WorldWideScience

Sample records for element approximation andnumerical

  1. Finite elements and approximation

    CERN Document Server

    Zienkiewicz, O C

    2006-01-01

    A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o

  2. Finite element approximation to the even-parity transport equation

    International Nuclear Information System (INIS)

    Lewis, E.E.

    1981-01-01

    This paper studies the finite element method, a procedure for reducing partial differential equations to sets of algebraic equations suitable for solution on a digital computer. The differential equation is cast into the form of a variational principle, the resulting domain then subdivided into finite elements. The dependent variable is then approximated by a simple polynomial, and these are linked across inter-element boundaries by continuity conditions. The finite element method is tailored to a variety of transport problems. Angular approximations are formulated, and the extent of ray effect mitigation is examined. Complex trial functions are introduced to enable the inclusion of buckling approximations. The ubiquitous curved interfaces of cell calculations, and coarse mesh methods are also treated. A concluding section discusses limitations of the work to date and suggests possible future directions

  3. Rules for matrix element evaluations in JWKB approximation

    International Nuclear Information System (INIS)

    Giler, S.

    1990-01-01

    Using the properties of the so-called fundamental solutions to the one-dimensional Schroedinger equation having Froeman and Froeman form the rules are formulated which allow one to evaluate matrix elements in the JWKB approximation and its generalizations. The rules apply to operators M(x, d/dx), M being polynomial functions of their arguments. The applicability of the rules depends on the properties of the so-called canonical indices introduced in this paper. The canonical indices are global characteristics of underlying Stokes graphs. If sufficiently small in comparison with unity they allow one to apply safely the JWKB approximation within the so-called ε-reduced canonical domains of a given Stokes graph. The Oth canonical index for the nth energy level Stokes graph corresponding to the harmonic oscillator potential is found to be ε CAN = 0.678/(2n+1). If the application of the rules is allowed then approximated matrix elements are obtained in an unambiguous way and with an accuracy controlled by corresponding canonical indices. Several examples of matrix elements are considered to illustrate how the rules should be used. Limitations to the rules are also discussed with the aid of suitably chosen examples. (author)

  4. Finite Element Approximation of the FENE-P Model

    OpenAIRE

    Barrett , John ,; Boyaval , Sébastien

    2017-01-01

    We extend our analysis on the Oldroyd-B model in Barrett and Boyaval [1] to consider the finite element approximation of the FENE-P system of equations, which models a dilute polymeric fluid, in a bounded domain $D $\\subset$ R d , d = 2 or 3$, subject to no flow boundary conditions. Our schemes are based on approximating the pressure and the symmetric conforma-tion tensor by either (a) piecewise constants or (b) continuous piecewise linears. In case (a) the velocity field is approximated by c...

  5. Quasi-planar elemental clusters in pair interactions approximation

    Directory of Open Access Journals (Sweden)

    Chkhartishvili Levan

    2016-01-01

    Full Text Available The pair-interactions approximation, when applied to describe elemental clusters, only takes into account bonding between neighboring atoms. According to this approach, isomers of wrapped forms of 2D clusters – nanotubular and fullerene-like structures – and truly 3D clusters, are generally expected to be more stable than their quasi-planar counterparts. This is because quasi-planar clusters contain more peripheral atoms with dangling bonds and, correspondingly, fewer atoms with saturated bonds. However, the differences in coordination numbers between central and peripheral atoms lead to the polarization of bonds. The related corrections to the molar binding energy can make small, quasi-planar clusters more stable than their 2D wrapped allotropes and 3D isomers. The present work provides a general theoretical frame for studying the relative stability of small elemental clusters within the pair interactions approximation.

  6. The complex variable boundary element method: Applications in determining approximative boundaries

    Science.gov (United States)

    Hromadka, T.V.

    1984-01-01

    The complex variable boundary element method (CVBEM) is used to determine approximation functions for boundary value problems of the Laplace equation such as occurs in potential theory. By determining an approximative boundary upon which the CVBEM approximator matches the desired constant (level curves) boundary conditions, the CVBEM is found to provide the exact solution throughout the interior of the transformed problem domain. Thus, the acceptability of the CVBEM approximation is determined by the closeness-of-fit of the approximative boundary to the study problem boundary. ?? 1984.

  7. Number-conserving random phase approximation with analytically integrated matrix elements

    International Nuclear Information System (INIS)

    Kyotoku, M.; Schmid, K.W.; Gruemmer, F.; Faessler, A.

    1990-01-01

    In the present paper a number conserving random phase approximation is derived as a special case of the recently developed random phase approximation in general symmetry projected quasiparticle mean fields. All the occurring integrals induced by the number projection are performed analytically after writing the various overlap and energy matrices in the random phase approximation equation as polynomials in the gauge angle. In the limit of a large number of particles the well-known pairing vibration matrix elements are recovered. We also present a new analytically number projected variational equation for the number conserving pairing problem

  8. The Fourier-finite-element approximation of the lame equations in axisymmetric domains with edges

    International Nuclear Information System (INIS)

    Nkemzil, Boniface

    2003-10-01

    This paper is concerned with a priori error estimates and convergence analysis of the Fourier-finite-element solutions of the Neumann problem for the Lame equations in axisymmetric domains Ω-circumflex is contained in R 3 with reentrant edges. The Fourier-FEM combines the approximating Fourier method with respect to the rotational angle using trigonometric polynomials of degree N (N →∞), with the finite-element method on the plane meridian domain of Ω-circumflex with mesh size h (h → 0) for approximating the Fourier coefficients. The asymptotic behavior of the solution near reentrant edges is described by singular functions in non-tensor product form and treated numerically by means of finite element method on locally graded meshes. For the right-hand side f-circumflex is an element of (L 2 (Ω-circumflex)) 3 , it is proved that the rate of convergence of the combined approximations in the norms of (W 2 1 (Ω-circumflex)) 3 is of the order O(h 2-l +N -(2-l) ) (l=0,1). (author)

  9. A study of the consistent and the lumped source approximations in finite element neutron diffusion calculations

    International Nuclear Information System (INIS)

    Ozgener, B.; Azgener, H.A.

    1991-01-01

    In finite element formulations for the solution of the within-group neutron diffusion equation, two different treatments are possible for the group source term: the consistent source approximation (CSA) and the lumped source approximation (LSA). CSA results in intra-group scattering and fission matrices which have the same nondiagonal structure as the global coefficient matrix. This situation might be regarded as a disadvantage, compared to the conventional (i.e. finite difference) methods where the intra-group scattering and fission matrices are diagonal. To overcome this disadvantage, LSA could be used to diagonalize these matrices. LSA is akin to the lumped mass approximation of continuum mechanics. We concentrate on two different aspects of the source approximations. Although it has been reported that LSA does not modify the asymptotic h 2 convergence behaviour for linear elements, the effect of LSA on convergence of higher degree elements has not been investigated. Thus, we would be interested in determining, p, the asymptotic order of convergence, in: Δk |k eff (analytical) -k eff (finite element)| = Ch p (1) for finite element approximations of varying degree (N) with both of the source approximations. Since (1) is valid in the asymptotic limit, we must use ultra-fine meshes and quadruple precision arithmetic. For our order of convergence study, we used infinite cylindrical geometry with azimuthal symmetry. Hence, the effects of singularities remain uninvestigated. The second aspect we dwell on is the performance of LSA in bilinear 3-D finite element calculations, compared to CSA. LSA has been used quite extensively in 1- and 2-D even-parity transport and diffusion calculations. In this work, we will try to assess the relative merits of LSA and CSA in 3-D problems. (author)

  10. Saint Petersburg International Conference on Integrated Navigation Systems, (9th), Held at St. Petersburg, Russia, on 27-29 May 2002

    Science.gov (United States)

    2002-05-01

    Dmitriev P.P., Shebshaevich V.S. Network satellite navigational systems. - M.:Radio and communication. 1982. 2. Harisov V.N., Petrov A.I., Boldin V.A...standardized LS-residuals) with a membership function which takes account of \\i- , introducing a weighting factor extracted from the elements of R and...numerical values of the blunders, we extract from the redundancy matrix R the diagonal and off-diagonal elements that correspond to the respective

  11. Finite element approximation to a model problem of transonic flow

    International Nuclear Information System (INIS)

    Tangmanee, S.

    1986-12-01

    A model problem of transonic flow ''the Tricomi equation'' in Ω is contained in IR 2 bounded by the rectangular-curve boundary is posed in the form of symmetric positive differential equations. The finite element method is then applied. When the triangulation of Ω-bar is made of quadrilaterals and the approximation space is the Lagrange polynomial, we get the error estimates. 14 refs, 1 fig

  12. Optimal convergence recovery for the Fourier-finite-element approximation of Maxwell's equations in non-smooth axisymmetric domains

    International Nuclear Information System (INIS)

    Nkemzi, B.

    2005-10-01

    Three-dimensional time-harmonic Maxwell's problems in axisymmetric domains Ω-circumflex with edges and conical points on the boundary are treated by means of the Fourier-finite-element method. The Fourier-fem combines the approximating Fourier series expansion of the solution with respect to the rotational angle using trigonometric polynomials of degree N (N → ∞), with the finite element approximation of the Fourier coefficients on the plane meridian domain Ω a is a subset of R + 2 of Ω-circumflex with mesh size h (h → 0). The singular behaviors of the Fourier coefficients near angular points of the domain Ω a are fully described by suitable singular functions and treated numerically by means of the singular function method with the finite element method on graded meshes. It is proved that the rate of convergence of the mixed approximations in H 1 (Ω-circumflex) 3 is of the order O (h+N -1 ) as known for the classical Fourier-finite-element approximation of problems with regular solutions. (author)

  13. Computational error estimates for Monte Carlo finite element approximation with log normal diffusion coefficients

    KAUST Repository

    Sandberg, Mattias

    2015-01-07

    The Monte Carlo (and Multi-level Monte Carlo) finite element method can be used to approximate observables of solutions to diffusion equations with log normal distributed diffusion coefficients, e.g. modelling ground water flow. Typical models use log normal diffusion coefficients with H¨older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible and can be larger than the computable low frequency error. This talk will address how the total error can be estimated by the computable error.

  14. Error estimates for the Fourier-finite-element approximation of the Lame system in nonsmooth axisymmetric domains

    International Nuclear Information System (INIS)

    Nkemzi, Boniface

    2003-10-01

    This paper is concerned with the effective implementation of the Fourier-finite-element method, which combines the approximating Fourier and the finite-element methods, for treating the Derichlet problem for the Lam.6 equations in axisymmetric domains Ω-circumflex is contained in R 3 with conical vertices and reentrant edges. The partial Fourier decomposition reduces the three-dimensional boundary value problem to an infinite sequence of decoupled two-dimensional boundary value problems on the plane meridian domain Ω α is contained in R + 2 of Ω-circumflex with solutions u, n (n = 0,1,2,...) being the Fourier coefficients of the solution u of the 3D problem. The asymptotic behavior of the Fourier coefficients near the angular points of Ω α , is described by appropriate singular vector-functions and treated numerically by linear finite elements on locally graded meshes. For the right-hand side function f-circumflex is an element of (L 2 (Ω-circumflex)) 3 it is proved that with appropriate mesh grading the rate of convergence of the combined approximations in (W 2 1 (Ω-circumflex)) 3 is of the order O(h + N -1 ), where h and N are the parameters of the finite-element and Fourier approximations, respectively, with h → 0 and N → ∞. (author)

  15. Finite element approximation for time-dependent diffusion with measure-valued source

    Czech Academy of Sciences Publication Activity Database

    Seidman, T.; Gobbert, M.; Trott, D.; Kružík, Martin

    2012-01-01

    Roč. 122, č. 4 (2012), s. 709-723 ISSN 0029-599X R&D Projects: GA AV ČR IAA100750802 Institutional support: RVO:67985556 Keywords : measure-valued source * diffusion equation Subject RIV: BA - General Mathematics Impact factor: 1.329, year: 2012 http://library.utia.cas.cz/separaty/2012/MTR/kruzik-finite element approximation for time - dependent diffusion with measure-valued source.pdf

  16. APPROX, 1-D and 2-D Function Approximation by Polynomials, Splines, Finite Elements Method

    International Nuclear Information System (INIS)

    Tollander, Bengt

    1975-01-01

    1 - Nature of physical problem solved: Approximates one- and two- dimensional functions using different forms of the approximating function, as polynomials, rational functions, Splines and (or) the finite element method. Different kinds of transformations of the dependent and (or) the independent variables can easily be made by data cards using a FORTRAN-like language. 2 - Method of solution: Approximations by polynomials, Splines and (or) the finite element method are made in L2 norm using the least square method by which the answer is directly given. For rational functions in one dimension the result given in L(infinite) norm is achieved by iterations moving the zero points of the error curve. For rational functions in two dimensions, the norm is L2 and the result is achieved by iteratively changing the coefficients of the denominator and then solving the coefficients of the numerator by the least square method. The transformation of the dependent and (or) independent variables is made by compiling the given transform data card(s) to an array of integers from which the transformation can be made

  17. Obtaining Approximate Values of Exterior Orientation Elements of Multi-Intersection Images Using Particle Swarm Optimization

    Science.gov (United States)

    Li, X.; Li, S. W.

    2012-07-01

    In this paper, an efficient global optimization algorithm in the field of artificial intelligence, named Particle Swarm Optimization (PSO), is introduced into close range photogrammetric data processing. PSO can be applied to obtain the approximate values of exterior orientation elements under the condition that multi-intersection photography and a small portable plane control frame are used. PSO, put forward by an American social psychologist J. Kennedy and an electrical engineer R.C. Eberhart, is a stochastic global optimization method based on swarm intelligence, which was inspired by social behavior of bird flocking or fish schooling. The strategy of obtaining the approximate values of exterior orientation elements using PSO is as follows: in terms of image coordinate observed values and space coordinates of few control points, the equations of calculating the image coordinate residual errors can be given. The sum of absolute value of each image coordinate is minimized to be the objective function. The difference between image coordinate observed value and the image coordinate computed through collinear condition equation is defined as the image coordinate residual error. Firstly a gross area of exterior orientation elements is given, and then the adjustment of other parameters is made to get the particles fly in the gross area. After iterative computation for certain times, the satisfied approximate values of exterior orientation elements are obtained. By doing so, the procedures like positioning and measuring space control points in close range photogrammetry can be avoided. Obviously, this method can improve the surveying efficiency greatly and at the same time can decrease the surveying cost. And during such a process, only one small portable control frame with a couple of control points is employed, and there are no strict requirements for the space distribution of control points. In order to verify the effectiveness of this algorithm, two experiments are

  18. OBTAINING APPROXIMATE VALUES OF EXTERIOR ORIENTATION ELEMENTS OF MULTI-INTERSECTION IMAGES USING PARTICLE SWARM OPTIMIZATION

    Directory of Open Access Journals (Sweden)

    X. Li

    2012-07-01

    Full Text Available In this paper, an efficient global optimization algorithm in the field of artificial intelligence, named Particle Swarm Optimization (PSO, is introduced into close range photogrammetric data processing. PSO can be applied to obtain the approximate values of exterior orientation elements under the condition that multi-intersection photography and a small portable plane control frame are used. PSO, put forward by an American social psychologist J. Kennedy and an electrical engineer R.C. Eberhart, is a stochastic global optimization method based on swarm intelligence, which was inspired by social behavior of bird flocking or fish schooling. The strategy of obtaining the approximate values of exterior orientation elements using PSO is as follows: in terms of image coordinate observed values and space coordinates of few control points, the equations of calculating the image coordinate residual errors can be given. The sum of absolute value of each image coordinate is minimized to be the objective function. The difference between image coordinate observed value and the image coordinate computed through collinear condition equation is defined as the image coordinate residual error. Firstly a gross area of exterior orientation elements is given, and then the adjustment of other parameters is made to get the particles fly in the gross area. After iterative computation for certain times, the satisfied approximate values of exterior orientation elements are obtained. By doing so, the procedures like positioning and measuring space control points in close range photogrammetry can be avoided. Obviously, this method can improve the surveying efficiency greatly and at the same time can decrease the surveying cost. And during such a process, only one small portable control frame with a couple of control points is employed, and there are no strict requirements for the space distribution of control points. In order to verify the effectiveness of this algorithm

  19. A 3 Year-Old Male Child Ingested Approximately 750 Grams of Elemental Mercury

    Directory of Open Access Journals (Sweden)

    Metin Uysalol

    2016-08-01

    Full Text Available Background: The oral ingestion of elemental mercury is unlikely to cause systemic toxicity, as it is poorly absorbed through the gastrointestinal system. However, abnormal gastrointestinal function or anatomy may allow elemental mercury into the bloodstream and the peritoneal space. Systemic effects of massive oral intake of mercury have rarely been reported. Case Report: In this paper, we are presenting the highest ingle oral intake of elemental mercury by a child aged 3 years. A Libyan boy aged 3 years ingested approximately 750 grams of elemental mercury and was still asymptomatic. Conclusion: The patient had no existing disease or abnormal gastrointestinal function or anatomy. The physical examination was normal. His serum mercury level was 91 μg/L (normal: <5 μg/L, and he showed no clinical manifestations. Exposure to mercury in children through different circumstances remains a likely occurrence.

  20. METHODS OF THE APPROXIMATE ESTIMATIONS OF FATIGUE DURABILITY OF COMPOSITE AIRFRAME COMPONENT TYPICAL ELEMENTS

    Directory of Open Access Journals (Sweden)

    V. E. Strizhius

    2015-01-01

    Full Text Available Methods of the approximate estimations of fatigue durability of composite airframe component typical elements which can be recommended for application at the stage of outline designing of the airplane are generated and presented.

  1. Computable error estimates for Monte Carlo finite element approximation of elliptic PDE with lognormal diffusion coefficients

    KAUST Repository

    Hall, Eric

    2016-01-09

    The Monte Carlo (and Multi-level Monte Carlo) finite element method can be used to approximate observables of solutions to diffusion equations with lognormal distributed diffusion coefficients, e.g. modeling ground water flow. Typical models use lognormal diffusion coefficients with H´ older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible and can be larger than the computable low frequency error. We address how the total error can be estimated by the computable error.

  2. Computational error estimates for Monte Carlo finite element approximation with log normal diffusion coefficients

    KAUST Repository

    Sandberg, Mattias

    2015-01-01

    log normal diffusion coefficients with H¨older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible

  3. The spectral element method for static neutron transport in AN approximation. Part I

    International Nuclear Information System (INIS)

    Barbarino, A.; Dulla, S.; Mund, E.H.; Ravetto, P.

    2013-01-01

    Highlights: ► Spectral elements methods (SEMs) are extended for the neutronics of nuclear reactor cores. ► The second-order, A N formulation of neutron trasport is adopted. ► Results for classical benchmark cases in 2D are presented and compared to finite elements. ► The advantages of SEM in terms of precision and convergence rate are illustrated. ► SEM consitutes a promising approach for the solution of neutron transport problems. - Abstract: Spectral elements methods provide very accurate solutions of elliptic problems. In this paper we apply the method to the A N (i.e. SP 2N−1 ) approximation of neutron transport. Numerical results for classical benchmark cases highlight its performance in comparison with finite element computations, in terms of accuracy per degree of freedom and convergence rate. All calculations presented in this paper refer to two-dimensional problems. The method can easily be extended to three-dimensional cases. The results illustrate promising features of the method for more complex transport problems

  4. Correlated random-phase approximation from densities and in-medium matrix elements

    Energy Technology Data Exchange (ETDEWEB)

    Trippel, Richard; Roth, Robert [Institut fuer Kernphysik, Technische Universitaet Darmstadt (Germany)

    2016-07-01

    The random-phase approximation (RPA) as well as the second RPA (SRPA) are established tools for the study of collective excitations in nuclei. Addressing the well known lack of correlations, we derived a universal framework for a fully correlated RPA based on the use of one- and two-body densities. We apply densities from coupled cluster theory and investigate the impact of correlations. As an alternative approach to correlations we use matrix elements transformed via in-medium similarity renormalization group (IM-SRG) in combination with RPA and SRPA. We find that within SRPA the use of IM-SRG matrix elements leads to the disappearance of instabilities of low-lying states. For the calculations we use normal-ordered two- plus three-body interactions derived from chiral effective field theory. We apply different Hamiltonians to a number of doubly-magic nuclei and calculate electric transition strengths.

  5. Computable Error Estimates for Finite Element Approximations of Elliptic Partial Differential Equations with Rough Stochastic Data

    KAUST Repository

    Hall, Eric Joseph

    2016-12-08

    We derive computable error estimates for finite element approximations of linear elliptic partial differential equations with rough stochastic coefficients. In this setting, the exact solutions contain high frequency content that standard a posteriori error estimates fail to capture. We propose goal-oriented estimates, based on local error indicators, for the pathwise Galerkin and expected quadrature errors committed in standard, continuous, piecewise linear finite element approximations. Derived using easily validated assumptions, these novel estimates can be computed at a relatively low cost and have applications to subsurface flow problems in geophysics where the conductivities are assumed to have lognormal distributions with low regularity. Our theory is supported by numerical experiments on test problems in one and two dimensions.

  6. Exact and approximate exchange potentials investigated in terms of their matrix elements with the Kohn-Sham orbitals

    International Nuclear Information System (INIS)

    Holas, A.; Cinal, M.

    2005-01-01

    Three approximate exchange potentials of high accuracy v x Y (r), Y=A,B,C, for the density-functional theory applications are obtained by replacing the matrix elements of the exact potential between the Kohn-Sham (KS) orbitals with such elements of the Fock exchange operator (within the virtual-occupied subset only) in three representations found for any local potential. A common identity is the base of these representations. The potential v x C happens to be the same as that derived by Harbola and Sahni, and v x A as that derived by Gritsenko and Baerends, and Della Sala and Goerling. The potentials obtained can be expressed in terms of occupied KS orbitals only. At large r, their asymptotic form -1/r is the same as that of the exact potential. The high quality of these three approximations is demonstrated by direct comparison with the exact potential and using various consistency tests. A common root established for the three approximations could be helpful in finding new and better approximations via modification of identities employed in the present investigation

  7. Computable Error Estimates for Finite Element Approximations of Elliptic Partial Differential Equations with Rough Stochastic Data

    KAUST Repository

    Hall, Eric Joseph; Hoel, Hå kon; Sandberg, Mattias; Szepessy, Anders; Tempone, Raul

    2016-01-01

    posteriori error estimates fail to capture. We propose goal-oriented estimates, based on local error indicators, for the pathwise Galerkin and expected quadrature errors committed in standard, continuous, piecewise linear finite element approximations

  8. An A Posteriori Error Analysis of Mixed Finite Element Galerkin Approximations to Second Order Linear Parabolic Problems

    KAUST Repository

    Memon, Sajid; Nataraj, Neela; Pani, Amiya Kumar

    2012-01-01

    In this article, a posteriori error estimates are derived for mixed finite element Galerkin approximations to second order linear parabolic initial and boundary value problems. Using mixed elliptic reconstructions, a posteriori error estimates in L∞(L2)- and L2(L2)-norms for the solution as well as its flux are proved for the semidiscrete scheme. Finally, based on a backward Euler method, a completely discrete scheme is analyzed and a posteriori error bounds are derived, which improves upon earlier results on a posteriori estimates of mixed finite element approximations to parabolic problems. Results of numerical experiments verifying the efficiency of the estimators have also been provided. © 2012 Society for Industrial and Applied Mathematics.

  9. Computable error estimates for Monte Carlo finite element approximation of elliptic PDE with lognormal diffusion coefficients

    KAUST Repository

    Hall, Eric; Haakon, Hoel; Sandberg, Mattias; Szepessy, Anders; Tempone, Raul

    2016-01-01

    lognormal diffusion coefficients with H´ older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible

  10. ABOUT SOLUTION OF MULTIPOINT BOUNDARY PROBLEMS OF TWO-DIMENSIONAL STRUCTURAL ANALYSIS WITH THE USE OF COMBINED APPLICATION OF FINITE ELEMENT METHOD AND DISCRETE-CONTINUAL FINITE ELEMENT METHOD PART 2: SPECIAL ASPECTS OF FINITE ELEMENT APPROXIMATION

    Directory of Open Access Journals (Sweden)

    Pavel A. Akimov

    2017-12-01

    Full Text Available As is well known, the formulation of a multipoint boundary problem involves three main components: a description of the domain occupied by the structure and the corresponding subdomains; description of the conditions inside the domain and inside the corresponding subdomains, the description of the conditions on the boundary of the domain, conditions on the boundaries between subdomains. This paper is a continuation of another work published earlier, in which the formulation and general principles of the approximation of the multipoint boundary problem of a static analysis of deep beam on the basis of the joint application of the finite element method and the discrete-continual finite element method were considered. It should be noted that the approximation within the fragments of a domain that have regular physical-geometric parameters along one of the directions is expedient to be carried out on the basis of the discrete-continual finite element method (DCFEM, and for the approximation of all other fragments it is necessary to use the standard finite element method (FEM. In the present publication, the formulas for the computing of displacements partial derivatives of displacements, strains and stresses within the finite element model (both within the finite element and the corresponding nodal values (with the use of averaging are presented. Boundary conditions between subdomains (respectively, discrete models and discrete-continual models and typical conditions such as “hinged support”, “free edge”, “perfect contact” (twelve basic (basic variants are available are under consideration as well. Governing formulas for computing of elements of the corresponding matrices of coefficients and vectors of the right-hand sides are given for each variant. All formulas are fully adapted for algorithmic implementation.

  11. An angularly refineable phase space finite element method with approximate sweeping procedure

    International Nuclear Information System (INIS)

    Kophazi, J.; Lathouwers, D.

    2013-01-01

    An angularly refineable phase space finite element method is proposed to solve the neutron transport equation. The method combines the advantages of two recently published schemes. The angular domain is discretized into small patches and patch-wise discontinuous angular basis functions are restricted to these patches, i.e. there is no overlap between basis functions corresponding to different patches. This approach yields block diagonal Jacobians with small block size and retains the possibility for S n -like approximate sweeping of the spatially discontinuous elements in order to provide efficient preconditioners for the solution procedure. On the other hand, the preservation of the full FEM framework (as opposed to collocation into a high-order S n scheme) retains the possibility of the Galerkin interpolated connection between phase space elements at arbitrary levels of discretization. Since the basis vectors are not orthonormal, a generalization of the Riemann procedure is introduced to separate the incoming and outgoing contributions in case of unstructured meshes. However, due to the properties of the angular discretization, the Riemann procedure can be avoided at a large fraction of the faces and this fraction rapidly increases as the level of refinement increases, contributing to the computational efficiency. In this paper the properties of the discretization scheme are studied with uniform refinement using an iterative solver based on the S 2 sweep order of the spatial elements. The fourth order convergence of the scalar flux is shown as anticipated from earlier schemes and the rapidly decreasing fraction of required Riemann faces is illustrated. (authors)

  12. Bent approximations to synchrotron radiation optics

    International Nuclear Information System (INIS)

    Heald, S.

    1981-01-01

    Ideal optical elements can be approximated by bending flats or cylinders. This paper considers the applications of these approximate optics to synchrotron radiation. Analytic and raytracing studies are used to compare their optical performance with the corresponding ideal elements. It is found that for many applications the performance is adequate, with the additional advantages of lower cost and greater flexibility. Particular emphasis is placed on obtaining the practical limitations on the use of the approximate elements in typical beamline configurations. Also considered are the possibilities for approximating very long length mirrors using segmented mirrors

  13. Lowest order Virtual Element approximation of magnetostatic problems

    Science.gov (United States)

    Beirão da Veiga, L.; Brezzi, F.; Dassi, F.; Marini, L. D.; Russo, A.

    2018-04-01

    We give here a simplified presentation of the lowest order Serendipity Virtual Element method, and show its use for the numerical solution of linear magneto-static problems in three dimensions. The method can be applied to very general decompositions of the computational domain (as is natural for Virtual Element Methods) and uses as unknowns the (constant) tangential component of the magnetic field $\\mathbf{H}$ on each edge, and the vertex values of the Lagrange multiplier $p$ (used to enforce the solenoidality of the magnetic induction $\\mathbf{B}=\\mu\\mathbf{H}$). In this respect the method can be seen as the natural generalization of the lowest order Edge Finite Element Method (the so-called "first kind N\\'ed\\'elec" elements) to polyhedra of almost arbitrary shape, and as we show on some numerical examples it exhibits very good accuracy (for being a lowest order element) and excellent robustness with respect to distortions.

  14. Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange finite elements

    KAUST Repository

    Bonito, Andrea; Guermond, Jean-Luc

    2011-01-01

    We propose and analyze an approximation technique for the Maxwell eigenvalue problem using H1-conforming finite elements. The key idea consists of considering a mixed method controlling the divergence of the electric field in a fractional Sobolev space H-α with α ∈ (1/2, 1). The method is shown to be convergent and spectrally correct. © 2011 American Mathematical Society.

  15. On approximation of non-Newtonian fluid flow by the finite element method

    Science.gov (United States)

    Svácek, Petr

    2008-08-01

    In this paper the problem of numerical approximation of non-Newtonian fluid flow with free surface is considered. Namely, the flow of fresh concrete is addressed. Industrial mixtures often behaves like non-Newtonian fluids exhibiting a yield stress that needs to be overcome for the flow to take place, cf. [R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids, vol. 1, Fluid Mechanics, Wiley, New York, 1987; R.P. Chhabra, J.F. Richardson, Non-Newtonian Flow in the Process Industries, Butterworth-Heinemann, London, 1999]. The main interest is paid to the mathematical formulation of the problem and to discretization with the aid of finite element method. The described numerical procedure is applied onto the solution of several problems.

  16. Extended Finite Element Method with Simplified Spherical Harmonics Approximation for the Forward Model of Optical Molecular Imaging

    Directory of Open Access Journals (Sweden)

    Wei Li

    2012-01-01

    Full Text Available An extended finite element method (XFEM for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SPN. In XFEM scheme of SPN equations, the signed distance function is employed to accurately represent the internal tissue boundary, and then it is used to construct the enriched basis function of the finite element scheme. Therefore, the finite element calculation can be carried out without the time-consuming internal boundary mesh generation. Moreover, the required overly fine mesh conforming to the complex tissue boundary which leads to excess time cost can be avoided. XFEM conveniences its application to tissues with complex internal structure and improves the computational efficiency. Phantom and digital mouse experiments were carried out to validate the efficiency of the proposed method. Compared with standard finite element method and classical Monte Carlo (MC method, the validation results show the merits and potential of the XFEM for optical imaging.

  17. Rolling element bearings diagnostics using the Symbolic Aggregate approXimation

    Science.gov (United States)

    Georgoulas, George; Karvelis, Petros; Loutas, Theodoros; Stylios, Chrysostomos D.

    2015-08-01

    Rolling element bearings are a very critical component in various engineering assets. Therefore it is of paramount importance the detection of possible faults, especially at an early stage, that may lead to unexpected interruptions of the production or worse, to severe accidents. This research work introduces a novel, in the field of bearing fault detection, method for the extraction of diagnostic representations of vibration recordings using the Symbolic Aggregate approXimation (SAX) framework and the related intelligent icons representation. SAX essentially transforms the original real valued time-series into a discrete one, which is then represented by a simple histogram form summarizing the occurrence of the chosen symbols/words. Vibration signals from healthy bearings and bearings with three different fault locations and with three different severity levels, as well as loading conditions, are analyzed. Considering the diagnostic problem as a classification one, the analyzed vibration signals and the resulting feature vectors feed simple classifiers achieving remarkably high classification accuracies. Moreover a sliding window scheme combined with a simple majority voting filter further increases the reliability and robustness of the diagnostic method. The results encourage the potential use of the proposed methodology for the diagnosis of bearing faults.

  18. A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging

    International Nuclear Information System (INIS)

    Lu Yujie; Zhu Banghe; Rasmussen, John C; Sevick-Muraca, Eva M; Shen Haiou; Wang Ge

    2010-01-01

    Fluorescence molecular imaging/tomography may play an important future role in preclinical research and clinical diagnostics. Time- and frequency-domain fluorescence imaging can acquire more measurement information than the continuous wave (CW) counterpart, improving the image quality of fluorescence molecular tomography. Although diffusion approximation (DA) theory has been extensively applied in optical molecular imaging, high-order photon migration models need to be further investigated to match quantitation provided by nuclear imaging. In this paper, a frequency-domain parallel adaptive finite element solver is developed with simplified spherical harmonics (SP N ) approximations. To fully evaluate the performance of the SP N approximations, a fast time-resolved tetrahedron-based Monte Carlo fluorescence simulator suitable for complex heterogeneous geometries is developed using a convolution strategy to realize the simulation of the fluorescence excitation and emission. The validation results show that high-order SP N can effectively correct the modeling errors of the diffusion equation, especially when the tissues have high absorption characteristics or when high modulation frequency measurements are used. Furthermore, the parallel adaptive mesh evolution strategy improves the modeling precision and the simulation speed significantly on a realistic digital mouse phantom. This solver is a promising platform for fluorescence molecular tomography using high-order approximations to the radiative transfer equation.

  19. Calculation of photon attenuation coefficients of elements and compounds from approximate semi-analytical formulae

    Energy Technology Data Exchange (ETDEWEB)

    Roteta, M; Baro, J; Fernandez-Varea, J M; Salvat, F

    1994-07-01

    The FORTRAN 77 code PHOTAC to compute photon attenuation coefficients of elements and compounds is described. The code is based on the semi analytical approximate atomic cross sections proposed by Baro et al. (1994). Photoelectric cross sections for coherent and incoherent scattering and for pair production are obtained as integrals of the corresponding differential cross sections. These integrals are evaluated, to a pre-selected accuracy, by using a 20-point Gauss adaptive integration algorithm. Calculated attenuation coefficients agree with recently compiled databases to within - 1%, in the energy range from 1 keV to 1 GeV. The complete source listing of the program PHOTAC is included. (Author) 14 refs.

  20. Calculation of photon attenuation coefficients of elements and compounds from approximate semi-analytical formulae

    International Nuclear Information System (INIS)

    Roteta, M.; Baro, J.; Fernandez-Varea, J. M.; Salvat, F.

    1994-01-01

    The FORTRAN 77 code PHOTAC to compute photon attenuation coefficients of elements and compounds is described. The code is based on the semi analytical approximate atomic cross sections proposed by Baro et al. (1994). Photoelectric cross sections for coherent and incoherent scattering and for pair production are obtained as integrals of the corresponding differential cross sections. These integrals are evaluated, to a pre-selected accuracy, by using a 20-point Gauss adaptive integration algorithm. Calculated attenuation coefficients agree with recently compiled databases to within - 1%, in the energy range from 1 keV to 1 GeV. The complete source listing of the program PHOTAC is included. (Author) 14 refs

  1. Nonlinear approximation with dictionaries I. Direct estimates

    DEFF Research Database (Denmark)

    Gribonval, Rémi; Nielsen, Morten

    2004-01-01

    We study various approximation classes associated with m-term approximation by elements from a (possibly) redundant dictionary in a Banach space. The standard approximation class associated with the best m-term approximation is compared to new classes defined by considering m-term approximation w...

  2. Calculation of photon attenuation coefficients of elements and compounds from approximate semi-analytical formulae

    International Nuclear Information System (INIS)

    Roteta, M.; Baro, J.; Fernandez-Varea, J.M.; Salvat, F.

    1994-01-01

    The FORTRAN 77 code PHOTAC to compute photon attenuation coefficients of elements and compounds is described. The code is based on the semi-analytical approximate atomic cross sections proposed by Baro et al. (1994). Photoelectric cross sections are calculated directly from a simple analytical expression. Atomic cross sections for coherent and incoherent scattering and for pair production are obtained as integrals of the corresponding differential cross sections. These integrals are evaluated, to a pre-selected accuracy, by using a 20-point Gauss adaptive integration algorithm. Calculated attenuation coefficients agree with recently compiled databases to within equal 1%, in the energy range from 1 KeV to 1 GeV. The complete source listing of the program PHOTAC is included

  3. An approximate method for calculating electron-phonon matrix element of a disordered transition metal and relevant comments on superconductivity

    International Nuclear Information System (INIS)

    Zhang, L.

    1981-08-01

    A method based on the tight-binding approximation is developed to calculate the electron-phonon matrix element for the disordered transition metals. With the method as a basis the experimental Tsub(c) data of the amorphous transition metal superconductors are re-analysed. Some comments on the superconductivity of the disordered materials are given

  4. A non-conformal finite element/finite volume scheme for the non-structured grid-based approximation of low Mach number flows; Un schema elements finis non-conformes/volumes finis pour l'approximation en maillages non-structures des ecoulements a faible nombre de Mach

    Energy Technology Data Exchange (ETDEWEB)

    Ansanay-Alex, G.

    2009-06-17

    The development of simulation codes aimed at a precise simulation of fires requires a precise approach of flame front phenomena by using very fine grids. The need to take different spatial scale into consideration leads to a local grid refinement and to a discretization with homogeneous grid for computing time and memory purposes. The author reports the approximation of the non-linear convection term, the scalar advection-diffusion in finite volumes, numerical simulations of a flow in a bent tube, of a three-dimensional laminar flame and of a low Mach number an-isotherm flow. Non conformal finite elements are also presented (Rannacher-Turek and Crouzeix-Raviart elements)

  5. About solution of multipoint boundary problem of static analysis of deep beam with the use of combined application of finite element method and discrete-continual finite element method. part 1: formulation of the problem and general principles of approximation

    Directory of Open Access Journals (Sweden)

    Lyakhovich Leonid

    2017-01-01

    Full Text Available This paper is devoted to formulation and general principles of approximation of multipoint boundary problem of static analysis of deep beam with the use of combined application of finite element method (FEM discrete-continual finite element method (DCFEM. The field of application of DCFEM comprises structures with regular physical and geometrical parameters in some dimension (“basic” dimension. DCFEM presupposes finite element approximation for non-basic dimension while in the basic dimension problem remains continual. DCFEM is based on analytical solutions of resulting multipoint boundary problems for systems of ordinary differential equations with piecewise-constant coefficients.

  6. Finite element approximation of the fields of bulk and interfacial line defects

    Science.gov (United States)

    Zhang, Chiqun; Acharya, Amit; Puri, Saurabh

    2018-05-01

    A generalized disclination (g.disclination) theory (Acharya and Fressengeas, 2015) has been recently introduced that goes beyond treating standard translational and rotational Volterra defects in a continuously distributed defects approach; it is capable of treating the kinematics and dynamics of terminating lines of elastic strain and rotation discontinuities. In this work, a numerical method is developed to solve for the stress and distortion fields of g.disclination systems. Problems of small and finite deformation theory are considered. The fields of a single disclination, a single dislocation treated as a disclination dipole, a tilt grain boundary, a misfitting grain boundary with disconnections, a through twin boundary, a terminating twin boundary, a through grain boundary, a star disclination/penta-twin, a disclination loop (with twist and wedge segments), and a plate, a lenticular, and a needle inclusion are approximated. It is demonstrated that while the far-field topological identity of a dislocation of appropriate strength and a disclination-dipole plus a slip dislocation comprising a disconnection are the same, the latter microstructure is energetically favorable. This underscores the complementary importance of all of topology, geometry, and energetics in understanding defect mechanics. It is established that finite element approximations of fields of interfacial and bulk line defects can be achieved in a systematic and routine manner, thus contributing to the study of intricate defect microstructures in the scientific understanding and predictive design of materials. Our work also represents one systematic way of studying the interaction of (g.)disclinations and dislocations as topological defects, a subject of considerable subtlety and conceptual importance (Aharoni et al., 2017; Mermin, 1979).

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

    Science.gov (United States)

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

    2018-04-01

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

  8. A non-conformal finite element/finite volume scheme for the non-structured grid-based approximation of low Mach number flows

    International Nuclear Information System (INIS)

    Ansanay-Alex, G.

