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

NASA Technical Reports Server (NTRS)

Skollermo, G.

1979-01-01

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

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.

The aggregated unfitted finite element method for elliptic problems

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

Thermal finite-element analysis of space shuttle main engine turbine blade

NASA Technical Reports Server (NTRS)

Abdul-Aziz, Ali; Tong, Michael T.; Kaufman, Albert

1987-01-01

Finite-element, transient heat transfer analyses were performed for the first-stage blades of the space shuttle main engine (SSME) high-pressure fuel turbopump. The analyses were based on test engine data provided by Rocketdyne. Heat transfer coefficients were predicted by performing a boundary-layer analysis at steady-state conditions with the STAN5 boundary-layer code. Two different peak-temperature overshoots were evaluated for the startup transient. Cutoff transient conditions were also analyzed. A reduced gas temperature profile based on actual thermocouple data was also considered. Transient heat transfer analyses were conducted with the MARC finite-element computer code.

Evaluation of stress distribution of implant-retained mandibular overdenture with different vertical restorative spaces: A finite element analysis

PubMed Central

Ebadian, Behnaz; Farzin, Mahmoud; Talebi, Saeid; Khodaeian, Niloufar

2012-01-01

Background: Available restorative space and bar height is an important factor in stress distribution of implant-supported overdentures. The purpose of this study was to evaluate the effect of different vertical restorative spaces and different bar heights on the stress distribution around implants by 3D finite element analysis. Materials and Methods: 3D finite element models were developed from mandibular overdentures with two implants in the interforaminal region. In these models, four different bar heights from gingival crest (0.5, 1, 1.5, 2 mm) with 15 mm occlusal plane height and three different occlusal plane heights from gingival crest (9, 12, 15 mm) with 2 mm bar height were analyzed. A vertical unilateral and a bilateral load of 150 N were applied to the central occlusal fossa of the first molar and the stress of bone around implant was analyzed by finite element analysis. Results: By increasing vertical restorative space, the maximum stress values around implants were found to be decreased in unilateral loading models but slightly increased in bilateral loading cases. By increasing bar height from gingival crest, the maximum stress values around implants were found to be increased in unilateral loading models but slightly decreased in bilateral loading cases. In unilateral loading models, maximum stress was found in a model with 9 mm occlusal plane height and 1.5 mm bar height (6.254 MPa), but in bilateral loading cases, maximum stress was found in a model with 15 mm occlusal plane height and 0.5 mm bar height (3.482 MPa). Conclusion: The reduction of bar height and increase in the thickness of acrylic resin base in implant-supported overdentures are biomechanically favorable and may result in less stress in periimplant bone. PMID:23559952

Finite-difference fluid dynamics computer mathematical models for the design and interpretation of experiments for space flight. [atmospheric general circulation experiment, convection in a float zone, and the Bridgman-Stockbarger crystal growing system

NASA Technical Reports Server (NTRS)

Roberts, G. O.; Fowlis, W. W.; Miller, T. L.

1984-01-01

Numerical methods are used to design a spherical baroclinic flow model experiment of the large scale atmosphere flow for Spacelab. The dielectric simulation of radial gravity is only dominant in a low gravity environment. Computer codes are developed to study the processes at work in crystal growing systems which are also candidates for space flight. Crystalline materials rarely achieve their potential properties because of imperfections and component concentration variations. Thermosolutal convection in the liquid melt can be the cause of these imperfections. Such convection is suppressed in a low gravity environment. Two and three dimensional finite difference codes are being used for this work. Nonuniform meshes and implicit iterative methods are used. The iterative method for steady solutions is based on time stepping but has the options of different time steps for velocity and temperature and of a time step varying smoothly with position according to specified powers of the mesh spacings. This allows for more rapid convergence. The code being developed for the crystal growth studies allows for growth of the crystal as the solid-liquid interface. The moving interface is followed using finite differences; shape variations are permitted. For convenience in applying finite differences in the solid and liquid, a time dependent coordinate transformation is used to make this interface a coordinate surface.

Optimum element density studies for finite-element thermal analysis of hypersonic aircraft structures

NASA Technical Reports Server (NTRS)

Ko, William L.; Olona, Timothy; Muramoto, Kyle M.

1990-01-01

Different finite element models previously set up for thermal analysis of the space shuttle orbiter structure are discussed and their shortcomings identified. Element density criteria are established for the finite element thermal modelings of space shuttle orbiter-type large, hypersonic aircraft structures. These criteria are based on rigorous studies on solution accuracies using different finite element models having different element densities set up for one cell of the orbiter wing. Also, a method for optimization of the transient thermal analysis computer central processing unit (CPU) time is discussed. Based on the newly established element density criteria, the orbiter wing midspan segment was modeled for the examination of thermal analysis solution accuracies and the extent of computation CPU time requirements. The results showed that the distributions of the structural temperatures and the thermal stresses obtained from this wing segment model were satisfactory and the computation CPU time was at the acceptable level. The studies offered the hope that modeling the large, hypersonic aircraft structures using high-density elements for transient thermal analysis is possible if a CPU optimization technique was used.

Second-order numerical solution of time-dependent, first-order hyperbolic equations

NASA Technical Reports Server (NTRS)

Shah, Patricia L.; Hardin, Jay

1995-01-01

A finite difference scheme is developed to find an approximate solution of two similar hyperbolic equations, namely a first-order plane wave and spherical wave problem. Finite difference approximations are made for both the space and time derivatives. The result is a conditionally stable equation yielding an exact solution when the Courant number is set to one.

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)

Bell - Kochen - Specker theorem for any finite dimension ?

NASA Astrophysics Data System (ADS)

Cabello, Adán; García-Alcaine, Guillermo

1996-03-01

The Bell - Kochen - Specker theorem against non-contextual hidden variables can be proved by constructing a finite set of `totally non-colourable' directions, as Kochen and Specker did in a Hilbert space of dimension n = 3. We generalize Kochen and Specker's set to Hilbert spaces of any finite dimension 0305-4470/29/5/016/img2, in a three-step process that shows the relationship between different kinds of proofs (`continuum', `probabilistic', `state-specific' and `state-independent') of the Bell - Kochen - Specker theorem. At the same time, this construction of a totally non-colourable set of directions in any dimension explicitly solves the question raised by Zimba and Penrose about the existence of such a set for n = 5.

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

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

Effect of joint spacing and joint dip on the stress distribution around tunnels using different numerical methods

NASA Astrophysics Data System (ADS)

Nikadat, Nooraddin; Fatehi Marji, Mohammad; Rahmannejad, Reza; Yarahmadi Bafghi, Alireza

2016-11-01

Different conditions may affect the stability of tunnels by the geometry (spacing and orientation) of joints in the surrounded rock mass. In this study, by comparing the results obtained by the three novel numerical methods i.e. finite element method (Phase2), discrete element method (UDEC) and indirect boundary element method (TFSDDM), the effects of joint spacing and joint dips on the stress distribution around rock tunnels are numerically studied. These comparisons indicate the validity of the stress analyses around circular rock tunnels. These analyses also reveal that for a semi-continuous environment, boundary element method gives more accurate results compared to the results of finite element and distinct element methods. In the indirect boundary element method, the displacements due to joints of different spacing and dips are estimated by using displacement discontinuity (DD) formulations and the total stress distribution around the tunnel are obtained by using fictitious stress (FS) formulations.

A k-space method for large-scale models of wave propagation in tissue.

PubMed

Mast, T D; Souriau, L P; Liu, D L; Tabei, M; Nachman, A I; Waag, R C

2001-03-01

Large-scale simulation of ultrasonic pulse propagation in inhomogeneous tissue is important for the study of ultrasound-tissue interaction as well as for development of new imaging methods. Typical scales of interest span hundreds of wavelengths; most current two-dimensional methods, such as finite-difference and finite-element methods, are unable to compute propagation on this scale with the efficiency needed for imaging studies. Furthermore, for most available methods of simulating ultrasonic propagation, large-scale, three-dimensional computations of ultrasonic scattering are infeasible. Some of these difficulties have been overcome by previous pseudospectral and k-space methods, which allow substantial portions of the necessary computations to be executed using fast Fourier transforms. This paper presents a simplified derivation of the k-space method for a medium of variable sound speed and density; the derivation clearly shows the relationship of this k-space method to both past k-space methods and pseudospectral methods. In the present method, the spatial differential equations are solved by a simple Fourier transform method, and temporal iteration is performed using a k-t space propagator. The temporal iteration procedure is shown to be exact for homogeneous media, unconditionally stable for "slow" (c(x) < or = c0) media, and highly accurate for general weakly scattering media. The applicability of the k-space method to large-scale soft tissue modeling is shown by simulating two-dimensional propagation of an incident plane wave through several tissue-mimicking cylinders as well as a model chest wall cross section. A three-dimensional implementation of the k-space method is also employed for the example problem of propagation through a tissue-mimicking sphere. Numerical results indicate that the k-space method is accurate for large-scale soft tissue computations with much greater efficiency than that of an analogous leapfrog pseudospectral method or a 2-4 finite difference time-domain method. However, numerical results also indicate that the k-space method is less accurate than the finite-difference method for a high contrast scatterer with bone-like properties, although qualitative results can still be obtained by the k-space method with high efficiency. Possible extensions to the method, including representation of absorption effects, absorbing boundary conditions, elastic-wave propagation, and acoustic nonlinearity, are discussed.

The method of space-time and conservation element and solution element: A new approach for solving the Navier-Stokes and Euler equations

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1995-01-01

A new numerical framework for solving conservation laws is being developed. This new framework differs substantially in both concept and methodology from the well-established methods, i.e., finite difference, finite volume, finite element, and spectral methods. It is conceptually simple and designed to overcome several key limitations of the above traditional methods. A two-level scheme for solving the convection-diffusion equation is constructed and used to illuminate the major differences between the present method and those previously mentioned. This explicit scheme, referred to as the a-mu scheme, has two independent marching variables.

A quasi-Lagrangian finite element method for the Navier-Stokes equations in a time-dependent domain

NASA Astrophysics Data System (ADS)

Lozovskiy, Alexander; Olshanskii, Maxim A.; Vassilevski, Yuri V.

2018-05-01

The paper develops a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-Lagrangian formulation of the problem. The paper provides stability and convergence analysis of the fully discrete (finite-difference in time and finite-element in space) method. The analysis does not assume any CFL time-step restriction, it rather needs mild conditions of the form $\\Delta t\\le C$, where $C$ depends only on problem data, and $h^{2m_u+2}\\le c\\,\\Delta t$, $m_u$ is polynomial degree of velocity finite element space. Both conditions result from a numerical treatment of practically important non-homogeneous boundary conditions. The theoretically predicted convergence rate is confirmed by a set of numerical experiments. Further we apply the method to simulate a flow in a simplified model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.

A comparison of the Method of Lines to finite difference techniques in solving time-dependent partial differential equations. [with applications to Burger equation and stream function-vorticity problem

NASA Technical Reports Server (NTRS)

Kurtz, L. A.; Smith, R. E.; Parks, C. L.; Boney, L. R.

1978-01-01

Steady state solutions to two time dependent partial differential systems have been obtained by the Method of Lines (MOL) and compared to those obtained by efficient standard finite difference methods: (1) Burger's equation over a finite space domain by a forward time central space explicit method, and (2) the stream function - vorticity form of viscous incompressible fluid flow in a square cavity by an alternating direction implicit (ADI) method. The standard techniques were far more computationally efficient when applicable. In the second example, converged solutions at very high Reynolds numbers were obtained by MOL, whereas solution by ADI was either unattainable or impractical. With regard to 'set up' time, solution by MOL is an attractive alternative to techniques with complicated algorithms, as much of the programming difficulty is eliminated.

Numerical simulation of rarefied gas flow through a slit

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Domain decomposition methods for systems of conservation laws: Spectral collocation approximations

NASA Technical Reports Server (NTRS)

Quarteroni, Alfio

1989-01-01

Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.

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

NASA Astrophysics Data System (ADS)

Wilkins, Mark L.

1993-05-01

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

A Random Finite Set Approach to Space Junk Tracking and Identification

DTIC Science & Technology

2014-09-03

Final 3. DATES COVERED (From - To) 31 Jan 13 – 29 Apr 14 4. TITLE AND SUBTITLE A Random Finite Set Approach to Space Junk Tracking and...01-2013 to 29-04-2014 4. TITLE AND SUBTITLE A Random Finite Set Approach to Space Junk Tracking and Identification 5a. CONTRACT NUMBER FA2386-13...Prescribed by ANSI Std Z39-18 A Random Finite Set Approach to Space Junk Tracking and Indentification Ba-Ngu Vo1, Ba-Tuong Vo1, 1Department of

POSTPROCESSING MIXED FINITE ELEMENT METHODS FOR SOLVING CAHN-HILLIARD EQUATION: METHODS AND ERROR ANALYSIS

PubMed Central

Wang, Wansheng; Chen, Long; Zhou, Jie

2015-01-01

A postprocessing technique for mixed finite element methods for the Cahn-Hilliard equation is developed and analyzed. Once the mixed finite element approximations have been computed at a fixed time on the coarser mesh, the approximations are postprocessed by solving two decoupled Poisson equations in an enriched finite element space (either on a finer grid or a higher-order space) for which many fast Poisson solvers can be applied. The nonlinear iteration is only applied to a much smaller size problem and the computational cost using Newton and direct solvers is negligible compared with the cost of the linear problem. The analysis presented here shows that this technique remains the optimal rate of convergence for both the concentration and the chemical potential approximations. The corresponding error estimate obtained in our paper, especially the negative norm error estimates, are non-trivial and different with the existing results in the literatures. PMID:27110063

Mathematical aspects of finite element methods for incompressible viscous flows

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.

1986-01-01

Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.

A simple finite-difference scheme for handling topography with the first-order wave equation

NASA Astrophysics Data System (ADS)

Mulder, W. A.; Huiskes, M. J.

2017-07-01

One approach to incorporate topography in seismic finite-difference codes is a local modification of the difference operators near the free surface. An earlier paper described an approach for modelling irregular boundaries in a constant-density acoustic finite-difference code, based on the second-order formulation of the wave equation that only involves the pressure. Here, a similar method is considered for the first-order formulation in terms of pressure and particle velocity, using a staggered finite-difference discretization both in space and in time. In one space dimension, the boundary conditions consist in imposing antisymmetry for the pressure and symmetry for particle velocity components. For the pressure, this means that the solution values as well as all even derivatives up to a certain order are zero on the boundary. For the particle velocity, all odd derivatives are zero. In 2D, the 1-D assumption is used along each coordinate direction, with antisymmetry for the pressure along the coordinate and symmetry for the particle velocity component parallel to that coordinate direction. Since the symmetry or antisymmetry should hold along the direction normal to the boundary rather than along the coordinate directions, this generates an additional numerical error on top of the time stepping errors and the errors due to the interior spatial discretization. Numerical experiments in 2D and 3D nevertheless produce acceptable results.

A conservative implicit finite difference algorithm for the unsteady transonic full potential equation

NASA Technical Reports Server (NTRS)

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

1980-01-01

An implicit finite difference procedure is developed to solve the unsteady full potential equation in conservation law form. Computational efficiency is maintained by use of approximate factorization techniques. The numerical algorithm is first order in time and second order in space. A circulation model and difference equations are developed for lifting airfoils in unsteady flow; however, thin airfoil body boundary conditions have been used with stretching functions to simplify the development of the numerical algorithm.

Semi-analytic valuation of stock loans with finite maturity

NASA Astrophysics Data System (ADS)

Lu, Xiaoping; Putri, Endah R. M.

2015-10-01

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

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).

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

NASA Technical Reports Server (NTRS)

Wieting, A. R.

1979-01-01

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

Finite Topological Spaces as a Pedagogical Tool

ERIC Educational Resources Information Center

Helmstutler, Randall D.; Higginbottom, Ryan S.

2012-01-01

We propose the use of finite topological spaces as examples in a point-set topology class especially suited to help students transition into abstract mathematics. We describe how carefully chosen examples involving finite spaces may be used to reinforce concepts, highlight pathologies, and develop students' non-Euclidean intuition. We end with a…

High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation

NASA Astrophysics Data System (ADS)

Anderson, R.; Dobrev, V.; Kolev, Tz.; Kuzmin, D.; Quezada de Luna, M.; Rieben, R.; Tomov, V.

2017-04-01

In this work we present a FCT-like Maximum-Principle Preserving (MPP) method to solve the transport equation. We use high-order polynomial spaces; in particular, we consider up to 5th order spaces in two and three dimensions and 23rd order spaces in one dimension. The method combines the concepts of positive basis functions for discontinuous Galerkin finite element spatial discretization, locally defined solution bounds, element-based flux correction, and non-linear local mass redistribution. We consider a simple 1D problem with non-smooth initial data to explain and understand the behavior of different parts of the method. Convergence tests in space indicate that high-order accuracy is achieved. Numerical results from several benchmarks in two and three dimensions are also reported.

Incremental analysis of large elastic deformation of a rotating cylinder

NASA Technical Reports Server (NTRS)

Buchanan, G. R.

1976-01-01

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

NATO Advanced Study Institute Granular Nanoelectronics Held in Ciocco, Italy on 23 July-4 August 1990. Poster Abstracts

DTIC Science & Technology

1990-08-04

approximation. The equations are solved with a finite - difference approximation scheme. A particular analysis has been devoted to the choice of the initial...closely spaced M. Grundmann, and D. Bimberg, Institut far Landau levels. With increasing field, the finiteness of Festkdrperphysik der Technischen...1990). formalism for phase coherent conductance between 4 F. Stern and W. E. Howard, Phys. Rev. 163, 816 different electron reservoirs: within the

Accurate Finite Difference Algorithms

NASA Technical Reports Server (NTRS)

Goodrich, John W.

1996-01-01

Two families of finite difference algorithms for computational aeroacoustics are presented and compared. All of the algorithms are single step explicit methods, they have the same order of accuracy in both space and time, with examples up to eleventh order, and they have multidimensional extensions. One of the algorithm families has spectral like high resolution. Propagation with high order and high resolution algorithms can produce accurate results after O(10(exp 6)) periods of propagation with eight grid points per wavelength.

A variational numerical method based on finite elements for the nonlinear solution characteristics of the periodically forced Chen system

NASA Astrophysics Data System (ADS)

Khan, Sabeel M.; Sunny, D. A.; Aqeel, M.

2017-09-01

Nonlinear dynamical systems and their solutions are very sensitive to initial conditions and therefore need to be approximated carefully. In this article, we present and analyze nonlinear solution characteristics of the periodically forced Chen system with the application of a variational method based on the concept of finite time-elements. Our approach is based on the discretization of physical time space into finite elements where each time-element is mapped to a natural time space. The solution of the system is then determined in natural time space using a set of suitable basis functions. The numerical algorithm is presented and implemented to compute and analyze nonlinear behavior at different time-step sizes. The obtained results show an excellent agreement with the classical RK-4 and RK-5 methods. The accuracy and convergence of the method is shown by comparing numerically computed results with the exact solution for a test problem. The presented method has shown a great potential in dealing with the solutions of nonlinear dynamical systems and thus can be utilized in delineating different features and characteristics of their solutions.

Subresolution Displacements in Finite Difference Simulations of Ultrasound Propagation and Imaging.

PubMed

Pinton, Gianmarco F

2017-03-01

Time domain finite difference simulations are used extensively to simulate wave propagation. They approximate the wave field on a discrete domain with a grid spacing that is typically on the order of a tenth of a wavelength. The smallest displacements that can be modeled by this type of simulation are thus limited to discrete values that are integer multiples of the grid spacing. This paper presents a method to represent continuous and subresolution displacements by varying the impedance of individual elements in a multielement scatterer. It is demonstrated that this method removes the limitations imposed by the discrete grid spacing by generating a continuum of displacements as measured by the backscattered signal. The method is first validated on an ideal perfect correlation case with a single scatterer. It is subsequently applied to a more complex case with a field of scatterers that model an acoustic radiation force-induced displacement used in ultrasound elasticity imaging. A custom finite difference simulation tool is used to simulate propagation from ultrasound imaging pulses in the scatterer field. These simulated transmit-receive events are then beamformed into images, which are tracked with a correlation-based algorithm to determine the displacement. A linear predictive model is developed to analytically describe the relationship between element impedance and backscattered phase shift. The error between model and simulation is λ/ 1364 , where λ is the acoustical wavelength. An iterative method is also presented that reduces the simulation error to λ/ 5556 over one iteration. The proposed technique therefore offers a computationally efficient method to model continuous subresolution displacements of a scattering medium in ultrasound imaging. This method has applications that include ultrasound elastography, blood flow, and motion tracking. This method also extends generally to finite difference simulations of wave propagation, such as electromagnetic or seismic waves.

Cascades of Particles Moving at Finite Velocity in Hyperbolic Spaces

NASA Astrophysics Data System (ADS)

Cammarota, V.; Orsingher, E.

2008-12-01

A branching process of particles moving at finite velocity over the geodesic lines of the hyperbolic space (Poincaré half-plane and Poincaré disk) is examined. Each particle can split into two particles only once at Poisson spaced times and deviates orthogonally when splitted. At time t, after N( t) Poisson events, there are N( t)+1 particles moving along different geodesic lines. We are able to obtain the exact expression of the mean hyperbolic distance of the center of mass of the cloud of particles. We derive such mean hyperbolic distance from two different and independent ways and we study the behavior of the relevant expression as t increases and for different values of the parameters c (hyperbolic velocity of motion) and λ (rate of reproduction). The mean hyperbolic distance of each moving particle is also examined and a useful representation, as the distance of a randomly stopped particle moving over the main geodesic line, is presented.

Documentation of the Fourth Order Band Model

NASA Technical Reports Server (NTRS)

Kalnay-Rivas, E.; Hoitsma, D.

1979-01-01

A general circulation model is presented which uses quadratically conservative, fourth order horizontal space differences on an unstaggered grid and second order vertical space differences with a forward-backward or a smooth leap frog time scheme to solve the primitive equations of motion. The dynamic equations for motion, finite difference equations, a discussion of the structure and flow chart of the program code, a program listing, and three relevent papers are given.

Valuation of financial models with non-linear state spaces

NASA Astrophysics Data System (ADS)

Webber, Nick

2001-02-01

A common assumption in valuation models for derivative securities is that the underlying state variables take values in a linear state space. We discuss numerical implementation issues in an interest rate model with a simple non-linear state space, formulating and comparing Monte Carlo, finite difference and lattice numerical solution methods. We conclude that, at least in low dimensional spaces, non-linear interest rate models may be viable.

Photonic time crystals.

PubMed

Zeng, Lunwu; Xu, Jin; Wang, Chengen; Zhang, Jianhua; Zhao, Yuting; Zeng, Jing; Song, Runxia

2017-12-07

When space (time) translation symmetry is spontaneously broken, the space crystal (time crystal) forms; when permittivity and permeability periodically vary with space (time), the photonic crystal (photonic time crystal) forms. We proposed the concept of photonic time crystal and rewritten the Maxwell's equations. Utilizing Finite Difference Time Domain (FDTD) method, we simulated electromagnetic wave propagation in photonic time crystal and photonic space-time crystal, the simulation results show that more intensive scatter fields can obtained in photonic time crystal and photonic space-time crystal.

Chiral anomaly and anomalous finite-size conductivity in graphene

NASA Astrophysics Data System (ADS)

Shen, Shun-Qing; Li, Chang-An; Niu, Qian

2017-09-01

Graphene is a monolayer of carbon atoms packed into a hexagon lattice to host two spin degenerate pairs of massless two-dimensional Dirac fermions with different chirality. It is known that the existence of non-zero electric polarization in reduced momentum space which is associated with a hidden chiral symmetry will lead to the zero-energy flat band of a zigzag nanoribbon and some anomalous transport properties. Here it is proposed that the Adler-Bell-Jackiw chiral anomaly or non-conservation of chiral charges of Dirac fermions at different valleys can be realized in a confined ribbon of finite width, even in the absence of a magnetic field. In the laterally diffusive regime, the finite-size correction to conductivity is always positive and is inversely proportional to the square of the lateral dimension W, which is different from the finite-size correction inversely proportional to W from the boundary modes. This anomalous finite-size conductivity reveals the signature of the chiral anomaly in graphene, and it is measurable experimentally. This finding provides an alternative platform to explore the purely quantum mechanical effect in graphene.

Simulating Space Capsule Water Landing with Explicit Finite Element Method

NASA Technical Reports Server (NTRS)

Wang, John T.; Lyle, Karen H.

2007-01-01

A study of using an explicit nonlinear dynamic finite element code for simulating the water landing of a space capsule was performed. The finite element model contains Lagrangian shell elements for the space capsule and Eulerian solid elements for the water and air. An Arbitrary Lagrangian Eulerian (ALE) solver and a penalty coupling method were used for predicting the fluid and structure interaction forces. The space capsule was first assumed to be rigid, so the numerical results could be correlated with closed form solutions. The water and air meshes were continuously refined until the solution was converged. The converged maximum deceleration predicted is bounded by the classical von Karman and Wagner solutions and is considered to be an adequate solution. The refined water and air meshes were then used in the models for simulating the water landing of a capsule model that has a flexible bottom. For small pitch angle cases, the maximum deceleration from the flexible capsule model was found to be significantly greater than the maximum deceleration obtained from the corresponding rigid model. For large pitch angle cases, the difference between the maximum deceleration of the flexible model and that of its corresponding rigid model is smaller. Test data of Apollo space capsules with a flexible heat shield qualitatively support the findings presented in this paper.

A Natural Language for AdS/CFT Correlators

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

Fitzpatrick, A.Liam; /Boston U.; Kaplan, Jared

2012-02-14

We provide dramatic evidence that 'Mellin space' is the natural home for correlation functions in CFTs with weakly coupled bulk duals. In Mellin space, CFT correlators have poles corresponding to an OPE decomposition into 'left' and 'right' sub-correlators, in direct analogy with the factorization channels of scattering amplitudes. In the regime where these correlators can be computed by tree level Witten diagrams in AdS, we derive an explicit formula for the residues of Mellin amplitudes at the corresponding factorization poles, and we use the conformal Casimir to show that these amplitudes obey algebraic finite difference equations. By analyzing the recursivemore » structure of our factorization formula we obtain simple diagrammatic rules for the construction of Mellin amplitudes corresponding to tree-level Witten diagrams in any bulk scalar theory. We prove the diagrammatic rules using our finite difference equations. Finally, we show that our factorization formula and our diagrammatic rules morph into the flat space S-Matrix of the bulk theory, reproducing the usual Feynman rules, when we take the flat space limit of AdS/CFT. Throughout we emphasize a deep analogy with the properties of flat space scattering amplitudes in momentum space, which suggests that the Mellin amplitude may provide a holographic definition of the flat space S-Matrix.« less

Demonstration Of Ultra HI-FI (UHF) Methods

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.

2004-01-01

Computational aero-acoustics (CAA) requires efficient, high-resolution simulation tools. Most current techniques utilize finite-difference approaches because high order accuracy is considered too difficult or expensive to achieve with finite volume or finite element methods. However, a novel finite volume approach (Ultra HI-FI or UHF) which utilizes Hermite fluxes is presented which can achieve both arbitrary accuracy and fidelity in space and time. The technique can be applied to unstructured grids with some loss of fidelity or with multi-block structured grids for maximum efficiency and resolution. In either paradigm, it is possible to resolve ultra-short waves (less than 2 PPW). This is demonstrated here by solving the 4th CAA workshop Category 1 Problem 1.

Finite Nilpotent BRST Transformations in Hamiltonian Formulation

NASA Astrophysics Data System (ADS)

Rai, Sumit Kumar; Mandal, Bhabani Prasad

2013-10-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

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

NASA Technical Reports Server (NTRS)

Stremel, P. M.

1984-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1983-01-01

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

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

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

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

2014-01-15

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

Four-level conservative finite-difference schemes for Boussinesq paradigm equation

NASA Astrophysics Data System (ADS)

Kolkovska, N.

2013-10-01

In this paper a two-parametric family of four level conservative finite difference schemes is constructed for the multidimensional Boussinesq paradigm equation. The schemes are explicit in the sense that no inner iterations are needed for evaluation of the numerical solution. The preservation of the discrete energy with this method is proved. The schemes have been numerically tested on one soliton propagation model and two solitons interaction model. The numerical experiments demonstrate that the proposed family of schemes has second order of convergence in space and time steps in the discrete maximal norm.

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

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

Basak, Subhasish; Bazavov, Alexei; Bernard, Claude

2014-09-25

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

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

NASA Astrophysics Data System (ADS)

Swidinsky, Andrei; Liu, Lifei

2017-11-01

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

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

Numerical integration and optimization of motions for multibody dynamic systems

NASA Astrophysics Data System (ADS)

Aguilar Mayans, Joan

This thesis considers the optimization and simulation of motions involving rigid body systems. It does so in three distinct parts, with the following topics: optimization and analysis of human high-diving motions, efficient numerical integration of rigid body dynamics with contacts, and motion optimization of a two-link robot arm using Finite-Time Lyapunov Analysis. The first part introduces the concept of eigenpostures, which we use to simulate and analyze human high-diving motions. Eigenpostures are used in two different ways: first, to reduce the complexity of the optimal control problem that we solve to obtain such motions, and second, to generate an eigenposture space to which we map existing real world motions to better analyze them. The benefits of using eigenpostures are showcased through different examples. The second part reviews an extensive list of integration algorithms used for the integration of rigid body dynamics. We analyze the accuracy and stability of the different integrators in the three-dimensional space and the rotation space SO(3). Integrators with an accuracy higher than first order perform more efficiently than integrators with first order accuracy, even in the presence of contacts. The third part uses Finite-time Lyapunov Analysis to optimize motions for a two-link robot arm. Finite-Time Lyapunov Analysis diagnoses the presence of time-scale separation in the dynamics of the optimized motion and provides the information and methodology for obtaining an accurate approximation to the optimal solution, avoiding the complications that timescale separation causes for alternative solution methods.

Flame trench analysis of NLS vehicles

NASA Technical Reports Server (NTRS)

Zeytinoglu, Nuri

1993-01-01

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

An optical flow-based state-space model of the vocal folds.

PubMed

Granados, Alba; Brunskog, Jonas

2017-06-01

High-speed movies of the vocal fold vibration are valuable data to reveal vocal fold features for voice pathology diagnosis. This work presents a suitable Bayesian model and a purely theoretical discussion for further development of a framework for continuum biomechanical features estimation. A linear and Gaussian nonstationary state-space model is proposed and thoroughly discussed. The evolution model is based on a self-sustained three-dimensional finite element model of the vocal folds, and the observation model involves a dense optical flow algorithm. The results show that the method is able to capture different deformation patterns between the computed optical flow and the finite element deformation, controlled by the choice of the model tissue parameters.

Algorithm development for Maxwell's equations for computational electromagnetism

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.

1990-01-01

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

Improved method for detecting local discontinuities in CMB data by finite differencing

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

Bowyer, Jude; Jaffe, Andrew H.

2011-01-15

An unexpected distribution of temperatures in the CMB could be a sign of new physics. In particular, the existence of cosmic defects could be indicated by temperature discontinuities via the Kaiser-Stebbins effect. In this paper, we show how performing finite differences on a CMB map, with the noise regularized in harmonic space, may expose such discontinuities, and we report the results of this process on the 7-year Wilkinson Microwave Anisotropy Probe data.

Stabilization of a finite slice in miscible displacement in homogeneous porous media

NASA Astrophysics Data System (ADS)

Pramanik, Satyajit; Mishra, Manoranjan

2016-11-01

We numerically studied the miscible displacement of a finite slice of variable viscosity and density. The stability of the finite slice depends on different flow parameters, such as displacement velocity U, mobility ratio R , and the density contrast. Series of numerical simulations corresponding to different ordered pair (R, U) in the parameter space, and a given density contrast reveal six different instability regions. We have shown that independent of the width of the slice, there always exists a region of stable displacement, and below a critical value of the slice width, this stable region increases with decreasing slice width. Further we observe that the viscous fingering (buoyancy-induced instability) at the upper interface induces buoyancy-induced instability (viscous fingering) at the lower interface. Besides the fundamental fluid dynamics understanding, our results can be helpful to model CO2 sequestration and chromatographic separation.

Linear finite-difference bond graph model of an ionic polymer actuator

NASA Astrophysics Data System (ADS)

Bentefrit, M.; Grondel, S.; Soyer, C.; Fannir, A.; Cattan, E.; Madden, J. D.; Nguyen, T. M. G.; Plesse, C.; Vidal, F.

2017-09-01

With the recent growing interest for soft actuation, many new types of ionic polymers working in air have been developed. Due to the interrelated mechanical, electrical, and chemical properties which greatly influence the characteristics of such actuators, their behavior is complex and difficult to understand, predict and optimize. In light of this challenge, an original linear multiphysics finite difference bond graph model was derived to characterize this ionic actuation. This finite difference scheme was divided into two coupled subparts, each related to a specific physical, electrochemical or mechanical domain, and then converted into a bond graph model as this language is particularly suited for systems from multiple energy domains. Simulations were then conducted and a good agreement with the experimental results was obtained. Furthermore, an analysis of the power efficiency of such actuators as a function of space and time was proposed and allowed to evaluate their performance.

Discretizing singular point sources in hyperbolic wave propagation problems

DOE PAGES

Petersson, N. Anders; O'Reilly, Ossian; Sjogreen, Bjorn; ...

2016-06-01

Here, we develop high order accurate source discretizations for hyperbolic wave propagation problems in first order formulation that are discretized by finite difference schemes. By studying the Fourier series expansions of the source discretization and the finite difference operator, we derive sufficient conditions for achieving design accuracy in the numerical solution. Only half of the conditions in Fourier space can be satisfied through moment conditions on the source discretization, and we develop smoothness conditions for satisfying the remaining accuracy conditions. The resulting source discretization has compact support in physical space, and is spread over as many grid points as themore » number of moment and smoothness conditions. In numerical experiments we demonstrate high order of accuracy in the numerical solution of the 1-D advection equation (both in the interior and near a boundary), the 3-D elastic wave equation, and the 3-D linearized Euler equations.« less

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

NASA Technical Reports Server (NTRS)

Collier, Richard S.

1997-01-01

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

Numerical simulation of conservation laws

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; To, Wai-Ming

1992-01-01

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

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.

FDDO and DSMC analyses of rarefied gas flow through 2D nozzles

NASA Technical Reports Server (NTRS)

Chung, Chan-Hong; De Witt, Kenneth J.; Jeng, Duen-Ren; Penko, Paul F.

1992-01-01

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas expanding through a two-dimensional nozzle and into a surrounding low-density environment. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, the variable hard sphere model is used as a molecular model and the no time counter method is employed as a collision sampling technique. The results of both the FDDO and the DSMC methods show good agreement. The FDDO method requires less computational effort than the DSMC method by factors of 10 to 40 in CPU time, depending on the degree of rarefaction.

Modeling and analysis of the space shuttle nose-gear tire with semianalytic finite elements

NASA Technical Reports Server (NTRS)

Kim, Kyun O.; Noor, Ahmed K.; Tanner, John A.

1990-01-01

A computational procedure is presented for the geometrically nonlinear analysis of aircraft tires. The Space Shuttle Orbiter nose gear tire was modeled by using a two-dimensional laminated anisotropic shell theory with the effects of variation in material and geometric parameters included. The four key elements of the procedure are: (1) semianalytic finite elements in which the shell variables are represented by Fourier series in the circumferential direction and piecewise polynominals in the meridional direction; (2) a mixed formulation with the fundamental unknowns consisting of strain parameters, stress-resultant parameters, and generalized displacements; (3) multilevel operator splitting to effect successive simplifications, and to uncouple the equations associated with different Fourier harmonics; and (4) multilevel iterative procedures and reduction techniques to generate the response of the shell. Numerical results of the Space Shuttle Orbiter nose gear tire model are compared with experimental measurements of the tire subjected to inflation loading.

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

PubMed

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

2017-01-01

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

Local existence of solutions to the Euler-Poisson system, including densities without compact support

NASA Astrophysics Data System (ADS)

Brauer, Uwe; Karp, Lavi

2018-01-01

Local existence and well posedness for a class of solutions for the Euler Poisson system is shown. These solutions have a density ρ which either falls off at infinity or has compact support. The solutions have finite mass, finite energy functional and include the static spherical solutions for γ = 6/5. The result is achieved by using weighted Sobolev spaces of fractional order and a new non-linear estimate which allows to estimate the physical density by the regularised non-linear matter variable. Gamblin also has studied this setting but using very different functional spaces. However we believe that the functional setting we use is more appropriate to describe a physical isolated body and more suitable to study the Newtonian limit.

Efficient assembly of finite-element subsystems with large relative rotations. [for rotorcraft dynamic characteristics

NASA Technical Reports Server (NTRS)

Fuh, Jon-Shen; Panda, Brahmananda; Peters, David A.

1988-01-01

A finite element approach is presented for the modeling of rotorcraft undergoing elastic deformation in addition to large rigid body motion with respect to inertial space, with particular attention given to the coupling of the rotor and fuselage subsystems subject to large relative rotations. The component synthesis technique used here allows the coupling of rotors to the fuselage for different rotorcraft configurations. The formulation is general and applicable to any rotorcraft vibration, aeroelasticity, and dynamics problem.

Generation of an incident focused light pulse in FDTD.

PubMed

Capoğlu, Ilker R; Taflove, Allen; Backman, Vadim

2008-11-10

A straightforward procedure is described for accurately creating an incident focused light pulse in the 3-D finite-difference time-domain (FDTD) electromagnetic simulation of the image space of an aplanatic converging lens. In this procedure, the focused light pulse is approximated by a finite sum of plane waves, and each plane wave is introduced into the FDTD simulation grid using the total-field/scattered-field (TF/SF) approach. The accuracy of our results is demonstrated by comparison with exact theoretical formulas.

Generation of an incident focused light pulse in FDTD

PubMed Central

Çapoğlu, İlker R.; Taflove, Allen; Backman, Vadim

2009-01-01

A straightforward procedure is described for accurately creating an incident focused light pulse in the 3-D finite-difference time-domain (FDTD) electromagnetic simulation of the image space of an aplanatic converging lens. In this procedure, the focused light pulse is approximated by a finite sum of plane waves, and each plane wave is introduced into the FDTD simulation grid using the total-field/scattered-field (TF/SF) approach. The accuracy of our results is demonstrated by comparison with exact theoretical formulas. PMID:19582013

Modelling of single walled carbon nanotube cylindrical structures with finite element method simulations

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

Günay, E.

In this study, the modulus of elasticity and shear modulus values of single-walled carbon nanotubes SWCNTs were modelled by using both finite element method and the Matlab code. Initially, cylindrical armchair and zigzag single walled 3D space frames were demonstrated as carbon nanostructures. Thereafter, macro programs were written by the Matlab code producing the space truss for zigzag and armchair models. 3D space frames were introduced to the ANSYS software and then tension, compression and additionally torsion tests were performed on zigzag and armchair carbon nanotubes with BEAM4 element in obtaining the exact values of elastic and shear modulus values.more » In this study, two different boundary conditions were tested and especially used in torsion loading. The equivalent shear modulus data was found by averaging the corresponding values obtained from ten different nodal points on the nanotube path. Finally, in this study it was determined that the elastic constant values showed proportional changes by increasing the carbon nanotube diameters up to a certain level but beyond this level these values remained stable.« less

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

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

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

USGS Publications Warehouse

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

1993-01-01

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

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

NASA Technical Reports Server (NTRS)

Cowsar, Lawrence C.

1993-01-01

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

Banach spaces that realize minimal fillings

NASA Astrophysics Data System (ADS)

Bednov, B. B.; Borodin, P. A.

2014-04-01

It is proved that a real Banach space realizes minimal fillings for all its finite subsets (a shortest network spanning a fixed finite subset always exists and has the minimum possible length) if and only if it is a predual of L_1. The spaces L_1 are characterized in terms of Steiner points (medians). Bibliography: 25 titles.

Electromagnetic synchronisation of clocks with finite separation in a rotating system

NASA Astrophysics Data System (ADS)

Cohen, J. M.; Moses, H. E.; Rosenblum, A.

1984-11-01

For clocks on the vertices of a triangle, it is shown that clock synchronisation using electromagnetic signals between finitely spaced clocks in a rotating frame leads to the same synchronization error as a closely spaced band of clocks along the same light path. In addition, the above result is generalized to n equally spaced clocks.

Wave chaos in a randomly inhomogeneous waveguide: spectral analysis of the finite-range evolution operator.

