one-dimensional statistical mechanics model for nucleosome positioning on genomic DNA.

PubMed

Tesoro, S; Ali, I; Morozov, A N; Sulaiman, N; Marenduzzo, D

2016-02-12

The first level of folding of DNA in eukaryotes is provided by the so-called '10 nm chromatin fibre', where DNA wraps around histone proteins (∼10 nm in size) to form nucleosomes, which go on to create a zig-zagging bead-on-a-string structure. In this work we present a one-dimensional statistical mechanics model to study nucleosome positioning within one such 10 nm fibre. We focus on the case of genomic sheep DNA, and we start from effective potentials valid at infinite dilution and determined from high-resolution in vitro salt dialysis experiments. We study positioning within a polynucleosome chain, and compare the results for genomic DNA to that obtained in the simplest case of homogeneous DNA, where the problem can be mapped to a Tonks gas. First, we consider the simple, analytically solvable, case where nucleosomes are assumed to be point-like. Then, we perform numerical simulations to gauge the effect of their finite size on the nucleosomal distribution probabilities. Finally we compare nucleosome distributions and simulated nuclease digestion patterns for the two cases (homogeneous and sheep DNA), thereby providing testable predictions of the effect of sequence on experimentally observable quantities in experiments on polynucleosome chromatin fibres reconstituted in vitro.

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

Aleman, S.E.

This report documents a finite element code designed to model subsurface flow and contaminant transport, named FACT. FACT is a transient three-dimensional, finite element code designed to simulate isothermal groundwater flow, moisture movement, and solute transport in variably saturated and fully saturated subsurface porous media.

Comparison of Gap Elements and Contact Algorithm for 3D Contact Analysis of Spiral Bevel Gears

NASA Technical Reports Server (NTRS)

Bibel, G. D.; Tiku, K.; Kumar, A.; Handschuh, R.

1994-01-01

Three dimensional stress analysis of spiral bevel gears in mesh using the finite element method is presented. A finite element model is generated by solving equations that identify tooth surface coordinates. Contact is simulated by the automatic generation of nonpenetration constraints. This method is compared to a finite element contact analysis conducted with gap elements.

Electronic part of the optical correlation function at finite temperature: the S-matrix expansion

NASA Astrophysics Data System (ADS)

Tavares, M.; Marques, G. E.; Tejedor, C.

1998-12-01

We present an extension to finite temperature of the Mahan-Nozières-De Dominicis framework to obtain the electronic part of the current-current correlation function. Its Fourier transform gives the absorption and emission spectra of doped low-dimensional semiconductors. We show the meaning of the new finite-temperature contributions characterizing the electronic part.

Nature of self-diffusion in two-dimensional fluids

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

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

Three-dimensional elastic-plastic finite-element analysis of fatigue crack propagation

NASA Technical Reports Server (NTRS)

Goglia, G. L.; Chermahini, R. G.

1985-01-01

Fatigue cracks are a major problem in designing structures subjected to cyclic loading. Cracks frequently occur in structures such as aircraft and spacecraft. The inspection intervals of many aircraft structures are based on crack-propagation lives. Therefore, improved prediction of propagation lives under flight-load conditions (variable-amplitude loading) are needed to provide more realistic design criteria for these structures. The main thrust was to develop a three-dimensional, nonlinear, elastic-plastic, finite element program capable of extending a crack and changing boundary conditions for the model under consideration. The finite-element model is composed of 8-noded (linear-strain) isoparametric elements. In the analysis, the material is assumed to be elastic-perfectly plastic. The cycle stress-strain curve for the material is shown Zienkiewicz's initial-stress method, von Mises's yield criterion, and Drucker's normality condition under small-strain assumptions are used to account for plasticity. The three-dimensional analysis is capable of extending the crack and changing boundary conditions under cyclic loading.

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

PubMed

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

2004-02-01

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

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

NASA Technical Reports Server (NTRS)

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

2007-01-01

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

Finite Element Model for Failure Study of Two-Dimensional Triaxially Braided Composite

NASA Technical Reports Server (NTRS)

Li, Xuetao; Binienda, Wieslaw K.; Goldberg, Robert K.

2010-01-01

A new three-dimensional finite element model of two-dimensional triaxially braided composites is presented in this paper. This meso-scale modeling technique is used to examine and predict the deformation and damage observed in tests of straight sided specimens. A unit cell based approach is used to take into account the braiding architecture as well as the mechanical properties of the fiber tows, the matrix and the fiber tow-matrix interface. A 0 deg / plus or minus 60 deg. braiding configuration has been investigated by conducting static finite element analyses. Failure initiation and progressive degradation has been simulated in the fiber tows by use of the Hashin failure criteria and a damage evolution law. The fiber tow-matrix interface was modeled by using a cohesive zone approach to capture any fiber-matrix debonding. By comparing the analytical results to those obtained experimentally, the applicability of the developed model was assessed and the failure process was investigated.

Nature of self-diffusion in two-dimensional fluids

DOE PAGES

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho; ...

2017-12-18

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

Finite dimensional approximation of a class of constrained nonlinear optimal control problems

NASA Technical Reports Server (NTRS)

Gunzburger, Max D.; Hou, L. S.

1994-01-01

An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.

Reductions in finite-dimensional integrable systems and special points of classical r-matrices

NASA Astrophysics Data System (ADS)

Skrypnyk, T.

2016-12-01

For a given 𝔤 ⊗ 𝔤-valued non-skew-symmetric non-dynamical classical r-matrices r(u, v) with spectral parameters, we construct the general form of 𝔤-valued Lax matrices of finite-dimensional integrable systems satisfying linear r-matrix algebra. We show that the reduction in the corresponding finite-dimensional integrable systems is connected with "the special points" of the classical r-matrices in which they become degenerated. We also propose a systematic way of the construction of additional integrals of the Lax-integrable systems associated with the symmetries of the corresponding r-matrices. We consider examples of the Lax matrices and integrable systems that are obtained in the framework of the general scheme. Among them there are such physically important systems as generalized Gaudin systems in an external magnetic field, ultimate integrable generalization of Toda-type chains (including "modified" or "deformed" Toda chains), generalized integrable Jaynes-Cummings-Dicke models, integrable boson models generalizing Bose-Hubbard dimer models, etc.

Solution of the two-dimensional spectral factorization problem

NASA Technical Reports Server (NTRS)

Lawton, W. M.

1985-01-01

An approximation theorem is proven which solves a classic problem in two-dimensional (2-D) filter theory. The theorem shows that any continuous two-dimensional spectrum can be uniformly approximated by the squared modulus of a recursively stable finite trigonometric polynomial supported on a nonsymmetric half-plane.

A parallel finite-difference method for computational aerodynamics

NASA Technical Reports Server (NTRS)

Swisshelm, Julie M.

1989-01-01

A finite-difference scheme for solving complex three-dimensional aerodynamic flow on parallel-processing supercomputers is presented. The method consists of a basic flow solver with multigrid convergence acceleration, embedded grid refinements, and a zonal equation scheme. Multitasking and vectorization have been incorporated into the algorithm. Results obtained include multiprocessed flow simulations from the Cray X-MP and Cray-2. Speedups as high as 3.3 for the two-dimensional case and 3.5 for segments of the three-dimensional case have been achieved on the Cray-2. The entire solver attained a factor of 2.7 improvement over its unitasked version on the Cray-2. The performance of the parallel algorithm on each machine is analyzed.

A MacCormack-TVD finite difference method to simulate the mass flow in mountainous terrain with variable computational domain

NASA Astrophysics Data System (ADS)

Ouyang, Chaojun; He, Siming; Xu, Qiang; Luo, Yu; Zhang, Wencheng

2013-03-01

A two-dimensional mountainous mass flow dynamic procedure solver (Massflow-2D) using the MacCormack-TVD finite difference scheme is proposed. The solver is implemented in Matlab on structured meshes with variable computational domain. To verify the model, a variety of numerical test scenarios, namely, the classical one-dimensional and two-dimensional dam break, the landslide in Hong Kong in 1993 and the Nora debris flow in the Italian Alps in 2000, are executed, and the model outputs are compared with published results. It is established that the model predictions agree well with both the analytical solution as well as the field observations.

Finite element analysis of steady and transiently moving/rolling nonlinear viscoelastic structure. II - Shell and three-dimensional simulations

NASA Technical Reports Server (NTRS)

Kennedy, Ronald; Padovan, Joe

1987-01-01

In a three-part series of papers, a generalized finite element solution strategy is developed to handle traveling load problems in rolling, moving and rotating structure. The main thrust of this section consists of the development of three-dimensional and shell type moving elements. In conjunction with this work, a compatible three-dimensional contact strategy is also developed. Based on these modeling capabilities, extensive analytical and experimental benchmarking is presented. Such testing includes traveling loads in rotating structure as well as low- and high-speed rolling contact involving standing wave-type response behavior. These point to the excellent modeling capabilities of moving element strategies.

Analytical modeling and analysis of magnetic field and torque for novel axial flux eddy current couplers with PM excitation

NASA Astrophysics Data System (ADS)

Li, Zhao; Wang, Dazhi; Zheng, Di; Yu, Linxin

2017-10-01

Rotational permanent magnet eddy current couplers are promising devices for torque and speed transmission without any mechanical contact. In this study, flux-concentration disk-type permanent magnet eddy current couplers with double conductor rotor are investigated. Given the drawback of the accurate three-dimensional finite element method, this paper proposes a mixed two-dimensional analytical modeling approach. Based on this approach, the closed-form expressions of magnetic field, eddy current, electromagnetic force and torque for such devices are obtained. Finally, a three-dimensional finite element method is employed to validate the analytical results. Besides, a prototype is manufactured and tested for the torque-speed characteristic.

Chaotic and regular instantons in helical shell models of turbulence

NASA Astrophysics Data System (ADS)

De Pietro, Massimo; Mailybaev, Alexei A.; Biferale, Luca

2017-03-01

Shell models of turbulence have a finite-time blowup in the inviscid limit, i.e., the enstrophy diverges while the single-shell velocities stay finite. The signature of this blowup is represented by self-similar instantonic structures traveling coherently through the inertial range. These solutions might influence the energy transfer and the anomalous scaling properties empirically observed for the forced and viscous models. In this paper we present a study of the instantonic solutions for a set of four shell models of turbulence based on the exact decomposition of the Navier-Stokes equations in helical eigenstates. We find that depending on the helical structure of each model, instantons are chaotic or regular. Some instantonic solutions tend to recover mirror symmetry for scales small enough. Models that have anomalous scaling develop regular nonchaotic instantons. Conversely, models that have nonanomalous scaling in the stationary regime are those that have chaotic instantons. The direction of the energy carried by each single instanton tends to coincide with the direction of the energy cascade in the stationary regime. Finally, we find that whenever the small-scale stationary statistics is intermittent, the instanton is less steep than the dimensional Kolmogorov scaling, independently of whether or not it is chaotic. Our findings further support the idea that instantons might be crucial to describe some aspects of the multiscale anomalous statistics of shell models.

Wigner analysis of three dimensional pupil with finite lateral aperture

PubMed Central

Chen, Hsi-Hsun; Oh, Se Baek; Zhai, Xiaomin; Tsai, Jui-Chang; Cao, Liang-Cai; Barbastathis, George; Luo, Yuan

2015-01-01

A three dimensional (3D) pupil is an optical element, most commonly implemented on a volume hologram, that processes the incident optical field on a 3D fashion. Here we analyze the diffraction properties of a 3D pupil with finite lateral aperture in the 4-f imaging system configuration, using the Wigner Distribution Function (WDF) formulation. Since 3D imaging pupil is finite in both lateral and longitudinal directions, the WDF of the volume holographic 4-f imager theoretically predicts distinct Bragg diffraction patterns in phase space. These result in asymmetric profiles of diffracted coherent point spread function between degenerate diffraction and Bragg diffraction, elucidating the fundamental performance of volume holographic imaging. Experimental measurements are also presented, confirming the theoretical predictions. PMID:25836443

Metriplectic integrators for the Landau collision operator

DOE PAGES

Kraus, Michael; Hirvijoki, Eero

2017-10-02

Here, we present a novel framework for addressing the nonlinear Landau collision integral in terms of finite element and other subspace projection methods. We employ the underlying metriplectic structure of the Landau collision integral and, using a Galerkin discretization for the velocity space, we transform the infinite-dimensional system into a finite-dimensional, time-continuous metriplectic system. Temporal discretization is accomplished using the concept of discrete gradients. The conservation of energy, momentum, and particle densities, as well as the production of entropy is demonstrated algebraically for the fully discrete system. Due to the generality of our approach, the conservation properties and the monotonicmore » behavior of entropy are guaranteed for finite element discretizations, in general, independently of the mesh configuration.« less

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

NASA Astrophysics Data System (ADS)

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

2016-05-01

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

New Multigrid Method Including Elimination Algolithm Based on High-Order Vector Finite Elements in Three Dimensional Magnetostatic Field Analysis

NASA Astrophysics Data System (ADS)

Hano, Mitsuo; Hotta, Masashi

A new multigrid method based on high-order vector finite elements is proposed in this paper. Low level discretizations in this method are obtained by using low-order vector finite elements for the same mesh. Gauss-Seidel method is used as a smoother, and a linear equation of lowest level is solved by ICCG method. But it is often found that multigrid solutions do not converge into ICCG solutions. An elimination algolithm of constant term using a null space of the coefficient matrix is also described. In three dimensional magnetostatic field analysis, convergence time and number of iteration of this multigrid method are discussed with the convectional ICCG method.

Three-dimensional vector modeling and restoration of flat finite wave tank radiometric measurements

NASA Technical Reports Server (NTRS)

Truman, W. M.; Balanis, C. A.; Holmes, J. J.

1977-01-01

In this paper, a three-dimensional Fourier transform inversion method describing the interaction between water surface emitted radiation from a flat finite wave tank and antenna radiation characteristics is reported. The transform technique represents the scanning of the antenna mathematically as a correlation. Computation time is reduced by using the efficient and economical fast Fourier transform algorithm. To verify the inversion method, computations have been made and compared with known data and other available results. The technique has been used to restore data of the finite wave tank system and other available antenna temperature measurements made at the Cape Cod Canal. The restored brightness temperatures serve as better representations of the emitted radiation than the measured antenna temperatures.

General response formula and application to topological insulator in quantum open system.

PubMed

Shen, H Z; Qin, M; Shao, X Q; Yi, X X

2015-11-01

It is well-known that the quantum linear response theory is based on the first-order perturbation theory for a system in thermal equilibrium. Hence, this theory breaks down when the system is in a steady state far from thermal equilibrium and the response up to higher order in perturbation is not negligible. In this paper, we develop a nonlinear response theory for such quantum open system. We first formulate this theory in terms of general susceptibility, after which we apply it to the derivation of Hall conductance for open system at finite temperature. As an example, the Hall conductance of the two-band model is derived. Then we calculate the Hall conductance for a two-dimensional ferromagnetic electron gas and a two-dimensional lattice model. The calculations show that the transition points of topological phase are robust against the environment. Our results provide a promising platform for the coherent manipulation of the nonlinear response in quantum open system, which has potential applications for quantum information processing and statistical physics.

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.

Statistical Energy Analysis (SEA) and Energy Finite Element Analysis (EFEA) Predictions for a Floor-Equipped Composite Cylinder

NASA Technical Reports Server (NTRS)

Grosveld, Ferdinand W.; Schiller, Noah H.; Cabell, Randolph H.

2011-01-01

Comet Enflow is a commercially available, high frequency vibroacoustic analysis software founded on Energy Finite Element Analysis (EFEA) and Energy Boundary Element Analysis (EBEA). Energy Finite Element Analysis (EFEA) was validated on a floor-equipped composite cylinder by comparing EFEA vibroacoustic response predictions with Statistical Energy Analysis (SEA) and experimental results. Statistical Energy Analysis (SEA) predictions were made using the commercial software program VA One 2009 from ESI Group. The frequency region of interest for this study covers the one-third octave bands with center frequencies from 100 Hz to 4000 Hz.

Thermal History and Mantle Dynamics of Venus

NASA Technical Reports Server (NTRS)

Hsui, Albert T.