    2009-01-01

    The development of simulation codes aimed at a precise simulation of fires requires a precise approach of flame front phenomena by using very fine grids. The need to take different spatial scale into consideration leads to a local grid refinement and to a discretization with homogeneous grid for computing time and memory purposes. The author reports the approximation of the non-linear convection term, the scalar advection-diffusion in finite volumes, numerical simulations of a flow in a bent tube, of a three-dimensional laminar flame and of a low Mach number an-isotherm flow. Non conformal finite elements are also presented (Rannacher-Turek and Crouzeix-Raviart elements)

  9. Repfinder: Finding approximately repeated scene elements for image editing

    KAUST Repository

    Cheng, Ming-Ming

    2010-07-26

    Repeated elements are ubiquitous and abundant in both manmade and natural scenes. Editing such images while preserving the repetitions and their relations is nontrivial due to overlap, missing parts, deformation across instances, illumination variation, etc. Manually enforcing such relations is laborious and error-prone. We propose a novel framework where user scribbles are used to guide detection and extraction of such repeated elements. Our detection process, which is based on a novel boundary band method, robustly extracts the repetitions along with their deformations. The algorithm only considers the shape of the elements, and ignores similarity based on color, texture, etc. We then use topological sorting to establish a partial depth ordering of overlapping repeated instances. Missing parts on occluded instances are completed using information from other instances. The extracted repeated instances can then be seamlessly edited and manipulated for a variety of high level tasks that are otherwise difficult to perform. We demonstrate the versatility of our framework on a large set of inputs of varying complexity, showing applications to image rearrangement, edit transfer, deformation propagation, and instance replacement. © 2010 ACM.

  10. Investigation of thermal energy transport from an anisotropic central heating element to the adjacent channels: A multipoint flux approximation

    KAUST Repository

    Salama, Amgad

    2015-02-01

    The problem of heat transfer from a central heating element pressed between two clad plates to cooling channels adjacent and outboard of the plates is investigated numerically. The aim of this work is to highlight the role of thermal conductivity anisotropy of the heating element and/or the encompassing plates on thermal energy transport to the fluid passing through the two channels. When the medium is anisotropic with respect to thermal conductivity; energy transport to the neighboring channels is no longer symmetric. This asymmetry in energy fluxes influence heat transfer to the coolant resulting in different patterns of temperature fields. In particular, it is found that the temperature fields are skewed towards the principal direction of anisotropy. In addition, the heat flux distributions along the edges of the heating element are also different as a manifestation of thermal conductivity anisotropy. Furthermore, the peak temperature at the channel walls change location and magnitude depending on the principal direction of anisotropy. Based on scaling arguments, it is found that, the ratio of width to the height of the heating system is a key parameter which can suggest when one may ignore the effect of the cross-diagonal terms of the full conductivity tensor. To account for anisotropy in thermal conductivity, the method of multipoint flux approximation (MPFA) is employed. Using this technique, it is possible to find a finite difference stencil which can handle full thermal conductivity tensor and in the same time enjoys the simplicity of finite difference approximation. Although the finite difference stencil based on MPFA is quite complex, in this work we apply the recently introduced experimenting field approach which construct the global problem automatically.

  11. The optimal XFEM approximation for fracture analysis

    International Nuclear Information System (INIS)

    Jiang Shouyan; Du Chengbin; Ying Zongquan

    2010-01-01

    The extended finite element method (XFEM) provides an effective tool for analyzing fracture mechanics problems. A XFEM approximation consists of standard finite elements which are used in the major part of the domain and enriched elements in the enriched sub-domain for capturing special solution properties such as discontinuities and singularities. However, two issues in the standard XFEM should specially be concerned: efficient numerical integration methods and an appropriate construction of the blending elements. In the paper, an optimal XFEM approximation is proposed to overcome the disadvantage mentioned above in the standard XFEM. The modified enrichment functions are presented that can reproduced exactly everywhere in the domain. The corresponding FORTRAN program is developed for fracture analysis. A classic problem of fracture mechanics is used to benchmark the program. The results indicate that the optimal XFEM can alleviate the errors and improve numerical precision.

  12. The matrix-elements of two-particle residual interaction in the shell-model formalism with the M.S.D.I. approximation. Part 2

    International Nuclear Information System (INIS)

    Jasielska, A.; Wiktor, S.

    1977-01-01

    The table of two-particle matrix elements calculated according to the formalism of MSDI approximation for the orbits 1fsub(7/2), 2psub(3/2), 2psub(1/2) and 1fsub(5/2) and published previously is now supplemented by inclusion of the 1gsub(9/2) orbit. (author)

  13. Coefficients Calculation in Pascal Approximation for Passive Filter Design

    Directory of Open Access Journals (Sweden)

    George B. Kasapoglu

    2018-02-01

    Full Text Available The recently modified Pascal function is further exploited in this paper in the design of passive analog filters. The Pascal approximation has non-equiripple magnitude, in contrast of the most well-known approximations, such as the Chebyshev approximation. A novelty of this work is the introduction of a precise method that calculates the coefficients of the Pascal function. Two examples are presented for the passive design to illustrate the advantages and the disadvantages of the Pascal approximation. Moreover, the values of the passive elements can be taken from tables, which are created to define the normalized values of these elements for the Pascal approximation, as Zverev had done for the Chebyshev, Elliptic, and other approximations. Although Pascal approximation can be implemented to both passive and active filter designs, a passive filter design is addressed in this paper, and the benefits and shortcomings of Pascal approximation are presented and discussed.

  14. Fate of pesticides in field ditches: the TOXSWA simulation model

    NARCIS (Netherlands)

    Adriaanse, P.I.

    1996-01-01

    The TOXSWA model describes the fate of pesticides entering field ditches by spray drift, atmospheric deposition, surface run-off, drainage or leaching. It considers four processes: transport, transformation, sorption and volatilization. Analytical andnumerical solutions corresponded well. A sample

  15. Well-Balanced Second-Order Approximation of the Shallow Water Equations With Friction via Continuous Galerkin Finite Elements

    Science.gov (United States)

    Quezada de Luna, M.; Farthing, M.; Guermond, J. L.; Kees, C. E.; Popov, B.

    2017-12-01

    The Shallow Water Equations (SWEs) are popular for modeling non-dispersive incompressible water waves where the horizontal wavelength is much larger than the vertical scales. They can be derived from the incompressible Navier-Stokes equations assuming a constant vertical velocity. The SWEs are important in Geophysical Fluid Dynamics for modeling surface gravity waves in shallow regimes; e.g., in the deep ocean. Some common geophysical applications are the evolution of tsunamis, river flooding and dam breaks, storm surge simulations, atmospheric flows and others. This work is concerned with the approximation of the time-dependent Shallow Water Equations with friction using explicit time stepping and continuous finite elements. The objective is to construct a method that is at least second-order accurate in space and third or higher-order accurate in time, positivity preserving, well-balanced with respect to rest states, well-balanced with respect to steady sliding solutions on inclined planes and robust with respect to dry states. Methods fulfilling the desired goals are common within the finite volume literature. However, to the best of our knowledge, schemes with the above properties are not well developed in the context of continuous finite elements. We start this work based on a finite element method that is second-order accurate in space, positivity preserving and well-balanced with respect to rest states. We extend it by: modifying the artificial viscosity (via the entropy viscosity method) to deal with issues of loss of accuracy around local extrema, considering a singular Manning friction term handled via an explicit discretization under the usual CFL condition, considering a water height regularization that depends on the mesh size and is consistent with the polynomial approximation, reducing dispersive errors introduced by lumping the mass matrix and others. After presenting the details of the method we show numerical tests that demonstrate the well

  16. Repfinder: Finding approximately repeated scene elements for image editing

    KAUST Repository

    Cheng, Ming-Ming; Zhang, Fanglue; Mitra, Niloy J.; Huang, Xiaolei; Hu, Shimin

    2010-01-01

    variation, etc. Manually enforcing such relations is laborious and error-prone. We propose a novel framework where user scribbles are used to guide detection and extraction of such repeated elements. Our detection process, which is based on a novel boundary

  17. Approximate Reanalysis in Topology Optimization

    DEFF Research Database (Denmark)

    Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole

    2009-01-01

    In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures...

  18. Simultaneous approximation in scales of Banach spaces

    International Nuclear Information System (INIS)

    Bramble, J.H.; Scott, R.

    1978-01-01

    The problem of verifying optimal approximation simultaneously in different norms in a Banach scale is reduced to verification of optimal approximation in the highest order norm. The basic tool used is the Banach space interpolation method developed by Lions and Peetre. Applications are given to several problems arising in the theory of finite element methods

  19. Uniform analytic approximation of Wigner rotation matrices

    Science.gov (United States)

    Hoffmann, Scott E.

    2018-02-01

    We derive the leading asymptotic approximation, for low angle θ, of the Wigner rotation matrix elements, dm1m2 j(θ ) , uniform in j, m1, and m2. The result is in terms of a Bessel function of integer order. We numerically investigate the error for a variety of cases and find that the approximation can be useful over a significant range of angles. This approximation has application in the partial wave analysis of wavepacket scattering.

  20. On badly approximable complex numbers

    DEFF Research Database (Denmark)

    Esdahl-Schou, Rune; Kristensen, S.

    We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably...

  1. Modeling the Elastic and Damping Properties of the Multilayered Torsion Bar-Blade Structure of Rotors of Light Helicopters of the New Generation. 1. Finite-Element Approximation of the Torsion Bar

    Science.gov (United States)

    Paimushin, V. N.; Shishkin, V. M.

    2015-11-01

    A prismatic semiquadratic element with a nonclassical approximation of its displacements is suggested for modeling the composite and soft layers of a torsion bar and multilayered plate-rod structures. The stiffness, weight, damping, and geometric stiffness matrices of the above-mentioned element are obtained. Expressions for computing stresses in the finite element under the action of static loads and vibrations in the resonance zone are presented. Test examples confirming the validity of the element suggested are given. An example of finite element determination of the dynamic response of a multilayered torsion bar in the resonant mode is considered.

  2. Approximate Noether symmetries and collineations for regular perturbative Lagrangians

    Science.gov (United States)

    Paliathanasis, Andronikos; Jamal, Sameerah

    2018-01-01

    Regular perturbative Lagrangians that admit approximate Noether symmetries and approximate conservation laws are studied. Specifically, we investigate the connection between approximate Noether symmetries and collineations of the underlying manifold. In particular we determine the generic Noether symmetry conditions for the approximate point symmetries and we find that for a class of perturbed Lagrangians, Noether symmetries are related to the elements of the Homothetic algebra of the metric which is defined by the unperturbed Lagrangian. Moreover, we discuss how exact symmetries become approximate symmetries. Finally, some applications are presented.

  3. Nonlinear Multigrid solver exploiting AMGe Coarse Spaces with Approximation Properties

    DEFF Research Database (Denmark)

    Christensen, Max la Cour; Villa, Umberto; Engsig-Karup, Allan Peter

    The paper introduces a nonlinear multigrid solver for mixed finite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstructured problems is the guaranteed approximation property of the AMGe coarse...... properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on unstructured meshes has the ability to be as powerful/successful as FAS on geometrically refined meshes. For comparison, Newton’s method and Picard iterations with an inner state-of-the-art linear solver...... are compared to FAS on a nonlinear saddle point problem with applications to porous media flow. It is demonstrated that FAS is faster than Newton’s method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate...

  4. Hybrid synchronization of two independent chaotic systems on ...

    Indian Academy of Sciences (India)

    One is how the same network node of the complex network was affected by different information sources. Another is how to achieve hybrid synchronization on the network. In this paper, the theoretical analysis andnumerical simulation on various complex networks are implemented. The results indicate that the hybrid ...

  5. Approximation theorems by Meyer-Koenig and Zeller type operators

    International Nuclear Information System (INIS)

    Ali Ozarslan, M.; Duman, Oktay

    2009-01-01

    This paper is mainly connected with the approximation properties of Meyer-Koenig and Zeller (MKZ) type operators. We first introduce a general sequence of MKZ operators based on q-integers and then obtain a Korovkin-type approximation theorem for these operators. We also compute their rates of convergence by means of modulus of continuity and the elements of Lipschitz class functionals. Furthermore, we give an rth order generalization of our operators in order to get some explicit approximation results.

  6. Approximate solution methods in engineering mechanics

    International Nuclear Information System (INIS)

    Boresi, A.P.; Cong, K.P.

    1991-01-01

    This is a short book of 147 pages including references and sometimes bibliographies at the end of each chapter, and subject and author indices at the end of the book. The test includes an introduction of 3 pages, 29 pages explaining approximate analysis, 41 pages on finite differences, 36 pages on finite elements, and 17 pages on specialized methods

  7. Finite approximations in fluid mechanics

    International Nuclear Information System (INIS)

    Hirschel, E.H.

    1986-01-01

    This book contains twenty papers on work which was conducted between 1983 and 1985 in the Priority Research Program ''Finite Approximations in Fluid Mechanics'' of the German Research Society (Deutsche Forschungsgemeinschaft). Scientists from numerical mathematics, fluid mechanics, and aerodynamics present their research on boundary-element methods, factorization methods, higher-order panel methods, multigrid methods for elliptical and parabolic problems, two-step schemes for the Euler equations, etc. Applications are made to channel flows, gas dynamical problems, large eddy simulation of turbulence, non-Newtonian flow, turbomachine flow, zonal solutions for viscous flow problems, etc. The contents include: multigrid methods for problems from fluid dynamics, development of a 2D-Transonic Potential Flow Solver; a boundary element spectral method for nonstationary viscous flows in 3 dimensions; navier-stokes computations of two-dimensional laminar flows in a channel with a backward facing step; calculations and experimental investigations of the laminar unsteady flow in a pipe expansion; calculation of the flow-field caused by shock wave and deflagration interaction; a multi-level discretization and solution method for potential flow problems in three dimensions; solutions of the conservation equations with the approximate factorization method; inviscid and viscous flow through rotating meridional contours; zonal solutions for viscous flow problems

  8. Discrete maximum principle for the P1 - P0 weak Galerkin finite element approximations

    Science.gov (United States)

    Wang, Junping; Ye, Xiu; Zhai, Qilong; Zhang, Ran

    2018-06-01

    This paper presents two discrete maximum principles (DMP) for the numerical solution of second order elliptic equations arising from the weak Galerkin finite element method. The results are established by assuming an h-acute angle condition for the underlying finite element triangulations. The mathematical theory is based on the well-known De Giorgi technique adapted in the finite element context. Some numerical results are reported to validate the theory of DMP.

  9. Finite element model updating of a prestressed concrete box girder bridge using subproblem approximation

    Science.gov (United States)

    Chen, G. W.; Omenzetter, P.

    2016-04-01

    This paper presents the implementation of an updating procedure for the finite element model (FEM) of a prestressed concrete continuous box-girder highway off-ramp bridge. Ambient vibration testing was conducted to excite the bridge, assisted by linear chirp sweepings induced by two small electrodynamic shakes deployed to enhance the excitation levels, since the bridge was closed to traffic. The data-driven stochastic subspace identification method was executed to recover the modal properties from measurement data. An initial FEM was developed and correlation between the experimental modal results and their analytical counterparts was studied. Modelling of the pier and abutment bearings was carefully adjusted to reflect the real operational conditions of the bridge. The subproblem approximation method was subsequently utilized to automatically update the FEM. For this purpose, the influences of bearing stiffness, and mass density and Young's modulus of materials were examined as uncertain parameters using sensitivity analysis. The updating objective function was defined based on a summation of squared values of relative errors of natural frequencies between the FEM and experimentation. All the identified modes were used as the target responses with the purpose of putting more constrains for the optimization process and decreasing the number of potentially feasible combinations for parameter changes. The updated FEM of the bridge was able to produce sufficient improvements in natural frequencies in most modes of interest, and can serve for a more precise dynamic response prediction or future investigation of the bridge health.

  10. Numerical Approximation of Elasticity Tensor Associated With Green-Naghdi Rate.

    Science.gov (United States)

    Liu, Haofei; Sun, Wei

    2017-08-01

    Objective stress rates are often used in commercial finite element (FE) programs. However, deriving a consistent tangent modulus tensor (also known as elasticity tensor or material Jacobian) associated with the objective stress rates is challenging when complex material models are utilized. In this paper, an approximation method for the tangent modulus tensor associated with the Green-Naghdi rate of the Kirchhoff stress is employed to simplify the evaluation process. The effectiveness of the approach is demonstrated through the implementation of two user-defined fiber-reinforced hyperelastic material models. Comparisons between the approximation method and the closed-form analytical method demonstrate that the former can simplify the material Jacobian evaluation with satisfactory accuracy while retaining its computational efficiency. Moreover, since the approximation method is independent of material models, it can facilitate the implementation of complex material models in FE analysis using shell/membrane elements in abaqus.

  11. NONLINEAR MULTIGRID SOLVER EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES

    Energy Technology Data Exchange (ETDEWEB)

    Christensen, Max La Cour [Technical Univ. of Denmark, Lyngby (Denmark); Villa, Umberto E. [Univ. of Texas, Austin, TX (United States); Engsig-Karup, Allan P. [Technical Univ. of Denmark, Lyngby (Denmark); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2016-01-22

    The paper introduces a nonlinear multigrid solver for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear solver is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a solver with the potential for mesh-independent convergence on general unstructured meshes.

  12. Square well approximation to the optical potential

    International Nuclear Information System (INIS)

    Jain, A.K.; Gupta, M.C.; Marwadi, P.R.

    1976-01-01

    Approximations for obtaining T-matrix elements for a sum of several potentials in terms of T-matrices for individual potentials are studied. Based on model calculations for S-wave for a sum of two separable non-local potentials of Yukawa type form factors and a sum of two delta function potentials, it is shown that the T-matrix for a sum of several potentials can be approximated satisfactorily over all the energy regions by the sum of T-matrices for individual potentials. Based on this, an approximate method for finding T-matrix for any local potential by approximating it by a sum of suitable number of square wells is presented. This provides an interesting way to calculate the T-matrix for any arbitary potential in terms of Bessel functions to a good degree of accuracy. The method is applied to the Saxon-Wood potentials and good agreement with exact results is found. (author)

  13. Multilayer shallow shelf approximation: Minimisation formulation, finite element solvers and applications

    Energy Technology Data Exchange (ETDEWEB)

    Jouvet, Guillaume, E-mail: jouvet@vaw.baug.ethz.ch [Institut für Mathematik, Freie Universität Berlin (Germany); Laboratory of Hydraulics, Hydrology and Glaciology, ETH Zurich (Switzerland)

    2015-04-15

    In this paper, a multilayer generalisation of the Shallow Shelf Approximation (SSA) is considered. In this recent hybrid ice flow model, the ice thickness is divided into thin layers, which can spread out, contract and slide over each other in such a way that the velocity profile is layer-wise constant. Like the SSA (1-layer model), the multilayer model can be reformulated as a minimisation problem. However, unlike the SSA, the functional to be minimised involves a new penalisation term for the interlayer jumps of the velocity, which represents the vertical shear stresses induced by interlayer sliding. Taking advantage of this reformulation, numerical solvers developed for the SSA can be naturally extended layer-wise or column-wise. Numerical results show that the column-wise extension of a Newton multigrid solver proves to be robust in the sense that its convergence is barely influenced by the number of layers and the type of ice flow. In addition, the multilayer formulation appears to be naturally better conditioned than the one of the first-order approximation to face the anisotropic conditions of the sliding-dominant ice flow of ISMIP-HOM experiments.

  14. Two-dimensional multigroup finite element calculation of fast reactor in diffusion approximation

    International Nuclear Information System (INIS)

    Schmid, J.

    1986-06-01

    When a linear element of triangular shape is used the actual finite element calculation is relatively simple. Extensive programs for mesh generation were written for easy inputting the configuration of reactors. A number of other programs were written for plotting neutron flux fields in individual groups, the power distribution, spatial plotting of fields, etc. The operation of selected programs, data preparation and operating instructions are described and examples given of data and results. All programs are written in GIER ALGOL. The used method and the developed programs have demonstrated that they are a useful instrument for the calculation of criticality and the distribution of neutron flux and power of both fast and thermal reactors. (J.B.)

  15. Space-angle approximations in the variational nodal method

    International Nuclear Information System (INIS)

    Lewis, E. E.; Palmiotti, G.; Taiwo, T.

    1999-01-01

    The variational nodal method is formulated such that the angular and spatial approximations maybe examined separately. Spherical harmonic, simplified spherical harmonic, and discrete ordinate approximations are coupled to the primal hybrid finite element treatment of the spatial variables. Within this framework, two classes of spatial trial functions are presented: (1) orthogonal polynomials for the treatment of homogeneous nodes and (2) bilinear finite subelement trial functions for the treatment of fuel assembly sized nodes in which fuel-pin cell cross sections are represented explicitly. Polynomial and subelement trial functions are applied to benchmark water-reactor problems containing MOX fuel using spherical harmonic and simplified spherical harmonic approximations. The resulting accuracy and computing costs are compared

  16. A Finite Element Analysis of Optimal Variable Thickness Sheets

    DEFF Research Database (Denmark)

    Petersson, Joakim S

    1996-01-01

    A quasimixed Finite Element (FE) method for maximum stiffness of variablethickness sheets is analysed. The displacement is approximated with ninenode Lagrange quadrilateral elements and the thickness is approximated aselementwise constant. One is guaranteed that the FE displacement solutionswill ...

  17. Bond charge approximation for valence electron density in elemental semiconductors

    International Nuclear Information System (INIS)

    Bashenov, V.K.; Gorbachov, V.E.; Marvakov, D.I.

    1985-07-01

    The spatial valence electron distribution in silicon and diamond is calculated in adiabatic bond charge approximation at zero temperature when bond charges have the Gaussian shape and their tensor character is taken into account. An agreement between theory and experiment has been achieved. For this purpose Xia's ionic pseudopotentials and Schulze-Unger's dielectric function are used. By two additional parameters Asub(B) and Zsub(B)sup(') we describe the spatial extent of the bond charge and local-field corrections, respectively. The parameter Zsub(B)sup(') accounts for the ratio between the Coulomb and exchange correlation interactions of the valence electrons and its silicon and diamond values have different signs. (author)

  18. Diophantine approximation and badly approximable sets

    DEFF Research Database (Denmark)

    Kristensen, S.; Thorn, R.; Velani, S.

    2006-01-01

    . The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...

  19. Finite element approximations of the stokes flow problem based upon various variational principles

    International Nuclear Information System (INIS)

    Franca, L.P.; Hughers, T.J.R.; Stenberg, R.

    1989-05-01

    Finite element methods are constructed by adding to the usual Galerkin method terms that are mesh-dependent least-squares forms of the Euler-Lagrange equations. The methods are consistent and possess additional stability compared to the Galerkin method. Finite element interpolations, which are unstable in the Galerkin approach, are now convergent. The methodology is applied to the velocity-pressure formulation, a.k.a., Herrmann's formulation, to the stress-velocity formulation, a.k.a., Hellinger-Reissner's formulation and to a new formulation based on augmented stress, pressure and velocity [pt

  20. Pade approximants for the Saxon-Woods potential

    International Nuclear Information System (INIS)

    Niculescu, V.I.R.; Catana, D.

    1995-01-01

    In the present work central Saxon-Woods (SW) potential and a uniform sphere Coulomb potential for protons are replaced with a Pade approximants. In this way expressions of the matrix elements of this potential form can be evaluated by the theory of complex functions. The methods assures satisfactory precision in a shorter computational time. (M.I.C) 1 fig., 2 tabs., 5 refs

  1. RCS estimation of linear and planar dipole phased arrays approximate model

    CERN Document Server

    Singh, Hema; Jha, Rakesh Mohan

    2016-01-01

    In this book, the RCS of a parallel-fed linear and planar dipole array is derived using an approximate method. The signal propagation within the phased array system determines the radar cross section (RCS) of phased array. The reflection and transmission coefficients for a signal at different levels of the phased-in scattering array system depend on the impedance mismatch and the design parameters. Moreover the mutual coupling effect in between the antenna elements is an important factor. A phased array system comprises of radiating elements followed by phase shifters, couplers, and terminating load impedance. These components lead to respective impedances towards the incoming signal that travels through them before reaching receive port of the array system. In this book, the RCS is approximated in terms of array factor, neglecting the phase terms. The mutual coupling effect is taken into account. The dependence of the RCS pattern on the design parameters is analyzed. The approximate model is established as a...

  2. Semiclassical approximation in Batalin-Vilkovisky formalism

    International Nuclear Information System (INIS)

    Schwarz, A.

    1993-01-01

    The geometry of supermanifolds provided with a Q-structure (i.e. with an odd vector field Q satisfying {Q, Q}=0), a P-structure (odd symplectic structure) and an S-structure (volume element) or with various combinations of these structures is studied. The results are applied to the analysis of the Batalin-Vilkovisky approach to the quantization of gauge theories. In particular the semiclassical approximation in this approach is expressed in terms of Reidemeister torsion. (orig.)

  3. Coulomb matrix elements in multi-orbital Hubbard models.

    Science.gov (United States)

    Bünemann, Jörg; Gebhard, Florian

    2017-04-26

    Coulomb matrix elements are needed in all studies in solid-state theory that are based on Hubbard-type multi-orbital models. Due to symmetries, the matrix elements are not independent. We determine a set of independent Coulomb parameters for a d-shell and an f-shell and all point groups with up to 16 elements (O h , O, T d , T h , D 6h , and D 4h ). Furthermore, we express all other matrix elements as a function of the independent Coulomb parameters. Apart from the solution of the general point-group problem we investigate in detail the spherical approximation and first-order corrections to the spherical approximation.

  4. Validity of the broken-pair approximation for N = 50, even-A nuclei

    International Nuclear Information System (INIS)

    Haq, S.; Gambhir, Y.K.

    1977-01-01

    The validity of the broken-pair approximation as an approximation to the seniority shell model is investigated. The results of the broken-pair approximation and the seniority shell model, obtained by employing identical input information (single-particle levels and their energies, effective two-body matrix elements, 88 Sr inert core) for N = 50, even-A nuclei are compared. A close agreement obtained between the calculated broken-pair approximation and the seniority shell model energies for 90 Zr, 92 Mo, 94 Ru, and 96 Pd nuclei and large (95--100 %) overlaps between the broken-pair approximation and the senority shell model wave functions for 92 Mo, demonstrates the validity of the broken-pair approximation in this region and in general its usefulness as a good approximation to the seniority shell model

  5. Pade approximants and the calculation of effective interactions

    International Nuclear Information System (INIS)

    Schucan, T.H.

    1975-01-01

    It is known that the series expansion of the effective interaction in nuclei diverges in practical applications due to the occurrence of low lying collective states. An approximation scheme which can be used to overcome the difficulties connected with this divergence is reviewed and it is shown that a continued fraction expansion can be used to calculate the eigenstate that has the larger overlap with the model space. An extension of this method is obtained by using Pade approximants (P.A.) which are then applied to the effective interaction, and to related matrices and matrix elements. Mathematical properties of the P.A. are discussed in light of these applications. 7 figures

  6. On the solvability of asymmetric quasilinear finite element approximate problems in nonlinear incompressible elasticity

    International Nuclear Information System (INIS)

    Ruas, V.

    1982-09-01

    A class of simplicial finite elements for solving incompressible elasticity problems in n-dimensional space, n=2 or 3, is presented. An asymmetric structure of the shape functions with respect to the centroid of the simplex, renders them particularly stable in the large strain case, in which the incompressibility condition is nonlinear. It is proved that under certain assembling conditions of the elements, there exists a solution to the corresponding discrete problems. Numerical examples illustrate the efficiency of the method. (Author) [pt

  7. Universal approximation in p-mean by neural networks

    NARCIS (Netherlands)

    Burton, R.M; Dehling, H.G

    A feedforward neural net with d input neurons and with a single hidden layer of n neurons is given by [GRAPHICS] where a(j), theta(j), w(ji) is an element of R. In this paper we study the approximation of arbitrary functions f: R-d --> R by a neural net in an L-p(mu) norm for some finite measure mu

  8. Finite-element time evolution operator for the anharmonic oscillator

    Science.gov (United States)

    Milton, Kimball A.

    1995-01-01

    The finite-element approach to lattice field theory is both highly accurate (relative errors approximately 1/N(exp 2), where N is the number of lattice points) and exactly unitary (in the sense that canonical commutation relations are exactly preserved at the lattice sites). In this talk I construct matrix elements for dynamical variables and for the time evolution operator for the anharmonic oscillator, for which the continuum Hamiltonian is H = p(exp 2)/2 + lambda q(exp 4)/4. Construction of such matrix elements does not require solving the implicit equations of motion. Low order approximations turn out to be extremely accurate. For example, the matrix element of the time evolution operator in the harmonic oscillator ground state gives a results for the anharmonic oscillator ground state energy accurate to better than 1 percent, while a two-state approximation reduces the error to less than 0.1 percent.

  9. Stress Intensity Factors for Cracked Metallic Structures Under Rapid Thermal Loading

    Science.gov (United States)

    1987-10-01

    solution algorithm was developed based on the influence function method, and numerical results were generated to show the variation of K with flaw size and...numerical algorithms developed can be executed on a desktop microcomputer illustrating the efficient and powerful characteristic of the influence function method... Function Method 3-6 Superposition and Crack Face Loading Equivalence 3-7 Influence Function Generation 3-10 Influence Functions For Two Cracked Body

  10. Approximating the r-process on earth with thermonuclear explosions

    International Nuclear Information System (INIS)

    Becker, S.A.

    1992-01-01

    The astrophysical r-process can be approximately simulated in certain types of thermonuclear explosions. Between 1952 and 1969 twenty-three nuclear tests were fielded by the United States which had as one of their objectives the production of heavy transuranic elements. Of these tests, fifteen were at least partially successful. Some of these shots were conducted under the project Plowshare Peaceful Nuclear Explosion Program as scientific research experiments. A review of the program, target nuclei used, and heavy element yields achieved, will be presented as well as discussion of plans for a new experiment in a future nuclear test

  11. Superconvergence of mixed finite element approximations to 3-D Maxwell's equations in metamaterials

    KAUST Repository

    Huang, Yunqing

    2011-09-01

    Numerical simulation of metamaterials has attracted more and more attention since 2000, after the first metamaterial with negative refraction index was successfully constructed. In this paper we construct a fully-discrete leap-frog type finite element scheme to solve the three-dimensional time-dependent Maxwell\\'s equations when metamaterials are involved. First, we obtain some superclose results between the interpolations of the analytical solutions and finite element solutions obtained using arbitrary orders of Raviart-Thomas-Nédélec mixed spaces on regular cubic meshes. Then we prove the superconvergence result in the discrete l2 norm achieved for the lowest-order Raviart-Thomas-Nédélec space. To our best knowledge, such superconvergence results have never been obtained elsewhere. Finally, we implement the leap-frog scheme and present numerical results justifying our theoretical analysis. © 2011 Elsevier Inc.

  12. Superconvergence of mixed finite element approximations to 3-D Maxwell's equations in metamaterials

    KAUST Repository

    Huang, Yunqing; Li, Jichun; Yang, Wei; Sun, Shuyu

    2011-01-01

    Numerical simulation of metamaterials has attracted more and more attention since 2000, after the first metamaterial with negative refraction index was successfully constructed. In this paper we construct a fully-discrete leap-frog type finite element scheme to solve the three-dimensional time-dependent Maxwell's equations when metamaterials are involved. First, we obtain some superclose results between the interpolations of the analytical solutions and finite element solutions obtained using arbitrary orders of Raviart-Thomas-Nédélec mixed spaces on regular cubic meshes. Then we prove the superconvergence result in the discrete l2 norm achieved for the lowest-order Raviart-Thomas-Nédélec space. To our best knowledge, such superconvergence results have never been obtained elsewhere. Finally, we implement the leap-frog scheme and present numerical results justifying our theoretical analysis. © 2011 Elsevier Inc.

  13. Quantum mean-field approximations for nuclear bound states and tunneling

    International Nuclear Information System (INIS)

    Negele, J.W.; Levit, S.; Paltiel, Z.; Massachusetts Inst. of Tech., Cambridge

    1979-01-01

    A conceptual framework has been presented in which observables are approximated in terms of a self-consistent quantum mean-field theory. Since the SPA (Stationary Phase Approximation) determines the optimal mean field to approximate a given observable, it is natural that when one changes the observable, the best mean field to describe it changes as well. Although the theory superficially appears applicable to any observable expressible in terms of an evolution operator, for example an S-matrix element, one would have to go far beyond the SPA to adequately approximate the overlap of two many-body wave functions. The most salient open problems thus concern quantitative assessment of the accuracy of the SPA, reformulation of the theory to accomodate hard cores, and selection of sensible expectation values of few-body operators to address in scattering problems

  14. Development of a discrete-ordinate approximation of the neutron transport equation for coupled xy-R-geometry

    International Nuclear Information System (INIS)

    Maertens, H.D.

    1982-01-01

    The inhomogenious structure of modern heavy water reactor fuel elements result in a strong spacial dependence of the neutron flux. The flux distribution can be calculated in detail by numerical methods, which describe exactly the geometrical heterogeniety and take into account the neutron flux anisotropy by higher transport theoretical approximations. Starting from the discrete ordinate method an approximation of the neutron transport equation has been developed, allowing for a cylindrical representation of the fuel-elements in a rectangular array of rods. The discretisation of the space variables, is based on the finite-difference approximation, defining a rectangular lattice in a two-dimensional cartesian coordinate system, which can be cut and replaced by circular mesh elements of a partially one-dimensional cylindrical coordinate system at arbitrary space points. To couple the two spacial regions the outer circle line of a cylindrical geometry is approximated in the cartesian system by a polygon with n >= 8. A cylindrical geometry is approximated in the cartesian system by a polygon with n>=8. A cylindrical geometry is thus enclosed by a system of two-dimensional rectangular, triangular and trapezoid mesh elements. The directional distribution of the neutron flux is conserved when switching from the xy-system to the cylindrical coordinate system. The angle discretisation by balanced sets of squares (EQsub(n)) allows a simple definition of transfer-coefficients for the redistribution of the neutron flux due to coordinate transformations. The procedure is verified and tested by selected problems. Possible applications and limits are discussed. (orig.) [de

  15. On the approximation of crack shapes found during inservice inspection

    International Nuclear Information System (INIS)

    Bhate, S.R.; Chawla, D.S.; Kushwaha, H.S.

    1997-01-01

    This paper addresses the characterization of axial internal flaw found during inservice inspection of a pipe. J-integral distribution for various flaw shapes is obtained using line spring finite, element method. The peak J-value and its distribution across the crack is found to be characteristic feature of each shape. The triangular shape yields peak J-value away from the center, the point of depth. The elliptic approximation results in large overestimate of J-value for unsymmetric flaws. Triangular approximation is recommended for such flaws so that further service can be obtained from the component

  16. On the approximation of crack shapes found during inservice inspection

    Energy Technology Data Exchange (ETDEWEB)

    Bhate, S.R.; Chawla, D.S.; Kushwaha, H.S. [Bhabha Atomic Research Centre, Bombay (India)] [and others

    1997-04-01

    This paper addresses the characterization of axial internal flaw found during inservice inspection of a pipe. J-integral distribution for various flaw shapes is obtained using line spring finite, element method. The peak J-value and its distribution across the crack is found to be characteristic feature of each shape. The triangular shape yields peak J-value away from the center, the point of depth. The elliptic approximation results in large overestimate of J-value for unsymmetric flaws. Triangular approximation is recommended for such flaws so that further service can be obtained from the component.

  17. Elasto-plastic stress/strain at notches, comparison of test and approximative computations

    International Nuclear Information System (INIS)

    Beste, A.; Seeger, T.

    1979-01-01

    The lifetime of cyclically loaded components is decisively determined by the value of the local load in the notch root. The determination of the elasto-plastic notch-stress and-strain is therefore an important element of recent methods of lifetime determination. These local loads are normally calculated with the help of approximation formulas. Yet there are no details about their accuracy. The basic construction of the approximation formulas is presented, along with some particulars. The use of approximations within the fully plastic range and for material laws which show a non-linear stress-strain (sigma-epsilon-)-behaviour from the beginning is explained. The use of approximation for cyclic loads is particularly discussed. Finally, the approximations are evaluated in terms of their exactness. The test results are compared with the results of the approximation calculations. (orig.) 891 RW/orig. 892 RKD [de

  18. Approximation to estimation of critical state

    International Nuclear Information System (INIS)

    Orso, Jose A.; Rosario, Universidad Nacional

    2011-01-01

    The position of the control rod for the critical state of the nuclear reactor depends on several factors; including, but not limited to the temperature and configuration of the fuel elements inside the core. Therefore, the position can not be known in advance. In this paper theoretical estimations are developed to obtain an equation that allows calculating the position of the control rod for the critical state (approximation to critical) of the nuclear reactor RA-4; and will be used to create a software performing the estimation by entering the count rate of the reactor pulse channel and the length obtained from the control rod (in cm). For the final estimation of the approximation to critical state, a function obtained experimentally indicating control rods reactivity according to the function of their position is used, work is done mathematically to obtain a linear function, which gets the length of the control rod, which has to be removed to get the reactor in critical position. (author) [es

  19. Optimal approximation of linear systems by artificial immune response

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    This paper puts forward a novel artificial immune response algorithm for optimal approximation of linear systems. A quaternion model of artificial immune response is proposed for engineering computing. The model abstracts four elements, namely, antigen, antibody, reaction rules among antibodies, and driving algorithm describing how the rules are applied to antibodies, to simulate the process of immune response. Some reaction rules including clonal selection rules, immunological memory rules and immune regulation rules are introduced. Using the theorem of Markov chain, it is proofed that the new model is convergent. The experimental study on the optimal approximation of a stable linear system and an unstable one show that the approximate models searched by the new model have better performance indices than those obtained by some existing algorithms including the differential evolution algorithm and the multi-agent genetic algorithm.

  20. A Gradient Weighted Moving Finite-Element Method with Polynomial Approximation of Any Degree

    Directory of Open Access Journals (Sweden)

    Ali R. Soheili

    2009-01-01

    Full Text Available A gradient weighted moving finite element method (GWMFE based on piecewise polynomial of any degree is developed to solve time-dependent problems in two space dimensions. Numerical experiments are employed to test the accuracy and effciency of the proposed method with nonlinear Burger equation.

  1. A set of pathological tests to validate new finite elements

    Indian Academy of Sciences (India)

    M. Senthilkumar (Newgen Imaging) 1461 1996 Oct 15 13:05:22

    The finite element method entails several approximations. Hence it ... researchers have designed several pathological tests to validate any new finite element. The .... Three dimensional thick shell elements using a hybrid/mixed formu- lation.

  2. United States Air Force Graduate Student Summer Support Program 1986. Program Technical Report. Volume 2

    Science.gov (United States)

    1986-12-01

    Dictionary and Handbook, Howard W. Sams and Company, Inc., Indianapolis, Indiana, 1980. 35. Sohr, Dana , "Better Software Manuals," Byte, vol. 8, no. 5, May...network which contains the desired properties. The use of a variational approach in adaptive grid generation was first used by Brackbill and Saltzman and...Numerical Grid Generation, edited by J. F. Thompson, North-Holland, 1982. 73-18 7. Saltzman , J., and Brackbill, J. U., "Application and Generalization

  3. Hierarchical low-rank approximation for high dimensional approximation

    KAUST Repository

    Nouy, Anthony

    2016-01-07

    Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.

  4. Hierarchical low-rank approximation for high dimensional approximation

    KAUST Repository

    Nouy, Anthony

    2016-01-01

    Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.