PubMed

Makarov, D V; Kon'kov, L E; Uleysky, M Yu; Petrov, P S

2013-01-01

The problem of sound propagation in a randomly inhomogeneous oceanic waveguide is considered. An underwater sound channel in the Sea of Japan is taken as an example. Our attention is concentrated on the domains of finite-range ray stability in phase space and their influence on wave dynamics. These domains can be found by means of the one-step Poincare map. To study manifestations of finite-range ray stability, we introduce the finite-range evolution operator (FREO) describing transformation of a wave field in the course of propagation along a finite segment of a waveguide. Carrying out statistical analysis of the FREO spectrum, we estimate the contribution of regular domains and explore their evanescence with increasing length of the segment. We utilize several methods of spectral analysis: analysis of eigenfunctions by expanding them over modes of the unperturbed waveguide, approximation of level-spacing statistics by means of the Berry-Robnik distribution, and the procedure used by A. Relano and coworkers [Relano et al., Phys. Rev. Lett. 89, 244102 (2002); Relano, Phys. Rev. Lett. 100, 224101 (2008)]. Comparing the results obtained with different methods, we find that the method based on the statistical analysis of FREO eigenfunctions is the most favorable for estimating the contribution of regular domains. It allows one to find directly the waveguide modes whose refraction is regular despite the random inhomogeneity. For example, it is found that near-axial sound propagation in the Sea of Japan preserves stability even over distances of hundreds of kilometers due to the presence of a shearless torus in the classical phase space. Increasing the acoustic wavelength degrades scattering, resulting in recovery of eigenfunction localization near periodic orbits of the one-step Poincaré map.

Characterization of the Coupling Between Adjacent Finite Ground Coplanar (FGC) Waveguides

NASA Technical Reports Server (NTRS)

Ponchak, George E.; Katehi, Linda P. B.; Tentzeris, Emmanouil M.

1997-01-01

Coupling between adjacent Finite Ground Coplanar (FGC) waveguides as a function of the line geometry is presented for the first time. A two Dimension-Finite Difference Time Domain (2D-FDTD) analysis and measurements are used to show that the coupling decreases as the line to line separation and the grOUnd plane width increases. Furthermore, it is shown that for a given spacing between the center lines of two FGC lines, the coupling is lower if the ground plane width is smaller Lastly, electric field plots generated from the 2D-FDTD technique are presented which demonstrate a strong slotline mode is established in the coupled FGC line.

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

NASA Technical Reports Server (NTRS)

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

1984-01-01

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

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

USGS Publications Warehouse

INTERA Environmental Consultants, Inc.

1979-01-01

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

Differential Calculus on h-Deformed Spaces

NASA Astrophysics Data System (ADS)

Herlemont, Basile; Ogievetsky, Oleg

2017-10-01

We construct the rings of generalized differential operators on the h-deformed vector space of gl-type. In contrast to the q-deformed vector space, where the ring of differential operators is unique up to an isomorphism, the general ring of h-deformed differential operators {Diff}_{h},σ(n) is labeled by a rational function σ in n variables, satisfying an over-determined system of finite-difference equations. We obtain the general solution of the system and describe some properties of the rings {Diff}_{h},σ(n).

Adjoint sensitivity analysis of a tumor growth model and its application to spatiotemporal radiotherapy optimization.

PubMed

Fujarewicz, Krzysztof; Lakomiec, Krzysztof

2016-12-01

We investigate a spatial model of growth of a tumor and its sensitivity to radiotherapy. It is assumed that the radiation dose may vary in time and space, like in intensity modulated radiotherapy (IMRT). The change of the final state of the tumor depends on local differences in the radiation dose and varies with the time and the place of these local changes. This leads to the concept of a tumor's spatiotemporal sensitivity to radiation, which is a function of time and space. We show how adjoint sensitivity analysis may be applied to calculate the spatiotemporal sensitivity of the finite difference scheme resulting from the partial differential equation describing the tumor growth. We demonstrate results of this approach to the tumor proliferation, invasion and response to radiotherapy (PIRT) model and we compare the accuracy and the computational effort of the method to the simple forward finite difference sensitivity analysis. Furthermore, we use the spatiotemporal sensitivity during the gradient-based optimization of the spatiotemporal radiation protocol and present results for different parameters of the model.

Particle-based simulation of charge transport in discrete-charge nano-scale systems: the electrostatic problem

PubMed Central

2012-01-01

The fast and accurate computation of the electric forces that drive the motion of charged particles at the nanometer scale represents a computational challenge. For this kind of system, where the discrete nature of the charges cannot be neglected, boundary element methods (BEM) represent a better approach than finite differences/finite elements methods. In this article, we compare two different BEM approaches to a canonical electrostatic problem in a three-dimensional space with inhomogeneous dielectrics, emphasizing their suitability for particle-based simulations: the iterative method proposed by Hoyles et al. and the Induced Charge Computation introduced by Boda et al. PMID:22338640

Particle-based simulation of charge transport in discrete-charge nano-scale systems: the electrostatic problem.

PubMed

Berti, Claudio; Gillespie, Dirk; Eisenberg, Robert S; Fiegna, Claudio

2012-02-16

The fast and accurate computation of the electric forces that drive the motion of charged particles at the nanometer scale represents a computational challenge. For this kind of system, where the discrete nature of the charges cannot be neglected, boundary element methods (BEM) represent a better approach than finite differences/finite elements methods. In this article, we compare two different BEM approaches to a canonical electrostatic problem in a three-dimensional space with inhomogeneous dielectrics, emphasizing their suitability for particle-based simulations: the iterative method proposed by Hoyles et al. and the Induced Charge Computation introduced by Boda et al.

FFT-based computation of the bioheat transfer equation for the HCC ultrasound surgery therapy modeling.

PubMed

Dillenseger, Jean-Louis; Esneault, Simon; Garnier, Carole

2008-01-01

This paper describes a modeling method of the tissue temperature evolution over time in hyperthermia. More precisely, this approach is used to simulate the hepatocellular carcinoma curative treatment by a percutaneous high intensity ultrasound surgery. The tissue temperature evolution over time is classically described by Pennes' bioheat transfer equation which is generally solved by a finite difference method. In this paper we will present a method where the bioheat transfer equation can be algebraically solved after a Fourier transformation over the space coordinates. The implementation and boundary conditions of this method will be shown and compared with the finite difference method.

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

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

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

2016-02-15

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

How to choose a subset of frequencies in frequency-domain finite-difference migration

NASA Astrophysics Data System (ADS)

Mulder, W. A.; Plessix, R.-E.

2004-09-01

Finite-difference migration with the two-way wave equation can be accelerated by an order of magnitude if the frequency domain rather than the time domain is used. This gain is mainly accomplished by using a subset of the available frequencies. The implicit assumption is that the data have a certain amount of redundancy in the frequency domain. The choice of frequencies cannot be arbitrary. If the frequencies are chosen with a constant increment and their spacing is too large, the well-known wrap-around that occurs when transforming back to the time domain will also show up in the migration to the depth domain, albeit in a more subtle way. Because migration involves propagation in a given background velocity model and summation over shots and receivers, the effects of wrap-around may disappear even when the Nyquist theorem is not obeyed. We have studied these effects analytically for the constant-velocity case and determined sampling conditions that avoid wrap-around artefacts. The conditions depend on the velocity, depth of the migration grid and offset range. They show that the spacing between subsequent frequencies can be larger than the inverse of the time range prescribed by the Nyquist theorem. A 2-D example has been used to test the validity of these conditions for a more realistic velocity model. Finite-difference migration with the one-way wave equation shows a similar behaviour.

Multiphysics elastodynamic finite element analysis of space debris deorbit stability and efficiency by electrodynamic tethers

NASA Astrophysics Data System (ADS)

Li, Gangqiang; Zhu, Zheng H.; Ruel, Stephane; Meguid, S. A.

2017-08-01

This paper developed a new multiphysics finite element method for the elastodynamic analysis of space debris deorbit by a bare flexible electrodynamic tether. Orbital motion limited theory and dynamics of flexible electrodynamic tethers are discretized by the finite element method, where the motional electric field is variant along the tether and coupled with tether deflection and motion. Accordingly, the electrical current and potential bias profiles of tether are solved together with the tether dynamics by the nodal position finite element method. The newly proposed multiphysics finite element method is applied to analyze the deorbit dynamics of space debris by electrodynamic tethers with a two-stage energy control strategy to ensure an efficient and stable deorbit process. Numerical simulations are conducted to study the coupled effect between the motional electric field and the tether dynamics. The results reveal that the coupling effect has a significant influence on the tether stability and the deorbit performance. It cannot be ignored when the libration and deflection of the tether are significant.

Does disc space height of fused segment affect adjacent degeneration in ALIF? A finite element study.

PubMed

Tang, Shujie; Meng, Xueying

2011-01-01

The restoration of disc space height of fused segment is essential in anterior lumbar interbody fusion, while the disc space height in many cases decreased postoperatively, which may adversely aggravate the adjacent segmental degeneration. However, no literature available focused on the issue. A normal healthy finite element model of L3-5 and four anterior lumbar interbody fusion models with different disc space height of fused segment were developed. 800 N compressive loading plus 10 Nm moments simulating flexion, extension, lateral bending and axial rotation were imposed on L3 superior endplate. The intradiscal pressure, the intersegmental rotation, the tresca stress and contact force of facet joints in L3-4 were investigated. Anterior lumbar interbody fusion with severely decreased disc space height presented with the highest values of the four parameters, and the normal healthy model presented with the lowest values except, under extension, the contact force of facet joints in normal healthy model is higher than that in normal anterior lumbar interbody fusion model. With disc space height decrease, the values of parameters in each anterior lumbar interbody fusion model increase gradually. Anterior lumbar interbody fusion with decreased disc space height aggravate the adjacent segmental degeneration more adversely.

Dynamic and thermal response finite element models of multi-body space structural configurations

NASA Technical Reports Server (NTRS)

Edighoffer, Harold H.

1987-01-01

Presented is structural dynamics modeling of two multibody space structural configurations. The first configuration is a generic space station model of a cylindrical habitation module, two solar array panels, radiator panel, and central connecting tube. The second is a 15-m hoop-column antenna. Discussed is the special joint elimination sequence used for these large finite element models, so that eigenvalues could be extracted. The generic space station model aided test configuration design and analysis/test data correlation. The model consisted of six finite element models, one of each substructure and one of all substructures as a system. Static analysis and tests at the substructure level fine-tuned the finite element models. The 15-m hoop-column antenna is a truss column and structural ring interconnected with tension stabilizing cables. To the cables, pretensioned mesh membrane elements were attached to form four parabolic shaped antennae, one per quadrant. Imposing thermal preloads in the cables and mesh elements produced pretension in the finite element model. Thermal preload variation in the 96 control cables was adjusted to maintain antenna shape within the required tolerance and to give pointing accuracy.

Efficient placement of structural dynamics sensors on the space station

NASA Technical Reports Server (NTRS)

Lepanto, Janet A.; Shepard, G. Dudley

1987-01-01

System identification of the space station dynamic model will require flight data from a finite number of judiciously placed sensors on it. The placement of structural dynamics sensors on the space station is a particularly challenging problem because the station will not be deployed in a single mission. Given that the build-up sequence and the final configuration for the space station are currently undetermined, a procedure for sensor placement was developed using the assembly flights 1 to 7 of the rephased dual keel space station as an example. The procedure presented approaches the problem of placing the sensors from an engineering, as opposed to a mathematical, point of view. In addition to locating a finite number of sensors, the procedure addresses the issues of unobserved structural modes, dominant structural modes, and the trade-offs involved in sensor placement for space station. This procedure for sensor placement will be applied to revised, and potentially more detailed, finite element models of the space station configuration and assembly sequence.

The finite element method scheme for a solution of an evolution variational inequality with a nonlocal space operator

NASA Astrophysics Data System (ADS)

Glazyrina, O. V.; Pavlova, M. F.

2016-11-01

We consider the parabolic inequality with monotone with respect to a gradient space operator, which is depended on integral with respect to space variables solution characteristic. We construct a two-layer differential scheme for this problem with use of penalty method, semidiscretization with respect to time variable method and the finite element method (FEM) with respect to space variables. We proved a convergence of constructed mothod.

Reentry heat transfer analysis of the space shuttle orbiter

NASA Technical Reports Server (NTRS)

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

1982-01-01

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

Effect of Finite Computational Domain on Turbulence Scaling Law in Both Physical and Spectral Spaces

NASA Technical Reports Server (NTRS)

Hou, Thomas Y.; Wu, Xiao-Hui; Chen, Shiyi; Zhou, Ye

1998-01-01

The well-known translation between the power law of energy spectrum and that of the correlation function or the second order structure function has been widely used in analyzing random data. Here, we show that the translation is valid only in proper scaling regimes. The regimes of valid translation are different for the correlation function and the structure function. Indeed, they do not overlap. Furthermore, in practice, the power laws exist only for a finite range of scales. We show that this finite range makes the translation inexact even in the proper scaling regime. The error depends on the scaling exponent. The current findings are applicable to data analysis in fluid turbulence and other stochastic systems.

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.

Least-squares finite element methods for compressible Euler equations

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Fermionic halos at finite temperature in AdS/CFT

NASA Astrophysics Data System (ADS)

Argüelles, Carlos R.; Grandi, Nicolás E.

2018-05-01

We explore the gravitational backreaction of a system consisting in a very large number of elementary fermions at finite temperature, in asymptotically AdS space. We work in the hydrodynamic approximation, and solve the Tolman-Oppenheimer-Volkoff equations with a perfect fluid whose equation of state takes into account both the relativistic effects of the fermionic constituents, as well as its finite temperature effects. We find a novel dense core-diluted halo structure for the density profiles in the AdS bulk, similarly as recently reported in flat space, for the case of astrophysical dark matter halos in galaxies. We further study the critical equilibrium configurations above which the core undergoes gravitational collapse towards a massive black hole, and calculate the corresponding critical central temperatures, for two qualitatively different central regimes of the fermions: the diluted-Fermi case, and the degenerate case. As a probe for the dual CFT, we construct the holographic two-point correlator of a scalar operator with large conformal dimension in the worldline limit, and briefly discuss on the boundary CFT effects at the critical points.

Explicit Finite Element Techniques Used to Characterize Splashdown of the Space Shuttle Solid Rocket Booster Aft Skirt

NASA Technical Reports Server (NTRS)

Melis, Matthew E.

2003-01-01

NASA Glenn Research Center s Structural Mechanics Branch has years of expertise in using explicit finite element methods to predict the outcome of ballistic impact events. Shuttle engineers from the NASA Marshall Space Flight Center and NASA Kennedy Space Flight Center required assistance in assessing the structural loads that a newly proposed thrust vector control system for the space shuttle solid rocket booster (SRB) aft skirt would expect to see during its recovery splashdown.

Exact Solution to Stationary Onset of Convection Due to Surface Tension Variation in a Multicomponent Fluid Layer With Interfacial Deformation

NASA Technical Reports Server (NTRS)

Skarda, J. Raymond Lee; McCaughan, Frances E.

1998-01-01

Stationary onset of convection due to surface tension variation in an unbounded multicomponent fluid layer is considered. Surface deformation is included and general flux boundary conditions are imposed on the stratifying agencies (temperature/composition) disturbance equations. Exact solutions are obtained to the general N-component problem for both finite and infinitesimal wavenumbers. Long wavelength instability may coexist with a finite wavelength instability for certain sets of parameter values, often referred to as frontier points. For an impermeable/insulated upper boundary and a permeable/conductive lower boundary, frontier boundaries are computed in the space of Bond number, Bo, versus Crispation number, Cr, over the range 5 x 10(exp -7) less than or equal to Bo less than or equal to 1. The loci of frontier points in (Bo, Cr) space for different values of N, diffusivity ratios, and, Marangoni numbers, collapsed to a single curve in (Bo, D(dimensional variable)Cr) space, where D(dimensional variable) is a Marangoni number weighted diffusivity ratio.

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.

Systems and Photosystems: Cellular Limits of Autotrophic Productivity in Cyanobacteria

PubMed Central

Burnap, Robert L.

2014-01-01

Recent advances in the modeling of microbial growth and metabolism have shown that growth rate critically depends upon the optimal allocation of finite proteomic resources among different cellular functions and that modeling growth rates becomes more realistic with the explicit accounting for the costs of macromolecular synthesis, most importantly, protein expression. The “proteomic constraint” is considered together with its application to understanding photosynthetic microbial growth. The central hypothesis is that physical limits of cellular space (and corresponding solvation capacity) in conjunction with cell surface-to-volume ratios represent the underlying constraints on the maximal rate of autotrophic microbial growth. The limitation of cellular space thus constrains the size the total complement of macromolecules, dissolved ions, and metabolites. To a first approximation, the upper limit in the cellular amount of the total proteome is bounded this space limit. This predicts that adaptation to osmotic stress will result in lower maximal growth rates due to decreased cellular concentrations of core metabolic proteins necessary for cell growth owing the accumulation of compatible osmolytes, as surmised previously. The finite capacity of membrane and cytoplasmic space also leads to the hypothesis that the species-specific differences in maximal growth rates likely reflect differences in the allocation of space to niche-specific proteins with the corresponding diminution of space devoted to other functions including proteins of core autotrophic metabolism, which drive cell reproduction. An optimization model for autotrophic microbial growth, the autotrophic replicator model, was developed based upon previous work investigating heterotrophic growth. The present model describes autotrophic growth in terms of the allocation protein resources among core functional groups including the photosynthetic electron transport chain, light-harvesting antennae, and the ribosome groups. PMID:25654078

Generalization of mixed multiscale finite element methods with applications

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

Lee, C S

Many science and engineering problems exhibit scale disparity and high contrast. The small scale features cannot be omitted in the physical models because they can affect the macroscopic behavior of the problems. However, resolving all the scales in these problems can be prohibitively expensive. As a consequence, some types of model reduction techniques are required to design efficient solution algorithms. For practical purpose, we are interested in mixed finite element problems as they produce solutions with certain conservative properties. Existing multiscale methods for such problems include the mixed multiscale finite element methods. We show that for complicated problems, the mixedmore » multiscale finite element methods may not be able to produce reliable approximations. This motivates the need of enrichment for coarse spaces. Two enrichment approaches are proposed, one is based on generalized multiscale finte element metthods (GMsFEM), while the other is based on spectral element-based algebraic multigrid (rAMGe). The former one, which is called mixed GMsFEM, is developed for both Darcy’s flow and linear elasticity. Application of the algorithm in two-phase flow simulations are demonstrated. For linear elasticity, the algorithm is subtly modified due to the symmetry requirement of the stress tensor. The latter enrichment approach is based on rAMGe. The algorithm differs from GMsFEM in that both of the velocity and pressure spaces are coarsened. Due the multigrid nature of the algorithm, recursive application is available, which results in an efficient multilevel construction of the coarse spaces. Stability, convergence analysis, and exhaustive numerical experiments are carried out to validate the proposed enrichment approaches. iii« less

Finite Element modelling of deformation induced by interacting volcanic sources

NASA Astrophysics Data System (ADS)

Pascal, Karen; Neuberg, Jürgen; Rivalta, Eleonora

2010-05-01

The displacement field due to magma movements in the subsurface is commonly modelled using the solutions for a point source (Mogi, 1958), a finite spherical source (McTigue, 1987), or a dislocation source (Okada, 1992) embedded in a homogeneous elastic half-space. When the magmatic system comprises more than one source, the assumption of homogeneity in the half-space is violated and several sources are combined, their respective deformation field being summed. We have investigated the effects of neglecting the interaction between sources on the surface deformation field. To do so, we calculated the vertical and horizontal displacements for models with adjacent sources and we tested them against the solutions of corresponding numerical 3D finite element models. We implemented several models combining spherical pressure sources and dislocation sources, varying their relative position. Furthermore we considered the impact of topography, loading, and magma compressibility. To quantify the discrepancies and compare the various models, we calculated the difference between analytical and numerical maximum horizontal or vertical surface displacements.We will demonstrate that for certain conditions combining analytical sources can cause an error of up to 20%. References: McTigue, D. F. (1987), Elastic Stress and Deformation Near a Finite Spherical Magma Body: Resolution of the Point Source Paradox, J. Geophys. Res. 92, 12931-12940. Mogi, K. (1958), Relations between the eruptions of various volcanoes and the deformations of the ground surfaces around them, Bull Earthquake Res Inst, Univ Tokyo 36, 99-134. Okada, Y. (1992), Internal Deformation Due to Shear and Tensile Faults in a Half-Space, Bulletin of the Seismological Society of America 82(2), 1018-1040.

Minimizing Actuator-Induced Residual Error in Active Space Telescope Primary Mirrors

DTIC Science & Technology

2010-09-01

actuator geometry, and rib-to-facesheet intersection geometry are exploited to achieve improved performance in silicon carbide ( SiC ) mirrors . A...are exploited to achieve improved performance in silicon carbide ( SiC ) mirrors . A parametric finite element model is used to explore the trade space...MOST) finite element model. The move to lightweight actively-controlled silicon carbide ( SiC ) mirrors is traced back to previous generations of space

Finite element analysis of a deployable space structure

NASA Technical Reports Server (NTRS)

Hutton, D. V.

1982-01-01

To assess the dynamic characteristics of a deployable space truss, a finite element model of the Scientific Applications Space Platform (SASP) truss has been formulated. The model incorporates all additional degrees of freedom associated with the pin-jointed members. Comparison of results with SPAR models of the truss show that the joints of the deployable truss significantly affect the vibrational modes of the structure only if the truss is relatively short.

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

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

2004-01-01

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

FDTD simulation of EM wave propagation in 3-D media

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

Wang, T.; Tripp, A.C.

1996-01-01

A finite-difference, time-domain solution to Maxwell`s equations has been developed for simulating electromagnetic wave propagation in 3-D media. The algorithm allows arbitrary electrical conductivity and permittivity variations within a model. The staggered grid technique of Yee is used to sample the fields. A new optimized second-order difference scheme is designed to approximate the spatial derivatives. Like the conventional fourth-order difference scheme, the optimized second-order scheme needs four discrete values to calculate a single derivative. However, the optimized scheme is accurate over a wider wavenumber range. Compared to the fourth-order scheme, the optimized scheme imposes stricter limitations on the time stepmore » sizes but allows coarser grids. The net effect is that the optimized scheme is more efficient in terms of computation time and memory requirement than the fourth-order scheme. The temporal derivatives are approximated by second-order central differences throughout. The Liao transmitting boundary conditions are used to truncate an open problem. A reflection coefficient analysis shows that this transmitting boundary condition works very well. However, it is subject to instability. A method that can be easily implemented is proposed to stabilize the boundary condition. The finite-difference solution is compared to closed-form solutions for conducting and nonconducting whole spaces and to an integral-equation solution for a 3-D body in a homogeneous half-space. In all cases, the finite-difference solutions are in good agreement with the other solutions. Finally, the use of the algorithm is demonstrated with a 3-D model. Numerical results show that both the magnetic field response and electric field response can be useful for shallow-depth and small-scale investigations.« less

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.

RAXBOD- INVISCID TRANSONIC FLOW OVER AXISYMMETRIC BODIES

NASA Technical Reports Server (NTRS)

Keller, J. D.

1994-01-01

The problem of axisymmetric transonic flow is of interest not only because of the practical application to missile and launch vehicle aerodynamics, but also because of its relation to fully three-dimensional flow in terms of the area rule. The RAXBOD computer program was developed for the analysis of steady, inviscid, irrotational, transonic flow over axisymmetric bodies in free air. RAXBOD uses a finite-difference relaxation method to numerically solve the exact formulation of the disturbance velocity potential with exact surface boundary conditions. Agreement with available experimental results has been good in cases where viscous effects and wind-tunnel wall interference are not important. The governing second-order partial differential equation describing the flow potential is replaced by a system of finite difference equations, including Jameson's "rotated" difference scheme at supersonic points. A stretching is applied to both the normal and tangential coordinates such that the infinite physical space is mapped onto a finite computational space. The boundary condition at infinity can be applied directly and there is no need for an asymptotic far-field solution. The system of finite difference equations is solved by a column relaxation method. In order to obtain both rapid convergence and any desired resolution, the relaxation is performed iteratively on successively refined grids. Input to RAXBOD consists of a description of the body geometry, the free stream conditions, and the desired resolution control parameters. Output from RAXBOD includes computed geometric parameters in the normal and tangential directions, iteration history information, drag coefficients, flow field data in the computational plane, and coordinates of the sonic line. This program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6600 computer with an overlayed central memory requirement of approximately 40K (octal) of 60 bit words. Optional plotted output can be generated for the Calcomp plotting system. The RAXBOD program was developed in 1976.

Computational strategies for tire monitoring and analysis

NASA Technical Reports Server (NTRS)

Danielson, Kent T.; Noor, Ahmed K.; Green, James S.

1995-01-01

Computational strategies are presented for the modeling and analysis of tires in contact with pavement. A procedure is introduced for simple and accurate determination of tire cross-sectional geometric characteristics from a digitally scanned image. Three new strategies for reducing the computational effort in the finite element solution of tire-pavement contact are also presented. These strategies take advantage of the observation that footprint loads do not usually stimulate a significant tire response away from the pavement contact region. The finite element strategies differ in their level of approximation and required amount of computer resources. The effectiveness of the strategies is demonstrated by numerical examples of frictionless and frictional contact of the space shuttle Orbiter nose-gear tire. Both an in-house research code and a commercial finite element code are used in the numerical studies.

Dark Soliton Solutions of Space-Time Fractional Sharma-Tasso-Olver and Potential Kadomtsev-Petviashvili Equations

NASA Astrophysics Data System (ADS)

Guner, Ozkan; Korkmaz, Alper; Bekir, Ahmet

2017-02-01

Dark soliton solutions for space-time fractional Sharma-Tasso-Olver and space-time fractional potential Kadomtsev-Petviashvili equations are determined by using the properties of modified Riemann-Liouville derivative and fractional complex transform. After reducing both equations to nonlinear ODEs with constant coefficients, the \\tanh ansatz is substituted into the resultant nonlinear ODEs. The coefficients of the solutions in the ansatz are calculated by algebraic computer computations. Two different solutions are obtained for the Sharma-Tasso-Olver equation as only one solution for the potential Kadomtsev-Petviashvili equation. The solution profiles are demonstrated in 3D plots in finite domains of time and space.

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

Doi-Peliti path integral methods for stochastic systems with partial exclusion

NASA Astrophysics Data System (ADS)

Greenman, Chris D.

2018-09-01

Doi-Peliti methods are developed for stochastic models with finite maximum occupation numbers per site. We provide a generalized framework for the different Fock spaces reported in the literature. Paragrassmannian techniques are then utilized to construct path integral formulations of factorial moments. We show that for many models of interest, a Magnus expansion is required to construct a suitable action, meaning actions containing a finite number of terms are not always feasible. However, for such systems, perturbative techniques are still viable, and for some examples, including carrying capacity population dynamics, and diffusion with partial exclusion, the expansions are exactly summable.

Partition of unity finite element method for quantum mechanical materials calculations

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

Pask, J. E.; Sukumar, N.

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

Partition of unity finite element method for quantum mechanical materials calculations

DOE PAGES

Pask, J. E.; Sukumar, N.

2016-11-09

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

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

NASA Astrophysics Data System (ADS)

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

2015-02-01

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

Geometrical Series and Phase Space in a Finite Oscillatory Motion

ERIC Educational Resources Information Center

Mareco, H. R. Olmedo

2006-01-01

This article discusses some interesting physical properties of oscillatory motion of a particle on two joined inclined planes. The geometrical series demonstrates that the particle will oscillate during a finite time. Another detail is the converging path to the origin of the phase space. Due to its simplicity, this motion may be used as a…

Finite difference time domain analysis of chirped dielectric gratings

NASA Technical Reports Server (NTRS)

Hochmuth, Diane H.; Johnson, Eric G.

1993-01-01

The finite difference time domain (FDTD) method for solving Maxwell's time-dependent curl equations is accurate, computationally efficient, and straight-forward to implement. Since both time and space derivatives are employed, the propagation of an electromagnetic wave can be treated as an initial-value problem. Second-order central-difference approximations are applied to the space and time derivatives of the electric and magnetic fields providing a discretization of the fields in a volume of space, for a period of time. The solution to this system of equations is stepped through time, thus, simulating the propagation of the incident wave. If the simulation is continued until a steady-state is reached, an appropriate far-field transformation can be applied to the time-domain scattered fields to obtain reflected and transmitted powers. From this information diffraction efficiencies can also be determined. In analyzing the chirped structure, a mesh is applied only to the area immediately around the grating. The size of the mesh is then proportional to the electric size of the grating. Doing this, however, imposes an artificial boundary around the area of interest. An absorbing boundary condition must be applied along the artificial boundary so that the outgoing waves are absorbed as if the boundary were absent. Many such boundary conditions have been developed that give near-perfect absorption. In this analysis, the Mur absorbing boundary conditions are employed. Several grating structures were analyzed using the FDTD method.

Three FORTRAN programs for finite-difference solutions to binary diffusion in one and two phases with composition-and time-dependent diffusion coefficients

USGS Publications Warehouse

Sanford, R.F.

1982-01-01

Geological examples of binary diffusion are numerous. They are potential indicators of the duration and rates of geological processes. Analytical solutions to the diffusion equations generally do not allow for variable diffusion coefficients, changing boundary conditions, and impingement of diffusion fields. The three programs presented here are based on Crank-Nicholson finite-difference approximations, which can take into account these complicating factors. Program 1 describes the diffusion of a component into an initially homogeneous phase that has a constant surface composition. Specifically it is written for Fe-Mg exchange in olivine at oxygen fugacities appropriate for the lunar crust, but other components, phases, or fugacities may be substituted by changing the values of the diffusion coefficient. Program 2 simulates the growth of exsolution lamellae. Program 3 describes the growth of reaction rims. These two programs are written for pseudobinary Ca-(Mg, Fe) exchange in pyroxenes. In all three programs, the diffusion coefficients and boundary conditions can be varied systematically with time. To enable users to employ widely different numerical values for diffusion coefficients and diffusion distance, the grid spacing in the space dimension and the increment by which the grid spacing in the time dimension is increased at each time step are input constants that can be varied each time the programs are run to yield a solution of the desired accuracy. ?? 1982.

Compatible-strain mixed finite element methods for incompressible nonlinear elasticity

NASA Astrophysics Data System (ADS)

Faghih Shojaei, Mostafa; Yavari, Arash

2018-05-01

We introduce a new family of mixed finite elements for incompressible nonlinear elasticity - compatible-strain mixed finite element methods (CSFEMs). Based on a Hu-Washizu-type functional, we write a four-field mixed formulation with the displacement, the displacement gradient, the first Piola-Kirchhoff stress, and a pressure-like field as the four independent unknowns. Using the Hilbert complexes of nonlinear elasticity, which describe the kinematics and the kinetics of motion, we identify the solution spaces of the independent unknown fields. In particular, we define the displacement in H1, the displacement gradient in H (curl), the stress in H (div), and the pressure field in L2. The test spaces of the mixed formulations are chosen to be the same as the corresponding solution spaces. Next, in a conforming setting, we approximate the solution and the test spaces with some piecewise polynomial subspaces of them. Among these approximation spaces are the tensorial analogues of the Nédélec and Raviart-Thomas finite element spaces of vector fields. This approach results in compatible-strain mixed finite element methods that satisfy both the Hadamard compatibility condition and the continuity of traction at the discrete level independently of the refinement level of the mesh. By considering several numerical examples, we demonstrate that CSFEMs have a good performance for bending problems and for bodies with complex geometries. CSFEMs are capable of capturing very large strains and accurately approximating stress and pressure fields. Using CSFEMs, we do not observe any numerical artifacts, e.g., checkerboarding of pressure, hourglass instability, or locking in our numerical examples. Moreover, CSFEMs provide an efficient framework for modeling heterogeneous solids.

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

PubMed

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

2012-09-01

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

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

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

1998-01-01

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

On orthogonal projectors induced by compact groups and Haar measures

NASA Astrophysics Data System (ADS)

Niezgoda, Marek

2008-02-01

We study the difference of two orthogonal projectors induced by compact groups of linear operators acting on a vector space. An upper bound for the difference is derived using the Haar measures of the groups. A particular attention is paid to finite groups. Some applications are given for complex matrices and unitarily invariant norms. Majorization inequalities of Fan and Hoffmann and of Causey are rediscovered.

Finite Rotation Analysis of Highly Thin and Flexible Structures

NASA Technical Reports Server (NTRS)

Clarke, Greg V.; Lee, Keejoo; Lee, Sung W.; Broduer, Stephen J. (Technical Monitor)

2001-01-01

Deployable space structures such as sunshields and solar sails are extremely thin and highly flexible with limited bending rigidity. For analytical investigation of their responses during deployment and operation in space, these structures can be modeled as thin shells. The present work examines the applicability of the solid shell element formulation to modeling of deployable space structures. The solid shell element formulation that models a shell as a three-dimensional solid is convenient in that no rotational parameters are needed for the description of kinematics of deformation. However, shell elements may suffer from element locking as the thickness becomes smaller unless special care is taken. It is shown that, when combined with the assumed strain formulation, the solid shell element formulation results in finite element models that are free of locking even for extremely thin structures. Accordingly, they can be used for analysis of highly flexible space structures undergoing geometrically nonlinear finite rotations.

Stable and unstable singularities in the unforced Hele-Shaw cell

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

Almgren, R.; Bertozzi, A.; Brenner, M.P.

We study singularity formation in the lubrication model for the unforced Hele-Shaw system, describing the breaking in two of a fluid droplet confined between two narrowly spaced glass plates. By varying the initial data, we exhibit four different scenarios: (1) the droplet breaks in finite time, with two pinch points moving toward each other and merging at the singular time; (2) the droplet breaks in finite time, with two asymmetric pinch points propagating away from each other; (3) the droplet breaks in finite time, with a single symmetric pinch point; or (4) the droplet relaxes to a stable equilibrium shapemore » without a finite time breakup. Each of the three singular scenarios has a self-similar structure with different scaling laws; the first scenario has not been observed before in other Hele-Shaw studies. We demonstrate instabilities of the second and third scenarios, in which the solution changes its behavior at a thickness that can be arbitrarily small depending on the initial condition. These transitions can be identified by examining the structure of the solution in the intermediate scaling region. {copyright} {ital 1996 American Institute of Physics.}« less

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.

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

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

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

Acoustic scattering from a finite cylindrical shell with evenly spaced stiffeners: Experimental investigation

NASA Astrophysics Data System (ADS)

Liétard, R.; Décultot, D.; Maze, G.; Tran-van-Nhieu, M.

2005-10-01

The influence of evenly spaced ribs (internal rings) on the acoustic scattering from a finite cylindrical shell is examined over the dimensionless frequency range 1

The dynamics of discrete-time computation, with application to recurrent neural networks and finite state machine extraction.

PubMed

Casey, M

1996-08-15

Recurrent neural networks (RNNs) can learn to perform finite state computations. It is shown that an RNN performing a finite state computation must organize its state space to mimic the states in the minimal deterministic finite state machine that can perform that computation, and a precise description of the attractor structure of such systems is given. This knowledge effectively predicts activation space dynamics, which allows one to understand RNN computation dynamics in spite of complexity in activation dynamics. This theory provides a theoretical framework for understanding finite state machine (FSM) extraction techniques and can be used to improve training methods for RNNs performing FSM computations. This provides an example of a successful approach to understanding a general class of complex systems that has not been explicitly designed, e.g., systems that have evolved or learned their internal structure.

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.

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.

Minimal measures for Euler-Lagrange flows on finite covering spaces

NASA Astrophysics Data System (ADS)

Wang, Fang; Xia, Zhihong

2016-12-01

In this paper we study the minimal measures for positive definite Lagrangian systems on compact manifolds. We are particularly interested in manifolds with more complicated fundamental groups. Mather’s theory classifies the minimal or action-minimizing measures according to the first (co-)homology group of a given manifold. We extend Mather’s notion of minimal measures to a larger class for compact manifolds with non-commutative fundamental groups, and use finite coverings to study the structure of these extended minimal measures. We also define action-minimizers and minimal measures in the homotopical sense. Our program is to study the structure of homotopical minimal measures by considering Mather’s minimal measures on finite covering spaces. Our goal is to show that, in general, manifolds with a non-commutative fundamental group have a richer set of minimal measures, hence a richer dynamical structure. As an example, we study the geodesic flow on surfaces of higher genus. Indeed, by going to the finite covering spaces, the set of minimal measures is much larger and more interesting.

Numerical simulation for solution of space-time fractional telegraphs equations with local fractional derivatives via HAFSTM

NASA Astrophysics Data System (ADS)

Pandey, Rishi Kumar; Mishra, Hradyesh Kumar

2017-11-01

In this paper, the semi-analytic numerical technique for the solution of time-space fractional telegraph equation is applied. This numerical technique is based on coupling of the homotopy analysis method and sumudu transform. It shows the clear advantage with mess methods like finite difference method and also with polynomial methods similar to perturbation and Adomian decomposition methods. It is easily transform the complex fractional order derivatives in simple time domain and interpret the results in same meaning.

Parallel Implementation of a High Order Implicit Collocation Method for the Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules; Halem, Milton (Technical Monitor)

2000-01-01

We combine a high order compact finite difference approximation and collocation techniques to numerically solve the two dimensional heat equation. The resulting method is implicit arid can be parallelized with a strategy that allows parallelization across both time and space. We compare the parallel implementation of the new method with a classical implicit method, namely the Crank-Nicolson method, where the parallelization is done across space only. Numerical experiments are carried out on the SGI Origin 2000.

The Blended Finite Element Method for Multi-fluid Plasma Modeling

DTIC Science & Technology

2016-07-01

Briefing Charts 3. DATES COVERED (From - To) 07 June 2016 - 01 July 2016 4. TITLE AND SUBTITLE The Blended Finite Element Method for Multi-fluid Plasma...BLENDED FINITE ELEMENT METHOD FOR MULTI-FLUID PLASMA MODELING Éder M. Sousa1, Uri Shumlak2 1ERC INC., IN-SPACE PROPULSION BRANCH (RQRS) AIR FORCE RESEARCH...MULTI-FLUID PLASMA MODEL 2 BLENDED FINITE ELEMENT METHOD Blended Finite Element Method Nodal Continuous Galerkin Modal Discontinuous Galerkin Model

Structural Modeling of a Five-Meter Thin Film Inflatable Antenna/Concentrator

NASA Technical Reports Server (NTRS)

Smalley, Kurt B.; Tinker, Michael L.; Taylor, W. Scott; Brunty, Joseph A. (Technical Monitor)

2002-01-01

Inflatable structures have been the subject of renewed interest in recent years for space applications such as communications antennas, solar thermal propulsion, and space solar power. A major advantage of using inflatable structures in space is their extremely light weight. An obvious second advantage is on-orbit deployability and related space savings in the launch configuration. A recent technology demonstrator flight for inflatable structures was the Inflatable Antenna Experiment (IAE) that was deployed on orbit from the Shuttle Orbiter. Although difficulty was encountered in the inflation/deployment phase, the flight was successful overall and provided valuable experience in the use of such structures. Several papers on static structural analysis of inflated cylinders have been written, describing different techniques such as linear shell theory, and nonlinear and variational methods, but very little work had been done in dynamics of inflatable structures until recent years. In 1988 Leonard indicated that elastic beam bending modes could be utilized in approximating lower-order frequencies of inflatable beams. Main, et al. wrote a very significant 1995 paper describing results of modal tests of inflated cantilever beams and the determination of effective material properties. Changes in material properties for different pressures were also discussed, and the beam model was used in a more complex structure. The paper demonstrated that conventional finite element analysis packages could be very useful in the analysis of complex inflatable structures. The purposes of this paper are to discuss the methodology for dynamically characterizing a large 5-meter thin film inflatable reflector, and to discuss the test arrangement and results. Nonlinear finite element modal results are compared to modal test data. The work is significant and of considerable interest to researchers because of 1) the large size of the structure, making it useful for scaling studies, and 2) application of commercially available finite element software for modeling pressurized thin-film structures.