1997-01-01

One objective of this research proposal is to develop a 3-D thermal history model for Venus. The basis of our study is a finite-element computer model to simulate thermal convection of fluids with highly temperature- and pressure-dependent viscosities in a three-dimensional spherical shell. A three-dimensional model for thermal history studies is necessary for the following reasons. To study planetary thermal evolution, one needs to consider global heat budgets of a planet throughout its evolution history. Hence, three-dimensional models are necessary. This is in contrasts to studies of some local phenomena or local structures where models of lower dimensions may be sufficient. There are different approaches to treat three-dimensional thermal convection problems. Each approach has its own advantages and disadvantages. Therefore, the choice of the various approaches is subjective and dependent on the problem addressed. In our case, we are interested in the effects of viscosities that are highly temperature dependent and that their magnitudes within the computing domain can vary over many orders of magnitude. In order to resolve the rapid change of viscosities, small grid spacings are often necessary. To optimize the amount of computing, variable grids become desirable. Thus, the finite-element numerical approach is chosen for its ability to place grid elements of different sizes over the complete computational domain. For this research proposal, we did not start from scratch and develop the finite element codes from the beginning. Instead, we adopted a finite-element model developed by Baumgardner, a collaborator of this research proposal, for three-dimensional thermal convection with constant viscosity. Over the duration supported by this research proposal, a significant amount of advancements have been accomplished.

Finite elements and finite differences for transonic flow calculations

NASA Technical Reports Server (NTRS)

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

1978-01-01

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

Three-dimensional analysis of tubular permanent magnet machines

NASA Astrophysics Data System (ADS)

Chai, J.; Wang, J.; Howe, D.

2006-04-01

This paper presents results from a three-dimensional finite element analysis of a tubular permanent magnet machine, and quantifies the influence of the laminated modules from which the stator core is assembled on the flux linkage and thrust force capability as well as on the self- and mutual inductances. The three-dimensional finite element (FE) model accounts for the nonlinear, anisotropic magnetization characteristic of the laminated stator structure, and for the voids which exist between the laminated modules. Predicted results are compared with those deduced from an axisymmetric FE model. It is shown that the emf and thrust force deduced from the three-dimensional model are significantly lower than those which are predicted from an axisymmetric field analysis, primarily as a consequence of the teeth and yoke being more highly saturated due to the presence of the voids in the laminated stator core.

A coupled sharp-interface immersed boundary-finite-element method for flow-structure interaction with application to human phonation.

PubMed

Zheng, X; Xue, Q; Mittal, R; Beilamowicz, S

2010-11-01

A new flow-structure interaction method is presented, which couples a sharp-interface immersed boundary method flow solver with a finite-element method based solid dynamics solver. The coupled method provides robust and high-fidelity solution for complex flow-structure interaction (FSI) problems such as those involving three-dimensional flow and viscoelastic solids. The FSI solver is used to simulate flow-induced vibrations of the vocal folds during phonation. Both two- and three-dimensional models have been examined and qualitative, as well as quantitative comparisons, have been made with established results in order to validate the solver. The solver is used to study the onset of phonation in a two-dimensional laryngeal model and the dynamics of the glottal jet in a three-dimensional model and results from these studies are also presented.

Simulation analysis of air flow and turbulence statistics in a rib grit roughened duct.

PubMed

Vogiatzis, I I; Denizopoulou, A C; Ntinas, G K; Fragos, V P

2014-01-01

The implementation of variable artificial roughness patterns on a surface is an effective technique to enhance the rate of heat transfer to fluid flow in the ducts of solar air heaters. Different geometries of roughness elements investigated have demonstrated the pivotal role that vortices and associated turbulence have on the heat transfer characteristics of solar air heater ducts by increasing the convective heat transfer coefficient. In this paper we investigate the two-dimensional, turbulent, unsteady flow around rectangular ribs of variable aspect ratios by directly solving the transient Navier-Stokes and continuity equations using the finite elements method. Flow characteristics and several aspects of turbulent flow are presented and discussed including velocity components and statistics of turbulence. The results reveal the impact that different rib lengths have on the computed mean quantities and turbulence statistics of the flow. The computed turbulence parameters show a clear tendency to diminish downstream with increasing rib length. Furthermore, the applied numerical method is capable of capturing small-scale flow structures resulting from the direct solution of Navier-Stokes and continuity equations.

Statistical mechanics of the vertex-cover problem

NASA Astrophysics Data System (ADS)

Hartmann, Alexander K.; Weigt, Martin

2003-10-01

We review recent progress in the study of the vertex-cover problem (VC). The VC belongs to the class of NP-complete graph theoretical problems, which plays a central role in theoretical computer science. On ensembles of random graphs, VC exhibits a coverable-uncoverable phase transition. Very close to this transition, depending on the solution algorithm, easy-hard transitions in the typical running time of the algorithms occur. We explain a statistical mechanics approach, which works by mapping the VC to a hard-core lattice gas, and then applying techniques such as the replica trick or the cavity approach. Using these methods, the phase diagram of the VC could be obtained exactly for connectivities c < e, where the VC is replica symmetric. Recently, this result could be confirmed using traditional mathematical techniques. For c > e, the solution of the VC exhibits full replica symmetry breaking. The statistical mechanics approach can also be used to study analytically the typical running time of simple complete and incomplete algorithms for the VC. Finally, we describe recent results for the VC when studied on other ensembles of finite- and infinite-dimensional graphs.

Measurement of Temperature and Soil Properties for Finite Element Model Verification

DOT National Transportation Integrated Search

2012-08-01

In recent years, ADOT&PF personnel have used TEMP/W, a commercially available two-dimensional finite element program, to conduct thermal modeling of various : embankment configurations in an effort to reduce the thawing of ice-rich permafrost through...

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

EPA Science Inventory

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

Diffusion of finite-sized hard-core interacting particles in a one-dimensional box: Tagged particle dynamics.

PubMed

Lizana, L; Ambjörnsson, T

2009-11-01

We solve a nonequilibrium statistical-mechanics problem exactly, namely, the single-file dynamics of N hard-core interacting particles (the particles cannot pass each other) of size Delta diffusing in a one-dimensional system of finite length L with reflecting boundaries at the ends. We obtain an exact expression for the conditional probability density function rhoT(yT,t|yT,0) that a tagged particle T (T=1,...,N) is at position yT at time t given that it at time t=0 was at position yT,0. Using a Bethe ansatz we obtain the N -particle probability density function and, by integrating out the coordinates (and averaging over initial positions) of all particles but particle T , we arrive at an exact expression for rhoT(yT,t|yT,0) in terms of Jacobi polynomials or hypergeometric functions. Going beyond previous studies, we consider the asymptotic limit of large N , maintaining L finite, using a nonstandard asymptotic technique. We derive an exact expression for rhoT(yT,t|yT,0) for a tagged particle located roughly in the middle of the system, from which we find that there are three time regimes of interest for finite-sized systems: (A) for times much smaller than the collision time ttaucoll but times smaller than the equilibrium time ttaue , rhoT(yT,t|yT,0) approaches a polynomial-type equilibrium probability density function. Notably, only regimes (A) and (B) are found in the previously considered infinite systems.

Applications of finite-size scaling for atomic and non-equilibrium systems

NASA Astrophysics Data System (ADS)

Antillon, Edwin A.

We apply the theory of Finite-size scaling (FSS) to an atomic and a non-equilibrium system in order to extract critical parameters. In atomic systems, we look at the energy dependence on the binding charge near threshold between bound and free states, where we seek the critical nuclear charge for stability. We use different ab initio methods, such as Hartree-Fock, Density Functional Theory, and exact formulations implemented numerically with the finite-element method (FEM). Using Finite-size scaling formalism, where in this case the size of the system is related to the number of elements used in the basis expansion of the wavefunction, we predict critical parameters in the large basis limit. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that this combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems. In the second part we look at non-equilibrium one-dimensional model known as the raise and peel model describing a growing surface which grows locally and has non-local desorption. For a specific values of adsorption ( ua) and desorption (ud) the model shows interesting features. At ua = ud, the model is described by a conformal field theory (with conformal charge c = 0) and its stationary probability can be mapped to the ground state of a quantum chain and can also be related a two dimensional statistical model. For ua ≥ ud, the model shows a scale invariant phase in the avalanche distribution. In this work we study the surface dynamics by looking at avalanche distributions using FSS formalism and explore the effect of changing the boundary conditions of the model. The model shows the same universality for the cases with and with our the wall for an odd number of tiles removed, but we find a new exponent in the presence of a wall for an even number of avalanches released. We provide new conjecture for the probability distribution of avalanches with a wall obtained by using exact diagonalization of small lattices and Monte-Carlo simulations.

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

NASA Technical Reports Server (NTRS)

Yu, Y.-Y.

1974-01-01

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

Nonequilibrium umbrella sampling in spaces of many order parameters

NASA Astrophysics Data System (ADS)

Dickson, Alex; Warmflash, Aryeh; Dinner, Aaron R.

2009-02-01

We recently introduced an umbrella sampling method for obtaining nonequilibrium steady-state probability distributions projected onto an arbitrary number of coordinates that characterize a system (order parameters) [A. Warmflash, P. Bhimalapuram, and A. R. Dinner, J. Chem. Phys. 127, 154112 (2007)]. Here, we show how our algorithm can be combined with the image update procedure from the finite-temperature string method for reversible processes [E. Vanden-Eijnden and M. Venturoli, "Revisiting the finite temperature string method for calculation of reaction tubes and free energies," J. Chem. Phys. (in press)] to enable restricted sampling of a nonequilibrium steady state in the vicinity of a path in a many-dimensional space of order parameters. For the study of transitions between stable states, the adapted algorithm results in improved scaling with the number of order parameters and the ability to progressively refine the regions of enforced sampling. We demonstrate the algorithm by applying it to a two-dimensional model of driven Brownian motion and a coarse-grained (Ising) model for nucleation under shear. It is found that the choice of order parameters can significantly affect the convergence of the simulation; local magnetization variables other than those used previously for sampling transition paths in Ising systems are needed to ensure that the reactive flux is primarily contained within a tube in the space of order parameters. The relation of this method to other algorithms that sample the statistics of path ensembles is discussed.

Comparing hard and soft prior bounds in geophysical inverse problems

NASA Technical Reports Server (NTRS)

Backus, George E.

1988-01-01

In linear inversion of a finite-dimensional data vector y to estimate a finite-dimensional prediction vector z, prior information about X sub E is essential if y is to supply useful limits for z. The one exception occurs when all the prediction functionals are linear combinations of the data functionals. Two forms of prior information are compared: a soft bound on X sub E is a probability distribution p sub x on X which describes the observer's opinion about where X sub E is likely to be in X; a hard bound on X sub E is an inequality Q sub x(X sub E, X sub E) is equal to or less than 1, where Q sub x is a positive definite quadratic form on X. A hard bound Q sub x can be softened to many different probability distributions p sub x, but all these p sub x's carry much new information about X sub E which is absent from Q sub x, and some information which contradicts Q sub x. Both stochastic inversion (SI) and Bayesian inference (BI) estimate z from y and a soft prior bound p sub x. If that probability distribution was obtained by softening a hard prior bound Q sub x, rather than by objective statistical inference independent of y, then p sub x contains so much unsupported new information absent from Q sub x that conclusions about z obtained with SI or BI would seen to be suspect.

Comparing hard and soft prior bounds in geophysical inverse problems

NASA Technical Reports Server (NTRS)

Backus, George E.

1987-01-01

In linear inversion of a finite-dimensional data vector y to estimate a finite-dimensional prediction vector z, prior information about X sub E is essential if y is to supply useful limits for z. The one exception occurs when all the prediction functionals are linear combinations of the data functionals. Two forms of prior information are compared: a soft bound on X sub E is a probability distribution p sub x on X which describeds the observer's opinion about where X sub E is likely to be in X; a hard bound on X sub E is an inequality Q sub x(X sub E, X sub E) is equal to or less than 1, where Q sub x is a positive definite quadratic form on X. A hard bound Q sub x can be softened to many different probability distributions p sub x, but all these p sub x's carry much new information about X sub E which is absent from Q sub x, and some information which contradicts Q sub x. Both stochastic inversion (SI) and Bayesian inference (BI) estimate z from y and a soft prior bound p sub x. If that probability distribution was obtained by softening a hard prior bound Q sub x, rather than by objective statistical inference independent of y, then p sub x contains so much unsupported new information absent from Q sub x that conclusions about z obtained with SI or BI would seen to be suspect.

The one-dimensional asymmetric persistent random walk

NASA Astrophysics Data System (ADS)

Rossetto, Vincent

2018-04-01

Persistent random walks are intermediate transport processes between a uniform rectilinear motion and a Brownian motion. They are formed by successive steps of random finite lengths and directions travelled at a fixed speed. The isotropic and symmetric 1D persistent random walk is governed by the telegrapher’s equation, also called the hyperbolic heat conduction equation. These equations have been designed to resolve the paradox of the infinite speed in the heat and diffusion equations. The finiteness of both the speed and the correlation length leads to several classes of random walks: Persistent random walk in one dimension can display anomalies that cannot arise for Brownian motion such as anisotropy and asymmetries. In this work we focus on the case where the mean free path is anisotropic, the only anomaly leading to a physics that is different from the telegrapher’s case. We derive exact expression of its Green’s function, for its scattering statistics and distribution of first-passage time at the origin. The phenomenology of the latter shows a transition for quantities like the escape probability and the residence time.

Fuzzy parametric uncertainty analysis of linear dynamical systems: A surrogate modeling approach

NASA Astrophysics Data System (ADS)

Chowdhury, R.; Adhikari, S.

2012-10-01

Uncertainty propagation engineering systems possess significant computational challenges. This paper explores the possibility of using correlated function expansion based metamodelling approach when uncertain system parameters are modeled using Fuzzy variables. In particular, the application of High-Dimensional Model Representation (HDMR) is proposed for fuzzy finite element analysis of dynamical systems. The HDMR expansion is a set of quantitative model assessment and analysis tools for capturing high-dimensional input-output system behavior based on a hierarchy of functions of increasing dimensions. The input variables may be either finite-dimensional (i.e., a vector of parameters chosen from the Euclidean space RM) or may be infinite-dimensional as in the function space CM[0,1]. The computational effort to determine the expansion functions using the alpha cut method scales polynomially with the number of variables rather than exponentially. This logic is based on the fundamental assumption underlying the HDMR representation that only low-order correlations among the input variables are likely to have significant impacts upon the outputs for most high-dimensional complex systems. The proposed method is integrated with a commercial Finite Element software. Modal analysis of a simplified aircraft wing with Fuzzy parameters has been used to illustrate the generality of the proposed approach. In the numerical examples, triangular membership functions have been used and the results have been validated against direct Monte Carlo simulations.

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

NASA Technical Reports Server (NTRS)

Kandil, Osama A.

1998-01-01

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

A 3-D Finite-Volume Non-hydrostatic Icosahedral Model (NIM)

NASA Astrophysics Data System (ADS)

Lee, Jin

2014-05-01

The Nonhydrostatic Icosahedral Model (NIM) formulates the latest numerical innovation of the three-dimensional finite-volume control volume on the quasi-uniform icosahedral grid suitable for ultra-high resolution simulations. NIM's modeling goal is to improve numerical accuracy for weather and climate simulations as well as to utilize the state-of-art computing architecture such as massive parallel CPUs and GPUs to deliver routine high-resolution forecasts in timely manner. NIM dynamic corel innovations include: * A local coordinate system remapped spherical surface to plane for numerical accuracy (Lee and MacDonald, 2009), * Grid points in a table-driven horizontal loop that allow any horizontal point sequence (A.E. MacDonald, et al., 2010), * Flux-Corrected Transport formulated on finite-volume operators to maintain conservative positive definite transport (J.-L, Lee, ET. Al., 2010), *Icosahedral grid optimization (Wang and Lee, 2011), * All differentials evaluated as three-dimensional finite-volume integrals around the control volume. The three-dimensional finite-volume solver in NIM is designed to improve pressure gradient calculation and orographic precipitation over complex terrain. NIM dynamical core has been successfully verified with various non-hydrostatic benchmark test cases such as internal gravity wave, and mountain waves in Dynamical Cores Model Inter-comparisons Projects (DCMIP). Physical parameterizations suitable for NWP are incorporated into NIM dynamical core and successfully tested with multimonth aqua-planet simulations. Recently, NIM has started real data simulations using GFS initial conditions. Results from the idealized tests as well as real-data simulations will be shown in the conference.

Statistics of dislocation pinning at localized obstacles

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

Dutta, A.; Bhattacharya, M., E-mail: mishreyee@vecc.gov.in; Barat, P.