  5. Calculation of the MSD two-step process with the sudden approximation

    Energy Technology Data Exchange (ETDEWEB)

    Yoshida, Shiro [Tohoku Univ., Sendai (Japan). Dept. of Physics; Kawano, Toshihiko [Kyushu Univ., Advanced Energy Engineering Science, Kasuga, Fukuoka (Japan)

    2000-03-01

    A calculation of the two-step process with the sudden approximation is described. The Green's function which connects the one-step matrix element to the two-step one is represented in {gamma}-space to avoid the on-energy-shell approximation. Microscopically calculated two-step cross sections are averaged together with an appropriate level density to give a two-step cross section. The calculated cross sections are compared with the experimental data, however the calculation still contains several simplifications at this moment. (author)

  6. Finite element analysis of three dimensional crack growth by the use of a boundary element sub model

    DEFF Research Database (Denmark)

    Lucht, Tore

    2009-01-01

    A new automated method to model non-planar three dimensional crack growth is proposed which combines the advantages of both the boundary element method and the finite element method. The proposed method links the two methods by a submodelling strategy in which the solution of a global finite...... element model containing an approximation of the crack is interpolated to a much smaller boundary element model containing a fine discretization of the real crack. The method is validated through several numerical comparisons and by comparison to crack growth measured in a test specimen for an engineering...

  7. Development of polygon elements based on the scaled boundary finite element method

    International Nuclear Information System (INIS)

    Chiong, Irene; Song Chongmin

    2010-01-01

    We aim to extend the scaled boundary finite element method to construct conforming polygon elements. The development of the polygonal finite element is highly anticipated in computational mechanics as greater flexibility and accuracy can be achieved using these elements. The scaled boundary polygonal finite element will enable new developments in mesh generation, better accuracy from a higher order approximation and better transition elements in finite element meshes. Polygon elements of arbitrary number of edges and order have been developed successfully. The edges of an element are discretised with line elements. The displacement solution of the scaled boundary finite element method is used in the development of shape functions. They are shown to be smooth and continuous within the element, and satisfy compatibility and completeness requirements. Furthermore, eigenvalue decomposition has been used to depict element modes and outcomes indicate the ability of the scaled boundary polygonal element to express rigid body and constant strain modes. Numerical tests are presented; the patch test is passed and constant strain modes verified. Accuracy and convergence of the method are also presented and the performance of the scaled boundary polygonal finite element is verified on Cook's swept panel problem. Results show that the scaled boundary polygonal finite element method outperforms a traditional mesh and accuracy and convergence are achieved from fewer nodes. The proposed method is also shown to be truly flexible, and applies to arbitrary n-gons formed of irregular and non-convex polygons.

  8. New elements

    International Nuclear Information System (INIS)

    Flerov, G.

    1976-01-01

    The history is briefly described of the investigation of superheavy elements at the Joint Institute for Nuclear Research at Dubna. The significance of the investigation is assessed from the point of view of the nuclear structure study and major problems encountered in experimental efforts are indicated. Current experimental methods aiming at the discovery or the production of superheavy nuclei with Z approximately 114 are listed. (I.W.)

  9. -Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations

    Directory of Open Access Journals (Sweden)

    Lee HyunYoung

    2010-01-01

    Full Text Available We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.

  10. The generalized gradient approximation in solids and molecules

    International Nuclear Information System (INIS)

    Haas, P.

    2010-01-01

    Today, most methods are based on theoretical calculations of the electronic structure of molecules, surfaces and solids on density functional theory (DFT) and the resulting Kohn-Sham equations. Unfortunately, the exact analytical expression for the exchange-correlation functional is not known and has to be approximated. The reliability of such a Kohn-Sham calculation depends i) from the numerical accuracy and ii) from the used approximation for the exchange-correlation energy. To solve the Kohn-Sham equations, the WIEN2k code, which is one of the most accurate methods for solid-state calculations, is used. The search for better approximations for the exchange-correlation energy is an intense field of research in chemistry and physics. The main objectives of the dissertation is the development, implementation and testing of advanced exchange-correlation functionals and the analysis of existing functionals. The focus of this work are GGA - functionals. Such GGA functionals are still the most widely used functionals, in particular because they are easy to implement and require little computational effort. Several recent studies have shown that an improvement of the GGA should be possible. A detailed analysis of the results will allow us to understand why a particular GGA approximation for a class of elements (compounds) works better than for another. (Kancsar) [de

  11. The nonconforming virtual element method for eigenvalue problems

    Energy Technology Data Exchange (ETDEWEB)

    Gardini, Francesca [Univ. of Pavia (Italy). Dept. of Mathematics; Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Vacca, Giuseppe [Univ. of Milano-Bicocca, Milan (Italy). Dept. of Mathematics and Applications

    2018-02-05

    We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible formulations of the discrete problem, derived respectively by the nonstabilized and stabilized approximation of the L2-inner product, and we study the convergence properties of the corresponding discrete eigenvalue problems. The proposed schemes provide a correct approximation of the spectrum and we prove optimal-order error estimates for the eigenfunctions and the usual double order of convergence of the eigenvalues. Finally we show a large set of numerical tests supporting the theoretical results, including a comparison with the conforming Virtual Element choice.

  12. Subshell stopping power of the elements for protons in the Born approximation

    International Nuclear Information System (INIS)

    McGuire, E.J.

    1982-01-01

    The generalized oscillator-strength formulation of the Born approximation was used to generate a large sample of subshell excitation and ionization generalized oscillator strengths across the periodic table. These were used to calculate the excitation and ionization contributions to the proton stopping power by individual subshells. The subshell ionization stopping powers are expressed in scaled form, depending on the subshell ionization energy. Detailed comparison of the calculated total proton stopping power is in good agreement with experiment across the periodic table. Detailed calculations show the importance of outer-shell ionization and excitation to the total stopping power for protons with energy less than 10 MeV

  13. Analysis of a finite PML approximation to the three dimensional elastic wave scattering problem

    KAUST Repository

    Bramble, James H.

    2010-01-01

    We consider the application of a perfectly matched layer (PML) technique to approximate solutions to the elastic wave scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift in spherical coordinates which leads to a variable complex coefficient equation for the displacement vector posed on an infinite domain (the complement of the scatterer). The rapid decay of the PML solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation (for the truncated problem). We prove existence and uniqueness of the solutions to the infinite domain and truncated domain PML equations (provided that the truncated domain is sufficiently large). We also show exponential convergence of the solution of the truncated PML problem to the solution of the original scattering problem in the region of interest. We then analyze a Galerkin numerical approximation to the truncated PML problem and prove that it is well posed provided that the PML damping parameter and mesh size are small enough. Finally, computational results illustrating the efficiency of the finite element PML approximation are presented. © 2010 American Mathematical Society.

  14. Trace Element Geochemistry of Martian Iddingsite in the Lafayette Meteorite

    Science.gov (United States)

    Treiman, Allan H.; Lindstrom, David J.

    1997-01-01

    The Lafayette meteorite contains abundant iddingsite, a fine-grained intergrowth of smectite clay, ferrihydrite, and ionic salt minerals. Both the meteorite and iddingsite formed on Mars. Samples of iddingsite, olivine, and augite pyroxene were extracted from Lafayette and analyzed for trace elements by instrumental neutron activation. Our results are comparable to independent analyses by electron and ion microbeam methods. Abundances of most elements in the iddingsite do not covary significantly. The iddingsite is extremely rich in Hg, which is probably terrestrial contamination. For the elements Si, Al, Fe, Mn, Ni, Co, and Zn, the composition of the iddingsite is close to a mixture of approximately 50% Lafayette olivine + approximately 40% Lafayette siliceous glass + approximately 1O% water. Concordant behavior among these elements is not compatible with element fractionations between smectite and water, but the hydrous nature and petrographic setting of the iddingsite clearly suggest an aqueous origin. These inferences are both consistent, however, with deposition of the iddingsite originally as a silicate gel, which then crystallized (neoformed) nearly isochemically. The iddingsite contains significantly more magnesium than implied by the model, which may suggest that the altering solutions were rich in Mg(2+).

  15. Technique for mass-spectrometric determination of moisture content in fuel elements and fuel element claddings

    International Nuclear Information System (INIS)

    Kurillovich, A.N.; Pimonov, Yu.I.; Biryukov, A.S.

    1988-01-01

    A technique for mass-spectroimetric determination of moisture content in fuel elements and fuek claddings in the 2x10 -4 -1.5x10 -2 g range is developed. The relative standard deviation is 0.13. A character of moisture extraction from oxide uranium fuels in the 20-700 deg C temperature range is studied. Approximately 80% of moisture is extracted from the fuels at 300 deg C. The moisture content in fuel elements with granular uranium oxide fuels is measured. Dependence of fuel element moisture content on conditions of hot vacuum drying is shown. The technique permits to optimize the fuel element fabrication process to decrease the moisture content in them. 4 refs.; 3 figs.; 2 tabs

  16. Postirradiation examinations of the BG-9 element

    International Nuclear Information System (INIS)

    Strain, R.V.; Renfro, C.W.; Neimark, L.A.

    1976-10-01

    Postirradiation examinations were performed on the GB-9 element irradiated in the Oak Ridge Reactor. This vented fuel element was irradiated to a peak burnup of 54,000 MWd/MT at a peak power rating of 14.8 kW/ft and a maximum outside surface temperature of 685 +- 15 0 C. The maximum diametral increase of the element was 0.2% ΔD/D. Volatile fission products migrated to the ends of the fuel column but had not been transported beyond the blanket region of the element. Fission-product attack of the cladding was found to a depth of 4.4 mils adjacent to the mixed-oxide fuel. The maximum fission-product attack (approximately 6.2 mils) was found adjacent to slightly hyperstoichiometric UO 2 pellets at the upper end of the fuel column. The more severe attack in this region has been attributed to the higher oxygen potential adjacent to the hyperstoichiometric UO 2 fuel. A stress-rupture test was performed on a section of the element. The cladding ruptured after 30 min at 700 0 C and approximately 21,500-psi loop stress, resulting in a diametral strain of 1.6%

  17. Parallel iterative procedures for approximate solutions of wave propagation by finite element and finite difference methods

    Energy Technology Data Exchange (ETDEWEB)

    Kim, S. [Purdue Univ., West Lafayette, IN (United States)

    1994-12-31

    Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.

  18. Some approximating formulae to the solution of an abstract evolution problem

    International Nuclear Information System (INIS)

    Ngongo, M.E.

    1991-12-01

    We consider discrete semigroups of operators associated with the first two primary sub-families of A-acceptable Norsett's rational approximations to e q , S 1 (γ;q) and S 2 (γ;q) with q is an element of C and γ a real parameter, and construct approximating formulae to the solution of an abstract evolution problem. The study of convergence is reduced to exploiting previous fundamental results of the author for this class of semigroups and this results, for associated numerical schemes, in a convergence independent of the regularity of the data of the problem. (author). 17 refs, 3 tabs

  19. Preconditioning for Mixed Finite Element Formulations of Elliptic Problems

    KAUST Repository

    Wildey, Tim; Xue, Guangri

    2013-01-01

    In this paper, we discuss a preconditioning technique for mixed finite element discretizations of elliptic equations. The technique is based on a block-diagonal approximation of the mass matrix which maintains the sparsity and positive definiteness of the corresponding Schur complement. This preconditioner arises from the multipoint flux mixed finite element method and is robust with respect to mesh size and is better conditioned for full permeability tensors than a preconditioner based on a diagonal approximation of the mass matrix. © Springer-Verlag Berlin Heidelberg 2013.

  20. Neutrinoless double-β decay of Se82 in the shell model: Beyond the closure approximation

    Science.gov (United States)

    Sen'kov, R. A.; Horoi, M.; Brown, B. A.

    2014-05-01

    We recently proposed a method [R. A. Senkov and M. Horoi, Phys. Rev. C 88, 064312 (2013), 10.1103/PhysRevC.88.064312] to calculate the standard nuclear matrix elements for neutrinoless double-β decay (0νββ) of Ca48 going beyond the closure approximation. Here we extend this analysis to the important case of Se82, which was chosen as the base isotope for the upcoming SuperNEMO experiment. We demonstrate that by using a mixed method that considers information from closure and nonclosure approaches, one can get excellent convergence properties for the nuclear matrix elements, which allows one to avoid unmanageable computational costs. We show that in contrast with the closure approximation the mixed approach has a very weak dependence on the average closure energy. The matrix elements for the heavy neutrino-exchange mechanism that could contribute to the 0νββ decay of Se82 are also presented.

  1. Approximate 2D inversion of airborne TEM data

    DEFF Research Database (Denmark)

    Christensen, N.B.; Wolfgram, Peter

    2006-01-01

    We propose an approximate two-dimensional inversion procedure for transient electromagnetic data. The method is a two-stage procedure, where data are first inverted with 1D multi-layer models. The 1D model section is then considered as data for the next inversion stage that produces the 2D model...... section. For moving platform data there is translational invariance and the second part of the inversion becomes a deconvolution. The convolution kernels are computed by perturbing one model element in an otherwise homogeneous 2D section and calculating full nonlinear responses. These responses...... are then inverted with 1D models to produce a 1D model section. This section is the convolution kernel for the deconvolution. Within its limitations, the approximate 2D inversion performs well. Theoretical modeling shows that it delivers model sections that are a definite improvement over 1D model sections...

  2. Parallel iterative solvers and preconditioners using approximate hierarchical methods

    Energy Technology Data Exchange (ETDEWEB)

    Grama, A.; Kumar, V.; Sameh, A. [Univ. of Minnesota, Minneapolis, MN (United States)

    1996-12-31

    In this paper, we report results of the performance, convergence, and accuracy of a parallel GMRES solver for Boundary Element Methods. The solver uses a hierarchical approximate matrix-vector product based on a hybrid Barnes-Hut / Fast Multipole Method. We study the impact of various accuracy parameters on the convergence and show that with minimal loss in accuracy, our solver yields significant speedups. We demonstrate the excellent parallel efficiency and scalability of our solver. The combined speedups from approximation and parallelism represent an improvement of several orders in solution time. We also develop fast and paralellizable preconditioners for this problem. We report on the performance of an inner-outer scheme and a preconditioner based on truncated Green`s function. Experimental results on a 256 processor Cray T3D are presented.

  3. Symmmetric double-well potential with Saxon-Woods tail and Pade approximations

    International Nuclear Information System (INIS)

    Niculescu, V.I.R.; Catana, D.

    1995-01-01

    In the present work we introduce a symmetric double-well potential with Woods-Saxon tail. The Woods-Saxon parts are replaced by Pade approximation.In this way the matrix elements of this potential form can be evaluated by the theory of complex functions. This results in a shorter computational time. (author). 1 fig., 1 tab., 7 refs

  4. Frames of exponentials:lower frame bounds for finite subfamilies, and approximation of the inverse frame operator

    DEFF Research Database (Denmark)

    Christensen, Ole; Lindner, Alexander M

    2001-01-01

    We give lower frame bounds for finite subfamilies of a frame of exponentials {e(i lambdak(.))}k is an element ofZ in L-2(-pi,pi). We also present a method for approximation of the inverse frame operator corresponding to {e(i lambdak(.))}k is an element ofZ, where knowledge of the frame bounds for...

  5. Soft dipole mode of neutron-rich light nuclei in asymptotic potential approximation

    International Nuclear Information System (INIS)

    Filippov, G.F.; Lashko, Yu.A.; Shvedov, L.P.

    2000-01-01

    Completely antisymmetrized 1''-continuum wave functions as well as the ground state wave function for ''6He have been constructed in asymptotic potential approximation. The behaviour of two-channel S-matrix elements shows on the existence of 1''- resonant state just above the three-body decay threshold of ''6He

  6. Bibliography for finite elements. [2200 references

    Energy Technology Data Exchange (ETDEWEB)

    Whiteman, J R [comp.

    1975-01-01

    This bibliography cites almost all of the significant papers on advances in the mathematical theory of finite elements. Reported are applications in aeronautical, civil, mechanical, nautical and nuclear engineering. Such topics as classical analysis, functional analysis, approximation theory, fluids, and diffusion are covered. Over 2200 references to publications up to the end of 1974 are included. Publications are listed alphabetically by author and also by keywords. In addition, finite element packages are listed.

  7. Spectral/ hp element methods: Recent developments, applications, and perspectives

    Science.gov (United States)

    Xu, Hui; Cantwell, Chris D.; Monteserin, Carlos; Eskilsson, Claes; Engsig-Karup, Allan P.; Sherwin, Spencer J.

    2018-02-01

    The spectral/ hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a C 0 - continuous expansion. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/ hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/ hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/ hp element method in more complex science and engineering applications are discussed.

  8. A finite element primer for beginners the basics

    CERN Document Server

    Zohdi, Tarek I

    2014-01-01

    The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are:(1) Weighted residual methods and Galerkin approximations,(2) A model problem for one-dimensional?linear elastostatics,(3) Weak formulations in one dimension,(4) Minimum principles in one dimension,(5) Error estimation in one dimension,(5) Construction of Finite Element basis functions in one dimension,(6) Gaussian Quadrature,(7) Iterative solvers and element by element data structures,(8) A model problem for th

  9. Aspects of approximate optimisation: overcoming the curse of dimensionality and design of experiments

    NARCIS (Netherlands)

    Trichon, Sophie; Bonte, M.H.A.; Ponthot, Jean-Philippe; van den Boogaard, Antonius H.

    2007-01-01

    Coupling optimisation algorithms to Finite Element Methods (FEM) is a very promising way to achieve optimal metal forming processes. However, many optimisation algorithms exist and it is not clear which of these algorithms to use. This paper investigates the sensitivity of a Sequential Approximate

  10. Adaptive ACMS: A robust localized Approximated Component Mode Synthesis Method

    OpenAIRE

    Madureira, Alexandre L.; Sarkis, Marcus

    2017-01-01

    We consider finite element methods of multiscale type to approximate solutions for two-dimensional symmetric elliptic partial differential equations with heterogeneous $L^\\infty$ coefficients. The methods are of Galerkin type and follows the Variational Multiscale and Localized Orthogonal Decomposition--LOD approaches in the sense that it decouples spaces into multiscale and fine subspaces. In a first method, the multiscale basis functions are obtained by mapping coarse basis functions, based...

  11. Spectral element method for wave propagation on irregular domains

    Indian Academy of Sciences (India)

    A spectral element approximation of acoustic propagation problems combined with a new mapping method on irregular domains is proposed. Following this method, the Gauss–Lobatto–Chebyshev nodes in the standard space are applied to the spectral element method (SEM). The nodes in the physical space are ...

  12. Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions

    International Nuclear Information System (INIS)

    Tarvainen, Tanja; Vauhkonen, Marko; Kolehmainen, Ville; Arridge, Simon R; Kaipio, Jari P

    2005-01-01

    In this paper, a coupled radiative transfer equation and diffusion approximation model is extended for light propagation in turbid medium with low-scattering and non-scattering regions. The light propagation is modelled with the radiative transfer equation in sub-domains in which the assumptions of the diffusion approximation are not valid. The diffusion approximation is used elsewhere in the domain. The two equations are coupled through their boundary conditions and they are solved simultaneously using the finite element method. The streamline diffusion modification is used to avoid the ray-effect problem in the finite element solution of the radiative transfer equation. The proposed method is tested with simulations. The results of the coupled model are compared with the finite element solutions of the radiative transfer equation and the diffusion approximation and with results of Monte Carlo simulation. The results show that the coupled model can be used to describe photon migration in turbid medium with low-scattering and non-scattering regions more accurately than the conventional diffusion model

  13. Analysis of the nine-point finite difference approximation for the heat conduction equation in a nuclear fuel element

    International Nuclear Information System (INIS)

    Kadri, M.

    1983-01-01

    The time dependent heat conduction equation in the x-y Cartesian geometry is formulated in terms of a nine-point finite difference relation using a Taylor series expansion technique. The accuracy of the nine-point formulation over the five-point formulation has been tested and evaluated for various reactor fuel-cladding plate configurations using a computer program. The results have been checked against analytical solutions for various model problems. The following cases were considered in the steady-state condition: (a) The thermal conductivity and the heat generation were uniform. (b) The thermal conductivity was constant, the heat generation variable. (c) The thermal conductivity varied linearly with the temperature, the heat generation was uniform. (d) Both thermal conductivity and heat generation vary. In case (a), approximately, for the same accuracy, 85% fewer grid points were needed for the nine-point relation which has a 14% higher convergence rate as compared to the five-point relation. In case (b), on the average, 84% fewer grid points were needed for the nine-point relation which has a 65% higher convergence rate as compared to the five-point relation. In case (c) and (d), there is significant accuracy (91% higher than the five-point relation) for the nine-point relation when a worse grid was used. The numerical solution of the nine-point formula in the time dependent case was also more accurate and converges faster than the numerical solution of the five-point formula for all comparative tests related to heat conduction problems in a nuclear fuel element

  14. Reduced-rank approximations to the far-field transform in the gridded fast multipole method

    Science.gov (United States)

    Hesford, Andrew J.; Waag, Robert C.

    2011-05-01

    The fast multipole method (FMM) has been shown to have a reduced computational dependence on the size of finest-level groups of elements when the elements are positioned on a regular grid and FFT convolution is used to represent neighboring interactions. However, transformations between plane-wave expansions used for FMM interactions and pressure distributions used for neighboring interactions remain significant contributors to the cost of FMM computations when finest-level groups are large. The transformation operators, which are forward and inverse Fourier transforms with the wave space confined to the unit sphere, are smooth and well approximated using reduced-rank decompositions that further reduce the computational dependence of the FMM on finest-level group size. The adaptive cross approximation (ACA) is selected to represent the forward and adjoint far-field transformation operators required by the FMM. However, the actual error of the ACA is found to be greater than that predicted using traditional estimates, and the ACA generally performs worse than the approximation resulting from a truncated singular-value decomposition (SVD). To overcome these issues while avoiding the cost of a full-scale SVD, the ACA is employed with more stringent accuracy demands and recompressed using a reduced, truncated SVD. The results show a greatly reduced approximation error that performs comparably to the full-scale truncated SVD without degrading the asymptotic computational efficiency associated with ACA matrix assembly.

  15. Spectral element method for wave propagation on irregular domains

    Indian Academy of Sciences (India)

    Yan Hui Geng

    2018-03-14

    Mar 14, 2018 ... Abstract. A spectral element approximation of acoustic propagation problems combined with a new mapping method on irregular domains is proposed. Following this method, the Gauss–Lobatto–Chebyshev nodes in the standard space are applied to the spectral element method (SEM). The nodes in the ...

  16. Modelling Convergence of Finite Element Analysis of Cantilever Beam

    African Journals Online (AJOL)

    Convergence studies are carried out by investigating the convergence of numerical results as the number of elements is increased. If convergence is not obtained, the engineer using the finite element method has absolutely no indication whether the results are indicative of a meaningful approximation to the correct solution ...

  17. Succinct Data Structures for Retrieval and Approximate Membership

    DEFF Research Database (Denmark)

    Dietzfelbinger, Martin; Pagh, Rasmus

    2008-01-01

    The retrieval problem is the problem of associating data with keys in a set. Formally, the data structure must store a function that has specified values on the elements of a given set S ⊆ U, |S| = n, but may have any value on elements outside S. All known methods (e. g. those based on perfect hash...... functions), induce a space overhead of Θ(n) bits over the optimum, regardless of the evaluation time. We show that for any k, query time O(k) can be achieved using space that is within a factor 1 + e − k of optimal, asymptotically for large n. The time to construct the data structure is O(n), expected....... If we allow logarithmic evaluation time, the additive overhead can be reduced to O(loglogn) bits whp. A general reduction transfers the results on retrieval into analogous results on approximate membership, a problem traditionally addressed using Bloom filters. Thus we obtain space bounds arbitrarily...

  18. L2-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations

    Directory of Open Access Journals (Sweden)

    Hyun Young Lee

    2010-01-01

    Full Text Available We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ℓ∞(L2 error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.

  19. Infinite elements for soil-structure interaction analysis in multi-layered halfspaces

    International Nuclear Information System (INIS)

    Yun, Chung Bang; Kim, Jae Min; Yang, Shin Chu

    1994-01-01

    This paper presents the theoretical aspects of a computer code (KIESSI) for soil-structure interaction analysis in a multi-layered halfspace using infinite elements. The shape functions of the infinite elements are derived from approximate expressions of the analytical solutions. Three different infinite elements are developed. They are the horizontal, the vertical and the comer infinite elements (HIE, VIE and CIE). Numerical example analyses are presented for demonstrating the effectiveness of the proposed infinite elements

  20. Mixed multiscale finite element methods using approximate global information based on partial upscaling

    KAUST Repository

    Jiang, Lijian

    2009-10-02

    The use of limited global information in multiscale simulations is needed when there is no scale separation. Previous approaches entail fine-scale simulations in the computation of the global information. The computation of the global information is expensive. In this paper, we propose the use of approximate global information based on partial upscaling. A requirement for partial homogenization is to capture long-range (non-local) effects present in the fine-scale solution, while homogenizing some of the smallest scales. The local information at these smallest scales is captured in the computation of basis functions. Thus, the proposed approach allows us to avoid the computations at the scales that can be homogenized. This results in coarser problems for the computation of global fields. We analyze the convergence of the proposed method. Mathematical formalism is introduced, which allows estimating the errors due to small scales that are homogenized. The proposed method is applied to simulate two-phase flows in heterogeneous porous media. Numerical results are presented for various permeability fields, including those generated using two-point correlation functions and channelized permeability fields from the SPE Comparative Project (Christie and Blunt, SPE Reserv Evalu Eng 4:308-317, 2001). We consider simple cases where one can identify the scales that can be homogenized. For more general cases, we suggest the use of upscaling on the coarse grid with the size smaller than the target coarse grid where multiscale basis functions are constructed. This intermediate coarse grid renders a partially upscaled solution that contains essential non-local information. Numerical examples demonstrate that the use of approximate global information provides better accuracy than purely local multiscale methods. © 2009 Springer Science+Business Media B.V.

  1. Stress analysis in pressure vessels by mixed finite element methods taking into account shear deformation

    International Nuclear Information System (INIS)

    Franca, L.P.; Toledo, E.M.; Loula, A.F.D.; Garcia, E.L.M.

    1988-12-01

    A new finite element method is employed to approximate axisymmetric shell problems. This formulation enhances stability and accuracy, from thin to moderately thick shells, compared to the correspondent Galerkin finite element approximations. Numerical results illustrate the good performance of the present method on some typical pressure vessels aplications. (author) [pt

  2. Self-similar factor approximants

    International Nuclear Information System (INIS)

    Gluzman, S.; Yukalov, V.I.; Sornette, D.

    2003-01-01

    The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving an improved type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are called self-similar factor approximants. These complement the obtained earlier self-similar exponential approximants and self-similar root approximants. The specific feature of self-similar factor approximants is that their control functions, providing convergence of the computational algorithm, are completely defined from the accuracy-through-order conditions. These approximants contain the Pade approximants as a particular case, and in some limit they can be reduced to the self-similar exponential approximants previously introduced by two of us. It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions, which include a variety of nonalgebraic functions. For other functions, not pertaining to this exactly reproducible class, the factor approximants provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Pade approximants. This is illustrated by a number of examples showing the generality and accuracy of the factor approximants even when conventional techniques meet serious difficulties

  3. Approximation of the unsteady Brinkman-Forchheimer equations by the pressure stabilization method

    KAUST Repository

    Louaked, Mohammed; Seloula, Nour; Trabelsi, Saber

    2017-01-01

    In this work, we propose and analyze the pressure stabilization method for the unsteady incompressible Brinkman-Forchheimer equations. We present a time discretization scheme which can be used with any consistent finite element space approximation. Second-order error estimate is proven. Some numerical results are also given.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2017

  4. Approximation of the unsteady Brinkman-Forchheimer equations by the pressure stabilization method

    KAUST Repository

    Louaked, Mohammed

    2017-07-20

    In this work, we propose and analyze the pressure stabilization method for the unsteady incompressible Brinkman-Forchheimer equations. We present a time discretization scheme which can be used with any consistent finite element space approximation. Second-order error estimate is proven. Some numerical results are also given.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2017

  5. Trace element emissions from coal

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    2012-09-15

    Trace elements are emitted during coal combustion. The quantity, in general, depends on the physical and chemical properties of the element itself, the concentration of the element in the coal, the combustion conditions and the type of particulate control device used, and its collection efficiency as a function of particle size. Some trace elements become concentrated in certain particle streams following combustion such as bottom ash, fly ash, and flue gas particulate matter, while others do not. Various classification schemes have been developed to describe this partitioning behaviour. These classification schemes generally distinguish between: Class 1: elements that are approximately equally concentrated in the fly ash and bottom ash, or show little or no fine particle enrichment, examples include Mn, Be, Co and Cr; Class 2: elements that are enriched in the fly ash relative to bottom ash, or show increasing enrichment with decreasing particle size, examples include As, Cd, Pb and Sb; Class 3: elements which are emitted in the gas phase (primarily Hg (not discussed in this review), and in some cases, Se). Control of class 1 trace elements is directly related to control of total particulate matter emissions, while control of the class 2 elements depends on collection of fine particulates. Due to the variability in particulate control device efficiencies, emission rates of these elements can vary substantially. The volatility of class 3 elements means that particulate controls have only a limited impact on the emissions of these elements.

  6. Modulated Pade approximant

    International Nuclear Information System (INIS)

    Ginsburg, C.A.

    1980-01-01

    In many problems, a desired property A of a function f(x) is determined by the behaviour of f(x) approximately equal to g(x,A) as x→xsup(*). In this letter, a method for resuming the power series in x of f(x) and approximating A (modulated Pade approximant) is presented. This new approximant is an extension of a resumation method for f(x) in terms of rational functions. (author)

  7. Approximate Dynamic Programming: Combining Regional and Local State Following Approximations.

    Science.gov (United States)

    Deptula, Patryk; Rosenfeld, Joel A; Kamalapurkar, Rushikesh; Dixon, Warren E

    2018-06-01

    An infinite-horizon optimal regulation problem for a control-affine deterministic system is solved online using a local state following (StaF) kernel and a regional model-based reinforcement learning (R-MBRL) method to approximate the value function. Unlike traditional methods such as R-MBRL that aim to approximate the value function over a large compact set, the StaF kernel approach aims to approximate the value function in a local neighborhood of the state that travels within a compact set. In this paper, the value function is approximated using a state-dependent convex combination of the StaF-based and the R-MBRL-based approximations. As the state enters a neighborhood containing the origin, the value function transitions from being approximated by the StaF approach to the R-MBRL approach. Semiglobal uniformly ultimately bounded (SGUUB) convergence of the system states to the origin is established using a Lyapunov-based analysis. Simulation results are provided for two, three, six, and ten-state dynamical systems to demonstrate the scalability and performance of the developed method.

  8. Finite element approximation of flow of fluids with shear-rate- and pressure-dependent viscosity

    Czech Academy of Sciences Publication Activity Database

    Hirn, A.; Lanzendörfer, Martin; Stebel, Jan

    2012-01-01

    Roč. 32, č. 4 (2012), s. 1604-1634 ISSN 0272-4979 R&D Projects: GA ČR GA201/09/0917; GA AV ČR IAA100300802; GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10300504; CEZ:AV0Z10190503 Keywords : non-Newtonian fluid * shear-rate- and pressure-dependent viscosity * finite element method * error analysis Subject RIV: BK - Fluid Dynamics Impact factor: 1.326, year: 2012

  9. Application of hexagonal element scheme in finite element method to three-dimensional diffusion problem of fast reactors

    International Nuclear Information System (INIS)

    Ishiguro, Misako; Higuchi, Kenji

    1983-01-01

    The finite element method is applied in Galerkin-type approximation to three-dimensional neutron diffusion equations of fast reactors. A hexagonal element scheme is adopted for treating the hexagonal lattice which is typical for fast reactors. The validity of the scheme is verified by applying the scheme as well as alternative schemes to the neutron diffusion calculation of a gas-cooled fast reactor of actual scale. The computed results are compared with corresponding values obtained using the currently applied triangular-element and also with conventional finite difference schemes. The hexagonal finite element scheme is found to yield a reasonable solution to the problem taken up here, with some merit in terms of saving in computing time, but the resulting multiplication factor differs by 1% and the flux by 9% compared with the triangular mesh finite difference scheme. The finite element method, even in triangular element scheme, would appear to incur error in inadmissible amount and which could not be easily eliminated by refining the nodes. (author)

  10. Optics of Water Microdroplets with Soot Inclusions: Exact Versus Approximate Results

    Science.gov (United States)

    Liu, Li; Mishchenko, Michael I.

    2016-01-01

    We use the recently generalized version of the multi-sphere superposition T-matrix method (STMM) to compute the scattering and absorption properties of microscopic water droplets contaminated by black carbon. The soot material is assumed to be randomly distributed throughout the droplet interior in the form of numerous small spherical inclusions. Our numerically-exact STMM results are compared with approximate ones obtained using the Maxwell-Garnett effective-medium approximation (MGA) and the Monte Carlo ray-tracing approximation (MCRTA). We show that the popular MGA can be used to calculate the droplet optical cross sections, single-scattering albedo, and asymmetry parameter provided that the soot inclusions are quasi-uniformly distributed throughout the droplet interior, but can fail in computations of the elements of the scattering matrix depending on the volume fraction of soot inclusions. The integral radiative characteristics computed with the MCRTA can deviate more significantly from their exact STMM counterparts, while accurate MCRTA computations of the phase function require droplet size parameters substantially exceeding 60.

  11. An approximate method to calculate ionization of LTE and non-LTE plasma

    International Nuclear Information System (INIS)

    Zhang Jun; Gu Peijun

    1987-01-01

    When matter, especially high Z element, is heated to high temperature, it will be ionized many times. The degree of ionization has a strong effect on many plasma properties. So an approximate method to calculate the mean ionization degree is needed for solving many practical problems. An analytical expression which is convenient for the approximate numerical calculation is given by fitting it to the scaling law and numerical results of the ionization potential of Thomas-Fermi statistical model. In LTE case, the ionization degree of Au calculated by using the approximate method is in agreement with that of the average ion model. By extending the approximate method to non-LTE case, the ionization degree of Au is similarly calculated according to Corona model and Collision-Radiatoin model(C-R). The results of Corona model agree with the published data quite well, while the results of C-R approach those of Corona model as the density is reduced and approach those of LTE as the density is increased. Finally, all approximately calculated results of ionization degree of Au and the comparision of them are given in figures and tables

  12. Vortex sheet approximation of boundary layers

    International Nuclear Information System (INIS)

    Chorin, A.J.

    1978-01-01

    a grid free method for approximating incomprssible boundary layers is introduced. The computational elements are segments of vortex sheets. The method is related to the earlier vortex method; simplicity is achieved at the cost of replacing the Navier-Stokes equations by the Prandtl boundary layer equations. A new method for generating vorticity at boundaries is also presented; it can be used with the earlier voartex method. The applications presented include (i) flat plate problems, and (ii) a flow problem in a model cylinder- piston assembly, where the new method is used near walls and an improved version of the random choice method is used in the interior. One of the attractive features of the new method is the ease with which it can be incorporated into hybrid algorithms

  13. Coefficients of viscosity for heavy impurity element in tokamak

    Energy Technology Data Exchange (ETDEWEB)

    El-Sharif, R N; Bekhit, A M [Plasma Physics dept., NRC, Atomic energy Authority, Cairo, (Egypt)

    1997-12-31

    The transport of heavy impurity element in to tokamak was studied theoretically. The viscosity coefficients of chromium impurities has been calculated in 13 and 21 moment approximation, in the limit of strong fields where is the gyrofrequency of species it was found that the off diagonal coefficient approximately tends to zero. This means that the friction force in the off-diagonal direction is very small, for the perpendicular viscosity coefficient the two approximation coincide to each other. 3 figs.

  14. On the trial functions in nested element method

    International Nuclear Information System (INIS)

    Altiparmakov, D.V.

    1985-01-01

    The R-function method is applied to the multidimensional steady-state neutron diffusion equation. Using a variational principle the nested element approximation is formulated. Trial functions taking into account the geometrical shape of material regions are constructed. The influence of both the surrounding regions and the corner singularities at the external boundary is incorporated into the approximate solution. Benchmark calculations show that such an approximation can yield satisfactory results. Moreover, in the case of complex geometry, the presented approach would result in a significant reduction of the number of unknowns compared to other methods

  15. Calculations of the properties of superconducting alloys via the average T-matrix approximation

    International Nuclear Information System (INIS)

    Chatterjee, P.

    1980-01-01

    The theoretical formula of McMillan, modified via the multiple-scattering theory by Gomersall and Gyorffy, has been very successful in computing the electron-phonon coupling constant (lambda) and the transition temperature (Tsub(c)) of many superconducting elements and compounds. For disordered solids, such as substitutional alloys, however, this theory fails because of the breakdown of the translational symmetry used in the multiple-scattering theory. Under these conditions the problem can still be solved if the t-matrix is averaged in the random phase approximation (average T-matrix approximation). Gomersall and Gyorffy's expression is reformulated for lambda in the random phase approximation. This theory is applied to calculate lambda and Tsub(c) of the binary substitutional NbMo alloy system at different concentrations. The results appear to be in fair agreement with experiments. (author)

  16. Mixed and mixed-hybrid elements for the diffusion equation

    International Nuclear Information System (INIS)

    Coulomb, F.; Fedon-Magnaud, C.

    1987-04-01

    To solve the diffusion equation, one often uses a Lagrangian finite element method. We want to introduce the mixed elements which allow a simultaneous approximation of the same order for the flux and its gradient. Though the linear systems are not positive definite, it is possible to make them so by eliminating some of the unknowns

  17. Approximate solutions of pulse transport in turbulent flow in narrow fuel element bundle geometries, using the FE method

    International Nuclear Information System (INIS)

    Kaiser, H.G.

    1985-01-01

    The author is concerned with the flow conditions in case of narrow fuel element grids of pressurised-water reactors. Starting from the mathematical formulation of the flow processes for incompressible, isothermal flows, models of the turbulence characteristics are being developed. Besides turbulence models, and network structure the finite element method is treated as numeric solution process. Finally the results are summarized and discussed. (HAG) [de

  18. Application of the probabilistic approximate analysis method to a turbopump blade analysis. [for Space Shuttle Main Engine

    Science.gov (United States)

    Thacker, B. H.; Mcclung, R. C.; Millwater, H. R.

    1990-01-01

    An eigenvalue analysis of a typical space propulsion system turbopump blade is presented using an approximate probabilistic analysis methodology. The methodology was developed originally to investigate the feasibility of computing probabilistic structural response using closed-form approximate models. This paper extends the methodology to structures for which simple closed-form solutions do not exist. The finite element method will be used for this demonstration, but the concepts apply to any numerical method. The results agree with detailed analysis results and indicate the usefulness of using a probabilistic approximate analysis in determining efficient solution strategies.

  19. Numerical Integration Techniques for Curved-Element Discretizations of Molecule–Solvent Interfaces

    Science.gov (United States)

    Bardhan, Jaydeep P.; Altman, Michael D.; Willis, David J.; Lippow, Shaun M.; Tidor, Bruce; White, Jacob K.

    2012-01-01

    Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, we have developed methods to model several important surface formulations using exact surface discretizations. Following and refining Zauhar’s work (J. Comp.-Aid. Mol. Des. 9:149-159, 1995), we define two classes of curved elements that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. We then present numerical integration techniques that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, we present a set of calculations that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planartriangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute–solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved

  20. Higher-order meshing of implicit geometries, Part II: Approximations on manifolds

    Science.gov (United States)

    Fries, T. P.; Schöllhammer, D.