Specialized Finite Set Statistics (FISST)-Based Estimation Methods to Enhance Space Situational Awareness in Medium Earth Orbit (MEO) and Geostationary Earth Orbit (GEO)

DTIC Science & Technology

2016-08-17

Research Laboratory AFRL /RVSV Space Vehicles Directorate 3550 Aberdeen Ave, SE 11. SPONSOR/MONITOR’S REPORT Kirtland AFB, NM 87117-5776 NUMBER(S) AFRL -RV...1 cy AFRL /RVIL Kirtland AFB, NM 87117-5776 2 cys Official Record Copy AFRL /RVSV/Richard S. Erwin 1 cy... AFRL -RV-PS- AFRL -RV-PS- TR-2016-0114 TR-2016-0114 SPECIALIZED FINITE SET STATISTICS (FISST)- BASED ESTIMATION METHODS TO ENHANCE SPACE SITUATIONAL

Ground State and Finite Temperature Lanczos Methods

NASA Astrophysics Data System (ADS)

Prelovšek, P.; Bonča, J.

The present review will focus on recent development of exact- diagonalization (ED) methods that use Lanczos algorithm to transform large sparse matrices onto the tridiagonal form. We begin with a review of basic principles of the Lanczos method for computing ground-state static as well as dynamical properties. Next, generalization to finite-temperatures in the form of well established finite-temperature Lanczos method is described. The latter allows for the evaluation of temperatures T>0 static and dynamic quantities within various correlated models. Several extensions and modification of the latter method introduced more recently are analysed. In particular, the low-temperature Lanczos method and the microcanonical Lanczos method, especially applicable within the high-T regime. In order to overcome the problems of exponentially growing Hilbert spaces that prevent ED calculations on larger lattices, different approaches based on Lanczos diagonalization within the reduced basis have been developed. In this context, recently developed method based on ED within a limited functional space is reviewed. Finally, we briefly discuss the real-time evolution of correlated systems far from equilibrium, which can be simulated using the ED and Lanczos-based methods, as well as approaches based on the diagonalization in a reduced basis.

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

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

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

2010-12-01

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

New Developments in the Method of Space-Time Conservation Element and Solution Element-Applications to Two-Dimensional Time-Marching Problems

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Wang, Xiao-Yen; Chow, Chuen-Yen

1994-01-01

A new numerical discretization method for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods, i.e., finite difference, finite volume, finite element, and spectral methods. It is motivated by several important physical/numerical considerations and designed to avoid several key limitations of the above traditional methods. As a result of the above considerations, a set of key principles for the design of numerical schemes was put forth in a previous report. These principles were used to construct several numerical schemes that model a 1-D time-dependent convection-diffusion equation. These schemes were then extended to solve the time-dependent Euler and Navier-Stokes equations of a perfect gas. It was shown that the above schemes compared favorably with the traditional schemes in simplicity, generality, and accuracy. In this report, the 2-D versions of the above schemes, except the Navier-Stokes solver, are constructed using the same set of design principles. Their constructions are simplified greatly by the use of a nontraditional space-time mesh. Its use results in the simplest stencil possible, i.e., a tetrahedron in a 3-D space-time with a vertex at the upper time level and other three at the lower time level. Because of the similarity in their design, each of the present 2-D solvers virtually shares with its 1-D counterpart the same fundamental characteristics. Moreover, it is shown that the present Euler solver is capable of generating highly accurate solutions for a famous 2-D shock reflection problem. Specifically, both the incident and the reflected shocks can be resolved by a single data point without the presence of numerical oscillations near the discontinuity.

State-Space Modeling of Dynamic Psychological Processes via the Kalman Smoother Algorithm: Rationale, Finite Sample Properties, and Applications

ERIC Educational Resources Information Center

Song, Hairong; Ferrer, Emilio

2009-01-01

This article presents a state-space modeling (SSM) technique for fitting process factor analysis models directly to raw data. The Kalman smoother via the expectation-maximization algorithm to obtain maximum likelihood parameter estimates is used. To examine the finite sample properties of the estimates in SSM when common factors are involved, a…

Finite-action solutions of Yang-Mills equations on de Sitter dS4 and anti-de Sitter AdS4 spaces

NASA Astrophysics Data System (ADS)

Ivanova, Tatiana A.; Lechtenfeld, Olaf; Popov, Alexander D.

2017-11-01

We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter dS4 and anti-de Sitter AdS4 spaces and construct various solutions to the Yang-Mills equations. On de Sitter space we reduce the Yang-Mills equations via an SU(2)-equivariant ansatz to Newtonian mechanics of a particle moving in R^3 under the influence of a quartic potential. Then we describe magnetic and electric-magnetic solutions, both Abelian and non-Abelian, all having finite energy and finite action. A similar reduction on anti-de Sitter space also yields Yang-Mills solutions with finite energy and action. We propose a lower bound for the action on both backgrounds. Employing another metric on AdS4, the SU(2) Yang-Mills equations are reduced to an analytic continuation of the above particle mechanics from R^3 to R^{2,1} . We discuss analytical solutions to these equations, which produce infinite-action configurations. After a Euclidean continuation of dS4 and AdS4 we also present self-dual (instanton-type) Yang-Mills solutions on these backgrounds.

Classical and special relativity in four steps

NASA Astrophysics Data System (ADS)

Browne, K. M.

2018-03-01

The most fundamental and pedagogically useful path to the space-time transformations of both classical and special relativity is to postulate the principle of relativity, derive the generalised or Ignatowsky transformation which contains both, then apply two different second postulates that give either the Galilean or Lorentz transformation. What is new here is (a) a simple two-step derivation of the Ignatowsky transformation, (b) a second postulate of universal time which yields the Galilean transformation, and (c) a different second postulate of finite universal lightspeed to give the Lorentz transformation using a simple Ignatowsky transformation of a light wave. This method demonstrates that the fundamental difference between Galilean and Lorentz transformations is not that lightspeed is universal (which is true for both) but whether the model requires lightspeed to be infinite or finite (as once mentioned by Einstein).

Noisy bases in Hilbert space: A new class of thermal coherent states and their properties

NASA Technical Reports Server (NTRS)

Vourdas, A.; Bishop, R. F.

1995-01-01

Coherent mixed states (or thermal coherent states) associated with the displaced harmonic oscillator at finite temperature, are introduced as a 'random' (or 'thermal' or 'noisy') basis in Hilbert space. A resolution of the identity for these states is proved and used to generalize the usual coherent state formalism for the finite temperature case. The Bargmann representation of an operator is introduced and its relation to the P and Q representations is studied. Generalized P and Q representations for the finite temperature case are also considered and several interesting relations among them are derived.

On the inequivalence of the CH and CHSH inequalities due to finite statistics

NASA Astrophysics Data System (ADS)

Renou, M. O.; Rosset, D.; Martin, A.; Gisin, N.

2017-06-01

Different variants of a Bell inequality, such as CHSH and CH, are known to be equivalent when evaluated on nonsignaling outcome probability distributions. However, in experimental setups, the outcome probability distributions are estimated using a finite number of samples. Therefore the nonsignaling conditions are only approximately satisfied and the robustness of the violation depends on the chosen inequality variant. We explain that phenomenon using the decomposition of the space of outcome probability distributions under the action of the symmetry group of the scenario, and propose a method to optimize the statistical robustness of a Bell inequality. In the process, we describe the finite group composed of relabeling of parties, measurement settings and outcomes, and identify correspondences between the irreducible representations of this group and properties of outcome probability distributions such as normalization, signaling or having uniform marginals.

A proof of the Woodward-Lawson sampling method for a finite linear array

NASA Technical Reports Server (NTRS)

Somers, Gary A.

1993-01-01

An extension of the continuous aperture Woodward-Lawson sampling theorem has been developed for a finite linear array of equidistant identical elements with arbitrary excitations. It is shown that by sampling the array factor at a finite number of specified points in the far field, the exact array factor over all space can be efficiently reconstructed in closed form. The specified sample points lie in real space and hence are measurable provided that the interelement spacing is greater than approximately one half of a wavelength. This paper provides insight as to why the length parameter used in the sampling formulas for discrete arrays is larger than the physical span of the lattice points in contrast with the continuous aperture case where the length parameter is precisely the physical aperture length.

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.

Dynamic earthquake rupture simulations on nonplanar faults embedded in 3D geometrically complex, heterogeneous elastic solids

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

Duru, Kenneth, E-mail: kduru@stanford.edu; Dunham, Eric M.; Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA

Dynamic propagation of shear ruptures on a frictional interface in an elastic solid is a useful idealization of natural earthquakes. The conditions relating discontinuities in particle velocities across fault zones and tractions acting on the fault are often expressed as nonlinear friction laws. The corresponding initial boundary value problems are both numerically and computationally challenging. In addition, seismic waves generated by earthquake ruptures must be propagated for many wavelengths away from the fault. Therefore, reliable and efficient numerical simulations require both provably stable and high order accurate numerical methods. We present a high order accurate finite difference method for: a)more » enforcing nonlinear friction laws, in a consistent and provably stable manner, suitable for efficient explicit time integration; b) dynamic propagation of earthquake ruptures along nonplanar faults; and c) accurate propagation of seismic waves in heterogeneous media with free surface topography. We solve the first order form of the 3D elastic wave equation on a boundary-conforming curvilinear mesh, in terms of particle velocities and stresses that are collocated in space and time, using summation-by-parts (SBP) finite difference operators in space. Boundary and interface conditions are imposed weakly using penalties. By deriving semi-discrete energy estimates analogous to the continuous energy estimates we prove numerical stability. The finite difference stencils used in this paper are sixth order accurate in the interior and third order accurate close to the boundaries. However, the method is applicable to any spatial operator with a diagonal norm satisfying the SBP property. Time stepping is performed with a 4th order accurate explicit low storage Runge–Kutta scheme, thus yielding a globally fourth order accurate method in both space and time. We show numerical simulations on band limited self-similar fractal faults revealing the complexity of rupture dynamics on rough faults.« less

Dynamic earthquake rupture simulations on nonplanar faults embedded in 3D geometrically complex, heterogeneous elastic solids

NASA Astrophysics Data System (ADS)

Duru, Kenneth; Dunham, Eric M.

2016-01-01

Dynamic propagation of shear ruptures on a frictional interface in an elastic solid is a useful idealization of natural earthquakes. The conditions relating discontinuities in particle velocities across fault zones and tractions acting on the fault are often expressed as nonlinear friction laws. The corresponding initial boundary value problems are both numerically and computationally challenging. In addition, seismic waves generated by earthquake ruptures must be propagated for many wavelengths away from the fault. Therefore, reliable and efficient numerical simulations require both provably stable and high order accurate numerical methods. We present a high order accurate finite difference method for: a) enforcing nonlinear friction laws, in a consistent and provably stable manner, suitable for efficient explicit time integration; b) dynamic propagation of earthquake ruptures along nonplanar faults; and c) accurate propagation of seismic waves in heterogeneous media with free surface topography. We solve the first order form of the 3D elastic wave equation on a boundary-conforming curvilinear mesh, in terms of particle velocities and stresses that are collocated in space and time, using summation-by-parts (SBP) finite difference operators in space. Boundary and interface conditions are imposed weakly using penalties. By deriving semi-discrete energy estimates analogous to the continuous energy estimates we prove numerical stability. The finite difference stencils used in this paper are sixth order accurate in the interior and third order accurate close to the boundaries. However, the method is applicable to any spatial operator with a diagonal norm satisfying the SBP property. Time stepping is performed with a 4th order accurate explicit low storage Runge-Kutta scheme, thus yielding a globally fourth order accurate method in both space and time. We show numerical simulations on band limited self-similar fractal faults revealing the complexity of rupture dynamics on rough faults.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Pasta phases in core-collapse supernova matter

NASA Astrophysics Data System (ADS)

Pais, Helena; Chiacchiera, Silvia; Providência, Constança

2016-04-01

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

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

NASA Technical Reports Server (NTRS)

Draine, B. T.; Goodman, Jeremy

1993-01-01

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

The Mimetic Finite Element Method and the Virtual Element Method for elliptic problems with arbitrary regularity.

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

Manzini, Gianmarco

2012-07-13

We develop and analyze a new family of virtual element methods on unstructured polygonal meshes for the diffusion problem in primal form, that use arbitrarily regular discrete spaces V{sub h} {contained_in} C{sup {alpha}} {element_of} N. The degrees of freedom are (a) solution and derivative values of various degree at suitable nodes and (b) solution moments inside polygons. The convergence of the method is proven theoretically and an optimal error estimate is derived. The connection with the Mimetic Finite Difference method is also discussed. Numerical experiments confirm the convergence rate that is expected from the theory.

On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. I - Nonstiff strongly dynamic problems

NASA Technical Reports Server (NTRS)

Harten, A.; Tal-Ezer, H.

1981-01-01

An implicit finite difference method of fourth order accuracy in space and time is introduced for the numerical solution of one-dimensional systems of hyperbolic conservation laws. The basic form of the method is a two-level scheme which is unconditionally stable and nondissipative. The scheme uses only three mesh points at level t and three mesh points at level t + delta t. The dissipative version of the basic method given is conditionally stable under the CFL (Courant-Friedrichs-Lewy) condition. This version is particularly useful for the numerical solution of problems with strong but nonstiff dynamic features, where the CFL restriction is reasonable on accuracy grounds. Numerical results are provided to illustrate properties of the proposed method.

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.

Finite size effects in the thermodynamics of a free neutral scalar field

NASA Astrophysics Data System (ADS)

Parvan, A. S.

2018-04-01

The exact analytical lattice results for the partition function of the free neutral scalar field in one spatial dimension in both the configuration and the momentum space were obtained in the framework of the path integral method. The symmetric square matrices of the bilinear forms on the vector space of fields in both configuration space and momentum space were found explicitly. The exact lattice results for the partition function were generalized to the three-dimensional spatial momentum space and the main thermodynamic quantities were derived both on the lattice and in the continuum limit. The thermodynamic properties and the finite volume corrections to the thermodynamic quantities of the free real scalar field were studied. We found that on the finite lattice the exact lattice results for the free massive neutral scalar field agree with the continuum limit only in the region of small values of temperature and volume. However, at these temperatures and volumes the continuum physical quantities for both massive and massless scalar field deviate essentially from their thermodynamic limit values and recover them only at high temperatures or/and large volumes in the thermodynamic limit.

Stabilization of a locally minimal forest

NASA Astrophysics Data System (ADS)

Ivanov, A. O.; Mel'nikova, A. E.; Tuzhilin, A. A.

2014-03-01

The method of partial stabilization of locally minimal networks, which was invented by Ivanov and Tuzhilin to construct examples of shortest trees with given topology, is developed. According to this method, boundary vertices of degree 2 are not added to all edges of the original locally minimal tree, but only to some of them. The problem of partial stabilization of locally minimal trees in a finite-dimensional Euclidean space is solved completely in the paper, that is, without any restrictions imposed on the number of edges remaining free of subdivision. A criterion for the realizability of such stabilization is established. In addition, the general problem of searching for the shortest forest connecting a finite family of boundary compact sets in an arbitrary metric space is formalized; it is shown that such forests exist for any family of compact sets if and only if for any finite subset of the ambient space there exists a shortest tree connecting it. The theory developed here allows us to establish further generalizations of the stabilization theorem both for arbitrary metric spaces and for metric spaces with some special properties. Bibliography: 10 titles.

A discrete model of a modified Burgers' partial differential equation

NASA Technical Reports Server (NTRS)

Mickens, R. E.; Shoosmith, J. N.

1990-01-01

A new finite-difference scheme is constructed for a modified Burger's equation. Three special cases of the equation are considered, and the 'exact' difference schemes for the space- and time-independent forms of the equation are presented, along with the diffusion-free case of Burger's equation modeled by a difference equation. The desired difference scheme is then obtained by imposing on any difference model of the initial equation the requirement that, in the appropriate limits, its difference scheme must reduce the results of the obtained equations.

Fourth-Order Conservative Vlasov-Maxwell Solver for Cartesian and Cylindrical Phase Space Coordinates

NASA Astrophysics Data System (ADS)

Vogman, Genia

Plasmas are made up of charged particles whose short-range and long-range interactions give rise to complex behavior that can be difficult to fully characterize experimentally. One of the most complete theoretical descriptions of a plasma is that of kinetic theory, which treats each particle species as a probability distribution function in a six-dimensional position-velocity phase space. Drawing on statistical mechanics, these distribution functions mathematically represent a system of interacting particles without tracking individual ions and electrons. The evolution of the distribution function(s) is governed by the Boltzmann equation coupled to Maxwell's equations, which together describe the dynamics of the plasma and the associated electromagnetic fields. When collisions can be neglected, the Boltzmann equation is reduced to the Vlasov equation. High-fidelity simulation of the rich physics in even a subset of the full six-dimensional phase space calls for low-noise high-accuracy numerical methods. To that end, this dissertation investigates a fourth-order finite-volume discretization of the Vlasov-Maxwell equation system, and addresses some of the fundamental challenges associated with applying these types of computationally intensive enhanced-accuracy numerical methods to phase space simulations. The governing equations of kinetic theory are described in detail, and their conservation-law weak form is derived for Cartesian and cylindrical phase space coordinates. This formulation is well known when it comes to Cartesian geometries, as it is used in finite-volume and finite-element discretizations to guarantee local conservation for numerical solutions. By contrast, the conservation-law weak form of the Vlasov equation in cylindrical phase space coordinates is largely unexplored, and to the author's knowledge has never previously been solved numerically. Thereby the methods described in this dissertation for simulating plasmas in cylindrical phase space coordinates present a new development in the field of computational plasma physics. A fourth-order finite-volume method for solving the Vlasov-Maxwell equation system is presented first for Cartesian and then for cylindrical phase space coordinates. Special attention is given to the treatment of the discrete primary variables and to the quadrature rule for evaluating the surface and line integrals that appear in the governing equations. The finite-volume treatment of conducting wall and axis boundaries is particularly nuanced when it comes to phase space coordinates, and is described in detail. In addition to the mechanics of each part of the finite-volume discretization in the two different coordinate systems, the complete algorithm is also presented. The Cartesian coordinate discretization is applied to several well-known test problems. Since even linear analysis of kinetic theory governing equations is complicated on account of velocity being an independent coordinate, few analytic or semi-analytic predictions exist. Benchmarks are particularly scarce for configurations that have magnetic fields and involve more than two phase space dimensions. Ensuring that simulations are true to the physics thus presents a difficulty in the development of robust numerical methods. The research described in this dissertation addresses this challenge through the development of more complete physics-based benchmarks based on the Dory-Guest-Harris instability. The instability is a special case of perpendicularly-propagating kinetic electrostatic waves in a warm uniformly magnetized plasma. A complete derivation of the closed-form linear theory dispersion relation for the instability is presented. The electric field growth rates and oscillation frequencies specified by the dispersion relation provide concrete measures against which simulation results can be quantitatively compared. Furthermore, a specialized form of perturbation is shown to strongly excite the fastest growing mode. The fourth-order finite-volume algorithm is benchmarked against the instability, and is demonstrated to have good convergence properties and close agreement with theoretical growth rate and oscillation frequency predictions. The Dory-Guest-Harris instability benchmark extends the scope of standard test problems by providing a substantive means of validating continuum kinetic simulations of warm magnetized plasmas in higher-dimensional 3D ( x,vx,vy) phase space. The linear theory analysis, initial conditions, algorithm description, and comparisons between theoretical predictions and simulation results are presented. The cylindrical coordinate finite-volume discretization is applied to model axisymmetric systems. Since mitigating the prohibitive computational cost of simulating six dimensions is another challenge in phase space simulations, the development of a robust means of exploiting symmetry is a major advance when it comes to numerically solving the Vlasov-Maxwell equation system. The discretization is applied to a uniform distribution function to assess the nature of the singularity at the axis, and is demonstrated to converge at fourth-order accuracy. The numerical method is then applied to simulate electrostatic ion confinement in an axisymmetric Z-pinch configuration. To the author's knowledge this presents the first instance of a conservative finite-volume discretization of the cylindrical coordinate Vlasov equation. The computational framework for the Vlasov-Maxwell solver is described, and an outlook for future research is presented.

A one-dimensional model of subsurface hillslope flow

Treesearch

Jason C. Fisher

1997-01-01

Abstract - A one-dimensional, finite difference model of saturated subsurface flow within a hillslope was developed. The model uses rainfall, elevation data, a hydraulic conductivity, and a storage coefficient to predict the saturated thickness in time and space. The model was tested against piezometric data collected in a swale located in the headwaters of the North...

A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2018-01-01

A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.

Quantum electron-vibrational dynamics at finite temperature: Thermo field dynamics approach

NASA Astrophysics Data System (ADS)

Borrelli, Raffaele; Gelin, Maxim F.

2016-12-01

Quantum electron-vibrational dynamics in molecular systems at finite temperature is described using an approach based on the thermo field dynamics theory. This formulation treats temperature effects in the Hilbert space without introducing the Liouville space. A comparison with the theoretically equivalent density matrix formulation shows the key numerical advantages of the present approach. The solution of thermo field dynamics equations with a novel technique for the propagation of tensor trains (matrix product states) is discussed. Numerical applications to model spin-boson systems show that the present approach is a promising tool for the description of quantum dynamics of complex molecular systems at finite temperature.

Recent Development of Multigrid Algorithms for Mixed and Noncomforming Methods for Second Order Elliptical Problems

NASA Technical Reports Server (NTRS)

Chen, Zhangxin; Ewing, Richard E.

1996-01-01

Multigrid algorithms for nonconforming and mixed finite element methods for second order elliptic problems on triangular and rectangular finite elements are considered. The construction of several coarse-to-fine intergrid transfer operators for nonconforming multigrid algorithms is discussed. The equivalence between the nonconforming and mixed finite element methods with and without projection of the coefficient of the differential problems into finite element spaces is described.

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

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

Pinto, Fabrizio

2009-10-15

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

Computer Program for Steady Transonic Flow over Thin Airfoils by Finite Elements

DTIC Science & Technology

1975-10-01

COMPUTER PROGRAM FOR STEADY JJ TRANSONIC FLOW OVER THIN AIRFOILS BY g FINITE ELEMENTS • *q^^ r ̂ c HUNTSVILLE RESEARCH & ENGINEERING CENTER...jglMMi B Jun’ INC ORGANIMTION NAME ANO ADDRESS Lö^kfteed Missiles & Space Company, Inc. Huntsville Research & Engineering Center,^ Huntsville, Alab...This report was prepared by personnel in the Computational Mechamcs Section of the Lockheed Missiles fc Space Company, Inc.. Huntsville Research

Slave finite elements: The temporal element approach to nonlinear analysis

NASA Technical Reports Server (NTRS)

Gellin, S.

1984-01-01

A formulation method for finite elements in space and time incorporating nonlinear geometric and material behavior is presented. The method uses interpolation polynomials for approximating the behavior of various quantities over the element domain, and only explicit integration over space and time. While applications are general, the plate and shell elements that are currently being programmed are appropriate to model turbine blades, vanes, and combustor liners.

Fractional finite Fourier transform.

PubMed

Khare, Kedar; George, Nicholas

2004-07-01

We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.

Implementing a Matrix-free Analytical Jacobian to Handle Nonlinearities in Models of 3D Lithospheric Deformation

NASA Astrophysics Data System (ADS)

Kaus, B.; Popov, A.

2015-12-01

The analytical expression for the Jacobian is a key component to achieve fast and robust convergence of the nonlinear Newton-Raphson iterative solver. Accomplishing this task in practice often requires a significant algebraic effort. Therefore it is quite common to use a cheap alternative instead, for example by approximating the Jacobian with a finite difference estimation. Despite its simplicity it is a relatively fragile and unreliable technique that is sensitive to the scaling of the residual and unknowns, as well as to the perturbation parameter selection. Unfortunately no universal rule can be applied to provide both a robust scaling and a perturbation. The approach we use here is to derive the analytical Jacobian for the coupled set of momentum, mass, and energy conservation equations together with the elasto-visco-plastic rheology and a marker in cell/staggered finite difference method. The software project LaMEM (Lithosphere and Mantle Evolution Model) is primarily developed for the thermo-mechanically coupled modeling of the 3D lithospheric deformation. The code is based on a staggered grid finite difference discretization in space, and uses customized scalable solvers form PETSc library to efficiently run on the massively parallel machines (such as IBM Blue Gene/Q). Currently LaMEM relies on the Jacobian-Free Newton-Krylov (JFNK) nonlinear solver, which approximates the Jacobian-vector product using a simple finite difference formula. This approach never requires an assembled Jacobian matrix and uses only the residual computation routine. We use an approximate Jacobian (Picard) matrix to precondition the Krylov solver with the Galerkin geometric multigrid. Because of the inherent problems of the finite difference Jacobian estimation, this approach doesn't always result in stable convergence. In this work we present and discuss a matrix-free technique in which the Jacobian-vector product is replaced by analytically-derived expressions and compare results with those obtained with a finite difference approximation of the Jacobian. This project is funded by ERC Starting Grant 258830 and computer facilities were provided by Jülich supercomputer center (Germany).

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

NASA Technical Reports Server (NTRS)

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

1996-01-01

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

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

NASA Technical Reports Server (NTRS)

McCutcheon, David Matthew

2017-01-01

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

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

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1996-01-01

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

Study of hypervelocity meteoroid impact on orbital space stations

NASA Technical Reports Server (NTRS)

Leimbach, K. R.; Prozan, R. J.

1973-01-01

Structural damage resulting in hypervelocity impact of a meteorite on a spacecraft is discussed. Of particular interest is the backside spallation caused by such a collision. To treat this phenomenon two numerical schemes were developed in the course of this study to compute the elastic-plastic flow fracture of a solid. The numerical schemes are a five-point finite difference scheme and a four-node finite element scheme. The four-node finite element scheme proved to be less sensitive to the type of boundary conditions and loadings. Although further development work is needed to improve the program versatility (generalization of the network topology, secondary storage for large systems, improving of the coding to reduce the run time, etc.), the basic framework is provided for a utilitarian computer program which may be used in a wide variety of situations. Analytic results showing the program output are given for several test cases.

Developments in the Gung Ho dynamical core

NASA Astrophysics Data System (ADS)

Melvin, Thomas

2017-04-01

Gung Ho is the new dynamical core being developed for the next generation Met Office weather and climate model, suitable for meeting the exascale challenge on emerging computer architectures. It builds upon the earlier collaborative project between the Met Office, NERC and STFC Daresbury of the same name to investigate suitable numerical methods for dynamical cores. A mixed-finite element approach is used, where different finite element spaces are used to represent various fields. This method provides a number of beneficial improvements over the current model, such a compatibility and inherent conservation on quasi-uniform unstructured meshes, whilst maintaining the accuracy and good dispersion properties of the staggered grid currently used. Furthermore, the mixed finite element approach allows a large degree of flexibility in the type of mesh, order of approximation and discretisation, providing a simple way to test alternative options to obtain the best model possible.

Coupling Between Microstrip Lines With Finite Width Ground Plane Embedded in Thin Film Circuits

NASA Technical Reports Server (NTRS)

Ponchak, George E.; Dalton, Edan; Tentzeris, Manos M.; Papapolymerou, John

2003-01-01

Three-dimensional (3D) interconnects built upon multiple layers of polyimide are required for constructing 3D circuits on CMOS (low resistivity) Si wafers, GaAs, and ceramic substrates. Thin film microstrip lines (TFMS) with finite width ground planes embedded in the polyimide are often used. However, the closely spaced TFMS lines a r e susceptible to high levels of coupling, which degrades circuit performance. In this paper, Finite Difference Time Domain (FDTD) analysis and experimental measurements a r e used to show that the ground planes must be connected by via holes to reduce coupling in both the forward and backward directions. Furthermore, it is shown that coupled microstrip lines establish a slotline type mode between the two ground planes and a dielectric waveguide type mode, and that the via holes recommended here eliminate these two modes.

Universal moduli spaces of Riemann surfaces

NASA Astrophysics Data System (ADS)

Ji, Lizhen; Jost, Jürgen

2017-04-01

We construct a moduli space for Riemann surfaces that is universal in the sense that it represents compact Riemann surfaces of any finite genus. This moduli space is a connected complex subspace of an infinite dimensional complex space, and is stratified according to genus such that each stratum has a compact closure, and it carries a metric and a measure that induce a Riemannian metric and a finite volume measure on each stratum. Applications to the Plateau-Douglas problem for minimal surfaces of varying genus and to the partition function of Bosonic string theory are outlined. The construction starts with a universal moduli space of Abelian varieties. This space carries a structure of an infinite dimensional locally symmetric space which is of interest in its own right. The key to our construction of the universal moduli space then is the Torelli map that assigns to every Riemann surface its Jacobian and its extension to the Satake-Baily-Borel compactifications.

Semigroup theory and numerical approximation for equations in linear viscoelasticity

NASA Technical Reports Server (NTRS)

Fabiano, R. H.; Ito, K.

1990-01-01

A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.

Applying CASE Tools for On-Board Software Development

NASA Astrophysics Data System (ADS)

Brammer, U.; Hönle, A.

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

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

USGS Publications Warehouse

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

1998-01-01

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

The Relation of Finite Element and Finite Difference Methods

NASA Technical Reports Server (NTRS)

Vinokur, M.

1976-01-01

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

Analysis of spurious oscillation modes for the shallow water and Navier-Stokes equations

USGS Publications Warehouse

Walters, R.A.; Carey, G.F.

1983-01-01

The origin and nature of spurious oscillation modes that appear in mixed finite element methods are examined. In particular, the shallow water equations are considered and a modal analysis for the one-dimensional problem is developed. From the resulting dispersion relations we find that the spurious modes in elevation are associated with zero frequency and large wave number (wavelengths of the order of the nodal spacing) and consequently are zero-velocity modes. The spurious modal behavior is the result of the finite spatial discretization. By means of an artificial compressibility and limiting argument we are able to resolve the similar problem for the Navier-Stokes equations. The relationship of this simpler analysis to alternative consistency arguments is explained. This modal approach provides an explanation of the phenomenon in question and permits us to deduce the cause of the very complex behavior of spurious modes observed in numerical experiments with the shallow water equations and Navier-Stokes equations. Furthermore, this analysis is not limited to finite element formulations, but is also applicable to finite difference formulations. ?? 1983.

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

NASA Technical Reports Server (NTRS)

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

2018-01-01

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

Finite Element Modeling of Deployment, and Foam Rigidization of Struts and Quarter Scale Shooting Star Experiment

NASA Technical Reports Server (NTRS)

Leigh, Larry, Jr.

2002-01-01

Inflated cylindrical struts constructed of kapton polyimide film and rigidized with foam have considerable practical application and potential for use as components of inflatable concentrator assemblies, antenna structures and space power systems, Because of their importance, it is of great interest to characterize the dynamic behavior of these components and structures both experimentally and analytically. It is very helpful to take a building-block approach to modeling and understanding inflatable assemblies by first investigating in detail the behavior of the components such as the struts. The foam material used for rigidization of such cylinders has varying modulus, which is a function of different factors, such as density of the foam. Thus, the primary motivation of the tests and analytical modeling efforts was to determine and understand the response of foam-rigidized cylinders for different densities, sizes, and construction methods, In recent years, inflatable structures have been the subject of renewed interest for space applications such as communications antennae, solar thermal propulsion, and space solar power. A major advantage of using inflatable structures in space is that they are extremely lightweight. This makes inflatables a perfect match for solar thermal propulsion because of the low thrust levels available. An obvious second advantage is on-orbit deployability and subsequent space savings in launch configuration. It can be seen that inflatable cylindrical struts and torus are critical components of structural assemblies. In view of this importance, structural dynamic and static behaviors of typical rigidized polyimide struts are investigated in this paper. The paper will focus on the finite element models that were used to model the behavior of the complete solar collector structure, and the results that they provided, as compared to test data.

Characteristics of chiral anomaly in view of various applications

NASA Astrophysics Data System (ADS)

Fujikawa, Kazuo

2018-01-01

In view of the recent applications of chiral anomaly to various fields beyond particle physics, we discuss some basic aspects of chiral anomaly which may help deepen our understanding of chiral anomaly in particle physics also. It is first shown that Berry's phase (and its generalization) for the Weyl model H =vFσ →.p →(t ) assumes a monopole form at the exact adiabatic limit but deviates from it off the adiabatic limit and vanishes in the high frequency limit of the Fourier transform of p →(t ) for bounded |p →(t )|. An effective action, which is consistent with the nonadiabatic limit of Berry's phase, combined with the Bjorken-Johnson-Low prescription, gives normal equal-time space-time commutators and no chiral anomaly. In contrast, an effective action with a monopole at the origin of the momentum space, which describes Berry's phase in the precise adiabatic limit but fails off the adiabatic limit, gives anomalous space-time commutators and a covariant anomaly to the gauge current. We regard this anomaly as an artifact of the postulated monopole and not a consequence of Berry's phase. As for the recent application of the chiral anomaly to the description of effective Weyl fermions in condensed matter and nuclear physics, which is closely related to the formulation of lattice chiral fermions, we point out that the chiral anomaly for each species doubler separately vanishes for a finite lattice spacing, contrary to the common assumption. Instead, a general form of pair creation associated with the spectral flow for the Dirac sea with finite depth takes place. This view is supported by the Ginsparg-Wilson fermion, which defines a single Weyl fermion without doublers on the lattice and gives a well-defined index (anomaly) even for a finite lattice spacing. A different use of anomaly in analogy to the partially conserved axial-vector current is also mentioned and could lead to an effect without fermion number nonconservation.

Differentiable representations of finite dimensional Lie groups in rigged Hilbert spaces

NASA Astrophysics Data System (ADS)

Wickramasekara, Sujeewa

The inceptive motivation for introducing rigged Hilbert spaces (RHS) in quantum physics in the mid 1960's was to provide the already well established Dirac formalism with a proper mathematical context. It has since become clear, however, that this mathematical framework is lissome enough to accommodate a class of solutions to the dynamical equations of quantum physics that includes some which are not possible in the normative Hilbert space theory. Among the additional solutions, in particular, are those which describe aspects of scattering and decay phenomena that have eluded the orthodox quantum physics. In this light, the RHS formulation seems to provide a mathematical rubric under which various phenomenological observations and calculational techniques, commonly known in the study of resonance scattering and decay as ``effective theories'' (e.g., the Wigner- Weisskopf method), receive a unified theoretical foundation. These observations lead to the inference that a theory founded upon the RHS mathematics may prove to be of better utility and value in understanding quantum physical phenomena. This dissertation primarily aims to contribute to the general formalism of the RHS theory of quantum mechanics by undertaking a study of differentiable representations of finite dimensional Lie groups. In particular, it is shown that a finite dimensional operator Lie algebra G in a rigged Hilbert space can be always integrated, provided one parameter integrability holds true for the elements of any basis for G . This result differs from and extends the well known integration theorem of E. Nelson and the subsequent works of others on unitary representations in that it does not require any assumptions on the existence of analytic vectors. Also presented here is a construction of a particular rigged Hilbert space of Hardy class functions that appears useful in formulating a relativistic version of the RHS theory of resonances and decay. As a contexture for the construction, a synopsis of the new relativistic theory is presented.

Finite element structural model of a large, thin, completely free, flat plate. [for large space structures

NASA Technical Reports Server (NTRS)

Joshi, S. M.; Groom, N. J.

1980-01-01

A finite element structural model of a 30.48 m x 30.48 m x 2.54 mm completely free aluminum plate is described and modal frequencies and mode shape data for the first 44 modes are presented. An explanation of the procedure for using the data is also presented. The model should prove useful for the investigation of controller design approaches for large flexible space structures.

Effect of element size on the solution accuracies of finite-element heat transfer and thermal stress analyses of space shuttle orbiter

NASA Technical Reports Server (NTRS)

Ko, William L.; Olona, Timothy

1987-01-01

The effect of element size on the solution accuracies of finite-element heat transfer and thermal stress analyses of space shuttle orbiter was investigated. Several structural performance and resizing (SPAR) thermal models and NASA structural analysis (NASTRAN) structural models were set up for the orbiter wing midspan bay 3. The thermal model was found to be the one that determines the limit of finite-element fineness because of the limitation of computational core space required for the radiation view factor calculations. The thermal stresses were found to be extremely sensitive to a slight variation of structural temperature distributions. The minimum degree of element fineness required for the thermal model to yield reasonably accurate solutions was established. The radiation view factor computation time was found to be insignificant compared with the total computer time required for the SPAR transient heat transfer analysis.

Global kinetic simulations of neoclassical toroidal viscosity in low-collisional perturbed tokamak plasmas

NASA Astrophysics Data System (ADS)

Matsuoka, Seikichi; Idomura, Yasuhiro; Satake, Shinsuke

2017-10-01

The neoclassical toroidal viscosity (NTV) caused by a non-axisymmetric magnetic field perturbation is numerically studied using two global kinetic simulations with different numerical approaches. Both simulations reproduce similar collisionality ( νb*) dependencies over wide νb * ranges. It is demonstrated that resonant structures in the velocity space predicted by the conventional superbanana-plateau theory exist in the small banana width limit, while the resonances diminish when the banana width becomes large. It is also found that fine scale structures are generated in the velocity space as νb* decreases in the large banana width simulations, leading to the νb* -dependency of the NTV. From the analyses of the particle orbit, it is found that the finite k∥ mode structure along the bounce motion appears owing to the finite orbit width, and it suffers from bounce phase mixing, suggesting the generation of the fine scale structures by the similar mechanism as the parallel phase mixing of passing particles.

Analysis and sizing of Mars aerobrake structure

NASA Technical Reports Server (NTRS)

Raju, I. S.; Craft, W. J.

1993-01-01

A cone-sphere aeroshell structure for aerobraking into Martian atmosphere is studied. Using this structural configuration, a space frame load-bearing structure is proposed. To generate this structure efficiently and to perform a variety of studies of several configurations, a mesh generator that utilizes only a few configurational parameters is developed. A finite element analysis program that analyzes space frame structures was developed. A sizing algorithm that arrives at a minimum mass configuration was developed and integrated into the finite element analysis program. A typical 135-ft-diam aerobrake configuration was analyzed and sized. The minimum mass obtained in this study using high modulus graphite/epoxy composite material members is compared with the masses obtained from two other aerobrake structures using lightweight erectable tetrahedral truss and part-spherical truss configurations. Excellent agreement for the minimum mass was obtained with the three different aerobrake structures. Also, the minimum mass using the present structure was obtained when the supports were not at the base but at about 75 percent of the base diameter.

Numerical difficulties and computational procedures for thermo-hydro-mechanical coupled problems of saturated porous media

NASA Astrophysics Data System (ADS)

Simoni, L.; Secchi, S.; Schrefler, B. A.

2008-12-01

This paper analyses the numerical difficulties commonly encountered in solving fully coupled numerical models and proposes a numerical strategy apt to overcome them. The proposed procedure is based on space refinement and time adaptivity. The latter, which in mainly studied here, is based on the use of a finite element approach in the space domain and a Discontinuous Galerkin approximation within each time span. Error measures are defined for the jump of the solution at each time station. These constitute the parameters allowing for the time adaptivity. Some care is however, needed for a useful definition of the jump measures. Numerical tests are presented firstly to demonstrate the advantages and shortcomings of the method over the more traditional use of finite differences in time, then to assess the efficiency of the proposed procedure for adapting the time step. The proposed method reveals its efficiency and simplicity to adapt the time step in the solution of coupled field problems.

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.

A phase space approach to imaging from limited data

NASA Astrophysics Data System (ADS)

Testorf, Markus E.

2015-09-01

The optical instrument function is used as the basis to develop optical system theory for imaging applications. The detection of optical signals is conveniently described as the overlap integral of the Wigner distribution functions of instrument and optical signal. Based on this framework various optical imaging systems, including plenoptic cameras, phase-retrieval algorithms, and Shack-Hartman sensors are shown to acquire information about a domain in phase-space, with finite extension and finite resolution. It is demonstrated how phase space optics can be used both to analyze imaging systems, as well as for designing methods for image reconstruction.

Free stream capturing in fluid conservation law for moving coordinates in three dimensions

NASA Technical Reports Server (NTRS)

Obayashi, Shigeru

1991-01-01

The free-stream capturing technique for both the finite-volume (FV) and finite-difference (FD) framework is summarized. For an arbitrary motion of the grid, the FV analysis shows that volumes swept by all six surfaces of the cell have to be computed correctly. This means that the free-stream capturing time-metric terms should be calculated not only from a surface vector of a cell at a single time level, but also from a volume swept by the cell surface in space and time. The FV free-stream capturing formulation is applicable to the FD formulation by proper translation from an FV cell to an FD mesh.

Computation of tightly-focused laser beams in the FDTD method

PubMed Central

Çapoğlu, İlker R.; Taflove, Allen; Backman, Vadim

2013-01-01

We demonstrate how a tightly-focused coherent TEMmn laser beam can be computed in the finite-difference time-domain (FDTD) method. The electromagnetic field around the focus is decomposed into a plane-wave spectrum, and approximated by a finite number of plane waves injected into the FDTD grid using the total-field/scattered-field (TF/SF) method. We provide an error analysis, and guidelines for the discrete approximation. We analyze the scattering of the beam from layered spaces and individual scatterers. The described method should be useful for the simulation of confocal microscopy and optical data storage. An implementation of the method can be found in our free and open source FDTD software (“Angora”). PMID:23388899

Computation of tightly-focused laser beams in the FDTD method.