2014-10-14

Pinning of dislocations at nanosized obstacles like precipitates, voids, and bubbles is a crucial mechanism in the context of phenomena like hardening and creep. The interaction between such an obstacle and a dislocation is often studied at fundamental level by means of analytical tools, atomistic simulations, and finite element methods. Nevertheless, the information extracted from such studies cannot be utilized to its maximum extent on account of insufficient information about the underlying statistics of this process comprising a large number of dislocations and obstacles in a system. Here, we propose a new statistical approach, where the statistics of pinning ofmore » dislocations by idealized spherical obstacles is explored by taking into account the generalized size-distribution of the obstacles along with the dislocation density within a three-dimensional framework. Starting with a minimal set of material parameters, the framework employs the method of geometrical statistics with a few simple assumptions compatible with the real physical scenario. The application of this approach, in combination with the knowledge of fundamental dislocation-obstacle interactions, has successfully been demonstrated for dislocation pinning at nanovoids in neutron irradiated type 316-stainless steel in regard to the non-conservative motion of dislocations. An interesting phenomenon of transition from rare pinning to multiple pinning regimes with increasing irradiation temperature is revealed.« less

One-Dimensional Czedli-Type Islands

ERIC Educational Resources Information Center

Horvath, Eszter K.; Mader, Attila; Tepavcevic, Andreja

2011-01-01

The notion of an island has surfaced in recent algebra and coding theory research. Discrete versions provide interesting combinatorial problems. This paper presents the one-dimensional case with finitely many heights, a topic convenient for student research.

Interactions between Magnetically Levitated Vehicles and Elevated Guideway Structures

DOT National Transportation Integrated Search

1992-07-01

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

Technique for evaluation of the strong potential Born approximation for electron capture

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

Sil, N.C.; McGuire, J.H.

1985-04-01

A technique is presented for evaluating differential cross sections in the strong potential Born (SPB) approximation. Our final expression is expressed as a finite sum of one-dimensional integrals, expressible as a finite sum of derivatives of hypergeometric functions.

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

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

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

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

Users manual for AUTOMESH-2D: A program of automatic mesh generation for two-dimensional scattering analysis by the finite element method

NASA Technical Reports Server (NTRS)

Hua, Chongyu; Volakis, John L.

1990-01-01

AUTOMESH-2D is a computer program specifically designed as a preprocessor for the scattering analysis of two dimensional bodies by the finite element method. This program was developed due to a need for reproducing the effort required to define and check the geometry data, element topology, and material properties. There are six modules in the program: (1) Parameter Specification; (2) Data Input; (3) Node Generation; (4) Element Generation; (5) Mesh Smoothing; and (5) Data File Generation.

Study on prestressed concrete reactor vessel structures. II-5: Crack analysis by three dimensional finite elements method of 1/20 multicavity type PCRV subjected to internal pressure

NASA Technical Reports Server (NTRS)

1978-01-01

A three-dimensional finite elements analysis is reported of the nonlinear behavior of PCRV subjected to internal pressure by comparing calculated results with test results. As the first stage, an analysis considering the nonlinearity of cracking in concrete was attempted. As a result, it is found possible to make an analysis up to three times the design pressure (50 kg/sqcm), and calculated results agree well with test results.

Vibration suppression with approximate finite dimensional compensators for distributed systems: Computational methods and experimental results

NASA Technical Reports Server (NTRS)

Banks, H. T.; Smith, Ralph C.; Wang, Yun

1994-01-01

Based on a distributed parameter model for vibrations, an approximate finite dimensional dynamic compensator is designed to suppress vibrations (multiple modes with a broad band of frequencies) of a circular plate with Kelvin-Voigt damping and clamped boundary conditions. The control is realized via piezoceramic patches bonded to the plate and is calculated from information available from several pointwise observed state variables. Examples from computational studies as well as use in laboratory experiments are presented to demonstrate the effectiveness of this design.

Incorporation of coupled nonequilibrium chemistry into a two-dimensional nozzle code (SEAGULL)

NASA Technical Reports Server (NTRS)

Ratliff, A. W.

1979-01-01

A two-dimensional multiple shock nozzle code (SEAGULL) was extended to include the effects of finite rate chemistry. The basic code that treats multiple shocks and contact surfaces was fully coupled with a generalized finite rate chemistry and vibrational energy exchange package. The modified code retains all of the original SEAGULL features plus the capability to treat chemical and vibrational nonequilibrium reactions. Any chemical and/or vibrational energy exchange mechanism can be handled as long as thermodynamic data and rate constants are available for all participating species.

Finite-Element Analysis of Residual Stresses Generated Under Nitriding Process: a Three-Dimensional Model

NASA Astrophysics Data System (ADS)

Sawicki, J.; Siedlaczek, P.; Staszczyk, A.

2018-03-01

A numerical three-dimensional model for computing residual stresses generated in cross section of steel 42CrMo4 after nitriding is presented. The diffusion process is analyzed by the finite-element method. The internal stresses are computed using the obtained profile of the distribution of the nitrogen concentration. The special features of the intricate geometry of the treated articles including edges and angles are considered. Comparative analysis of the results of the simulation and of the experimental measurement of residual stresses is performed by the Waisman-Philips method.

Three-dimensional finite element analysis of acoustic instability of solid propellant rocket motors

NASA Technical Reports Server (NTRS)

Hackett, R. M.; Juruf, R. S.

1976-01-01

A three dimensional finite element solution of the acoustic vibration problem in a solid propellant rocket motor is presented. The solution yields the natural circular frequencies of vibration and the corresponding acoustic pressure mode shapes, considering the coupled response of the propellant grain to the acoustic oscillations occurring in the motor cavity. The near incompressibility of the solid propellant is taken into account in the formulation. A relatively simple example problem is solved in order to illustrate the applicability of the analysis and the developed computer code.

Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules

1999-01-01

In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.

High dimensional linear regression models under long memory dependence and measurement error

NASA Astrophysics Data System (ADS)

Kaul, Abhishek

This dissertation consists of three chapters. The first chapter introduces the models under consideration and motivates problems of interest. A brief literature review is also provided in this chapter. The second chapter investigates the properties of Lasso under long range dependent model errors. Lasso is a computationally efficient approach to model selection and estimation, and its properties are well studied when the regression errors are independent and identically distributed. We study the case, where the regression errors form a long memory moving average process. We establish a finite sample oracle inequality for the Lasso solution. We then show the asymptotic sign consistency in this setup. These results are established in the high dimensional setup (p> n) where p can be increasing exponentially with n. Finally, we show the consistency, n½ --d-consistency of Lasso, along with the oracle property of adaptive Lasso, in the case where p is fixed. Here d is the memory parameter of the stationary error sequence. The performance of Lasso is also analysed in the present setup with a simulation study. The third chapter proposes and investigates the properties of a penalized quantile based estimator for measurement error models. Standard formulations of prediction problems in high dimension regression models assume the availability of fully observed covariates and sub-Gaussian and homogeneous model errors. This makes these methods inapplicable to measurement errors models where covariates are unobservable and observations are possibly non sub-Gaussian and heterogeneous. We propose weighted penalized corrected quantile estimators for the regression parameter vector in linear regression models with additive measurement errors, where unobservable covariates are nonrandom. The proposed estimators forgo the need for the above mentioned model assumptions. We study these estimators in both the fixed dimension and high dimensional sparse setups, in the latter setup, the dimensionality can grow exponentially with the sample size. In the fixed dimensional setting we provide the oracle properties associated with the proposed estimators. In the high dimensional setting, we provide bounds for the statistical error associated with the estimation, that hold with asymptotic probability 1, thereby providing the ℓ1-consistency of the proposed estimator. We also establish the model selection consistency in terms of the correctly estimated zero components of the parameter vector. A simulation study that investigates the finite sample accuracy of the proposed estimator is also included in this chapter.

Statistics based sampling for controller and estimator design

NASA Astrophysics Data System (ADS)

Tenne, Dirk

The purpose of this research is the development of statistical design tools for robust feed-forward/feedback controllers and nonlinear estimators. This dissertation is threefold and addresses the aforementioned topics nonlinear estimation, target tracking and robust control. To develop statistically robust controllers and nonlinear estimation algorithms, research has been performed to extend existing techniques, which propagate the statistics of the state, to achieve higher order accuracy. The so-called unscented transformation has been extended to capture higher order moments. Furthermore, higher order moment update algorithms based on a truncated power series have been developed. The proposed techniques are tested on various benchmark examples. Furthermore, the unscented transformation has been utilized to develop a three dimensional geometrically constrained target tracker. The proposed planar circular prediction algorithm has been developed in a local coordinate framework, which is amenable to extension of the tracking algorithm to three dimensional space. This tracker combines the predictions of a circular prediction algorithm and a constant velocity filter by utilizing the Covariance Intersection. This combined prediction can be updated with the subsequent measurement using a linear estimator. The proposed technique is illustrated on a 3D benchmark trajectory, which includes coordinated turns and straight line maneuvers. The third part of this dissertation addresses the design of controller which include knowledge of parametric uncertainties and their distributions. The parameter distributions are approximated by a finite set of points which are calculated by the unscented transformation. This set of points is used to design robust controllers which minimize a statistical performance of the plant over the domain of uncertainty consisting of a combination of the mean and variance. The proposed technique is illustrated on three benchmark problems. The first relates to the design of prefilters for a linear and nonlinear spring-mass-dashpot system and the second applies a feedback controller to a hovering helicopter. Lastly, the statistical robust controller design is devoted to a concurrent feed-forward/feedback controller structure for a high-speed low tension tape drive.

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

NASA Technical Reports Server (NTRS)

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

1978-01-01

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

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.

Study of propellant dynamics in a shuttle type launch vehicle

NASA Technical Reports Server (NTRS)

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

1972-01-01

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

Constitutive Behavior and Finite Element Analysis of FRP Composite and Concrete Members.

PubMed

Ann, Ki Yong; Cho, Chang-Geun

2013-09-10

The present study concerns compressive and flexural constitutive models incorporated into an isoparametric beam finite element scheme for fiber reinforced polymer (FRP) and concrete composites, using their multi-axial constitutive behavior. The constitutive behavior of concrete was treated in triaxial stress states as an orthotropic hypoelasticity-based formulation to determine the confinement effect of concrete from a three-dimensional failure surface in triaxial stress states. The constitutive behavior of the FRP composite was formulated from the two-dimensional classical lamination theory. To predict the flexural behavior of circular cross-section with FRP sheet and concrete composite, a layered discretization of cross-sections was incorporated into nonlinear isoparametric beam finite elements. The predicted constitutive behavior was validated by a comparison to available experimental results in the compressive and flexural beam loading test.

Scattering and radiation analysis of three-dimensional cavity arrays via a hybrid finite element method

NASA Technical Reports Server (NTRS)

Jin, Jian-Ming; Volakis, John L.

1992-01-01

A hybrid numerical technique is presented for a characterization of the scattering and radiation properties of three-dimensional cavity arrays recessed in a ground plane. The technique combines the finite element and boundary integral methods and invokes Floquet's representation to formulate a system of equations for the fields at the apertures and those inside the cavities. The system is solved via the conjugate gradient method in conjunction with the Fast Fourier Transform (FFT) thus achieving an O(N) storage requirement. By virtue of the finite element method, the proposed technique is applicable to periodic arrays comprised of cavities having arbitrary shape and filled with inhomogeneous dielectrics. Several numerical results are presented, along with new measured data, which demonstrate the validity, efficiency, and capability of the technique.

A finite element approach for solution of the 3D Euler equations

NASA Technical Reports Server (NTRS)

Thornton, E. A.; Ramakrishnan, R.; Dechaumphai, P.

1986-01-01

Prediction of thermal deformations and stresses has prime importance in the design of the next generation of high speed flight vehicles. Aerothermal load computations for complex three-dimensional shapes necessitate development of procedures to solve the full Navier-Stokes equations. This paper details the development of a three-dimensional inviscid flow approach which can be extended for three-dimensional viscous flows. A finite element formulation, based on a Taylor series expansion in time, is employed to solve the compressible Euler equations. Model generation and results display are done using a commercially available program, PATRAN, and vectorizing strategies are incorporated to ensure computational efficiency. Sample problems are presented to demonstrate the validity of the approach for analyzing high speed compressible flows.

Temperature distributions and thermal stresses in a graded zirconia/metal gas path seal system for aircraft gas turbine engines

NASA Technical Reports Server (NTRS)

Taylor, C. M.; Bill, R. C.

1978-01-01

A ceramic/metallic aircraft gas turbine outer gas path seal designed for improved engine performance was studied. Transient temperature and stress profiles in a test seal geometry were determined by numerical analysis. During a simulated engine deceleration cycle from sea-level takeoff to idle conditions, the maximum seal temperature occurred below the seal surface, therefore the top layer of the seal was probably subjected to tensile stresses exceeding the modulus of rupture. In the stress analysis both two- and three-dimensional finite element computer programs were used. Predicted trends of the simpler and more easily usable two-dimensional element programs were borne out by the three-dimensional finite element program results.

Recurrence relations in one-dimensional Ising models.

PubMed

da Conceição, C M Silva; Maia, R N P

2017-09-01

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

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

NASA Astrophysics Data System (ADS)

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

1989-03-01

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

Dynamical decoupling of unbounded Hamiltonians

NASA Astrophysics Data System (ADS)

Arenz, Christian; Burgarth, Daniel; Facchi, Paolo; Hillier, Robin

2018-03-01

We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, is known to work for bounded interactions, but physical environments such as bosonic heat baths are usually modeled with unbounded interactions; hence, here, we initiate a systematic study of dynamical decoupling for unbounded operators. We develop a sufficient decoupling criterion for arbitrary Hamiltonians and a necessary decoupling criterion for semibounded Hamiltonians. We give examples for unbounded Hamiltonians where decoupling works and the limiting evolution as well as the convergence speed can be explicitly computed. We show that decoupling does not always work for unbounded interactions and we provide both physically and mathematically motivated examples.

Finite element probabilistic risk assessment of transmission line insulation flashovers caused by lightning strokes

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

Bacvarov, D.C.

1981-01-01

A new method for probabilistic risk assessment of transmission line insulation flashovers caused by lightning strokes is presented. The utilized approach of applying the finite element method for probabilistic risk assessment is demonstrated to be very powerful. The reasons for this are two. First, the finite element method is inherently suitable for analysis of three dimensional spaces where the parameters, such as three variate probability densities of the lightning currents, are non-uniformly distributed. Second, the finite element method permits non-uniform discretization of the three dimensional probability spaces thus yielding high accuracy in critical regions, such as the area of themore » low probability events, while at the same time maintaining coarse discretization in the non-critical areas to keep the number of grid points and the size of the problem to a manageable low level. The finite element probabilistic risk assessment method presented here is based on a new multidimensional search algorithm. It utilizes an efficient iterative technique for finite element interpolation of the transmission line insulation flashover criteria computed with an electro-magnetic transients program. Compared to other available methods the new finite element probabilistic risk assessment method is significantly more accurate and approximately two orders of magnitude computationally more efficient. The method is especially suited for accurate assessment of rare, very low probability events.« less

Computation of the transonic perturbation flow fields around two- and three-dimensional oscillating wings

NASA Technical Reports Server (NTRS)

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

1975-01-01

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about an harmonically oscillating wing are presented along with a discussion of the development of a pilot program for three-dimensional flow. In addition, some two- and three-dimensional examples are presented.

An alternative view of continuous forest inventories

Treesearch

Francis A. Roesch

2008-01-01

A generalized three-dimensional concept of continuous forest inventories applicable to all common forest sample designs is presented and discussed. The concept recognizes the forest through time as a three-dimensional population, two dimensions in land area and the third in time. The sample is selected from a finite three-dimensional partitioning of the population. The...

Three-dimensional modeling of flexible pavements : executive summary, August 2001.

DOT National Transportation Integrated Search

2001-08-01

A linear viscoelastic model has been incorporated into a three-dimensional finite element program for analysis of flexible pavements. Linear and quadratic versions of hexahedral elements and quadrilateral axisymmetrix elements are provided. Dynamic p...

Three dimensional modeling of flexible pavements : final report, March 2002.

DOT National Transportation Integrated Search

2001-08-01

A linear viscoelastic model has been incorporated into a three-dimensional finite element program for analysis of flexible pavements. Linear and quadratic versions of hexahedral elements and quadrilateral axisymmetrix elements are provided. Dynamic p...

A FINITE-DIFFERENCE, DISCRETE-WAVENUMBER METHOD FOR CALCULATING RADAR TRACES

EPA Science Inventory

A hybrid of the finite-difference method and the discrete-wavenumber method is developed to calculate radar traces. The method is based on a three-dimensional model defined in the Cartesian coordinate system; the electromagnetic properties of the model are symmetric with respect ...

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for high Reynolds number laminar flows

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook

1988-01-01

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables were interpolated using complete quadratic shape functions and the pressure was interpolated using linear shape functions. For the two dimensional case, the pressure is defined on a triangular element which is contained inside the complete biquadratic element for velocity variables; and for the three dimensional case, the pressure is defined on a tetrahedral element which is again contained inside the complete tri-quadratic element. Thus the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow for Reynolds number of 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorable with those of the finite difference methods as well as experimental data available. A finite elememt computer program for incompressible, laminar flows is presented.