    2017-11-01

    A new concept for the higher-order accurate approximation of partial differential equations on manifolds is proposed where a surface mesh composed by higher-order elements is automatically generated based on level-set data. Thereby, it enables a completely automatic workflow from the geometric description to the numerical analysis without any user-intervention. A master level-set function defines the shape of the manifold through its zero-isosurface which is then restricted to a finite domain by additional level-set functions. It is ensured that the surface elements are sufficiently continuous and shape regular which is achieved by manipulating the background mesh. The numerical results show that optimal convergence rates are obtained with a moderate increase in the condition number compared to handcrafted surface meshes.

  1. Drying damaged K West fuel elements (Summary of whole element furnace runs 1 through 8); TOPICAL

    International Nuclear Information System (INIS)

    LAWRENCE, L.A.

    1998-01-01

    N Reactor fuel elements stored in the Hanford K Basins were subjected to high temperatures and vacuum conditions to remove water. Results of the first series of whole element furnace tests i.e., Runs 1 through 8 were collected in this summary report. The report focuses on the six tests with breached fuel from the K West Basin which ranged from a simple fracture at the approximate mid-point to severe damage with cladding breaches at the top and bottom ends with axial breaches and fuel loss. Results of the tests are summarized and compared for moisture released during cold vacuum drying, moisture remaining after drying, effects of drying on the fuel element condition, and hydrogen and fission product release

  2. Dataset concerning the analytical approximation of the Ae3 temperature

    Directory of Open Access Journals (Sweden)

    B.L. Ennis

    2017-02-01

    The dataset includes the terms of the function and the values for the polynomial coefficients for major alloying elements in steel. A short description of the approximation method used to derive and validate the coefficients has also been included. For discussion and application of this model, please refer to the full length article entitled “The role of aluminium in chemical and phase segregation in a TRIP-assisted dual phase steel” 10.1016/j.actamat.2016.05.046 (Ennis et al., 2016 [1].

  3. In-Depth Study Of European Union Fiscal Approximation

    Directory of Open Access Journals (Sweden)

    Andreea Roxana TOMI

    2011-05-01

    Full Text Available The current study presents a viewpoint on the EU fiscal policy contents, advocating the need for an in-depth understanding and acceleration of the 27 national fiscal system components and the creation of the EU Tax System that would enable the Single Market operation and the enforcement of the four fundamental liberties within the European Union. In the author’s opinion, the extant common fiscal policy elements are only marginal, while the actions aimed at an in-depth understanding of a broad fiscal policy are essential to the extent they point at both direct and indirect taxation aspects whose approximation is a priority.

  4. Rigid muffin-tin approximation for the electron-phonon interaction in transition metals

    International Nuclear Information System (INIS)

    Butler, W.H.

    1980-01-01

    Progress in calculating the electron-phonon parameters of transition metals has been based on either the rigid muffin-tin approximation (RMTA) or the fitted modified tight-binding approximation (FMTBA). The RMTA has been shown to be remarkably accurate for average electron-phonon properties, but there are indications that RMTA matrix elements may be too small at low momentum transfer. An attempt is made to demonstrate these assertions concerning the accuracy of RMTA and the numerous electron-phonon calculations are placed in a broader perspective by a demonstration of how they can be used to explain the trends in the strength of the electron-phonon coupling among the transition metals and the A-15 compounds

  5. Rigid muffin-tin approximation for the electron-phonon interaction in transition metals

    Energy Technology Data Exchange (ETDEWEB)

    Butler, W.H.

    1980-01-01

    Progress in calculating the electron-phonon parameters of transition metals has been based on either the rigid muffin-tin approximation (RMTA) or the fitted modified tight-binding approximation (FMTBA). The RMTA has been shown to be remarkably accurate for average electron-phonon properties, but there are indications that RMTA matrix elements may be too small at low momentum transfer. An attempt is made to demonstrate these assertions concerning the accuracy of RMTA and the numerous electron-phonon calculations are placed in a broader perspective by a demonstration of how they can be used to explain the trends in the strength of the electron-phonon coupling among the transition metals and the A-15 compounds. (GHT)

  6. Collective nuclear excitations with Skyrme-second random-phase approximation

    International Nuclear Information System (INIS)

    Gambacurta, D.; Catara, F.; Grasso, M.

    2010-01-01

    Second random-phase approximation (RPA) calculations with a Skyrme force are performed to describe both high- and low-lying excited states in 16 O. The coupling between one particle-one hole and two particle-two hole as well as that between two particle-two hole configurations among themselves are fully taken into account, and the residual interaction is never neglected; we do not resort therefore to a generally used approximate scheme where only the first kind of coupling is considered. The issue of the rearrangement terms in the matrix elements beyond the standard RPA will be considered in detail in a forthcoming paper. Two approximations are employed here for these rearrangement terms: they are either neglected or evaluated with the RPA procedure. As a general feature of second RPA results, a several-MeV shift of the strength distribution to lower energies is systematically found with respect to RPA distributions. A much more important fragmentation of the strength is also naturally provided by the second RPA owing to the huge number of two particle-two hole configurations. A better description of the excitation energies of the low-lying 0 + and 2 + states is obtained with the second RPA than with the RPA.

  7. Random-phase approximation and broken symmetry

    International Nuclear Information System (INIS)

    Davis, E.D.; Heiss, W.D.

    1986-01-01

    The validity of the random-phase approximation (RPA) in broken-symmetry bases is tested in an appropriate many-body system for which exact solutions are available. Initially the regions of stability of the self-consistent quasiparticle bases in this system are established and depicted in a 'phase' diagram. It is found that only stable bases can be used in an RPA calculation. This is particularly true for those RPA modes which are not associated with the onset of instability of the basis; it is seen that these modes do not describe any excited state when the basis is unstable, although from a formal point of view they remain acceptable. The RPA does well in a stable broken-symmetry basis provided one is not too close to a point where a phase transition occurs. This is true for both energies and matrix elements. (author)

  8. Construction and assessment of hierarchical edge elements for three-dimensional computations of eddy currents

    Energy Technology Data Exchange (ETDEWEB)

    Midtgaard, Ole-Morten

    1997-12-31

    This thesis considers the feasibility of doing calculations to optimize electrical machines without the need to build expensive prototypes. It deals with the construction and assessment of new, hierarchical, hexahedral edge elements for three-dimensional computations of eddy currents with the electric vector potential formulation. The new elements, five in all, gave up to second-order approximations for both the magnetic field and the current density. Theoretical arguments showed these elements to be more economical for a given polynomial order of the approximated fields than the serendipity family of nodal elements. Further it was pointed out how the support of a source field computed by using edge elements could be made very small provided that a proper spanning tree was used in the edge element mesh. This was exploited for the voltage forcing technique, where source fields were used as basis functions, with unknown total currents in voltage forced conductors as degrees of freedom. The practical assessment of the edge elements proved the accuracy to improve with increasing polynomial order, both for local and global quantities. The most economical element was, however, one giving only complete first-order approximations for both fields. Further, the edge elements turned out to be better than the nodal elements also in practice. For the voltage forcing technique, source field basis functions which had small support, resulted in large reduction of the CPU-time for solving the main equation system, compared to source fields which had large support. The new elements can be used in a p-type adaptive scheme, and they should also be applicable for other tangentially continuous field problems. 67 refs., 34 figs., 10 tabs.

  9. Stabilized and Block Approximate Inverse Preconditioners for Problems in Solid and Structural Mechanics

    Czech Academy of Sciences Publication Activity Database

    Benzi, M.; Kouhia, R.; Tůma, Miroslav

    2001-01-01

    Roč. 190, - (2001), s. 6533-6554 ISSN 0045-7825 R&D Projects: GA AV ČR IAA2030801; GA ČR GA201/00/0080 Institutional research plan: AV0Z1030915 Keywords : preconditioning * conjugate gradient * factorized sparse approximate inverse * block algorithms * finite elements * shells Subject RIV: BA - General Mathematics Impact factor: 0.913, year: 2001

  10. Superconvergence of Finite Element Approximations to Parabolic and Hyperbolic Integro-Differential Equations%抛物型和双曲型积分-微分方程有限元逼近的超收敛性质

    Institute of Scientific and Technical Information of China (English)

    张铁; 李长军

    2001-01-01

    The object of this paper is to investigate the superconvergence properties of finite element approximations to parabolic and hyperbolic integro-differential equations. The quasi projection technique introduced earlier by Douglas et al. is developed to derive the O(h2r) order knot superconvergence in the case of a single space variable, and to show the optimal order negative norm estimates in the case of several space variables.

  11. Relativistic atomic matrix elements of rq for arbitrary states in the quantum-defect approximation

    International Nuclear Information System (INIS)

    Owono Owono, L.C.; Owona Angue, M.L.C.; Kwato Njock, M.G.; Oumarou, B.

    2004-01-01

    Recurrence relations used in the calculation of matrix elements of r q for arbitrary q and states of the relativistic one-electron atom with a point-like ionic core are obtained with Dirac and quasirelativistic effective radial Hamiltonians. The phenomenological and supersymmetry-inspired quantum-defect approaches introduced in previous works to model the electron-core interactions are employed. The formulas worked out on the basis of a hypervirial inspired method may be viewed as a generalization to off-diagonal cases of our recently reported results on the evaluation of expectation values of r q

  12. Coupling multipoint flux mixed finite element methodswith continuous Galerkin methods for poroelasticity

    KAUST Repository

    Wheeler, Mary

    2013-11-16

    We study the numerical approximation on irregular domains with general grids of the system of poroelasticity, which describes fluid flow in deformable porous media. The flow equation is discretized by a multipoint flux mixed finite element method and the displacements are approximated by a continuous Galerkin finite element method. First-order convergence in space and time is established in appropriate norms for the pressure, velocity, and displacement. Numerical results are presented that illustrate the behavior of the method. © Springer Science+Business Media Dordrecht 2013.

  13. A simple finite element method for linear hyperbolic problems

    International Nuclear Information System (INIS)

    Mu, Lin; Ye, Xiu

    2017-01-01

    Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.

  14. Universal resources for approximate and stochastic measurement-based quantum computation

    International Nuclear Information System (INIS)

    Mora, Caterina E.; Piani, Marco; Miyake, Akimasa; Van den Nest, Maarten; Duer, Wolfgang; Briegel, Hans J.

    2010-01-01

    We investigate which quantum states can serve as universal resources for approximate and stochastic measurement-based quantum computation in the sense that any quantum state can be generated from a given resource by means of single-qubit (local) operations assisted by classical communication. More precisely, we consider the approximate and stochastic generation of states, resulting, for example, from a restriction to finite measurement settings or from possible imperfections in the resources or local operations. We show that entanglement-based criteria for universality obtained in M. Van den Nest et al. [New J. Phys. 9, 204 (2007)] for the exact, deterministic case can be lifted to the much more general approximate, stochastic case. This allows us to move from the idealized situation (exact, deterministic universality) considered in previous works to the practically relevant context of nonperfect state preparation. We find that any entanglement measure fulfilling some basic requirements needs to reach its maximum value on some element of an approximate, stochastic universal family of resource states, as the resource size grows. This allows us to rule out various families of states as being approximate, stochastic universal. We prove that approximate, stochastic universality is in general a weaker requirement than deterministic, exact universality and provide resources that are efficient approximate universal, but not exact deterministic universal. We also study the robustness of universal resources for measurement-based quantum computation under realistic assumptions about the (imperfect) generation and manipulation of entangled states, giving an explicit expression for the impact that errors made in the preparation of the resource have on the possibility to use it for universal approximate and stochastic state preparation. Finally, we discuss the relation between our entanglement-based criteria and recent results regarding the uselessness of states with a high

  15. Trace elements in the human endometrium and decidua

    International Nuclear Information System (INIS)

    Hagenfeldt, K.; Landgren, B.-M.; Plantin, L.-O.; Diczfalusy, E.

    1977-01-01

    By means of neutron activation analysis, 25 trace elements, which are usually present in biological material, were estimated in 31 specimens of human endometrial tissue obtained at various phases of the menstrual cycle and in 14 specimens of decidua from the 12th to 18th week of pregnancy. Among the 13 trace elements invariably found in all specimens, the levels of copper, potassium, rubidium, antimony and zinc were significantly higher and those of bromine, selenium and sodium significantly lower in the endometrium than in the decidua. No difference was found in the levels of gold, calcium, cobalt, cesiuj and iron. Among the 12 trace elements which were found only occasionally, chromium, mercury, silver and cadmium were detected in approximately half and cerium and scandium in approximately one-fourth of the 45 samples studied. Arsenic, barium, lanthanum, molybdenum, samarium and strontium were detected only rarely. The cyclic variations in the endometrial levels of calcium, rubidium and copper were highly significant and those in the levels of gold, cesium, iron, potassium and zinc probably significant. (author)

  16. High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics [High Order Curvilinear Finite Elements for Lagrangian Hydrodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Dobrev, Veselin A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kolev, Tzanio V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Rieben, Robert N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2012-09-20

    The numerical approximation of the Euler equations of gas dynamics in a movingLagrangian frame is at the heart of many multiphysics simulation algorithms. Here, we present a general framework for high-order Lagrangian discretization of these compressible shock hydrodynamics equations using curvilinear finite elements. This method is an extension of the approach outlined in [Dobrev et al., Internat. J. Numer. Methods Fluids, 65 (2010), pp. 1295--1310] and can be formulated for any finite dimensional approximation of the kinematic and thermodynamic fields, including generic finite elements on two- and three-dimensional meshes with triangular, quadrilateral, tetrahedral, or hexahedral zones. We discretize the kinematic variables of position and velocity using a continuous high-order basis function expansion of arbitrary polynomial degree which is obtained via a corresponding high-order parametric mapping from a standard reference element. This enables the use of curvilinear zone geometry, higher-order approximations for fields within a zone, and a pointwise definition of mass conservation which we refer to as strong mass conservation. Moreover, we discretize the internal energy using a piecewise discontinuous high-order basis function expansion which is also of arbitrary polynomial degree. This facilitates multimaterial hydrodynamics by treating material properties, such as equations of state and constitutive models, as piecewise discontinuous functions which vary within a zone. To satisfy the Rankine--Hugoniot jump conditions at a shock boundary and generate the appropriate entropy, we introduce a general tensor artificial viscosity which takes advantage of the high-order kinematic and thermodynamic information available in each zone. Finally, we apply a generic high-order time discretization process to the semidiscrete equations to develop the fully discrete numerical algorithm. Our method can be viewed as the high-order generalization of the so-called staggered

  17. Approximate symmetries of Hamiltonians

    Science.gov (United States)

    Chubb, Christopher T.; Flammia, Steven T.

    2017-08-01

    We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.

  18. A CAREM type fuel element dynamic analysis

    International Nuclear Information System (INIS)

    Magoia, J.E.

    1990-01-01

    A first analysis on the dynamic behaviour of a fuel element designed for the CAREM nuclear reactor (Central Argentina de Elementos Modulares) was performed. The model used to represent this dynamic behaviour was satisfactorily evaluated. Using primary estimations for some of its numerical parameters, a first approximation to its natural vibrational modes was obtained. Results obtained from fuel elements frequently used in nuclear power plants of the PWR (Pressurized Water Reactors) type, are compared with values resulting from similar analysis. (Author) [es

  19. Extending the Matrix Element Method beyond the Born approximation: calculating event weights at next-to-leading order accuracy

    International Nuclear Information System (INIS)

    Martini, Till; Uwer, Peter

    2015-01-01

    In this article we illustrate how event weights for jet events can be calculated efficiently at next-to-leading order (NLO) accuracy in QCD. This is a crucial prerequisite for the application of the Matrix Element Method in NLO. We modify the recombination procedure used in jet algorithms, to allow a factorisation of the phase space for the real corrections into resolved and unresolved regions. Using an appropriate infrared regulator the latter can be integrated numerically. As illustration, we reproduce differential distributions at NLO for two sample processes. As further application and proof of concept, we apply the Matrix Element Method in NLO accuracy to the mass determination of top quarks produced in e"+e"− annihilation. This analysis is relevant for a future Linear Collider. We observe a significant shift in the extracted mass depending on whether the Matrix Element Method is used in leading or next-to-leading order.

  20. Performance Characteristics of PTC Elements for an Electric Vehicle Heating System

    Directory of Open Access Journals (Sweden)

    Yoon Hyuk Shin

    2016-10-01

    Full Text Available A high-voltage positive temperature coefficient (PTC heater has a simple structure and a swift response. Therefore, for cabin heating in electric vehicles (EVs, such heaters are used either on their own or with a heat pump system. In this study, the sintering process in the manufacturing of PTC elements for an EV heating system was improved to enhance surface uniformity. The electrode production process entailing thin-film sputtering deposition was applied to ensure the high heating performance of PTC elements and reduce the electrode thickness. The allowable voltage and surface heat temperature of the high-voltage PTC elements with thin-film electrodes were 800 V and 172 °C, respectively. The electrode layer thickness was uniform at approximately 3.8 μm or less, approximately 69% less electrode materials were required compared to that before process improvement. Furthermore, a heater for the EV heating system was manufactured using the developed high-voltage PTC elements to verify performance and reliability.

  1. Mixed finite element - discontinuous finite volume element discretization of a general class of multicontinuum models

    Science.gov (United States)

    Ruiz-Baier, Ricardo; Lunati, Ivan

    2016-10-01

    We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation

  2. Mixed finite element simulations in two-dimensional groundwater flow problems

    International Nuclear Information System (INIS)

    Kimura, Hideo

    1989-01-01

    A computer code of groundwater flow in two-dimensional porous media based on the mixed finite element method was developed for accurate approximations of Darcy velocities in safety evaluation of radioactive waste disposal. The mixed finite element procedure solves for both the Darcy velocities and pressure heads simultaneously in the Darcy equation and continuity equation. Numerical results of a single well pumping at a constant rate in a uniform flow field showed that the mixed finite element method gives more accurate Darcy velocities nearly 50 % on average error than standard finite element method. (author)

  3. Sensitivity analysis of the Galerkin finite element method neutron diffusion solver to the shape of the elements

    Energy Technology Data Exchange (ETDEWEB)

    Hosseini, Seyed Abolfaz [Dept. of Energy Engineering, Sharif University of Technology, Tehran (Iran, Islamic Republic of)

    2017-02-15

    The purpose of the present study is the presentation of the appropriate element and shape function in the solution of the neutron diffusion equation in two-dimensional (2D) geometries. To this end, the multigroup neutron diffusion equation is solved using the Galerkin finite element method in both rectangular and hexagonal reactor cores. The spatial discretization of the equation is performed using unstructured triangular and quadrilateral finite elements. Calculations are performed using both linear and quadratic approximations of shape function in the Galerkin finite element method, based on which results are compared. Using the power iteration method, the neutron flux distributions with the corresponding eigenvalue are obtained. The results are then validated against the valid results for IAEA-2D and BIBLIS-2D benchmark problems. To investigate the dependency of the results to the type and number of the elements, and shape function order, a sensitivity analysis of the calculations to the mentioned parameters is performed. It is shown that the triangular elements and second order of the shape function in each element give the best results in comparison to the other states.

  4. Approximate Schur complement preconditioning of the lowest order nodal discretizations

    Energy Technology Data Exchange (ETDEWEB)

    Moulton, J.D.; Ascher, U.M. [Univ. of British Columbia, Vancouver, British Columbia (Canada); Morel, J.E. [Los Alamos National Lab., NM (United States)

    1996-12-31

    Particular classes of nodal methods and mixed hybrid finite element methods lead to equivalent, robust and accurate discretizations of 2nd order elliptic PDEs. However, widespread popularity of these discretizations has been hindered by the awkward linear systems which result. The present work exploits this awkwardness, which provides a natural partitioning of the linear system, by defining two optimal preconditioners based on approximate Schur complements. Central to the optimal performance of these preconditioners is their sparsity structure which is compatible with Dendy`s black box multigrid code.

  5. Geometric approximation algorithms

    CERN Document Server

    Har-Peled, Sariel

    2011-01-01

    Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.

  6. Extending the Matrix Element Method beyond the Born approximation: calculating event weights at next-to-leading order accuracy

    Energy Technology Data Exchange (ETDEWEB)

    Martini, Till; Uwer, Peter [Humboldt-Universität zu Berlin, Institut für Physik,Newtonstraße 15, 12489 Berlin (Germany)

    2015-09-14

    In this article we illustrate how event weights for jet events can be calculated efficiently at next-to-leading order (NLO) accuracy in QCD. This is a crucial prerequisite for the application of the Matrix Element Method in NLO. We modify the recombination procedure used in jet algorithms, to allow a factorisation of the phase space for the real corrections into resolved and unresolved regions. Using an appropriate infrared regulator the latter can be integrated numerically. As illustration, we reproduce differential distributions at NLO for two sample processes. As further application and proof of concept, we apply the Matrix Element Method in NLO accuracy to the mass determination of top quarks produced in e{sup +}e{sup −} annihilation. This analysis is relevant for a future Linear Collider. We observe a significant shift in the extracted mass depending on whether the Matrix Element Method is used in leading or next-to-leading order.

  7. Time dependent mean field approximation to the many-body S-matrix

    International Nuclear Information System (INIS)

    Alhassid, Y.; Koonin, S.E.

    1980-01-01

    Time-dependent Hartree-Fock (TDHF) calculations are a good description of some inclusive properties of deep inelastic heavy-ion collisions. The first steps toward a mean-field theory that approximates specific elements of the many-body S matrix are presented. A many-body system with pairwise interactions excited by an external, time-dependent one-body field is considered. The methods are used to solve the forced Lipkin model. The moduli of elastic and excitation amplitudes are plotted. 3 figures

  8. Nonlinear dynamic analysis using Petrov-Galerkin natural element method

    International Nuclear Information System (INIS)

    Lee, Hong Woo; Cho, Jin Rae

    2004-01-01

    According to our previous study, it is confirmed that the Petrov-Galerkin Natural Element Method (PG-NEM) completely resolves the numerical integration inaccuracy in the conventional Bubnov-Galerkin Natural Element Method (BG-NEM). This paper is an extension of PG-NEM to two-dimensional nonlinear dynamic problem. For the analysis, a constant average acceleration method and a linearized total Lagrangian formulation is introduced with the PG-NEM. At every time step, the grid points are updated and the shape functions are reproduced from the relocated nodal distribution. This process enables the PG-NEM to provide more accurate and robust approximations. The representative numerical experiments performed by the test Fortran program, and the numerical results confirmed that the PG-NEM effectively and accurately approximates the nonlinear dynamic problem

  9. Elemental composition of solar energetic particles

    International Nuclear Information System (INIS)

    Cook, W.R. III.

    1981-01-01

    The Low Energy Telescopes on the Voyager spacecraft are used to measure the elemental composition (2 less than or equal to Z less than or equal to 28) and energy spectra (5 to 15 MeV/nucleon) of solar energetic particles (SEPs) in seven large flare events. Four flare events are selected which have SEP abundance ratios approximately independent of energy/nucleon. The abundances for these events are compared from flare to flare and are compared to solar abundances from other sources - spectroscopy of the photosphere and corona, and solar wind measurements. The selected SEP composition results may be described by an average composition plus a systematic flare-to-flare deviation about the average. For each of the four events, the ratios of the SEP abundances to the four-flare average SEP abundances are approximately monotonic functions of nuclear charge Z in the range 6 less than or equal to Z less than or equal to 28. An exception to this Z-dependent trend occurs for He, whose abundance relative to Si is nearly the same in all four events. The four-flare average SEP composition is significantly different from the solar composition determined by photospheric spectroscopy: the elements C, N and O are depleted in SEPs by a factor of about five relative to the elements Na, Mg, Al, Si, Ca, Cr, Fe, and Ni. For some elemental abundance ratios (e.g. Mg/O), the difference between SEP and photospheric results is persistent from flare to flare and is apparently not due to a systematic difference in SEP energy/nucleon spectra between the elements, nor to propagation effects which would result in a time-dependent abundance ratio in individual flare events

  10. Sparse approximation with bases

    CERN Document Server

    2015-01-01

    This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications.  The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...

  11. TRIGA fuel element burnup determination by measurement and calculation

    International Nuclear Information System (INIS)

    Zagar, T.; Ravnik, M.; Persic, A.; Jeraj, R.

    2000-01-01

    To estimate the accuracy of the fuel element burnup calculation different factors influencing the calculation were studied. To cover different aspects of burnup calculations, two in-house developed computer codes were used in calculations. The first (TRIGAP) is based on a one-dimensional two-group diffusion approximation, and the second (TRIGLAV) is based on a two-dimensional four-group diffusion equation. Both codes use WIMSD program with different libraries forunit-cell cross section data calculation. The burnup accumulated during the operating history of the TRIGA reactor at Josef Stefan Institute was calculated for all fuel elements. Elements used in the core during this period were standard SS 8.5% fuel elements, standard SS 12% fuel elements and highly enriched FLIP fuel elements. During the considerable period of operational history, FLIP and standard fuel elements were used simultaneously in mixed cores. (authors)

  12. Application of a 2-D approximation technique for solving stress analyses problem in FEM

    Directory of Open Access Journals (Sweden)

    H Khawaja

    2016-10-01

    Full Text Available With the advent of computational techniques and methods like finite element method, complex engineering problems are no longer difficult to solve. These methods have helped engineers and designers to simulate and solve engineering problems in much more details than possible with experimental techniques. However, applying these techniques is not a simple task and require lots of acumen, understanding, and experience in obtaining a solution that is as close to an exact solution as possible with minimum computer resources. In this work using the finite element (FE method, stress analyzes of the low-pressure turbine of a small turbofan engine is carried out by employing two different techniques. Initially, a complete solid model of the turbine is prepared which is then finite element modelled with the eight-node brick element. Stresses are calculated using this model. Subsequently, the same turbine is modelled with four-node shell element for calculation of stresses. Material properties, applied loads (inertial, aerodynamic, and thermal, and constraints were same for both the cases. Authors have developed a “2-D approximation technique” to approximate a 3-D problem into a 2-D problem to study the saving invaluable computational time and resources. In this statistics technique, the 3-D domain of variable thickness is divided into many small areas of constant thickness. It is ensured that the value of the thickness for each sub-area is the correct representative thickness of that sub area, and it is within three sigma limit. The results revealed that technique developed is accurate, less time consuming and computational effort saving; the stresses obtained by 2-D technique are within five percent of 3-D results. The solution is obtained in CPU time which is six times less than the 3-D model. Similarly, the number of nodes and elements are more than ten times less than that of the 3-D model. ANSYS ® was used in this work.

  13. Selectable six-element multicoil array for entire spine imaging

    International Nuclear Information System (INIS)

    Byrne, J.W.; Bluma-Walter, J.; Prorok, R.J.

    1990-01-01

    This article introduces a new multicoil array that can provide entire spine imaging in two acquisitions with no need to manually reposition either the coil or the patient. A selectable contoured multicoil array with six elements was used to obtain coverage of the entire spine. The first four elements were used for imaging the upper spine region (cervical/thoracic) during the first acquisition, and the last four elements were used for imaging the lower spine region (thoracic/lumbar) during the second acquisition. The overall coil length was approximately 75 cm

  14. Finite element simulation and testing of ISW CFRP anchorage

    DEFF Research Database (Denmark)

    Schmidt, Jacob Wittrup; Goltermann, Per; Hertz, Kristian Dahl

    2013-01-01

    is modelled in the 3D finite Element program ABAQUS, just as digital image correlation (DIC) testing was performed to verify the finite element simulation. Also a new optimized design was produced to ensure that the finite element simulation and anchorage behaviour correlated well. It is seen....... This paper presents a novel mechanical integrated sleeve wedge anchorage which seem very promising when perusing the scope of ultimate utilization of CFRP 8mm rods (with a tension capacity of approximately 140kN). Compression transverse to the CFRP is evaluated to prevent premature failure. The anchorage...

  15. Ring-element analysis of layered orthotropic bodies

    DEFF Research Database (Denmark)

    Jørgensen, O.

    1993-01-01

    For the analysis of arbitrarily laminated circular bodies, a displacement-based ring-element is presented. The analysis is performed in a cylindrical coordinate system. The method of analysis requires the boundary conditions as well as the external forces to be pi-periodic. The element formulation...... accounts for a desired degree of approximation of the displacement field in the direction of the circumference. This is done by a truncated Fourier expansion of the angular dependence of the displacements in terms of trigonometric functions. Thus the Fourier expansion coefficients are the unknowns...... to that of solutions obtained by traditional 3D elements. A scheme for analytical integration of the angular dependence of the stiffness matrix is given....

  16. Approximate techniques for predicting size effects on cleavage fracture toughness (Jc)

    International Nuclear Information System (INIS)

    Kirk, M.T.; Dodds, R.H. Jr.

    1993-07-01

    This investigation examines the ability of an elastic T-stress analysis coupled with modified boundary layer (MBL) solution to predict stresses ahead of a crack tip in a variety of planar geometries. The approximate stresses are used as input to estimate the effective driving force for cleavage fracture (J 0 ) using the micromechanically based approach introduced by Dodds and Anderson. Finite element analyses for a wide variety of planar cracked geometries are conducted which have elastic biaxiality parameters (β) ranging from -0.99 (very low constraint) to +2.96 (very high constraint). The magnitude and sign of β indicate the rate at which crack-tip constraint changes with increasing applied load. All results pertain to a moderately strain hardening material (strain hardening exponent (η) of 10). These analyses suggest that β is an effective indicator of both the accuracy of T-MBL estimates of J 0 and of applicability limits on evolving fracture analysis methodologies (i.e. T-MBL, J-Q, and J/J 0 ). Specifically, when 1β1>0.4 these analyses show that the T-MBL approximation of J 0 is accurate to within 20% of a detailed finite-element analysis. As ''structural type'' configurations, i.e. shallow cracks in tension, generally have 1β1>0.4, it appears that only an elastic analysis may be needed to determine reasonably accurate J 0 values for structural conditions

  17. Finite size effects of a pion matrix element

    International Nuclear Information System (INIS)

    Guagnelli, M.; Jansen, K.; Palombi, F.; Petronzio, R.; Shindler, A.; Wetzorke, I.

    2004-01-01

    We investigate finite size effects of the pion matrix element of the non-singlet, twist-2 operator corresponding to the average momentum of non-singlet quark densities. Using the quenched approximation, they come out to be surprisingly large when compared to the finite size effects of the pion mass. As a consequence, simulations of corresponding nucleon matrix elements could be affected by finite size effects even stronger which could lead to serious systematic uncertainties in their evaluation

  18. Approximating distributions from moments

    Science.gov (United States)

    Pawula, R. F.

    1987-11-01

    A method based upon Pearson-type approximations from statistics is developed for approximating a symmetric probability density function from its moments. The extended Fokker-Planck equation for non-Markov processes is shown to be the underlying foundation for the approximations. The approximation is shown to be exact for the beta probability density function. The applicability of the general method is illustrated by numerous pithy examples from linear and nonlinear filtering of both Markov and non-Markov dichotomous noise. New approximations are given for the probability density function in two cases in which exact solutions are unavailable, those of (i) the filter-limiter-filter problem and (ii) second-order Butterworth filtering of the random telegraph signal. The approximate results are compared with previously published Monte Carlo simulations in these two cases.

  19. Investigation of trace elements in coal

    International Nuclear Information System (INIS)

    Gluskoter, H.J.; Cahil, R.A.; Miller, W.G.; Ruch, R.R.; Shimp, N.F.

    1976-01-01

    A variety of coal samples is currently being extensively analyzed for constituents, including many trace elements, at the Illinois State Geological Survey. The samples include whole coals, washed coals, and bench samples. Among the many determinations made on each sample are analyses for approximately 60 elements, almost twice the number of elements previously determined. The increase is in part the result of the addition of instrumental neutron activation analysis (INAA) equipment to the laboratory. Twenty-five samples of Herrin (No. 6) Coal that had been analyzed previously were subjected to INAA analysis and were found to include Ba, Ce, Cs, Dy, Eu, Au, Hf, I, In, La, Lu, Rb, Sm, Sc, Ag, Sr, Ta, Tb, Th, W, U, and Yb, none of which were reported by previous techniques. These elements generally are present in very small amounts and, with the exception of barium, exhibit no wide range in concentration. The rare earth elements are among those having the narrowest ranges. Wide variations in element content have been observed in bench sets of coals (samples of vertical segments of the coal seam). Many elements, notably germanium, are concentrated at the top and/or bottom of the seam, the high concentrations of Ge being found there in all four bench sets analyzed to date

  20. New realisation of Preisach model using adaptive polynomial approximation

    Science.gov (United States)

    Liu, Van-Tsai; Lin, Chun-Liang; Wing, Home-Young

    2012-09-01

    Modelling system with hysteresis has received considerable attention recently due to the increasing accurate requirement in engineering applications. The classical Preisach model (CPM) is the most popular model to demonstrate hysteresis which can be represented by infinite but countable first-order reversal curves (FORCs). The usage of look-up tables is one way to approach the CPM in actual practice. The data in those tables correspond with the samples of a finite number of FORCs. This approach, however, faces two major problems: firstly, it requires a large amount of memory space to obtain an accurate prediction of hysteresis; secondly, it is difficult to derive efficient ways to modify the data table to reflect the timing effect of elements with hysteresis. To overcome, this article proposes the idea of using a set of polynomials to emulate the CPM instead of table look-up. The polynomial approximation requires less memory space for data storage. Furthermore, the polynomial coefficients can be obtained accurately by using the least-square approximation or adaptive identification algorithm, such as the possibility of accurate tracking of hysteresis model parameters.

  1. General Rytov approximation.

    Science.gov (United States)

    Potvin, Guy

    2015-10-01

    We examine how the Rytov approximation describing log-amplitude and phase fluctuations of a wave propagating through weak uniform turbulence can be generalized to the case of turbulence with a large-scale nonuniform component. We show how the large-scale refractive index field creates Fermat rays using the path integral formulation for paraxial propagation. We then show how the second-order derivatives of the Fermat ray action affect the Rytov approximation, and we discuss how a numerical algorithm would model the general Rytov approximation.

  2. FINELM: a multigroup finite element diffusion code

    International Nuclear Information System (INIS)

    Higgs, C.E.; Davierwalla, D.M.

    1981-06-01

    FINELM is a FORTRAN IV program to solve the Neutron Diffusion Equation in X-Y, R-Z, R-theta, X-Y-Z and R-theta-Z geometries using the method of Finite Elements. Lagrangian elements of linear or higher degree to approximate the spacial flux distribution have been provided. The method of dissections, coarse mesh rebalancing and Chebyshev acceleration techniques are available. Simple user defined input is achieved through extensive input subroutines. The input preparation is described followed by a program structure description. Sample test cases are provided. (Auth.)

  3. An upwind space-time conservation element and solution element scheme for solving dusty gas flow model

    Science.gov (United States)

    Rehman, Asad; Ali, Ishtiaq; Qamar, Shamsul

    An upwind space-time conservation element and solution element (CE/SE) scheme is extended to numerically approximate the dusty gas flow model. Unlike central CE/SE schemes, the current method uses the upwind procedure to derive the numerical fluxes through the inner boundary of conservation elements. These upwind fluxes are utilized to calculate the gradients of flow variables. For comparison and validation, the central upwind scheme is also applied to solve the same dusty gas flow model. The suggested upwind CE/SE scheme resolves the contact discontinuities more effectively and preserves the positivity of flow variables in low density flows. Several case studies are considered and the results of upwind CE/SE are compared with the solutions of central upwind scheme. The numerical results show better performance of the upwind CE/SE method as compared to the central upwind scheme.

  4. The physical-optics approximation and its application to light backscattering by hexagonal ice crystals

    International Nuclear Information System (INIS)

    Borovoi, A.; Konoshonkin, A.; Kustova, N.

    2014-01-01

    The physical-optics approximation in the problem of light scattering by large particles is so defined that it includes the classical physical optics concerning the problem of light penetration through a large aperture in an opaque screen. In the second part of the paper, the problem of light backscattering by quasi-horizontally oriented atmospheric ice crystals is considered where conformity between the physical-optics and geometric-optics approximations is discussed. The differential scattering cross section as well as the polarization elements of the Mueller matrix for quasi-horizontally oriented hexagonal ice plates has been calculated in the physical-optics approximation for the case of vertically pointing lidars. - Highlights: • The physical-optics Mueller matrix is a smoothed geometric-optics counterpart. • Backscatter by partially oriented hexagonal ice plates has been calculated. • Depolarization ratio for partially oriented hexagonal ice plates is negligible

  5. Rigorous numerical approximation of Ruelle–Perron–Frobenius operators and topological pressure of expanding maps

    International Nuclear Information System (INIS)

    Terhesiu, Dalia; Froyland, Gary

    2008-01-01

    It is well known that for different classes of transformations, including the class of piecewise C 2 expanding maps T : [0, 1] O, Ulam's method is an efficient way to numerically approximate the absolutely continuous invariant measure of T. We develop a new extension of Ulam's method and prove that this extension can be used for the numerical approximation of the Ruelle–Perron–Frobenius operator associated with T and the potential φ β = −β log |T | |, where β element of R. In particular, we prove that our extended Ulam's method is a powerful tool for computing the topological pressure P(T, φ β ) and the density of the equilibrium state

  6. Novel porcine repetitive elements

    Directory of Open Access Journals (Sweden)

    Nonneman Dan J

    2006-12-01

    Full Text Available Abstract Background Repetitive elements comprise ~45% of mammalian genomes and are increasingly known to impact genomic function by contributing to the genomic architecture, by direct regulation of gene expression and by affecting genomic size, diversity and evolution. The ubiquity and increasingly understood importance of repetitive elements contribute to the need to identify and annotate them. We set out to identify previously uncharacterized repetitive DNA in the porcine genome. Once found, we characterized the prevalence of these repeats in other mammals. Results We discovered 27 repetitive elements in 220 BACs covering 1% of the porcine genome (Comparative Vertebrate Sequencing Initiative; CVSI. These repeats varied in length from 55 to 1059 nucleotides. To estimate copy numbers, we went to an independent source of data, the BAC-end sequences (Wellcome Trust Sanger Institute, covering approximately 15% of the porcine genome. Copy numbers in BAC-ends were less than one hundred for 6 repeat elements, between 100 and 1000 for 16 and between 1,000 and 10,000 for 5. Several of the repeat elements were found in the bovine genome and we have identified two with orthologous sites, indicating that these elements were present in their common ancestor. None of the repeat elements were found in primate, rodent or dog genomes. We were unable to identify any of the replication machinery common to active transposable elements in these newly identified repeats. Conclusion The presence of both orthologous and non-orthologous sites indicates that some sites existed prior to speciation and some were generated later. The identification of low to moderate copy number repetitive DNA that is specific to artiodactyls will be critical in the assembly of livestock genomes and studies of comparative genomics.

  7. Finite element prediction of elastic strains in beryllium compact tension specimens

    International Nuclear Information System (INIS)

    Guerra, F.; Varma, R.; Bourke, M.

    1997-01-01

    Three-dimensional finite element (FE) calculations using ABAQUS version 5.5.9 were compared to neutron diffraction measurements of a loaded, pre-cracked beryllium compact tension (CT) specimens. The objective was to validate the FE results with the experimental open-quotes elastic strainclose quotes measurements. Then the FE calculations could be used to study residual stress and other aspects of these problems in the unloaded state and the crack tip stress in the loaded state which is hard to measure experimentally. A graded FE mesh was focused on the regions containing high strain gradients, the smallest elements were approximately 0.5 mm x 0.5 mm x 0.4 mm. A standard 20-node brick element model was complemented by a model with 1/4-point elements at the crack tip. Since the neutron diffraction measurements provided a volume average of approximately a cube of edge 3.0 mm, various averaging (or integrating) techniques were used on the FE results. Several integration schemes showed good agreement with the experimental results

  8. Local Projection-Based Stabilized Mixed Finite Element Methods for Kirchhoff Plate Bending Problems

    Directory of Open Access Journals (Sweden)

    Xuehai Huang

    2013-01-01

    Full Text Available Based on stress-deflection variational formulation, we propose a family of local projection-based stabilized mixed finite element methods for Kirchhoff plate bending problems. According to the error equations, we obtain the error estimates of the approximation to stress tensor in energy norm. And by duality argument, error estimates of the approximation to deflection in H1-norm are achieved. Then we design an a posteriori error estimator which is closely related to the equilibrium equation, constitutive equation, and nonconformity of the finite element spaces. With the help of Zienkiewicz-Guzmán-Neilan element spaces, we prove the reliability of the a posteriori error estimator. And the efficiency of the a posteriori error estimator is proved by standard bubble function argument.