PubMed

Capoğlu, Ilker R; Taflove, Allen; Backman, Vadim

2013-01-14

We demonstrate how a tightly-focused coherent TEMmn laser beam can be computed in the finite-difference time-domain (FDTD) method. The electromagnetic field around the focus is decomposed into a plane-wave spectrum, and approximated by a finite number of plane waves injected into the FDTD grid using the total-field/scattered-field (TF/SF) method. We provide an error analysis, and guidelines for the discrete approximation. We analyze the scattering of the beam from layered spaces and individual scatterers. The described method should be useful for the simulation of confocal microscopy and optical data storage. An implementation of the method can be found in our free and open source FDTD software ("Angora").

Black-Scholes finite difference modeling in forecasting of call warrant prices in Bursa Malaysia

NASA Astrophysics Data System (ADS)

Mansor, Nur Jariah; Jaffar, Maheran Mohd

2014-07-01

Call warrant is a type of structured warrant in Bursa Malaysia. It gives the holder the right to buy the underlying share at a specified price within a limited period of time. The issuer of the structured warrants usually uses European style to exercise the call warrant on the maturity date. Warrant is very similar to an option. Usually, practitioners of the financial field use Black-Scholes model to value the option. The Black-Scholes equation is hard to solve analytically. Therefore the finite difference approach is applied to approximate the value of the call warrant prices. The central in time and central in space scheme is produced to approximate the value of the call warrant prices. It allows the warrant holder to forecast the value of the call warrant prices before the expiry date.

A FORTRAN program for calculating nonlinear seismic ground response

USGS Publications Warehouse

Joyner, William B.

1977-01-01

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

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

DOE PAGES

Nutaro, James; Kuruganti, Teja

2017-02-24

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

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).…

A generalization of Fatou's lemma for extended real-valued functions on σ-finite measure spaces: with an application to infinite-horizon optimization in discrete time.

PubMed

Kamihigashi, Takashi

2017-01-01

Given a sequence [Formula: see text] of measurable functions on a σ -finite measure space such that the integral of each [Formula: see text] as well as that of [Formula: see text] exists in [Formula: see text], we provide a sufficient condition for the following inequality to hold: [Formula: see text] Our condition is considerably weaker than sufficient conditions known in the literature such as uniform integrability (in the case of a finite measure) and equi-integrability. As an application, we obtain a new result on the existence of an optimal path for deterministic infinite-horizon optimization problems in discrete time.

Structural weights analysis of advanced aerospace vehicles using finite element analysis

NASA Technical Reports Server (NTRS)

Bush, Lance B.; Lentz, Christopher A.; Rehder, John J.; Naftel, J. Chris; Cerro, Jeffrey A.

1989-01-01

A conceptual/preliminary level structural design system has been developed for structural integrity analysis and weight estimation of advanced space transportation vehicles. The system includes a three-dimensional interactive geometry modeler, a finite element pre- and post-processor, a finite element analyzer, and a structural sizing program. Inputs to the system include the geometry, surface temperature, material constants, construction methods, and aerodynamic and inertial loads. The results are a sized vehicle structure capable of withstanding the static loads incurred during assembly, transportation, operations, and missions, and a corresponding structural weight. An analysis of the Space Shuttle external tank is included in this paper as a validation and benchmark case of the system.

A combined dislocation fan-finite element (DF-FE) method for stress field simulation of dislocations emerging at the free surfaces of 3D elastically anisotropic crystals

NASA Astrophysics Data System (ADS)

Balusu, K.; Huang, H.

2017-04-01

A combined dislocation fan-finite element (DF-FE) method is presented for efficient and accurate simulation of dislocation nodal forces in 3D elastically anisotropic crystals with dislocations intersecting the free surfaces. The finite domain problem is decomposed into half-spaces with singular traction stresses, an infinite domain, and a finite domain with non-singular traction stresses. As such, the singular and non-singular parts of the traction stresses are addressed separately; the dislocation fan (DF) method is introduced to balance the singular traction stresses in the half-spaces while the finite element method (FEM) is employed to enforce the non-singular boundary conditions. The accuracy and efficiency of the DF method is demonstrated using a simple isotropic test case, by comparing it with the analytical solution as well as the FEM solution. The DF-FE method is subsequently used for calculating the dislocation nodal forces in a finite elastically anisotropic crystal, which produces dislocation nodal forces that converge rapidly with increasing mesh resolutions. In comparison, the FEM solution fails to converge, especially for nodes closer to the surfaces.

An Implicit Characteristic Based Method for Electromagnetics

NASA Technical Reports Server (NTRS)

Beggs, John H.; Briley, W. Roger

2001-01-01

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

Some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers of finite extent

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

Li, K., E-mail: likai@imech.ac.cn; University of Chinese Academy of Sciences, Beijing 100190; Xun, B.

2016-05-15

As a part of the preliminary studies for the future space experiment (Zona-K) in the Russian module of the International Space Station, some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers filled with 10 cSt silicone oil have been numerically studied in this paper. As the laterally applied temperature difference is raised, variations in the spatial structure and temporal evolution of the thermocapillary convection and a complex sequence of transitions are observed. The results show that the finite extent of the liquid layer significantly influences the tempo-spatial evolution of the thermocapillary convection. Moreover, the bifurcation route ofmore » the thermocapillary convection changes very sensitively by the aspect ratio of the liquid layer. With the increasing Reynolds number (applied temperature difference), the steady thermocapillary convection experiences two consecutive transitions from periodic oscillatory state to quasi-periodic oscillatory state with frequency-locking before emergence of chaotic convection in a liquid layer of aspect ratio 14.25, and the thermocapillary convection undergoes period-doubling cascades leading to chaotic convection in a liquid layer of aspect ratio 13.0.« less

Strange Quark Magnetic Moment of the Nucleon at the Physical Point.

PubMed

Sufian, Raza Sabbir; Yang, Yi-Bo; Alexandru, Andrei; Draper, Terrence; Liang, Jian; Liu, Keh-Fei

2017-01-27

We report a lattice QCD calculation of the strange quark contribution to the nucleon's magnetic moment and charge radius. This analysis presents the first direct determination of strange electromagnetic form factors including at the physical pion mass. We perform a model-independent extraction of the strange magnetic moment and the strange charge radius from the electromagnetic form factors in the momentum transfer range of 0.051  GeV^{2}≲Q^{2}≲1.31  GeV^{2}. The finite lattice spacing and finite volume corrections are included in a global fit with 24 valence quark masses on four lattices with different lattice spacings, different volumes, and four sea quark masses including one at the physical pion mass. We obtain the strange magnetic moment G_{M}^{s}(0)=-0.064(14)(09)μ_{N}. The four-sigma precision in statistics is achieved partly due to low-mode averaging of the quark loop and low-mode substitution to improve the statistics of the nucleon propagator. We also obtain the strange charge radius ⟨r_{s}^{2}⟩_{E}=-0.0043(16)(14)  fm^{2}.

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

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

Development of cost-effective surfactant flooding technology. Final report

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

Pope, G.A.; Sepehrnoori, K.

1996-11-01

Task 1 of this research was the development of a high-resolution, fully implicit, finite-difference, multiphase, multicomponent, compositional simulator for chemical flooding. The major physical phenomena modeled in this simulator are dispersion, heterogeneous permeability and porosity, adsorption, interfacial tension, relative permeability and capillary desaturation, compositional phase viscosity, compositional phase density and gravity effects, capillary pressure, and aqueous-oleic-microemulsion phase behavior. Polymer and its non-Newtonian rheology properties include shear-thinning viscosity, permeability reduction, inaccessible pore volume, and adsorption. Options of constant or variable space grids and time steps, constant-pressure or constant-rate well conditions, horizontal and vertical wells, and multiple slug injections are also availablemore » in the simulator. The solution scheme used in this simulator is fully implicit. The pressure equation and the mass-conservation equations are solved simultaneously for the aqueous-phase pressure and the total concentrations of each component. A third-order-in-space, second-order-in-time finite-difference method and a new total-variation-diminishing (TVD) third-order flux limiter are used that greatly reduce numerical dispersion effects. Task 2 was the optimization of surfactant flooding. The code UTCHEM was used to simulate surfactant polymer flooding.« less

A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes

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

Dorda, Antonius, E-mail: dorda@tugraz.at; Schürrer, Ferdinand, E-mail: ferdinand.schuerrer@tugraz.at

2015-03-01

We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of themore » phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations.« less

A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes

PubMed Central

Dorda, Antonius; Schürrer, Ferdinand

2015-01-01

We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of the phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations. PMID:25892748

A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes.

PubMed

Dorda, Antonius; Schürrer, Ferdinand

2015-03-01

We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of the phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations.

An Optimal Order Nonnested Mixed Multigrid Method for Generalized Stokes Problems

NASA Technical Reports Server (NTRS)

Deng, Qingping

1996-01-01

A multigrid algorithm is developed and analyzed for generalized Stokes problems discretized by various nonnested mixed finite elements within a unified framework. It is abstractly proved by an element-independent analysis that the multigrid algorithm converges with an optimal order if there exists a 'good' prolongation operator. A technique to construct a 'good' prolongation operator for nonnested multilevel finite element spaces is proposed. Its basic idea is to introduce a sequence of auxiliary nested multilevel finite element spaces and define a prolongation operator as a composite operator of two single grid level operators. This makes not only the construction of a prolongation operator much easier (the final explicit forms of such prolongation operators are fairly simple), but the verification of the approximate properties for prolongation operators is also simplified. Finally, as an application, the framework and technique is applied to seven typical nonnested mixed finite elements.

Probabilistic Structural Analysis Theory Development

NASA Technical Reports Server (NTRS)

Burnside, O. H.

1985-01-01

The objective of the Probabilistic Structural Analysis Methods (PSAM) project is to develop analysis techniques and computer programs for predicting the probabilistic response of critical structural components for current and future space propulsion systems. This technology will play a central role in establishing system performance and durability. The first year's technical activity is concentrating on probabilistic finite element formulation strategy and code development. Work is also in progress to survey critical materials and space shuttle mian engine components. The probabilistic finite element computer program NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) is being developed. The final probabilistic code will have, in the general case, the capability of performing nonlinear dynamic of stochastic structures. It is the goal of the approximate methods effort to increase problem solving efficiency relative to finite element methods by using energy methods to generate trial solutions which satisfy the structural boundary conditions. These approximate methods will be less computer intensive relative to the finite element approach.

Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Kumar, Vivek; Raghurama Rao, S. V.

2008-04-01

Non-standard finite difference methods (NSFDM) introduced by Mickens [ Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791-797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250-2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235-276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter ( λ) is chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.

Constructing space difference schemes which satisfy a cell entropy inequality

NASA Technical Reports Server (NTRS)

Merriam, Marshal L.

1989-01-01

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

Sensitivity of finite helical axis parameters to temporally varying realistic motion utilizing an idealized knee model.

PubMed

Johnson, T S; Andriacchi, T P; Erdman, A G

2004-01-01

Various uses of the screw or helical axis have previously been reported in the literature in an attempt to quantify the complex displacements and coupled rotations of in vivo human knee kinematics. Multiple methods have been used by previous authors to calculate the axis parameters, and it has been theorized that the mathematical stability and accuracy of the finite helical axis (FHA) is highly dependent on experimental variability and rotation increment spacing between axis calculations. Previous research has not addressed the sensitivity of the FHA for true in vivo data collection, as required for gait laboratory analysis. This research presents a controlled series of experiments simulating continuous data collection as utilized in gait analysis to investigate the sensitivity of the three-dimensional finite screw axis parameters of rotation, displacement, orientation and location with regard to time step increment spacing, utilizing two different methods for spatial location. Six-degree-of-freedom motion parameters are measured for an idealized rigid body knee model that is constrained to a planar motion profile for the purposes of error analysis. The kinematic data are collected using a multicamera optoelectronic system combined with an error minimization algorithm known as the point cluster method. Rotation about the screw axis is seen to be repeatable, accurate and time step increment insensitive. Displacement along the axis is highly dependent on time step increment sizing, with smaller rotation angles between calculations producing more accuracy. Orientation of the axis in space is accurate with only a slight filtering effect noticed during motion reversal. Locating the screw axis by a projected point onto the screw axis from the mid-point of the finite displacement is found to be less sensitive to motion reversal than finding the intersection of the axis with a reference plane. A filtering effect of the spatial location parameters was noted for larger time step increments during periods of little or no rotation.

Scattering characteristics of electromagnetic waves in time and space inhomogeneous weakly ionized dusty plasma sheath

NASA Astrophysics Data System (ADS)

Guo, Li-xin; Chen, Wei; Li, Jiang-ting; Ren, Yi; Liu, Song-hua

2018-05-01

The dielectric coefficient of a weakly ionised dusty plasma is used to establish a three-dimensional time and space inhomogeneous dusty plasma sheath. The effects of scattering on electromagnetic (EM) waves in this dusty plasma sheath are investigated using the auxiliary differential equation finite-difference time-domain method. Backward radar cross-sectional values of various parameters, including the dust particle radius, charging frequency of dust particles, dust particle concentration, effective collision frequency, rate of the electron density variation with time, angle of EM wave incidence, and plasma frequency, are analysed within the time and space inhomogeneous plasma sheath. The results show the noticeable effects of dusty plasma parameters on EM waves.

On real-space Density Functional Theory for non-orthogonal crystal systems: Kronecker product formulation of the kinetic energy operator

NASA Astrophysics Data System (ADS)

Sharma, Abhiraj; Suryanarayana, Phanish

2018-05-01

We present an accurate and efficient real-space Density Functional Theory (DFT) framework for the ab initio study of non-orthogonal crystal systems. Specifically, employing a local reformulation of the electrostatics, we develop a novel Kronecker product formulation of the real-space kinetic energy operator that significantly reduces the number of operations associated with the Laplacian-vector multiplication, the dominant cost in practical computations. In particular, we reduce the scaling with respect to finite-difference order from quadratic to linear, thereby significantly bridging the gap in computational cost between non-orthogonal and orthogonal systems. We verify the accuracy and efficiency of the proposed methodology through selected examples.

Long-time asymptotic solution structure of Camassa-Holm equation subject to an initial condition with non-zero reflection coefficient of the scattering data

NASA Astrophysics Data System (ADS)

Chang, Chueh-Hsin; Yu, Ching-Hao; Sheu, Tony Wen-Hann

2016-10-01

In this article, we numerically revisit the long-time solution behavior of the Camassa-Holm equation ut - uxxt + 2ux + 3uux = 2uxuxx + uuxxx. The finite difference solution of this integrable equation is sought subject to the newly derived initial condition with Delta-function potential. Our underlying strategy of deriving a numerical phase accurate finite difference scheme in time domain is to reduce the numerical dispersion error through minimization of the derived discrepancy between the numerical and exact modified wavenumbers. Additionally, to achieve the goal of conserving Hamiltonians in the completely integrable equation of current interest, a symplecticity-preserving time-stepping scheme is developed. Based on the solutions computed from the temporally symplecticity-preserving and the spatially wavenumber-preserving schemes, the long-time asymptotic CH solution characters can be accurately depicted in distinct regions of the space-time domain featuring with their own quantitatively very different solution behaviors. We also aim to numerically confirm that in the two transition zones their long-time asymptotics can indeed be described in terms of the theoretically derived Painlevé transcendents. Another attempt of this study is to numerically exhibit a close connection between the presently predicted finite-difference solution and the solution of the Painlevé ordinary differential equation of type II in two different transition zones.

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

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-07-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved space-times. In this paper, we assume the background space-time to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local time-stepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed space-times. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

Assessment of the performance of rigid pavement back-calculation through finite element modeling

NASA Astrophysics Data System (ADS)

Shoukry, Samir N.; William, Gergis W.; Martinelli, David R.

1999-02-01

This study focuses on examining the behavior of rigid pavement layers during the Falling Weight Deflectometer (FWD) test. Factors affecting the design of a concrete slab, such as whether the joints are doweled or undoweled and the spacing between the transverse joints, were considered in this study. Explicit finite element analysis was employed to investigate pavement layers' responses to the action of the impulse of the FWD test. Models of various dimensions were developed to satisfy the factors under consideration. The accuracy of the finite element models developed in this investigation was verified by comparing the finite element- generated deflection basin with that experimentally measured during an actual test. The results showed that the measured deflection basin can be reproduced through finite element modeling of the pavement structure. The resulting deflection basins from the use FE modeling was processed in order to backcalculate pavement layer moduli. This approach provides a method for the evaluation of the performance of existing backcalculation programs which are based on static elastic layer analysis. Based upon the previous studies conducted for the selection of software, three different backcalculation programs were chosen for the evaluation: MODULUS5.0, EVERCALC4.0, and MODCOMP3. The results indicate that ignoring the dynamic nature of the load may lead to crude results, especially during backcalculation procedures.

Numerical investigation of implementation of air-earth boundary by acoustic-elastic boundary approach

USGS Publications Warehouse

Xu, Y.; Xia, J.; Miller, R.D.

2007-01-01

The need for incorporating the traction-free condition at the air-earth boundary for finite-difference modeling of seismic wave propagation has been discussed widely. A new implementation has been developed for simulating elastic wave propagation in which the free-surface condition is replaced by an explicit acoustic-elastic boundary. Detailed comparisons of seismograms with different implementations for the air-earth boundary were undertaken using the (2,2) (the finite-difference operators are second order in time and space) and the (2,6) (second order in time and sixth order in space) standard staggered-grid (SSG) schemes. Methods used in these comparisons to define the air-earth boundary included the stress image method (SIM), the heterogeneous approach, the scheme of modifying material properties based on transversely isotropic medium approach, the acoustic-elastic boundary approach, and an analytical approach. The method proposed achieves the same or higher accuracy of modeled body waves relative to the SIM. Rayleigh waves calculated using the explicit acoustic-elastic boundary approach differ slightly from those calculated using the SIM. Numerical results indicate that when using the (2,2) SSG scheme for SIM and our new method, a spatial step of 16 points per minimum wavelength is sufficient to achieve 90% accuracy; 32 points per minimum wavelength achieves 95% accuracy in modeled Rayleigh waves. When using the (2,6) SSG scheme for the two methods, a spatial step of eight points per minimum wavelength achieves 95% accuracy in modeled Rayleigh waves. Our proposed method is physically reasonable and, based on dispersive analysis of simulated seismographs from a layered half-space model, is highly accurate. As a bonus, our proposed method is easy to program and slightly faster than the SIM. ?? 2007 Society of Exploration Geophysicists.

Finite Element Modeling of a Semi-Rigid Hybrid Mirror and a Highly Actuated Membrane Mirror as Candidates for the Next Generation Space Telescope

NASA Technical Reports Server (NTRS)

Craig, Larry; Jacobson, Dave; Mosier, Gary; Nein, Max; Page, Timothy; Redding, Dave; Sutherlin, Steve; Wilkerson, Gary

2000-01-01

Advanced space telescopes, which will eventually replace the Hubble Space Telescope (HTS), will have apertures of 8 - 20 n. Primary mirrors of these dimensions will have to be foldable to fit into the space launcher. By necessity these mirrors will be extremely light weight and flexible and the historical approaches to mirror designs, where the mirror is made as rigid as possible to maintain figure and to serve as the anchor for the entire telescope, cannot be applied any longer. New design concepts and verifications will depend entirely on analytical methods to predict optical performance. Finite element modeling of the structural and thermal behavior of such mirrors is becoming the tool for advanced space mirror designs. This paper discusses some of the preliminary tasks and study results, which are currently the basis for the design studies of the Next Generation Space Telescope.

Directional radiation pattern in structural-acoustic coupled system

NASA Astrophysics Data System (ADS)

Seo, Hee-Seon; Kim, Yang-Hann

2005-07-01

In this paper we demonstrate the possibility of designing a radiator using structural-acoustic interaction by predicting the pressure distribution and radiation pattern of a structural-acoustic coupling system that is composed by a wall and two spaces. If a wall separates spaces, then the wall's role in transporting the acoustic characteristics of the spaces is important. The spaces can be categorized as bounded finite space and unbounded infinite space. The wall considered in this study composes two plates and an opening, and the wall separates one space that is highly reverberant and the other that is unbounded without any reflection. This rather hypothetical circumstance is selected to study the general coupling problem between the finite and infinite acoustic domains. We developed an equation that predicts the energy distribution and energy flow in the two spaces separated by a wall, and its computational examples are presented. Three typical radiation patterns that include steered, focused, and omnidirected are presented. A designed radiation pattern is also presented by using the optimal design algorithm.

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

Simulation of Aluminum Micro-mirrors for Space Applications at Cryogenic Temperatures

NASA Technical Reports Server (NTRS)

Kuhn, J. L.; Dutta, S. B.; Greenhouse, M. A.; Mott, D. B.

2000-01-01

Closed form and finite element models are developed to predict the device response of aluminum electrostatic torsion micro-mirrors fabricated on silicon substrate for space applications at operating temperatures of 30K. Initially, closed form expressions for electrostatic pressure arid mechanical restoring torque are used to predict the pull-in and release voltages at room temperature. Subsequently, a detailed mechanical finite element model is developed to predict stresses and vertical beam deflection induced by the electrostatic and thermal loads. An incremental and iterative solution method is used in conjunction with the nonlinear finite element model and closed form electrostatic equations to solve. the coupled electro-thermo-mechanical problem. The simulation results are compared with experimental measurements at room temperature of fabricated micro-mirror devices.

Values of the phase space factors for double beta decay

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

Stoica, Sabin, E-mail: stoica@theory.nipne.ro; Mirea, Mihai; Horia Hulubei National Institute of Physics and Nuclear Engineering, 30 Reactorului street, P.O. Box MG6, Magurele

2015-10-28

We report an up-date list of the experimentally most interesting phase space factors for double beta decay (DBD). The electron/positron wave functions are obtained by solving the Dirac equations with a Coulomb potential derived from a realistic proton density distribution in nucleus and with inclusion of the finite nuclear size (FNS) and electron screening (ES) effects. We build up new numerical routines which allow us a good control of the accuracy of calculations. We found several notable differences as compared with previous results reported in literature and possible sources of these discrepancies are discussed.

Principles of magnetohydrodynamic simulation in space plasmas

NASA Technical Reports Server (NTRS)

Sato, T.

1985-01-01

Attention is given to the philosophical as well as physical principles that are essential to the establishment of MHD simulation studies for solar plasma research, assuming the capabilities of state-of-the-art computers and emphasizing the importance of 'local' MHD simulation. Solar-terrestrial plasma space is divided into several elementary regions where a macroscopic elementary energy conversion process could conceivably occur; the local MHD simulation is defined as self-contained in each of the regions. The importance of, and the difficulties associated with, the boundary condition are discussed in detail. The roles of diagnostics and of the finite difference method are noted.

Analysis of SIR-A antenna tests

NASA Technical Reports Server (NTRS)

Carver, K. R.; Post, C. C.

1979-01-01

The purpose of this report is: (1) to provide an analysis of antenna test procedures used at JPL for measurement of the SIR-A antenna and (2) to point out that the measured E-plane patterns differ in some significant respects from the true pattern as experienced during the OFT-2 space deployment; this results principally from the finite range length associated with the JPL far-field range.

Nondestructive analysis and development

NASA Technical Reports Server (NTRS)

Moslehy, Faissal A.

1993-01-01

This final report summarizes the achievements of project #4 of the NASA/UCF Cooperative Agreement from January 1990 to December 1992. The objectives of this project are to review NASA's NDE program at Kennedy Space Center (KSC) and recommend means for enhancing the present testing capabilities through the use of improved or new technologies. During the period of the project, extensive development of a reliable nondestructive, non-contact vibration technique to determine and quantify the bond condition of the thermal protection system (TPS) tiles of the Space Shuttle Orbiter was undertaken. Experimental modal analysis (EMA) is used as a non-destructive technique for the evaluation of Space Shuttle thermal protection system (TPS) tile bond integrity. Finite element (FE) models for tile systems were developed and were used to generate their vibration characteristics (i.e. natural frequencies and mode shapes). Various TPS tile assembly configurations as well as different bond conditions were analyzed. Results of finite element analyses demonstrated a drop in natural frequencies and a change in mode shapes which correlate with both size and location of disbond. Results of experimental testing of tile panels correlated with FE results and demonstrated the feasibility of EMA as a viable technique for tile bond verification. Finally, testing performed on the Space Shuttle Columbia using a laser doppler velocimeter demonstrated the application of EMA, when combined with FE modeling, as a non-contact, non-destructive bond evaluation technique.

On conforming mixed finite element methods for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D; Nicolaides, R. A.; Peterson, J. S.

1982-01-01

The application of conforming mixed finite element methods to obtain approximate solutions of linearized Navier-Stokes equations is examined. Attention is given to the convergence rates of various finite element approximations of the pressure and the velocity field. The optimality of the convergence rates are addressed in terms of comparisons of the approximation convergence to a smooth solution in relation to the best approximation available for the finite element space used. Consideration is also devoted to techniques for efficient use of a Gaussian elimination algorithm to obtain a solution to a system of linear algebraic equations derived by finite element discretizations of linear partial differential equations.

New developments in the method of space-time conservation element and solution element: Applications to the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1993-01-01

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods--i.e., finite difference, finite volume, finite element, and spectral methods. It is conceptually simple and designed to avoid several key limitations to the above traditional methods. An explicit model scheme for solving a simple 1-D unsteady convection-diffusion equation is constructed and used to illuminate major differences between the current method and those mentioned above. Unexpectedly, its amplification factors for the pure convection and pure diffusion cases are identical to those of the Leapfrog and the DuFort-Frankel schemes, respectively. Also, this explicit scheme and its Navier-Stokes extension have the unusual property that their stabilities are limited only by the CFL condition. Moreover, despite the fact that it does not use any flux-limiter or slope-limiter, the Navier-Stokes solver is capable of generating highly accurate shock tube solutions with shock discontinuities being resolved within one mesh interval. An accurate Euler solver also is constructed through another extension. It has many unusual properties, e.g., numerical diffusion at all mesh points can be controlled by a set of local parameters.

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

NASA Astrophysics Data System (ADS)

Gyrya, V.; Lipnikov, K.

2017-11-01

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

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

NASA Astrophysics Data System (ADS)

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

2000-06-01

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

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

DOE PAGES

Gyrya, V.; Lipnikov, K.

2017-07-18

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

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

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

Gyrya, V.; Lipnikov, K.

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

Finite-difference simulation and visualization of elastodynamics in time-evolving generalized curvilinear coordinates

NASA Technical Reports Server (NTRS)

Kaul, Upender K. (Inventor)

2009-01-01

Modeling and simulation of free and forced structural vibrations is essential to an overall structural health monitoring capability. In the various embodiments, a first principles finite-difference approach is adopted in modeling a structural subsystem such as a mechanical gear by solving elastodynamic equations in generalized curvilinear coordinates. Such a capability to generate a dynamic structural response is widely applicable in a variety of structural health monitoring systems. This capability (1) will lead to an understanding of the dynamic behavior of a structural system and hence its improved design, (2) will generate a sufficiently large space of normal and damage solutions that can be used by machine learning algorithms to detect anomalous system behavior and achieve a system design optimization and (3) will lead to an optimal sensor placement strategy, based on the identification of local stress maxima all over the domain.

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.

A Note on Multigrid Theory for Non-nested Grids and/or Quadrature

NASA Technical Reports Server (NTRS)

Douglas, C. C.; Douglas, J., Jr.; Fyfe, D. E.

1996-01-01

We provide a unified theory for multilevel and multigrid methods when the usual assumptions are not present. For example, we do not assume that the solution spaces or the grids are nested. Further, we do not assume that there is an algebraic relationship between the linear algebra problems on different levels. What we provide is a computationally useful theory for adaptively changing levels. Theory is provided for multilevel correction schemes, nested iteration schemes, and one way (i.e., coarse to fine grid with no correction iterations) schemes. We include examples showing the applicability of this theory: finite element examples using quadrature in the matrix assembly and finite volume examples with non-nested grids. Our theory applies directly to other discretizations as well.

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

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

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.

Diagnosing hyperuniformity in two-dimensional, disordered, jammed packings of soft spheres.

PubMed

Dreyfus, Remi; Xu, Ye; Still, Tim; Hough, L A; Yodh, A G; Torquato, Salvatore

2015-01-01

Hyperuniformity characterizes a state of matter for which (scaled) density fluctuations diminish towards zero at the largest length scales. However, the task of determining whether or not an image of an experimental system is hyperuniform is experimentally challenging due to finite-resolution, noise, and sample-size effects that influence characterization measurements. Here we explore these issues, employing video optical microscopy to study hyperuniformity phenomena in disordered two-dimensional jammed packings of soft spheres. Using a combination of experiment and simulation we characterize the possible adverse effects of particle polydispersity, image noise, and finite-size effects on the assignment of hyperuniformity, and we develop a methodology that permits improved diagnosis of hyperuniformity from real-space measurements. The key to this improvement is a simple packing reconstruction algorithm that incorporates particle polydispersity to minimize the free volume. In addition, simulations show that hyperuniformity in finite-sized samples can be ascertained more accurately in direct space than in reciprocal space. Finally, our experimental colloidal packings of soft polymeric spheres are shown to be effectively hyperuniform.

Maximum-entropy reconstruction method for moment-based solution of the Boltzmann equation

NASA Astrophysics Data System (ADS)

Summy, Dustin; Pullin, Dale

2013-11-01

We describe a method for a moment-based solution of the Boltzmann equation. This starts with moment equations for a 10 + 9 N , N = 0 , 1 , 2 . . . -moment representation. The partial-differential equations (PDEs) for these moments are unclosed, containing both higher-order moments and molecular-collision terms. These are evaluated using a maximum-entropy construction of the velocity distribution function f (c , x , t) , using the known moments, within a finite-box domain of single-particle-velocity (c) space. Use of a finite-domain alleviates known problems (Junk and Unterreiter, Continuum Mech. Thermodyn., 2002) concerning existence and uniqueness of the reconstruction. Unclosed moments are evaluated with quadrature while collision terms are calculated using a Monte-Carlo method. This allows integration of the moment PDEs in time. Illustrative examples will include zero-space- dimensional relaxation of f (c , t) from a Mott-Smith-like initial condition toward equilibrium and one-space dimensional, finite Knudsen number, planar Couette flow. Comparison with results using the direct-simulation Monte-Carlo method will be presented.

Diagnosing hyperuniformity in two-dimensional, disordered, jammed packings of soft spheres

NASA Astrophysics Data System (ADS)

Dreyfus, Remi; Xu, Ye; Still, Tim; Hough, L. A.; Yodh, A. G.; Torquato, Salvatore

2015-01-01

Hyperuniformity characterizes a state of matter for which (scaled) density fluctuations diminish towards zero at the largest length scales. However, the task of determining whether or not an image of an experimental system is hyperuniform is experimentally challenging due to finite-resolution, noise, and sample-size effects that influence characterization measurements. Here we explore these issues, employing video optical microscopy to study hyperuniformity phenomena in disordered two-dimensional jammed packings of soft spheres. Using a combination of experiment and simulation we characterize the possible adverse effects of particle polydispersity, image noise, and finite-size effects on the assignment of hyperuniformity, and we develop a methodology that permits improved diagnosis of hyperuniformity from real-space measurements. The key to this improvement is a simple packing reconstruction algorithm that incorporates particle polydispersity to minimize the free volume. In addition, simulations show that hyperuniformity in finite-sized samples can be ascertained more accurately in direct space than in reciprocal space. Finally, our experimental colloidal packings of soft polymeric spheres are shown to be effectively hyperuniform.

Effect of roof strength in injury mitigation during pole impact.

PubMed

Friedman, Keith; Hutchinson, John; Mihora, Dennis; Kumar, Sri; Frieder, Russell; Sances, Anthony

2007-01-01

Motor vehicle accidents involving pole impacts often result in serious head and neck injuries to occupants. Pole impacts are typically associated with rollover and side collisions. During such events, the roof structure is often deformed into the occupant survival space. The existence of a strengthened roof structure would reduce roof deformation and accordingly provide better protection to occupants. The present study examines the effect of reinforced (strengthened) roofs using experimental crash study and computer model simulation. The experimental study includes the production cab structure of a pickup truck. The cab structure was loaded using an actual telephone pole under controlled laboratory conditions. The cab structure was subjected to two separate load conditions at the A-pillar and door frame. The contact force and deformation were measured using a force gauge and potentiometer, respectively. A computer finite element model was created to simulate the experimental studies. The results of finite element model matched well with experimental data during two different load conditions. The validated finite element model was then used to simulate a reinforced roof structure. The reinforced roof significantly reduced the structural deformations compared to those observed in the production roof. The peak deformation was reduced by approximately 75% and peak velocity was reduced by approximately 50%. Such a reduction in the deformation of the roof structure helps to maintain a safe occupant survival space.

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.

1992-01-01

The Penn State Finite Difference Time Domain Electromagnetic Scattering Code version D is a 3-D numerical electromagnetic scattering code based upon the finite difference time domain technique (FDTD). The 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 D code capabilities; a brief description of the default scattering geometry; a brief description of each subroutine; a description of the include file; a section briefly discussing Radar Cross Section computations; a section discussing some scattering results; a sample problem setup section; a new problem checklist; references and figure titles. The FDTD technique models transient electromagnetic scattering and interactions with objects of arbitrary shape and/or material composition. In the FDTD method, Maxwell's curl equations are discretized in time-space and all derivatives (temporal and spatial) are approximated by central differences.

A symplectic integration method for elastic filaments

NASA Astrophysics Data System (ADS)

Ladd, Tony; Misra, Gaurav

2009-03-01

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

Theoretical analysis of a dual-probe scanning tunneling microscope setup on graphene.

PubMed

Settnes, Mikkel; Power, Stephen R; Petersen, Dirch H; Jauho, Antti-Pekka

2014-03-07

Experimental advances allow for the inclusion of multiple probes to measure the transport properties of a sample surface. We develop a theory of dual-probe scanning tunneling microscopy using a Green's function formalism, and apply it to graphene. Sampling the local conduction properties at finite length scales yields real space conductance maps which show anisotropy for pristine graphene systems and quantum interference effects in the presence of isolated impurities. Spectral signatures in the Fourier transforms of real space conductance maps include characteristics that can be related to different scattering processes. We compute the conductance maps of graphene systems with different edge geometries or height fluctuations to determine the effects of nonideal graphene samples on dual-probe measurements.

Finite element analysis of space debris removal by high-power lasers

NASA Astrophysics Data System (ADS)

Xue, Li; Jiang, Guanlei; Yu, Shuang; Li, Ming

2015-08-01

With the development of space station technologies, irradiation of space debris by space-based high-power lasers, can locally generate high-temperature plasmas and micro momentum, which may achieve the removal of debris through tracking down. Considered typical square-shaped space debris of material Ti with 5cm×5cm size, whose thermal conductivity, density, specific heat capacity and emissivity are 7.62W/(m·°C), 4500kg/m3, 0.52J/(kg·°C) and 0.3,respectively, based on the finite element analysis of ANSYS, each irradiation of space debris by high-power lasers with power density 106W/m2 and weapons-grade lasers with power density 3000W/m2 are simulated under space environment, and the temperature curves due to laser thermal irradiation are obtained and compared. Results show only 2s is needed for high-power lasers to make the debris temperature reach to about 10000K, which is the threshold temperature for plasmas-state conversion. While for weapons-grade lasers, it is 13min needed. Using two line elements (TLE), and combined with the coordinate transformation from celestial coordinate system to site coordinate system, the visible period of space debris is calculated as 5-10min. That is, in order to remove space debris by laser plasmas, the laser power density should be further improved. The article provides an intuitive and visual feasibility analysis method of space debris removal, and the debris material and shape, laser power density and spot characteristics are adjustable. This finite element analysis method is low-cost, repeatable and adaptable, which has an engineering-prospective applications.

A three-dimensional finite element evaluation of magnetic attachment attractive force and the influence of the magnetic circuit.

PubMed

Kumano, Hirokazu; Nakamura, Yoshinori; Kanbara, Ryo; Takada, Yukyo; Ochiai, Kent T; Tanaka, Yoshinobu

2014-01-01

The finite element method has been considered to be excellent evaluative technique to study magnetic circuit optimization. The present study analyzed and quantitatively evaluated the different effects of magnetic circuit on attractive force and magnetic flux density using a three-dimensional finite element method for comparative evaluation. The diameter of a non-magnetic material in the shield disk of a magnetic assembly was variably increased by 0.1 mm to a maximum 2.0 mm in this study design. The analysis results demonstrate that attractive force increases until the diameter of the non-magnetic spacing material reaches a diameter of 0.5 mm where it peaks and then decreases as the overall diameter increases over 0.5 mm. The present analysis suggested that the attractive force for a magnetic attachment is optimized with an appropriate magnetic assembly shield disk diameter using a non-magnetic material to effectively change the magnetic circuit efficiency and resulting retention.

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

DOE PAGES

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

1995-01-01

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

Chiral phase transition at finite chemical potential in 2 +1 -flavor soft-wall anti-de Sitter space QCD

NASA Astrophysics Data System (ADS)

Bartz, Sean P.; Jacobson, Theodore

2018-04-01

The phase transition from hadronic matter to chirally symmetric quark-gluon plasma is expected to be a rapid crossover at zero quark chemical potential (μ ), becoming first order at some finite value of μ , indicating the presence of a critical point. Using a three-flavor soft-wall model of anti-de Sitter/QCD, we investigate the effect of varying the light and strange quark masses on the order of the chiral phase transition. At zero quark chemical potential, we reproduce the Columbia Plot, which summarizes the results of lattice QCD and other holographic models. We then extend this holographic model to examine the effects of finite quark chemical potential. We find that the the chemical potential does not affect the critical line that separates first-order from rapid crossover transitions. This excludes the possibility of a critical point in this model, suggesting that a different setup is necessary to reproduce all the features of the QCD phase diagram.

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

NASA Technical Reports Server (NTRS)

Blosser, Max L.

2012-01-01

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

Principal component analysis for fermionic critical points

NASA Astrophysics Data System (ADS)

Costa, Natanael C.; Hu, Wenjian; Bai, Z. J.; Scalettar, Richard T.; Singh, Rajiv R. P.

2017-11-01

We use determinant quantum Monte Carlo (DQMC), in combination with the principal component analysis (PCA) approach to unsupervised learning, to extract information about phase transitions in several of the most fundamental Hamiltonians describing strongly correlated materials. We first explore the zero-temperature antiferromagnet to singlet transition in the periodic Anderson model, the Mott insulating transition in the Hubbard model on a honeycomb lattice, and the magnetic transition in the 1/6-filled Lieb lattice. We then discuss the prospects for learning finite temperature superconducting transitions in the attractive Hubbard model, for which there is no sign problem. Finally, we investigate finite temperature charge density wave (CDW) transitions in the Holstein model, where the electrons are coupled to phonon degrees of freedom, and carry out a finite size scaling analysis to determine Tc. We examine the different behaviors associated with Hubbard-Stratonovich auxiliary field configurations on both the entire space-time lattice and on a single imaginary time slice, or other quantities, such as equal-time Green's and pair-pair correlation functions.

A pseudo energy-invariant method for relativistic wave equations with Riesz space-fractional derivatives

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.; Hendy, A. S.; De Staelen, R. H.

2018-03-01

In this work, we investigate a general nonlinear wave equation with Riesz space-fractional derivatives that generalizes various classical hyperbolic models, including the sine-Gordon and the Klein-Gordon equations from relativistic quantum mechanics. A finite-difference discretization of the model is provided using fractional centered differences. The method is a technique that is capable of preserving an energy-like quantity at each iteration. Some computational comparisons against solutions available in the literature are performed in order to assess the capability of the method to preserve the invariant. Our experiments confirm that the technique yields good approximations to the solutions considered. As an application of our scheme, we provide simulations that confirm, for the first time in the literature, the presence of the phenomenon of nonlinear supratransmission in Riesz space-fractional Klein-Gordon equations driven by a harmonic perturbation at the boundary.