Discontinuous dual-primal mixed finite elements for elliptic problems

NASA Technical Reports Server (NTRS)

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

2000-01-01

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

An efficicient data structure for three-dimensional vertex based finite volume method

NASA Astrophysics Data System (ADS)

Akkurt, Semih; Sahin, Mehmet

2017-11-01

A vertex based three-dimensional finite volume algorithm has been developed using an edge based data structure.The mesh data structure of the given algorithm is similar to ones that exist in the literature. However, the data structures are redesigned and simplied in order to fit requirements of the vertex based finite volume method. In order to increase the cache efficiency, the data access patterns for the vertex based finite volume method are investigated and these datas are packed/allocated in a way that they are close to each other in the memory. The present data structure is not limited with tetrahedrons, arbitrary polyhedrons are also supported in the mesh without putting any additional effort. Furthermore, the present data structure also supports adaptive refinement and coarsening. For the implicit and parallel implementation of the FVM algorithm, PETSc and MPI libraries are employed. The performance and accuracy of the present algorithm are tested for the classical benchmark problems by comparing the CPU time for the open source algorithms.

Computation of three-dimensional nozzle-exhaust flow fields with the GIM code

NASA Technical Reports Server (NTRS)

Spradley, L. W.; Anderson, P. G.

1978-01-01

A methodology is introduced for constructing numerical analogs of the partial differential equations of continuum mechanics. A general formulation is provided which permits classical finite element and many of the finite difference methods to be derived directly. The approach, termed the General Interpolants Method (GIM), can combined the best features of finite element and finite difference methods. A quasi-variational procedure is used to formulate the element equations, to introduce boundary conditions into the method and to provide a natural assembly sequence. A derivation is given in terms of general interpolation functions from this procedure. Example computations for transonic and supersonic flows in two and three dimensions are given to illustrate the utility of GIM. A three-dimensional nozzle-exhaust flow field is solved including interaction with the freestream and a coupled treatment of the shear layer. Potential applications of the GIM code to a variety of computational fluid dynamics problems is then discussed in terms of existing capability or by extension of the methodology.

Unified control/structure design and modeling research

NASA Technical Reports Server (NTRS)

Mingori, D. L.; Gibson, J. S.; Blelloch, P. A.; Adamian, A.

1986-01-01

To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed.

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

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

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

2005-11-15

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

Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Luo, Li-Shi

2007-01-01

In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.

Two-dimensional finite-element analyses of simulated rotor-fragment impacts against rings and beams compared with experiments

NASA Technical Reports Server (NTRS)

Stagliano, T. R.; Witmer, E. A.; Rodal, J. J. A.

1979-01-01

Finite element modeling alternatives as well as the utility and limitations of the two dimensional structural response computer code CIVM-JET 4B for predicting the transient, large deflection, elastic plastic, structural responses of two dimensional beam and/or ring structures which are subjected to rigid fragment impact were investigated. The applicability of the CIVM-JET 4B analysis and code for the prediction of steel containment ring response to impact by complex deformable fragments from a trihub burst of a T58 turbine rotor was studied. Dimensional analysis considerations were used in a parametric examination of data from engine rotor burst containment experiments and data from sphere beam impact experiments. The use of the CIVM-JET 4B computer code for making parametric structural response studies on both fragment-containment structure and fragment-deflector structure was illustrated. Modifications to the analysis/computation procedure were developed to alleviate restrictions.

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.

Irreducible representations of finitely generated nilpotent groups

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

Beloshapka, I V; Gorchinskiy, S O

2016-01-31

We prove that irreducible complex representations of finitely generated nilpotent groups are monomial if and only if they have finite weight, which was conjectured by Parshin. Note that we consider (possibly infinite-dimensional) representations without any topological structure. In addition, we prove that for certain induced representations, irreducibility is implied by Schur irreducibility. Both results are obtained in a more general form for representations over an arbitrary field. Bibliography: 21 titles.

Numerical Methods for 2-Dimensional Modeling

DTIC Science & Technology

1980-12-01

high-order finite element methods, and a multidimensional version of the method of lines, both utilizing an optimized stiff integrator for the time...integration. The finite element methods have proved disappointing, but the method of lines has provided an unexpectedly large gain in speed. Two...diffusion problems with the same number of unknowns (a 21 x 41 grid), solved by second-order finite element methods, took over seven minutes on the Cray-i

An algorithm for the basis of the finite Fourier transform

NASA Technical Reports Server (NTRS)

Santhanam, Thalanayar S.

1995-01-01

The Finite Fourier Transformation matrix (F.F.T.) plays a central role in the formulation of quantum mechanics in a finite dimensional space studied by the author over the past couple of decades. An outstanding problem which still remains open is to find a complete basis for F.F.T. In this paper we suggest a simple algorithm to find the eigenvectors of F.T.T.

United States Air Force Graduate Student Research Program. Program Management Report

DTIC Science & Technology

1988-12-01

PRELIMINARY STRUCTURAL DESIGN/OPTIMIZATION by Richard A. Swift ABSTRACT Finite element analysis for use in structural design has advanced to the point where...Plates Subjected Gregory Schoeppner to Low Velocity Impact *** Same Report as Prof. William Wolfe * 57 Finite Element Analysis for Preliminary Richard...and dynamic load conditions using both radial and bias- ply tires. A detailed three-dimensional finite - element model of the wheel was generated for

Affine.m—Mathematica package for computations in representation theory of finite-dimensional and affine Lie algebras

NASA Astrophysics Data System (ADS)

Nazarov, Anton

2012-11-01

In this paper we present Affine.m-a program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. The algorithms are based on the properties of weights and Weyl symmetry. Computation of weight multiplicities in irreducible and Verma modules, branching of representations and tensor product decomposition are the most important problems for us. These problems have numerous applications in physics and we provide some examples of these applications. The program is implemented in the popular computer algebra system Mathematica and works with finite-dimensional and affine Lie algebras. Catalogue identifier: AENA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENB_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, UK Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 24 844 No. of bytes in distributed program, including test data, etc.: 1 045 908 Distribution format: tar.gz Programming language: Mathematica. Computer: i386-i686, x86_64. Operating system: Linux, Windows, Mac OS, Solaris. RAM: 5-500 Mb Classification: 4.2, 5. Nature of problem: Representation theory of finite-dimensional Lie algebras has many applications in different branches of physics, including elementary particle physics, molecular physics, nuclear physics. Representations of affine Lie algebras appear in string theories and two-dimensional conformal field theory used for the description of critical phenomena in two-dimensional systems. Also Lie symmetries play a major role in a study of quantum integrable systems. Solution method: We work with weights and roots of finite-dimensional and affine Lie algebras and use Weyl symmetry extensively. Central problems which are the computations of weight multiplicities, branching and fusion coefficients are solved using one general recurrent algorithm based on generalization of Weyl character formula. We also offer alternative implementation based on the Freudenthal multiplicity formula which can be faster in some cases. Restrictions: Computational complexity grows fast with the rank of an algebra, so computations for algebras of ranks greater than 8 are not practical. Unusual features: We offer the possibility of using a traditional mathematical notation for the objects in representation theory of Lie algebras in computations if Affine.m is used in the Mathematica notebook interface. Running time: From seconds to days depending on the rank of the algebra and the complexity of the representation.

Interacting steps with finite-range interactions: Analytical approximation and numerical results

NASA Astrophysics Data System (ADS)

Jaramillo, Diego Felipe; Téllez, Gabriel; González, Diego Luis; Einstein, T. L.

2013-05-01

We calculate an analytical expression for the terrace-width distribution P(s) for an interacting step system with nearest- and next-nearest-neighbor interactions. Our model is derived by mapping the step system onto a statistically equivalent one-dimensional system of classical particles. The validity of the model is tested with several numerical simulations and experimental results. We explore the effect of the range of interactions q on the functional form of the terrace-width distribution and pair correlation functions. For physically plausible interactions, we find modest changes when next-nearest neighbor interactions are included and generally negligible changes when more distant interactions are allowed. We discuss methods for extracting from simulated experimental data the characteristic scale-setting terms in assumed potential forms.

Exact Large-Deviation Statistics for a Nonequilibrium Quantum Spin Chain

NASA Astrophysics Data System (ADS)

Žnidarič, Marko

2014-01-01

We consider a one-dimensional XX spin chain in a nonequilibrium setting with a Lindblad-type boundary driving. By calculating large-deviation rate function in the thermodynamic limit, a generalization of free energy to a nonequilibrium setting, we obtain a complete distribution of current, including closed expressions for lower-order cumulants. We also identify two phase-transition-like behaviors in either the thermodynamic limit, at which the current probability distribution becomes discontinuous, or at maximal driving, when the range of possible current values changes discontinuously. In the thermodynamic limit the current has a finite upper and lower bound. We also explicitly confirm nonequilibrium fluctuation relation and show that the current distribution is the same under mapping of the coupling strength Γ→1/Γ.

Finite-data-size study on practical universal blind quantum computation

NASA Astrophysics Data System (ADS)

Zhao, Qiang; Li, Qiong

2018-07-01

The universal blind quantum computation with weak coherent pulses protocol is a practical scheme to allow a client to delegate a computation to a remote server while the computation hidden. However, in the practical protocol, a finite data size will influence the preparation efficiency in the remote blind qubit state preparation (RBSP). In this paper, a modified RBSP protocol with two decoy states is studied in the finite data size. The issue of its statistical fluctuations is analyzed thoroughly. The theoretical analysis and simulation results show that two-decoy-state case with statistical fluctuation is closer to the asymptotic case than the one-decoy-state case with statistical fluctuation. Particularly, the two-decoy-state protocol can achieve a longer communication distance than the one-decoy-state case in this statistical fluctuation situation.

Harnessing Multivariate Statistics for Ellipsoidal Data in Structural Geology

NASA Astrophysics Data System (ADS)

Roberts, N.; Davis, J. R.; Titus, S.; Tikoff, B.

2015-12-01

Most structural geology articles do not state significance levels, report confidence intervals, or perform regressions to find trends. This is, in part, because structural data tend to include directions, orientations, ellipsoids, and tensors, which are not treatable by elementary statistics. We describe a full procedural methodology for the statistical treatment of ellipsoidal data. We use a reconstructed dataset of deformed ooids in Maryland from Cloos (1947) to illustrate the process. Normalized ellipsoids have five degrees of freedom and can be represented by a second order tensor. This tensor can be permuted into a five dimensional vector that belongs to a vector space and can be treated with standard multivariate statistics. Cloos made several claims about the distribution of deformation in the South Mountain fold, Maryland, and we reexamine two particular claims using hypothesis testing: 1) octahedral shear strain increases towards the axial plane of the fold; 2) finite strain orientation varies systematically along the trend of the axial trace as it bends with the Appalachian orogen. We then test the null hypothesis that the southern segment of South Mountain is the same as the northern segment. This test illustrates the application of ellipsoidal statistics, which combine both orientation and shape. We report confidence intervals for each test, and graphically display our results with novel plots. This poster illustrates the importance of statistics in structural geology, especially when working with noisy or small datasets.

Geometric MCMC for infinite-dimensional inverse problems

NASA Astrophysics Data System (ADS)

Beskos, Alexandros; Girolami, Mark; Lan, Shiwei; Farrell, Patrick E.; Stuart, Andrew M.

2017-04-01

Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement, when the finite-dimensional approximations become more accurate. Such methods are typically forced to reduce step-sizes as the discretization gets finer, and thus are expensive as a function of dimension. Recently, a new class of MCMC methods with mesh-independent convergence times has emerged. However, few of them take into account the geometry of the posterior informed by the data. At the same time, recently developed geometric MCMC algorithms have been found to be powerful in exploring complicated distributions that deviate significantly from elliptic Gaussian laws, but are in general computationally intractable for models defined in infinite dimensions. In this work, we combine geometric methods on a finite-dimensional subspace with mesh-independent infinite-dimensional approaches. Our objective is to speed up MCMC mixing times, without significantly increasing the computational cost per step (for instance, in comparison with the vanilla preconditioned Crank-Nicolson (pCN) method). This is achieved by using ideas from geometric MCMC to probe the complex structure of an intrinsic finite-dimensional subspace where most data information concentrates, while retaining robust mixing times as the dimension grows by using pCN-like methods in the complementary subspace. The resulting algorithms are demonstrated in the context of three challenging inverse problems arising in subsurface flow, heat conduction and incompressible flow control. The algorithms exhibit up to two orders of magnitude improvement in sampling efficiency when compared with the pCN method.

External Boundary Conditions for Three-Dimensional Problems of Computational Aerodynamics

NASA Technical Reports Server (NTRS)

Tsynkov, Semyon V.

1997-01-01

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

Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method.

PubMed

Deng, Yongbo; Korvink, Jan G

2016-05-01

This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.

Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method

PubMed Central

Korvink, Jan G.

2016-01-01

This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable. PMID:27279766

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

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

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

1985-09-01

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

Modeling dam-break flows using finite volume method on unstructured grid

USDA-ARS?s Scientific Manuscript database

Two-dimensional shallow water models based on unstructured finite volume method and approximate Riemann solvers for computing the intercell fluxes have drawn growing attention because of their robustness, high adaptivity to complicated geometry and ability to simulate flows with mixed regimes and di...

Improved Design of Tunnel Supports : Volume 3 : Finite Element Analysis of the Peachtree Center Station in Atlanta

DOT National Transportation Integrated Search

1980-06-01

Volume 3 contains the application of the three-dimensional (3-D) finite element program, Automatic Dynamic Incremental Nonlinear Analysis (ADINA), which was designed to replace the traditional 2-D plane strain analysis, to a specific location. The lo...

A FINITE-DIFFERENCE, DISCRETE-WAVENUMBER METHOD FOR CALCULATING RADAR TRACES

EPA Science Inventory

A hybrid of the finite-difference method and the discrete-wavenumber method is developed to calculate radar traces. The method is based on a three-dimensional model defined in the Cartesian coordinate system; the electromag-netic properties of the model are symmetric with respect...

Asymptotic symmetries of Rindler space at the horizon and null infinity

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

Chung, Hyeyoun

2010-08-15

We investigate the asymptotic symmetries of Rindler space at null infinity and at the event horizon using both systematic and ad hoc methods. We find that the approaches that yield infinite-dimensional asymptotic symmetry algebras in the case of anti-de Sitter and flat spaces only give a finite-dimensional algebra for Rindler space at null infinity. We calculate the charges corresponding to these symmetries and confirm that they are finite, conserved, and integrable, and that the algebra of charges gives a representation of the asymptotic symmetry algebra. We also use relaxed boundary conditions to find infinite-dimensional asymptotic symmetry algebras for Rindler spacemore » at null infinity and at the event horizon. We compute the charges corresponding to these symmetries and confirm that they are finite and integrable. We also determine sufficient conditions for the charges to be conserved on-shell, and for the charge algebra to give a representation of the asymptotic symmetry algebra. In all cases, we find that the central extension of the charge algebra is trivial.« less

A new conformal absorbing boundary condition for finite element meshes and parallelization of FEMATS

NASA Technical Reports Server (NTRS)

Chatterjee, A.; Volakis, J. L.; Nguyen, J.; Nurnberger, M.; Ross, D.

1993-01-01

Some of the progress toward the development and parallelization of an improved version of the finite element code FEMATS is described. This is a finite element code for computing the scattering by arbitrarily shaped three dimensional surfaces composite scatterers. The following tasks were worked on during the report period: (1) new absorbing boundary conditions (ABC's) for truncating the finite element mesh; (2) mixed mesh termination schemes; (3) hierarchical elements and multigridding; (4) parallelization; and (5) various modeling enhancements (antenna feeds, anisotropy, and higher order GIBC).

A statistical mechanical model of economics

NASA Astrophysics Data System (ADS)

Lubbers, Nicholas Edward Williams

Statistical mechanics pursues low-dimensional descriptions of systems with a very large number of degrees of freedom. I explore this theme in two contexts. The main body of this dissertation explores and extends the Yard Sale Model (YSM) of economic transactions using a combination of simulations and theory. The YSM is a simple interacting model for wealth distributions which has the potential to explain the empirical observation of Pareto distributions of wealth. I develop the link between wealth condensation and the breakdown of ergodicity due to nonlinear diffusion effects which are analogous to the geometric random walk. Using this, I develop a deterministic effective theory of wealth transfer in the YSM that is useful for explaining many quantitative results. I introduce various forms of growth to the model, paying attention to the effect of growth on wealth condensation, inequality, and ergodicity. Arithmetic growth is found to partially break condensation, and geometric growth is found to completely break condensation. Further generalizations of geometric growth with growth in- equality show that the system is divided into two phases by a tipping point in the inequality parameter. The tipping point marks the line between systems which are ergodic and systems which exhibit wealth condensation. I explore generalizations of the YSM transaction scheme to arbitrary betting functions to develop notions of universality in YSM-like models. I find that wealth vi condensation is universal to a large class of models which can be divided into two phases. The first exhibits slow, power-law condensation dynamics, and the second exhibits fast, finite-time condensation dynamics. I find that the YSM, which exhibits exponential dynamics, is the critical, self-similar model which marks the dividing line between the two phases. The final chapter develops a low-dimensional approach to materials microstructure quantification. Modern materials design harnesses complex microstructure effects to develop high-performance materials, but general microstructure quantification is an unsolved problem. Motivated by statistical physics, I envision microstructure as a low-dimensional manifold, and construct this manifold by leveraging multiple machine learning approaches including transfer learning, dimensionality reduction, and computer vision breakthroughs with convolutional neural networks.