  9. The scattering matrix element of the three body reactive collision

    International Nuclear Information System (INIS)

    Morsy, M.W.; Hilal, A.A.; El-Sabagh, M.A.

    1980-08-01

    The optical model approximation has been applied to a previously derived set of coupled equations representing the dynamics of the three-body reactive scattering. The Schroedinger equation obtained describing the scattering problem has then been solved by inserting the effective mass approximation. The asymptotic requirements for both the entrance and exit channels, respectively, have been supplied to give the scattering matrix element of the reactive collision. (author)

  10. Finite element analysis of an inflatable torus considering air mass structural element

    Science.gov (United States)

    Gajbhiye, S. C.; Upadhyay, S. H.; Harsha, S. P.

    2014-01-01

    Inflatable structures, also known as gossamer structures, are at high boom in the current space technology due to their low mass and compact size comparing to the traditional spacecraft designing. Internal pressure becomes the major source of strength and rigidity, essentially stiffen the structure. However, inflatable space based membrane structure are at high risk to the vibration disturbance due to their low structural stiffness and material damping. Hence, the vibration modes of the structure should be known to a high degree of accuracy in order to provide better control authority. In the past, most of the studies conducted on the vibration analysis of gossamer structures used inaccurate or approximate theories in modeling the internal pressure. The toroidal shaped structure is one of the important key element in space application, helps to support the reflector in space application. This paper discusses the finite-element analysis of an inflated torus. The eigen-frequencies are obtained via three-dimensional small-strain elasticity theory, based on extremum energy principle. The two finite-element model (model-1 and model-2) have cases have been generated using a commercial finite-element package. The structure model-1 with shell element and model-2 with the combination of the mass of enclosed fluid (air) added to the shell elements have been taken for the study. The model-1 is computed with present analytical approach to understand the convergence rate and the accuracy. The convergence study is made available for the symmetric modes and anti-symmetric modes about the centroidal-axis plane, meeting the eigen-frequencies of an inflatable torus with the circular cross section. The structural model-2 is introduced with air mass element and analyzed its eigen-frequency with different aspect ratio and mode shape response using in-plane and out-plane loading condition are studied.

  11. Mean field approximation versus exact treatment of collisions in few-body systems

    International Nuclear Information System (INIS)

    Lemm, J.; Weiguny, A.; Giraud, B.G.

    1990-01-01

    A variational principle for calculating matrix elements of the full resolvent operator for a many-body system is studied. Its mean field approximation results in non-linear equations of Hartree (-Fock) type, with initial and final channel wave functions as driving terms. The mean field equations will in general have many solutions whereas the exact problem being linear, has a unique solution. In a schematic model with separable forces the mean field equations are analytically soluble, and for the exact problem the resulting integral equations are solved numerically. Comparing exact and mean field results over a wide range of system parameters, the mean field approach proves to be a very reliable approximation, which is not plagued by the notorious problem of defining asymptotic channels in the time-dependent mean field method. (orig.)

  12. Accuracy of finite-element models for the stress analysis of multiple-holed moderator blocks

    International Nuclear Information System (INIS)

    Smith, P.D.; Sullivan, R.M.; Lewis, A.C.; Yu, H.J.

    1981-01-01

    Two steps have been taken to quantify and improve the accuracy in the analysis. First, the limitations of various approximation techniques have been studied with the aid of smaller benchmark problems containing fewer holes. Second, a new family of computer programs has been developed for handling such large problems. This paper describes the accuracy studies and the benchmark problems. A review is given of some proposed modeling techniques including local mesh refinement, homogenization, a special-purpose finite element, and substructuring. Some limitations of these approaches are discussed. The new finite element programs and the features that contribute to their efficiency are discussed. These include a standard architecture for out-of-core data processing and an equation solver that operates on a peripheral array processor. The central conclusions of the paper are: (1) modeling approximation methods such as local mesh refinement and homogenization tend to be unreliable, and they should be justified by a fine mesh benchmark analysis; and (2) finite element codes are now available that can achieve accurate solutions at a reasonable cost, and there is no longer a need to employ modeling approximations in the two-dimensional analysis of HTGR fuel elements. 10 figures

  13. Finite element approximation of a new variational principle for compressible and incompressible linear isotropic elasticity

    International Nuclear Information System (INIS)

    Franca, L.P.; Stenberg, R.

    1989-06-01

    Stability conditions are described to analyze a variational formulation emanating from a variational principle for linear isotropic elasticity. The variational principle is based on four dependent variables (namely, the strain tensor, augmented stress, pressure and displacement) and is shown to be valid for any compressibility including the incompressible limit. An improved convergence error analysis is established for a Galerkin-least-squares method based upon these four variables. The analysis presented establishes convergence for a wide choice of combinations of finite element interpolations. (author) [pt

  14. Chaos and its Role in Design and Simulation of Railway Vehicles

    DEFF Research Database (Denmark)

    True, Hans

    1996-01-01

    First certain important properties of nonlinear problems are discussed. Thenthe concept of chaos is described. It can only appear in nonlinear systemsand it is very common in the real world. Certain characteristic features ofdeterministic chaos and in relation hereto tests for the existence...... of chaos indynamical systems are presented.\\ Next the relevance of chaos for railwaydynamics is discussed and examples of chaotic oscillations in railwaydynamical model are shown, whereby the distinction between a chaoticattractor and transient chaos is introduces. Some causes of chaos in railwaytechnology...... are discussed. Finally the effects of chaos on field tests andnumerical simulations are discussed....

  15. Validity of the Aluminum Equivalent Approximation in Space Radiation Shielding

    Science.gov (United States)

    Badavi, Francis F.; Adams, Daniel O.; Wilson, John W.

    2009-01-01

    The origin of the aluminum equivalent shield approximation in space radiation analysis can be traced back to its roots in the early years of the NASA space programs (Mercury, Gemini and Apollo) wherein the primary radiobiological concern was the intense sources of ionizing radiation causing short term effects which was thought to jeopardize the safety of the crew and hence the mission. Herein, it is shown that the aluminum equivalent shield approximation, although reasonably well suited for that time period and to the application for which it was developed, is of questionable usefulness to the radiobiological concerns of routine space operations of the 21 st century which will include long stays onboard the International Space Station (ISS) and perhaps the moon. This is especially true for a risk based protection system, as appears imminent for deep space exploration where the long-term effects of Galactic Cosmic Ray (GCR) exposure is of primary concern. The present analysis demonstrates that sufficiently large errors in the interior particle environment of a spacecraft result from the use of the aluminum equivalent approximation, and such approximations should be avoided in future astronaut risk estimates. In this study, the aluminum equivalent approximation is evaluated as a means for estimating the particle environment within a spacecraft structure induced by the GCR radiation field. For comparison, the two extremes of the GCR environment, the 1977 solar minimum and the 2001 solar maximum, are considered. These environments are coupled to the Langley Research Center (LaRC) deterministic ionized particle transport code High charge (Z) and Energy TRaNsport (HZETRN), which propagates the GCR spectra for elements with charges (Z) in the range I aluminum equivalent approximation for a good polymeric shield material such as genetic polyethylene (PE). The shield thickness is represented by a 25 g/cm spherical shell. Although one could imagine the progression to greater

  16. Approximation techniques for engineers

    CERN Document Server

    Komzsik, Louis

    2006-01-01

    Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.

  17. International Conference Approximation Theory XV

    CERN Document Server

    Schumaker, Larry

    2017-01-01

    These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, a...

  18. Final Report of the Project "From the finite element method to the virtual element method"

    Energy Technology Data Exchange (ETDEWEB)

    Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Gyrya, Vitaliy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2017-12-20

    The Finite Element Method (FEM) is a powerful numerical tool that is being used in a large number of engineering applications. The FEM is constructed on triangular/tetrahedral and quadrilateral/hexahedral meshes. Extending the FEM to general polygonal/polyhedral meshes in straightforward way turns out to be extremely difficult and leads to very complex and computationally expensive schemes. The reason for this failure is that the construction of the basis functions on elements with a very general shape is a non-trivial and complex task. In this project we developed a new family of numerical methods, dubbed the Virtual Element Method (VEM) for the numerical approximation of partial differential equations (PDE) of elliptic type suitable to polygonal and polyhedral unstructured meshes. We successfully formulated, implemented and tested these methods and studied both theoretically and numerically their stability, robustness and accuracy for diffusion problems, convection-reaction-diffusion problems, the Stokes equations and the biharmonic equations.

  19. Mixed hybrid finite elements and streamline computation for the potential flow problem

    NARCIS (Netherlands)

    Kaasschieter, E.F.; Huijben, A.J.M.

    1992-01-01

    An important class of problems in mathematical physics involves equations of the form -¿ · (A¿¿) = f. In a variety of problems it is desirable to obtain an accurate approximation of the flow quantity u = -A¿¿. Such an accurate approximation can be determined by the mixed finite element method. In

  20. Ordered cones and approximation

    CERN Document Server

    Keimel, Klaus

    1992-01-01

    This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.

  1. Investigation of the Behavior of Steel Shear Walls Using Finite Elements Analysis

    OpenAIRE

    Abubakri, K.; Veladi, H.

    2016-01-01

    Currently, steel shear walls are considered by engineers as an economic method against lateral loads imposed by wind and earthquake in tall structures. Accordingly, there is a growing need to develop accurate methods alongside approximation methods to estimate the behavior of these structural elements. The finite element technique is one of the strongest numerical methods in analysis of solid mechanics problems. Finite element analysis however requires high technical knowledge of the behavior...

  2. Rational bases and generalized barycentrics applications to finite elements and graphics

    CERN Document Server

    Wachspress, Eugene

    2016-01-01

    This three-part volume explores theory for construction of rational interpolation functions for continuous patchwork approximation.  Authored by the namesake of the Wachspress Coordinates, the book develops construction of basis functions for a broad class of elements which have widespread graphics and finite element application. Part one is the 1975 book A Rational Finite Element Basis (with minor updates and corrections) written by Dr. Wachspress.  Part two describes theoretical advances since 1975 and includes analysis of elements not considered previously.  Part three consists of annotated MATLAB programs implementing theory presented in parts one and two.

  3. An isoparametric shell of revolution finite element for harmonic loadings of any order

    International Nuclear Information System (INIS)

    Johnson, J.J.; Charman, C.M.

    1981-01-01

    A general isoparametric shell of revolution finite element subjected to any order harmonic loading is presented. Derivation of the element properties, its implementation in a general purpose finite element program, and its application to a sample problem are discussed. The element is isoparametric, that is, the variation of the displacements along the meridian of the shell and the shape of the meridian itself are approximated in an identical manner. The element has been implemented in the computer program MODSAP. A sample problem of a cooling tower subjected to wind loading is presented. (orig./HP)

  4. The time-dependent relativistic mean-field theory and the random phase approximation

    International Nuclear Information System (INIS)

    Ring, P.; Ma, Zhong-yu; Van Giai, Nguyen; Vretenar, D.; Wandelt, A.; Cao, Li-gang

    2001-01-01

    The Relativistic Random Phase Approximation (RRPA) is derived from the Time-Dependent Relativistic Mean-Field (TD RMF) theory in the limit of small amplitude oscillations. In the no-sea approximation of the RMF theory, the RRPA configuration space includes not only the usual particle-hole ph-states, but also αh-configurations, i.e. pairs formed from occupied states in the Fermi sea and empty negative-energy states in the Dirac sea. The contribution of the negative-energy states to the RRPA matrices is examined in a schematic model, and the large effect of Dirac-sea states on isoscalar strength distributions is illustrated for the giant monopole resonance in 116 Sn. It is shown that, because the matrix elements of the time-like component of the vector-meson fields which couple the αh-configurations with the ph-configurations are strongly reduced with respect to the corresponding matrix elements of the isoscalar scalar meson field, the inclusion of states with unperturbed energies more than 1.2 GeV below the Fermi energy has a pronounced effect on giant resonances with excitation energies in the MeV region. The influence of nuclear magnetism, i.e. the effect of the spatial components of the vector fields is examined, and the difference between the nonrelativistic and relativistic RPA predictions for the nuclear matter compression modulus is explained

  5. Multidisciplinary Inverse Reliability Analysis Based on Collaborative Optimization with Combination of Linear Approximations

    Directory of Open Access Journals (Sweden)

    Xin-Jia Meng

    2015-01-01

    Full Text Available Multidisciplinary reliability is an important part of the reliability-based multidisciplinary design optimization (RBMDO. However, it usually has a considerable amount of calculation. The purpose of this paper is to improve the computational efficiency of multidisciplinary inverse reliability analysis. A multidisciplinary inverse reliability analysis method based on collaborative optimization with combination of linear approximations (CLA-CO is proposed in this paper. In the proposed method, the multidisciplinary reliability assessment problem is first transformed into a problem of most probable failure point (MPP search of inverse reliability, and then the process of searching for MPP of multidisciplinary inverse reliability is performed based on the framework of CLA-CO. This method improves the MPP searching process through two elements. One is treating the discipline analyses as the equality constraints in the subsystem optimization, and the other is using linear approximations corresponding to subsystem responses as the replacement of the consistency equality constraint in system optimization. With these two elements, the proposed method realizes the parallel analysis of each discipline, and it also has a higher computational efficiency. Additionally, there are no difficulties in applying the proposed method to problems with nonnormal distribution variables. One mathematical test problem and an electronic packaging problem are used to demonstrate the effectiveness of the proposed method.

  6. Distribution of trace elements in Western Canadian coal ashes

    Energy Technology Data Exchange (ETDEWEB)

    Kronberg, B I; Brown, J R; Fyfe, W S; Peirce, M; Winder, C G

    1981-01-01

    Concentrations of 52 minor elements in coal ash were determined using spark source mass spectroscopy. Hg levels in raw coal were investigated by cold vapour atomic absorption spectrophotometry. The concentration of elements are compared to other available data and to levels in the Earth's crust. F levels in coal ash exceed 500/sub g-1/ and may be greater than 1 wt% om raw coal. Approximately half the elements (B, S, Ni, Zn, Ga, Se, Sr, Y, Mo, Sn, Sb, I, Ba, Pr, Nd, Sm, Eu, Ho, Hf, Pt, Hg, Pb, Tl, Bi, U) investigated are enriched in the coal ash with respect to the Earth's crust. The ranges in minor element concentrations in coal ash and coal from different global regions are very similar.

  7. Elements of the interacting boson approximation

    International Nuclear Information System (INIS)

    Cseh, Jozsef

    1985-01-01

    The main features of the interacting boson model family are briefly summarized. The main tool of the model is the group theory; its basic useful results (symmetry groups, spectrum generating algebra, dynamic groups and symmetries, tensor representations, broken symmetries, subgroup chains) are summarized. The emission and annihilation operators of the individual boson degrees of freedom form a U(n) algebra. Its reprezentation theory can be used to classify the basic states and energy levels of the system. A simple variant of the interacting boson model is analyzed in detail. The genealogy of different interacting boson models from vibron model to supersymmetric ones is surveyed. (D.Gy.)

  8. Back-propagation neural network-based approximate analysis of true stress-strain behaviors of high-strength metallic material

    International Nuclear Information System (INIS)

    Doh, Jaeh Yeok; Lee, Jong Soo; Lee, Seung Uk

    2016-01-01

    In this study, a Back-propagation neural network (BPN) is employed to conduct an approximation of a true stress-strain curve using the load-displacement experimental data of DP590, a high-strength material used in automobile bodies and chassis. The optimized interconnection weights are obtained with hidden layers and output layers of the BPN through intelligent learning and training of the experimental data; by using these weights, a mathematical model of the material's behavior is suggested through this feed-forward neural network. Generally, the material properties from the tensile test cannot be acquired until the fracture regions, since it is difficult to measure the cross-section area of a specimen after diffusion necking. For this reason, the plastic properties of the true stress-strain are extrapolated using the weighted-average method after diffusion necking. The accuracies of BPN-based meta-models for predicting material properties are validated in terms of the Root mean square error (RMSE). By applying the approximate material properties, the reliable finite element solution can be obtained to realize the different shapes of the finite element models. Furthermore, the sensitivity analysis of the approximate meta-model is performed using the first-order approximate derivatives of the BPN and is compared with the results of the finite difference method. In addition, we predict the tension velocity's effect on the material property through a first-order sensitivity analysis.

  9. Linear and nonlinear symmetrically loaded shells of revolution approximated with the finite element method

    International Nuclear Information System (INIS)

    Cook, W.A.

    1978-10-01

    Nuclear Material shipping containers have shells of revolution as a basic structural component. Analytically modeling the response of these containers to severe accident impact conditions requires a nonlinear shell-of-revolution model that accounts for both geometric and material nonlinearities. Present models are limited to large displacements, small rotations, and nonlinear materials. This report discusses a first approach to developing a finite element nonlinear shell of revolution model that accounts for these nonlinear geometric effects. The approach uses incremental loads and a linear shell model with equilibrium iterations. Sixteen linear models are developed, eight using the potential energy variational principle and eight using a mixed variational principle. Four of these are suitable for extension to nonlinear shell theory. A nonlinear shell theory is derived, and a computational technique used in its solution is presented

  10. Global sensitivity analysis using low-rank tensor approximations

    International Nuclear Information System (INIS)

    Konakli, Katerina; Sudret, Bruno

    2016-01-01

    In the context of global sensitivity analysis, the Sobol' indices constitute a powerful tool for assessing the relative significance of the uncertain input parameters of a model. We herein introduce a novel approach for evaluating these indices at low computational cost, by post-processing the coefficients of polynomial meta-models belonging to the class of low-rank tensor approximations. Meta-models of this class can be particularly efficient in representing responses of high-dimensional models, because the number of unknowns in their general functional form grows only linearly with the input dimension. The proposed approach is validated in example applications, where the Sobol' indices derived from the meta-model coefficients are compared to reference indices, the latter obtained by exact analytical solutions or Monte-Carlo simulation with extremely large samples. Moreover, low-rank tensor approximations are confronted to the popular polynomial chaos expansion meta-models in case studies that involve analytical rank-one functions and finite-element models pertinent to structural mechanics and heat conduction. In the examined applications, indices based on the novel approach tend to converge faster to the reference solution with increasing size of the experimental design used to build the meta-model. - Highlights: • A new method is proposed for global sensitivity analysis of high-dimensional models. • Low-rank tensor approximations (LRA) are used as a meta-modeling technique. • Analytical formulas for the Sobol' indices in terms of LRA coefficients are derived. • The accuracy and efficiency of the approach is illustrated in application examples. • LRA-based indices are compared to indices based on polynomial chaos expansions.

  11. COMPUTER EXPERIMENTS WITH FINITE ELEMENTS OF HIGHER ORDER

    Directory of Open Access Journals (Sweden)

    Khomchenko A.

    2017-12-01

    Full Text Available The paper deals with the problem of constructing the basic functions of a quadrilateral finite element of the fifth order by the means of the computer algebra system Maple. The Lagrangian approximation of such a finite element contains 36 nodes: 20 nodes perimeter and 16 internal nodes. Alternative models with reduced number of internal nodes are considered. Graphs of basic functions and cognitive portraits of lines of zero level are presented. The work is aimed at studying the possibilities of using modern information technologies in the teaching of individual mathematical disciplines.

  12. Relativistic pseudopotential model for superheavy elements: applications to chemistry of eka-Hg and eka-Pb

    Energy Technology Data Exchange (ETDEWEB)

    Zaitsevskii, Andrei V [Institute of Hydrogen Energetics and Plasma Technologies, Russian Research Centre ' Kurchatov Institute' (Russian Federation); Wuellen, C van [Technische Universitaet Kaiserslautern (Germany); Titov, A V [B P Konstantinov Petersburg Nuclear Physics Institute, Russian Academy of Sciences (Russian Federation)

    2009-12-31

    Relativistic pseudopotential approach to the electronic structure simulation of superheavy elements (SHE) compounds is presented. Advanced formulations of this approach leaving both valence and outer-core electronic shells for explicit treatment give rise to simple and efficient computational techniques ensuring highly accurate description of most chemical properties of SHE. At present, the errors due to the use of approximate methods for solving the correlation problem for a subsystem of valence electrons are much larger than those stemming from the pseudopotential approximation itself. Recent applications to the studies of the chemistry of elements 112 (eka-Hg) and 114 (eka-Pb) are reviewed; properties of these elements and their lighter homologues, Hg and Pb, are compared.

  13. Compatible-strain mixed finite element methods for incompressible nonlinear elasticity

    Science.gov (United States)

    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.

  14. A 1372-element Large Scale Hemispherical Ultrasound Phased Array Transducer for Noninvasive Transcranial Therapy

    International Nuclear Information System (INIS)

    Song, Junho; Hynynen, Kullervo

    2009-01-01

    Noninvasive transcranial therapy using high intensity focused ultrasound transducers has attracted high interest as a promising new modality for the treatments of brain related diseases. We describe the development of a 1372 element large scale hemispherical ultrasound phased array transducer operating at a resonant frequency of 306 kHz. The hemispherical array has a diameter of 31 cm and a 15.5 cm radius of curvature. It is constructed with piezoelectric (PZT-4) tube elements of a 10 mm in diameter, 6 mm in length and 1.4 mm wall thickness. Each element is quasi-air backed by attaching a cork-rubber membrane on the back of the element. The acoustic efficiency of the element is determined to be approximately 50%. The large number of the elements delivers high power ultrasound and offers better beam steering and focusing capability. Comparisons of sound pressure-squared field measurements with theoretical calculations in water show that the array provides good beam steering and tight focusing capability over an efficient volume of approximately 100x100x80 mm 3 with nominal focal spot size of approximately 2.3 mm in diameter at -6 dB. We also present its beam steering and focusing capability through an ex vivo human skull by measuring pressure-squared amplitude after phase corrections. These measurements show the same efficient volume range and focal spot sizes at -6 dB as the ones in water without the skull present. These results indicate that the array is sufficient for use in noninvasive transcranial ultrasound therapy.

  15. Fuel-element failures in Hanford single-pass reactors 1944--1971

    Energy Technology Data Exchange (ETDEWEB)

    Gydesen, S.P.

    1993-07-01

    The primary objective of the Hanford Environmental Dose Reconstruction (HEDR) Project is to estimate the radiation dose that individuals could have received as a result of emissions since 1944 from the US Department of Energy`s (DOE) Hanford Site near Richland, Washington. To estimate the doses, the staff of the Source Terms Task use operating information from historical documents to approximate the radioactive emissions. One source of radioactive emissions to the Columbia River came from leaks in the aluminum cladding of the uranium metal fuel elements in single-pass reactors. The purpose of this letter report is to provide photocopies of the documents that recorded these failures. The data from these documents will be used by the Source Terms Task to determine the contribution of single-pass reactor fuel-element failures to the radioactivity of the reactor effluent from 1944 through 1971. Each referenced fuel-element failure occurring in the Hanford single-pass reactors is addressed. The first recorded failure was in 1948, the last in 1970. No records of fuel-element failures were found in documents prior to 1948. Data on the approximately 2000 failures which occurred during the 28 years (1944--1971) of Hanford single-pass reactor operations are provided in this report.

  16. An upwind space-time conservation element and solution element scheme for solving dusty gas flow model

    Directory of Open Access Journals (Sweden)

    Asad Rehman

    Full Text Available An upwind space-time conservation element and solution element (CE/SE scheme is extended to numerically approximate the dusty gas flow model. Unlike central CE/SE schemes, the current method uses the upwind procedure to derive the numerical fluxes through the inner boundary of conservation elements. These upwind fluxes are utilized to calculate the gradients of flow variables. For comparison and validation, the central upwind scheme is also applied to solve the same dusty gas flow model. The suggested upwind CE/SE scheme resolves the contact discontinuities more effectively and preserves the positivity of flow variables in low density flows. Several case studies are considered and the results of upwind CE/SE are compared with the solutions of central upwind scheme. The numerical results show better performance of the upwind CE/SE method as compared to the central upwind scheme. Keywords: Dusty gas flow, Solid particles, Upwind schemes, Rarefaction wave, Shock wave, Contact discontinuity

  17. CONTRIBUTIONS TO RATIONAL APPROXIMATION,

    Science.gov (United States)

    Some of the key results of linear Chebyshev approximation theory are extended to generalized rational functions. Prominent among these is Haar’s...linear theorem which yields necessary and sufficient conditions for uniqueness. Some new results in the classic field of rational function Chebyshev...Furthermore a Weierstrass type theorem is proven for rational Chebyshev approximation. A characterization theorem for rational trigonometric Chebyshev approximation in terms of sign alternation is developed. (Author)

  18. Temperature Analysis and Failure Probability of the Fuel Element in HTR-PM

    International Nuclear Information System (INIS)

    Yang Lin; Liu Bing; Tang Chunhe

    2014-01-01

    Spherical fuel element is applied in the 200-MW High Temperature Reactor-Pebble-bed Modular (HTR-PM). Each spherical fuel element contains approximately 12,000 coated fuel particles in the inner graphite matrix with a diameter of 50mm to form the fuel zone, while the outer shell with a thickness of 5mm is a fuel-free zone made up of the same graphite material. Under high burnup irradiation, the temperature of fuel element rises and the stress will result in the damage of fuel element. The purpose of this study is to analyze the temperature of fuel element and to discuss the stress and failure probability. (author)

  19. Thermal stresses in rectangular plates: variational and finite element solutions

    International Nuclear Information System (INIS)

    Laura, P.A.A.; Gutierrez, R.H.; Sanchez Sarmiento, G.; Basombrio, F.G.

    1978-01-01

    This paper deals with the development of an approximate method for the analysis of thermal stresses in rectangular plates (plane stress problem) and an evaluation of the relative accuracy of the finite element method. The stress function is expanded in terms of polynomial coordinate functions which identically satisfy the boundary conditions, and a variational approach is used to determine the expansion coefficients. The results are in good agreement with a finite element approach. (Auth.)

  20. Exact constants in approximation theory

    CERN Document Server

    Korneichuk, N

    1991-01-01

    This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base

  1. Examining the best-fit paradigm for FEM at element level

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    mathematical physics that are not always amenable to analytical methods. ... Invoking the virtual work principle, one can use an approximate ...... Reddy J N 2003 An introduction to the finite element method (New Delhi: Tata McGraw-Hill).

  2. Linear finite element method for one-dimensional diffusion problems

    Energy Technology Data Exchange (ETDEWEB)

    Brandao, Michele A.; Dominguez, Dany S.; Iglesias, Susana M., E-mail: micheleabrandao@gmail.com, E-mail: dany@labbi.uesc.br, E-mail: smiglesias@uesc.br [Universidade Estadual de Santa Cruz (LCC/DCET/UESC), Ilheus, BA (Brazil). Departamento de Ciencias Exatas e Tecnologicas. Laboratorio de Computacao Cientifica

    2011-07-01

    We describe in this paper the fundamentals of Linear Finite Element Method (LFEM) applied to one-speed diffusion problems in slab geometry. We present the mathematical formulation to solve eigenvalue and fixed source problems. First, we discretized a calculus domain using a finite set of elements. At this point, we obtain the spatial balance equations for zero order and first order spatial moments inside each element. Then, we introduce the linear auxiliary equations to approximate neutron flux and current inside the element and architect a numerical scheme to obtain the solution. We offer numerical results for fixed source typical model problems to illustrate the method's accuracy for coarse-mesh calculations in homogeneous and heterogeneous domains. Also, we compare the accuracy and computational performance of LFEM formulation with conventional Finite Difference Method (FDM). (author)

  3. An approximative solution for limit load of piping branch junctions with circumferential crack and finite element validation

    International Nuclear Information System (INIS)

    Xuan Fuzhen; Liu Changjun; Li Peining

    2005-01-01

    This paper is concerned with the prediction of limit load of the piping branch junctions with circumferential crack under internal pressure. Recently, we have developed a new approach for predicting the limit load of two-cylinder intersection structures with diameter ratio larger than 0.5, which has been successfully applied to defect free cases under various loading conditions. In the present work, we consider the extension of the approach to cover cracked piping branch junctions. On the basis of stress analysis in the vicinity of intersection line, a closed form of limit load solution for piping branch junctions with circumferential crack was developed. Then, 36 finite element (FE) models of piping branch junction with various dimensions of structure and crack were analyzed by using nonlinear finite element software. The limit loads from FE analysis and the proposed solution are compared with each other. Overall good agreement between the estimated solutions and the FE results provides confidence in the use of the proposed formulae for defect assessment of piping branch junctions in practice

  4. Iterative approximation of the solution of a monotone operator equation in certain Banach spaces

    International Nuclear Information System (INIS)

    Chidume, C.E.

    1988-01-01

    Let X=L p (or l p ), p ≥ 2. The solution of the equation Ax=f, f is an element of X is approximated in X by an iteration process in each of the following two cases: (i) A is a bounded linear mapping of X into itself which is also bounded below; and, (ii) A is a nonlinear Lipschitz mapping of X into itself and satisfies ≥ m |x-y| 2 , for some constant m > 0 and for all x, y in X, where j is the single-valued normalized duality mapping of X into X* (the dual space of X). A related result deals with the iterative approximation of the fixed point of a Lipschitz strictly pseudocontractive mapping in X. (author). 12 refs

  5. Optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation

    DEFF Research Database (Denmark)

    Sadegh, Payman; Spall, J. C.

    1998-01-01

    simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo...

  6. Approximate kernel competitive learning.

    Science.gov (United States)

    Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang

    2015-03-01

    Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches. Copyright © 2014 Elsevier Ltd. All rights reserved.

  7. ACGT-containing abscisic acid response element (ABRE) and coupling element 3 (CE3) are functionally equivalent.

    Science.gov (United States)

    Hobo, T; Asada, M; Kowyama, Y; Hattori, T

    1999-09-01

    ACGT-containing ABA response elements (ABREs) have been functionally identified in the promoters of various genes. In addition, single copies of ABRE have been found to require a cis-acting, coupling element to achieve ABA induction. A coupling element 3 (CE3) sequence, originally identified as such in the barley HVA1 promoter, is found approximately 30 bp downstream of motif A (ACGT-containing ABRE) in the promoter of the Osem gene. The relationship between these two elements was further defined by linker-scan analyses of a 55 bp fragment of the Osem promoter, which is sufficient for ABA-responsiveness and VP1 activation. The analyses revealed that both motif A and CE3 sequence were required not only for ABA-responsiveness but also for VP1 activation. Since the sequences of motif A and CE3 were found to be similar, motif-exchange experiments were carried out. The experiments demonstrated that motif A and CE3 were interchangeable by each other with respect to both ABA and VP1 regulation. In addition, both sequences were shown to be recognized by a VP1-interacting, ABA-responsive bZIP factor TRAB1. These results indicate that ACGT-containing ABREs and CE3 are functionally equivalent cis-acting elements. Furthermore, TRAB1 was shown to bind two other non-ACGT ABREs. Based on these results, all these ABREs including CE3 are proposed to be categorized into a single class of cis-acting elements.

  8. Conversion and matched filter approximations for serial minimum-shift keyed modulation

    Science.gov (United States)

    Ziemer, R. E.; Ryan, C. R.; Stilwell, J. H.

    1982-01-01

    Serial minimum-shift keyed (MSK) modulation, a technique for generating and detecting MSK using series filtering, is ideally suited for high data rate applications provided the required conversion and matched filters can be closely approximated. Low-pass implementations of these filters as parallel inphase- and quadrature-mixer structures are characterized in this paper in terms of signal-to-noise ratio (SNR) degradation from ideal and envelope deviation. Several hardware implementation techniques utilizing microwave devices or lumped elements are presented. Optimization of parameter values results in realizations whose SNR degradation is less than 0.5 dB at error probabilities of .000001.

  9. Essential and toxic trace elements in the chinese medicine

    International Nuclear Information System (INIS)

    Wang, C.F.; Jenq Yann Yang; Ming-Jenq Duo; Chang, E.E.

    1996-01-01

    The concentration of certain toxic and essential elements in various raw materials of Chinese herbs and 'scientific Chinese medicine' were determined by atomic absorption spectrometry (AAS) and instrumental neutron activation analysis (INAA). Correlation of these elements as they exist in the raw materials and in the prescription of medicine were investigated and the approximate intake of elements by patients were estimated. Values of elements determined both by AAS and INAA presented excellent agreement. The ranges of elemental concentrations were found to vary from 10 4 to 10 -1 mg/kg in different kinds of herbs. All herbs exhibit extraordinary enrichment capabilities from the environment for elements such as Mn, Zn, Ca, K, Mg, Cd, Cu, Pb and As. Higher contents of Cd, Pb and As in herbs may be attributed to the uptake of these elements from polluted soil due to industrial and anthropogenic activities. It was found that commercial scientific Chinese medicine, SCDBT, contains more elemental concentrations than that of herbs used in the prescription, which may indicate that possible contamination could be caused by unknown ingredients added in the process. A much higher toxic elemental content, such as Pb, Cd and As, has been found in CFH and the daily intake of these elements by the patient will exceed the PTDI values. (author)

  10. Numerical approximations of flow induced vibrations of vocal folds

    Directory of Open Access Journals (Sweden)

    Sváček Petr

    2017-01-01

    Full Text Available The paper focus on mathematical modelling of incompressible fluid flow interacting with vibrations of an elastic vocal fold. The flow in moving domain is modelled by the incompressible Navier-Stokes equations written in the Arbitrary Lagrangian-Eulerian (ALE form. The channel geometry is an approximation of the human glottal region. The flow model is coupled with a simplified structure model. The problem is mathematically described and the resulting fluid-structure interaction problem is discretized by a stabilized finite element method. A strong coupling algorithm is applied for solution of the coupled fluid-structure problem. The choice of boundary conditions is discussed, particularly the choice of different artificial inlet/outlet boundary conditions is described in details. The numerical results are shown.

  11. Numerical approximations of flow induced vibrations of vocal folds

    Science.gov (United States)

    Sváček, Petr

    The paper focus on mathematical modelling of incompressible fluid flow interacting with vibrations of an elastic vocal fold. The flow in moving domain is modelled by the incompressible Navier-Stokes equations written in the Arbitrary Lagrangian-Eulerian (ALE) form. The channel geometry is an approximation of the human glottal region. The flow model is coupled with a simplified structure model. The problem is mathematically described and the resulting fluid-structure interaction problem is discretized by a stabilized finite element method. A strong coupling algorithm is applied for solution of the coupled fluid-structure problem. The choice of boundary conditions is discussed, particularly the choice of different artificial inlet/outlet boundary conditions is described in details. The numerical results are shown.

  12. Mathematical aspects of finite element methods for incompressible viscous flows

    Science.gov (United States)

    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.

  13. Approximate cohomology in Banach algebras | Pourabbas ...

    African Journals Online (AJOL)

    We introduce the notions of approximate cohomology and approximate homotopy in Banach algebras and we study the relation between them. We show that the approximate homotopically equivalent cochain complexes give the same approximate cohomologies. As a special case, approximate Hochschild cohomology is ...

  14. International Conference Approximation Theory XIV

    CERN Document Server

    Schumaker, Larry

    2014-01-01

    This volume developed from papers presented at the international conference Approximation Theory XIV,  held April 7–10, 2013 in San Antonio, Texas. The proceedings contains surveys by invited speakers, covering topics such as splines on non-tensor-product meshes, Wachspress and mean value coordinates, curvelets and shearlets, barycentric interpolation, and polynomial approximation on spheres and balls. Other contributed papers address a variety of current topics in approximation theory, including eigenvalue sequences of positive integral operators, image registration, and support vector machines. This book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.

  15. Forms of Approximate Radiation Transport

    CERN Document Server

    Brunner, G

    2002-01-01

    Photon radiation transport is described by the Boltzmann equation. Because this equation is difficult to solve, many different approximate forms have been implemented in computer codes. Several of the most common approximations are reviewed, and test problems illustrate the characteristics of each of the approximations. This document is designed as a tutorial so that code users can make an educated choice about which form of approximate radiation transport to use for their particular simulation.

  16. Approximate and renormgroup symmetries

    International Nuclear Information System (INIS)

    Ibragimov, Nail H.; Kovalev, Vladimir F.

    2009-01-01

    ''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)

  17. Finite element approximation of a sharp interface approach for gradient flow dynamics of two-phase biomembranes

    OpenAIRE

    Barrett, John W.; Garcke, Harald; Nürnberg, Robert

    2017-01-01

    A finite element method for the evolution of a two-phase membrane in a sharp interface formulation is introduced. The evolution equations are given as an $L^2$--gradient flow of an energy involving an elastic bending energy and a line energy. In the two phases Helfrich-type evolution equations are prescribed, and on the interface, an evolving curve on an evolving surface, highly nonlinear boundary conditions have to hold. Here we consider both $C^0$-- and $C^1$--matching conditions for the su...

  18. Investigation of the Behavior of Steel Shear Walls Using Finite Elements Analysis

    Directory of Open Access Journals (Sweden)

    K. Abubakri

    2016-10-01

    Full Text Available Currently, steel shear walls are considered by engineers as an economic method against lateral loads imposed by wind and earthquake in tall structures. Accordingly, there is a growing need to develop accurate methods alongside approximation methods to estimate the behavior of these structural elements. The finite element technique is one of the strongest numerical methods in analysis of solid mechanics problems. Finite element analysis however requires high technical knowledge of the behavioral models of materials. Therefore, it is less used by designers for certain structural elements such as steel shear walls. This study examines the failure mechanism of steel shear walls using finite elements analysis and validates this modeling by comparing the results with experimental studies.

  19. An approximate Kalman filter for ocean data assimilation: An example with an idealized Gulf Stream model

    Science.gov (United States)

    Fukumori, Ichiro; Malanotte-Rizzoli, Paola

    1995-04-01

    A practical method of data assimilation for use with large, nonlinear, ocean general circulation models is explored. A Kaiman filter based on approximations of the state error covariance matrix is presented, employing a reduction of the effective model dimension, the error's asymptotic steady state limit, and a time-invariant linearization of the dynamic model for the error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. We examine the utility of the approximate filter in assimilating different measurement types using a twin experiment of an idealized Gulf Stream. A nonlinear primitive equation model of an unstable east-west jet is studied with a state dimension exceeding 170,000 elements. Assimilation of various pseudomeasurements are examined, including velocity, density, and volume transport at localized arrays and realistic distributions of satellite altimetry and acoustic tomography observations. Results are compared in terms of their effects on the accuracies of the estimation. The approximate filter is shown to outperform an empirical nudging scheme used in a previous study. The examples demonstrate that useful approximate estimation errors can be computed in a practical manner for general circulation models.

  20. Ground-state properties of third-row elements with nonlocal density functionals

    International Nuclear Information System (INIS)

    Bagno, P.; Jepsen, O.; Gunnarsson, O.