Updating the Finite Element Model of the Aerostructures Test Wing Using Ground Vibration Test Data

NASA Technical Reports Server (NTRS)

Lung, Shun-Fat; Pak, Chan-Gi

2009-01-01

Improved and/or accelerated decision making is a crucial step during flutter certification processes. Unfortunately, most finite element structural dynamics models have uncertainties associated with model validity. Tuning the finite element model using measured data to minimize the model uncertainties is a challenging task in the area of structural dynamics. The model tuning process requires not only satisfactory correlations between analytical and experimental results, but also the retention of the mass and stiffness properties of the structures. Minimizing the difference between analytical and experimental results is a type of optimization problem. By utilizing the multidisciplinary design, analysis, and optimization (MDAO) tool in order to optimize the objective function and constraints; the mass properties, the natural frequencies, and the mode shapes can be matched to the target data to retain the mass matrix orthogonality. This approach has been applied to minimize the model uncertainties for the structural dynamics model of the aerostructures test wing (ATW), which was designed and tested at the National Aeronautics and Space Administration Dryden Flight Research Center (Edwards, California). This study has shown that natural frequencies and corresponding mode shapes from the updated finite element model have excellent agreement with corresponding measured data.

Updating the Finite Element Model of the Aerostructures Test Wing using Ground Vibration Test Data

NASA Technical Reports Server (NTRS)

Lung, Shun-fat; Pak, Chan-gi

2009-01-01

Improved and/or accelerated decision making is a crucial step during flutter certification processes. Unfortunately, most finite element structural dynamics models have uncertainties associated with model validity. Tuning the finite element model using measured data to minimize the model uncertainties is a challenging task in the area of structural dynamics. The model tuning process requires not only satisfactory correlations between analytical and experimental results, but also the retention of the mass and stiffness properties of the structures. Minimizing the difference between analytical and experimental results is a type of optimization problem. By utilizing the multidisciplinary design, analysis, and optimization (MDAO) tool in order to optimize the objective function and constraints; the mass properties, the natural frequencies, and the mode shapes can be matched to the target data to retain the mass matrix orthogonality. This approach has been applied to minimize the model uncertainties for the structural dynamics model of the Aerostructures Test Wing (ATW), which was designed and tested at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center (DFRC) (Edwards, California). This study has shown that natural frequencies and corresponding mode shapes from the updated finite element model have excellent agreement with corresponding measured data.

A New Linearized Crank-Nicolson Mixed Element Scheme for the Extended Fisher-Kolmogorov Equation

PubMed Central

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L 2(Ω))2 space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L 2 and H 1-norm for both the scalar unknown u and the diffusion term w = −Δu and a priori error estimates in (L 2)2-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes. PMID:23864831

A new linearized Crank-Nicolson mixed element scheme for the extended Fisher-Kolmogorov equation.

PubMed

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei; Liu, Yang

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L²(Ω))² space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L² and H¹-norm for both the scalar unknown u and the diffusion term w = -Δu and a priori error estimates in (L²)²-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes.

Coupled Loads Analysis of the Modified NASA Barge Pegasus and Space Launch System Hardware

NASA Technical Reports Server (NTRS)

Knight, J. Brent

2015-01-01

A Coupled Loads Analysis (CLA) has been performed for barge transport of Space Launch System hardware on the recently modified NASA barge Pegasus. The barge re-design was facilitated with detailed finite element analyses by the ARMY Corps of Engineers - Marine Design Center. The Finite Element Model (FEM) utilized in the design was also used in the subject CLA. The Pegasus FEM and CLA results are presented as well as a comparison of the analysis process to that of a payload being transported to space via the Space Shuttle. Discussion of the dynamic forcing functions is included as well. The process of performing a dynamic CLA of NASA hardware during marine transport is thought to be a first and can likely support minimization of undue conservatism.

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

On Replacing "Quantum Thinking" with Counterfactual Reasoning

NASA Astrophysics Data System (ADS)

Narens, Louis

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

Effect of Lamina Thickness of Prepreg on the Surface Accuracy of Carbon Fiber Composite Space Mirrors

NASA Astrophysics Data System (ADS)

Yang, Zhiyong; Tang, Zhanwen; Xie, Yongjie; Shi, Hanqiao; Zhang, Boming; Guo, Hongjun

2018-02-01

Composite space mirror can completely replicate the high-precision surface of mould by replication process, but the actual surface accuracy of the replication composite mirror always decreases. Lamina thickness of prepreg affects the layers and layup sequence of composite space mirror, and which would affect surface accuracy of space mirror. In our research, two groups of contrasting cases through finite element analyses (FEA) and comparative experiments were studied; the effect of different lamina thicknesses of prepreg and corresponding lay-up sequences was focused as well. We describe a special analysis model, validated process and result analysis. The simulated and measured surface figures both get the same conclusion. Reducing lamina thickness of prepreg used in replicating composite space mirror is propitious to optimal design of layup sequence for fabricating composite mirror, and could improve its surface accuracy.

A study of the effect of space-dependent neutronics on stochastically-induced bifurcations in BWR dynamics

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

Analytis, G.T.

1995-09-01

A non-linear one-group space-dependent neutronic model for a finite one-dimensional core is coupled with a simple BWR feed-back model. In agreement with results obtained by the authors who originally developed the point-kinetics version of this model, we shall show numerically that stochastic reactivity excitations may result in limit-cycles and eventually in a chaotic behaviour, depending on the magnitude of the feed-back coefficient K. In the framework of this simple space-dependent model, the effect of the non-linearities on the different spatial harmonics is studied and the importance of the space-dependent effects is exemplified and assessed in terms of the importance ofmore » the higher harmonics. It is shown that under certain conditions, when the limit-cycle-type develop, the neutron spectra may exhibit strong space-dependent effects.« less

Scattering of targets over layered half space using a semi-analytic method in conjunction with FDTD algorithm.

PubMed

Cao, Le; Wei, Bing

2014-08-25

Finite-difference time-domain (FDTD) algorithm with a new method of plane wave excitation is used to investigate the RCS (Radar Cross Section) characteristics of targets over layered half space. Compare with the traditional excitation plane wave method, the calculation memory and time requirement is greatly decreased. The FDTD calculation is performed with a plane wave incidence, and the RCS of far field is obtained by extrapolating the currently calculated data on the output boundary. However, methods available for extrapolating have to evaluate the half space Green function. In this paper, a new method which avoids using the complex and time-consuming half space Green function is proposed. Numerical results show that this method is in good agreement with classic algorithm and it can be used in the fast calculation of scattering and radiation of targets over layered half space.

Near-field investigation of the effect of the array edge on the resonance of loop frequency selective surface elements at mid-infrared wavelengths.

PubMed

Tucker, Eric; D' Archangel, Jeffrey; Raschke, Markus B; Boreman, Glenn

2015-05-04

Mid-infrared scattering scanning near-field optical microscopy, in combination with far-field infrared spectroscopy, and simulations, was employed to investigate the effect of mutual-element coupling towards the edge of arrays of loop elements acting as frequency selective surfaces (FSSs). Two different square loop arrays on ZnS over a ground plane, resonant at 10.3 µm, were investigated. One array had elements that were closely spaced while the other array had elements with greater inter-element spacing. In addition to the dipolar resonance, we observed a new emergent resonance associated with the edge of the closely-spaced array as a finite size effect, due to the broken translational invariance.

Hybrid finite difference/finite element immersed boundary method.

PubMed

E Griffith, Boyce; Luo, Xiaoyu

2017-12-01

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International  Journal  for  Numerical  Methods  in  Biomedical  Engineering Published by John Wiley & Sons Ltd.

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

NASA Astrophysics Data System (ADS)

Aguirre, E. E.; Karchewski, B.

2017-12-01

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

The Quantized Geometry of Visual Space: The Coherent Computation of Depth, Form, and Lightness. Revised Version.

DTIC Science & Technology

1982-08-01

of sensitivity with background luminance, and the finitE capacity of visual short term memory are discussed in terms of a small set of ...binocular rivalry, reflectance rivalry, Fechner’s paradox, decrease of threshold contrast with increased number of cycles in a grating pattern, hysteresis...adaptation level tuning, Weber law modulation, shift of sensitivity with background luminance, and the finite capacity of visual

Solution of the Average-Passage Equations for the Incompressible Flow through Multiple-Blade-Row Turbomachinery

DTIC Science & Technology

1994-02-01

numerical treatment. An explicit numerical procedure based on Runqe-Kutta time stepping for cell-centered, hexahedral finite volumes is...An explicit numerical procedure based on Runge-Kutta time stepping for cell-centered, hexahedral finite volumes is outlined for the approximate...Discretization 16 3.1 Cell-Centered Finite -Volume Discretization in Space 16 3.2 Artificial Dissipation 17 3.3 Time Integration 21 3.4 Convergence

A more accurate modeling of the effects of actuators in large space structures

NASA Technical Reports Server (NTRS)

Hablani, H. B.

1981-01-01

The paper deals with finite actuators. A nonspinning three-axis stabilized space vehicle having a two-dimensional large structure and a rigid body at the center is chosen for analysis. The torquers acting on the vehicle are modeled as antisymmetric forces distributed in a small but finite area. In the limit they represent point torquers which also are treated as a special case of surface distribution of dipoles. Ordinary and partial differential equations governing the forced vibrations of the vehicle are derived by using Hamilton's principle. Associated modal inputs are obtained for both the distributed moments and the distributed forces. It is shown that the finite torquers excite the higher modes less than the point torquers. Modal cost analysis proves to be a suitable methodology to this end.

Dynamic analysis of Space Shuttle/RMS configuration using continuum approach

NASA Technical Reports Server (NTRS)

Ramakrishnan, Jayant; Taylor, Lawrence W., Jr.

1994-01-01

The initial assembly of Space Station Freedom involves the Space Shuttle, its Remote Manipulation System (RMS) and the evolving Space Station Freedom. The dynamics of this coupled system involves both the structural and the control system dynamics of each of these components. The modeling and analysis of such an assembly is made even more formidable by kinematic and joint nonlinearities. The current practice of modeling such flexible structures is to use finite element modeling in which the mass and interior dynamics is ignored between thousands of nodes, for each major component. The model characteristics of only tens of modes are kept out of thousands which are calculated. The components are then connected by approximating the boundary conditions and inserting the control system dynamics. In this paper continuum models are used instead of finite element models because of the improved accuracy, reduced number of model parameters, the avoidance of model order reduction, and the ability to represent the structural and control system dynamics in the same system of equations. Dynamic analysis of linear versions of the model is performed and compared with finite element model results. Additionally, the transfer matrix to continuum modeling is presented.

A finite state projection algorithm for the stationary solution of the chemical master equation.

PubMed

Gupta, Ankit; Mikelson, Jan; Khammash, Mustafa

2017-10-21

The chemical master equation (CME) is frequently used in systems biology to quantify the effects of stochastic fluctuations that arise due to biomolecular species with low copy numbers. The CME is a system of ordinary differential equations that describes the evolution of probability density for each population vector in the state-space of the stochastic reaction dynamics. For many examples of interest, this state-space is infinite, making it difficult to obtain exact solutions of the CME. To deal with this problem, the Finite State Projection (FSP) algorithm was developed by Munsky and Khammash [J. Chem. Phys. 124(4), 044104 (2006)], to provide approximate solutions to the CME by truncating the state-space. The FSP works well for finite time-periods but it cannot be used for estimating the stationary solutions of CMEs, which are often of interest in systems biology. The aim of this paper is to develop a version of FSP which we refer to as the stationary FSP (sFSP) that allows one to obtain accurate approximations of the stationary solutions of a CME by solving a finite linear-algebraic system that yields the stationary distribution of a continuous-time Markov chain over the truncated state-space. We derive bounds for the approximation error incurred by sFSP and we establish that under certain stability conditions, these errors can be made arbitrarily small by appropriately expanding the truncated state-space. We provide several examples to illustrate our sFSP method and demonstrate its efficiency in estimating the stationary distributions. In particular, we show that using a quantized tensor-train implementation of our sFSP method, problems admitting more than 100 × 10 6 states can be efficiently solved.

A finite state projection algorithm for the stationary solution of the chemical master equation

NASA Astrophysics Data System (ADS)

Gupta, Ankit; Mikelson, Jan; Khammash, Mustafa

2017-10-01

The chemical master equation (CME) is frequently used in systems biology to quantify the effects of stochastic fluctuations that arise due to biomolecular species with low copy numbers. The CME is a system of ordinary differential equations that describes the evolution of probability density for each population vector in the state-space of the stochastic reaction dynamics. For many examples of interest, this state-space is infinite, making it difficult to obtain exact solutions of the CME. To deal with this problem, the Finite State Projection (FSP) algorithm was developed by Munsky and Khammash [J. Chem. Phys. 124(4), 044104 (2006)], to provide approximate solutions to the CME by truncating the state-space. The FSP works well for finite time-periods but it cannot be used for estimating the stationary solutions of CMEs, which are often of interest in systems biology. The aim of this paper is to develop a version of FSP which we refer to as the stationary FSP (sFSP) that allows one to obtain accurate approximations of the stationary solutions of a CME by solving a finite linear-algebraic system that yields the stationary distribution of a continuous-time Markov chain over the truncated state-space. We derive bounds for the approximation error incurred by sFSP and we establish that under certain stability conditions, these errors can be made arbitrarily small by appropriately expanding the truncated state-space. We provide several examples to illustrate our sFSP method and demonstrate its efficiency in estimating the stationary distributions. In particular, we show that using a quantized tensor-train implementation of our sFSP method, problems admitting more than 100 × 106 states can be efficiently solved.

Design optimization of space structures

NASA Technical Reports Server (NTRS)

Felippa, Carlos

1991-01-01

The topology-shape-size optimization of space structures is investigated through Kikuchi's homogenization method. The method starts from a 'design domain block,' which is a region of space into which the structure is to materialize. This domain is initially filled with a finite element mesh, typically regular. Force and displacement boundary conditions corresponding to applied loads and supports are applied at specific points in the domain. An optimal structure is to be 'carved out' of the design under two conditions: (1) a cost function is to be minimized, and (2) equality or inequality constraints are to be satisfied. The 'carving' process is accomplished by letting microstructure holes develop and grow in elements during the optimization process. These holes have a rectangular shape in two dimensions and a cubical shape in three dimensions, and may also rotate with respect to the reference axes. The properties of the perforated element are obtained through an homogenization procedure. Once a hole reaches the volume of the element, that element effectively disappears. The project has two phases. In the first phase the method was implemented as the combination of two computer programs: a finite element module, and an optimization driver. In the second part, focus is on the application of this technique to planetary structures. The finite element part of the method was programmed for the two-dimensional case using four-node quadrilateral elements to cover the design domain. An element homogenization technique different from that of Kikuchi and coworkers was implemented. The optimization driver is based on an augmented Lagrangian optimizer, with the volume constraint treated as a Courant penalty function. The optimizer has to be especially tuned to this type of optimization because the number of design variables can reach into the thousands. The driver is presently under development.

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

PubMed

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

2015-03-01

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

Efficient development and processing of thermal math models of very large space truss structures

NASA Technical Reports Server (NTRS)

Warren, Andrew H.; Arelt, Joseph E.; Lalicata, Anthony L.

1993-01-01

As the spacecraft moves along the orbit, the truss members are subjected to direct and reflected solar, albedo and planetary infra-red (IR) heating rates, as well as IR heating and shadowing from other spacecraft components. This is a transient process with continuously changing heating loads and the shadowing effects. The resulting nonuniform temperature distribution may cause nonuniform thermal expansion, deflection and stress in the truss elements, truss warping and thermal distortions. There are three challenges in the thermal-structural analysis of the large truss structures. The first is the development of the thermal and structural math models, the second - model processing, and the third - the data transfer between the models. All three tasks require considerable time and computer resources to be done because of a very large number of components involved. To address these challenges a series of techniques of automated thermal math modeling and efficient processing of very large space truss structures were developed. In the process the finite element and finite difference methods are interfaced. A very substantial reduction of the quantity of computations was achieved while assuring a desired accuracy of the results. The techniques are illustrated on the thermal analysis of a segment of the Space Station main truss.

Molecular Dynamics Investigation of Each Bubble Behavior in Coarsening of Cavitation Bubbles in a Finite Space

NASA Astrophysics Data System (ADS)

Tsuda, Shin-Ichi; Nakano, Yuta; Watanabe, Satoshi

2017-11-01

Recently, several studies using Molecular Dynamics (MD) simulation have been conducted for investigation of Ostwald ripening of cavitation bubbles in a finite space. The previous studies focused a characteristic length of bubbles as one of the spatially-averaged quantities, but each bubble behavior was not been investigated in detail. The objective of this study is clarification of the characteristics of each bubble behavior in Ostwald ripening, and we conducted MD simulation of a Lennard-Jones fluid in a semi-confined space. As a result, the time dependency of the characteristic length of bubbles as a spatially-averaged quantity suggested that the driving force of the Ostwald ripening is Evaporation/Condensation (EC) across liquid-vapor surface, which is the same result as the previous works. The radius change of the relatively larger bubbles also showed the same tendency to a classical EC model. However, the sufficiently smaller bubbles than the critical size, e.g., the bubbles just before collapsing, showed a different characteristic from the classical EC model. Those smaller bubbles has a tendency to be limited by mechanical non-equilibrium in which viscosity of liquid is dominant rather than by EC across liquid-vapor surface. This work was supported by JSPS KAKENHI Grant Number JP16K06085.

Finite Difference Model of a Four-Electrode Conductivity Measurement System

DTIC Science & Technology

2016-05-27

for an infinite half space with electrodes placed on the air/media boundary : 1 Less...8) The left hand side of Equation (8) can be converted to a surface integral using Green’s theorem : − � ∇ ∙ �σ���∇ϕ...adjacent to a boundary between two conductivities. The discretized solutions for each face are summed to comprise the surface integral: − � σ

Some Aspects of Essentially Nonoscillatory (ENO) Formulations for the Euler Equations, Part 3

NASA Technical Reports Server (NTRS)

Chakravarthy, Sukumar R.

1990-01-01

An essentially nonoscillatory (ENO) formulation is described for hyperbolic systems of conservation laws. ENO approaches are based on smart interpolation to avoid spurious numerical oscillations. ENO schemes are a superset of Total Variation Diminishing (TVD) schemes. In the recent past, TVD formulations were used to construct shock capturing finite difference methods. At extremum points of the solution, TVD schemes automatically reduce to being first-order accurate discretizations locally, while away from extrema they can be constructed to be of higher order accuracy. The new framework helps construct essentially non-oscillatory finite difference methods without recourse to local reductions of accuracy to first order. Thus arbitrarily high orders of accuracy can be obtained. The basic general ideas of the new approach can be specialized in several ways and one specific implementation is described based on: (1) the integral form of the conservation laws; (2) reconstruction based on the primitive functions; (3) extension to multiple dimensions in a tensor product fashion; and (4) Runge-Kutta time integration. The resulting method is fourth-order accurate in time and space and is applicable to uniform Cartesian grids. The construction of such schemes for scalar equations and systems in one and two space dimensions is described along with several examples which illustrate interesting aspects of the new approach.

Classifier performance prediction for computer-aided diagnosis using a limited dataset.

PubMed

Sahiner, Berkman; Chan, Heang-Ping; Hadjiiski, Lubomir

2008-04-01

In a practical classifier design problem, the true population is generally unknown and the available sample is finite-sized. A common approach is to use a resampling technique to estimate the performance of the classifier that will be trained with the available sample. We conducted a Monte Carlo simulation study to compare the ability of the different resampling techniques in training the classifier and predicting its performance under the constraint of a finite-sized sample. The true population for the two classes was assumed to be multivariate normal distributions with known covariance matrices. Finite sets of sample vectors were drawn from the population. The true performance of the classifier is defined as the area under the receiver operating characteristic curve (AUC) when the classifier designed with the specific sample is applied to the true population. We investigated methods based on the Fukunaga-Hayes and the leave-one-out techniques, as well as three different types of bootstrap methods, namely, the ordinary, 0.632, and 0.632+ bootstrap. The Fisher's linear discriminant analysis was used as the classifier. The dimensionality of the feature space was varied from 3 to 15. The sample size n2 from the positive class was varied between 25 and 60, while the number of cases from the negative class was either equal to n2 or 3n2. Each experiment was performed with an independent dataset randomly drawn from the true population. Using a total of 1000 experiments for each simulation condition, we compared the bias, the variance, and the root-mean-squared error (RMSE) of the AUC estimated using the different resampling techniques relative to the true AUC (obtained from training on a finite dataset and testing on the population). Our results indicated that, under the study conditions, there can be a large difference in the RMSE obtained using different resampling methods, especially when the feature space dimensionality is relatively large and the sample size is small. Under this type of conditions, the 0.632 and 0.632+ bootstrap methods have the lowest RMSE, indicating that the difference between the estimated and the true performances obtained using the 0.632 and 0.632+ bootstrap will be statistically smaller than those obtained using the other three resampling methods. Of the three bootstrap methods, the 0.632+ bootstrap provides the lowest bias. Although this investigation is performed under some specific conditions, it reveals important trends for the problem of classifier performance prediction under the constraint of a limited dataset.

Finite Element Analysis of Wrinkled Membrane Structures for Sunshield Applications

NASA Technical Reports Server (NTRS)

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

2002-01-01

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

Reduced Uncertainties in the Flutter Analysis of the Aerostructures Test Wing

NASA Technical Reports Server (NTRS)

Pak, Chan-gi; Lung, Shun-fat

2010-01-01

Tuning the finite element model using measured data to minimize the model uncertainties is a challenging task in the area of structural dynamics. A test validated finite element model can provide a reliable flutter analysis to define the flutter placard speed to which the aircraft can be flown prior to flight flutter testing. Minimizing the difference between numerical and experimental results is a type of optimization problem. Through the use of the National Aeronautics and Space Administration Dryden Flight Research Center s (Edwards, California, USA) multidisciplinary design, analysis, and optimization tool to optimize the objective function and constraints; the mass properties, the natural frequencies, and the mode shapes are matched to the target data and the mass matrix orthogonality is retained. The approach in this study has been applied to minimize the model uncertainties for the structural dynamic model of the aerostructures test wing, which was designed, built, and tested at the National Aeronautics and Space Administration Dryden Flight Research Center. A 25-percent change in flutter speed has been shown after reducing the uncertainties

Non-reciprocal elastic wave propagation in 2D phononic membranes with spatiotemporally varying material properties

NASA Astrophysics Data System (ADS)

Attarzadeh, M. A.; Nouh, M.

2018-05-01

One-dimensional phononic materials with material fields traveling simultaneously in space and time have been shown to break elastodynamic reciprocity resulting in unique wave propagation features. In the present work, a comprehensive mathematical analysis is presented to characterize and fully predict the non-reciprocal wave dispersion in two-dimensional space. The analytical dispersion relations, in the presence of the spatiotemporal material variations, are validated numerically using finite 2D membranes with a prescribed number of cells. Using omnidirectional excitations at the membrane's center, wave propagations are shown to exhibit directional asymmetry that increases drastically in the direction of the material travel and vanishes in the direction perpendicular to it. The topological nature of the predicted dispersion in different propagation directions are evaluated using the computed Chern numbers. Finally, the degree of the 2D non-reciprocity is quantified using a non-reciprocity index (NRI) which confirms the theoretical dispersion predictions as well as the finite simulations. The presented framework can be extended to plate-type structures as well as 3D spatiotemporally modulated phononic crystals.

Reduced Uncertainties in the Flutter Analysis of the Aerostructures Test Wing

NASA Technical Reports Server (NTRS)

Pak, Chan-Gi; Lung, Shun Fat

2011-01-01

Tuning the finite element model using measured data to minimize the model uncertainties is a challenging task in the area of structural dynamics. A test validated finite element model can provide a reliable flutter analysis to define the flutter placard speed to which the aircraft can be flown prior to flight flutter testing. Minimizing the difference between numerical and experimental results is a type of optimization problem. Through the use of the National Aeronautics and Space Administration Dryden Flight Research Center's (Edwards, California) multidisciplinary design, analysis, and optimization tool to optimize the objective function and constraints; the mass properties, the natural frequencies, and the mode shapes are matched to the target data, and the mass matrix orthogonality is retained. The approach in this study has been applied to minimize the model uncertainties for the structural dynamic model of the aerostructures test wing, which was designed, built, and tested at the National Aeronautics and Space Administration Dryden Flight Research Center. A 25 percent change in flutter speed has been shown after reducing the uncertainties.

Light diffusion in N-layered turbid media: steady-state domain.

PubMed

Liemert, André; Kienle, Alwin

2010-01-01

We deal with light diffusion in N-layered turbid media. The steady-state diffusion equation is solved for N-layered turbid media having a finite or an infinitely thick N'th layer. Different refractive indices are considered in the layers. The Fourier transform formalism is applied to derive analytical solutions of the fluence rate in Fourier space. The inverse Fourier transform is calculated using four different methods to test their performance and accuracy. Further, to avoid numerical errors, approximate formulas in Fourier space are derived. Fast solutions for calculation of the spatially resolved reflectance and transmittance from the N-layered turbid media ( approximately 10 ms) with small relative differences (<10(-7)) are found. Additionally, the solutions of the diffusion equation are compared to Monte Carlo simulations for turbid media having up to 20 layers.

Gels and gel-derived glasses in the Na2O-B2O3-SiO2 system. [containerless melting in space

NASA Technical Reports Server (NTRS)

Mukherjee, S. P.

1982-01-01

The containerless melting of high-purity multicomponent homogeneous gels and gel-monoliths offers a unique approach to making ultrapure multicomponent optical glasses in the reduced gravity environment of space. Procedures for preparing and characterizing gels and gel-derived glasses in the Na2O-B2O3-SiO2 system are described. Preparation is based on the polymerization reactions of alkoxysilane with trimethyl borate or boric acid and a suitable sodium compound. The chemistry of the gelling process is discussed in terms of process parameters and the gel compositions. The physicochemical nature of gels prepared by three different procedures were found to be significantly different. IR absorption spectra indicate finite differences in the molecular structures of the different gels. The melting of the gel powders and the transformation of porous gel-monoliths to transparent 'glass' without melting are described.

A direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D

NASA Astrophysics Data System (ADS)

Boscheri, Walter; Dumbser, Michael

2014-10-01

In this paper we present a new family of high order accurate Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial differential equations with stiff source terms on moving tetrahedral meshes in three space dimensions. A WENO reconstruction technique is used to achieve high order of accuracy in space, while an element-local space-time Discontinuous Galerkin finite element predictor on moving curved meshes is used to obtain a high order accurate one-step time discretization. Within the space-time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space-time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space-time nodes. Since our algorithm is cell-centered, the final mesh motion is computed by using a suitable node solver algorithm. A rezoning step as well as a flattener strategy are used in some of the test problems to avoid mesh tangling or excessive element deformations that may occur when the computation involves strong shocks or shear waves. The ALE algorithm presented in this article belongs to the so-called direct ALE methods because the final Lagrangian finite volume scheme is based directly on a space-time conservation formulation of the governing PDE system, with the rezoned geometry taken already into account during the computation of the fluxes. We apply our new high order unstructured ALE schemes to the 3D Euler equations of compressible gas dynamics, for which a set of classical numerical test problems has been solved and for which convergence rates up to sixth order of accuracy in space and time have been obtained. We furthermore consider the equations of classical ideal magnetohydrodynamics (MHD) as well as the non-conservative seven-equation Baer-Nunziato model of compressible multi-phase flows with stiff relaxation source terms.

Giant Linear Nonreciprocity, Zero Reflection, and Zero Band Gap in Equilibrated Space-Time-Varying Media

NASA Astrophysics Data System (ADS)

Taravati, Sajjad

2018-06-01

This article presents a class of space-time-varying media with giant linear nonreciprocity, zero space-time local reflections, and zero photonic band gap. This is achieved via equilibrium in the electric and magnetic properties of unidirectionally space-time-modulated media. The enhanced nonreciprocity is accompanied by a larger sonic regime interval which provides extra design freedom for achieving strong nonreciprocity by a weak pumping strength. We show that the width of photonic band gaps in general periodic space-time permittivity- and permeability-modulated media is proportional to the absolute difference between the electric and magnetic pumping strengths. We derive a rigorous analytical solution for investigation of wave propagation and scattering from general periodic space-time permittivity- and permeability-modulated media. In contrast with weak photonic transitions, from the excited mode to its two adjacent modes, in conventional space-time permittivity-modulated media, in an equilibrated space-time-varying medium, strong photonic transitions occur from the excited mode to its four adjacent modes. We study the enhanced nonreciprocity and zero band gap in equilibrated space-time-modulated media by analysis of their dispersion diagrams. In contrast to conventional space-time permittivity-modulated media, equilibrated space-time media exhibit different phase and group velocities for forward and backward harmonics. Furthermore, the numerical simulation scheme of general space-time permittivity- and permeability-modulated media is presented, which is based on the finite-difference time-domain technique. Our analytical and numerical results provide insights into general space-time refractive-index-modulated media, paving the way toward optimal isolators, nonreciprocal integrated systems, and subharmonic frequency generators.

A System of Poisson Equations for a Nonconstant Varadhan Functional on a Finite State Space

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

Cavazos-Cadena, Rolando; Hernandez-Hernandez, Daniel

2006-01-15

Given a discrete-time Markov chain with finite state space and a stationary transition matrix, a system of 'local' Poisson equations characterizing the (exponential) Varadhan's functional J(.) is given. The main results, which are derived for an arbitrary transition structure so that J(.) may be nonconstant, are as follows: (i) Any solution to the local Poisson equations immediately renders Varadhan's functional, and (ii) a solution of the system always exist. The proof of this latter result is constructive and suggests a method to solve the local Poisson equations.

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).

Dispersion analysis of the Pn -Pn-1DG mixed finite element pair for atmospheric modelling

NASA Astrophysics Data System (ADS)

Melvin, Thomas

2018-02-01

Mixed finite element methods provide a generalisation of staggered grid finite difference methods with a framework to extend the method to high orders. The ability to generate a high order method is appealing for applications on the kind of quasi-uniform grids that are popular for atmospheric modelling, so that the method retains an acceptable level of accuracy even around special points in the grid. The dispersion properties of such schemes are important to study as they provide insight into the numerical adjustment to imbalance that is an important component in atmospheric modelling. This paper extends the recent analysis of the P2 - P1DG pair, that is a quadratic continuous and linear discontinuous finite element pair, to higher polynomial orders and also spectral element type pairs. In common with the previously studied element pair, and also with other schemes such as the spectral element and discontinuous Galerkin methods, increasing the polynomial order is found to provide a more accurate dispersion relation for the well resolved part of the spectrum but at the cost of a number of unphysical spectral gaps. The effects of these spectral gaps are investigated and shown to have a varying impact depending upon the width of the gap. Finally, the tensor product nature of the finite element spaces is exploited to extend the dispersion analysis into two-dimensions.

Thermodynamic theory of intrinsic finite-size effects in PbTiO3 nanocrystals. I. Nanoparticle size-dependent tetragonal phase stability

NASA Astrophysics Data System (ADS)

Akdogan, E. K.; Safari, A.

2007-03-01

We propose a phenomenological intrinsic finite-size effect model for single domain, mechanically free, and surface charge compensated ΔG-P ⃗s-ξ space, which describes the decrease in tetragonal phase stability with decreasing ξ rigorously.

Statistical mechanics of free particles on space with Lie-type noncommutativity

NASA Astrophysics Data System (ADS)

Shariati, Ahmad; Khorrami, Mohammad; Fatollahi, Amir H.

2010-07-01

Effects of Lie-type noncommutativity on thermodynamic properties of a system of free identical particles are investigated. A definition for finite volume of the configuration space is given, and the grandcanonical partition function in the thermodynamic limit is calculated. Two possible definitions for the pressure are discussed, which are equivalent when the noncommutativity vanishes. The thermodynamic observables are extracted from the partition function. Different limits are discussed where either the noncommutativity or the quantum effects are important. Finally, specific cases are discussed where the group is SU(2) or SO(3), and the partition function of a nondegenerate gas is calculated.

Impact on the earth, ocean and atmosphere

NASA Technical Reports Server (NTRS)

Ahrens, Thomas J.; O'Keefe, John D.

1987-01-01

On the basis of finite-difference techniques, cratering flow calculations are used to obtain the spatial attenuation of shock pressure with radius along the impact axis for the impact of silicate rock and iron impactors on a silicate half-space at speeds of 5 to 45 km/sec. Upon impact of a 10 to 30 km diameter silicate or water object onto a 5 km deep ocean overlying a silicate half-space planet at 30 km/sec, it is found that from 12 to 15 percent of the incident energy is coupled into the water. The mass of atmosphere lost due to impacts of 1 to 5 km radius projectiles is calculated.

Laser diode initiated detonators for space applications

NASA Technical Reports Server (NTRS)

Ewick, David W.; Graham, J. A.; Hawley, J. D.

1993-01-01

Ensign Bickford Aerospace Company (EBAC) has over ten years of experience in the design and development of laser ordnance systems. Recent efforts have focused on the development of laser diode ordnance systems for space applications. Because the laser initiated detonators contain only insensitive secondary explosives, a high degree of system safety is achieved. Typical performance characteristics of a laser diode initiated detonator are described in this paper, including all-fire level, function time, and output. A finite difference model used at EBAC to predict detonator performance, is described and calculated results are compared to experimental data. Finally, the use of statistically designed experiments to evaluate performance of laser initiated detonators is discussed.

Finite-frequency sensitivity kernels for head waves

NASA Astrophysics Data System (ADS)

Zhang, Zhigang; Shen, Yang; Zhao, Li

2007-11-01

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

On the dynamics of approximating schemes for dissipative nonlinear equations

NASA Technical Reports Server (NTRS)

Jones, Donald A.

1993-01-01

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

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.

A method for solution of the Euler-Bernoulli beam equation in flexible-link robotic systems

NASA Technical Reports Server (NTRS)

Tzes, Anthony P.; Yurkovich, Stephen; Langer, F. Dieter

1989-01-01

An efficient numerical method for solving the partial differential equation (PDE) governing the flexible manipulator control dynamics is presented. A finite-dimensional model of the equation is obtained through discretization in both time and space coordinates by using finite-difference approximations to the PDE. An expert program written in the Macsyma symbolic language is utilized in order to embed the boundary conditions into the program, accounting for a mass carried at the tip of the manipulator. The advantages of the proposed algorithm are many, including the ability to (1) include any distributed actuation term in the partial differential equation, (2) provide distributed sensing of the beam displacement, (3) easily modify the boundary conditions through an expert program, and (4) modify the structure for running under a multiprocessor environment.

Novel quadrilateral elements based on explicit Hermite polynomials for bending of Kirchhoff-Love plates

NASA Astrophysics Data System (ADS)

Beheshti, Alireza

2018-03-01

The contribution addresses the finite element analysis of bending of plates given the Kirchhoff-Love model. To analyze the static deformation of plates with different loadings and geometries, the principle of virtual work is used to extract the weak form. Following deriving the strain field, stresses and resultants may be obtained. For constructing four-node quadrilateral plate elements, the Hermite polynomials defined with respect to the variables in the parent space are applied explicitly. Based on the approximated field of displacement, the stiffness matrix and the load vector in the finite element method are obtained. To demonstrate the performance of the subparametric 4-node plate elements, some known, classical examples in structural mechanics are solved and there are comparisons with the analytical solutions available in the literature.

NPLOT: an Interactive Plotting Program for NASTRAN Finite Element Models

NASA Technical Reports Server (NTRS)

Jones, G. K.; Mcentire, K. J.

1985-01-01

The NPLOT (NASTRAN Plot) is an interactive computer graphics program for plotting undeformed and deformed NASTRAN finite element models. Developed at NASA's Goddard Space Flight Center, the program provides flexible element selection and grid point, ASET and SPC degree of freedom labelling. It is easy to use and provides a combination menu and command driven user interface. NPLOT also provides very fast hidden line and haloed line algorithms. The hidden line algorithm in NPLOT proved to be both very accurate and several times faster than other existing hidden line algorithms. A fast spatial bucket sort and horizon edge computation are used to achieve this high level of performance. The hidden line and the haloed line algorithms are the primary features that make NPLOT different from other plotting programs.

The improvement of GaN-based light-emitting diodes using nanopatterned sapphire substrate with small pattern spacing

NASA Astrophysics Data System (ADS)

Zhang, Yonghui; Wei, Tongbo; Wang, Junxi; Lan, Ding; Chen, Yu; Hu, Qiang; Lu, Hongxi; Li, Jinmin

2014-02-01

Self-assembly SiO2 nanosphere monolayer template is utilized to fabricate nanopatterned sapphire substrates (NPSSs) with 0-nm, 50-nm, and 120-nm spacing, receptively. The GaN growth on top of NPSS with 0-nm spacing has the best crystal quality because of laterally epitaxial overgrowth. However, GaN growth from pattern top is more difficult to get smooth surface than from pattern bottom. The rougher surface may result in a higher work voltage. The stimulation results of finite-difference time-domain (FDTD) display that too large or too small spacing lead to the reduced light extracted efficiency (LEE) of LEDs. Under a driving current 350 mA, the external quantum efficiencies (EQE) of GaN-based LEDs grown on NPSSs with 0-nm, 50-nm, and 120-nm spacing increase by 43.3%, 50.6%, and 39.1%, respectively, compared to that on flat sapphire substrate (FSS). The optimized pattern spacing is 50 nm for the NPSS with 600-nm pattern period.

Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method

DOE PAGES

Kalchev, Delyan Z.; Lee, C. S.; Villa, U.; ...

2016-09-22

Here, we propose two multilevel spectral techniques for constructing coarse discretization spaces for saddle-point problems corresponding to PDEs involving a divergence constraint, with a focus on mixed finite element discretizations of scalar self-adjoint second order elliptic equations on general unstructured grids. We use element agglomeration algebraic multigrid (AMGe), which employs coarse elements that can have nonstandard shape since they are agglomerates of fine-grid elements. The coarse basis associated with each agglomerated coarse element is constructed by solving local eigenvalue problems and local mixed finite element problems. This construction leads to stable upscaled coarse spaces and guarantees the inf-sup compatibility ofmore » the upscaled discretization. Also, the approximation properties of these upscaled spaces improve by adding more local eigenfunctions to the coarse spaces. The higher accuracy comes at the cost of additional computational effort, as the sparsity of the resulting upscaled coarse discretization (referred to as operator complexity) deteriorates when we introduce additional functions in the coarse space. We also provide an efficient solver for the coarse (upscaled) saddle-point system by employing hybridization, which leads to a symmetric positive definite (s.p.d.) reduced system for the Lagrange multipliers, and to solve the latter s.p.d. system, we use our previously developed spectral AMGe solver. Numerical experiments, in both two and three dimensions, are provided to illustrate the efficiency of the proposed upscaling technique.« less

Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method

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

Kalchev, Delyan Z.; Lee, C. S.; Villa, U.

Here, we propose two multilevel spectral techniques for constructing coarse discretization spaces for saddle-point problems corresponding to PDEs involving a divergence constraint, with a focus on mixed finite element discretizations of scalar self-adjoint second order elliptic equations on general unstructured grids. We use element agglomeration algebraic multigrid (AMGe), which employs coarse elements that can have nonstandard shape since they are agglomerates of fine-grid elements. The coarse basis associated with each agglomerated coarse element is constructed by solving local eigenvalue problems and local mixed finite element problems. This construction leads to stable upscaled coarse spaces and guarantees the inf-sup compatibility ofmore » the upscaled discretization. Also, the approximation properties of these upscaled spaces improve by adding more local eigenfunctions to the coarse spaces. The higher accuracy comes at the cost of additional computational effort, as the sparsity of the resulting upscaled coarse discretization (referred to as operator complexity) deteriorates when we introduce additional functions in the coarse space. We also provide an efficient solver for the coarse (upscaled) saddle-point system by employing hybridization, which leads to a symmetric positive definite (s.p.d.) reduced system for the Lagrange multipliers, and to solve the latter s.p.d. system, we use our previously developed spectral AMGe solver. Numerical experiments, in both two and three dimensions, are provided to illustrate the efficiency of the proposed upscaling technique.« less

Viewing hybrid systems as products of control systems and automata

NASA Technical Reports Server (NTRS)

Grossman, R. L.; Larson, R. G.

1992-01-01

The purpose of this note is to show how hybrid systems may be modeled as products of nonlinear control systems and finite state automata. By a hybrid system, we mean a network of consisting of continuous, nonlinear control system connected to discrete, finite state automata. Our point of view is that the automata switches between the control systems, and that this switching is a function of the discrete input symbols or letters that it receives. We show how a nonlinear control system may be viewed as a pair consisting of a bialgebra of operators coding the dynamics, and an algebra of observations coding the state space. We also show that a finite automata has a similar representation. A hybrid system is then modeled by taking suitable products of the bialgebras coding the dynamics and the observation algebras coding the state spaces.