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

NASA Astrophysics Data System (ADS)

Pekşen, Ertan; Yas, Türker; Kıyak, Alper

2014-09-01

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

A non-linear dimension reduction methodology for generating data-driven stochastic input models

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

Ganapathysubramanian, Baskar; Zabaras, Nicholas

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem ofmore » manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space R{sup n}. An isometric mapping F from M to a low-dimensional, compact, connected set A is contained in R{sup d}(d<

Comments on the Diffusive Behavior of Two Upwind Schemes

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1998-01-01

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and locally one-dimensional finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2.5 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a speedup of 29 over finite volume.

Finite element area and line integral transforms for generalization of aperture function and geometry in Kirchhoff scalar diffraction theory

NASA Astrophysics Data System (ADS)

Kraus, Hal G.

1993-02-01

Two finite element-based methods for calculating Fresnel region and near-field region intensities resulting from diffraction of light by two-dimensional apertures are presented. The first is derived using the Kirchhoff area diffraction integral and the second is derived using a displaced vector potential to achieve a line integral transformation. The specific form of each of these formulations is presented for incident spherical waves and for Gaussian laser beams. The geometry of the two-dimensional diffracting aperture(s) is based on biquadratic isoparametric elements, which are used to define apertures of complex geometry. These elements are also used to build complex amplitude and phase functions across the aperture(s), which may be of continuous or discontinuous form. The finite element transform integrals are accurately and efficiently integrated numerically using Gaussian quadrature. The power of these methods is illustrated in several examples which include secondary obstructions, secondary spider supports, multiple mirror arrays, synthetic aperture arrays, apertures covered by screens, apodization, phase plates, and off-axis apertures. Typically, the finite element line integral transform results in significant gains in computational efficiency over the finite element Kirchhoff transform method, but is also subject to some loss in generality.

Vibration Response Models of a Stiffened Aluminum Plate Excited by a Shaker

NASA Technical Reports Server (NTRS)

Cabell, Randolph H.

2008-01-01

Numerical models of structural-acoustic interactions are of interest to aircraft designers and the space program. This paper describes a comparison between two energy finite element codes, a statistical energy analysis code, a structural finite element code, and the experimentally measured response of a stiffened aluminum plate excited by a shaker. Different methods for modeling the stiffeners and the power input from the shaker are discussed. The results show that the energy codes (energy finite element and statistical energy analysis) accurately predicted the measured mean square velocity of the plate. In addition, predictions from an energy finite element code had the best spatial correlation with measured velocities. However, predictions from a considerably simpler, single subsystem, statistical energy analysis model also correlated well with the spatial velocity distribution. The results highlight a need for further work to understand the relationship between modeling assumptions and the prediction results.

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

ERIC Educational Resources Information Center

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

2010-01-01

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

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

EPA Science Inventory

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

Progress in multi-dimensional upwind differencing

NASA Technical Reports Server (NTRS)

Vanleer, Bram

1992-01-01

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

Poisson traces, D-modules, and symplectic resolutions

NASA Astrophysics Data System (ADS)

Etingof, Pavel; Schedler, Travis

2018-03-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

Poisson traces, D-modules, and symplectic resolutions.

PubMed

Etingof, Pavel; Schedler, Travis

2018-01-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

Element-topology-independent preconditioners for parallel finite element computations

NASA Technical Reports Server (NTRS)

Park, K. C.; Alexander, Scott

1992-01-01

A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.

Recent Progress in the p and h-p Version of the Finite Element Method.

DTIC Science & Technology

1987-07-01

code PROBE which was developed recently by NOETIC Technologies, St. Louis £54]. PROBE solves two dimensional problems of linear elasticity, stationary...of the finite element method was studied in detail from various point of view. We will mention here some essential illustrative results. In one...28) Bathe, K. J., Brezzi, F., Studies of finite element procedures - the INF-SUP condition, equivalent forms and applications in Reliability of

Constitutive Behavior and Finite Element Analysis of FRP Composite and Concrete Members

PubMed Central

Ann, Ki Yong; Cho, Chang-Geun

2013-01-01

The present study concerns compressive and flexural constitutive models incorporated into an isoparametric beam finite element scheme for fiber reinforced polymer (FRP) and concrete composites, using their multi-axial constitutive behavior. The constitutive behavior of concrete was treated in triaxial stress states as an orthotropic hypoelasticity-based formulation to determine the confinement effect of concrete from a three-dimensional failure surface in triaxial stress states. The constitutive behavior of the FRP composite was formulated from the two-dimensional classical lamination theory. To predict the flexural behavior of circular cross-section with FRP sheet and concrete composite, a layered discretization of cross-sections was incorporated into nonlinear isoparametric beam finite elements. The predicted constitutive behavior was validated by a comparison to available experimental results in the compressive and flexural beam loading test. PMID:28788312

Design of Beneficial Wave Dynamics for Engine Life and Operability Enhancement

DTIC Science & Technology

2010-07-30

ST^(A), where S is the Dirac delta measure. Stochastic transition 9 function can be used to define two linear transfer operators called as Perron ... Frobenius and Koopman operators. Here we consider the finite dimensional approximation of the P-F operator. To do this we consider the finite

Convergence of an hp-Adaptive Finite Element Strategy in Two and Three Space-Dimensions

NASA Astrophysics Data System (ADS)

Bürg, Markus; Dörfler, Willy

2010-09-01

We show convergence of an automatic hp-adaptive refinement strategy for the finite element method on the elliptic boundary value problem. The strategy is a generalization of a refinement strategy proposed for one-dimensional situations to problems in two and three space-dimensions.

1+1 dimensional compactifications of string theory.

PubMed

Goheer, Naureen; Kleban, Matthew; Susskind, Leonard

2004-05-14

We argue that stable, maximally symmetric compactifications of string theory to 1+1 dimensions are in conflict with holography. In particular, the finite horizon entropies of the Rindler wedge in 1+1 dimensional Minkowski and anti-de Sitter space, and of the de Sitter horizon in any dimension, are inconsistent with the symmetries of these spaces. The argument parallels one made recently by the same authors, in which we demonstrated the incompatibility of the finiteness of the entropy and the symmetries of de Sitter space in any dimension. If the horizon entropy is either infinite or zero, the conflict is resolved.

Stability and Existence Results for Quasimonotone Quasivariational Inequalities in Finite Dimensional Spaces

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

Castellani, Marco; Giuli, Massimiliano, E-mail: massimiliano.giuli@univaq.it

2016-02-15

We study pseudomonotone and quasimonotone quasivariational inequalities in a finite dimensional space. In particular we focus our attention on the closedness of some solution maps associated to a parametric quasivariational inequality. From this study we derive two results on the existence of solutions of the quasivariational inequality. On the one hand, assuming the pseudomonotonicity of the operator, we get the nonemptiness of the set of the classical solutions. On the other hand, we show that the quasimonoticity of the operator implies the nonemptiness of the set of nonzero solutions. An application to traffic network is also considered.

Linear and nonlinear pattern selection in Rayleigh-Benard stability problems

NASA Technical Reports Server (NTRS)

Davis, Sanford S.

1993-01-01

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

A History of the Description of the Three-Dimensional Finite Rotation

NASA Astrophysics Data System (ADS)

Fraiture, Luc

2009-01-01

A history of the description of a three-dimensional finite rotation is given starting with Cardano in the middle of the sixteenth century and ending with Bryan in the beginning of the past century. Description means both a textual description and/or a mathematical representation. To appreciate the historical context of the milestones reached over the centuries, the background and personality of the main players in this history are given. At the end, a short critical discussion is added, reviewing the present names of rotation parameters in use related to the scientists which have been considered here.

MHOST version 4.2. Volume 1: Users' manual

NASA Technical Reports Server (NTRS)

Nakazawa, Shohei

1989-01-01

This manual describes the user options available for running the MHOST finite element analysis package. MHOST is a solid and structural analysis program based on mixed finite element technology, and is specifically designed for three-dimensional inelastic analysis. A family of two- and three-dimensional continuum elements along with beam and shell structural elements can be utilized. Many options are available in the constitutive equation library, the solution algorithms and the analysis capabilities. An overview of the algorithms, a general description of the input data formats, and a discussion of input data for selecting solution algorithms are given.

First Instances of Generalized Expo-Rational Finite Elements on Triangulations

NASA Astrophysics Data System (ADS)

Dechevsky, Lubomir T.; Zanaty, Peter; Laksa˚, Arne; Bang, Børre

2011-12-01

In this communication we consider a construction of simplicial finite elements on triangulated two-dimensional polygonal domains. This construction is, in some sense, dual to the construction of generalized expo-rational B-splines (GERBS). The main result is in the obtaining of new polynomial simplicial patches of the first several lowest possible total polynomial degrees which exhibit Hermite interpolatory properties. The derivation of these results is based on the theory of piecewise polynomial GERBS called Euler Beta-function B-splines. We also provide 3-dimensional visualization of the graphs of the new polynomial simplicial patches and their control polygons.

Many-body delocalization in a strongly disordered system with long-range interactions: Finite-size scaling

NASA Astrophysics Data System (ADS)

Burin, Alexander L.

2015-03-01

Many-body localization in a disordered system of interacting spins coupled by the long-range interaction 1 /Rα is investigated combining analytical theory considering resonant interactions and a finite-size scaling of exact numerical solutions with number of spins N . The numerical results for a one-dimensional system are consistent with the general expectations of analytical theory for a d -dimensional system including the absence of localization in the infinite system at α <2 d and a universal scaling of a critical energy disordering Wc∝N2/d -α d .

75 FR 48815 - Medicaid Program and Children's Health Insurance Program (CHIP); Revisions to the Medicaid...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-08-11

... size may be reduced by the finite population correction factor. The finite population correction is a statistical formula utilized to determine sample size where the population is considered finite rather than... program may notify us and the annual sample size will be reduced by the finite population correction...

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.

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

NASA Astrophysics Data System (ADS)

Bischoff, Jan-Moritz; Jeckelmann, Eric

2017-11-01

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

A computer code for three-dimensional incompressible flows using nonorthogonal body-fitted coordinate systems

NASA Technical Reports Server (NTRS)

Chen, Y. S.

1986-01-01

In this report, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BFC) systems has been developed. The equations of motion are transformed to a generalized curvilinear coordinate system from which the transformed equations are discretized using finite difference approximations in the transformed domain. The hybrid scheme is used to approximate the convection terms in the governing equations. Solutions of the finite difference equations are obtained iteratively by using a pressure-velocity correction algorithm (SIMPLE-C). Numerical examples of two- and three-dimensional, laminar and turbulent flow problems are employed to evaluate the accuracy and efficiency of the present computer code. The user's guide and computer program listing of the present code are also included.

The program FANS-3D (finite analytic numerical simulation 3-dimensional) and its applications

NASA Technical Reports Server (NTRS)

Bravo, Ramiro H.; Chen, Ching-Jen

1992-01-01

In this study, the program named FANS-3D (Finite Analytic Numerical Simulation-3 Dimensional) is presented. FANS-3D was designed to solve problems of incompressible fluid flow and combined modes of heat transfer. It solves problems with conduction and convection modes of heat transfer in laminar flow, with provisions for radiation and turbulent flows. It can solve singular or conjugate modes of heat transfer. It also solves problems in natural convection, using the Boussinesq approximation. FANS-3D was designed to solve heat transfer problems inside one, two and three dimensional geometries that can be represented by orthogonal planes in a Cartesian coordinate system. It can solve internal and external flows using appropriate boundary conditions such as symmetric, periodic and user specified.

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

NASA Astrophysics Data System (ADS)

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

2012-10-01

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

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

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

Gacs quantum algorithmic entropy in infinite dimensional Hilbert spaces

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

Benatti, Fabio, E-mail: benatti@ts.infn.it; Oskouei, Samad Khabbazi, E-mail: kh.oskuei@ut.ac.ir; Deh Abad, Ahmad Shafiei, E-mail: shafiei@khayam.ut.ac.ir

We extend the notion of Gacs quantum algorithmic entropy, originally formulated for finitely many qubits, to infinite dimensional quantum spin chains and investigate the relation of this extension with two quantum dynamical entropies that have been proposed in recent years.

Development of Composite Materials with High Passive Damping Properties

DTIC Science & Technology

2006-05-15

frequency response function analysis. Sound transmission through sandwich panels was studied using the statistical energy analysis (SEA). Modal density...2.2.3 Finite element models 14 2.2.4 Statistical energy analysis method 15 CHAPTER 3 ANALYSIS OF DAMPING IN SANDWICH MATERIALS. 24 3.1 Equation of...sheets and the core. 2.2.4 Statistical energy analysis method Finite element models are generally only efficient for problems at low and middle frequencies

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

PubMed

Campbell, J Q; Petrella, A J

2016-09-06

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

A finite element: Boundary integral method for electromagnetic scattering. Ph.D. Thesis Technical Report, Feb. - Sep. 1992

NASA Technical Reports Server (NTRS)

Collins, J. D.; Volakis, John L.

1992-01-01

A method that combines the finite element and boundary integral techniques for the numerical solution of electromagnetic scattering problems is presented. The finite element method is well known for requiring a low order storage and for its capability to model inhomogeneous structures. Of particular emphasis in this work is the reduction of the storage requirement by terminating the finite element mesh on a boundary in a fashion which renders the boundary integrals in convolutional form. The fast Fourier transform is then used to evaluate these integrals in a conjugate gradient solver, without a need to generate the actual matrix. This method has a marked advantage over traditional integral equation approaches with respect to the storage requirement of highly inhomogeneous structures. Rectangular, circular, and ogival mesh termination boundaries are examined for two-dimensional scattering. In the case of axially symmetric structures, the boundary integral matrix storage is reduced by exploiting matrix symmetries and solving the resulting system via the conjugate gradient method. In each case several results are presented for various scatterers aimed at validating the method and providing an assessment of its capabilities. Important in methods incorporating boundary integral equations is the issue of internal resonance. A method is implemented for their removal, and is shown to be effective in the two-dimensional and three-dimensional applications.

The Statistical Mechanics of Ideal Homogeneous Turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2002-01-01

Plasmas, such as those found in the space environment or in plasma confinement devices, are often modeled as electrically conducting fluids. When fluids and plasmas are energetically stirred, regions of highly nonlinear, chaotic behavior known as turbulence arise. Understanding the fundamental nature of turbulence is a long-standing theoretical challenge. The present work describes a statistical theory concerning a certain class of nonlinear, finite dimensional, dynamical models of turbulence. These models arise when the partial differential equations describing incompressible, ideal (i.e., nondissipative) homogeneous fluid and magnetofluid (i.e., plasma) turbulence are Fourier transformed into a very large set of ordinary differential equations. These equations define a divergenceless flow in a high-dimensional phase space, which allows for the existence of a Liouville theorem, guaranteeing a distribution function based on constants of the motion (integral invariants). The novelty of these particular dynamical systems is that there are integral invariants other than the energy, and that some of these invariants behave like pseudoscalars under two of the discrete symmetry transformations of physics, parity, and charge conjugation. In this work the 'rugged invariants' of ideal homogeneous turbulence are shown to be the only significant scalar and pseudoscalar invariants. The discovery that pseudoscalar invariants cause symmetries of the original equations to be dynamically broken and induce a nonergodic structure on the associated phase space is the primary result presented here. Applicability of this result to dissipative turbulence is also discussed.

Statistical Machine Learning for Structured and High Dimensional Data

DTIC Science & Technology

2014-09-17

AFRL-OSR-VA-TR-2014-0234 STATISTICAL MACHINE LEARNING FOR STRUCTURED AND HIGH DIMENSIONAL DATA Larry Wasserman CARNEGIE MELLON UNIVERSITY Final...Re . 8-98) v Prescribed by ANSI Std. Z39.18 14-06-2014 Final Dec 2009 - Aug 2014 Statistical Machine Learning for Structured and High Dimensional...area of resource-constrained statistical estimation. machine learning , high-dimensional statistics U U U UU John Lafferty 773-702-3813 > Research under

The Use of Sparse Direct Solver in Vector Finite Element Modeling for Calculating Two Dimensional (2-D) Magnetotelluric Responses in Transverse Electric (TE) Mode

NASA Astrophysics Data System (ADS)

Yihaa Roodhiyah, Lisa’; Tjong, Tiffany; Nurhasan; Sutarno, D.