    1989-01-01

    The cohesive energy, the lattice parameter, and the bulk modulus of third-row elements are calculated using the Langreth-Mehl-Hu (LMH), the Perdew-Wang (PW), and the gradient expansion functionals. The PW functional is found to give somewhat better results than the LMH functional and both are found to typically remove half the errors in the local-spin-density (LSD) approximation, while the gradient expansion gives worse results than the local-density approximation. For Fe both the LMH and PW functionals correctly predict a ferromagnetic bcc ground state, while the LSD approximation and the gradient expansion predict a nonmagnetic fcc ground state

  1. Cosmological implications of light element abundances: theory.

    Science.gov (United States)

    Schramm, D N

    1993-06-01

    Primordial nucleosynthesis provides (with the microwave background radiation) one of the two quantitative experimental tests of the hot Big Bang cosmological model (versus alternative explanations for the observed Hubble expansion). The standard homogeneous-isotropic calculation fits the light element abundances ranging from 1H at 76% and 4He at 24% by mass through 2H and 3He at parts in 105 down to 7Li at parts in 1010. It is also noted how the recent Large Electron Positron Collider (and Stanford Linear Collider) results on the number of neutrinos (Nnu) are a positive laboratory test of this standard Big Bang scenario. The possible alternate scenario of quark-hadron-induced inhomogeneities is also discussed. It is shown that when this alternative scenario is made to fit the observed abundances accurately, the resulting conclusions on the baryonic density relative to the critical density (Omegab) remain approximately the same as in the standard homogeneous case, thus adding to the robustness of the standard model and the conclusion that Omegab approximately 0.06. This latter point is the driving force behind the need for nonbaryonic dark matter (assuming total density Omegatotal = 1) and the need for dark baryonic matter, since the density of visible matter Omegavisible < Omegab. The recent Population II B and Be observations are also discussed and shown to be a consequence of cosmic ray spallation processes rather than primordial nucleosynthesis. The light elements and Nnu successfully probe the cosmological model at times as early as 1 sec and a temperature (T) of approximately 10(10) K (approximately 1 MeV). Thus, they provided the first quantitative arguments that led to the connections of cosmology to nuclear and particle physics.

  2. Approximations of Fuzzy Systems

    Directory of Open Access Journals (Sweden)

    Vinai K. Singh

    2013-03-01

    Full Text Available A fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. Such results can be viewed as an existence of optimal fuzzy systems. Li-Xin Wang discussed a similar problem using Gaussian membership function and Stone-Weierstrass Theorem. He established that fuzzy systems, with product inference, centroid defuzzification and Gaussian functions are capable of approximating any real continuous function on a compact set to arbitrary accuracy. In this paper we study a similar approximation problem by using exponential membership functions

  3. Approximate and renormgroup symmetries

    Energy Technology Data Exchange (ETDEWEB)

    Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling

    2009-07-01

    ''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)

  4. Electronic structure of the Fe2 molecule in the local-spin-density approximation

    International Nuclear Information System (INIS)

    Dhar, S.; Kestner, N.R.

    1988-01-01

    Ab initio self-consistent all-electron spin-polarized calculations have been performed for the ground-state properties of the Fe 2 molecule using the local-spin-density approximation. A Gaussian orbital basis is employed and all the two-electron integrals are evaluated analytically. The matrix elements of the exchange-correlation potential are computed numerically. The total energy, the binding energy, the equilibrium distance, vibrational frequency, and the ground-state configurations are reported and compared with other calculations and experimental results

  5. Fast multipole acceleration of the MEG/EEG boundary element method

    International Nuclear Information System (INIS)

    Kybic, Jan; Clerc, Maureen; Faugeras, Olivier; Keriven, Renaud; Papadopoulo, Theo

    2005-01-01

    The accurate solution of the forward electrostatic problem is an essential first step before solving the inverse problem of magneto- and electroencephalography (MEG/EEG). The symmetric Galerkin boundary element method is accurate but cannot be used for very large problems because of its computational complexity and memory requirements. We describe a fast multipole-based acceleration for the symmetric boundary element method (BEM). It creates a hierarchical structure of the elements and approximates far interactions using spherical harmonics expansions. The accelerated method is shown to be as accurate as the direct method, yet for large problems it is both faster and more economical in terms of memory consumption

  6. An Improved Direction Finding Algorithm Based on Toeplitz Approximation

    Directory of Open Access Journals (Sweden)

    Qing Wang

    2013-01-01

    Full Text Available In this paper, a novel direction of arrival (DOA estimation algorithm called the Toeplitz fourth order cumulants multiple signal classification method (TFOC-MUSIC algorithm is proposed through combining a fast MUSIC-like algorithm termed the modified fourth order cumulants MUSIC (MFOC-MUSIC algorithm and Toeplitz approximation. In the proposed algorithm, the redundant information in the cumulants is removed. Besides, the computational complexity is reduced due to the decreased dimension of the fourth-order cumulants matrix, which is equal to the number of the virtual array elements. That is, the effective array aperture of a physical array remains unchanged. However, due to finite sampling snapshots, there exists an estimation error of the reduced-rank FOC matrix and thus the capacity of DOA estimation degrades. In order to improve the estimation performance, Toeplitz approximation is introduced to recover the Toeplitz structure of the reduced-dimension FOC matrix just like the ideal one which has the Toeplitz structure possessing optimal estimated results. The theoretical formulas of the proposed algorithm are derived, and the simulations results are presented. From the simulations, in comparison with the MFOC-MUSIC algorithm, it is concluded that the TFOC-MUSIC algorithm yields an excellent performance in both spatially-white noise and in spatially-color noise environments.

  7. SPLAI: Computational Finite Element Model for Sensor Networks

    Directory of Open Access Journals (Sweden)

    Ruzana Ishak

    2006-01-01

    Full Text Available Wireless sensor network refers to a group of sensors, linked by a wireless medium to perform distributed sensing task. The primary interest is their capability in monitoring the physical environment through the deployment of numerous tiny, intelligent, wireless networked sensor nodes. Our interest consists of a sensor network, which includes a few specialized nodes called processing elements that can perform some limited computational capabilities. In this paper, we propose a model called SPLAI that allows the network to compute a finite element problem where the processing elements are modeled as the nodes in the linear triangular approximation problem. Our model also considers the case of some failures of the sensors. A simulation model to visualize this network has been developed using C++ on the Windows environment.

  8. High order curvilinear finite elements for elastic–plastic Lagrangian dynamics

    International Nuclear Information System (INIS)

    Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N.

    2014-01-01

    This paper presents a high-order finite element method for calculating elastic–plastic flow on moving curvilinear meshes and is an extension of our general high-order curvilinear finite element approach for solving the Euler equations of gas dynamics in a Lagrangian frame [1,2]. In order to handle transition to plastic flow, we formulate the stress–strain relation in rate (or incremental) form and augment our semi-discrete equations for Lagrangian hydrodynamics with an additional evolution equation for the deviatoric stress which is valid for arbitrary order spatial discretizations of the kinematic and thermodynamic variables. The semi-discrete equation for the deviatoric stress rate is developed for 2D planar, 2D axisymmetric and full 3D geometries. For each case, the strain rate is approximated via a collocation method at zone quadrature points while the deviatoric stress is approximated using an L 2 projection onto the thermodynamic basis. We apply high order, energy conserving, explicit time stepping methods to the semi-discrete equations to develop the fully discrete method. We conclude with numerical results from an extensive series of verification tests that demonstrate several practical advantages of using high-order finite elements for elastic–plastic flow

  9. Discontinuous finite element treatment of duct problems in transport calculations

    International Nuclear Information System (INIS)

    Mirza, A. M.; Qamar, S.

    1998-01-01

    A discontinuous finite element approach is presented to solve the even-parity Boltzmann transport equation for duct problems. Presence of ducts in a system results in the streaming of particles and hence requires the employment of higher order angular approximations to model the angular flux. Conventional schemes based on the use of continuous trial functions require the same order of angular approximations to be used everywhere in the system, resulting in wastage of computational resources. Numerical investigations for the test problems presented in this paper indicate that the discontinuous finite elements eliminate the above problems and leads to computationally efficient and economical methods. They are also found to be more suitable for treating the sharp changes in the angular flux at duct-observer interfaces. The new approach provides a single-pass alternate to extrapolation and interactive schemes which need multiple passes of the solution strategy to acquire convergence. The method has been tested with the help of two case studies, namely straight and dog-leg duct problems. All results have been verified against those obtained from Monte Carlo simulations and K/sup +/ continuous finite element method. (author)

  10. Cosmological applications of Padé approximant

    International Nuclear Information System (INIS)

    Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan

    2014-01-01

    As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation

  11. Cosmological applications of Padé approximant

    Science.gov (United States)

    Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan

    2014-01-01

    As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation.

  12. Prestack wavefield approximations

    KAUST Repository

    Alkhalifah, Tariq

    2013-01-01

    The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.

  13. Prestack wavefield approximations

    KAUST Repository

    Alkhalifah, Tariq

    2013-09-01

    The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.

  14. Improved approximate inspirals of test bodies into Kerr black holes

    International Nuclear Information System (INIS)

    Gair, Jonathan R; Glampedakis, Kostas

    2006-01-01

    We present an improved version of the approximate scheme for generating inspirals of test bodies into a Kerr black hole recently developed by Glampedakis, Hughes and Kennefick. Their original 'hybrid' scheme was based on combining exact relativistic expressions for the evolution of the orbital elements (the semilatus rectum p and eccentricity e) with an approximate, weak-field, formula for the energy and angular momentum fluxes, amended by the assumption of constant inclination angle ι during the inspiral. Despite the fact that the resulting inspirals were overall well behaved, certain pathologies remained for orbits in the strong-field regime and for orbits which are nearly circular and/or nearly polar. In this paper we eliminate these problems by incorporating an array of improvements in the approximate fluxes. First, we add certain corrections which ensure the correct behavior of the fluxes in the limit of vanishing eccentricity and/or 90 deg. inclination. Second, we use higher order post-Newtonian formulas, adapted for generic orbits. Third, we drop the assumption of constant inclination. Instead, we first evolve the Carter constant by means of an approximate post-Newtonian expression and subsequently extract the evolution of ι. Finally, we improve the evolution of circular orbits by using fits to the angular momentum and inclination evolution determined by Teukolsky-based calculations. As an application of our improved scheme, we provide a sample of generic Kerr inspirals which we expect to be the most accurate to date, and for the specific case of nearly circular orbits we locate the critical radius where orbits begin to decircularize under radiation reaction. These easy-to-generate inspirals should become a useful tool for exploring LISA data analysis issues and may ultimately play a role in the detection of inspiral signals in the LISA data

  15. A Comparative Analysis of Nutrients and Mineral Elements Content ...

    African Journals Online (AJOL)

    (Mg), Iron (Fe), Copper (Cu) and Zinc (Zn) content, while P. pedicellatum has high ... INTRODUCTION ... central to animal production and productivity. .... for growth and serve as structural element in all plant ... the animal's body, it ensured correct maintenance of ... Ash content because Ash is the approximation of total.

  16. Expectation Consistent Approximate Inference

    DEFF Research Database (Denmark)

    Opper, Manfred; Winther, Ole

    2005-01-01

    We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability dis...

  17. Approximate number and approximate time discrimination each correlate with school math abilities in young children.

    Science.gov (United States)

    Odic, Darko; Lisboa, Juan Valle; Eisinger, Robert; Olivera, Magdalena Gonzalez; Maiche, Alejandro; Halberda, Justin

    2016-01-01

    What is the relationship between our intuitive sense of number (e.g., when estimating how many marbles are in a jar), and our intuitive sense of other quantities, including time (e.g., when estimating how long it has been since we last ate breakfast)? Recent work in cognitive, developmental, comparative psychology, and computational neuroscience has suggested that our representations of approximate number, time, and spatial extent are fundamentally linked and constitute a "generalized magnitude system". But, the shared behavioral and neural signatures between number, time, and space may alternatively be due to similar encoding and decision-making processes, rather than due to shared domain-general representations. In this study, we investigate the relationship between approximate number and time in a large sample of 6-8 year-old children in Uruguay by examining how individual differences in the precision of number and time estimation correlate with school mathematics performance. Over four testing days, each child completed an approximate number discrimination task, an approximate time discrimination task, a digit span task, and a large battery of symbolic math tests. We replicate previous reports showing that symbolic math abilities correlate with approximate number precision and extend those findings by showing that math abilities also correlate with approximate time precision. But, contrary to approximate number and time sharing common representations, we find that each of these dimensions uniquely correlates with formal math: approximate number correlates more strongly with formal math compared to time and continues to correlate with math even when precision in time and individual differences in working memory are controlled for. These results suggest that there are important differences in the mental representations of approximate number and approximate time and further clarify the relationship between quantity representations and mathematics. Copyright

  18. Approximation and Computation

    CERN Document Server

    Gautschi, Walter; Rassias, Themistocles M

    2011-01-01

    Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg

  19. Domain decomposition method for nonconforming finite element approximations of anisotropic elliptic problems on nonmatching grids

    Energy Technology Data Exchange (ETDEWEB)

    Maliassov, S.Y. [Texas A& M Univ., College Station, TX (United States)

    1996-12-31

    An approach to the construction of an iterative method for solving systems of linear algebraic equations arising from nonconforming finite element discretizations with nonmatching grids for second order elliptic boundary value problems with anisotropic coefficients is considered. The technique suggested is based on decomposition of the original domain into nonoverlapping subdomains. The elliptic problem is presented in the macro-hybrid form with Lagrange multipliers at the interfaces between subdomains. A block diagonal preconditioner is proposed which is spectrally equivalent to the original saddle point matrix and has the optimal order of arithmetical complexity. The preconditioner includes blocks for preconditioning subdomain and interface problems. It is shown that constants of spectral equivalence axe independent of values of coefficients and mesh step size.

  20. Aspects of Finite Element Simulation of Axi-Symmetric Hydromechanical Deep Drawing

    DEFF Research Database (Denmark)

    Jensen, Morten Rikard; Olovsson, Lars; Danckert, Joachim

    1999-01-01

    A new approach for the Finite Element modelling of the hydromechanical deep drawing process is evaluated. In the model a Finite Difference approximation of Reynold’s equation is solved for the fluid flow between the blank and the draw die in the flange region. The approach is implemented...... as a contact algorithm in an explicit Finite Element code, Exhale2D. The developed model is verified against experiments and good agreement is obtained. It is concluded that the developed model is a promising approach for simulating the hydromechanical deep drawing process using the Finite Element Method....

  1. Numerical Multilevel Upscaling for Incompressible Flow in Reservoir Simulation: An Element-based Algebraic Multigrid (AMGe) Approach

    DEFF Research Database (Denmark)

    Christensen, Max la Cour; Villa, Umberto; Engsig-Karup, Allan Peter

    2017-01-01

    associated with non-planar interfaces between agglomerates, the coarse velocity space has guaranteed approximation properties. The employed AMGe technique provides coarse spaces with desirable local mass conservation and stability properties analogous to the original pair of Raviart-Thomas and piecewise......We study the application of a finite element numerical upscaling technique to the incompressible two-phase porous media total velocity formulation. Specifically, an element agglomeration based Algebraic Multigrid (AMGe) technique with improved approximation proper ties [37] is used, for the first...... discontinuous polynomial spaces, resulting in strong mass conservation for the upscaled systems. Due to the guaranteed approximation properties and the generic nature of the AMGe method, recursive multilevel upscaling is automatically obtained. Furthermore, this technique works for both structured...

  2. COMPARISONS OF THE FINITE-ELEMENT-WITH-DISCONTIGUOUS-SUPPORT METHOD TO CONTINUOUS-ENERGY MONTE CARLO FOR PIN-CELL PROBLEMS

    Energy Technology Data Exchange (ETDEWEB)

    A. T. Till; M. Hanuš; J. Lou; J. E. Morel; M. L. Adams

    2016-05-01

    The standard multigroup (MG) method for energy discretization of the transport equation can be sensitive to approximations in the weighting spectrum chosen for cross-section averaging. As a result, MG often inaccurately treats important phenomena such as self-shielding variations across a material. From a finite-element viewpoint, MG uses a single fixed basis function (the pre-selected spectrum) within each group, with no mechanism to adapt to local solution behavior. In this work, we introduce the Finite-Element-with-Discontiguous-Support (FEDS) method, whose only approximation with respect to energy is that the angular flux is a linear combination of unknowns multiplied by basis functions. A basis function is non-zero only in the discontiguous set of energy intervals associated with its energy element. Discontiguous energy elements are generalizations of bands and are determined by minimizing a norm of the difference between snapshot spectra and their averages over the energy elements. We begin by presenting the theory of the FEDS method. We then compare to continuous-energy Monte Carlo for one-dimensional slab and two-dimensional pin-cell problem. We find FEDS to be accurate and efficient at producing quantities of interest such as reaction rates and eigenvalues. Results show that FEDS converges at a rate that is approximately first-order in the number of energy elements and that FEDS is less sensitive to weighting spectrum than standard MG.

  3. Approximate Dynamic Programming in Tracking Control of a Robotic Manipulator

    Directory of Open Access Journals (Sweden)

    Marcin Szuster

    2016-02-01

    Full Text Available This article focuses on the implementation of an approximate dynamic programming algorithm in the discrete tracking control system of the three-degrees of freedom Scorbot-ER 4pc robotic manipulator. The controlled system is included in an articulated robots group which uses rotary joints to access their work space. The main part of the control system is a dual heuristic dynamic programming algorithm that consists of two structures designed in the form of neural networks: an actor and a critic. The actor generates the suboptimal control law while the critic approximates the difference of the value function from Bellman's equation with respect to the state. The residual elements of the control system are the PD controller, the supervisory term and an additional control signal. The structure of the supervisory term derives from the stability analysis performed using the Lyapunov stability theorem. The control system works online, the neural networks' weights-adaptation procedure is performed in every iteration step, and the neural networks' preliminary learning process is not required. The performance of the control system was verified by a series of computer simulations and experiments performed using the Scorbot-ER 4pc robotic manipulator.

  4. Finite element analysis of nonlinear creeping flows

    International Nuclear Information System (INIS)

    Loula, A.F.D.; Guerreiro, J.N.C.

    1988-12-01

    Steady-state creep problems with monotone constitutive laws are studied. Finite element approximations are constructed based on mixed Petrov-Galerkin formulations for constrained problems. Stability, convergence and a priori error estimates are proved for equal-order discontinuous stress and continuous velocity interpolations. Numerical results are presented confirming the rates of convergence predicted in the analysis and the good performance of this formulation. (author) [pt

  5. Constrained Optimization via Stochastic approximation with a simultaneous perturbation gradient approximation

    DEFF Research Database (Denmark)

    Sadegh, Payman

    1997-01-01

    This paper deals with a projection algorithm for stochastic approximation using simultaneous perturbation gradient approximation for optimization under inequality constraints where no direct gradient of the loss function is available and the inequality constraints are given as explicit functions...... of the optimization parameters. It is shown that, under application of the projection algorithm, the parameter iterate converges almost surely to a Kuhn-Tucker point, The procedure is illustrated by a numerical example, (C) 1997 Elsevier Science Ltd....

  6. A finite element method for neutron transport

    International Nuclear Information System (INIS)

    Ackroyd, R.T.

    1978-01-01

    A variational treatment of the finite element method for neutron transport is given based on a version of the even-parity Boltzmann equation which does not assume that the differential scattering cross-section has a spherical harmonic expansion. The theory of minimum and maximum principles is based on the Cauchy-Schwartz equality and the properties of a leakage operator G and a removal operator C. For systems with extraneous sources, two maximum and one minimum principles are given in boundary free form, to ease finite element computations. The global error of an approximate variational solution is given, the relationship of one the maximum principles to the method of least squares is shown, and the way in which approximate solutions converge locally to the exact solution is established. A method for constructing local error bounds is given, based on the connection between the variational method and the method of the hypercircle. The source iteration technique and a maximum principle for a system with extraneous sources suggests a functional for a variational principle for a self-sustaining system. The principle gives, as a consequence of the properties of G and C, an upper bound to the lowest eigenvalue. A related functional can be used to determine both upper and lower bounds for the lowest eigenvalue from an inspection of any approximate solution for the lowest eigenfunction. The basis for the finite element is presented in a general form so that two modes of exploitation can be undertaken readily. The model can be in phase space, with positional and directional co-ordinates defining points of the model, or it can be restricted to the positional co-ordinates and an expansion in orthogonal functions used for the directional co-ordinates. Suitable sets of functions are spherical harmonics and Walsh functions. The latter set is appropriate if a discrete direction representation of the angular flux is required. (author)

  7. Some results in Diophantine approximation

    DEFF Research Database (Denmark)

    Pedersen, Steffen Højris

    the basic concepts on which the papers build. Among other it introduces metric Diophantine approximation, Mahler’s approach on algebraic approximation, the Hausdorff measure, and properties of the formal Laurent series over Fq. The introduction ends with a discussion on Mahler’s problem when considered......This thesis consists of three papers in Diophantine approximation, a subbranch of number theory. Preceding these papers is an introduction to various aspects of Diophantine approximation and formal Laurent series over Fq and a summary of each of the three papers. The introduction introduces...

  8. Mathematical considerations regarding the stability of the trace element systems by linear regressions

    International Nuclear Information System (INIS)

    Mihai, Maria; Popescu, I.V.

    2002-01-01

    In this paper we present a mathematical model that would describe the stability and instability conditions, respectively of the organs of human body assumed as a living cybernetic system with feedback. We tested the theoretical model on the following trace elements: Mn, Zn and As. The trace elements were determined from the nose-pharyngeal carcinoma. We utilise the linear approximation to describe the dependencies between the trace elements determined in the hair of the patient. We present the results graphically. (authors)

  9. Bounded-Degree Approximations of Stochastic Networks

    Energy Technology Data Exchange (ETDEWEB)

    Quinn, Christopher J.; Pinar, Ali; Kiyavash, Negar

    2017-06-01

    We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with speci ed in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identify the r-best approximations among these classes, enabling robust decision making.

  10. Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media

    Energy Technology Data Exchange (ETDEWEB)

    Mohamed, M. Shadi, E-mail: m.s.mohamed@durham.ac.uk [School of Engineering and Computing Sciences, University of Durham, South Road, Durham DH1 3LE (United Kingdom); Seaid, Mohammed; Trevelyan, Jon [School of Engineering and Computing Sciences, University of Durham, South Road, Durham DH1 3LE (United Kingdom); Laghrouche, Omar [Institute for Infrastructure and Environment, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom)

    2013-10-15

    We investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media. The coupled equations are integrated in time using a semi-implicit method in the finite element framework. We show that for the considered problems, a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method. It is illustrated that this approach can be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls. The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction–radiation problems in two space dimensions.

  11. [Preliminary attempt at the speciation of 25-elements in the Chinese medicinal herbs].

    Science.gov (United States)

    Wang, Jing-Yu; Li, Ouyang; Liu, Ya-Qiong; Xie, Qing; Huang, Zhuo; Tu, Peng-Fei; Guo, Xu-Lin; Liu, Hu-Sheng

    2004-08-01

    To make an attempt at the multi-element speciation in the Chinese medicinal herbs by determining the concentrations of 25 elements in different extraction solutions. Firstly, five Chinese medicinal herbs (Buddleja officinalis, Dictamnus dasycarpus, Myristica fragrans, Albizia judibrissin and Inula japonica) from the same region of China were treated to obtain water-soluble phase, lipid-soluble phase and non-soluble phase by water extraction, organic solvent extraction and acid digestion, respectively. Secondly, Phytolacca acinosa, a Chinese medicinal herb collected from 9 regions of China, was extracted by 0% EtOH, 50% EtOH, 75% EtOH, 95% EtOH, respectively, referring the Chinese Pharmacopoeia. Finally, the concentrations of 25 elements, such as Be, Cr, Cu, Zn, Ge, Sr, Y, Mo, Cd, Tl, Pb and REEs, in the above three phases were determined by ICP-MS. Under the optimal conditions, all the 25 elements could be determined with detection limits ranged from 0.003 to 0.71 ng x g(-1). The average recoveries of the elements in P. acinosa were 88% approximately 119%, with the relative standard deviations 1.7% approximately 13.3%. It was observed that the determined 25 elements distributed in all the water-soluble, lipid-soluble and non-soluble phases, indicating that the inorganic species, organicspecies, as well as the protein bound species were coexisted in the herbs. Big differences of the element extraction rates could be found by using different ethanol solutions. With the aid of the obtained results, we may increase the extraction of necessary elements while decrease that of the toxic elements from the herbs by choosing a suitable solvent during the drug production.

  12. Low Multilinear Rank Approximation of Tensors and Application in Missing Traffic Data

    Directory of Open Access Journals (Sweden)

    Huachun Tan

    2014-02-01

    Full Text Available The problem of missing data in multiway arrays (i.e., tensors is common in many fields such as bibliographic data analysis, image processing, and computer vision. We consider the problems of approximating a tensor by another tensor with low multilinear rank in the presence of missing data and possibly reconstructing it (i.e., tensor completion. In this paper, we propose a weighted Tucker model which models only the known elements for capturing the latent structure of the data and reconstructing the missing elements. To treat the nonuniqueness of the proposed weighted Tucker model, a novel gradient descent algorithm based on a Grassmann manifold, which is termed Tucker weighted optimization (Tucker-Wopt, is proposed for guaranteeing the global convergence to a local minimum of the problem. Based on extensive experiments, Tucker-Wopt is shown to successfully reconstruct tensors with noise and up to 95% missing data. Furthermore, the experiments on traffic flow volume data demonstrate the usefulness of our algorithm on real-world application.

  13. Extrachromosomal genetic elements in Micrococcus.

    Science.gov (United States)

    Dib, Julián Rafael; Liebl, Wolfgang; Wagenknecht, Martin; Farías, María Eugenia; Meinhardt, Friedhelm

    2013-01-01

    Micrococci are Gram-positive G + C-rich, nonmotile, nonspore-forming actinomycetous bacteria. Micrococcus comprises ten members, with Micrococcus luteus being the type species. Representatives of the genus play important roles in the biodegradation of xenobiotics, bioremediation processes, production of biotechnologically important enzymes or bioactive compounds, as test strains in biological assays for lysozyme and antibiotics, and as infective agents in immunocompromised humans. The first description of plasmids dates back approximately 28 years, when several extrachromosomal elements ranging in size from 1.5 to 30.2 kb were found in Micrococcus luteus. Up to the present, a number of circular plasmids conferring antibiotic resistance, the ability to degrade aromatic compounds, and osmotolerance are known, as well as cryptic elements with unidentified functions. Here, we review the Micrococcus extrachromosomal traits reported thus far including phages and the only quite recently described large linear extrachromosomal genetic elements, termed linear plasmids, which range in size from 75 kb (pJD12) to 110 kb (pLMA1) and which confer putative advantageous capabilities, such as antibiotic or heavy metal resistances (inferred from sequence analyses and curing experiments). The role of the extrachromosomal elements for the frequently proven ecological and biotechnological versatility of the genus will be addressed as well as their potential for the development and use as genetic tools.

  14. Approximation by planar elastic curves

    DEFF Research Database (Denmark)

    Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge

    2016-01-01

    We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient......-driven optimization is then used to find the approximating elastic curve....

  15. Limitations of shallow nets approximation.

    Science.gov (United States)

    Lin, Shao-Bo

    2017-10-01

    In this paper, we aim at analyzing the approximation abilities of shallow networks in reproducing kernel Hilbert spaces (RKHSs). We prove that there is a probability measure such that the achievable lower bound for approximating by shallow nets can be realized for all functions in balls of reproducing kernel Hilbert space with high probability, which is different with the classical minimax approximation error estimates. This result together with the existing approximation results for deep nets shows the limitations for shallow nets and provides a theoretical explanation on why deep nets perform better than shallow nets. Copyright © 2017 Elsevier Ltd. All rights reserved.

  16. Finite elements methods in mechanics

    CERN Document Server

    Eslami, M Reza

    2014-01-01

    This book covers all basic areas of mechanical engineering, such as fluid mechanics, heat conduction, beams, and elasticity with detailed derivations for the mass, stiffness, and force matrices. It is especially designed to give physical feeling to the reader for finite element approximation by the introduction of finite elements to the elevation of elastic membrane. A detailed treatment of computer methods with numerical examples are provided. In the fluid mechanics chapter, the conventional and vorticity transport formulations for viscous incompressible fluid flow with discussion on the method of solution are presented. The variational and Galerkin formulations of the heat conduction, beams, and elasticity problems are also discussed in detail. Three computer codes are provided to solve the elastic membrane problem. One of them solves the Poisson’s equation. The second computer program handles the two dimensional elasticity problems, and the third one presents the three dimensional transient heat conducti...

  17. Generalized multiscale finite element method. Symmetric interior penalty coupling

    KAUST Repository

    Efendiev, Yalchin R.; Galvis, Juan; Lazarov, Raytcho D.; Moon, M.; Sarkis, Marcus V.

    2013-01-01

    Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the "mass" matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. © 2013 Elsevier Inc.

  18. Generalized multiscale finite element method. Symmetric interior penalty coupling

    KAUST Repository

    Efendiev, Yalchin R.

    2013-12-01

    Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the "mass" matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. © 2013 Elsevier Inc.

  19. Linear and Nonlinear Finite Elements.

    Science.gov (United States)

    1983-12-01

    Metzler. Con/ ugte rapdent solution of a finite element elastic problem with high Poson rato without scaling and once with the global stiffness matrix K...nonzero c, that makes u(0) = 1. According to the linear, small deflection theory of the membrane the central displacement given to the membrane is not... theory is possible based on the approximations (l-y 2 )t = +y’ 2 +y𔃾 , (1-y𔃼)’ 1-y’ 2 - y" (6) that change eq. (5) to V𔃺) = , [yŖ(1 + y") - Qy𔃼

  20. Application of the integral method to modelling the oxidation of defected fuel elements

    International Nuclear Information System (INIS)

    Kolar, M.

    1995-06-01

    The starting point for this report is the discrepancy reported in previous work between the reaction-diffusion calculations and the CEX-1 experiment, which involves storage of defected fuel elements in air at 150 deg C. This discrepancy is considerably diminished here by a more critical choice of theoretical parameters, and by taking into account the fact that different CEX-1 fuel elements were oxidized at very different rates and that the fuel element used previously for comparison with theoretical calculations actually underwent two limited-oxygen-supply cycles. Much better agreement is obtained here between the theory and the third, unlimited-air, storage period of the CEX-1 experiment. The approximate integral method is used extensively for the solution of the one-dimensional diffusion moving-boundary problems that may describe various storage periods of the CEX-1 experiment. In some cases it is easy to extend this method to arbitrary precision by using higher moments of the diffusion equation. Using this method, the validity of quasi-steady-state approximation is verified. Diffusion-controlled oxidation is also studied. In this case, for the unlimited oxygen supply, the integral method leads to an exact analytical solution for linear geometry, and to a good analytical approximation of the solution for the spherically symmetric geometry. These solutions may have some application in the analysis of experiments on the oxidation of small UO 2 fragments or powders when the individual UO 2 grains may be considered to be approximately spherical. (author). 23 refs., 5 tabs., 11 figs

  1. Approximate circuits for increased reliability

    Science.gov (United States)

    Hamlet, Jason R.; Mayo, Jackson R.

    2015-08-18

    Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.

  2. Mapping moveout approximations in TI media

    KAUST Repository

    Stovas, Alexey; Alkhalifah, Tariq Ali

    2013-01-01

    Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.

  3. Analytical approximation of neutron physics data

    International Nuclear Information System (INIS)

    Badikov, S.A.; Vinogradov, V.A.; Gaj, E.V.; Rabotnov, N.S.

    1984-01-01

    The method for experimental neutron-physical data analytical approximation by rational functions based on the Pade approximation is suggested. It is shown that the existence of the Pade approximation specific properties in polar zones is an extremely favourable analytical property essentially extending the convergence range and increasing its rate as compared with polynomial approximation. The Pade approximation is the particularly natural instrument for resonance curve processing as the resonances conform to the complex poles of the approximant. But even in a general case analytical representation of the data in this form is convenient and compact. Thus representation of the data on the neutron threshold reaction cross sections (BOSPOR constant library) in the form of rational functions lead to approximately twenty fold reduction of the storaged numerical information as compared with the by-point calculation at the same accWracy

  4. Mapping moveout approximations in TI media

    KAUST Repository

    Stovas, Alexey

    2013-11-21

    Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.

  5. Nuclear Hartree-Fock approximation testing and other related approximations

    International Nuclear Information System (INIS)

    Cohenca, J.M.

    1970-01-01

    Hartree-Fock, and Tamm-Dancoff approximations are tested for angular momentum of even-even nuclei. Wave functions, energy levels and momenta are comparatively evaluated. Quadripole interactions are studied following the Elliott model. Results are applied to Ne 20 [pt

  6. An h-p Taylor-Galerkin finite element method for compressible Euler equations

    Science.gov (United States)

    Demkowicz, L.; Oden, J. T.; Rachowicz, W.; Hardy, O.

    1991-01-01

    An extension of the familiar Taylor-Galerkin method to arbitrary h-p spatial approximations is proposed. Boundary conditions are analyzed, and a linear stability result for arbitrary meshes is given, showing the unconditional stability for the parameter of implicitness alpha not less than 0.5. The wedge and blunt body problems are solved with both linear, quadratic, and cubic elements and h-adaptivity, showing the feasibility of higher orders of approximation for problems with shocks.

  7. WELWING, Material Buckling for HWR with Annular Fuel Elements

    International Nuclear Information System (INIS)

    Grosskopf, O.G.P.

    1973-01-01

    1 - Nature of the physical problem solved: WELWING was developed to calculate the material buckling of reactor systems consisting of annular fuel elements in heavy water as moderator for various moderator to fuel ratios. The moderator to fuel ratio for the maximum material buckling for the particular system is selected automatically and the corresponding material buckling is calculated. 2 - Method of solution: The method used is an analytical solution of the one-group diffusion equations with various corrections and approximations. 3 - Restrictions on the complexity of the problem: Up to 32 different materials in the fuel element may be used

  8. Investigation of thermal energy transport from an anisotropic central heating element to the adjacent channels: A multipoint flux approximation

    KAUST Repository

    Salama, Amgad; Sun, Shuyu; El-Amin, Mohamed

    2015-01-01

    anisotropy of the heating element and/or the encompassing plates on thermal energy transport to the fluid passing through the two channels. When the medium is anisotropic with respect to thermal conductivity; energy transport to the neighboring channels

  9. Exact and approximate interior corner problem in neutron diffusion by integral transform methods

    International Nuclear Information System (INIS)

    Bareiss, E.H.; Chang, K.S.J.; Constatinescu, D.A.

    1976-09-01

    The mathematical solution of the neutron diffusion equation exhibits singularities in its derivatives at material corners. A mathematical treatment of the nature of these singularities and its impact on coarse network approximation methods in computational work is presented. The mathematical behavior is deduced from Green's functions, based on a generalized theory for two space dimensions, and the resulting systems of integral equations, as well as from the Kontorovich--Lebedev Transform. The effect on numerical calculations is demonstrated for finite difference and finite element methods for a two-region corner problem

  10. Review of fuel element development for nuclear rocket engines

    International Nuclear Information System (INIS)

    Taub, J.M.

    1975-06-01

    The Los Alamos Scientific Laboratory (LASL) entered the nuclear propulsion field in 1955 and began work on all aspects of a nuclear propulsion program involving uranium-loaded graphite fuels, hydrogen propellant, and a target exhaust temperature of approximately 2500 0 C. A very extensive uranium-loaded graphite fuel element technology evolved from the program. Selection and composition of raw materials for the extrusion mix had to be coupled with heat treatment studies to give optimum element properties. The highly enriched uranium in the element was incorporated as UO 2 , pyrocarbon-coated UC 2 , or solid solution UC . ZrC particles. An extensive development program resulted in successful NbC or ZrC coatings on elements to withstand hydrogen corrosion at elevated temperatures. Hot gas, thermal shock, thermal stress, and NDT evaluation procedures were developed to monitor progress in preparation of elements with optimum properties. Final evaluation was made in reactor tests at NRDS. Aerojet-General, Westinghouse Astronuclear Laboratory, and the Oak Ridge Y-12 Plant of Union Carbide Nuclear Company entered the program in the early 1960's, and their activities paralleled those of LASL in fuel element development. (U.S.)

  11. Fuel element burnup determination in HEU-LEU mixed TRIGA research reactor core

    International Nuclear Information System (INIS)

    Zagar, Tomaz; Ravnik, Matjaz

    2000-01-01

    This paper presents the results of a burnup calculations and burnup measurements for TRIGA FLIP HEU fuel elements and standard TRIGA LEU fuel elements used simultaneously in small TRIGA Mark II research reactor in Ljubljana, Slovenija. The fuel element burnup for approximately 15 years of operation was calculated with two different in house computer codes TRIGAP and TRIGLAV (both codes are available at OECD NEA Data Bank). The calculation is performed in one-dimensional radial geometry in TRIGAP and in two-dimensional (r,φ) geometry in TRIGLAV. Inter-comparison of results shows important influence of in-core water gaps, irradiation channels and mixed rings on burnup calculation accuracy. Burnup of 5 HEU and 27 LEU fuel elements was also measured with reactivity method. Measured and calculated burnup values are inter-compared for these elements (author)

  12. Approximate Implicitization Using Linear Algebra

    Directory of Open Access Journals (Sweden)

    Oliver J. D. Barrowclough

    2012-01-01

    Full Text Available We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.

  13. Domain decomposition solvers for nonlinear multiharmonic finite element equations

    KAUST Repository

    Copeland, D. M.

    2010-01-01

    In many practical applications, for instance, in computational electromagnetics, the excitation is time-harmonic. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple elliptic equation for the amplitude. This is true for linear problems, but not for nonlinear problems. However, due to the periodicity of the solution, we can expand the solution in a Fourier series. Truncating this Fourier series and approximating the Fourier coefficients by finite elements, we arrive at a large-scale coupled nonlinear system for determining the finite element approximation to the Fourier coefficients. The construction of fast solvers for such systems is very crucial for the efficiency of this multiharmonic approach. In this paper we look at nonlinear, time-harmonic potential problems as simple model problems. We construct and analyze almost optimal solvers for the Jacobi systems arising from the Newton linearization of the large-scale coupled nonlinear system that one has to solve instead of performing the expensive time-integration procedure. © 2010 de Gruyter.

  14. Risk approximation in decision making: approximative numeric abilities predict advantageous decisions under objective risk.

    Science.gov (United States)

    Mueller, Silke M; Schiebener, Johannes; Delazer, Margarete; Brand, Matthias

    2018-01-22

    Many decision situations in everyday life involve mathematical considerations. In decisions under objective risk, i.e., when explicit numeric information is available, executive functions and abilities to handle exact numbers and ratios are predictors of objectively advantageous choices. Although still debated, exact numeric abilities, e.g., normative calculation skills, are assumed to be related to approximate number processing skills. The current study investigates the effects of approximative numeric abilities on decision making under objective risk. Participants (N = 153) performed a paradigm measuring number-comparison, quantity-estimation, risk-estimation, and decision-making skills on the basis of rapid dot comparisons. Additionally, a risky decision-making task with exact numeric information was administered, as well as tasks measuring executive functions and exact numeric abilities, e.g., mental calculation and ratio processing skills, were conducted. Approximative numeric abilities significantly predicted advantageous decision making, even beyond the effects of executive functions and exact numeric skills. Especially being able to make accurate risk estimations seemed to contribute to superior choices. We recommend approximation skills and approximate number processing to be subject of future investigations on decision making under risk.

  15. A study on discontinuous Galerkin finite element methods for elliptic problems

    NARCIS (Netherlands)

    Janivita Joto Sudirham, J.J.S.; Sudirham, J.J.; van der Vegt, Jacobus J.W.; van Damme, Rudolf M.J.