The weight hierarchies and chain condition of a class of codes from varieties over finite fields

NASA Technical Reports Server (NTRS)

Wu, Xinen; Feng, Gui-Liang; Rao, T. R. N.

1996-01-01

The generalized Hamming weights of linear codes were first introduced by Wei. These are fundamental parameters related to the minimal overlap structures of the subcodes and very useful in several fields. It was found that the chain condition of a linear code is convenient in studying the generalized Hamming weights of the product codes. In this paper we consider a class of codes defined over some varieties in projective spaces over finite fields, whose generalized Hamming weights can be determined by studying the orbits of subspaces of the projective spaces under the actions of classical groups over finite fields, i.e., the symplectic groups, the unitary groups and orthogonal groups. We give the weight hierarchies and generalized weight spectra of the codes from Hermitian varieties and prove that the codes satisfy the chain condition.

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

USGS Publications Warehouse

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

1998-01-01

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

Turbulent cascade in a two-ion plasma

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

Qiu, Xin; Faculty of Information Engineering, Jiangxi University of Science and Technology, Ganzhou 341000; Liu, San-Qiu, E-mail: sqlgroup@ncu.edu.cn

2014-11-15

It is shown that small but finite-amplitude drift wave turbulence in a two-ion-species plasma can be modeled by a Hasegawa-Mima equation. The mode cascade process and resulting turbulent spectrum are investigated. The spectrum is found to be similar to that of a two-component plasma, but the space and time scales of the turbulent cascade process can be quite different since they are rescaled by the presence of the second ion species.

ADE-FDTD Scattered-Field Formulation for Dispersive Materials

PubMed Central

Kong, Soon-Cheol; Simpson, Jamesina J.; Backman, Vadim

2009-01-01

This Letter presents a scattered-field formulation for modeling dispersive media using the finite-difference time-domain (FDTD) method. Specifically, the auxiliary differential equation method is applied to Drude and Lorentz media for a scattered field FDTD model. The present technique can also be applied in a straightforward manner to Debye media. Excellent agreement is achieved between the FDTD-calculated and exact theoretical results for the reflection coefficient in half-space problems. PMID:19844602

ADE-FDTD Scattered-Field Formulation for Dispersive Materials.

PubMed

Kong, Soon-Cheol; Simpson, Jamesina J; Backman, Vadim

2008-01-01

This Letter presents a scattered-field formulation for modeling dispersive media using the finite-difference time-domain (FDTD) method. Specifically, the auxiliary differential equation method is applied to Drude and Lorentz media for a scattered field FDTD model. The present technique can also be applied in a straightforward manner to Debye media. Excellent agreement is achieved between the FDTD-calculated and exact theoretical results for the reflection coefficient in half-space problems.

Charged boson stars and black holes with nonminimal coupling to gravity

NASA Astrophysics Data System (ADS)

Verbin, Y.; Brihaye, Y.

2018-02-01

We find new spherically symmetric charged boson star solutions of a complex scalar field coupled nonminimally to gravity by a "John-type" term of Horndeski theory, that is a coupling between the kinetic scalar term and Einstein tensor. We study the parameter space of the solutions and find two distinct families according to their position in parameter space. More widespread is the family of solutions (which we call branch 1) existing for a finite interval of the central value of the scalar field starting from zero and ending at some finite maximal value. This branch contains as a special case the charged boson stars of the minimally coupled theory. In some regions of parameter space we find a new second branch ("branch 2") of solutions which are more massive and more stable than those of branch 1. This second branch exists also in a finite interval of the central value of the scalar field, but its end points (either both or in some cases only one) are extremal Reissner-Nordström black hole solutions.

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

NASA Technical Reports Server (NTRS)

Fisher, Travis C.; Carpenter, Mark H.

2013-01-01

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

Survival probability of a truncated radial oscillator subject to periodic kicks

NASA Astrophysics Data System (ADS)

Tanabe, Seiichi; Watanabe, Shinichi; Saif, Farhan; Matsuzawa, Michio

2002-03-01

Classical and quantum survival probabilities are compared for a truncated radial oscillator undergoing impulsive interactions with periodic laser pulses represented here as kicks. The system is truncated in the sense that the harmonic potential is made valid only within a finite range; the rest of the space is treated as a perfect absorber. Exploring extended values of the parameters of this model [Phys. Rev. A 63, 052721 (2001)], we supplement discussions on classical and quantum features near resonances. The classical system proves to be quasi-integrable and preserves phase-space area despite the momentum transfered by the kicks, exhibiting simple yet rich phase-space features. A geometrical argument reveals quantum-classical correspondence in the locations of minima in the paired survival probabilities while the ``ionization'' rates differ due to quantum tunneling.

From Large Deviations to Semidistances of Transport and Mixing: Coherence Analysis for Finite Lagrangian Data

NASA Astrophysics Data System (ADS)

Koltai, Péter; Renger, D. R. Michiel

2018-06-01

One way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport and mixing, finite time coherent sets play an important role. These are time-parametrized families of sets with unlikely transport to and from their surroundings under small or vanishing random perturbations of the dynamics. Here we propose, as a measure of transport and mixing for purely advective (i.e., deterministic) flows, (semi)distances that arise under vanishing perturbations in the sense of large deviations. Analogously, for given finite Lagrangian trajectory data we derive a discrete-time-and-space semidistance that comes from the "best" approximation of the randomly perturbed process conditioned on this limited information of the deterministic flow. It can be computed as shortest path in a graph with time-dependent weights. Furthermore, we argue that coherent sets are regions of maximal farness in terms of transport and mixing, and hence they occur as extremal regions on a spanning structure of the state space under this semidistance—in fact, under any distance measure arising from the physical notion of transport. Based on this notion, we develop a tool to analyze the state space (or the finite trajectory data at hand) and identify coherent regions. We validate our approach on idealized prototypical examples and well-studied standard cases.

A Ring Construction Using Finite Directed Graphs

ERIC Educational Resources Information Center

Bardzell, Michael

2012-01-01

In this paper we discuss an interesting class of noncommutative rings which can be constructed using finite directed graphs. This construction also creates a vector space. These structures provide undergraduate students connections between ring theory and graph theory and, among other things, allow them to see a ring unity element that looks quite…

Analytical Proof That There is no Effect of Confinement or Curvature on the Maxwell-Boltzmann Collision Frequency

NASA Astrophysics Data System (ADS)

Carnio, Brett N.; Elliott, Janet A. W.

2014-08-01

The number of Maxwell-Boltzmann particles that hit a flat wall in infinite space per unit area per unit time is a well-known result. As new applications are arising in micro and nanotechnologies there are a number of situations in which a rarefied gas interacts with either a flat or curved surface in a small confined geometry. Thus, it is necessary to prove that the Maxwell-Boltzmann collision frequency result holds even if a container's dimensions are on the order of nanometers and also that this result is valid for both a finite container with flat walls (a rectangular container) and a finite container with a curved wall (a cylindrical container). An analytical proof confirms that the Maxwell-Boltzmann collision frequencies for either a finite rectangular container or a finite cylindrical container are both equal to the well-known result obtained for a flat wall in infinite space. A major aspect of this paper is the introduction of a mathematical technique to solve the arising infinite sum of integrals whose integrands depend on the Maxwell-Boltzmann velocity distribution.

Micromorphic approach for gradient-extended thermo-elastic-plastic solids in the logarithmic strain space

NASA Astrophysics Data System (ADS)

Aldakheel, Fadi

2017-11-01

The coupled thermo-mechanical strain gradient plasticity theory that accounts for microstructure-based size effects is outlined within this work. It extends the recent work of Miehe et al. (Comput Methods Appl Mech Eng 268:704-734, 2014) to account for thermal effects at finite strains. From the computational viewpoint, the finite element design of the coupled problem is not straightforward and requires additional strategies due to the difficulties near the elastic-plastic boundaries. To simplify the finite element formulation, we extend it toward the micromorphic approach to gradient thermo-plasticity model in the logarithmic strain space. The key point is the introduction of dual local-global field variables via a penalty method, where only the global fields are restricted by boundary conditions. Hence, the problem of restricting the gradient variable to the plastic domain is relaxed, which makes the formulation very attractive for finite element implementation as discussed in Forest (J Eng Mech 135:117-131, 2009) and Miehe et al. (Philos Trans R Soc A Math Phys Eng Sci 374:20150170, 2016).

Computational modeling of human head under blast in confined and open spaces: primary blast injury.

PubMed

Rezaei, A; Salimi Jazi, M; Karami, G

2014-01-01

In this paper, a computational modeling for biomechanical analysis of primary blast injuries is presented. The responses of the brain in terms of mechanical parameters under different blast spaces including open, semi-confined, and confined environments are studied. In the study, the effect of direct and indirect blast waves from the neighboring walls in the confined environments will be taken into consideration. A 50th percentile finite element head model is exposed to blast waves of different intensities. In the open space, the head experiences a sudden intracranial pressure (ICP) change, which vanishes in a matter of a few milliseconds. The situation is similar in semi-confined space, but in the confined space, the reflections from the walls will create a number of subsequent peaks in ICP with a longer duration. The analysis procedure is based on a simultaneous interaction simulation of the deformable head and its components with the blast wave propagations. It is concluded that compared with the open and semi-confined space settings, the walls in the confined space scenario enhance the risk of primary blast injuries considerably because of indirect blast waves transferring a larger amount of damaging energy to the head. Copyright © 2013 John Wiley & Sons, Ltd.

Inferring the Limit Behavior of Some Elementary Cellular Automata

NASA Astrophysics Data System (ADS)

Ruivo, Eurico L. P.; de Oliveira, Pedro P. B.

Cellular automata locally define dynamical systems, discrete in space, time and in the state variables, capable of displaying arbitrarily complex global emergent behavior. One core question in the study of cellular automata refers to their limit behavior, that is, to the global dynamical features in an infinite time evolution. Previous works have shown that for finite time evolutions, the dynamics of one-dimensional cellular automata can be described by regular languages and, therefore, by finite automata. Such studies have shown the existence of growth patterns in the evolution of such finite automata for some elementary cellular automata rules and also inferred the limit behavior of such rules based upon the growth patterns; however, the results on the limit behavior were obtained manually, by direct inspection of the structures that arise during the time evolution. Here we present the formalization of an automatic method to compute such structures. Based on this, the rules of the elementary cellular automata space were classified according to the existence of a growth pattern in their finite automata. Also, we present a method to infer the limit graph of some elementary cellular automata rules, derived from the analysis of the regular expressions that describe their behavior in finite time. Finally, we analyze some attractors of two rules for which we could not compute the whole limit set.

On thick domain walls in general relativity

NASA Technical Reports Server (NTRS)

Goetz, Guenter; Noetzold, Dirk

1989-01-01

Planar scalar field configurations in general relativity differ considerably from those in flat space. It is shown that static domain walls of finite thickness in curved space-time do not possess a reflection symmetry. At infinity, the space-time tends to the Taub vacuum on one side of the wall and to the Minkowski vacuum (Rindler space-time) on the other. Massive test particles are always accelerated towards the Minkowski side, i.e., domain walls are attractive on the Taub side, but repulsive on the Minkowski side (Taub-vacuum cleaner). It is also proved that the pressure in all directions is always negative. Finally, a brief comment is made concerning the possibility of infinite, i.e., bigger than horizon size, domain walls in our universe. All of the results are independent of the form of the potential V(phi) greater than or equal to 0 of the scalar field phi.

Influence of Layup Sequence on the Surface Accuracy of Carbon Fiber Composite Space Mirrors

NASA Astrophysics Data System (ADS)

Yang, Zhiyong; Liu, Qingnian; Zhang, Boming; Xu, Liang; Tang, Zhanwen; Xie, Yongjie

2018-04-01

Layup sequence is directly related to stiffness and deformation resistance of the composite space mirror, and error caused by layup sequence can affect the surface precision of composite mirrors evidently. Variation of layup sequence with the same total thickness of composite space mirror changes surface form of the composite mirror, which is the focus of our study. In our research, the influence of varied quasi-isotropic stacking sequences and random angular deviation on the surface accuracy of composite space mirrors was investigated through finite element analyses (FEA). We established a simulation model for the studied concave mirror with 500 mm diameter, essential factors of layup sequences and random angular deviations on different plies were discussed. Five guiding findings were described in this study. Increasing total plies, optimizing stacking sequence and keeping consistency of ply alignment in ply placement are effective to improve surface accuracy of composite mirror.

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

DTIC Science & Technology

1993-06-01

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

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.

Domain decomposition for a mixed finite element method in three dimensions

USGS Publications Warehouse

Cai, Z.; Parashkevov, R.R.; Russell, T.F.; Wilson, J.D.; Ye, X.

2003-01-01

We consider the solution of the discrete linear system resulting from a mixed finite element discretization applied to a second-order elliptic boundary value problem in three dimensions. Based on a decomposition of the velocity space, these equations can be reduced to a discrete elliptic problem by eliminating the pressure through the use of substructures of the domain. The practicality of the reduction relies on a local basis, presented here, for the divergence-free subspace of the velocity space. We consider additive and multiplicative domain decomposition methods for solving the reduced elliptic problem, and their uniform convergence is established.

Properties of highly frustrated magnetic molecules studied by the finite-temperature Lanczos method

NASA Astrophysics Data System (ADS)

Schnack, J.; Wendland, O.

2010-12-01

The very interesting magnetic properties of frustrated magnetic molecules are often hardly accessible due to the prohibitive size of the related Hilbert spaces. The finite-temperature Lanczos method is able to treat spin systems for Hilbert space sizes up to 109. Here we first demonstrate for exactly solvable systems that the method is indeed accurate. Then we discuss the thermal properties of one of the biggest magnetic molecules synthesized to date, the icosidodecahedron with antiferromagnetically coupled spins of s = 1/2. We show how genuine quantum features such as the magnetization plateau behave as a function of temperature.

Design of invisibility cloaks with an open tunnel.

PubMed

Ako, Thomas; Yan, Min; Qiu, Min

2010-12-20

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

The effects of topography on magma chamber deformation models: Application to Mt. Etna and radar interferometry

NASA Astrophysics Data System (ADS)

Williams, Charles A.; Wadge, Geoff

We have used a three-dimensional elastic finite element model to examine the effects of topography on the surface deformation predicted by models of magma chamber deflation. We used the topography of Mt. Etna to control the geometry of our model, and compared the finite element results to those predicted by an analytical solution for a pressurized sphere in an elastic half-space. Topography has a significant effect on the predicted surface deformation for both displacement profiles and synthetic interferograms. Not only are the predicted displacement magnitudes significantly different, but also the map-view patterns of displacement. It is possible to match the predicted displacement magnitudes fairly well by adjusting the elevation of a reference surface; however, the horizontal pattern of deformation is still significantly different. Thus, inversions based on constant-elevation reference surfaces may not properly estimate the horizontal position of a magma chamber. We have investigated an approach where the elevation of the reference surface varies for each computation point, corresponding to topography. For vertical displacements and tilts this method provides a good fit to the finite element results, and thus may form the basis for an inversion scheme. For radial displacements, a constant reference elevation provides a better fit to the numerical results.

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

NASA Astrophysics Data System (ADS)

Adib, Arash; Poorveis, Davood; Mehraban, Farid

2018-03-01

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

Modeling 3D Dynamic Rupture on Arbitrarily-Shaped faults by Boundary-Conforming Finite Difference Method

NASA Astrophysics Data System (ADS)

Zhu, D.; Zhu, H.; Luo, Y.; Chen, X.

2008-12-01

We use a new finite difference method (FDM) and the slip-weakening law to model the rupture dynamics of a non-planar fault embedded in a 3-D elastic media with free surface. The new FDM, based on boundary- conforming grid, sets up the mapping equations between the curvilinear coordinate and the Cartesian coordinate and transforms irregular physical space to regular computational space; it also employs a higher- order non-staggered DRP/opt MacCormack scheme which is of low dispersion and low dissipation so that the high accuracy and stability of our rupture modeling are guaranteed. Compared with the previous methods, not only we can compute the spontaneous rupture of an arbitrarily shaped fault, but also can model the influence of the surface topography on the rupture process of earthquake. In order to verify the feasibility of this method, we compared our results and other previous results, and found out they matched perfectly. Thanks to the boundary-conforming FDM, problems such as dynamic rupture with arbitrary dip, strike and rake over an arbitrary curved plane can be handled; and supershear or subshear rupture can be simulated with different parameters such as the initial stresses and the critical slip displacement Dc. Besides, our rupture modeling is economical to be implemented owing to its high efficiency and does not suffer from displacement leakage. With the help of inversion data of rupture by field observations, this method is convenient to model rupture processes and seismograms of natural earthquakes.

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.

Characterizing the importance of free space in the numerical human body models.

PubMed

Chebil, Omar; Arnoux, Pierre-Jean; Behr, Michel

2015-03-01

The geometric fidelity of the inner organs on finite-element model (FEM) of the human body and the choice to use discontinuous mesh engender the appearance of empty spaces that do not reflect the real-life situation of human body cavities. The aim of this study is to assess the influence of these empty spaces on the behavior of a simplified FEM built with three different structures in interaction which properties are relevant with the abdominal cavity. This FEM is made up of a large sphere (peritoneum) containing two hemispheres (liver and spleen). The space between peritoneum and inner organs was defined with two different approaches and assessed under impact conditions. The first is a meshfree space (Mfs) approach, e.g., consider the space as a perfect gas. The second approach, meshed space (MS), entailed adding volumetric elements in the empty space. From each approach, one optimal configuration was identified regarding the recorded force versus compression, the mobility of inner organs, and the space incompressibility. This space has a considerable influence on the behavior of the FEM and mainly on the applied loadings of inner organs (difference reaching 70% according to the configuration). For the first approach, the incompressible gas is designated because it guarantees space incompressibility (vf/vi = 1) and inner organs loading with the lowest delay (for high impact velocity: Peak force = 89 N, compression 47%). For the second approach, the discontinuous volumetric mesh is preferred because it promotes space incompressibility (vf/vi = 0.94) and acceptable force reaction (for high impact velocity: Peak force = 97 N, compression 49%). The current study shows the importance of this space on the human FEMs cavities behavior and proposes two configurations able to be used in a future study including detailed FEM.

Existence of Lipschitz selections of the Steiner map

NASA Astrophysics Data System (ADS)

Bednov, B. B.; Borodin, P. A.; Chesnokova, K. V.

2018-02-01

This paper is concerned with the problem of the existence of Lipschitz selections of the Steiner map {St}_n, which associates with n points of a Banach space X the set of their Steiner points. The answer to this problem depends on the geometric properties of the unit sphere S(X) of X, its dimension, and the number n. For n≥slant 4 general conditions are obtained on the space X under which {St}_n admits no Lipschitz selection. When X is finite dimensional it is shown that, if n≥slant 4 is even, the map {St}_n has a Lipschitz selection if and only if S(X) is a finite polytope; this is not true if n≥slant 3 is odd. For n=3 the (single-valued) map {St}_3 is shown to be Lipschitz continuous in any smooth strictly-convex two-dimensional space; this ceases to be true in three-dimensional spaces. Bibliography: 21 titles.

Space-coiling fractal metamaterial with multi-bandgaps on subwavelength scale

NASA Astrophysics Data System (ADS)

Man, Xianfeng; Liu, Tingting; Xia, Baizhan; Luo, Zhen; Xie, Longxiang; Liu, Jian

2018-06-01

Acoustic metamaterials are remarkably different from conventional materials, as they can flexibly manipulate and control the propagation of sound waves. Unlike the locally resonant metamaterials introduced in earlier studies, we designed an ultraslow artificial structure with a sound speed much lower than that in air. In this paper, the space-coiling approach is proposed for achieving artificial metamaterial for extremely low-frequency airborne sound. In addition, the self-similar fractal technique is utilized for designing space-coiling Mie-resonance-based metamaterials (MRMMs) to obtain a band-dispersive spectrum. The band structures of two-dimensional (2D) acoustic metamaterials with different fractal levels are illustrated using the finite element method. The low-frequency bandgap can easily be formed, and multi-bandgap properties are observed in high-level fractals. Furthermore, the designed MRMMs with higher order fractal space coiling shows a good robustness against irregular arrangement. Besides, the proposed artificial structure was found to modify and control the radiation field arbitrarily. Thus, this work provides useful guidelines for the design of acoustic filtering devices and acoustic wavefront shaping applications on the subwavelength scale.

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

PubMed

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

2016-11-01

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

On solving wave equations on fixed bounded intervals involving Robin boundary conditions with time-dependent coefficients

NASA Astrophysics Data System (ADS)

van Horssen, Wim T.; Wang, Yandong; Cao, Guohua

2018-06-01

In this paper, it is shown how characteristic coordinates, or equivalently how the well-known formula of d'Alembert, can be used to solve initial-boundary value problems for wave equations on fixed, bounded intervals involving Robin type of boundary conditions with time-dependent coefficients. A Robin boundary condition is a condition that specifies a linear combination of the dependent variable and its first order space-derivative on a boundary of the interval. Analytical methods, such as the method of separation of variables (SOV) or the Laplace transform method, are not applicable to those types of problems. The obtained analytical results by applying the proposed method, are in complete agreement with those obtained by using the numerical, finite difference method. For problems with time-independent coefficients in the Robin boundary condition(s), the results of the proposed method also completely agree with those as for instance obtained by the method of separation of variables, or by the finite difference method.

a Bounded Finite-Difference Discretization of a Two-Dimensional Diffusion Equation with Logistic Nonlinear Reaction

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

In the present manuscript, we introduce a finite-difference scheme to approximate solutions of the two-dimensional version of Fisher's equation from population dynamics, which is a model for which the existence of traveling-wave fronts bounded within (0,1) is a well-known fact. The method presented here is a nonstandard technique which, in the linear regime, approximates the solutions of the original model with a consistency of second order in space and first order in time. The theory of M-matrices is employed here in order to elucidate conditions under which the method is able to preserve the positivity and the boundedness of solutions. In fact, our main result establishes relatively flexible conditions under which the preservation of the positivity and the boundedness of new approximations is guaranteed. Some simulations of the propagation of a traveling-wave solution confirm the analytical results derived in this work; moreover, the experiments evince a good agreement between the numerical result and the analytical solutions.

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

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

We present an Augmented Lagrangian formulation and its real-space implementation for non-periodic Orbital-Free Density Functional Theory (OF-DFT) calculations. In particular, we rewrite the constrained minimization problem of OF-DFT as a sequence of minimization problems without any constraint, thereby making it amenable to powerful unconstrained optimization algorithms. Further, we develop a parallel implementation of this approach for the Thomas–Fermi–von Weizsacker (TFW) kinetic energy functional in the framework of higher-order finite-differences and the conjugate gradient method. With this implementation, we establish that the Augmented Lagrangian approach is highly competitive compared to the penalty and Lagrange multiplier methods. Additionally, we show that higher-ordermore » finite-differences represent a computationally efficient discretization for performing OF-DFT simulations. Overall, we demonstrate that the proposed formulation and implementation are both efficient and robust by studying selected examples, including systems consisting of thousands of atoms. We validate the accuracy of the computed energies and forces by comparing them with those obtained by existing plane-wave methods.« less

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.

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

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

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

Numerical Analysis of an H 1-Galerkin Mixed Finite Element Method for Time Fractional Telegraph Equation

PubMed Central

Wang, Jinfeng; Zhao, Meng; Zhang, Min; Liu, Yang; Li, Hong

2014-01-01

We discuss and analyze an H 1-Galerkin mixed finite element (H 1-GMFE) method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H 1-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H 1-GMFE method. Based on the discussion on the theoretical error analysis in L 2-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H 1-norm. Moreover, we derive and analyze the stability of H 1-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure. PMID:25184148

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.

1989-01-01

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

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

NASA Astrophysics Data System (ADS)

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

2012-09-01

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

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.

Structural Evaluation of a Space Shuttle Main Engine (SSME) High Pressure Fuel Turbopump Turbine Blade

NASA Technical Reports Server (NTRS)

Abdul-Aziz, Ali

1996-01-01

Thermal and structural finite-element analyses were performed on the first high pressure fuel turbopump turbine blade of the space shuttle main engine (SSME). A two-dimensional (2-D) finite-element model of the blade and firtree disk attachment was analyzed using the general purpose MARC (finite-element) code. The loading history applied is a typical test stand engine cycle mission, which consists of a startup condition with two thermal spikes, a steady state and a shutdown transient. The blade material is a directionally solidified (DS) Mar-M 246 alloy, the blade rotor is forged with waspalloy material. Thermal responses under steady-state and transient conditions were calculated. The stresses and strains under the influence of mechanical and thermal loadings were also determined. The critical regions that exhibited high stresses and severe localized plastic deformation were the blade-rotor gaps.

Viscoelastic reciprocating contacts in presence of finite rough interfaces: A numerical investigation

NASA Astrophysics Data System (ADS)

Putignano, Carmine; Carbone, Giuseppe

2018-05-01

Viscoelastic reciprocating contacts are crucial in a number of systems, ranging from sealing components to viscoelastic dampers. Roughness plays in these conditions a central role, but no exhaustive assessment in terms of influence on area, separation and friction has been drawn so far. This is due to the huge number of time and space scales involved in the problem. By means of an innovative Boundary Element methodology, which treats the time as a parameter and then requires only to discretize the space domain, we investigate the viscoelastic reciprocating contact mechanics between rough solids. In particular, we consider the alternate contact of a rigid finite-size rough punch over a viscoelastic layer: the importance of the domain finiteness in the determination of the contact area and the contact solution anisotropy is enlightened. Implications on real system may be drawn on this basis. Finally, we focus on the hysteretic cycle related to the viscoelastic tangential forces.

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

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

Besse, Nicolas; Latu, Guillaume; Ghizzo, Alain

In this paper we present a new method for the numerical solution of the relativistic Vlasov-Maxwell system on a phase-space grid using an adaptive semi-Lagrangian method. The adaptivity is performed through a wavelet multiresolution analysis, which gives a powerful and natural refinement criterion based on the local measurement of the approximation error and regularity of the distribution function. Therefore, the multiscale expansion of the distribution function allows to get a sparse representation of the data and thus save memory space and CPU time. We apply this numerical scheme to reduced Vlasov-Maxwell systems arising in laser-plasma physics. Interaction of relativistically strongmore » laser pulses with overdense plasma slabs is investigated. These Vlasov simulations revealed a rich variety of phenomena associated with the fast particle dynamics induced by electromagnetic waves as electron trapping, particle acceleration, and electron plasma wavebreaking. However, the wavelet based adaptive method that we developed here, does not yield significant improvements compared to Vlasov solvers on a uniform mesh due to the substantial overhead that the method introduces. Nonetheless they might be a first step towards more efficient adaptive solvers based on different ideas for the grid refinement or on a more efficient implementation. Here the Vlasov simulations are performed in a two-dimensional phase-space where the development of thin filaments, strongly amplified by relativistic effects requires an important increase of the total number of points of the phase-space grid as they get finer as time goes on. The adaptive method could be more useful in cases where these thin filaments that need to be resolved are a very small fraction of the hyper-volume, which arises in higher dimensions because of the surface-to-volume scaling and the essentially one-dimensional structure of the filaments. Moreover, the main way to improve the efficiency of the adaptive method is to increase the local character in phase-space of the numerical scheme, by considering multiscale reconstruction with more compact support and by replacing the semi-Lagrangian method with more local - in space - numerical scheme as compact finite difference schemes, discontinuous-Galerkin method or finite element residual schemes which are well suited for parallel domain decomposition techniques.« less

Multipartite entanglement in fermionic systems via a geometric measure

NASA Astrophysics Data System (ADS)

Lari, Behzad; Durganandini, P.; Joag, Pramod S.

2010-12-01

We study multipartite entanglement in a system consisting of indistinguishable fermions. Specifically, we have proposed a geometric entanglement measure for N spin-(1)/(2) fermions distributed over 2L modes (single-particle states). The measure is defined on the 2L qubit space isomorphic to the Fock space for 2L single-particle states. This entanglement measure is defined for a given partition of 2L modes containing m⩾2 subsets. Thus this measure applies to m⩽2L partite fermionic systems where L is any finite number, giving the number of sites. The Hilbert spaces associated with these subsets may have different dimensions. Further, we have defined the local quantum operations with respect to a given partition of modes. This definition is generic and unifies different ways of dividing a fermionic system into subsystems. We have shown, using a representative case, that the geometric measure is invariant under local unitary operators corresponding to a given partition. We explicitly demonstrate the use of the measure to calculate multipartite entanglement in some correlated electron systems.

Space-time-modulated stochastic processes

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

Starting from the physical problem associated with the Lorentzian transformation of a Poisson-Kac process in inertial frames, the concept of space-time-modulated stochastic processes is introduced for processes possessing finite propagation velocity. This class of stochastic processes provides a two-way coupling between the stochastic perturbation acting on a physical observable and the evolution of the physical observable itself, which in turn influences the statistical properties of the stochastic perturbation during its evolution. The definition of space-time-modulated processes requires the introduction of two functions: a nonlinear amplitude modulation, controlling the intensity of the stochastic perturbation, and a time-horizon function, which modulates its statistical properties, providing irreducible feedback between the stochastic perturbation and the physical observable influenced by it. The latter property is the peculiar fingerprint of this class of models that makes them suitable for extension to generic curved-space times. Considering Poisson-Kac processes as prototypical examples of stochastic processes possessing finite propagation velocity, the balance equations for the probability density functions associated with their space-time modulations are derived. Several examples highlighting the peculiarities of space-time-modulated processes are thoroughly analyzed.

Computer-Aided Engineering of Semiconductor Integrated Circuits

DTIC Science & Technology

1979-07-01

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

Efficient design of nanoplasmonic waveguide devices using the space mapping algorithm.

PubMed

Dastmalchi, Pouya; Veronis, Georgios

2013-12-30

We show that the space mapping algorithm, originally developed for microwave circuit optimization, can enable the efficient design of nanoplasmonic waveguide devices which satisfy a set of desired specifications. Space mapping utilizes a physics-based coarse model to approximate a fine model accurately describing a device. Here the fine model is a full-wave finite-difference frequency-domain (FDFD) simulation of the device, while the coarse model is based on transmission line theory. We demonstrate that simply optimizing the transmission line model of the device is not enough to obtain a device which satisfies all the required design specifications. On the other hand, when the iterative space mapping algorithm is used, it converges fast to a design which meets all the specifications. In addition, full-wave FDFD simulations of only a few candidate structures are required before the iterative process is terminated. Use of the space mapping algorithm therefore results in large reductions in the required computation time when compared to any direct optimization method of the fine FDFD model.

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

PubMed

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

2011-11-02

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

Optimization with Fuzzy Data via Evolutionary Algorithms

NASA Astrophysics Data System (ADS)

Kosiński, Witold

2010-09-01

Order fuzzy numbers (OFN) that make possible to deal with fuzzy inputs quantitatively, exactly in the same way as with real numbers, have been recently defined by the author and his 2 coworkers. The set of OFN forms a normed space and is a partially ordered ring. The case when the numbers are presented in the form of step functions, with finite resolution, simplifies all operations and the representation of defuzzification functionals. A general optimization problem with fuzzy data is formulated. Its fitness function attains fuzzy values. Since the adjoint space to the space of OFN is finite dimensional, a convex combination of all linear defuzzification functionals may be used to introduce a total order and a real-valued fitness function. Genetic operations on individuals representing fuzzy data are defined.

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

NASA Technical Reports Server (NTRS)

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

1996-01-01

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

A Robust Absorbing Boundary Condition for Compressible Flows

NASA Technical Reports Server (NTRS)

Loh, Ching Y.; orgenson, Philip C. E.

2005-01-01

An absorbing non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented with theoretical proof. This paper is a continuation and improvement of a previous paper by the author. The absorbing NRBC technique is based on a first principle of non reflecting, which contains the essential physics that a plane wave solution of the Euler equations remains intact across the boundary. The technique is theoretically shown to work for a large class of finite volume approaches. When combined with the hyperbolic conservation laws, the NRBC is simple, robust and truly multi-dimensional; no additional implementation is needed except the prescribed physical boundary conditions. Several numerical examples in multi-dimensional spaces using two different finite volume schemes are illustrated to demonstrate its robustness in practical computations. Limitations and remedies of the technique are also discussed.

Acoustic Parametric Array for Identifying Standoff Targets

NASA Astrophysics Data System (ADS)

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

2010-02-01

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

Possible higher order phase transition in large-N gauge theory at finite temperature

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

Nishimura, Hiromichi

2017-08-07

We analyze the phase structure of SU(¥) gauge theory at finite temperature using matrix models. Our basic assumption is that the effective potential is dominated by double-trace terms for the Polyakov loops. As a function of the temperature, a background field for the Polyakov loop, and a quartic coupling, it exhibits a universal structure: in the large portion of the parameter space, there is a continuous phase transition analogous to the third-order phase transition of Gross,Witten and Wadia, but the order of phase transition can be higher than third. We show that different confining potentials give rise to drastically differentmore » behavior of the eigenvalue density and the free energy. Therefore lattice simulations at large N could probe the order of phase transition and test our results. Critical« less

Bloch-Nordsieck thermometers: one-loop exponentiation in finite temperature QED

NASA Astrophysics Data System (ADS)

Gupta, Sourendu; Indumathi, D.; Mathews, Prakash; Ravindran, V.

1996-02-01

We study the scattering of hard external particles in a heat bath in a real-time formalism for finite temperature QED. We investigate the distribution of the 4-momentum difference of initial and final hard particles in a fully covariant manner when the scale of the process, Q, is much larger than the temperature, T. Our computations are valid for all T subject to this constraint. We exponentiate the leading infra-red term at one-loop order through a resummation of soft (thermal) photon emissions and absorptions. For T > 0, we find that tensor structures arise which are not present at T = 0. These cant' thermal signatures. As a result, external particles can serve as thermometers introduced into the heat bath. We investigate the phase space origin of log( Q/ m) and log ( Q/ T) teens.

Research on the winding losses based on finite element method for transformer

NASA Astrophysics Data System (ADS)

Li, Wenpeng; Lai, Wenqing; Ye, Ligang; Luo, Hanwu; Luo, Changjiang; Cui, Shigang; Wang, Yongqiang

2018-04-01

Transformer loss can cause the transformer to overheat. Under the action of high frequency current, the loss of transformer windings will be aggravated due to proximity effect and skin effect. In this paper, a three-dimensional model of high frequency transformer windings is established. Considering of the proximity effect and skin effect, the eddy current effects loss in the transformer windings are simulated based on finite element method. And the winding losses of the transformer windings are obtained under different arrangements. The influence of the winding layout on the winding losses is given. Finally, the trend of winding loss with current frequency, winding thickness and inter layer spacing is obtained through calculation. The winding loss initially decreases as the thickness of the winding increases, but when it reaches a certain level, this reduction becomes insignificant.

Metamaterials with gradient negative index of refraction.

PubMed

Pinchuk, Anatoliy O; Schatz, George C

2007-10-01

We propose a new metamaterial with a gradient negative index of refraction, which can focus a collimated beam of light coming from a distant object. A slab of the negative refractive index metamaterial has a focal length that can be tuned by changing the gradient of the negative refractive index. A thin metal film pierced with holes of appropriate size or spacing between them can be used as a metamaterial with the gradient negative index of refraction. We use finite-difference time-domain calculations to show the focusing of a plane electromagnetic wave passing through a system of equidistantly spaced holes in a metal slab with decreasing diameters toward the edges of the slab.

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

NASA Technical Reports Server (NTRS)

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

1999-01-01

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

Asymptotic behavior and interpretation of virtual states: The effects of confinement and of basis sets

NASA Astrophysics Data System (ADS)

Boffi, Nicholas M.; Jain, Manish; Natan, Amir

2016-02-01

A real-space high order finite difference method is used to analyze the effect of spherical domain size on the Hartree-Fock (and density functional theory) virtual eigenstates. We show the domain size dependence of both positive and negative virtual eigenvalues of the Hartree-Fock equations for small molecules. We demonstrate that positive states behave like a particle in spherical well and show how they approach zero. For the negative eigenstates, we show that large domains are needed to get the correct eigenvalues. We compare our results to those of Gaussian basis sets and draw some conclusions for real-space, basis-sets, and plane-waves calculations.

A Hierarchical Framework for State-Space Matrix Inference and Clustering.

PubMed

Zuo, Chandler; Chen, Kailei; Hewitt, Kyle J; Bresnick, Emery H; Keleş, Sündüz

2016-09-01

In recent years, a large number of genomic and epigenomic studies have been focusing on the integrative analysis of multiple experimental datasets measured over a large number of observational units. The objectives of such studies include not only inferring a hidden state of activity for each unit over individual experiments, but also detecting highly associated clusters of units based on their inferred states. Although there are a number of methods tailored for specific datasets, there is currently no state-of-the-art modeling framework for this general class of problems. In this paper, we develop the MBASIC ( M atrix B ased A nalysis for S tate-space I nference and C lustering) framework. MBASIC consists of two parts: state-space mapping and state-space clustering. In state-space mapping, it maps observations onto a finite state-space, representing the activation states of units across conditions. In state-space clustering, MBASIC incorporates a finite mixture model to cluster the units based on their inferred state-space profiles across all conditions. Both the state-space mapping and clustering can be simultaneously estimated through an Expectation-Maximization algorithm. MBASIC flexibly adapts to a large number of parametric distributions for the observed data, as well as the heterogeneity in replicate experiments. It allows for imposing structural assumptions on each cluster, and enables model selection using information criterion. In our data-driven simulation studies, MBASIC showed significant accuracy in recovering both the underlying state-space variables and clustering structures. We applied MBASIC to two genome research problems using large numbers of datasets from the ENCODE project. The first application grouped genes based on transcription factor occupancy profiles of their promoter regions in two different cell types. The second application focused on identifying groups of loci that are similar to a GATA2 binding site that is functional at its endogenous locus by utilizing transcription factor occupancy data and illustrated applicability of MBASIC in a wide variety of problems. In both studies, MBASIC showed higher levels of raw data fidelity than analyzing these data with a two-step approach using ENCODE results on transcription factor occupancy data.

Universal entanglement spectra of gapped one-dimensional field theories

NASA Astrophysics Data System (ADS)

Cho, Gil Young; Ludwig, Andreas W. W.; Ryu, Shinsei

2017-03-01

We discuss the entanglement spectrum of the ground state of a (1+1)-dimensional system in a gapped phase near a quantum phase transition. In particular, in proximity to a quantum phase transition described by a conformal field theory (CFT), the system is represented by a gapped Lorentz invariant field theory in the "scaling limit" (correlation length ξ much larger than microscopic "lattice" scale "a "), and can be thought of as a CFT perturbed by a relevant perturbation. We show that for such (1+1) gapped Lorentz invariant field theories in infinite space, the low-lying entanglement spectrum obtained by tracing out, say, left half-infinite space, is precisely equal to the physical spectrum of the unperturbed gapless, i.e., conformal field theory defined on a finite interval of length Lξ=ln(ξ /a ) with certain boundary conditions. In particular, the low-lying entanglement spectrum of the gapped theory is the finite-size spectrum of a boundary conformal field theory, and is always discrete and universal. Each relevant perturbation, and thus each gapped phase in proximity to the quantum phase transition, maps into a particular boundary condition. A similar property has been known to hold for Baxter's corner transfer matrices in a very special class of fine-tuned, namely, integrable off-critical lattice models, for the entire entanglement spectrum and independent of the scaling limit. In contrast, our result applies to completely general gapped Lorentz invariant theories in the scaling limit, without the requirement of integrability, for the low-lying entanglement spectrum. While the entanglement spectrum of the ground state of a gapped theory on a finite interval of length 2 R with suitable boundary conditions, bipartitioned into two equal pieces, turns out to exhibit a crossover between the finite-size spectra of the same CFT with in general different boundary conditions as the system size R crosses the correlation length from the "critical regime'' R ≪ξ to the "gapped regime'' R ≫ξ , the physical spectrum on a finite interval of length R with the same boundary conditions, on the other hand, is known to undergo a dramatic reorganization during the same crossover from being discrete to being continuous.