2018-04-01

The late research, linear matrices of vector finite element in two dimensional(2-D) magnetotelluric (MT) responses modeling was solved by non-sparse direct solver in TE mode. Nevertheless, there is some weakness which have to be improved especially accuracy in the low frequency (10-3 Hz-10-5 Hz) which is not achieved yet and high cost computation in dense mesh. In this work, the solver which is used is sparse direct solver instead of non-sparse direct solverto overcome the weaknesses of solving linear matrices of vector finite element metod using non-sparse direct solver. Sparse direct solver will be advantageous in solving linear matrices of vector finite element method because of the matrix properties which is symmetrical and sparse. The validation of sparse direct solver in solving linear matrices of vector finite element has been done for a homogen half-space model and vertical contact model by analytical solution. Thevalidation result of sparse direct solver in solving linear matrices of vector finite element shows that sparse direct solver is more stable than non-sparse direct solver in computing linear problem of vector finite element method especially in low frequency. In the end, the accuracy of 2D MT responses modelling in low frequency (10-3 Hz-10-5 Hz) has been reached out under the efficient allocation memory of array and less computational time consuming.

Dimensional stability of curved panels with cocured stiffeners and cobonded frames

NASA Technical Reports Server (NTRS)

Mabson, G. E.; Flynn, B. W.; Swanson, G. D.; Lundquist, R. C.; Rupp, P. L.

1993-01-01

Closed form and finite element analyses are presented for axial direction and transverse direction dimensional stability of skin/stringer panels. Several sensitivity studies are presented to illustrate the influence of various design parameters on the dimensional stability of these panels. Panel geometry, material properties (stiffness and coefficient of thermal expansion), restraint conditions and local details, such as resin fillets, all combine to influence dimensional stability, residual and assembly forces.

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

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

A new procedure for investigating three-dimensional stress fields in a thin plate with a through-the-thickness crack

NASA Astrophysics Data System (ADS)

Yi, Dake; Wang, TzuChiang

2018-06-01

In the paper, a new procedure is proposed to investigate three-dimensional fracture problems of a thin elastic plate with a long through-the-thickness crack under remote uniform tensile loading. The new procedure includes a new analytical method and high accurate finite element simulations. In the part of theoretical analysis, three-dimensional Maxwell stress functions are employed in order to derive three-dimensional crack tip fields. Based on the theoretical analysis, an equation which can describe the relationship among the three-dimensional J-integral J( z), the stress intensity factor K( z) and the tri-axial stress constraint level T z ( z) is derived first. In the part of finite element simulations, a fine mesh including 153360 elements is constructed to compute the stress field near the crack front, J( z) and T z ( z). Numerical results show that in the plane very close to the free surface, the K field solution is still valid for in-plane stresses. Comparison with the numerical results shows that the analytical results are valid.

Contact Stress Analysis of Spiral Bevel Gears Using Finite Element Analysis

NASA Technical Reports Server (NTRS)

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

1995-01-01

A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the finite element method. The procedure involves generating a finite element model by solving equations that identify tooth surface coordinates. Coordinate transformations are used to orientate the gear and pinion for gear meshing. Contact boundary conditions are simulated with gap elements. A solution technique for correct orientation of the gap elements is given. Example models and results are presented.

Finite-surface method for the Maxwell equations with corner singularities

NASA Technical Reports Server (NTRS)

Vinokur, Marcel; Yarrow, Maurice

1994-01-01

The finite-surface method for the two-dimensional Maxwell equations in generalized coordinates is extended to treat perfect conductor boundaries with sharp corners. Known singular forms of the grid and the electromagnetic fields in the neighborhood of each corner are used to obtain accurate approximations to the surface and line integrals appearing in the method. Numerical results are presented for a harmonic plane wave incident on a finite flat plate. Comparisons with exact solutions show good agreement.

FIESTA ROC: A new finite element analysis program for solar cell simulation

NASA Technical Reports Server (NTRS)

Clark, Ralph O.

1991-01-01

The Finite Element Semiconductor Three-dimensional Analyzer by Ralph O. Clark (FIESTA ROC) is a computational tool for investigating in detail the performance of arbitrary solar cell structures. As its name indicates, it uses the finite element technique to solve the fundamental semiconductor equations in the cell. It may be used for predicting the performance (thereby dictating the design parameters) of a proposed cell or for investigating the limiting factors in an established design.

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

PubMed

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

2014-10-01

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

Computer aided stress analysis of long bones utilizing computer tomography

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

Marom, S.A.

1986-01-01

A computer aided analysis method, utilizing computed tomography (CT) has been developed, which together with a finite element program determines the stress-displacement pattern in a long bone section. The CT data file provides the geometry, the density and the material properties for the generated finite element model. A three-dimensional finite element model of a tibial shaft is automatically generated from the CT file by a pre-processing procedure for a finite element program. The developed pre-processor includes an edge detection algorithm which determines the boundaries of the reconstructed cross-sectional images of the scanned bone. A mesh generation procedure than automatically generatesmore » a three-dimensional mesh of a user-selected refinement. The elastic properties needed for the stress analysis are individually determined for each model element using the radiographic density (CT number) of each pixel with the elemental borders. The elastic modulus is determined from the CT radiographic density by using an empirical relationship from the literature. The generated finite element model, together with applied loads, determined from existing gait analysis and initial displacements, comprise a formatted input for the SAP IV finite element program. The output of this program, stresses and displacements at the model elements and nodes, are sorted and displayed by a developed post-processor to provide maximum and minimum values at selected locations in the model.« less

Biomechanical evaluation of one-piece and two-piece small-diameter dental implants: In-vitro experimental and three-dimensional finite element analyses.

PubMed

Wu, Aaron Yu-Jen; Hsu, Jui-Ting; Chee, Winston; Lin, Yun-Te; Fuh, Lih-Jyh; Huang, Heng-Li

2016-09-01

Small-diameter dental implants are associated with a higher risk of implant failure. This study used both three-dimensional finite-element (FE) simulations and in-vitro experimental tests to analyze the stresses and strains in both the implant and the surrounding bone when using one-piece (NobelDirect) and two-piece (NobelReplace) small-diameter implants, with the aim of understanding the underlying biomechanical mechanisms. Six experimental artificial jawbone models and two FE models were prepared for one-piece and two-piece 3.5-mm diameter implants. Rosette strain gauges were used for in-vitro tests, with peak values of the principal bone strain recorded with a data acquisition system. Implant stability as quantified by Periotest values (PTV) were also recorded for both types of implants. Experimental data were analyzed statistically using Wilcoxon's rank-sum test. In FE simulations, the peak value and distribution of von-Mises stresses in the implant and bone were selected for evaluation. In in-vitro tests, the peak bone strain was 42% lower for two-piece implants than for one-piece implants. The PTV was slightly lower for one-piece implants (PTV = -6) than for two-piece implants (PTV = -5). In FE simulations, the stresses in the bone and implant were about 23% higher and 12% lower, respectively, for one-piece implants than those for two-piece implants. Due to the higher peri-implant bone stresses and strains, one-piece implants (NobelDirect) might be not suitable for use as small-diameter implants. Copyright © 2016. Published by Elsevier B.V.

Stresses and strains in thick perforated orthotropic plates

Treesearch

A. Alshaya; John Hunt; R. Rowlands

2016-01-01

Stress and strain concentrations and in-plane and out-of-plane stress constraint factors associated with a circular hole in thick, loaded orthotropic composite plates are determined by three-dimensional finite element method. The plate has essentially infinite in-plane geometry but finite thickness. Results for Sitka Spruce wood are emphasized, although some for carbon...

Development Of A Navier-Stokes Computer Code

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Kwak, Dochan

1993-01-01

Report discusses aspects of development of CENS3D computer code, solving three-dimensional Navier-Stokes equations of compressible, viscous, unsteady flow. Implements implicit finite-difference or finite-volume numerical-integration scheme, called "lower-upper symmetric-Gauss-Seidel" (LU-SGS), offering potential for very low computer time per iteration and for fast convergence.

Computational procedure for finite difference solution of one-dimensional heat conduction problems reduces computer time

NASA Technical Reports Server (NTRS)

Iida, H. T.

1966-01-01

Computational procedure reduces the numerical effort whenever the method of finite differences is used to solve ablation problems for which the surface recession is large relative to the initial slab thickness. The number of numerical operations required for a given maximum space mesh size is reduced.

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.

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

NASA Astrophysics Data System (ADS)

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

2016-01-01

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

A hybrid-stress finite element approach for stress and vibration analysis in linear anisotropic elasticity

NASA Technical Reports Server (NTRS)

Oden, J. Tinsley; Fly, Gerald W.; Mahadevan, L.

1987-01-01

A hybrid stress finite element method is developed for accurate stress and vibration analysis of problems in linear anisotropic elasticity. A modified form of the Hellinger-Reissner principle is formulated for dynamic analysis and an algorithm for the determination of the anisotropic elastic and compliance constants from experimental data is developed. These schemes were implemented in a finite element program for static and dynamic analysis of linear anisotropic two dimensional elasticity problems. Specific numerical examples are considered to verify the accuracy of the hybrid stress approach and compare it with that of the standard displacement method, especially for highly anisotropic materials. It is that the hybrid stress approach gives much better results than the displacement method. Preliminary work on extensions of this method to three dimensional elasticity is discussed, and the stress shape functions necessary for this extension are included.

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

NASA Technical Reports Server (NTRS)

Jin, Jian-Ming; Volakis, John L.

1990-01-01

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

Integrated Nondestructive Evaluation and Finite Element Analysis Predicts Crack Location and Shape

NASA Technical Reports Server (NTRS)

Abdul-Azia, Ali; Baaklini, George Y.; Trudell, Jeffrey J.

2002-01-01

This study describes the finite-element analyses and the NDE modality undertaken on two flywheel rotors that were spun to burst speed. Computed tomography and dimensional measurements were used to nondestructively evaluate the rotors before and/or after they were spun to the first crack detection. Computed tomography data findings of two- and three-dimensional crack formation were used to conduct finite-element (FEA) and fracture mechanics analyses. A procedure to extend these analyses to estimate the life of these components is also outlined. NDE-FEA results for one of the rotors are presented in the figures. The stress results, which represent the radial stresses in the rim, clearly indicate that the maximum stress region is within the section defined by the computed tomography scan. Furthermore, the NDE data correlate well with the FEA results. In addition, the measurements reported show that the NDE and FEA data are in parallel.

Factors Influencing Progressive Failure Analysis Predictions for Laminated Composite Structure

NASA Technical Reports Server (NTRS)

Knight, Norman F., Jr.

2008-01-01

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

Finite analytic numerical solution of heat transfer and flow past a square channel cavity

NASA Technical Reports Server (NTRS)

Chen, C.-J.; Obasih, K.

1982-01-01

A numerical solution of flow and heat transfer characteristics is obtained by the finite analytic method for a two dimensional laminar channel flow over a two-dimensional square cavity. The finite analytic method utilizes the local analytic solution in a small element of the problem region to form the algebraic equation relating an interior nodal value with its surrounding nodal values. Stable and rapidly converged solutions were obtained for Reynolds numbers ranging to 1000 and Prandtl number to 10. Streamfunction, vorticity and temperature profiles are solved. Local and mean Nusselt number are given. It is found that the separation streamlines between the cavity and channel flow are concave into the cavity at low Reynolds number and convex at high Reynolds number (Re greater than 100) and for square cavity the mean Nusselt number may be approximately correlated with Peclet number as Nu(m) = 0.365 Pe exp 0.2.

Realistic finite temperature simulations of magnetic systems using quantum statistics

NASA Astrophysics Data System (ADS)

Bergqvist, Lars; Bergman, Anders

2018-01-01

We have performed realistic atomistic simulations at finite temperatures using Monte Carlo and atomistic spin dynamics simulations incorporating quantum (Bose-Einstein) statistics. The description is much improved at low temperatures compared to classical (Boltzmann) statistics normally used in these kind of simulations, while at higher temperatures the classical statistics are recovered. This corrected low-temperature description is reflected in both magnetization and the magnetic specific heat, the latter allowing for improved modeling of the magnetic contribution to free energies. A central property in the method is the magnon density of states at finite temperatures, and we have compared several different implementations for obtaining it. The method has no restrictions regarding chemical and magnetic order of the considered materials. This is demonstrated by applying the method to elemental ferromagnetic systems, including Fe and Ni, as well as Fe-Co random alloys and the ferrimagnetic system GdFe3.

Mesh generation for two-dimensional regions using the Tektronix DVST (direct view storage tube) graphics terminal

NASA Technical Reports Server (NTRS)

Gabrielson, V. K.

1975-01-01

The computer program DVMESH and the use of the Tektronix DVST graphics terminal were described for applications of preparing mesh data for use in various two-dimensional axisymmetric finite element stress analysis and heat transfer codes.

Three dimensional modeling of rigid pavement : executive summary, February 1995.

DOT National Transportation Integrated Search

1995-02-17

A finite-element program has been developed to model the response of rigid pavement to both static loads and temperature changes. The program is fully three-dimensional and incorporates not only the common twenty-node brick element but also a thin in...

Three-dimensional modeling of rigid pavement : final report, September 1995.

DOT National Transportation Integrated Search

1995-02-17

A finite-element program has been developed to model the response of rigid pavement to both static loads and temperature changes. The program is fully three-dimensional and incorporates not only the common twenty-node brick element but also a thin in...

DENSITY-DEPENDENT FLOW IN ONE-DIMENSIONAL VARIABLY-SATURATED MEDIA

EPA Science Inventory

A one-dimensional finite element is developed to simulate density-dependent flow of saltwater in variably saturated media. The flow and solute equations were solved in a coupled mode (iterative), in a partially coupled mode (non-iterative), and in a completely decoupled mode. P...

Evaluation of HFIR LEU Fuel Using the COMSOL Multiphysics Platform

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

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

2009-03-01

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

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.

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

PubMed

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

2009-11-01

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

Numerical study of anomalous dynamic scaling behaviour of (1+1)-dimensional Das Sarma-Tamborenea model

NASA Astrophysics Data System (ADS)

Xun, Zhi-Peng; Tang, Gang; Han, Kui; Hao, Da-Peng; Xia, Hui; Zhou, Wei; Yang, Xi-Quan; Wen, Rong-Ji; Chen, Yu-Ling

2010-07-01

In order to discuss the finite-size effect and the anomalous dynamic scaling behaviour of Das Sarma-Tamborenea growth model, the (1+1)-dimensional Das Sarma-Tamborenea model is simulated on a large length scale by using the kinetic Monte-Carlo method. In the simulation, noise reduction technique is used in order to eliminate the crossover effect. Our results show that due to the existence of the finite-size effect, the effective global roughness exponent of the (1+1)-dimensional Das Sarma-Tamborenea model systematically decreases with system size L increasing when L > 256. This finding proves the conjecture by Aarao Reis[Aarao Reis F D A 2004 Phys. Rev. E 70 031607]. In addition, our simulation results also show that the Das Sarma-Tamborenea model in 1+1 dimensions indeed exhibits intrinsic anomalous scaling behaviour.

Spillover, nonlinearity, and flexible structures

NASA Technical Reports Server (NTRS)

Bass, Robert W.; Zes, Dean

1991-01-01

Many systems whose evolution in time is governed by Partial Differential Equations (PDEs) are linearized around a known equilibrium before Computer Aided Control Engineering (CACE) is considered. In this case, there are infinitely many independent vibrational modes, and it is intuitively evident on physical grounds that infinitely many actuators would be needed in order to control all modes. A more precise, general formulation of this grave difficulty (spillover problem) is due to A.V. Balakrishnan. A possible route to circumvention of this difficulty lies in leaving the PDE in its original nonlinear form, and adding the essentially finite dimensional control action prior to linearization. One possibly applicable technique is the Liapunov Schmidt rigorous reduction of singular infinite dimensional implicit function problems to finite dimensional implicit function problems. Omitting details of Banach space rigor, the formalities of this approach are given.

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

USGS Publications Warehouse

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

1993-01-01

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

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

Observable measure of quantum coherence in finite dimensional systems.

PubMed

Girolami, Davide

2014-10-24

Quantum coherence is the key resource for quantum technology, with applications in quantum optics, information processing, metrology, and cryptography. Yet, there is no universally efficient method for quantifying coherence either in theoretical or in experimental practice. I introduce a framework for measuring quantum coherence in finite dimensional systems. I define a theoretical measure which satisfies the reliability criteria established in the context of quantum resource theories. Then, I present an experimental scheme implementable with current technology which evaluates the quantum coherence of an unknown state of a d-dimensional system by performing two programmable measurements on an ancillary qubit, in place of the O(d2) direct measurements required by full state reconstruction. The result yields a benchmark for monitoring quantum effects in complex systems, e.g., certifying nonclassicality in quantum protocols and probing the quantum behavior of biological complexes.