    2003-01-01

    In this report we study several approaches of the discontinuous Galerkin finite element methods for elliptic problems. An important aspect in these formulations is the use of a lifting operator, for which we present an efficient numerical approximation technique. Numerical experiments for two

  16. Phase reduction and synchronization of a network of coupled dynamical elements exhibiting collective oscillations

    Science.gov (United States)

    Nakao, Hiroya; Yasui, Sho; Ota, Masashi; Arai, Kensuke; Kawamura, Yoji

    2018-04-01

    A general phase reduction method for a network of coupled dynamical elements exhibiting collective oscillations, which is applicable to arbitrary networks of heterogeneous dynamical elements, is developed. A set of coupled adjoint equations for phase sensitivity functions, which characterize the phase response of the collective oscillation to small perturbations applied to individual elements, is derived. Using the phase sensitivity functions, collective oscillation of the network under weak perturbation can be described approximately by a one-dimensional phase equation. As an example, mutual synchronization between a pair of collectively oscillating networks of excitable and oscillatory FitzHugh-Nagumo elements with random coupling is studied.

  17. Coupling multipoint flux mixed finite element methodswith continuous Galerkin methods for poroelasticity

    KAUST Repository

    Wheeler, Mary; Xue, Guangri; Yotov, Ivan

    2013-01-01

    We study the numerical approximation on irregular domains with general grids of the system of poroelasticity, which describes fluid flow in deformable porous media. The flow equation is discretized by a multipoint flux mixed finite element method

  18. Synthesis of new thermoelectrics using modulated elemental reactants

    Energy Technology Data Exchange (ETDEWEB)

    Hornbostel, M D; Sellinschegg, H; Johnson, D C

    1997-07-01

    A series of new, metastable ternary crystalline compounds with the skutterudite crystal structure have been synthesized using modulated elemental reactants. The initial reactants are made up of multiple repeats of a {approximately}25 {angstrom} thick unit containing elemental layers of the desired ternary metal, iron and antimony. Low temperature annealing (150 C) results in interdiffusion of the elemental layers to form amorphous reaction intermediates. Annealing these intermediates at temperatures between 200 C and 250 C results in exothermic crystallization of the desired skutterudite crystal structure. Most of the new compounds prepared are only kinetically stable, decomposing exothermically to form thermodynamically more stable mixtures of binary compounds and elements. Low angle x-ray diffraction studies show that the resulting films are exceedingly smooth. These films have an ideal geometry for measuring properties of importance for thermoelectric devices--the Seebeck coefficient and the electrical conductivity. Thermal conductivity can be measured using a modification of the 3{omega} technique of Cahill. Samples can be produced rapidly, allowing for systematic screening and subsequent optimization as a function of composition and doping levels.

  19. Quantitative microwave impedance microscopy with effective medium approximations

    Directory of Open Access Journals (Sweden)

    T. S. Jones

    2017-02-01

    Full Text Available Microwave impedance microscopy (MIM is a scanning probe technique to measure local changes in tip-sample admittance. The imaginary part of the reported change is calibrated with finite element simulations and physical measurements of a standard capacitive sample, and thereafter the output ΔY is given a reference value in siemens. Simulations also provide a means of extracting sample conductivity and permittivity from admittance, a procedure verified by comparing the estimated permittivity of polytetrafluoroethlyene (PTFE to the accepted value. Simulations published by others have investigated the tip-sample system for permittivity at a given conductivity, or conversely conductivity and a given permittivity; here we supply the full behavior for multiple values of both parameters. Finally, the well-known effective medium approximation of Bruggeman is considered as a means of estimating the volume fractions of the constituents in inhomogeneous two-phase systems. Specifically, we consider the estimation of porosity in carbide-derived carbon, a nanostructured material known for its use in energy storage devices.

  20. Two Scales, Hybrid Model for Soils, Involving Artificial Neural Network and Finite Element Procedure

    Directory of Open Access Journals (Sweden)

    Krasiński Marcin

    2015-02-01

    Full Text Available A hybrid ANN-FE solution is presented as a result of two level analysis of soils: a level of a laboratory sample and a level of engineering geotechnical problem. Engineering properties of soils (sands are represented directly in the form of ANN (this is in contrast with our former paper where ANN approximated constitutive relationships. Initially the ANN is trained with Duncan formula (Duncan and Chang [2], then it is re-trained (calibrated with some available experimental data, specific for the soil considered. The obtained approximation of the constitutive parameters is used directly in finite element method at the level of a single element at the scale of the laboratory sample to check the correct representation of the laboratory test. Then, the finite element that was successfully tested at the level of laboratory sample is used at the macro level to solve engineering problems involving the soil for which it was calibrated.

  1. A simple finite element method for boundary value problems with a Riemann–Liouville derivative

    KAUST Repository

    Jin, Bangti; Lazarov, Raytcho; Lu, Xiliang; Zhou, Zhi

    2016-01-01

    © 2015 Elsevier B.V. All rights reserved. We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order α∈(3/2,2) on the unit interval (0,1). The standard Galerkin finite element approximation converges slowly due to the presence of singularity term xα-1 in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value problem with nonlocal low order terms, whose solution can reconstruct directly the solution to the original problem. The stability of the variational formulation, and the optimal regularity pickup of the solution are analyzed. A novel Galerkin finite element method with piecewise linear or quadratic finite elements is developed, and L2(D) error estimates are provided. The approach is then applied to the corresponding fractional Sturm-Liouville problem, and error estimates of the eigenvalue approximations are given. Extensive numerical results fully confirm our theoretical study.

  2. A simple finite element method for boundary value problems with a Riemann–Liouville derivative

    KAUST Repository

    Jin, Bangti

    2016-02-01

    © 2015 Elsevier B.V. All rights reserved. We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order α∈(3/2,2) on the unit interval (0,1). The standard Galerkin finite element approximation converges slowly due to the presence of singularity term xα-1 in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value problem with nonlocal low order terms, whose solution can reconstruct directly the solution to the original problem. The stability of the variational formulation, and the optimal regularity pickup of the solution are analyzed. A novel Galerkin finite element method with piecewise linear or quadratic finite elements is developed, and L2(D) error estimates are provided. The approach is then applied to the corresponding fractional Sturm-Liouville problem, and error estimates of the eigenvalue approximations are given. Extensive numerical results fully confirm our theoretical study.

  3. A 3000 element lead-glass electromagnetic calorimeter

    International Nuclear Information System (INIS)

    Crittenden, R.R.; Dzierba, A.R.; Gunter, J.; Lindenbusch, R.; Rust, D.R.; Scott, E.; Smith, P.T.; Sulanke, T.; Teige, S.; Brabson, B.B.; Adams, T.; Bishop, J.M.; Cason, N.M.; LoSecco, J.M.; Manak, J.J.; Sanjari, A.H.; Shephard, W.D.; Steinike, D.L.; Taegar, S.A.; Thompson, D.R.; Chung, S.U.; Hackenburg, R.W.; Olchanski, C.; Weygand, D.P.; Willutzki, H.J.; Denisov, S.; Dushkin, A.; Kochetkov, V.; Lipaev, V.; Popov, A.; Shein, I.; Soldatov, A.; Bar-Yam, Z.; Cummings, J.P.; Dowd, J.P.; Eugenio, P.; Hayek, M.; Kern, W.; King, E.; Anoshina, E.V.; Bodyagin, V.A.; Demianov, A.I.; Gribushin, A.M.; Kodolova, O.L.; Korotkikh, V.L.; Kostin, M.A.; Ostrovidov, A.I.; Sarycheva, L.I.; Sinev, N.B.; Vardanyan, I.N.; Yershov, A.A.; Brown, D.S.; Pedlar, T.K.; Seth, K.K.; Wise, J.; Zhao, D.; Adams, G.S.; Napolitano, J.; Nozar, M.; Smith, J.A.; Witkowski, M.

    1997-01-01

    A 3045 element lead glass calorimeter and an associated fast trigger processor have been constructed, tested and implemented in BNL experiment E852 in conjunction with the multi-particle spectrometer (MPS). Approximately, 10 9 all-neutral and neutral plus charged triggers were recorded with this apparatus during data runs in 1994 and 1995. This paper reports on the construction, testing and performance of this lead glass calorimeter and the associated trigger processor. (orig.)

  4. The fingerprint element analysis on provenance of ancient chinese Jun porcelain

    International Nuclear Information System (INIS)

    Gao Zhengyao; Chen Songhua; Wang Jie; Huang Zhongxiang; Jia Xiuqin; Han Song

    1997-01-01

    Forty-three samples of ancient Jun porcelains and so on were chosen. Neutron activation analysis (NAA) was used to measure the 36 trace elements in every sample. Seven elements were chosen as the 'fingerprint elements'. The provenance of the glazes and bodies of ancient Chinese Jun porcelain were investigated by the fingerprint element analysis method. The result shows that although the ancient Chinese Jun porcelain samples have been leapt over six hundred years, and glaze colors are utterly different and are from many different kilns, there are long term, stable and same mainly raw material source. The near provenance relation between ancient Jun porcelain and ancient Ru porcelain is preliminarily analyzed. A few modern Jun porcelains approximate from ancient Jun porcelains, the majority become estranged from ancient Jun porcelain

  5. Trace element assessment in water of river kassa system, jos ...

    African Journals Online (AJOL)

    The value of index of geoaccumulation (Igeo) is approximately 2; for Zn and Pb which indicates, moderate contamination. Areas of the river system with anomalous value of trace element concentrations are those where mine tailings have been deposited close to the river channel or places where run off from adjoining ...

  6. Phase unwrapping algorithm using polynomial phase approximation and linear Kalman filter.

    Science.gov (United States)

    Kulkarni, Rishikesh; Rastogi, Pramod

    2018-02-01

    A noise-robust phase unwrapping algorithm is proposed based on state space analysis and polynomial phase approximation using wrapped phase measurement. The true phase is approximated as a two-dimensional first order polynomial function within a small sized window around each pixel. The estimates of polynomial coefficients provide the measurement of phase and local fringe frequencies. A state space representation of spatial phase evolution and the wrapped phase measurement is considered with the state vector consisting of polynomial coefficients as its elements. Instead of using the traditional nonlinear Kalman filter for the purpose of state estimation, we propose to use the linear Kalman filter operating directly with the wrapped phase measurement. The adaptive window width is selected at each pixel based on the local fringe density to strike a balance between the computation time and the noise robustness. In order to retrieve the unwrapped phase, either a line-scanning approach or a quality guided strategy of pixel selection is used depending on the underlying continuous or discontinuous phase distribution, respectively. Simulation and experimental results are provided to demonstrate the applicability of the proposed method.

  7. Spline approximation, Part 1: Basic methodology

    Science.gov (United States)

    Ezhov, Nikolaj; Neitzel, Frank; Petrovic, Svetozar

    2018-04-01

    In engineering geodesy point clouds derived from terrestrial laser scanning or from photogrammetric approaches are almost never used as final results. For further processing and analysis a curve or surface approximation with a continuous mathematical function is required. In this paper the approximation of 2D curves by means of splines is treated. Splines offer quite flexible and elegant solutions for interpolation or approximation of "irregularly" distributed data. Depending on the problem they can be expressed as a function or as a set of equations that depend on some parameter. Many different types of splines can be used for spline approximation and all of them have certain advantages and disadvantages depending on the approximation problem. In a series of three articles spline approximation is presented from a geodetic point of view. In this paper (Part 1) the basic methodology of spline approximation is demonstrated using splines constructed from ordinary polynomials and splines constructed from truncated polynomials. In the forthcoming Part 2 the notion of B-spline will be explained in a unique way, namely by using the concept of convex combinations. The numerical stability of all spline approximation approaches as well as the utilization of splines for deformation detection will be investigated on numerical examples in Part 3.

  8. The approximation of asymptotic potential and the soft dipole mode of the 6He

    International Nuclear Information System (INIS)

    Filippov, G.F.; Lashko, Yu.A.; Shvrdov, L.P.; Kato, K.

    1999-01-01

    The soft dipole mode of a three-cluster 6 He nucleus is investigated on the basis of the generalized version of the zero-radius nuclear forces approximation, taking into account a slowly decreasing asymptotic potential and influence of the Paulo exclusion principle on the asymptotic of the wave function, and also the fact of degeneration of 1 - continuous spectrum states. The issue of the behaviour of matrix elements of the two-channel S-matrix and problem of existence of the super-threshold 1 - resonance are discussed [ru

  9. A collapse mode of failure in powder-filled fuel elements

    International Nuclear Information System (INIS)

    Feraday, M.A.; Chalder, G.H.

    1964-01-01

    Two swaged fuel elements containing crushed, fused UO 2 powder were irradiated in a pressurized water loop at high heat ratings (∫Kdθ = 48 w/cm). The fuel elements were 2.0 cm in diameter and were sheathed in nickel-free Zircaloy--2 of 0.038 cm thickness. One element failed when the sheath ruptured at the top of a longitudinal ridge in the sheath after a burn-up of approximately 2550 MWd/TeU. No evidence was found that outgassing of the UO 2 contributed to the failure. Dimensional and structural changes observed in the fuel elements led to the conclusion that ridging of the sheath resulted from the action of coolant pressure on the diametral clearance formed by sintering and shrinkage of the UO 2 . Failure resulted due to severe local deformation accompanying one or more power cycles following ridge formation. (author)

  10. A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries

    Science.gov (United States)

    Heumann, Holger; Rapetti, Francesca

    2017-04-01

    Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients. As a consequence, the location of critical points of the poloidal flux, that are of paramount importance in tokamak engineering, is constrained to nodes of the mesh leading to undesired jumps in transient problems. Moreover, recent numerical results for the self-consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map. In this work we propose a mortar element method that employs two overlapping meshes. One mesh with Cartesian quadrilaterals covers the vacuum chamber domain accessible by the plasma and one mesh with triangles discretizes the region outside. The two meshes overlap in a narrow region. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details outside this region. The continuity of the numerical solution in the region of overlap is weakly enforced by a mortar-like mapping.

  11. Beyond chemical accuracy: The pseudopotential approximation in diffusion Monte Carlo calculations of the HCP to BCC phase transition in beryllium.

    Energy Technology Data Exchange (ETDEWEB)

    Shulenburger, Luke [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Mattsson, Thomas Kjell Rene [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Desjarlais, Michael Paul [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2015-01-01

    Motivated by the disagreement between recent diffusion Monte Carlo calculations of the phase transition pressure between the ambient and beta-Sn phases of silicon and experiments, we present a study of the HCP to BCC phase transition in beryllium. This lighter element provides an opportunity for directly testing many of the approximations required for calculations on silicon and may suggest a path towards increasing the practical accuracy of diffusion Monte Carlo calculations of solids in general. We demonstrate that the single largest approximation in these calculations is the pseudopotential approximation and after removing this we find excellent agreement with experiment for the ambient HCP phase and results similar to careful calculations using density functional theory for the phase transition pressure.

  12. Test Functions for Three-Dimensional Control-Volume Mixed Finite-Element Methods on Irregular Grids

    National Research Council Canada - National Science Library

    Naff, R. L; Russell, T. F; Wilson, J. D

    2000-01-01

    .... For control-volume mixed finite-element methods, vector shape functions are used to approximate the distribution of velocities across cells and vector test functions are used to minimize the error...

  13. Training Future Entrepreneurs Using European Funds. A Descriptive Research on Start-Up Romania Programs

    Directory of Open Access Journals (Sweden)

    Cristina Nicolau

    2016-01-01

    Full Text Available This paper focuses on the mutual relationship among the concepts of entrepreneurship, trainingpersonnel and business start-up and development. From our point of view, Romania shallencourage as much as possible entrepreneurship so as to create SMEs, the most flexible andnumerous in number in the Romanian total number of companies. Hence, the main objective of thispaper is to highlight the importance of accessing European funds in increasing the number ofRomanians properly trained so as to become successful entrepreneurs and to manage successfulbusinesses. At the same time, another main objective is to present the need of entrepreneurshiptraining and support in business start-up and development by using the descriptive method ofresearch.

  14. An approximate dynamic programming approach to resource management in multi-cloud scenarios

    Science.gov (United States)

    Pietrabissa, Antonio; Priscoli, Francesco Delli; Di Giorgio, Alessandro; Giuseppi, Alessandro; Panfili, Martina; Suraci, Vincenzo

    2017-03-01

    The programmability and the virtualisation of network resources are crucial to deploy scalable Information and Communications Technology (ICT) services. The increasing demand of cloud services, mainly devoted to the storage and computing, requires a new functional element, the Cloud Management Broker (CMB), aimed at managing multiple cloud resources to meet the customers' requirements and, simultaneously, to optimise their usage. This paper proposes a multi-cloud resource allocation algorithm that manages the resource requests with the aim of maximising the CMB revenue over time. The algorithm is based on Markov decision process modelling and relies on reinforcement learning techniques to find online an approximate solution.

  15. Domain Decomposition Solvers for Frequency-Domain Finite Element Equations

    KAUST Repository

    Copeland, Dylan

    2010-10-05

    The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method. © 2011 Springer-Verlag Berlin Heidelberg.

  16. Analysis of trace elements in human hair by PIXE

    International Nuclear Information System (INIS)

    Baptista, G.B.; Montenegro, E.C.; Paschoa, A.S.; Barros Leite, C.V. de.

    1980-10-01

    The PIXE method was applied to the analysis of trace elements in scalp hair using two methods for target preparation. In the first method eigth hair strands each with nearly cylindrical geommetry and approximately the same diameter were selected and placed on an aluminum frame. In the second method a given mass of hair was dissolved with nitric acid and a known amount of strontium was added to the solution and dripped on a membrane filter using a micropipet. The results for the concentrations of trace elements in hair obtained by the two methods are compared and several aspects of the analysis is discussed. (Author) [pt

  17. Domain Decomposition Solvers for Frequency-Domain Finite Element Equations

    KAUST Repository

    Copeland, Dylan; Kolmbauer, Michael; Langer, Ulrich

    2010-01-01

    The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method. © 2011 Springer-Verlag Berlin Heidelberg.

  18. Study on elastic scattering of 412 KeV γ radiation in elements of different atomic numbers

    International Nuclear Information System (INIS)

    Goncalves, O.D.

    1977-01-01

    The differentials cross sections for elastic scattering of 412 KeV γ rays was measured with Ge-Li detectors for elements of z = 78, 74, 56, 48 and 47. For the elements of z 78, 56 and 48 don't exist former measurements, while for z 74 and 48 exist only measurements done with NaI detectors, of poor resolution. Approximated theories calculated through H.F.S.D. form factors are discussed. From the analysis of the experimental and theoretical results, anomalies early pointed in this approximation could be explained. The experimental results presented good agreement with recent theoretical calculations done with second order perturbation theory. (author)

  19. A multipoint flux approximation of the steady-state heat conduction equation in anisotropic media

    KAUST Repository

    Salama, Amgad; Sun, Shuyu; El-Amin, M. F.

    2013-01-01

    In this work, we introduce multipoint flux (MF) approximation method to the problem of conduction heat transfer in anisotropic media. In such media, the heat flux vector is no longer coincident with the temperature gradient vector. In this case, thermal conductivity is described as a second order tensor that usually requires, at least, six quantities to be fully defined in general three-dimensional problems. The two-point flux finite differences approximation may not handle such anisotropy and essentially more points need to be involved to describe the heat flux vector. In the framework of mixed finite element method (MFE), the MFMFE methods are locally conservative with continuous normal fluxes. We consider the lowest order Brezzi-Douglas-Marini (BDM) mixed finite element method with a special quadrature rule that allows for nodal velocity elimination resulting in a cell-centered system for the temperature. We show comparisons with some analytical solution of the problem of conduction heat transfer in anisotropic long strip. We also consider the problem of heat conduction in a bounded, rectangular domain with different anisotropy scenarios. It is noticed that the temperature field is significantly affected by such anisotropy scenarios. Also, the technique used in this work has shown that it is possible to use the finite difference settings to handle heat transfer in anisotropic media. In this case, heat flux vectors, for the case of rectangular mesh, generally require six points to be described. Copyright © 2013 by ASME.

  20. A multipoint flux approximation of the steady-state heat conduction equation in anisotropic media

    KAUST Repository

    Salama, Amgad

    2013-03-20

    In this work, we introduce multipoint flux (MF) approximation method to the problem of conduction heat transfer in anisotropic media. In such media, the heat flux vector is no longer coincident with the temperature gradient vector. In this case, thermal conductivity is described as a second order tensor that usually requires, at least, six quantities to be fully defined in general three-dimensional problems. The two-point flux finite differences approximation may not handle such anisotropy and essentially more points need to be involved to describe the heat flux vector. In the framework of mixed finite element method (MFE), the MFMFE methods are locally conservative with continuous normal fluxes. We consider the lowest order Brezzi-Douglas-Marini (BDM) mixed finite element method with a special quadrature rule that allows for nodal velocity elimination resulting in a cell-centered system for the temperature. We show comparisons with some analytical solution of the problem of conduction heat transfer in anisotropic long strip. We also consider the problem of heat conduction in a bounded, rectangular domain with different anisotropy scenarios. It is noticed that the temperature field is significantly affected by such anisotropy scenarios. Also, the technique used in this work has shown that it is possible to use the finite difference settings to handle heat transfer in anisotropic media. In this case, heat flux vectors, for the case of rectangular mesh, generally require six points to be described. Copyright © 2013 by ASME.

  1. Acoustical topology optimization of Zwicker's loudness with Padé approximation

    DEFF Research Database (Denmark)

    Kook, Junghwan; Jensen, Jakob Søndergaard; Wang, Semyung

    2013-01-01

    Zwicker's loudness is a conventional standard index for measuring human hearing annoyance and has been widely considered in many industrial fields for noise evaluations. The calculation of Zwicker's loudness, which is needed for a wide range of frequency responses with a fine frequency resolution......, this approach imposes prohibitively high computational costs. In this research, we propose a computationally-efficient approach to resolve the computational issue in the computation and optimization of Zwicker's loudness. We present an efficient approach which combines the finite element method (FEM......) with the Padé approximation (PA) procedure for obtaining Zwicker's loudness and for applying it in a gradient-based acoustical topology optimization procedure applied to the design of acoustic devices to minimize Zwicker's loudness. In this respect, the calculation of Zwicker's loudness is represented by the PA...

  2. Applicability of the successive approximation methods in the control elements treatment in nuclear systems with irregular geometry

    International Nuclear Information System (INIS)

    El Maftoum, W.R.

    1983-01-01

    The solution of the steady-state wave equation was found by a Fourier series expansion in an arbitrarily shaped n-dimensional domain. This solution, subject to a homogeneous boundary condition (Dirichlet), was applied to a reactor with partially inserted control rods. A Fortran IV program was developed which solves the equation for two media. Criticality calculations were carried out and the worth of partially inserted rod was determined for several problems with an accuracy comparable with that in the existing literature. As a further consequence the technique, associated with the method of sucessive approximations, allowed to derive perturbative formulas for the eigenvalues of the wave equation and related equations. (Author) [pt

  3. Criteria for the reliability of numerical approximations to the solution of fluid flow problems

    International Nuclear Information System (INIS)

    Foias, C.

    1986-01-01

    The numerical approximation of the solutions of fluid flows models is a difficult problem in many cases of energy research. In all numerical methods implementable on digital computers, a basic question is if the number N of elements (Galerkin modes, finite-difference cells, finite-elements, etc.) is sufficient to describe the long time behavior of the exact solutions. It was shown using several approaches that some of the estimates based on physical intuition of N are rigorously valid under very general conditions and follow directly from the mathematical theory of the Navier-Stokes equations. Among the mathematical approaches to these estimates, the most promising (which can be and was already applied to many other dissipative partial differential systems) consists in giving upper estimates to the fractal dimension of the attractor associated to one (or all) solution(s) of the respective partial differential equations. 56 refs

  4. Essential Boundary Conditions with Straight C1 Finite Elements in Curved Domains

    International Nuclear Information System (INIS)

    Ferraro, N.M.; Jardin, S.C.; Luo, X.

    2010-01-01

    The implementation of essential boundary conditions in C1 finite element analysis requires proper treatment of both the boundary conditions on second-order differentials of the solution and the curvature of the domain boundary. A method for the imposition of essential boundary conditions using straight elements (where the elements are not deformed to approximate a curved domain) is described. It is shown that pre-multiplication of the matrix equation by the local rotation matrix at each boundary node is not the optimal transformation. The uniquely optimal transformation is found, which does not take the form of a similarity transformation due to the non-orthogonality of the transformation to curved coordinates.

  5. Reliability of Structural Systems with Correlated Elements

    DEFF Research Database (Denmark)

    Thoft-Christensen, Palle; Sørensen, John Dalsgaard

    1982-01-01

    Calculation of the probability of failure of a system with correlation members is usually a difficult and time-consuming numerical problem. However, for some types of systems with equally correlated elements this calculation can be performed in a simple way. This has suggested two new methods bas...... on so-called average and equivalent correlation coefficients. By using these methods approximate values for the probability of failure can easily be calculated. The accuracy of these methods is illustrated with examples....

  6. The efficiency of Flory approximation

    International Nuclear Information System (INIS)

    Obukhov, S.P.

    1984-01-01

    The Flory approximation for the self-avoiding chain problem is compared with a conventional perturbation theory expansion. While in perturbation theory each term is averaged over the unperturbed set of configurations, the Flory approximation is equivalent to the perturbation theory with the averaging over the stretched set of configurations. This imposes restrictions on the integration domain in higher order terms and they can be treated self-consistently. The accuracy δν/ν of Flory approximation for self-avoiding chain problems is estimated to be 2-5% for 1 < d < 4. (orig.)

  7. Analysis of arab ore phosphate, for macro, micro and toxic elements using INAA method

    International Nuclear Information System (INIS)

    El-Ghawi, U.M.; Abugassa, I.O.; Alfakhri, S.M.

    2003-01-01

    Natural phosphates are used on large scale in the fertilizer industry and large quantities of phosphates are processed each year all over the world from fertilizer production. At present world usage of rock phosphates is approximately 90 million tons per annum. Because natural phosphates are a source of some valuable elements besides phosphorus used in fertilizers production, the objective of this paper is to check the level of radioactive elements of uranium and thorium, and the stable environmental pollutants like As and Cr in natural arab phosphate. In addition, rare earth elements (REEs) and other elements like (Fe, K, Mn, Na and Ti) were determined

  8. Efficient lensing element for x-rays

    International Nuclear Information System (INIS)

    Ceglio, N.M.; Smith, H.I.

    1977-01-01

    An efficient x-ray lens with an effective speed of order less than approximately f/50 for lambda greater than approximately 10 A x-rays is described. Fabrication of this lensing element appears feasible using existing microfabrication technology. Diffraction and refraction are coupled in a single element to achieve efficient x-ray concentration into a single order focal spot. Diffraction is used to produce efficient ray bending (without absorption) while refraction is used only to provide appropriate phase adjustment among the various diffraction orders to insure what is essentially a single order output. The mechanism for ray bending (diffraction) is decoupled from the absorption mechanism. Refraction is used only to achieve small shifts in phase so that the associated attenuation need not be prohibitive. The x-ray lens might be described as a Blazed Fresnel Phase Plate (BFPP) with a spatially distributed phase shift within each Fresnel zone. The spatial distribution of the phase shifts is chosen to concentrate essentially all of the unabsorbed energy into a single focal spot. The BFPP transforms the incident plane wave into a converging spherical wave having an amplitude modulation which is periodic in r 2 . As a result of the periodic amplitude modulation, the BFPP will diffract energy into foci other than the first order real focus. In cases of small absorption such effects are negligible and practically all the unabsorbed energy is directed into the first order real focus

  9. Spectral element method for vector radiative transfer equation

    International Nuclear Information System (INIS)

    Zhao, J.M.; Liu, L.H.; Hsu, P.-F.; Tan, J.Y.

    2010-01-01

    A spectral element method (SEM) is developed to solve polarized radiative transfer in multidimensional participating medium. The angular discretization is based on the discrete-ordinates approach, and the spatial discretization is conducted by spectral element approach. Chebyshev polynomial is used to build basis function on each element. Four various test problems are taken as examples to verify the performance of the SEM. The effectiveness of the SEM is demonstrated. The h and the p convergence characteristics of the SEM are studied. The convergence rate of p-refinement follows the exponential decay trend and is superior to that of h-refinement. The accuracy and efficiency of the higher order approximation in the SEM is well demonstrated for the solution of the VRTE. The predicted angular distribution of brightness temperature and Stokes vector by the SEM agree very well with the benchmark solutions in references. Numerical results show that the SEM is accurate, flexible and effective to solve multidimensional polarized radiative transfer problems.

  10. A New Approximation Method for Solving Variational Inequalities and Fixed Points of Nonexpansive Mappings

    Directory of Open Access Journals (Sweden)

    Klin-eam Chakkrid

    2009-01-01

    Full Text Available Abstract A new approximation method for solving variational inequalities and fixed points of nonexpansive mappings is introduced and studied. We prove strong convergence theorem of the new iterative scheme to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality for the inverse-strongly monotone mapping which solves some variational inequalities. Moreover, we apply our main result to obtain strong convergence to a common fixed point of nonexpansive mapping and strictly pseudocontractive mapping in a Hilbert space.

  11. Annotations on the virtual element method for second-order elliptic problems

    Energy Technology Data Exchange (ETDEWEB)

    Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2017-01-03

    This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the numerical discretization of Partial Differential Equations (PDEs) and, in particular, the Finite Element Method (FEM). This document is not an introduction to the FEM, for which many textbooks (also free on the internet) are available. Eventually, this document is intended to evolve into a tutorial introduction to the VEM (but this is really a long-term goal).

  12. Scattering Light by а Cylindrical Capsule with Arbitrary End Caps in the Rayleigh-Gans-Debye Approximation

    Directory of Open Access Journals (Sweden)

    K. A. Shapovalov

    2015-01-01

    Full Text Available The paper concerns the light scattering problem of biological objects of complicated structure.It considers optically “soft” (having a refractive index close to that of a surrounding medium homogeneous cylindrical capsules, composed of three parts: central one that is cylindrical and two symmetrical rounding end caps. Such capsules can model more broad class of biological objects than the ordinary shapes of a spheroid or sphere. But, unfortunately, if a particle has other than a regular geometrical shape, then it is very difficult or impossible to solve the scattering problem analytically in its most general form that oblige us to use numerical and approximate analytical methods. The one of such approximate analytical method is the Rayleigh-Gans-Debye approximation (or the first Born approximation.So, the Rayleigh-Gans-Debye approximation is valid for different objects having size from nanometer to millimeter and depending on wave length and refractive index of an object under small phase shift of central ray.The formulas for light scattering amplitude of cylindrical capsule with arbitrary end caps in the Rayleigh-Gans-Debye approximation in scalar form are obtained. Then the light scattering phase function [or element of scattering matrix f11] for natural incident light (unpolarized or arbitrary polarized light is calculated.Numerical results for light scattering phase functions of cylindrical capsule with conical, spheroidal, paraboloidal ends in the Rayleigh-Gans-Debye approximation are compared. Also numerical results for light scattering phase function of cylindrical capsule with conical ends in the Rayleigh-Gans-Debye approximation and in the method of Purcell-Pennypacker (or Discrete Dipole method are compared. The good agreement within an application range of the RayleighGans-Debye approximation is obtained.Further continuation of the work, perhaps, is a consideration of multilayer cylindrical capsule in the Rayleigh

  13. Predicting thermal distortion of synchrotron radiation mirrors with finite element analysis

    International Nuclear Information System (INIS)

    DiGennaro, R.; Edwards, W.R.; Hoyer, E.

    1985-10-01

    High power and high power densities due to absorbed radiation are significant design considerations which can limit performance of mirrors receiving highly collimated synchrotron radiation from insertion devices and bending magnet sources. Although the grazing incidence angles needed for x-ray optics spread the thermal load, localized, non-uniform heating can cause distortions which exceed allowable surface figure errors and limit focusing resolution. This paper discusses the suitability of numerical approximations using finite element methods for heat transfer, deformation, and stress analysis of optical elements. The primary analysis objectives are (1) to estimate optical surface figure under maximum heat loads, (2) to correctly predict thermal stresses in order to select suitable materials and mechanical design configurations, and (3) to minimize fabrication costs by specifying appropriate tolerances for surface figure. Important factors which determine accuracy of results include finite element model mesh refinement, accuracy of boundary condition modeling, and reliability of material property data. Some methods to verify accuracy are suggested. Design analysis for an x-ray mirror is presented. Some specific configurations for internal water-cooling are evaluated in order to determine design sensitivity with respect to structural geometry, material properties, fabrication tolerances, absorbed heat magnitude and distribution, and heat transfer approximations. Estimated accuracy of these results is discussed

  14. Weighted approximation with varying weight

    CERN Document Server

    Totik, Vilmos

    1994-01-01

    A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.

  15. Spectral Element Method for the Simulation of Unsteady Compressible Flows

    Science.gov (United States)

    Diosady, Laslo Tibor; Murman, Scott M.

    2013-01-01

    This work uses a discontinuous-Galerkin spectral-element method (DGSEM) to solve the compressible Navier-Stokes equations [1{3]. The inviscid ux is computed using the approximate Riemann solver of Roe [4]. The viscous fluxes are computed using the second form of Bassi and Rebay (BR2) [5] in a manner consistent with the spectral-element approximation. The method of lines with the classical 4th-order explicit Runge-Kutta scheme is used for time integration. Results for polynomial orders up to p = 15 (16th order) are presented. The code is parallelized using the Message Passing Interface (MPI). The computations presented in this work are performed using the Sandy Bridge nodes of the NASA Pleiades supercomputer at NASA Ames Research Center. Each Sandy Bridge node consists of 2 eight-core Intel Xeon E5-2670 processors with a clock speed of 2.6Ghz and 2GB per core memory. On a Sandy Bridge node the Tau Benchmark [6] runs in a time of 7.6s.

  16. Spectral response of multi-element silicon detectors

    Energy Technology Data Exchange (ETDEWEB)

    Ludewigt, B.A.; Rossington, C.S.; Chapman, K. [Univ. of California, Berkeley, CA (United States)

    1997-04-01

    Multi-element silicon strip detectors, in conjunction with integrated circuit pulse-processing electronics, offer an attractive alternative to conventional lithium-drifted silicon Si(Li) and high purity germanium detectors (HPGe) for high count rate, low noise synchrotron x-ray fluorescence applications. One of the major differences between the segmented Si detectors and the commercially available single-element Si(Li) or HPGe detectors is that hundreds of elements can be fabricated on a single Si substrate using standard silicon processing technologies. The segmentation of the detector substrate into many small elements results in very low noise performance at or near, room temperature, and the count rate of the detector is increased many-fold due to the multiplication in the total number of detectors. Traditionally, a single channel of detector with electronics can handle {approximately}100 kHz count rates while maintaining good energy resolution; the segmented detectors can operate at greater than MHz count rates merely due to the multiplication in the number of channels. One of the most critical aspects in the development of the segmented detectors is characterizing the charge sharing and charge loss that occur between the individual detector strips, and determining how these affect the spectral response of the detectors.

  17. A Kohn–Sham equation solver based on hexahedral finite elements

    International Nuclear Information System (INIS)

    Fang Jun; Gao Xingyu; Zhou Aihui

    2012-01-01

    We design a Kohn–Sham equation solver based on hexahedral finite element discretizations. The solver integrates three schemes proposed in this paper. The first scheme arranges one a priori locally-refined hexahedral mesh with appropriate multiresolution. The second one is a modified mass-lumping procedure which accelerates the diagonalization in the self-consistent field iteration. The third one is a finite element recovery method which enhances the eigenpair approximations with small extra work. We carry out numerical tests on each scheme to investigate the validity and efficiency, and then apply them to calculate the ground state total energies of nanosystems C 60 , C 120 , and C 275 H 172 . It is shown that our solver appears to be computationally attractive for finite element applications in electronic structure study.

  18. INTOR cost approximation

    International Nuclear Information System (INIS)

    Knobloch, A.F.

    1980-01-01

    A simplified cost approximation for INTOR parameter sets in a narrow parameter range is shown. Plausible constraints permit the evaluation of the consequences of parameter variations on overall cost. (orig.) [de

  19. Implementation of the Vanka-type multigrid solver for the finite element approximation of the Navier-Stokes equations on GPU

    Czech Academy of Sciences Publication Activity Database

    Bauer, Petr; Klement, V.; Oberhuber, T.; Žabka, V.

    2016-01-01

    Roč. 200, March (2016), s. 50-56 ISSN 0010-4655 R&D Projects: GA ČR GB14-36566G Institutional support: RVO:61388998 Keywords : Navier–Stokes equations * mixed finite elements * multigrid * Vanka-type smoothers * Gauss–Seidel * red–black coloring * parallelization * GPU Subject RIV: BK - Fluid Dynamics Impact factor: 3.936, year: 2016

  20. Solar power satellite rectenna design study: Directional receiving elements and parallel-series combining analysis

    Science.gov (United States)

    Gutmann, R. J.; Borrego, J. M.

    1978-01-01

    Rectenna conversion efficiencies (RF to dc) approximating 85 percent were demonstrated on a small scale, clearly indicating the feasibility and potential of efficiency of microwave power to dc. The overall cost estimates of the solar power satellite indicate that the baseline rectenna subsystem will be between 25 to 40 percent of the system cost. The directional receiving elements and element extensions were studied, along with power combining evaluation and evaluation extensions.

  1. Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells

    Directory of Open Access Journals (Sweden)

    Humberto Breves Coda

    2009-01-01

    Full Text Available This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples.

  2. Plastic profiled sealing element for household refrigeration appliances

    Energy Technology Data Exchange (ETDEWEB)

    Wunderlich, E; Robl, G

    1988-12-28

    A plastic profiled sealing element for household refrigeration appliances, such as freezers, refrigerators, and freezer compartments, includes a sealing bellows having a hose-shaped cross section. The sealing bellows is provided with two side walls and a covering wall, and is made of a plastic that has been set by means of a softener so as to be continuously flexible. Further, the profiled sealing element is provided with an anchor member made of a plastic of the same or different material hardness, with the sealing bellows and the anchor member being connected with one another to form a unit. The cross sections of the two side walls of the sealing bellows narrow as the side walls rise from the region of the connection of the side walls with the covering wall of the anchor member to approximately half the height of the sealing bellows, so that the side walls become increasingly thinner. Thereafter, the cross sections of the side walls increase again to the edges of the covering wall of the sealing bellows, until the side walls again reach approximately their initial cross sections. The side walls, on the one hand, and the covering wall, on the other hand, are kept flexible by means of softeners having different characteristics.

  3. A unified approach to the Darwin approximation

    International Nuclear Information System (INIS)

    Krause, Todd B.; Apte, A.; Morrison, P. J.

    2007-01-01

    There are two basic approaches to the Darwin approximation. The first involves solving the Maxwell equations in Coulomb gauge and then approximating the vector potential to remove retardation effects. The second approach approximates the Coulomb gauge equations themselves, then solves these exactly for the vector potential. There is no a priori reason that these should result in the same approximation. Here, the equivalence of these two approaches is investigated and a unified framework is provided in which to view the Darwin approximation. Darwin's original treatment is variational in nature, but subsequent applications of his ideas in the context of Vlasov's theory are not. We present here action principles for the Darwin approximation in the Vlasov context, and this serves as a consistency check on the use of the approximation in this setting

  4. An Approximate Approach to Automatic Kernel Selection.

    Science.gov (United States)

    Ding, Lizhong; Liao, Shizhong

    2016-02-02

    Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.

  5. Mixed-hybrid finite element method for the transport equation and diffusion approximation of transport problems

    International Nuclear Information System (INIS)

    Cartier, J.