Hybrid simulation combining two space-time discretization of the discrete-velocity Boltzmann equation

NASA Astrophysics Data System (ADS)

Horstmann, Jan Tobias; Le Garrec, Thomas; Mincu, Daniel-Ciprian; Lévêque, Emmanuel

2017-11-01

Despite the efficiency and low dissipation of the stream-collide scheme of the discrete-velocity Boltzmann equation, which is nowadays implemented in many lattice Boltzmann solvers, a major drawback exists over alternative discretization schemes, i.e. finite-volume or finite-difference, that is the limitation to Cartesian uniform grids. In this paper, an algorithm is presented that combines the positive features of each scheme in a hybrid lattice Boltzmann method. In particular, the node-based streaming of the distribution functions is coupled with a second-order finite-volume discretization of the advection term of the Boltzmann equation under the Bhatnagar-Gross-Krook approximation. The algorithm is established on a multi-domain configuration, with the individual schemes being solved on separate sub-domains and connected by an overlapping interface of at least 2 grid cells. A critical parameter in the coupling is the CFL number equal to unity, which is imposed by the stream-collide algorithm. Nevertheless, a semi-implicit treatment of the collision term in the finite-volume formulation allows us to obtain a stable solution for this condition. The algorithm is validated in the scope of three different test cases on a 2D periodic mesh. It is shown that the accuracy of the combined discretization schemes agrees with the order of each separate scheme involved. The overall numerical error of the hybrid algorithm in the macroscopic quantities is contained between the error of the two individual algorithms. Finally, we demonstrate how such a coupling can be used to adapt to anisotropic flows with some gradual mesh refinement in the FV domain.

An Aeroelastic Analysis of a Thin Flexible Membrane

NASA Technical Reports Server (NTRS)

Scott, Robert C.; Bartels, Robert E.; Kandil, Osama A.

2007-01-01

Studies have shown that significant vehicle mass and cost savings are possible with the use of ballutes for aero-capture. Through NASA's In-Space Propulsion program, a preliminary examination of ballute sensitivity to geometry and Reynolds number was conducted, and a single-pass coupling between an aero code and a finite element solver was used to assess the static aeroelastic effects. There remain, however, a variety of open questions regarding the dynamic aeroelastic stability of membrane structures for aero-capture, with the primary challenge being the prediction of the membrane flutter onset. The purpose of this paper is to describe and begin addressing these issues. The paper includes a review of the literature associated with the structural analysis of membranes and membrane utter. Flow/structure analysis coupling and hypersonic flow solver options are also discussed. An approach is proposed for tackling this problem that starts with a relatively simple geometry and develops and evaluates analysis methods and procedures. This preliminary study considers a computationally manageable 2-dimensional problem. The membrane structural models used in the paper include a nonlinear finite-difference model for static and dynamic analysis and a NASTRAN finite element membrane model for nonlinear static and linear normal modes analysis. Both structural models are coupled with a structured compressible flow solver for static aeroelastic analysis. For dynamic aeroelastic analyses, the NASTRAN normal modes are used in the structured compressible flow solver and 3rd order piston theories were used with the finite difference membrane model to simulate utter onset. Results from the various static and dynamic aeroelastic analyses are compared.

Linear quadratic tracking problems in Hilbert space - Application to optimal active noise suppression

NASA Technical Reports Server (NTRS)

Banks, H. T.; Silcox, R. J.; Keeling, S. L.; Wang, C.

1989-01-01

A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.

Moving GIS Research Indoors: Spatiotemporal Analysis of Agricultural Animals

PubMed Central

Daigle, Courtney L.; Banerjee, Debasmit; Montgomery, Robert A.; Biswas, Subir; Siegford, Janice M.

2014-01-01

A proof of concept applying wildlife ecology techniques to animal welfare science in intensive agricultural environments was conducted using non-cage laying hens. Studies of wildlife ecology regularly use Geographic Information Systems (GIS) to assess wild animal movement and behavior within environments with relatively unlimited space and finite resources. However, rather than depicting landscapes, a GIS could be developed in animal production environments to provide insight into animal behavior as an indicator of animal welfare. We developed a GIS-based approach for studying agricultural animal behavior in an environment with finite space and unlimited resources. Concurrent data from wireless body-worn location tracking sensor and video-recording systems, which depicted spatially-explicit behavior of hens (135 hens/room) in two identical indoor enclosures, were collected. The spatial configuration of specific hen behaviors, variation in home range patterns, and variation in home range overlap show that individual hens respond to the same environment differently. Such information could catalyze management practice adjustments (e.g., modifying feeder design and/or location). Genetically-similar hens exhibited diverse behavioral and spatial patterns via a proof of concept approach enabling detailed examinations of individual non-cage laying hen behavior and welfare. PMID:25098421

Helicopter time-domain electromagnetic numerical simulation based on Leapfrog ADI-FDTD

NASA Astrophysics Data System (ADS)

Guan, S.; Ji, Y.; Li, D.; Wu, Y.; Wang, A.

2017-12-01

We present a three-dimension (3D) Alternative Direction Implicit Finite-Difference Time-Domain (Leapfrog ADI-FDTD) method for the simulation of helicopter time-domain electromagnetic (HTEM) detection. This method is different from the traditional explicit FDTD, or ADI-FDTD. Comparing with the explicit FDTD, leapfrog ADI-FDTD algorithm is no longer limited by Courant-Friedrichs-Lewy(CFL) condition. Thus, the time step is longer. Comparing with the ADI-FDTD, we reduce the equations from 12 to 6 and .the Leapfrog ADI-FDTD method will be easier for the general simulation. First, we determine initial conditions which are adopted from the existing method presented by Wang and Tripp(1993). Second, we derive Maxwell equation using a new finite difference equation by Leapfrog ADI-FDTD method. The purpose is to eliminate sub-time step and retain unconditional stability characteristics. Third, we add the convolution perfectly matched layer (CPML) absorbing boundary condition into the leapfrog ADI-FDTD simulation and study the absorbing effect of different parameters. Different absorbing parameters will affect the absorbing ability. We find the suitable parameters after many numerical experiments. Fourth, We compare the response with the 1-Dnumerical result method for a homogeneous half-space to verify the correctness of our algorithm.When the model contains 107*107*53 grid points, the conductivity is 0.05S/m. The results show that Leapfrog ADI-FDTD need less simulation time and computer storage space, compared with ADI-FDTD. The calculation speed decreases nearly four times, memory occupation decreases about 32.53%. Thus, this algorithm is more efficient than the conventional ADI-FDTD method for HTEM detection, and is more precise than that of explicit FDTD in the late time.

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.

Finite element modeling of truss structures with frequency-dependent material damping

NASA Technical Reports Server (NTRS)

Lesieutre, George A.

1991-01-01

A physically motivated modelling technique for structural dynamic analysis that accommodates frequency dependent material damping was developed. Key features of the technique are the introduction of augmenting thermodynamic fields (AFT) to interact with the usual mechanical displacement field, and the treatment of the resulting coupled governing equations using finite element analysis methods. The AFT method is fully compatible with current structural finite element analysis techniques. The method is demonstrated in the dynamic analysis of a 10-bay planar truss structure, a structure representative of those contemplated for use in future space systems.

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

NASA Astrophysics Data System (ADS)

Sun, Xuwei; Lu, Dinghui

2017-08-01

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

Effect of girder spacing on bridge deck response.

DOT National Transportation Integrated Search

2000-12-01

The purpose of this investigation was to evaluate the use of the commercial finite element code ABAQUS for analysis of reinforced concrete bridge decks and to employ this analysis package to determine the effect of girder spacing on deck response. A ...

Very large virtual compound spaces: construction, storage and utility in drug discovery.

PubMed

Peng, Zhengwei

2013-09-01

Recent activities in the construction, storage and exploration of very large virtual compound spaces are reviewed by this report. As expected, the systematic exploration of compound spaces at the highest resolution (individual atoms and bonds) is intrinsically intractable. By contrast, by staying within a finite number of reactions and a finite number of reactants or fragments, several virtual compound spaces have been constructed in a combinatorial fashion with sizes ranging from 10(11)11 to 10(20)20 compounds. Multiple search methods have been developed to perform searches (e.g. similarity, exact and substructure) into those compound spaces without the need for full enumeration. The up-front investment spent on synthetic feasibility during the construction of some of those virtual compound spaces enables a wider adoption by medicinal chemists to design and synthesize important compounds for drug discovery. Recent activities in the area of exploring virtual compound spaces via the evolutionary approach based on Genetic Algorithm also suggests a positive shift of focus from method development to workflow, integration and ease of use, all of which are required for this approach to be widely adopted by medicinal chemists.

Numeric simulation model for long-term orthodontic tooth movement with contact boundary conditions using the finite element method.

PubMed

Hamanaka, Ryo; Yamaoka, Satoshi; Anh, Tuan Nguyen; Tominaga, Jun-Ya; Koga, Yoshiyuki; Yoshida, Noriaki

2017-11-01

Although many attempts have been made to simulate orthodontic tooth movement using the finite element method, most were limited to analyses of the initial displacement in the periodontal ligament and were insufficient to evaluate the effect of orthodontic appliances on long-term tooth movement. Numeric simulation of long-term tooth movement was performed in some studies; however, neither the play between the brackets and archwire nor the interproximal contact forces were considered. The objectives of this study were to simulate long-term orthodontic tooth movement with the edgewise appliance by incorporating those contact conditions into the finite element model and to determine the force system when the space is closed with sliding mechanics. We constructed a 3-dimensional model of maxillary dentition with 0.022-in brackets and 0.019 × 0.025-in archwire. Forces of 100 cN simulating sliding mechanics were applied. The simulation was accomplished on the assumption that bone remodeling correlates with the initial tooth displacement. This method could successfully represent the changes in the moment-to-force ratio: the tooth movement pattern during space closure. We developed a novel method that could simulate the long-term orthodontic tooth movement and accurately determine the force system in the course of time by incorporating contact boundary conditions into finite element analysis. It was also suggested that friction is progressively increased during space closure in sliding mechanics. Copyright © 2017. Published by Elsevier Inc.

The finite state projection algorithm for the solution of the chemical master equation.

PubMed

Munsky, Brian; Khammash, Mustafa

2006-01-28

This article introduces the finite state projection (FSP) method for use in the stochastic analysis of chemically reacting systems. One can describe the chemical populations of such systems with probability density vectors that evolve according to a set of linear ordinary differential equations known as the chemical master equation (CME). Unlike Monte Carlo methods such as the stochastic simulation algorithm (SSA) or tau leaping, the FSP directly solves or approximates the solution of the CME. If the CME describes a system that has a finite number of distinct population vectors, the FSP method provides an exact analytical solution. When an infinite or extremely large number of population variations is possible, the state space can be truncated, and the FSP method provides a certificate of accuracy for how closely the truncated space approximation matches the true solution. The proposed FSP algorithm systematically increases the projection space in order to meet prespecified tolerance in the total probability density error. For any system in which a sufficiently accurate FSP exists, the FSP algorithm is shown to converge in a finite number of steps. The FSP is utilized to solve two examples taken from the field of systems biology, and comparisons are made between the FSP, the SSA, and tau leaping algorithms. In both examples, the FSP outperforms the SSA in terms of accuracy as well as computational efficiency. Furthermore, due to very small molecular counts in these particular examples, the FSP also performs far more effectively than tau leaping methods.

Moisture Transport in Composites during Repair Work,

DTIC Science & Technology

1983-09-01

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

Finite element analysis of the Space Shuttle 2.5-inch frangible nut

NASA Technical Reports Server (NTRS)

McKinnis, Darin N.

1994-01-01

Finite element analysis of the Space Shuttle 2.5-inch frangible nut was conducted to improve understanding of the current design and proposed design changes to this explosively-actuated nut. The 2.5-inch frangible nut is used in two places to attach the aft end of the Space Shuttle Orbiter to the External Tank. Both 2.5-inch frangible nuts must function to complete safe separation. The 2.5-inch frangible nut contains two explosive boosters containing RDX explosive each capable of splitting the nut in half, on command from the Orbiter computers. To ensure separation, the boosters are designed to be redundant. The detonation of one booster is sufficient to split the nut in half. However, beginning in 1987 some production lots of 2.5-inch frangible nuts have demonstrated an inability to separate using only a single booster. The cause of the failure has been attributed to differences in the material properties and response of the Inconel 718 from which the 2.5-inch frangible nut is manufactured. Subsequent tests have resulted in design modifications of the boosters and frangible nut. Model development and initial analysis was conducted by Sandia National Laboratories (SNL) under funding from NASA Lyndon B. Johnson Space Center (NASA-JSC) starting in 1992. Modeling codes previously developed by SNL were transferred to NASA-JSC for further analysis on this and other devices. An explosive bolt with NASA Standard Detonator (NSD) charge, a 3/4-inch frangible nut, and the Super*Zip linear separation system are being modeled by NASA-JSC.

Non-adiabatic pumping in an oscillating-piston model

NASA Astrophysics Data System (ADS)

Chuchem, Maya; Dittrich, Thomas; Cohen, Doron

2012-05-01

We consider the prototypical "piston pump" operating on a ring, where a circulating current is induced by means of an AC driving. This can be regarded as a generalized Fermi-Ulam model, incorporating a finite-height moving wall (piston) and non-trivial topology (ring). The amount of particles transported per cycle is determined by a layered structure of phase space. Each layer is characterized by a different drift velocity. We discuss the differences compared with the adiabatic and Boltzmann pictures, and highlight the significance of the "diabatic" contribution that might lead to a counter-stirring effect.

Crystallization of isotactic polypropylene in different shear regimes

NASA Astrophysics Data System (ADS)

Spina, Roberto; Spekowius, Marcel; Hopmann, Christian

2017-10-01

The investigation of the shear-induced crystallization of isotactic polypropylene in isothermal conditions in different shear regimes is the aim of the present research. A multiscale framework is developed and implemented to compute the nucleation and growth of spherulites, based on material parameters needed to connect crystallization kinetics to the molecular material properties. The framework consists of a macro-model based on a Finite Element Method linked to a micro-model based on Cellular Automata. The main results are the evolution of the crystallization degree and spherulite space filling as a function of imposed temperature ash shear rate.

Computational design of the basic dynamical processes of the UCLA general circulation model

NASA Technical Reports Server (NTRS)

Arakawa, A.; Lamb, V. R.

1977-01-01

The 12-layer UCLA general circulation model encompassing troposphere and stratosphere (and superjacent 'sponge layer') is described. Prognostic variables are: surface pressure, horizontal velocity, temperature, water vapor and ozone in each layer, planetary boundary layer (PBL) depth, temperature, moisture and momentum discontinuities at PBL top, ground temperature and water storage, and mass of snow on ground. Selection of space finite-difference schemes for homogeneous incompressible flow, with/without a free surface, nonlinear two-dimensional nondivergent flow, enstrophy conserving schemes, momentum advection schemes, vertical and horizontal difference schemes, and time differencing schemes are discussed.

Effects of damping on mode shapes, volume 2

NASA Technical Reports Server (NTRS)

Gates, R. M.; Merchant, D. H.; Arnquist, J. L.

1977-01-01

Displacement, velocity, and acceleration admittances were calculated for a realistic NASTRAN structural model of space shuttle for three conditions: liftoff, maximum dynamic pressure and end of solid rocket booster burn. The realistic model of the orbiter, external tank, and solid rocket motors included the representation of structural joint transmissibilities by finite stiffness and damping elements. Data values for the finite damping elements were assigned to duplicate overall low-frequency modal damping values taken from tests of similar vehicles. For comparison with the calculated admittances, position and rate gains were computed for a conventional shuttle model for the liftoff condition. Dynamic characteristics and admittances for the space shuttle model are presented.

Thermal-structural analyses of Space Shuttle Main Engine (SSME) hot section components

NASA Technical Reports Server (NTRS)

Abdul-Aziz, Ali; Thompson, Robert L.

1988-01-01

Three dimensional nonlinear finite element heat transfer and structural analyses were performed for the first stage high pressure fuel turbopump (HPFTP) blade of the space shuttle main engine (SSME). Directionally solidified (DS) MAR-M 246 and single crystal (SC) PWA-1480 material properties were used for the analyses. Analytical conditions were based on a typical test stand engine cycle. Blade temperature and stress strain histories were calculated by using the MARC finite element computer code. The structural response of an SSME turbine blade was assessed and a greater understanding of blade damage mechanisms, convective cooling effects, and thermal mechanical effects was gained.

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.

Effects of damping on mode shapes, volume 1

NASA Technical Reports Server (NTRS)

Gates, R. M.

1977-01-01

Displacement, velocity, and acceleration admittances were calculated for a realistic NASTRAN structural model of space shuttle for three conditions: liftoff, maximum dynamic pressure and end of solid rocket booster burn. The realistic model of the orbiter, external tank, and solid rocket motors included the representation of structural joint transmissibilities by finite stiffness and damping elements. Methods developed to incorporate structural joints and their damping characteristics into a finite element model of the space shuttle, to determine the point damping parameters required to produce realistic damping in the primary modes, and to calculate the effect of distributed damping on structural resonances through the calculation of admittances.

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.

Decomposition of Fuzzy Soft Sets with Finite Value Spaces

PubMed Central

Jun, Young Bae

2014-01-01

The notion of fuzzy soft sets is a hybrid soft computing model that integrates both gradualness and parameterization methods in harmony to deal with uncertainty. The decomposition of fuzzy soft sets is of great importance in both theory and practical applications with regard to decision making under uncertainty. This study aims to explore decomposition of fuzzy soft sets with finite value spaces. Scalar uni-product and int-product operations of fuzzy soft sets are introduced and some related properties are investigated. Using t-level soft sets, we define level equivalent relations and show that the quotient structure of the unit interval induced by level equivalent relations is isomorphic to the lattice consisting of all t-level soft sets of a given fuzzy soft set. We also introduce the concepts of crucial threshold values and complete threshold sets. Finally, some decomposition theorems for fuzzy soft sets with finite value spaces are established, illustrated by an example concerning the classification and rating of multimedia cell phones. The obtained results extend some classical decomposition theorems of fuzzy sets, since every fuzzy set can be viewed as a fuzzy soft set with a single parameter. PMID:24558342

Decomposition of fuzzy soft sets with finite value spaces.

PubMed

Feng, Feng; Fujita, Hamido; Jun, Young Bae; Khan, Madad

2014-01-01

The notion of fuzzy soft sets is a hybrid soft computing model that integrates both gradualness and parameterization methods in harmony to deal with uncertainty. The decomposition of fuzzy soft sets is of great importance in both theory and practical applications with regard to decision making under uncertainty. This study aims to explore decomposition of fuzzy soft sets with finite value spaces. Scalar uni-product and int-product operations of fuzzy soft sets are introduced and some related properties are investigated. Using t-level soft sets, we define level equivalent relations and show that the quotient structure of the unit interval induced by level equivalent relations is isomorphic to the lattice consisting of all t-level soft sets of a given fuzzy soft set. We also introduce the concepts of crucial threshold values and complete threshold sets. Finally, some decomposition theorems for fuzzy soft sets with finite value spaces are established, illustrated by an example concerning the classification and rating of multimedia cell phones. The obtained results extend some classical decomposition theorems of fuzzy sets, since every fuzzy set can be viewed as a fuzzy soft set with a single parameter.

Kuramoto model with uniformly spaced frequencies: Finite-N asymptotics of the locking threshold.

PubMed

Ottino-Löffler, Bertrand; Strogatz, Steven H

2016-06-01

We study phase locking in the Kuramoto model of coupled oscillators in the special case where the number of oscillators, N, is large but finite, and the oscillators' natural frequencies are evenly spaced on a given interval. In this case, stable phase-locked solutions are known to exist if and only if the frequency interval is narrower than a certain critical width, called the locking threshold. For infinite N, the exact value of the locking threshold was calculated 30 years ago; however, the leading corrections to it for finite N have remained unsolved analytically. Here we derive an asymptotic formula for the locking threshold when N≫1. The leading correction to the infinite-N result scales like either N^{-3/2} or N^{-1}, depending on whether the frequencies are evenly spaced according to a midpoint rule or an end-point rule. These scaling laws agree with numerical results obtained by Pazó [D. Pazó, Phys. Rev. E 72, 046211 (2005)PLEEE81539-375510.1103/PhysRevE.72.046211]. Moreover, our analysis yields the exact prefactors in the scaling laws, which also match the numerics.

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.

Processing and Modeling of Porous Copper Using Sintering Dissolution Process

NASA Astrophysics Data System (ADS)

Salih, Mustafa Abualgasim Abdalhakam

The growth of porous metal has produced materials with improved properties as compared to non-metals and solid metals. Porous metal can be classified as either open cell or closed cell. Open cell allows a fluid media to pass through it. Closed cell is made up of adjacent sealed pores with shared cell walls. Metal foams offer higher strength to weight ratios, increased impact energy absorption, and a greater tolerance to high temperatures and adverse environmental conditions when compared to bulk materials. Copper and its alloys are examples of these, well known for high strength and good mechanical, thermal and electrical properties. In the present study, the porous Cu was made by a powder metallurgy process, using three different space holders, sodium chloride, sodium carbonate and potassium carbonate. Several different samples have been produced, using different ratios of volume fraction. The densities of the porous metals have been measured and compared to the theoretical density calculated using an equation developed for these foams. The porous structure was determined with the removal of spacer materials through sintering process. The sintering process of each spacer material depends on the melting point of the spacer material. Processing, characterization, and mechanical properties were completed. These tests include density measurements, compression tests, computed tomography (CT) and scanning electron microscopy (SEM). The captured morphological images are utilized to generate the object-oriented finite element (OOF) analysis for the porous copper. Porous copper was formed with porosities in the range of 40-66% with density ranges from 3 to 5.2 g/cm3. A study of two different methods to measure porosity was completed. OOF (Object Oriented Finite Elements) is a desktop software application for studying the relationship between the microstructure of a material and its overall mechanical, dielectric, or thermal properties using finite element models based on real or simulated micrographs. OOF provides methods for segmenting images, creating meshes and solving of complex geometries using finite element models, and visualizing 2D results.

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

NASA Astrophysics Data System (ADS)

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

2015-10-01

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

On some theoretical and practical aspects of multigrid methods. [to solve finite element systems from elliptic equations

NASA Technical Reports Server (NTRS)

Nicolaides, R. A.

1979-01-01

A description and explanation of a simple multigrid algorithm for solving finite element systems is given. Numerical results for an implementation are reported for a number of elliptic equations, including cases with singular coefficients and indefinite equations. The method shows the high efficiency, essentially independent of the grid spacing, predicted by the theory.

Finite mode analysis through harmonic waveguides

PubMed

Alieva; Wolf

2000-08-01

The mode analysis of signals in a multimodal shallow harmonic waveguide whose eigenfrequencies are equally spaced and finite can be performed by an optoelectronic device, of which the optical part uses the guide to sample the wave field at a number of sensors along its axis and the electronic part computes their fast Fourier transform. We illustrate this process with the Kravchuk transform.

Finite temperature dynamics of a Holstein polaron: The thermo-field dynamics approach

NASA Astrophysics Data System (ADS)

Chen, Lipeng; Zhao, Yang

2017-12-01

Combining the multiple Davydov D2 Ansatz with the method of thermo-field dynamics, we study finite temperature dynamics of a Holstein polaron on a lattice. It has been demonstrated, using the hierarchy equations of motion method as a benchmark, that our approach provides an efficient, robust description of finite temperature dynamics of the Holstein polaron in the simultaneous presence of diagonal and off-diagonal exciton-phonon coupling. The method of thermo-field dynamics handles temperature effects in the Hilbert space with key numerical advantages over other treatments of finite-temperature dynamics based on quantum master equations in the Liouville space or wave function propagation with Monte Carlo importance sampling. While for weak to moderate diagonal coupling temperature increases inhibit polaron mobility, it is found that off-diagonal coupling induces phonon-assisted transport that dominates at high temperatures. Results on the mean square displacements show that band-like transport features dominate the diagonal coupling cases, and there exists a crossover from band-like to hopping transport with increasing temperature when including off-diagonal coupling. As a proof of concept, our theory provides a unified treatment of coherent and incoherent transport in molecular crystals and is applicable to any temperature.

Impact cratering calculations

NASA Technical Reports Server (NTRS)

Ahrens, Thomas J.; Okeefe, J. D.; Smither, C.; Takata, T.

1991-01-01

In the course of carrying out finite difference calculations, it was discovered that for large craters, a previously unrecognized type of crater (diameter) growth occurred which was called lip wave propagation. This type of growth is illustrated for an impact of a 1000 km (2a) silicate bolide at 12 km/sec (U) onto a silicate half-space at earth gravity (1 g). The von Misses crustal strength is 2.4 kbar. The motion at the crater lip associated with this wave type phenomena is up, outward, and then down, similar to the particle motion of a surface wave. It is shown that the crater diameter has grown d/a of approximately 25 to d/a of approximately 4 via lip propagation from Ut/a = 5.56 to 17.0 during the time when rebound occurs. A new code is being used to study partitioning of energy and momentum and cratering efficiency with self gravity for finite-sized objects rather than the previously discussed planetary half-space problems. These are important and fundamental subjects which can be addressed with smoothed particle hydrodynamic (SPH) codes. The SPH method was used to model various problems in astrophysics and planetary physics. The initial work demonstrates that the energy budget for normal and oblique impacts are distinctly different than earlier calculations for silicate projectile impact on a silicate half space. Motivated by the first striking radar images of Venus obtained by Magellan, the effect of the atmosphere on impact cratering was studied. In order the further quantify the processes of meteor break-up and trajectory scattering upon break-up, the reentry physics of meteors striking Venus' atmosphere versus that of the Earth were studied.

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

PubMed

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

2011-11-01

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

Finite length filters with maximally confined spectral power

NASA Technical Reports Server (NTRS)

Knight, J. W.; Newman, C. E.

1975-01-01

The problem of finding a function which, in addition to being zero outside a specified range in x-space, has its spectral power well confined to a certain range in k-space is solved numerically. Properties of the solutions are also discussed.

Efficient Computation of Anharmonic Force Constants via q-space, with Application to Graphene

NASA Astrophysics Data System (ADS)

Kornbluth, Mordechai; Marianetti, Chris

We present a new approach for extracting anharmonic force constants from a sparse sampling of the anharmonic dynamical tensor. We calculate the derivative of the energy with respect to q-space displacements (phonons) and strain, which guarantees the absence of supercell image errors. Central finite differences provide a well-converged quadratic error tail for each derivative, separating the contribution of each anharmonic order. These derivatives populate the anharmonic dynamical tensor in a sparse mesh that bounds the Brillouin Zone, which ensures comprehensive sampling of q-space while exploiting small-cell calculations for efficient, high-throughput computation. This produces a well-converged and precisely-defined dataset, suitable for big-data approaches. We transform this sparsely-sampled anharmonic dynamical tensor to real-space anharmonic force constants that obey full space-group symmetries by construction. Machine-learning techniques identify the range of real-space interactions. We show the entire process executed for graphene, up to and including the fifth-order anharmonic force constants. This method successfully calculates strain-based phonon renormalization in graphene, even under large strains, which solves a major shortcoming of previous potentials.

The improvement of GaN-based light-emitting diodes using nanopatterned sapphire substrate with small pattern spacing

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

Zhang, Yonghui; Wei, Tongbo, E-mail: tbwei@semi.ac.cn; Wang, Junxi

2014-02-15

Self-assembly SiO{sub 2} nanosphere monolayer template is utilized to fabricate nanopatterned sapphire substrates (NPSSs) with 0-nm, 50-nm, and 120-nm spacing, receptively. The GaN growth on top of NPSS with 0-nm spacing has the best crystal quality because of laterally epitaxial overgrowth. However, GaN growth from pattern top is more difficult to get smooth surface than from pattern bottom. The rougher surface may result in a higher work voltage. The stimulation results of finite-difference time-domain (FDTD) display that too large or too small spacing lead to the reduced light extracted efficiency (LEE) of LEDs. Under a driving current 350 mA, themore » external quantum efficiencies (EQE) of GaN-based LEDs grown on NPSSs with 0-nm, 50-nm, and 120-nm spacing increase by 43.3%, 50.6%, and 39.1%, respectively, compared to that on flat sapphire substrate (FSS). The optimized pattern spacing is 50 nm for the NPSS with 600-nm pattern period.« less

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

NASA Technical Reports Server (NTRS)

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

1973-01-01

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

A New Discretization Method of Order Four for the Numerical Solution of One-Space Dimensional Second-Order Quasi-Linear Hyperbolic Equation

ERIC Educational Resources Information Center

Mohanty, R. K.; Arora, Urvashi

2002-01-01

Three level-implicit finite difference methods of order four are discussed for the numerical solution of the mildly quasi-linear second-order hyperbolic equation A(x, t, u)u[subscript xx] + 2B(x, t, u)u[subscript xt] + C(x, t, u)u[subscript tt] = f(x, t, u, u[subscript x], u[subscript t]), 0 less than x less than 1, t greater than 0 subject to…

Stability Analysis of Finite Difference Approximations to Hyperbolic Systems,and Problems in Applied and Computational Matrix and Operator Theory

DTIC Science & Technology

1990-12-07

Fundaqao Calouste Gulbenkian, Instituto Gulbenkian de Ci~ncia, Centro de C6lculo Cientifico , Coimbra, 1973. 28, Dirac, P. A. M., Spinors in Hilbert Space...Office of Scientific Research grants 1965 Mathematical Association of America Editorial Prize for the article entitled: "Linear Transformations on...matrices" 1966 L.R. Ford Memorial Prize awarded by the Mathematical Association of America for the article , "Permanents" 1989 Outstanding Computer

The uncertainty principle and quantum chaos

NASA Technical Reports Server (NTRS)

Chirikov, Boris V.

1993-01-01

The conception of quantum chaos is described in some detail. The most striking feature of this novel phenomenon is that all the properties of classical dynamical chaos persist here but, typically, on the finite and different time scales only. The ultimate origin of such a universal quantum stability is in the fundamental uncertainty principle which makes discrete the phase space and, hence, the spectrum of bounded quantum motion. Reformulation of the ergodic theory, as a part of the general theory of dynamical systems, is briefly discussed.

Numerical simulation of steady supersonic flow. [spatial marching

NASA Technical Reports Server (NTRS)

Schiff, L. B.; Steger, J. L.

1981-01-01

A noniterative, implicit, space-marching, finite-difference algorithm was developed for the steady thin-layer Navier-Stokes equations in conservation-law form. The numerical algorithm is applicable to steady supersonic viscous flow over bodies of arbitrary shape. In addition, the same code can be used to compute supersonic inviscid flow or three-dimensional boundary layers. Computed results from two-dimensional and three-dimensional versions of the numerical algorithm are in good agreement with those obtained from more costly time-marching techniques.

Active Vibration damping of Smart composite beams based on system identification technique

NASA Astrophysics Data System (ADS)

Bendine, Kouider; Satla, Zouaoui; Boukhoulda, Farouk Benallel; Nouari, Mohammed

2018-03-01

In the present paper, the active vibration control of a composite beam using piezoelectric actuator is investigated. The space state equation is determined using system identification technique based on the structure input output response provided by ANSYS APDL finite element package. The Linear Quadratic (LQG) control law is designed and integrated into ANSYS APDL to perform closed loop simulations. Numerical examples for different types of excitation loads are presented to test the efficiency and the accuracy of the proposed model.

Propagation of Bessel-X pulses in a hybrid photonic crystal

NASA Astrophysics Data System (ADS)

Chung, K. B.

2018-05-01

We report the propagation of Bessel-X pulses in a two-dimensional hybrid photonic crystal, investigated by the finite-difference time-domain method, in which broadband super-collimation and the propagation of self-collimated ultrashort pulses were reported. We first show the propagation of Bessel-X pulses in two-dimensional free space, whose transverse branches diverge rapidly with propagation. We then show that Bessel-X pulses propagate with their transverse and longitudinal shapes almost unchanged in the hybrid photonic crystal.

Large-scale tidal effect on redshift-space power spectrum in a finite-volume survey

NASA Astrophysics Data System (ADS)

Akitsu, Kazuyuki; Takada, Masahiro; Li, Yin

2017-04-01

Long-wavelength matter inhomogeneities contain cleaner information on the nature of primordial perturbations as well as the physics of the early Universe. The large-scale coherent overdensity and tidal force, not directly observable for a finite-volume galaxy survey, are both related to the Hessian of large-scale gravitational potential and therefore are of equal importance. We show that the coherent tidal force causes a homogeneous anisotropic distortion of the observed distribution of galaxies in all three directions, perpendicular and parallel to the line-of-sight direction. This effect mimics the redshift-space distortion signal of galaxy peculiar velocities, as well as a distortion by the Alcock-Paczynski effect. We quantify its impact on the redshift-space power spectrum to the leading order, and discuss its importance for ongoing and upcoming galaxy surveys.

Bacterial Fission, Powers of Two, Sociology, Environmental Science, Public Health, Biology, Mathematics: An Integration of Constructivism, Discovery, and Inquiry

ERIC Educational Resources Information Center

Schlenker, Richard; Tierney, Kathleen

2006-01-01

Students examine the bacterial expansion pattern and attempt to relate what they discover to expanding powers of two. They also relate what they see and discover to increasing living space requirements in a world of infinite space and finite space to discover that living space decreases as a function of one over expanding powers of two. The…

On the frames of spaces of finite-dimensional Lie algebras of dimension at most 6

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

Gorbatsevich, V V

2014-05-31

In this paper, the frames of spaces of complex n-dimensional Lie algebras (that is, the intersections of all irreducible components of these spaces) are studied. A complete description of the frames and their projectivizations for n ≤ 6 is given. It is also proved that for n ≤ 6 the projectivizations of these spaces are simply connected. Bibliography: 7 titles.

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

NASA Technical Reports Server (NTRS)

Sparrow, Victor W.

1993-01-01

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

State Machine Modeling of the Space Launch System Solid Rocket Boosters

NASA Technical Reports Server (NTRS)

Harris, Joshua A.; Patterson-Hine, Ann

2013-01-01

The Space Launch System is a Shuttle-derived heavy-lift vehicle currently in development to serve as NASA's premiere launch vehicle for space exploration. The Space Launch System is a multistage rocket with two Solid Rocket Boosters and multiple payloads, including the Multi-Purpose Crew Vehicle. Planned Space Launch System destinations include near-Earth asteroids, the Moon, Mars, and Lagrange points. The Space Launch System is a complex system with many subsystems, requiring considerable systems engineering and integration. To this end, state machine analysis offers a method to support engineering and operational e orts, identify and avert undesirable or potentially hazardous system states, and evaluate system requirements. Finite State Machines model a system as a finite number of states, with transitions between states controlled by state-based and event-based logic. State machines are a useful tool for understanding complex system behaviors and evaluating "what-if" scenarios. This work contributes to a state machine model of the Space Launch System developed at NASA Ames Research Center. The Space Launch System Solid Rocket Booster avionics and ignition subsystems are modeled using MATLAB/Stateflow software. This model is integrated into a larger model of Space Launch System avionics used for verification and validation of Space Launch System operating procedures and design requirements. This includes testing both nominal and o -nominal system states and command sequences.

Finite Volume Algorithms for Heat Conduction

DTIC Science & Technology

2010-05-01

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

A Kirchhoff Approach to Seismic Modeling and Prestack Depth Migration

DTIC Science & Technology

1993-05-01

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

A 2D multi-term time and space fractional Bloch-Torrey model based on bilinear rectangular finite elements

NASA Astrophysics Data System (ADS)

Qin, Shanlin; Liu, Fawang; Turner, Ian W.

2018-03-01

The consideration of diffusion processes in magnetic resonance imaging (MRI) signal attenuation is classically described by the Bloch-Torrey equation. However, many recent works highlight the distinct deviation in MRI signal decay due to anomalous diffusion, which motivates the fractional order generalization of the Bloch-Torrey equation. In this work, we study the two-dimensional multi-term time and space fractional diffusion equation generalized from the time and space fractional Bloch-Torrey equation. By using the Galerkin finite element method with a structured mesh consisting of rectangular elements to discretize in space and the L1 approximation of the Caputo fractional derivative in time, a fully discrete numerical scheme is derived. A rigorous analysis of stability and error estimation is provided. Numerical experiments in the square and L-shaped domains are performed to give an insight into the efficiency and reliability of our method. Then the scheme is applied to solve the multi-term time and space fractional Bloch-Torrey equation, which shows that the extra time derivative terms impact the relaxation process.

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

PubMed

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

2018-01-01

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

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.

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.

A comparative study of finite element and finite difference methods for Cauchy-Riemann type equations

NASA Technical Reports Server (NTRS)

Fix, G. J.; Rose, M. E.

1983-01-01

A least squares formulation of the system divu = rho, curlu = zeta is surveyed from the viewpoint of both finite element and finite difference methods. Closely related arguments are shown to establish convergence estimates.

Fracture prediction using modified mohr coulomb theory for non-linear strain paths using AA3104-H19

NASA Astrophysics Data System (ADS)

Dick, Robert; Yoon, Jeong Whan

2016-08-01

Experiment results from uniaxial tensile tests, bi-axial bulge tests, and disk compression tests for a beverage can AA3104-H19 material are presented. The results from the experimental tests are used to determine material coefficients for both Yld2000 and Yld2004 models. Finite element simulations are developed to study the influence of materials model on the predicted earing profile. It is shown that only the YLD2004 model is capable of accurately predicting the earing profile as the YLD2000 model only predicts 4 ears. Excellent agreement with the experimental data for earing is achieved using the AA3104-H19 material data and the Yld2004 constitutive model. Mechanical tests are also conducted on the AA3104-H19 to generate fracture data under different stress triaxiality conditions. Tensile tests are performed on specimens with a central hole and notched specimens. Torsion of a double bridge specimen is conducted to generate points near pure shear conditions. The Nakajima test is utilized to produce points in bi-axial tension. The data from the experiments is used to develop the fracture locus in the principal strain space. Mapping from principal strain space to stress triaxiality space, principal stress space, and polar effective plastic strain space is accomplished using a generalized mapping technique. Finite element modeling is used to validate the Modified Mohr-Coulomb (MMC) fracture model in the polar space. Models of a hole expansion during cup drawing and a cup draw/reverse redraw/expand forming sequence demonstrate the robustness of the modified PEPS fracture theory for the condition with nonlinear forming paths and accurately predicts the onset of failure. The proposed methods can be widely used for predicting failure for the examples which undergo nonlinear strain path including rigid-packaging and automotive forming.

Using SpaceClaimTD Direct for Modeling Components with Complex Geometries for the Thermal Desktop-Based Advanced Stirling Radioisotope Generator Model

NASA Technical Reports Server (NTRS)

Fabanich, William A., Jr.

2014-01-01

SpaceClaim/TD Direct has been used extensively in the development of the Advanced Stirling Radioisotope Generator (ASRG) thermal model. This paper outlines the workflow for that aspect of the task and includes proposed best practices and lessons learned. The ASRG thermal model was developed to predict component temperatures and power output and to provide insight into the prime contractor's thermal modeling efforts. The insulation blocks, heat collectors, and cold side adapter flanges (CSAFs) were modeled with this approach. The model was constructed using mostly TD finite difference (FD) surfaces/solids. However, some complex geometry could not be reproduced with TD primitives while maintaining the desired degree of geometric fidelity. Using SpaceClaim permitted the import of original CAD files and enabled the defeaturing/repair of those geometries. TD Direct (a SpaceClaim add-on from CRTech) adds features that allowed the "mark-up" of that geometry. These so-called "mark-ups" control how finite element (FE) meshes are to be generated through the "tagging" of features (e.g. edges, solids, surfaces). These tags represent parameters that include: submodels, material properties, material orienters, optical properties, and radiation analysis groups. TD aliases were used for most tags to allow analysis to be performed with a variety of parameter values. "Domain-tags" were also attached to individual and groups of surfaces and solids to allow them to be used later within TD to populate objects like, for example, heaters and contactors. These tools allow the user to make changes to the geometry in SpaceClaim and then easily synchronize the mesh in TD without having to redefine the objects each time as one would if using TDMesher. The use of SpaceClaim/TD Direct helps simplify the process for importing existing geometries and in the creation of high fidelity FE meshes to represent complex parts. It also saves time and effort in the subsequent analysis.