User's manual for two dimensional FDTD version TEA and TMA codes for scattering from frequency-independent dielectic materials

NASA Technical Reports Server (NTRS)

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

1991-01-01

The Penn State Finite Difference Time Domain Electromagnetic Scattering Code Versions TEA and TMA are two dimensional numerical electromagnetic scattering codes based upon the Finite Difference Time Domain Technique (FDTD) first proposed by Yee in 1966. The supplied version of the codes are two versions of our current two dimensional FDTD code set. This manual provides a description of the codes and corresponding results for the default scattering problem. The manual is organized into eleven sections: introduction, Version TEA and TMA code capabilities, a brief description of the default scattering geometry, a brief description of each subroutine, a description of the include files (TEACOM.FOR TMACOM.FOR), a section briefly discussing scattering width computations, a section discussing the scattering results, a sample problem set section, a new problem checklist, references and figure titles.

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

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

Flexible Models for Solar Sail Control

NASA Technical Reports Server (NTRS)

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

2005-01-01

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

Reaction-diffusion on the fully-connected lattice: A+A\\rightarrow A

NASA Astrophysics Data System (ADS)

Turban, Loïc; Fortin, Jean-Yves

2018-04-01

Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong fluctuations in low dimensions. In this work we study this problem on the fully-connected lattice, an infinite-dimensional system in the thermodynamic limit, for which mean-field behaviour is expected. Exact expressions for the particle density distribution at a given time and survival time distribution for a given number of particles are obtained. In particular, we show that the time needed to reach a finite number of surviving particles (vanishing density in the scaling limit) displays strong fluctuations and extreme value statistics, characterized by a universal class of non-Gaussian distributions with singular behaviour.

Finite element analysis in fluids; Proceedings of the Seventh International Conference on Finite Element Methods in Flow Problems, University of Alabama, Huntsville, Apr. 3-7, 1989

NASA Technical Reports Server (NTRS)

Chung, T. J. (Editor); Karr, Gerald R. (Editor)

1989-01-01

Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on finite-element methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume finite elements, crystal growth, domain decomposition, EM-field problems, FDM/FEM, and fluid-structure interactions. Consideration is given to free-boundary problems with heat transfer, free surface flow, geophysical flow problems, heat and mass transfer, high-speed flow, incompressible flow, inverse design methods, MHD problems, the mathematics of finite elements, and mesh generation. Also discussed are mixed finite elements, multigrid methods, non-Newtonian fluids, numerical dissipation, parallel vector processing, reservoir simulation, seepage, shallow-water problems, spectral methods, supercomputer architectures, three-dimensional problems, and turbulent flows.

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 finite-element method for large-amplitude, two-dimensional panel flutter at hypersonic speeds

NASA Technical Reports Server (NTRS)

Mei, Chuh; Gray, Carl E.

1989-01-01

The nonlinear flutter behavior of a two-dimensional panel in hypersonic flow is investigated analytically. An FEM formulation based unsteady third-order piston theory (Ashley and Zartarian, 1956; McIntosh, 1970) and taking nonlinear structural and aerodynamic phenomena into account is derived; the solution procedure is outlined; and typical results are presented in extensive tables and graphs. A 12-element finite-element solution obtained using an alternative method for linearizing the assumed limit-cycle time function is shown to give predictions in good agreement with classical analytical results for large-amplitude vibration in a vacuum and large-amplitude panel flutter, using linear aerodynamics.

Conformal Nets II: Conformal Blocks

NASA Astrophysics Data System (ADS)

Bartels, Arthur; Douglas, Christopher L.; Henriques, André

2017-08-01

Conformal nets provide a mathematical formalism for conformal field theory. Associated to a conformal net with finite index, we give a construction of the `bundle of conformal blocks', a representation of the mapping class groupoid of closed topological surfaces into the category of finite-dimensional projective Hilbert spaces. We also construct infinite-dimensional spaces of conformal blocks for topological surfaces with smooth boundary. We prove that the conformal blocks satisfy a factorization formula for gluing surfaces along circles, and an analogous formula for gluing surfaces along intervals. We use this interval factorization property to give a new proof of the modularity of the category of representations of a conformal net.

Application of Laser Ranging and VLBI Data to a Study of Plate Tectonic Driving Forces

NASA Technical Reports Server (NTRS)

Solomon, S. C.

1980-01-01

The conditions under which changes in plate driving or resistive forces associated with plate boundary earthquakes are measurable with laser ranging or very long base interferometry were investigated. Aspects of plate forces that can be characterized by such measurements were identified. Analytic solutions for two dimensional stress diffusion in a viscoelastic plate following earthquake faulting on a finite fault, finite element solutions for three dimensional stress diffusion in a viscoelastic Earth following earthquake faulting, and quantitative constraints from modeling of global intraplate stress on the magnitude of deviatoric stress in the lithosphere are among the topics discussed.

Finite element analysis of electromagnetic propagation in an absorbing wave guide

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.

1986-01-01

Wave guides play a significant role in microwave space communication systems. The attenuation per unit length of the guide depends on its construction and design frequency range. A finite element Galerkin formulation has been developed to study TM electromagnetic propagation in complex two-dimensional absorbing wave guides. The analysis models the electromagnetic absorptive characteristics of a general wave guide which could be used to determine wall losses or simulate resistive terminations fitted into the ends of a guide. It is believed that the general conclusions drawn by using this simpler two-dimensional geometry will be fundamentally the same for other geometries.

Analysis of Aerospike Plume Induced Base-Heating Environment

NASA Technical Reports Server (NTRS)

Wang, Ten-See

1998-01-01

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

STARS: A general-purpose finite element computer program for analysis of engineering structures

NASA Technical Reports Server (NTRS)

Gupta, K. K.

1984-01-01

STARS (Structural Analysis Routines) is primarily an interactive, graphics-oriented, finite-element computer program for analyzing the static, stability, free vibration, and dynamic responses of damped and undamped structures, including rotating systems. The element library consists of one-dimensional (1-D) line elements, two-dimensional (2-D) triangular and quadrilateral shell elements, and three-dimensional (3-D) tetrahedral and hexahedral solid elements. These elements enable the solution of structural problems that include truss, beam, space frame, plane, plate, shell, and solid structures, or any combination thereof. Zero, finite, and interdependent deflection boundary conditions can be implemented by the program. The associated dynamic response analysis capability provides for initial deformation and velocity inputs, whereas the transient excitation may be either forces or accelerations. An effective in-core or out-of-core solution strategy is automatically employed by the program, depending on the size of the problem. Data input may be at random within a data set, and the program offers certain automatic data-generation features. Input data are formatted as an optimal combination of free and fixed formats. Interactive graphics capabilities enable convenient display of nodal deformations, mode shapes, and element stresses.

Superfluid transition of homogeneous and trapped two-dimensional Bose gases.

PubMed

Holzmann, Markus; Baym, Gordon; Blaizot, Jean-Paul; Laloë, Franck

2007-01-30

Current experiments on atomic gases in highly anisotropic traps present the opportunity to study in detail the low temperature phases of two-dimensional inhomogeneous systems. Although, in an ideal gas, the trapping potential favors Bose-Einstein condensation at finite temperature, interactions tend to destabilize the condensate, leading to a superfluid Kosterlitz-Thouless-Berezinskii phase with a finite superfluid mass density but no long-range order, as in homogeneous fluids. The transition in homogeneous systems is conveniently described in terms of dissociation of topological defects (vortex-antivortex pairs). However, trapped two-dimensional gases are more directly approached by generalizing the microscopic theory of the homogeneous gas. In this paper, we first derive, via a diagrammatic expansion, the scaling structure near the phase transition in a homogeneous system, and then study the effects of a trapping potential in the local density approximation. We find that a weakly interacting trapped gas undergoes a Kosterlitz-Thouless-Berezinskii transition from the normal state at a temperature slightly below the Bose-Einstein transition temperature of the ideal gas. The characteristic finite superfluid mass density of a homogeneous system just below the transition becomes strongly suppressed in a trapped gas.

Comparative Evaluation of Stress Distribution in Experimentally Designed Nickel-titanium Rotary Files with Varying Cross Sections: A Finite Element Analysis.

PubMed

Basheer Ahamed, Shadir Bughari; Vanajassun, Purushothaman Pranav; Rajkumar, Kothandaraman; Mahalaxmi, Sekar

2018-04-01

Single cross-sectional nickel-titanium (NiTi) rotary instruments during continuous rotations are subjected to constant and variable stresses depending on the canal anatomy. This study was intended to create 2 new experimental, theoretic single-file designs with combinations of triple U (TU), triangle (TR), and convex triangle (CT) cross sections and to compare their bending stresses in simulated root canals with a single cross-sectional instrument using finite element analysis. A 3-dimensional model of the simulated root canal with 45° curvature and NiTi files with 5 cross-sectional designs were created using Pro/ENGINEER Wildfire 4.0 software (PTC Inc, Needham, MA) and ANSYS software (version 17; ANSYS, Inc, Canonsburg, PA) for finite element analysis. The NiTi files of 3 groups had single cross-sectional shapes of CT, TR, and TU designs, and 2 experimental groups had a CT, TR, and TU (CTU) design and a TU, TR, and CT (UTC) design. The file was rotated in simulated root canals to analyze the bending stress, and the von Mises stress value for every file was recorded in MPa. Statistical analysis was performed using the Kruskal-Wallis test and the Bonferroni-adjusted Mann-Whitney test for multiple pair-wise comparison with a P value <.05 (95 %). The maximum bending stress of the rotary file was observed in the apical third of the CT design, whereas comparatively less stress was recorded in the CTU design. The TU and TR designs showed a similar stress pattern at the curvature, whereas the UTC design showed greater stress in the apical and middle thirds of the file in curved canals. All the file designs showed a statistically significant difference. The CTU designed instruments showed the least bending stress on a 45° angulated simulated root canal when compared with all the other tested designs. Copyright © 2017 American Association of Endodontists. Published by Elsevier Inc. All rights reserved.

Identification of elastic, dielectric, and piezoelectric constants in piezoceramic disks.

PubMed

Perez, Nicolas; Andrade, Marco A B; Buiochi, Flavio; Adamowski, Julio C

2010-12-01

Three-dimensional modeling of piezoelectric devices requires a precise knowledge of piezoelectric material parameters. The commonly used piezoelectric materials belong to the 6mm symmetry class, which have ten independent constants. In this work, a methodology to obtain precise material constants over a wide frequency band through finite element analysis of a piezoceramic disk is presented. Given an experimental electrical impedance curve and a first estimate for the piezoelectric material properties, the objective is to find the material properties that minimize the difference between the electrical impedance calculated by the finite element method and that obtained experimentally by an electrical impedance analyzer. The methodology consists of four basic steps: experimental measurement, identification of vibration modes and their sensitivity to material constants, a preliminary identification algorithm, and final refinement of the material constants using an optimization algorithm. The application of the methodology is exemplified using a hard lead zirconate titanate piezoceramic. The same methodology is applied to a soft piezoceramic. The errors in the identification of each parameter are statistically estimated in both cases, and are less than 0.6% for elastic constants, and less than 6.3% for dielectric and piezoelectric constants.

Two-Dimensional Model for Reactive-Sorption Columns of Cylindrical Geometry: Analytical Solutions and Moment Analysis.

PubMed

Khan, Farman U; Qamar, Shamsul

2017-05-01

A set of analytical solutions are presented for a model describing the transport of a solute in a fixed-bed reactor of cylindrical geometry subjected to the first (Dirichlet) and third (Danckwerts) type inlet boundary conditions. Linear sorption kinetic process and first-order decay are considered. Cylindrical geometry allows the use of large columns to investigate dispersion, adsorption/desorption and reaction kinetic mechanisms. The finite Hankel and Laplace transform techniques are adopted to solve the model equations. For further analysis, statistical temporal moments are derived from the Laplace-transformed solutions. The developed analytical solutions are compared with the numerical solutions of high-resolution finite volume scheme. Different case studies are presented and discussed for a series of numerical values corresponding to a wide range of mass transfer and reaction kinetics. A good agreement was observed in the analytical and numerical concentration profiles and moments. The developed solutions are efficient tools for analyzing numerical algorithms, sensitivity analysis and simultaneous determination of the longitudinal and transverse dispersion coefficients from a laboratory-scale radial column experiment. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

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

NASA Technical Reports Server (NTRS)

Hooper, Steven J.

1989-01-01

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

Stress Recovery and Error Estimation for 3-D Shell Structures

NASA Technical Reports Server (NTRS)

Riggs, H. R.

2000-01-01

The C1-continuous stress fields obtained from finite element analyses are in general lower- order accurate than are the corresponding displacement fields. Much effort has focussed on increasing their accuracy and/or their continuity, both for improved stress prediction and especially error estimation. A previous project developed a penalized, discrete least squares variational procedure that increases the accuracy and continuity of the stress field. The variational problem is solved by a post-processing, 'finite-element-type' analysis to recover a smooth, more accurate, C1-continuous stress field given the 'raw' finite element stresses. This analysis has been named the SEA/PDLS. The recovered stress field can be used in a posteriori error estimators, such as the Zienkiewicz-Zhu error estimator or equilibrium error estimators. The procedure was well-developed for the two-dimensional (plane) case involving low-order finite elements. It has been demonstrated that, if optimal finite element stresses are used for the post-processing, the recovered stress field is globally superconvergent. Extension of this work to three dimensional solids is straightforward. Attachment: Stress recovery and error estimation for shell structure (abstract only). A 4-node, shear-deformable flat shell element developed via explicit Kirchhoff constraints (abstract only). A novel four-node quadrilateral smoothing element for stress enhancement and error estimation (abstract only).

Contact stress analysis of spiral bevel gears using nonlinear finite element static analysis

NASA Technical Reports Server (NTRS)

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

1993-01-01

A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the finite element method. The procedure involves generating a finite element model by solving equations that identify tooth surface coordinates. Coordinate transformations are used to orientate the gear and pinion for gear meshing. Contact boundary conditions are simulated with gap elements. A solution technique for correct orientation of the gap elements is given. Example models and results are presented.

Computation of canonical correlation and best predictable aspect of future for time series

NASA Technical Reports Server (NTRS)

Pourahmadi, Mohsen; Miamee, A. G.

1989-01-01

The canonical correlation between the (infinite) past and future of a stationary time series is shown to be the limit of the canonical correlation between the (infinite) past and (finite) future, and computation of the latter is reduced to a (generalized) eigenvalue problem involving (finite) matrices. This provides a convenient and essentially, finite-dimensional algorithm for computing canonical correlations and components of a time series. An upper bound is conjectured for the largest canonical correlation.

Finite-element analysis of dynamic fracture

NASA Technical Reports Server (NTRS)

Aberson, J. A.; Anderson, J. M.; King, W. W.

1976-01-01

Applications of the finite element method to the two dimensional elastodynamics of cracked structures are presented. Stress intensity factors are computed for two problems involving stationary cracks. The first serves as a vehicle for discussing lumped-mass and consistent-mass characterizations of inertia. In the second problem, the behavior of a photoelastic dynamic tear test specimen is determined for the time prior to crack propagation. Some results of a finite element simulation of rapid crack propagation in an infinite body are discussed.

A Discontinuous Galerkin Finite Element Method for Hamilton-Jacobi Equations

NASA Technical Reports Server (NTRS)

Hu, Changqing; Shu, Chi-Wang

1998-01-01

In this paper, we present a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the Runge-Kutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method.

Avalanches, loading and finite size effects in 2D amorphous plasticity: results from a finite element model

NASA Astrophysics Data System (ADS)

Sandfeld, Stefan; Budrikis, Zoe; Zapperi, Stefano; Fernandez Castellanos, David

2015-02-01

Crystalline plasticity is strongly interlinked with dislocation mechanics and nowadays is relatively well understood. Concepts and physical models of plastic deformation in amorphous materials on the other hand—where the concept of linear lattice defects is not applicable—still are lagging behind. We introduce an eigenstrain-based finite element lattice model for simulations of shear band formation and strain avalanches. Our model allows us to study the influence of surfaces and finite size effects on the statistics of avalanches. We find that even with relatively complex loading conditions and open boundary conditions, critical exponents describing avalanche statistics are unchanged, which validates the use of simpler scalar lattice-based models to study these phenomena.

A 3-dimensional mass conserving element for compressible flows

NASA Technical Reports Server (NTRS)

Fix, G.; Suri, M.

1985-01-01

A variety of finite element schemes has been used in the numerical approximation of compressible flows particularly in underwater acoustics. In many instances instabilities have been generated due to the lack of mass conservation. Two- and three-dimensional elements are developed which avoid these problems.