Using SpaceClaim/TD Direct for Modeling Components with Complex Geometries for the Thermal Desktop-Based Advanced Stirling Radioisotope Generator Model

NASA Technical Reports Server (NTRS)

Fabanich, William

2014-01-01

SpaceClaim/TD Direct has been used extensively in the development of the Advanced Stirling Radioisotope Generator (ASRG) thermal model. This paper outlines the workflow for that aspect of the task and includes proposed best practices and lessons learned. The ASRG thermal model was developed to predict component temperatures and power output and to provide insight into the prime contractors thermal modeling efforts. The insulation blocks, heat collectors, and cold side adapter flanges (CSAFs) were modeled with this approach. The model was constructed using mostly TD finite difference (FD) surfaces solids. However, some complex geometry could not be reproduced with TD primitives while maintaining the desired degree of geometric fidelity. Using SpaceClaim permitted the import of original CAD files and enabled the defeaturing repair of those geometries. TD Direct (a SpaceClaim add-on from CRTech) adds features that allowed the mark-up of that geometry. These so-called mark-ups control how finite element (FE) meshes were generated and allowed the tagging of features (e.g. edges, solids, surfaces). These tags represent parameters that include: submodels, material properties, material orienters, optical properties, and radiation analysis groups. TD aliases were used for most tags to allow analysis to be performed with a variety of parameter values. Domain-tags were also attached to individual and groups of surfaces and solids to allow them to be used later within TD to populate objects like, for example, heaters and contactors. These tools allow the user to make changes to the geometry in SpaceClaim and then easily synchronize the mesh in TD without having to redefine these objects each time as one would if using TD Mesher.The use of SpaceClaim/TD Direct has helped simplify the process for importing existing geometries and in the creation of high fidelity FE meshes to represent complex parts. It has also saved time and effort in the subsequent analysis.

Speciation in the Derrida-Higgs model with finite genomes and spatial populations

NASA Astrophysics Data System (ADS)

de Aguiar, Marcus A. M.

2017-02-01

The speciation model proposed by Derrida and Higgs demonstrated that a sexually reproducing population can split into different species in the absence of natural selection or any type of geographic isolation, provided that mating is assortative and the number of genes involved in the process is infinite. Here we revisit this model and simulate it for finite genomes, focusing on the question of how many genes it actually takes to trigger neutral sympatric speciation. We find that, for typical parameters used in the original model, it takes the order of 105 genes. We compare the results with a similar spatially explicit model where about 100 genes suffice for speciation. We show that when the number of genes is small the species that emerge are strongly segregated in space. For a larger number of genes, on the other hand, the spatial structure of the population is less important and the species distribution overlap considerably.

Predicting financial market crashes using ghost singularities.

PubMed

Smug, Damian; Ashwin, Peter; Sornette, Didier

2018-01-01

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

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

Robust optimization of front members in a full frontal car impact

NASA Astrophysics Data System (ADS)

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

2013-03-01

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

Predicting financial market crashes using ghost singularities

PubMed Central

2018-01-01

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

Ion-Conserving Modified Poisson-Boltzmann Theory Considering a Steric Effect in an Electrolyte

NASA Astrophysics Data System (ADS)

Sugioka, Hideyuki

2016-12-01

The modified Poisson-Nernst-Planck (MPNP) and modified Poisson-Boltzmann (MPB) equations are well known as fundamental equations that consider a steric effect, which prevents unphysical ion concentrations. However, it is unclear whether they are equivalent or not. To clarify this problem, we propose an improved free energy formulation that considers a steric limit with an ion-conserving condition and successfully derive the ion-conserving modified Poisson-Boltzmann (IC-MPB) equations that are equivalent to the MPNP equations. Furthermore, we numerically examine the equivalence by comparing between the IC-MPB solutions obtained by the Newton method and the steady MPNP solutions obtained by the finite-element finite-volume method. A surprising aspect of our finding is that the MPB solutions are much different from the MPNP (IC-MPB) solutions in a confined space. We consider that our findings will significantly contribute to understanding the surface science between solids and liquids.

Correlation Results for a Mass Loaded Vehicle Panel Test Article Finite Element Models and Modal Survey Tests

NASA Technical Reports Server (NTRS)

Maasha, Rumaasha; Towner, Robert L.

2012-01-01

High-fidelity Finite Element Models (FEMs) were developed to support a recent test program at Marshall Space Flight Center (MSFC). The FEMs correspond to test articles used for a series of acoustic tests. Modal survey tests were used to validate the FEMs for five acoustic tests (a bare panel and four different mass-loaded panel configurations). An additional modal survey test was performed on the empty test fixture (orthogrid panel mounting fixture, between the reverb and anechoic chambers). Modal survey tests were used to test-validate the dynamic characteristics of FEMs used for acoustic test excitation. Modal survey testing and subsequent model correlation has validated the natural frequencies and mode shapes of the FEMs. The modal survey test results provide a basis for the analysis models used for acoustic loading response test and analysis comparisons

A discontinuous control volume finite element method for multi-phase flow in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Salinas, P.; Pavlidis, D.; Xie, Z.; Osman, H.; Pain, C. C.; Jackson, M. D.

2018-01-01

We present a new, high-order, control-volume-finite-element (CVFE) method for multiphase porous media flow with discontinuous 1st-order representation for pressure and discontinuous 2nd-order representation for velocity. The method has been implemented using unstructured tetrahedral meshes to discretize space. The method locally and globally conserves mass. However, unlike conventional CVFE formulations, the method presented here does not require the use of control volumes (CVs) that span the boundaries between domains with differing material properties. We demonstrate that the approach accurately preserves discontinuous saturation changes caused by permeability variations across such boundaries, allowing efficient simulation of flow in highly heterogeneous models. Moreover, accurate solutions are obtained at significantly lower computational cost than using conventional CVFE methods. We resolve a long-standing problem associated with the use of classical CVFE methods to model flow in highly heterogeneous porous media.

Transition from two-dimensional photonic crystals to dielectric metasurfaces in the optical diffraction with a fine structure

PubMed Central

Rybin, Mikhail V.; Samusev, Kirill B.; Lukashenko, Stanislav Yu.; Kivshar, Yuri S.; Limonov, Mikhail F.

2016-01-01

We study experimentally a fine structure of the optical Laue diffraction from two-dimensional periodic photonic lattices. The periodic photonic lattices with the C4v square symmetry, orthogonal C2v symmetry, and hexagonal C6v symmetry are composed of submicron dielectric elements fabricated by the direct laser writing technique. We observe surprisingly strong optical diffraction from a finite number of elements that provides an excellent tool to determine not only the symmetry but also exact number of particles in the finite-length structure and the sample shape. Using different samples with orthogonal C2v symmetry and varying the lattice spacing, we observe experimentally a transition between the regime of multi-order diffraction, being typical for photonic crystals to the regime where only the zero-order diffraction can be observed, being is a clear fingerprint of dielectric metasurfaces characterized by effective parameters. PMID:27491952

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.

System Identification of Damped Truss-Like Space Structures. Ph.D. Thesis - Cleveland State Univ., Mar. 1994

NASA Technical Reports Server (NTRS)

Armand, Sasan

1995-01-01

A spacecraft payload flown on a launch vehicle experiences dynamic loads. The dynamic loads are caused by various phenomena ranging from the start-up of the launch vehicle engine to wind gusts. A spacecraft payload should be designed to meet launch vehicle dynamic loads. One of the major steps taken towards determining the dynamic loads is to correlate the finite element model of the spacecraft with the test results of a modal survey test. A test-verified finite element model of the spacecraft should possess the same spatial properties (stiffness, mass, and damping) and modal properties (frequencies and mode shapes) as the test hardware representing the spacecraft. The test-verified and correlated finite element model of the spacecraft is then coupled with the finite element model of the launch vehicle for analysis of loads and stress. Modal survey testing, verification of a finite element model, and modification of the finite element model to match the modal survey test results can easily be accomplished if the spacecraft structure is simple. However, this is rarely the case. A simple structure here is defined as a structure where the influence of nonlinearity between force and displacement (uncertainty in a test, for example, with errors in input and output), and the influence of damping (structural, coulomb, and viscous) are not pronounced. The objective of this study is to develop system identification and correlation methods with the focus on the structural systems that possess nonproportional damping. Two approaches to correct the nonproportional damping matrix of a truss structure were studied, and have been implemented on truss-like structures such as the National Aeronautics and Space Administration's space station truss. The results of this study showed nearly 100 percent improvement of the correlated eigensystem over the analytical eigensystem. The first method showed excellent results with up to three modes used in the system identification process. The second method could handle more modes, but required more computer usage time, and the results were less accurate than those of the first method.

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

NASA Astrophysics Data System (ADS)

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

2015-09-01

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

Periodic trim solutions with hp-version finite elements in time

NASA Technical Reports Server (NTRS)

Peters, David A.; Hou, Lin-Jun

1990-01-01

Finite elements in time as an alternative strategy for rotorcraft trim problems are studied. The research treats linear flap and linearized flap-lag response both for quasi-trim and trim cases. The connection between Fourier series analysis and hp-finite elements for periodic a problem is also examined. It is proved that Fourier series is a special case of space-time finite elements in which one element is used with a strong displacement formulation. Comparisons are made with respect to accuracy among Fourier analysis, displacement methods, and mixed methods over a variety parameters. The hp trade-off is studied for the periodic trim problem to provide an optimum step size and order of polynomial for a given error criteria. It is found that finite elements in time can outperform Fourier analysis for periodic problems, and for some given error criteria. The mixed method provides better results than does the displacement method.

A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition

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

Gerritsma, Marc; Bochev, Pavel

Formulation of locally conservative least-squares finite element methods (LSFEMs) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require non-standard boundary conditions (Bochev and Gunzburger, 2009 [3]), while methods that admit the no-slip condition satisfy the incompressibility equation only approximately (Bochev and Gunzburger, 2009 [4, Chapter 7]). Here we address this problem by proving a new non-standard stability bound for the velocity–vorticity–pressure Stokes system augmented with a no-slip boundary condition. This bound gives rise to a norm-equivalent least-squares functional in which the velocity can be approximatedmore » by div-conforming finite element spaces, thereby enabling a locally-conservative approximations of this variable. Here, we also provide a practical realization of the new LSFEM using high-order spectral mimetic finite element spaces (Kreeft et al., 2011) and report several numerical tests, which confirm its mimetic properties.« less

Stress analysis of the space telescope focal plane structure joint

NASA Technical Reports Server (NTRS)

Foster, W. A., Jr.; Shoemaker, W. L.

1985-01-01

Two major efforts were begun concerning the Space Telescope focal plane structure joint. The 3-D solid finite element modeling of the bipod flexure plate was carried out. Conceptual models were developed for the load transfer through the three major bolts to the flexure plate. The flexure plate drawings were reconstructed using DADAM for the purpose of developing a file from which the coordinates of any point on the flexure plate could be determined and also to locate the attachment points of the various components which connect with the flexure plate. For modeling convenience the CADAM drawing of the flexure plate has been divided into several regions which will be subdivided into finite elements using MSGMESH, which is a finite element mesh generator available with MSC/NASTRAN. In addition to the CADAM work on the flexure plate, an effort was also begun to develop computer aided drawings of the peripheral beam which will be used to assist in modeling the connection between it and the flexure plate.

Split Space-Marching Finite-Volume Method for Chemically Reacting Supersonic Flow

NASA Technical Reports Server (NTRS)

Rizzi, Arthur W.; Bailey, Harry E.

1976-01-01

A space-marching finite-volume method employing a nonorthogonal coordinate system and using a split differencing scheme for calculating steady supersonic flow over aerodynamic shapes is presented. It is a second-order-accurate mixed explicit-implicit procedure that solves the inviscid adiabatic and nondiffusive equations for chemically reacting flow in integral conservation-law form. The relationship between the finite-volume and differential forms of the equations is examined and the relative merits of each discussed. The method admits initial Cauchy data situated on any arbitrary surface and integrates them forward along a general curvilinear coordinate, distorting and deforming the surface as it advances. The chemical kinetics term is split from the convective terms which are themselves dimensionally split, thereby freeing the fluid operators from the restricted step size imposed by the chemical reactions and increasing the computational efficiency. The accuracy of this splitting technique is analyzed, a sufficient stability criterion is established, a representative flow computation is discussed, and some comparisons are made with another method.

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.

A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition

DOE PAGES

Gerritsma, Marc; Bochev, Pavel

2016-03-22

Formulation of locally conservative least-squares finite element methods (LSFEMs) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require non-standard boundary conditions (Bochev and Gunzburger, 2009 [3]), while methods that admit the no-slip condition satisfy the incompressibility equation only approximately (Bochev and Gunzburger, 2009 [4, Chapter 7]). Here we address this problem by proving a new non-standard stability bound for the velocity–vorticity–pressure Stokes system augmented with a no-slip boundary condition. This bound gives rise to a norm-equivalent least-squares functional in which the velocity can be approximatedmore » by div-conforming finite element spaces, thereby enabling a locally-conservative approximations of this variable. Here, we also provide a practical realization of the new LSFEM using high-order spectral mimetic finite element spaces (Kreeft et al., 2011) and report several numerical tests, which confirm its mimetic properties.« less

A linear shock cell model for jets of arbitrary exit geometry

NASA Technical Reports Server (NTRS)

Morris, P. J.; Bhat, T. R. S.; Chen, G.

1989-01-01

The shock cell structures of single supersonic non-ideally expanded jets with arbitrary exit geometry are studied. Both vortex sheets and realistic mean profiles are considered for the jet shear layer. The boundary element method is used to predict the shock spacing and screech tones in a vortex sheet model of a single jet. This formulation enables the calculations to be performed only on the vortex sheet. This permits the efficient and convenient study of complicated jet geometries. Results are given for circular, elliptic and rectangular jets and the results are compared with analysis and experiment. The agreement between the predictions and measurements is very good but depends on the assumptions made to predict the geometry of the fully expanded jet. A finite diffference technique is used to examine the effect of finite mixing layer thickness for a single jet. The finite thickness of the mixing layer is found to decrease the shock spacing by approximately 20 percent over the length of the jet potential core.

Periodically driven ergodic and many-body localized quantum systems

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

Ponte, Pedro; Department of Physics and Astronomy, University of Waterloo, ON N2L 3G1; Chandran, Anushya

2015-02-15

We study dynamics of isolated quantum many-body systems whose Hamiltonian is switched between two different operators periodically in time. The eigenvalue problem of the associated Floquet operator maps onto an effective hopping problem. Using the effective model, we establish conditions on the spectral properties of the two Hamiltonians for the system to localize in energy space. We find that ergodic systems always delocalize in energy space and heat up to infinite temperature, for both local and global driving. In contrast, many-body localized systems with quenched disorder remain localized at finite energy. We support our conclusions by numerical simulations of disorderedmore » spin chains. We argue that our results hold for general driving protocols, and discuss their experimental implications.« less

Numerical computation of space shuttle orbiter flow field

NASA Technical Reports Server (NTRS)

Tannehill, John C.

1988-01-01

A new parabolized Navier-Stokes (PNS) code has been developed to compute the hypersonic, viscous chemically reacting flow fields around 3-D bodies. The flow medium is assumed to be a multicomponent mixture of thermally perfect but calorically imperfect gases. The new PNS code solves the gas dynamic and species conservation equations in a coupled manner using a noniterative, implicit, approximately factored, finite difference algorithm. The space-marching method is made well-posed by special treatment of the streamwise pressure gradient term. The code has been used to compute hypersonic laminar flow of chemically reacting air over cones at angle of attack. The results of the computations are compared with the results of reacting boundary-layer computations and show excellent agreement.

Low-rank approximation in the numerical modeling of the Farley-Buneman instability in ionospheric plasma

NASA Astrophysics Data System (ADS)

Dolgov, S. V.; Smirnov, A. P.; Tyrtyshnikov, E. E.

2014-04-01

We consider numerical modeling of the Farley-Buneman instability in the Earth's ionosphere plasma. The ion behavior is governed by the kinetic Vlasov equation with the BGK collisional term in the four-dimensional phase space, and since the finite difference discretization on a tensor product grid is used, this equation becomes the most computationally challenging part of the scheme. To relax the complexity and memory consumption, an adaptive model reduction using the low-rank separation of variables, namely the Tensor Train format, is employed. The approach was verified via a prototype MATLAB implementation. Numerical experiments demonstrate the possibility of efficient separation of space and velocity variables, resulting in the solution storage reduction by a factor of order tens.

Time domain simulation of harmonic ultrasound images and beam patterns in 3D using the k-space pseudospectral method.

PubMed

Treeby, Bradley E; Tumen, Mustafa; Cox, B T

2011-01-01

A k-space pseudospectral model is developed for the fast full-wave simulation of nonlinear ultrasound propagation through heterogeneous media. The model uses a novel equation of state to account for nonlinearity in addition to power law absorption. The spectral calculation of the spatial gradients enables a significant reduction in the number of required grid nodes compared to finite difference methods. The model is parallelized using a graphical processing unit (GPU) which allows the simulation of individual ultrasound scan lines using a 256 x 256 x 128 voxel grid in less than five minutes. Several numerical examples are given, including the simulation of harmonic ultrasound images and beam patterns using a linear phased array transducer.

Struggle for space: viral extinction through competition for cells.

PubMed

Cuesta, José A; Aguirre, Jacobo; Capitán, José A; Manrubia, Susanna C

2011-01-14

The design of protocols to suppress the propagation of viral infections is an enduring enterprise, especially hindered by limited knowledge of the mechanisms leading to viral extinction. Here we report on infection extinction due to intraspecific competition to infect susceptible hosts. Beneficial mutations increase the production of viral progeny, while the host cell may develop defenses against infection. For an unlimited number of host cells, a feedback runaway coevolution between host resistance and progeny production occurs. However, physical space limits the advantage that the virus obtains from increasing offspring numbers; thus, infection clearance may result from an increase in host defenses beyond a finite threshold. Our results might be relevant to devise improved control strategies in environments with mobility constraints or different geometrical properties.

An iterative phase-space explicit discontinuous Galerkin method for stellar radiative transfer in extended atmospheres

NASA Astrophysics Data System (ADS)

de Almeida, Valmor F.

2017-07-01

A phase-space discontinuous Galerkin (PSDG) method is presented for the solution of stellar radiative transfer problems. It allows for greater adaptivity than competing methods without sacrificing generality. The method is extensively tested on a spherically symmetric, static, inverse-power-law scattering atmosphere. Results for different sizes of atmospheres and intensities of scattering agreed with asymptotic values. The exponentially decaying behavior of the radiative field in the diffusive-transparent transition region, and the forward peaking behavior at the surface of extended atmospheres were accurately captured. The integrodifferential equation of radiation transfer is solved iteratively by alternating between the radiative pressure equation and the original equation with the integral term treated as an energy density source term. In each iteration, the equations are solved via an explicit, flux-conserving, discontinuous Galerkin method. Finite elements are ordered in wave fronts perpendicular to the characteristic curves so that elemental linear algebraic systems are solved quickly by sweeping the phase space element by element. Two implementations of a diffusive boundary condition at the origin are demonstrated wherein the finite discontinuity in the radiation intensity is accurately captured by the proposed method. This allows for a consistent mechanism to preserve photon luminosity. The method was proved to be robust and fast, and a case is made for the adequacy of parallel processing. In addition to classical two-dimensional plots, results of normalized radiation intensity were mapped onto a log-polar surface exhibiting all distinguishing features of the problem studied.

Nonlinear Aeroacoustics Computations by the Space-Time CE/SE Method

NASA Technical Reports Server (NTRS)

Loh, Ching Y.

2003-01-01

The Space-Time Conservation Element and Solution Element Method, or CE/SE Method for short, is a recently developed numerical method for conservation laws. Despite its second order accuracy in space and time, it possesses low dispersion errors and low dissipation. The method is robust enough to cover a wide range of compressible flows: from weak linear acoustic waves to strong discontinuous waves (shocks). An outstanding feature of the CE/SE scheme is its truly multi-dimensional, simple but effective non-reflecting boundary condition (NRBC), which is particularly valuable for computational aeroacoustics (CAA). In nature, the method may be categorized as a finite volume method, where the conservation element (CE) is equivalent to a finite control volume (or cell) and the solution element (SE) can be understood as the cell interface. However, due to its careful treatment of the surface fluxes and geometry, it is different from the existing schemes. Currently, the CE/SE scheme has been developed to a matured stage that a 3-D unstructured CE/SE Navier-Stokes solver is already available. However, in the present review paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen and sketched in section 2. Then applications of the 2-D and 3-D CE/SE schemes to linear, and in particular, nonlinear aeroacoustics are depicted in sections 3, 4, and 5 to demonstrate its robustness and capability.

Space Shuttle Main Engine structural analysis and data reduction/evaluation. Volume 5: Main Injector LOX Inlet analysis

NASA Technical Reports Server (NTRS)

Violett, Rebeca S.

1989-01-01

The analysis performed on the Main Injector LOX Inlet Assembly located on the Space Shuttle Main Engine is summarized. An ANSYS finite element model of the inlet assemably was built and executed. Static stress analysis was also performed.

Modeling and control of flexible space structures

NASA Technical Reports Server (NTRS)

Wie, B.; Bryson, A. E., Jr.

1981-01-01

The effects of actuator and sensor locations on transfer function zeros are investigated, using uniform bars and beams as generic models of flexible space structures. It is shown how finite element codes may be used directly to calculate transfer function zeros. The impulse response predicted by finite-dimensional models is compared with the exact impulse response predicted by the infinite dimensional models. It is shown that some flexible structures behave as if there were a direct transmission between actuator and sensor (equal numbers of zeros and poles in the transfer function). Finally, natural damping models for a vibrating beam are investigated since natural damping has a strong influence on the appropriate active control logic for a flexible structure.

A Maximal Element Theorem in FWC-Spaces and Its Applications

PubMed Central

Hu, Qingwen; Miao, Yulin

2014-01-01

A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWC-spaces. The results represented in this paper unify and extend some known results in the literature. PMID:24782672

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

NASA Technical Reports Server (NTRS)

Stein, M.; Housner, J. D.

1978-01-01

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

Heating of foods in space-vehicle environments. [by conductive heat transfer

NASA Technical Reports Server (NTRS)

Bannerot, R. B.; Cox, J. E.; Chen, C. K.; Heidelbaugh, N. D.

1973-01-01

In extended space missions, foods will be heated to enhance the psychological as well as the physiological well-being of the crew. In the low-gravity space environment natural convection is essentially absent so that the heat transfer within the food is by conduction alone. To prevent boiling in reduced pressure environments the maximum temperature of the heating system is severely limited. The Skylab food-heating system utilizes a tray with receptables for the food containers. The walls of the receptacles are lined with thermally controlled, electrical-resistance, blanket-type heating elements. A finite difference model is employed to perform parametric studies on the food-heating system. The effects on heating time of the (1) thermophysical properties of the food, (2) heater power level, (3) initial food temperatures, (4) container geometry, and (5) heater control temperature are presented graphically. The optimal heater power level and container geometry are determined.

A parallel variable metric optimization algorithm

NASA Technical Reports Server (NTRS)

Straeter, T. A.

1973-01-01

An algorithm, designed to exploit the parallel computing or vector streaming (pipeline) capabilities of computers is presented. When p is the degree of parallelism, then one cycle of the parallel variable metric algorithm is defined as follows: first, the function and its gradient are computed in parallel at p different values of the independent variable; then the metric is modified by p rank-one corrections; and finally, a single univariant minimization is carried out in the Newton-like direction. Several properties of this algorithm are established. The convergence of the iterates to the solution is proved for a quadratic functional on a real separable Hilbert space. For a finite-dimensional space the convergence is in one cycle when p equals the dimension of the space. Results of numerical experiments indicate that the new algorithm will exploit parallel or pipeline computing capabilities to effect faster convergence than serial techniques.

Experimental demonstration of revival of oscillations from death in coupled nonlinear oscillators.

PubMed

Senthilkumar, D V; Suresh, K; Chandrasekar, V K; Zou, Wei; Dana, Syamal K; Kathamuthu, Thamilmaran; Kurths, Jürgen

2016-04-01

We experimentally demonstrate that a processing delay, a finite response time, in the coupling can revoke the stability of the stable steady states, thereby facilitating the revival of oscillations in the same parameter space where the coupled oscillators suffered the quenching of oscillation. This phenomenon of reviving of oscillations is demonstrated using two different prototype electronic circuits. Further, the analytical critical curves corroborate that the spread of the parameter space with stable steady state is diminished continuously by increasing the processing delay. Finally, the death state is completely wiped off above a threshold value by switching the stability of the stable steady state to retrieve sustained oscillations in the same parameter space. The underlying dynamical mechanism responsible for the decrease in the spread of the stable steady states and the eventual reviving of oscillation as a function of the processing delay is explained using analytical results.

On the Huygens absorbing boundary conditions for electromagnetics

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

Berenger, Jean-Pierre

A new absorbing boundary condition (ABC) is presented for the solution of Maxwell equations in unbounded spaces. Called the Huygens ABC, this condition is a generalization of two previously published ABCs, namely the multiple absorbing surfaces (MAS) and the re-radiating boundary condition (rRBC). The properties of the Huygens ABC are derived theoretically in continuous spaces and in the finite-difference (FDTD) discretized space. A solution is proposed to render the Huygens ABC effective for the absorption of evanescent waves. Numerical experiments with the FDTD method show that the effectiveness of the Huygens ABC is close to that of the PML ABCmore » in some realistic problems of numerical electromagnetics. It is also shown in the paper that a combination of the Huygens ABC with the PML ABC is very well suited to the solution of some particular problems.« less

Preliminary study of the effects of a reversible chemical reaction on gas bubble dissolution. [for space glass refining

NASA Technical Reports Server (NTRS)

Weinberg, M. C.

1982-01-01

A preliminary investigation is carried out of the effects of a reversible chemical reaction on the dissolution of an isolated, stationary gas bubble in a glass melt. The exact governing equations for the model system are formulated and analyzed. The approximate quasi-steady-state version of these equations is solved analytically, and a calculation is made of bubble dissolution rates. The results are then compared with numerical solutions obtained from the finite difference form of the exact governing equations. It is pointed out that in the microgravity condition of space, the buoyant rise of a gas bubble in a glass melt will be negligible on the time scale of most experiments. For this reason, a determination of the behavior of a stationary gas bubble in a melt is relevant for an understanding of glass refining in space.

Experimental demonstration of revival of oscillations from death in coupled nonlinear oscillators

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

Senthilkumar, D. V., E-mail: skumarusnld@gmail.com; Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA University, Thanjavur 613 401; Suresh, K.

We experimentally demonstrate that a processing delay, a finite response time, in the coupling can revoke the stability of the stable steady states, thereby facilitating the revival of oscillations in the same parameter space where the coupled oscillators suffered the quenching of oscillation. This phenomenon of reviving of oscillations is demonstrated using two different prototype electronic circuits. Further, the analytical critical curves corroborate that the spread of the parameter space with stable steady state is diminished continuously by increasing the processing delay. Finally, the death state is completely wiped off above a threshold value by switching the stability of themore » stable steady state to retrieve sustained oscillations in the same parameter space. The underlying dynamical mechanism responsible for the decrease in the spread of the stable steady states and the eventual reviving of oscillation as a function of the processing delay is explained using analytical results.« less

The Space-Time Conservative Schemes for Large-Scale, Time-Accurate Flow Simulations with Tetrahedral Meshes

NASA Technical Reports Server (NTRS)

Venkatachari, Balaji Shankar; Streett, Craig L.; Chang, Chau-Lyan; Friedlander, David J.; Wang, Xiao-Yen; Chang, Sin-Chung

2016-01-01

Despite decades of development of unstructured mesh methods, high-fidelity time-accurate simulations are still predominantly carried out on structured, or unstructured hexahedral meshes by using high-order finite-difference, weighted essentially non-oscillatory (WENO), or hybrid schemes formed by their combinations. In this work, the space-time conservation element solution element (CESE) method is used to simulate several flow problems including supersonic jet/shock interaction and its impact on launch vehicle acoustics, and direct numerical simulations of turbulent flows using tetrahedral meshes. This paper provides a status report for the continuing development of the space-time conservation element solution element (CESE) numerical and software framework under the Revolutionary Computational Aerosciences (RCA) project. Solution accuracy and large-scale parallel performance of the numerical framework is assessed with the goal of providing a viable paradigm for future high-fidelity flow physics simulations.

Rarefied gas flow through two-dimensional nozzles

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

Invariant measures in brain dynamics

NASA Astrophysics Data System (ADS)

Boyarsky, Abraham; Góra, Paweł

2006-10-01

This note concerns brain activity at the level of neural ensembles and uses ideas from ergodic dynamical systems to model and characterize chaotic patterns among these ensembles during conscious mental activity. Central to our model is the definition of a space of neural ensembles and the assumption of discrete time ensemble dynamics. We argue that continuous invariant measures draw the attention of deeper brain processes, engendering emergent properties such as consciousness. Invariant measures supported on a finite set of ensembles reflect periodic behavior, whereas the existence of continuous invariant measures reflect the dynamics of nonrepeating ensemble patterns that elicit the interest of deeper mental processes. We shall consider two different ways to achieve continuous invariant measures on the space of neural ensembles: (1) via quantum jitters, and (2) via sensory input accompanied by inner thought processes which engender a “folding” property on the space of ensembles.

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

NASA Technical Reports Server (NTRS)

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

1978-01-01

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

Mechanical properties and motion of the cupula of the human semicircular canal.

PubMed

Selva, Pierre; Oman, Charles M; Stone, Howard A

2009-01-01

The mathematical model for the dynamics of the cupula-endolymph system of the inner ear semicircular canal, as elaborated by numerous investigators, remains a foundational tool in all of vestibular physiology. Most models represent the cupula as a linear spring-like element of stiffness K=DeltaP/DeltaV, where DeltaV is the volume displaced upon application of a pressure difference DeltaP. The parameter K directly influences the long time constant of the cupula-endolymph system. Given estimates of K based on experiments, we use thick and thin bending membrane theory, and also finite-element simulations based on more realistic cupula morphologies, to estimate the human cupula's Young's modulus E approximately 5.4 Pa. We show that for a model morphology, thick bending membrane theory and finite-element predictions are in good agreement, and conclude that the morphology of the attachment of the cupula to the slope of the crista should not greatly influence the volume displacement. We note, however, that other biological materials with very low E are hydrogels that have significant viscoelastic properties. Experiments to directly measure E and investigate potential viscoelastic behavior ultimately may be needed. In addition, based on experimental images we study two other different shapes for the cupula and quantify their impact on the deflection of the cupula. We also use a three-dimensional finite-element model to analyze both the shear strain distribution and its time evolution near the sensory epithelium. We conclude that stimulation of sensory hair cells probably begins at the centre of the crista and spreads toward the periphery of the cupula and down the sides of the crista. Thus, spatio-temporal variations in the shearing stimulus are predicted to impact subsequent transduction and encoding. Finally, modeling the fluid-filled vertical channels believed to lie within the cupula, we investigate the impact of different tube diameters on the transverse displacement field. We show that, for the assumed diameters and grid spacing, cupula displacements should be highly sensitive to the diameter of the tubes. Experiments to verify the existence of cupular channels and accurately measure their diameter and spacing are needed.

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

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

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

Solution of the advection-dispersion equation by a finite-volume eulerian-lagrangian local adjoint method

USGS Publications Warehouse

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

1992-01-01

A finite-volume Eulerian-Lagrangian local adjoint method for solution of the advection-dispersion equation is developed and discussed. The method is mass conservative and can solve advection-dominated ground-water solute-transport problems accurately and efficiently. An integrated finite-difference approach is used in the method. A key component of the method is that the integral representing the mass-storage term is evaluated numerically at the current time level. Integration points, and the mass associated with these points, are then forward tracked up to the next time level. The number of integration points required to reach a specified level of accuracy is problem dependent and increases as the sharpness of the simulated solute front increases. Integration points are generally equally spaced within each grid cell. For problems involving variable coefficients it has been found to be advantageous to include additional integration points at strategic locations in each well. These locations are determined by backtracking. Forward tracking of boundary fluxes by the method alleviates problems that are encountered in the backtracking approaches of most characteristic methods. A test problem is used to illustrate that the new method offers substantial advantages over other numerical methods for a wide range of problems.

Efficient FEM simulation of static and free vibration behavior of single walled boron nitride nanotubes

NASA Astrophysics Data System (ADS)

Giannopoulos, Georgios I.; Kontoni, Denise-Penelope N.; Georgantzinos, Stylianos K.

2016-08-01

This paper describes the static and free vibration behavior of single walled boron nitride nanotubes using a structural mechanics based finite element method. First, depending on the type of nanotube under investigation, its three dimensional nanostructure is developed according to the well-known corresponding positions of boron and nitride atoms as well as boron nitride bonds. Then, appropriate point masses are assigned to the atomic positions of the developed space frame. Next, these point masses are suitably interconnected with two-noded, linear, spring-like, finite elements. In order to simulate effectively the interactions observed between boron and nitride atoms within the nanotube, appropriate potential energy functions are introduced for these finite elements. In this manner, various atomistic models for both armchair and zigzag nanotubes with different aspect ratios are numerically analyzed and their effective elastic modulus as well as their natural frequencies and corresponding mode shapes are obtained. Regarding the free vibration analysis, the computed results reveal bending, breathing and axial modes of vibration depending on the nanotube size and chirality as well as the applied boundary support conditions. The longitudinal stiffness of the boron nitride nanotubes is found also sensitive to their geometric characteristics.

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

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

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

2016-01-15

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

Reconstruction of finite-valued sparse signals

NASA Astrophysics Data System (ADS)

Keiper, Sandra; Kutyniok, Gitta; Lee, Dae Gwan; Pfander, Götz

2017-08-01

The need of reconstructing discrete-valued sparse signals from few measurements, that is solving an undetermined system of linear equations, appears frequently in science and engineering. Those signals appear, for example, in error correcting codes as well as massive Multiple-Input Multiple-Output (MIMO) channel and wideband spectrum sensing. A particular example is given by wireless communications, where the transmitted signals are sequences of bits, i.e., with entries in f0; 1g. Whereas classical compressed sensing algorithms do not incorporate the additional knowledge of the discrete nature of the signal, classical lattice decoding approaches do not utilize sparsity constraints. In this talk, we present an approach that incorporates a discrete values prior into basis pursuit. In particular, we address finite-valued sparse signals, i.e., sparse signals with entries in a finite alphabet. We will introduce an equivalent null space characterization and show that phase transition takes place earlier than when using the classical basis pursuit approach. We will further discuss robustness of the algorithm and show that the nonnegative case is very different from the bipolar one. One of our findings is that the positioning of the zero in the alphabet - i.e., whether it is a boundary element or not - is crucial.

Numerical solution of the wave equation with variable wave speed on nonconforming domains by high-order difference potentials

NASA Astrophysics Data System (ADS)

Britt, S.; Tsynkov, S.; Turkel, E.

2018-02-01

We solve the wave equation with variable wave speed on nonconforming domains with fourth order accuracy in both space and time. This is accomplished using an implicit finite difference (FD) scheme for the wave equation and solving an elliptic (modified Helmholtz) equation at each time step with fourth order spatial accuracy by the method of difference potentials (MDP). High-order MDP utilizes compact FD schemes on regular structured grids to efficiently solve problems on nonconforming domains while maintaining the design convergence rate of the underlying FD scheme. Asymptotically, the computational complexity of high-order MDP scales the same as that for FD.

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.

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

NASA Astrophysics Data System (ADS)

Barnett, D. A., Jr.

1991-02-01

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

The Benard problem: A comparison of finite difference and spectral collocation eigen value solutions

NASA Technical Reports Server (NTRS)

Skarda, J. Raymond Lee; Mccaughan, Frances E.; Fitzmaurice, Nessan

1995-01-01

The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2nd order finite difference scheme. An exact solution to the Marangoni-Benard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.

Configuration-shape-size optimization of space structures by material redistribution

NASA Technical Reports Server (NTRS)

Vandenbelt, D. N.; Crivelli, L. A.; Felippa, C. A.

1993-01-01

This project investigates the configuration-shape-size optimization (CSSO) of orbiting and planetary space structures. The project embodies three phases. In the first one the material-removal CSSO method introduced by Kikuchi and Bendsoe (KB) is further developed to gain understanding of finite element homogenization techniques as well as associated constrained optimization algorithms that must carry along a very large number (thousands) of design variables. In the CSSO-KB method an optimal structure is 'carved out' of a design domain initially filled with finite elements, by allowing perforations (microholes) to develop, grow and merge. The second phase involves 'materialization' of space structures from the void, thus reversing the carving process. The third phase involves analysis of these structures for construction and operational constraints, with emphasis in packaging and deployment. The present paper describes progress in selected areas of the first project phase and the start of the second one.

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

NASA Astrophysics Data System (ADS)

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

2011-11-01

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

Finite-element modelling of thermal micracking in fresh and consolidated marbles

NASA Astrophysics Data System (ADS)

Weiss, T.; Fuller, E.; Siegesmund, S.

2003-04-01

The initial stage of marble weathering is supposed to be controlled by thermal microcracking. Due to the anisotropy of the thermal expansion coefficients of calcite, the main rock forming mineral in marble, stresses are caused which lead to thermally-induced microcracking, especially along the grain boundaries. The so-called "granular disintegration" is a frequent weathering phenomenon observed for marbles. The controlling parameters are the grain size, grain shape and grain orientation. We use a finite-element approach to constrain magnitude and directional dependence of thermal degradation. Therefore, different assumptions are validated including the fracture toughness of the grain boundaries, the effects of the grain-to-grain orientation and bulk lattice preferred orientation (here referred to as texture). The resulting thermal microcracking and bulk rock thermal expansion anisotropy are validated. It is evident that thermal degradation depends on the texture. Strongly textured marbles exhibit a clear directional dependence of thermal degradation and a smaller bulk thermal degradation than randomly oriented ones. The effect of different stone consolidants in the pore space of degraded marble is simulated and its influence on mechanical properties such as tensile strength are evaluated.

An analysis for high Reynolds number inviscid/viscid interactions in cascades

NASA Technical Reports Server (NTRS)

Barnett, Mark; Verdon, Joseph M.; Ayer, Timothy C.

1993-01-01

An efficient steady analysis for predicting strong inviscid/viscid interaction phenomena such as viscous-layer separation, shock/boundary-layer interaction, and trailing-edge/near-wake interaction in turbomachinery blade passages is needed as part of a comprehensive analytical blade design prediction system. Such an analysis is described. It uses an inviscid/viscid interaction approach, in which the flow in the outer inviscid region is assumed to be potential, and that in the inner or viscous-layer region is governed by Prandtl's equations. The inviscid solution is determined using an implicit, least-squares, finite-difference approximation, the viscous-layer solution using an inverse, finite-difference, space-marching method which is applied along the blade surfaces and wake streamlines. The inviscid and viscid solutions are coupled using a semi-inverse global iteration procedure, which permits the prediction of boundary-layer separation and other strong-interaction phenomena. Results are presented for three cascades, with a range of inlet flow conditions considered for one of them, including conditions leading to large-scale flow separations. Comparisons with Navier-Stokes solutions and experimental data are also given.

A finite element model development for simulation of the impact of slab thickness, joints, and membranes on indoor radon concentration.

PubMed

Muñoz, E; Frutos, B; Olaya, M; Sánchez, J

2017-10-01

The focus of this study is broadly to define the physics involved in radon generation and transport through the soil and other materials using different parameter-estimation tools from the literature. The effect of moisture in the soil and radon transport via water in the pore space was accounted for with the application of a porosity correction coefficient. A 2D finite element model is created, which reproduces the diffusion and advection mechanisms resulting from specified boundary conditions. A comparison between the model and several analytical and numerical solutions obtained from the literature and field studies validates the model. Finally, the results demonstrate that the model can predict radon entry through different building boundary conditions, such as concrete slabs with or without joints, variable slab thicknesses and diffusion coefficients, and the use of several radon barrier membranes. Cracks in the concrete or the radon barrier membrane have been studied to understand how indoor concentration is affected by these issues. Copyright © 2017 Elsevier Ltd. All rights reserved.

Unconditionally stable finite-difference time-domain methods for modeling the Sagnac effect

NASA Astrophysics Data System (ADS)

Novitski, Roman; Scheuer, Jacob; Steinberg, Ben Z.

2013-02-01

We present two unconditionally stable finite-difference time-domain (FDTD) methods for modeling the Sagnac effect in rotating optical microsensors. The methods are based on the implicit Crank-Nicolson scheme, adapted to hold in the rotating system reference frame—the rotating Crank-Nicolson (RCN) methods. The first method (RCN-2) is second order accurate in space whereas the second method (RCN-4) is fourth order accurate. Both methods are second order accurate in time. We show that the RCN-4 scheme is more accurate and has better dispersion isotropy. The numerical results show good correspondence with the expression for the classical Sagnac resonant frequency splitting when using group refractive indices of the resonant modes of a microresonator. Also we show that the numerical results are consistent with the perturbation theory for the rotating degenerate microcavities. We apply our method to simulate the effect of rotation on an entire Coupled Resonator Optical Waveguide (CROW) consisting of a set of coupled microresonators. Preliminary results validate the formation of a rotation-induced gap at the center of a transfer function of a CROW.