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

PubMed

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

2017-06-01

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

A Finite-Volume "Shaving" Method for Interfacing NASA/DAO''s Physical Space Statistical Analysis System to the Finite-Volume GCM with a Lagrangian Control-Volume Vertical Coordinate

NASA Technical Reports Server (NTRS)

Lin, Shian-Jiann; DaSilva, Arlindo; Atlas, Robert (Technical Monitor)

2001-01-01

Toward the development of a finite-volume Data Assimilation System (fvDAS), a consistent finite-volume methodology is developed for interfacing the NASA/DAO's Physical Space Statistical Analysis System (PSAS) to the joint NASA/NCAR finite volume CCM3 (fvCCM3). To take advantage of the Lagrangian control-volume vertical coordinate of the fvCCM3, a novel "shaving" method is applied to the lowest few model layers to reflect the surface pressure changes as implied by the final analysis. Analysis increments (from PSAS) to the upper air variables are then consistently put onto the Lagrangian layers as adjustments to the volume-mean quantities during the analysis cycle. This approach is demonstrated to be superior to the conventional method of using independently computed "tendency terms" for surface pressure and upper air prognostic variables.

Fast mean and variance computation of the diffuse sound transmission through finite-sized thick and layered wall and floor systems

NASA Astrophysics Data System (ADS)

Decraene, Carolina; Dijckmans, Arne; Reynders, Edwin P. B.

2018-05-01

A method is developed for computing the mean and variance of the diffuse field sound transmission loss of finite-sized layered wall and floor systems that consist of solid, fluid and/or poroelastic layers. This is achieved by coupling a transfer matrix model of the wall or floor to statistical energy analysis subsystem models of the adjacent room volumes. The modal behavior of the wall is approximately accounted for by projecting the wall displacement onto a set of sinusoidal lateral basis functions. This hybrid modal transfer matrix-statistical energy analysis method is validated on multiple wall systems: a thin steel plate, a polymethyl methacrylate panel, a thick brick wall, a sandwich panel, a double-leaf wall with poro-elastic material in the cavity, and a double glazing. The predictions are compared with experimental data and with results obtained using alternative prediction methods such as the transfer matrix method with spatial windowing, the hybrid wave based-transfer matrix method, and the hybrid finite element-statistical energy analysis method. These comparisons confirm the prediction accuracy of the proposed method and the computational efficiency against the conventional hybrid finite element-statistical energy analysis method.

A three-dimensional finite-element thermal/mechanical analytical technique for high-performance traveling wave tubes

NASA Technical Reports Server (NTRS)

Bartos, Karen F.; Fite, E. Brian; Shalkhauser, Kurt A.; Sharp, G. Richard

1991-01-01

Current research in high-efficiency, high-performance traveling wave tubes (TWT's) has led to the development of novel thermal/ mechanical computer models for use with helical slow-wave structures. A three-dimensional, finite element computer model and analytical technique used to study the structural integrity and thermal operation of a high-efficiency, diamond-rod, K-band TWT designed for use in advanced space communications systems. This analysis focused on the slow-wave circuit in the radiofrequency section of the TWT, where an inherent localized heating problem existed and where failures were observed during earlier cold compression, or 'coining' fabrication technique that shows great potential for future TWT development efforts. For this analysis, a three-dimensional, finite element model was used along with MARC, a commercially available finite element code, to simulate the fabrication of a diamond-rod TWT. This analysis was conducted by using component and material specifications consistent with actual TWT fabrication and was verified against empirical data. The analysis is nonlinear owing to material plasticity introduced by the forming process and also to geometric nonlinearities presented by the component assembly configuration. The computer model was developed by using the high efficiency, K-band TWT design but is general enough to permit similar analyses to be performed on a wide variety of TWT designs and styles. The results of the TWT operating condition and structural failure mode analysis, as well as a comparison of analytical results to test data are presented.

A three-dimensional finite-element thermal/mechanical analytical technique for high-performance traveling wave tubes

NASA Technical Reports Server (NTRS)

Shalkhauser, Kurt A.; Bartos, Karen F.; Fite, E. B.; Sharp, G. R.

1992-01-01

Current research in high-efficiency, high-performance traveling wave tubes (TWT's) has led to the development of novel thermal/mechanical computer models for use with helical slow-wave structures. A three-dimensional, finite element computer model and analytical technique used to study the structural integrity and thermal operation of a high-efficiency, diamond-rod, K-band TWT designed for use in advanced space communications systems. This analysis focused on the slow-wave circuit in the radiofrequency section of the TWT, where an inherent localized heating problem existed and where failures were observed during earlier cold compression, or 'coining' fabrication technique that shows great potential for future TWT development efforts. For this analysis, a three-dimensional, finite element model was used along with MARC, a commercially available finite element code, to simulate the fabrication of a diamond-rod TWT. This analysis was conducted by using component and material specifications consistent with actual TWT fabrication and was verified against empirical data. The analysis is nonlinear owing to material plasticity introduced by the forming process and also to geometric nonlinearities presented by the component assembly configuration. The computer model was developed by using the high efficiency, K-band TWT design but is general enough to permit similar analyses to be performed on a wide variety of TWT designs and styles. The results of the TWT operating condition and structural failure mode analysis, as well as a comparison of analytical results to test data are presented.

Trading spaces: building three-dimensional nets from two-dimensional tilings

PubMed Central

Castle, Toen; Evans, Myfanwy E.; Hyde, Stephen T.; Ramsden, Stuart; Robins, Vanessa

2012-01-01

We construct some examples of finite and infinite crystalline three-dimensional nets derived from symmetric reticulations of homogeneous two-dimensional spaces: elliptic (S2), Euclidean (E2) and hyperbolic (H2) space. Those reticulations are edges and vertices of simple spherical, planar and hyperbolic tilings. We show that various projections of the simplest symmetric tilings of those spaces into three-dimensional Euclidean space lead to topologically and geometrically complex patterns, including multiple interwoven nets and tangled nets that are otherwise difficult to generate ab initio in three dimensions. PMID:24098839

A Selective Overview of Variable Selection in High Dimensional Feature Space

PubMed Central

Fan, Jianqing

2010-01-01

High dimensional statistical problems arise from diverse fields of scientific research and technological development. Variable selection plays a pivotal role in contemporary statistical learning and scientific discoveries. The traditional idea of best subset selection methods, which can be regarded as a specific form of penalized likelihood, is computationally too expensive for many modern statistical applications. Other forms of penalized likelihood methods have been successfully developed over the last decade to cope with high dimensionality. They have been widely applied for simultaneously selecting important variables and estimating their effects in high dimensional statistical inference. In this article, we present a brief account of the recent developments of theory, methods, and implementations for high dimensional variable selection. What limits of the dimensionality such methods can handle, what the role of penalty functions is, and what the statistical properties are rapidly drive the advances of the field. The properties of non-concave penalized likelihood and its roles in high dimensional statistical modeling are emphasized. We also review some recent advances in ultra-high dimensional variable selection, with emphasis on independence screening and two-scale methods. PMID:21572976

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

USGS Publications Warehouse

Gray, William G.

1978-01-01

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

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.

User's manual for the FLORA equilibrium and stability code

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

Freis, R.P.; Cohen, B.I.

1985-04-01

This document provides a user's guide to the content and use of the two-dimensional axisymmetric equilibrium and stability code FLORA. FLORA addresses the low-frequency MHD stability of long-thin axisymmetric tandem mirror systems with finite pressure and finite-larmor-radius effects. FLORA solves an initial-value problem for interchange, rotational, and ballooning stability.

Finite element solution of lubrication problems

NASA Technical Reports Server (NTRS)

Reddi, M. M.

1971-01-01

A variational formulation of the transient lubrication problem is presented and the corresponding finite element equations derived for three and six point triangles, and, four and eight point quadrilaterals. Test solutions for a one dimensional slider bearing used in validating the computer program are given. Utility of the method is demonstrated by a solution of the shrouded step bearing.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.

Determination of apparent coupling factors for adhesive bonded acrylic plates using SEAL approach

NASA Astrophysics Data System (ADS)

Pankaj, Achuthan. C.; Shivaprasad, M. V.; Murigendrappa, S. M.

2018-04-01

Apparent coupling loss factors (CLF) and velocity responses has been computed for two lap joined adhesive bonded plates using finite element and experimental statistical energy analysis like approach. A finite element model of the plates has been created using ANSYS software. The statistical energy parameters have been computed using the velocity responses obtained from a harmonic forced excitation analysis. Experiments have been carried out for two different cases of adhesive bonded joints and the results have been compared with the apparent coupling factors and velocity responses obtained from finite element analysis. The results obtained from the studies signify the importance of modeling of adhesive bonded joints in computation of the apparent coupling factors and its further use in computation of energies and velocity responses using statistical energy analysis like approach.

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

EPA Science Inventory

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

Developments in the simulation of compressible inviscid and viscous flow on supercomputers

NASA Technical Reports Server (NTRS)

Steger, J. L.; Buning, P. G.

1985-01-01

In anticipation of future supercomputers, finite difference codes are rapidly being extended to simulate three-dimensional compressible flow about complex configurations. Some of these developments are reviewed. The importance of computational flow visualization and diagnostic methods to three-dimensional flow simulation is also briefly discussed.

Infinite Dimensional Dynamical Systems and their Finite Dimensional Analogues.

DTIC Science & Technology

1987-01-01

Rolla ____t___e ___o, __.Paul Steen Cornell Univ.Andrew Szeri Cornell Univ. ByEdriss Titi Univ. of Chicago _Distributi-on/ -S. Tsaltas Unvcrsity of...Cornell University Ithaca, NY 14853 Edriss Titi University of Chicago Dept. of Mathematics 5734 S. University Ave.Chicago, IL 60637 Spiros Tsaltas Dept

Parallel Computation and Visualization of Three-dimensional, Time-dependent, Thermal Convective Flows

NASA Technical Reports Server (NTRS)

Wang, P.; Li, P.

1998-01-01

A high-resolution numerical study on parallel systems is reported on three-dimensional, time-dependent, thermal convective flows. A parallel implentation on the finite volume method with a multigrid scheme is discussed, and a parallel visualization systemm is developed on distributed systems for visualizing the flow.

A finite element conjugate gradient FFT method for scattering

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

Computer animation of modal and transient vibrations

NASA Technical Reports Server (NTRS)

Lipman, Robert R.

1987-01-01

An interactive computer graphics processor is described that is capable of generating input to animate modal and transient vibrations of finite element models on an interactive graphics system. The results from NASTRAN can be postprocessed such that a three dimensional wire-frame picture, in perspective, of the finite element mesh is drawn on the graphics display. Modal vibrations of any mode shape or transient motions over any range of steps can be animated. The finite element mesh can be color-coded by any component of displacement. Viewing parameters and the rate of vibration of the finite element model can be interactively updated while the structure is vibrating.

Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms

NASA Technical Reports Server (NTRS)

Kurdila, Andrew J.; Sharpley, Robert C.

1999-01-01

This paper presents a final report on Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms. The focus of this research is to derive and implement: 1) Wavelet based methodologies for the compression, transmission, decoding, and visualization of three dimensional finite element geometry and simulation data in a network environment; 2) methodologies for interactive algorithm monitoring and tracking in computational mechanics; and 3) Methodologies for interactive algorithm steering for the acceleration of large scale finite element simulations. Also included in this report are appendices describing the derivation of wavelet based Particle Image Velocity algorithms and reduced order input-output models for nonlinear systems by utilizing wavelet approximations.

Hybrid-finite-element analysis of some nonlinear and 3-dimensional problems of engineering fracture mechanics

NASA Technical Reports Server (NTRS)

Atluri, S. N.; Nakagaki, M.; Kathiresan, K.

1980-01-01

In this paper, efficient numerical methods for the analysis of crack-closure effects on fatigue-crack-growth-rates, in plane stress situations, and for the solution of stress-intensity factors for arbitrary shaped surface flaws in pressure vessels, are presented. For the former problem, an elastic-plastic finite element procedure valid for the case of finite deformation gradients is developed and crack growth is simulated by the translation of near-crack-tip elements with embedded plastic singularities. For the latter problem, an embedded-elastic-singularity hybrid finite element method, which leads to a direct evaluation of K-factors, is employed.

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

USGS Publications Warehouse

Torak, L.J.

1993-01-01

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

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

USGS Publications Warehouse

Torak, Lynn J.

1992-01-01

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

Eroding dipoles and vorticity growth for Euler flows in {{{R}}}^{3}: the hairpin geometry as a model for finite-time blowup

NASA Astrophysics Data System (ADS)

Childress, Stephen; Gilbert, Andrew D.

2018-02-01

A theory of an eroding ‘hairpin’ vortex dipole structure in three-dimensions is developed, extending our previous study of an axisymmetric eroding dipole without swirl. The axisymmetric toroidal dipole was found to lead to maximal growth of vorticity, as {t}4/3. The hairpin is here similarly proposed as a model to produce large ‘self-stretching’ of vorticity, with the possibility of finite-time blow-up. We derive a system of partial differential equations of ‘generalized’ form, involving contour averaging of a locally two-dimensional Euler flow. We do not attempt here to solve the system exactly, but point out that non-existence of physically acceptable solutions would most probably be a result of the axial flow. Because of the axial flow the vorticity distribution within the dipole eddies is no longer of the simple Sadovskii type (vorticity constant over a cross-section) obtained in the axisymmetric problem. Thus the solution of the system depends upon the existence of a larger class of propagating two-dimensional dipoles. The hairpin model is obtained by formal asymptotic analysis. As in the axisymmetric problem a local transformation to ‘shrinking’ coordinates is introduced, but now in a self-similar form appropriate to the study of a possible finite-time singularity. We discuss some properties of the model, including a study of the helicity and a first step in iterating toward a solution from the Sadovskii structure. We also present examples of two-dimensional propagating dipoles not previously studied, which have a vorticity profile consistent with our model. Although no rigorous results can be given, and analysis of the system is only partial, the formal calculations are consistent with the possibility of a finite time blowup of vorticity at a point of vanishing circulation of the dipole eddies, but depending upon the existence of the necessary two-dimensional propagating dipole. Our results also suggest that conservation of kinetic energy as realized in the eroding hairpin excludes a finite time blowup for the corresponding Navier-Stokes model.

A boundary element alternating method for two-dimensional mixed-mode fracture problems

NASA Technical Reports Server (NTRS)

Raju, I. S.; Krishnamurthy, T.

1992-01-01

A boundary element alternating method, denoted herein as BEAM, is presented for two dimensional fracture problems. This is an iterative method which alternates between two solutions. An analytical solution for arbitrary polynomial normal and tangential pressure distributions applied to the crack faces of an embedded crack in an infinite plate is used as the fundamental solution in the alternating method. A boundary element method for an uncracked finite plate is the second solution. For problems of edge cracks a technique of utilizing finite elements with BEAM is presented to overcome the inherent singularity in boundary element stress calculation near the boundaries. Several computational aspects that make the algorithm efficient are presented. Finally, the BEAM is applied to a variety of two dimensional crack problems with different configurations and loadings to assess the validity of the method. The method gives accurate stress intensity factors with minimal computing effort.

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

Giorda, Paolo; Zanardi, Paolo; Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

We analyze the dynamical-algebraic approach to universal quantum control introduced in P. Zanardi and S. Lloyd, e-print quant-ph/0305013. The quantum state space H encoding information decomposes into irreducible sectors and subsystems associated with the group of available evolutions. If this group coincides with the unitary part of the group algebra CK of some group K then universal control is achievable over the K-irreducible components of H. This general strategy is applied to different kinds of bosonic systems. We first consider massive bosons in a double well and show how to achieve universal control over all finite-dimensional Fock sectors. We thenmore » discuss a multimode massless case giving the conditions for generating the whole infinite-dimensional multimode Heisenberg-Weyl enveloping algebra. Finally we show how to use an auxiliary bosonic mode coupled to finite-dimensional systems to generate high-order nonlinearities needed for universal control.« less

A novel modelling approach to energy transport in a respiratory system.

PubMed

Nithiarasu, Perumal; Sazonov, Igor

2017-10-01

In this paper, energy transport in a respiratory tract is modelled using the finite element method for the first time. The upper and lower respiratory tracts are approximated as a 1-dimensional domain with varying cross-sectional and surface areas, and the radial heat conduction in the tissue is approximated using the 1-dimensional cylindrical coordinate system. The governing equations are solved using 1-dimensional linear finite elements with convective and evaporative boundary conditions on the wall. The results obtained for the exhalation temperature of the respiratory system have been compared with the available animal experiments. The study of a full breathing cycle indicates that evaporation is the main mode of heat transfer, and convection plays almost negligible role in the energy transport. This is in-line with the results obtained from animal experiments. Copyright © 2016 John Wiley & Sons, Ltd.

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

PubMed

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

2015-04-01

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