    2006-04-01

    This thesis focuses on mathematical analysis, numerical resolution and modelling of the transport equations. First of all, we deal with numerical approximation of the solution of the transport equations by using a mixed-hybrid scheme. We derive and study a mixed formulation of the transport equation, then we analyse the related variational problem and present the discretization and the main properties of the scheme. We particularly pay attention to the behavior of the scheme and we show its efficiency in the diffusion limit (when the mean free path is small in comparison with the characteristic length of the physical domain). We present academical benchmarks in order to compare our scheme with other methods in many physical configurations and validate our method on analytical test cases. Unstructured and very distorted meshes are used to validate our scheme. The second part of this thesis deals with two transport problems. The first one is devoted to the study of diffusion due to boundary conditions in a transport problem between two plane plates. The second one consists in modelling and simulating radiative transfer phenomenon in case of the industrial context of inertial confinement fusion. (author)

  6. Approximate error conjugation gradient minimization methods

    Science.gov (United States)

    Kallman, Jeffrey S

    2013-05-21

    In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.

  7. Nonempirical Calculation of Superconducting Transition Temperatures in Light-Element Superconductors.

    Science.gov (United States)

    Arita, Ryotaro; Koretsune, Takashi; Sakai, Shiro; Akashi, Ryosuke; Nomura, Yusuke; Sano, Wataru

    2017-07-01

    Recent progress in the fully nonempirical calculation of the superconducting transition temperature (T c ) is reviewed. Especially, this study focuses on three representative light-element high-T c superconductors, i.e., elemental Li, sulfur hydrides, and alkali-doped fullerides. Here, it is discussed how crucial it is to develop the beyond Migdal-Eliashberg (ME) methods. For Li, a scheme of superconducting density functional theory for the plasmon mechanism is formulated and it is found that T c is dramatically enhanced by considering the frequency dependence of the screened Coulomb interaction. For sulfur hydrides, it is essential to go beyond not only the static approximation for the screened Coulomb interaction, but also the constant density-of-states approximation for electrons, the harmonic approximation for phonons, and the Migdal approximation for the electron-phonon vertex, all of which have been employed in the standard ME calculation. It is also shown that the feedback effect in the self-consistent calculation of the self-energy and the zero point motion considerably affect the calculation of T c . For alkali-doped fullerides, the interplay between electron-phonon coupling and electron correlations becomes more nontrivial. It has been demonstrated that the combination of density functional theory and dynamical mean field theory with the ab initio downfolding scheme for electron-phonon coupled systems works successfully. This study not only reproduces the experimental phase diagram but also obtains a unified view of the high-T c superconductivity and the Mott-Hubbard transition in the fullerides. The results for these high-T c superconductors will provide a firm ground for future materials design of new superconductors. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  8. Polygonal-path approximations on the path spaces of quantum-mechanical systems: properties of the polygonal paths

    International Nuclear Information System (INIS)

    Exner, P.; Kolerov, G.I.

    1981-01-01

    Properties of the subset of polygonal paths in the Hilbert space H of paths referring to a d-dimensional quantum-mechanical system are examined. Using the reproduction kernel technique we prove that each element of H is approximated by polygonal paths uniformly with respect to the ''norm'' of time-interval partitions. This result will be applied in the second part of the present paper to prove consistency of the uniform polygonal-path extension of the Feynman maps [ru

  9. Self-similar continued root approximants

    International Nuclear Information System (INIS)

    Gluzman, S.; Yukalov, V.I.

    2012-01-01

    A novel method of summing asymptotic series is advanced. Such series repeatedly arise when employing perturbation theory in powers of a small parameter for complicated problems of condensed matter physics, statistical physics, and various applied problems. The method is based on the self-similar approximation theory involving self-similar root approximants. The constructed self-similar continued roots extrapolate asymptotic series to finite values of the expansion parameter. The self-similar continued roots contain, as a particular case, continued fractions and Padé approximants. A theorem on the convergence of the self-similar continued roots is proved. The method is illustrated by several examples from condensed-matter physics.

  10. Analysis of a Cartesian PML approximation to acoustic scattering problems in and

    KAUST Repository

    Bramble, James H.

    2013-08-01

    We consider the application of a perfectly matched layer (PML) technique applied in Cartesian geometry to approximate solutions of the acoustic scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift ("stretching") and leads to a variable complex coefficient equation for the acoustic wave posed on an infinite domain, the complement of the bounded scatterer. The use of Cartesian geometry leads to a PML operator with simple coefficients, although, still complex symmetric (non-Hermitian). The PML reformulation results in a problem whose solution coincides with the original solution inside the PML layer while decaying exponentially outside. The rapid decay of the PML solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation (for the truncated problem). This paper provides new stability estimates for the Cartesian PML approximations both on the infinite and the truncated domain. We first investigate the stability of the infinite PML approximation as a function of the PML strength σ0. This is done for PML methods which involve continuous piecewise smooth stretching as well as piecewise constant stretching functions. We next introduce a truncation parameter M which determines the size of the PML layer. Our analysis shows that the truncated PML problem is stable provided that the product of Mσ0 is sufficiently large, in which case the solution of the problem on the truncated domain converges exponentially to that of the original problem in the domain of interest near the scatterer. This justifies the simple computational strategy of selecting a fixed PML layer and increasing σ0 to obtain the desired accuracy. The results of numerical experiments varying M and σ0 are given which illustrate the theoretically predicted behavior. © 2013 Elsevier B.V. All rights reserved.

  11. Exact and approximate formulas for neutrino mixing and oscillations with non-standard interactions

    International Nuclear Information System (INIS)

    Meloni, Davide; Ohlsson, Tommy; Zhang, He

    2009-01-01

    We present, both exactly and approximately, a complete set of mappings between the vacuum (or fundamental) leptonic mixing parameters and the effective ones in matter with non-standard neutrino interaction (NSI) effects included. Within the three-flavor neutrino framework and a constant matter density profile, a full set of sum rules is established, which enables us to reconstruct the moduli of the effective leptonic mixing matrix elements, in terms of the vacuum mixing parameters in order to reproduce the neutrino oscillation probabilities for future long-baseline experiments. Very compact, but quite accurate, approximate mappings are obtained based on series expansions in the neutrino mass hierarchy parameter η ≡ Δm 2 21 /Δm 2 31 , the vacuum leptonic mixing parameter s 13 ≡ sin θ 13 , and the NSI parameters ε αβ . A detailed numerical analysis about how the NSIs affect the smallest leptonic mixing angle θ 13 , the deviation of the leptonic mixing angle θ 23 from its maximal mixing value, and the transition probabilities useful for future experiments are performed using our analytical results.

  12.  Higher Order Improvements for Approximate Estimators

    DEFF Research Database (Denmark)

    Kristensen, Dennis; Salanié, Bernard

    Many modern estimation methods in econometrics approximate an objective function, through simulation or discretization for instance. The resulting "approximate" estimator is often biased; and it always incurs an efficiency loss. We here propose three methods to improve the properties of such appr......Many modern estimation methods in econometrics approximate an objective function, through simulation or discretization for instance. The resulting "approximate" estimator is often biased; and it always incurs an efficiency loss. We here propose three methods to improve the properties...... of such approximate estimators at a low computational cost. The first two methods correct the objective function so as to remove the leading term of the bias due to the approximation. One variant provides an analytical bias adjustment, but it only works for estimators based on stochastic approximators......, such as simulation-based estimators. Our second bias correction is based on ideas from the resampling literature; it eliminates the leading bias term for non-stochastic as well as stochastic approximators. Finally, we propose an iterative procedure where we use Newton-Raphson (NR) iterations based on a much finer...

  13. Finite element analysis of ARPS structures

    International Nuclear Information System (INIS)

    Ruhkamp, J.D.; McDougal, J.R.; Kramer, D.P.

    1998-01-01

    Algor finite element software was used to determine the stresses and deflections in the metallic walls of Advanced Radioisotope Power Systems (ARPS) designs. The preliminary design review of these systems often neglects the structural integrity of the design which can effect fabrication and the end use of the design. Before finite element analysis (FEA) was run on the canister walls of the thermophotovoltaic (TPV) generator, hand calculations were used to approximate the stresses and deflections in a flat plate. These results compared favorably to the FEA results of a similar size flat plate. The AMTEC (Alkali Metal Thermal-to-Electric Conversion) cells were analyzed by FEA and the results compared to two cells that were mechanically tested. The mechanically tested cells buckled in the thin sections, one at the top and one in the lower section. The FEA predicted similar stress and shape results but the critical buckling load was found to be very shape dependent

  14. Exact and approximate multiple diffraction calculations

    International Nuclear Information System (INIS)

    Alexander, Y.; Wallace, S.J.; Sparrow, D.A.

    1976-08-01

    A three-body potential scattering problem is solved in the fixed scatterer model exactly and approximately to test the validity of commonly used assumptions of multiple scattering calculations. The model problem involves two-body amplitudes that show diffraction-like differential scattering similar to high energy hadron-nucleon amplitudes. The exact fixed scatterer calculations are compared to Glauber approximation, eikonal-expansion results and a noneikonal approximation

  15. A point-value enhanced finite volume method based on approximate delta functions

    Science.gov (United States)

    Xuan, Li-Jun; Majdalani, Joseph

    2018-02-01

    We revisit the concept of an approximate delta function (ADF), introduced by Huynh (2011) [1], in the form of a finite-order polynomial that holds identical integral properties to the Dirac delta function when used in conjunction with a finite-order polynomial integrand over a finite domain. We show that the use of generic ADF polynomials can be effective at recovering and generalizing several high-order methods, including Taylor-based and nodal-based Discontinuous Galerkin methods, as well as the Correction Procedure via Reconstruction. Based on the ADF concept, we then proceed to formulate a Point-value enhanced Finite Volume (PFV) method, which stores and updates the cell-averaged values inside each element as well as the unknown quantities and, if needed, their derivatives on nodal points. The sharing of nodal information with surrounding elements saves the number of degrees of freedom compared to other compact methods at the same order. To ensure conservation, cell-averaged values are updated using an identical approach to that adopted in the finite volume method. Here, the updating of nodal values and their derivatives is achieved through an ADF concept that leverages all of the elements within the domain of integration that share the same nodal point. The resulting scheme is shown to be very stable at successively increasing orders. Both accuracy and stability of the PFV method are verified using a Fourier analysis and through applications to the linear wave and nonlinear Burgers' equations in one-dimensional space.

  16. Approximating transcranial magnetic stimulation with electric stimulation in mouse: a simulation study.

    Science.gov (United States)

    Barnes, Walter L; Lee, Won Hee; Peterchev, Angel V

    2014-01-01

    Rodent models are valuable for preclinical examination of novel therapeutic techniques, including transcranial magnetic stimulation (TMS). However, comparison of TMS effects in rodents and humans is confounded by inaccurate scaling of the spatial extent of the induced electric field in rodents. The electric field is substantially less focal in rodent models of TMS due to the technical restrictions of making very small coils that can handle the currents required for TMS. We examine the electric field distributions generated by various electrode configurations of electric stimulation in an inhomogeneous high-resolution finite element mouse model, and show that the electric field distributions produced by human TMS can be approximated by electric stimulation in mouse. Based on these results and the limits of magnetic stimulation in mice, we argue that the most practical and accurate way to model focal TMS in mice is electric stimulation through either cortical surface electrodes or electrodes implanted halfway through the mouse cranium. This approach could allow much more accurate approximation of the human TMS electric field focality and strength than that offered by TMS in mouse, enabling, for example, focal targeting of specific cortical regions, which is common in human TMS paradigms.

  17. On Covering Approximation Subspaces

    Directory of Open Access Journals (Sweden)

    Xun Ge

    2009-06-01

    Full Text Available Let (U';C' be a subspace of a covering approximation space (U;C and X⊂U'. In this paper, we show that and B'(X⊂B(X∩U'. Also, iff (U;C has Property Multiplication. Furthermore, some connections between outer (resp. inner definable subsets in (U;C and outer (resp. inner definable subsets in (U';C' are established. These results answer a question on covering approximation subspace posed by J. Li, and are helpful to obtain further applications of Pawlak rough set theory in pattern recognition and artificial intelligence.

  18. An Atomistic Modeling Study of Alloying Element Impurity Element, and Transmutation Products on the cohesion of A Nickel E5 {001} Twist Grain Boundary

    International Nuclear Information System (INIS)

    Young, G.A. Jr.; Najafabadi, R.; Strohmayer, W.; Baldrey, D.G.; Hamm, B.; Harris, J.; Sticht, J.; Wimmer, E.

    2003-01-01

    Atomistic modeling methods were employed to investigate the effects of impurity elements on the metallurgy, irradiation embrittlement, and environmentally assisted cracking of nickel-base alloys exposed to nuclear environments. Calculations were performed via ab initio atomistic modeling methods to ensure the accuracy and reliability of the results. A Griffith-type fracture criterion was used to quantitatively assess the effect of elements or element pairs on the grain boundary cohesive strength. In order of most embrittling to most strengthening, the elements are ranked as: He, Li, S, H, C, Zr, P, Fe, Mn, Nb, Cr, and B. Helium is strongly embrittling (-2.04 eV/atom lowering of the Griffith energy), phosphorus has little effect on the grain boundary (0.1 eV/atom), and boron offers appreciable strengthening (1.03 eV/atom increase in the Griffith energy). Calculations for pairs of elements (H-Li, H-B, H-C, H-P, and H-S) show little interaction on the grain boundary cohesive energy, so that for the conditions studied, linear superposition of elemental effects is a good approximation. These calculations help explain metallurgical effects (e.g. why boron can strengthen grain boundaries), irradiation embrittlement (e.g. how boron transmutation results in grain boundary embrittlement), as well as how grain boundary impurity elements can affect environmentally assisted cracking (i.e. low temperature crack propagation and stress corrosion cracking) of nickel-base alloys

  19. A Nash-Hörmander iteration and boundary elements for the Molodensky problem

    DEFF Research Database (Denmark)

    Costea, Adrian; Gimperlein, Heiko; Stephan, Ernst P.

    2014-01-01

    evaluation of the Hessian of the gravitational potential on the surface, using a representation in terms of a hypersingular integral.Aboundary element method is used to solve the exterior problem. Numerical results compare the error between the approximation and the exact solution in a model problem....

  20. Goal-Oriented Self-Adaptive hp Finite Element Simulation of 3D DC Borehole Resistivity Simulations

    KAUST Repository

    Calo, Victor M.; Pardo, David; Paszyński, Maciej R.

    2011-01-01

    (adjusting polynomial orders of approximation) or hp (both) refinements on the finite elements. The new parallel implementation utilizes a computational mesh shared between multiple processors. All computational algorithms, including automatic hp goal

  1. Decision trees with minimum average depth for sorting eight elements

    KAUST Repository

    AbouEisha, Hassan M.

    2015-11-19

    We prove that the minimum average depth of a decision tree for sorting 8 pairwise different elements is equal to 620160/8!. We show also that each decision tree for sorting 8 elements, which has minimum average depth (the number of such trees is approximately equal to 8.548×10^326365), has also minimum depth. Both problems were considered by Knuth (1998). To obtain these results, we use tools based on extensions of dynamic programming which allow us to make sequential optimization of decision trees relative to depth and average depth, and to count the number of decision trees with minimum average depth.

  2. Partitioning of elements during coal combustion and leaching experiments

    Energy Technology Data Exchange (ETDEWEB)

    Wang Wen-feng; Qin Yong; Song Dang-yu; Wang Jun-yi [China University of Mining & Technology, Xuzhou (China). School of Resources and Earth Science

    2009-04-15

    The mineral component and content of sulfur and 42 major and trace elements of the feed coal, fly and bottom ashes collected from Shizuishan coal-fired power plant, Ningxia, China were analyzed using AFS, INAA, ICP-MS, ICP-AES, XRD. Based on the coal combustion and leaching experiments, the partitioning of these elements during coal combustion and the leaching behavior of the 11 potentially hazardous elements, including As, Cd, Co, Cr, Hg, Mo, Ni, Pb, Se, Th and U were investigated. The results show that the distribution of elements in the fly and bottom ashes is controlled by their volatilities and modes of occurrence in the coal. The degree of volatilization of elements may be mainly associated with boiling/melting points of these elements and their compounds. The elements easily volatilized, organically bound or associated with sub-micrometer and nano minerals (e.g. Al and Na) tend to be enriched in the fine fractions of fly ash, and most elements do not vaporize which are approximately equally partitioned in the fly and bottom ashes. The emission rates of As, Cr, K, Mg, Mn, Mo, Pb, Sb, and Zn are notably influenced by the temperature ranging from 877 to 1300{sup o}C. The leaching behavior of elements depend significantly on their geochemical properties and modes of occurrence. The elements with a low degree of volatilization are not easily leached, while volatile elements easily leached under the acid conditions. Arsenic, B Br, Cd, Cu, Hg, Pb, S, Sb and Se show a higher emission rate during coal combustion, and the leached concentrations of Cd, Co, Mo, Ni and U in the acid media exceed their limited concentrations recommended in relevant environment quality standards for water, which will harm the environment. 32 refs., 4 figs., 4 tabs.

  3. Reduced trace element concentrations in fast-growing juvenile Atlantic salmon in natural streams.

    Science.gov (United States)

    Ward, Darren M; Nislow, Keith H; Chen, Celia Y; Folt, Carol L

    2010-05-01

    To assess the effect of rapid individual growth on trace element concentrations in fish, we measured concentrations of seven trace elements (As, Cd, Cs, Hg, Pb, Se, Zn) in stream-dwelling Atlantic salmon (Salmo salar) from 15 sites encompassing a 10-fold range in salmon growth. All salmon were hatched under uniform conditions, released into streams, and sampled approximately 120 days later for trace element analysis. For most elements, element concentrations in salmon tracked those in their prey. Fast-growing salmon had lower concentrations of all elements than slow growers, after accounting for prey concentrations. This pattern held for essential and nonessential elements, as well as elements that accumulate from food and those that can accumulate from water. At the sites with the fastest salmon growth, trace element concentrations in salmon were 37% (Cs) to 86% (Pb) lower than at sites where growth was suppressed. Given that concentrations were generally below levels harmful to salmon and that the pattern was consistent across all elements, we suggest that dilution of elements in larger biomass led to lower concentrations in fast-growing fish. Streams that foster rapid, efficient fish growth may produce fish with lower concentrations of elements potentially toxic for human and wildlife consumers.

  4. Effect of lattice deformation on temperature fields and heat transfer in the fuel elements of characteristic zones for a model of fast reactor fuel assembly

    International Nuclear Information System (INIS)

    Zhukov, A.V.; Matyukhin, N.M.; Sviridenko, E.Ya.

    1980-01-01

    Given are the experimental results for temperature fields in the model assembly in nonribbed simulators of the BN-600-type reactor fuel elements in the course of deformation of the lattice caused by shifting of the central and peripheral (lateral, angular) fuel elements by the value of the gap between the fuel elements (the limiting case when the fuel elements touch each other along the whole length). An assembly consisting of 37 electroheated pipes arranged in a triangular lattice with a relative step of S/d=1.185 is used as a model. The experiments were carried out on the sodium stand at constant energy release along the length of the fuel element simulators and at the Pe number changing in the 14-700 range. The data obtained show considerable increase of nonuniformities of the fuel element temperatures for characteristic zones of the fuel cassette assembly models of the fast reactor at deviations of the lattice geometric sizes from the nominal ones. For the central nonribbed element the temperature nonuniformity increases approximately 7.5 times and for the lateral element approximately 6 times when the elements touch each other along the whole length. The shift the central nonribbed element by the value of the gap between the fu.el elements leads to the decrease of heat transfer in comparison with heat transfer at the nominal geometry approximately 3-7 times in the 10-450 range for the Pe numbers. It is shown that the coolant temperature distribution along the assembly radius has a complex character (with a peak between the centre and the perifery) caused by redistribution of coolant consumptions due to fuel element lattice deformation

  5. Prestack traveltime approximations

    KAUST Repository

    Alkhalifah, Tariq Ali

    2011-01-01

    Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach. © 2011 Society of Exploration Geophysicists.

  6. Approximation methods in probability theory

    CERN Document Server

    Čekanavičius, Vydas

    2016-01-01

    This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.

  7. A numerical approximation to the elastic properties of sphere-reinforced composites

    Science.gov (United States)

    Segurado, J.; Llorca, J.

    2002-10-01

    Three-dimensional cubic unit cells containing 30 non-overlapping identical spheres randomly distributed were generated using a new, modified random sequential adsortion algorithm suitable for particle volume fractions of up to 50%. The elastic constants of the ensemble of spheres embedded in a continuous and isotropic elastic matrix were computed through the finite element analysis of the three-dimensional periodic unit cells, whose size was chosen as a compromise between the minimum size required to obtain accurate results in the statistical sense and the maximum one imposed by the computational cost. Three types of materials were studied: rigid spheres and spherical voids in an elastic matrix and a typical composite made up of glass spheres in an epoxy resin. The moduli obtained for different unit cells showed very little scatter, and the average values obtained from the analysis of four unit cells could be considered very close to the "exact" solution to the problem, in agreement with the results of Drugan and Willis (J. Mech. Phys. Solids 44 (1996) 497) referring to the size of the representative volume element for elastic composites. They were used to assess the accuracy of three classical analytical models: the Mori-Tanaka mean-field analysis, the generalized self-consistent method, and Torquato's third-order approximation.

  8. Finite element modelling

    International Nuclear Information System (INIS)

    Tonks, M.R.; Williamson, R.; Masson, R.

    2015-01-01

    The Finite Element Method (FEM) is a numerical technique for finding approximate solutions to boundary value problems. While FEM is commonly used to solve solid mechanics equations, it can be applied to a large range of BVPs from many different fields. FEM has been used for reactor fuels modelling for many years. It is most often used for fuel performance modelling at the pellet and pin scale, however, it has also been used to investigate properties of the fuel material, such as thermal conductivity and fission gas release. Recently, the United Stated Department Nuclear Energy Advanced Modelling and Simulation Program has begun using FEM as the basis of the MOOSE-BISON-MARMOT Project that is developing a multi-dimensional, multi-physics fuel performance capability that is massively parallel and will use multi-scale material models to provide a truly predictive modelling capability. (authors)

  9. U.S. Department Of Energy's nuclear engineering education research: highlights of recent and current research-II. 1. Comparison of Angular Approximations for PWR Cell Calculations

    International Nuclear Information System (INIS)

    Smith, M.A.; Tsoulfanidis, N.; Lewis, E.E.; Palmiotti, G.

    2001-01-01

    Increasing computer power is allowing higher-order angular approximations to replace diffusion theory methods in whole core reactor physics computations. Spherical harmonic (P n ), simplified spherical harmonic (SP n ), and discrete ordinates (S n ) methods are capable of performing such calculations in three dimensions. Most advantages of such transport methods are gained by eliminating fuel assembly homogenization, thus allowing pin powers to be calculated directly. A further step, currently under investigation, is the elimination of spatial homogenization at the pin cell level as well. The fuel-moderator interfaces may be treated explicitly in P n , S n , or SP n calculations by applying triangular finite elements (FEM) to the spatial variables. Early results using a modified form of the VARIANT code, however, indicate that without pin cell homogenization, high-order angular approximations may be required to represent the lattice effects accurately within the whole-core calculations. To examine these lattice effects further, a modified form of VARIANT was created to use the spatial triangular finite element scheme. The program was set up to treat a single heterogeneous pin cell coupled with P n , SP n , or S n angular approximations. Additional modifications replaced the nodal interface approximations with exact reflected boundary conditions to increase the accuracy of the results. Several pressurized water reactor pin cells, taken from a previous benchmark specification, were examined. However, the results shown here focus only on the most severe case, i.e., a pin cell containing 8.7% mixed-oxide enriched fuel. The DRAGON collision probability code was used to collapse a 69-group cross-section library to a more manageable 7-group library that contained cross sections for the fuel-cladding mixture and for the water. Eigenvalue results are shown in Figs. 1 and 2 using the modified VARIANT code with P n , SP n , and S n angular approximations. A 7-group MCNP Monte

  10. Comparison of the Born series and rational approximants in potential scattering. [Pade approximants, Yikawa and exponential potential

    Energy Technology Data Exchange (ETDEWEB)

    Garibotti, C R; Grinstein, F F [Rosario Univ. Nacional (Argentina). Facultad de Ciencias Exactas e Ingenieria

    1976-05-08

    It is discussed the real utility of Born series for the calculation of atomic collision processes in the Born approximation. It is suggested to make use of Pade approximants and it is shown that this approach provides very fast convergent sequences over all the energy range studied. Yukawa and exponential potential are explicitly considered and the results are compared with high-order Born approximation.

  11. Spherical Approximation on Unit Sphere

    Directory of Open Access Journals (Sweden)

    Eman Samir Bhaya

    2018-01-01

    Full Text Available In this paper we introduce a Jackson type theorem for functions in LP spaces on sphere And study on best approximation of  functions in  spaces defined on unit sphere. our central problem is to describe the approximation behavior of functions in    spaces for  by modulus of smoothness of functions.

  12. Analysis of corrections to the eikonal approximation

    Science.gov (United States)

    Hebborn, C.; Capel, P.

    2017-11-01

    Various corrections to the eikonal approximations are studied for two- and three-body nuclear collisions with the goal to extend the range of validity of this approximation to beam energies of 10 MeV/nucleon. Wallace's correction does not improve much the elastic-scattering cross sections obtained at the usual eikonal approximation. On the contrary, a semiclassical approximation that substitutes the impact parameter by a complex distance of closest approach computed with the projectile-target optical potential efficiently corrects the eikonal approximation. This opens the possibility to analyze data measured down to 10 MeV/nucleon within eikonal-like reaction models.

  13. Low-complexity computation of plate eigenmodes with Vekua approximations and the method of particular solutions

    Science.gov (United States)

    Chardon, Gilles; Daudet, Laurent

    2013-11-01

    This paper extends the method of particular solutions (MPS) to the computation of eigenfrequencies and eigenmodes of thin plates, in the framework of the Kirchhoff-Love plate theory. Specific approximation schemes are developed, with plane waves (MPS-PW) or Fourier-Bessel functions (MPS-FB). This framework also requires a suitable formulation of the boundary conditions. Numerical tests, on two plates with various boundary conditions, demonstrate that the proposed approach provides competitive results with standard numerical schemes such as the finite element method, at reduced complexity, and with large flexibility in the implementation choices.

  14. High-order harmonic propagation in gases within the discrete dipole approximation

    International Nuclear Information System (INIS)

    Hernandez-Garcia, C.; Perez-Hernandez, J. A.; Ramos, J.; Jarque, E. Conejero; Plaja, L.; Roso, L.

    2010-01-01

    We present an efficient approach for computing high-order harmonic propagation based on the discrete dipole approximation. In contrast with other approaches, our strategy is based on computing the total field as the superposition of the driving field with the field radiated by the elemental emitters of the sample. In this way we avoid the numerical integration of the wave equation, as Maxwell's equations have an analytical solution for an elementary (pointlike) emitter. The present strategy is valid for low-pressure gases interacting with strong fields near the saturation threshold (i.e., partially ionized), which is a common situation in the experiments of high-order harmonic generation. We use this tool to study the dependence of phase matching of high-order harmonics with the relative position between the beam focus and the gas jet.

  15. Design method for low order two-degree-of-freedom controller based on Pade approximation of the denominator series expansion

    International Nuclear Information System (INIS)

    Ishikawa, Nobuyuki; Suzuki, Katsuo

    1999-01-01

    Having advantages of setting independently feedback characteristics such as disturbance rejection specification and reference response characteristics, two-degree-of-freedom (2DOF) control is widely utilized to improve the control performance. The ordinary design method such as model matching usually derives high-ordered feedforward element of 2DOF controller. In this paper, we propose a new design method for low order feedforward element which is based on Pade approximation of the denominator series expansion. The features of the proposed method are as follows: (1) it is suited to realize reference response characteristics in low frequency region, (2) the order of the feedforward element can be selected apart from the feedback element. These are essential to the 2DOF controller design. With this method, 2DOF reactor power controller is designed and its control performance is evaluated by numerical simulation with reactor dynamics model. For this evaluation, it is confirmed that the controller designed by the proposed method possesses equivalent control characteristics to the controller by the ordinary model matching method. (author)

  16. Composition of the earth's upper mantle. II - Volatile trace elements in ultramafic xenoliths

    Science.gov (United States)

    Morgan, J. W.; Wandless, G. A.; Petrie, R. K.; Irving, A. J.

    1980-01-01

    Radiochemical neutron activation analysis was used to determine the nine volatile elements Ag, Bi, Cd, In, Sb, Se, Te, Tl, and Zn in 19 ultramafic rocks, consisting mainly of spinel and garnet lherzolites. A sheared garnet lherzolite, PHN 1611, may approximate undepleted mantle material and tends to have a higher volatile element content than the depleted mantle material represented by spinel lherzolites. Comparisons of continental basalts with PHN 1611 and of oceanic ridge basalts with spinel lherzolites show similar basalt: source material partition factors for eight of the nine volatile elements, Sb being the exception. The strong depletion of Te and Se in the mantle, relative to lithophile elements of similar volatility, suggests that 97% of the earth's S, Se and Te may be in the outer core.

  17. Ancilla-approximable quantum state transformations

    International Nuclear Information System (INIS)

    Blass, Andreas; Gurevich, Yuri

    2015-01-01

    We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined system. Measure the state of the auxiliary subsystem. If (and only if) it is in a specified final state, consider the process successful, and take the resulting state of the original (principal) system as the result of the process. We review known information about exact realization of transformations by such a process. Then we present results about approximate realization of finite partial transformations. We not only consider primarily the issue of approximation to within a specified positive ε, but also address the question of arbitrarily close approximation

  18. Ancilla-approximable quantum state transformations

    Energy Technology Data Exchange (ETDEWEB)

    Blass, Andreas [Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109 (United States); Gurevich, Yuri [Microsoft Research, Redmond, Washington 98052 (United States)

    2015-04-15

    We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined system. Measure the state of the auxiliary subsystem. If (and only if) it is in a specified final state, consider the process successful, and take the resulting state of the original (principal) system as the result of the process. We review known information about exact realization of transformations by such a process. Then we present results about approximate realization of finite partial transformations. We not only consider primarily the issue of approximation to within a specified positive ε, but also address the question of arbitrarily close approximation.

  19. Recognition of computerized facial approximations by familiar assessors.

    Science.gov (United States)

    Richard, Adam H; Monson, Keith L

    2017-11-01

    Studies testing the effectiveness of facial approximations typically involve groups of participants who are unfamiliar with the approximated individual(s). This limitation requires the use of photograph arrays including a picture of the subject for comparison to the facial approximation. While this practice is often necessary due to the difficulty in obtaining a group of assessors who are familiar with the approximated subject, it may not accurately simulate the thought process of the target audience (friends and family members) in comparing a mental image of the approximated subject to the facial approximation. As part of a larger process to evaluate the effectiveness and best implementation of the ReFace facial approximation software program, the rare opportunity arose to conduct a recognition study using assessors who were personally acquainted with the subjects of the approximations. ReFace facial approximations were generated based on preexisting medical scans, and co-workers of the scan donors were tested on whether they could accurately pick out the approximation of their colleague from arrays of facial approximations. Results from the study demonstrated an overall poor recognition performance (i.e., where a single choice within a pool is not enforced) for individuals who were familiar with the approximated subjects. Out of 220 recognition tests only 10.5% resulted in the assessor selecting the correct approximation (or correctly choosing not to make a selection when the array consisted only of foils), an outcome that was not significantly different from the 9% random chance rate. When allowed to select multiple approximations the assessors felt resembled the target individual, the overall sensitivity for ReFace approximations was 16.0% and the overall specificity was 81.8%. These results differ markedly from the results of a previous study using assessors who were unfamiliar with the approximated subjects. Some possible explanations for this disparity in

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

    Science.gov (United States)

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

    2015-06-21

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

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

    Science.gov (United States)

    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.

  2. Massive black holes and light-element nucleosynthesis in a baryonic universe

    Science.gov (United States)

    Gnedin, Nickolay Y.; Ostriker, Jeremiah P.; Rees, Martin J.

    1995-01-01

    We reexamine the model proposed by Gnedin & Ostriker (1992) in which Jeans mass black holes (M(sub BH) approximately = 10(exp 6) solar mass) form shortly after decoupling. There is no nonbaryonic dark matter in this model, but we examine the possibility that Omega(sub b) is considerably larger than given by normal nucleosynthesis. Here we allow for the fact that much of the high baryon-to-photon ratio material will collapse leaving the universe of remaining material with light-element abundances more in accord with the residual baryonic density (approximately = 10(exp -2)) than with Omega(sub 0) and the initial baryonic density (approximately = 10(exp -1)). We find that no reasonable model can be made with random-phase density fluctuations, if the power on scales smaller than 10(exp 6) solar mass is as large as expected. However, phase-correlated models of the type that might occur in connection with topological singularities can be made with Omega(sub b) h(exp 2) = 0.013 +/- 0.001, 0.15 approximately less than Omega(sub 0) approximately less than 0.4, which are either flat (Omega(sub lambda) = 1 - Omega(sub 0)) or open (Omega(sub lambda) = 0) and which satisfy all the observational constraints which we apply, including the large baryon-to-total mass ratio found in the X-ray clusters. The remnant baryon density is thus close to that obtained in the standard picture (Omega(sub b) h(exp 2) = 0.0125 +/- 0.0025; Walker et al. 1991). The spectral index implied for fluctuations in the baryonic isocurvature scenario, -1 less than m less than 0, is in the range expected by other arguments based on large-scale structure and microwave fluctuation constraints. The dark matter in this picture is in the form of massive black holes. Accretion onto them at early epochs releases high-energy photons which significantly heat and reionize the universe. But photodissociation does not materially change light-element abundances. A typical model gives bar-y approximately = 1 x 10(exp -5

  3. Approximating The DCM

    DEFF Research Database (Denmark)

    Madsen, Rasmus Elsborg

    2005-01-01

    The Dirichlet compound multinomial (DCM), which has recently been shown to be well suited for modeling for word burstiness in documents, is here investigated. A number of conceptual explanations that account for these recent results, are provided. An exponential family approximation of the DCM...

  4. A New Approach to Sequence Analysis Exemplified by Identification of cis-Elements in Abscisic Acid Inducible Promoters

    DEFF Research Database (Denmark)

    Busk, Peter Kamp; Hallin, Peter Fischer; Salomon, Jesper

    -regulatory elements. We have developed a method for identifying short, conserved motifs in biological sequences such as proteins, DNA and RNA5. This method was used for analysis of approximately 2000 Arabidopsis thaliana promoters that have been shown by DNA array analysis to be induced by abscisic acid6....... These promoters were compared to 28000 promoters that are not induced by abscisic acid. The analysis identified previously described ABA-inducible promoter elements such as ABRE, CE3 and CRT1 but also new cis-elements were found. Furthermore, the list of DNA elements could be used to predict ABA...

  5. An approximation for kanban controlled assembly systems

    NARCIS (Netherlands)

    Topan, E.; Avsar, Z.M.

    2011-01-01

    An approximation is proposed to evaluate the steady-state performance of kanban controlled two-stage assembly systems. The development of the approximation is as follows. The considered continuous-time Markov chain is aggregated keeping the model exact, and this aggregate model is approximated

  6. SEE rate estimation based on diffusion approximation of charge collection

    Science.gov (United States)

    Sogoyan, Armen V.; Chumakov, Alexander I.; Smolin, Anatoly A.

    2018-03-01

    The integral rectangular parallelepiped (IRPP) method remains the main approach to single event rate (SER) prediction for aerospace systems, despite the growing number of issues impairing method's validity when applied to scaled technology nodes. One of such issues is uncertainty in parameters extraction in the IRPP method, which can lead to a spread of several orders of magnitude in the subsequently calculated SER. The paper presents an alternative approach to SER estimation based on diffusion approximation of the charge collection by an IC element and geometrical interpretation of SEE cross-section. In contrast to the IRPP method, the proposed model includes only two parameters which are uniquely determined from the experimental data for normal incidence irradiation at an ion accelerator. This approach eliminates the necessity of arbitrary decisions during parameter extraction and, thus, greatly simplifies calculation procedure and increases the robustness of the forecast.

  7. Low Rank Approximation Algorithms, Implementation, Applications

    CERN Document Server

    Markovsky, Ivan

    2012-01-01

    Matrix low-rank approximation is intimately related to data modelling; a problem that arises frequently in many different fields. Low Rank Approximation: Algorithms, Implementation, Applications is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory. Applications described include: system and control theory: approximate realization, model reduction, output error, and errors-in-variables identification; signal processing: harmonic retrieval, sum-of-damped exponentials, finite impulse response modeling, and array processing; machine learning: multidimensional scaling and recommender system; computer vision: algebraic curve fitting and fundamental matrix estimation; bioinformatics for microarray data analysis; chemometrics for multivariate calibration; ...

  8. Two-Dimensional Nonlinear Finite Element Analysis of CMC Microstructures

    Science.gov (United States)

    Mital, Subodh K.; Goldberg, Robert K.; Bonacuse, Peter J.

    2012-01-01

    A research program has been developed to quantify the effects of the microstructure of a woven ceramic matrix composite and its variability on the effective properties and response of the material. In order to characterize and quantify the variations in the microstructure of a five harness satin weave, chemical vapor infiltrated (CVI) SiC/SiC composite material, specimens were serially sectioned and polished to capture images that detailed the fiber tows, matrix, and porosity. Open source quantitative image analysis tools were then used to isolate the constituents, from which two dimensional finite element models were generated which approximated the actual specimen section geometry. A simplified elastic-plastic model, wherein all stress above yield is redistributed to lower stress regions, is used to approximate the progressive damage behavior for each of the composite constituents. Finite element analyses under in-plane tensile loading were performed to examine how the variability in the local microstructure affected the macroscopic stress-strain response of the material as well as the local initiation and progression of damage. The macroscopic stress-strain response appeared to be minimally affected by the variation in local microstructure, but the locations where damage initiated and propagated appeared to be linked to specific aspects of the local microstructure.

  9. TRANSFORMED GENERATE APPROXIMATION METHOD FOR ...

    African Journals Online (AJOL)

    Ignatius & Ebimene

    generalized boundary value problems with first-kind Chebychev polynomials as trial ... For this course, we will consider the generalized boundary value problem of the form: ... 0(1)( − 1), are finite real constants and is the .... b. Ax = (10) where the elements of , and (with elements denoted as ,.

  10. Shearlets and Optimally Sparse Approximations

    DEFF Research Database (Denmark)

    Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q

    2012-01-01

    Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations...... optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction...... to and a survey about sparse approximations of cartoon-like images by band-limited and also compactly supported shearlet frames as well as a reference for the state-of-the-art of this research field....

  11. Approximate Waveforms for Extreme-Mass-Ratio Inspirals: The Chimera Scheme

    International Nuclear Information System (INIS)

    Sopuerta, Carlos F; Yunes, Nicolás

    2012-01-01

    We describe a new kludge scheme to model the dynamics of generic extreme-mass-ratio inspirals (EMRIs; stellar compact objects spiraling into a spinning supermassive black hole) and their gravitational-wave emission. The Chimera scheme is a hybrid method that combines tools from different approximation techniques in General Relativity: (i) A multipolar, post-Minkowskian expansion for the far-zone metric perturbation (the gravitational waveforms) and for the local prescription of the self-force; (ii) a post-Newtonian expansion for the computation of the multipole moments in terms of the trajectories; and (iii) a BH perturbation theory expansion when treating the trajectories as a sequence of self-adjusting Kerr geodesies. The EMRI trajectory is made out of Kerr geodesic fragments joined via the method of osculating elements as dictated by the multipolar post-Minkowskian radiation-reaction prescription. We implemented the proper coordinate mapping between Boyer-Lindquist coordinates, associated with the Kerr geodesies, and harmonic coordinates, associated with the multipolar post-Minkowskian decomposition. The Chimera scheme is thus a combination of approximations that can be used to model generic inspirals of systems with extreme to intermediate mass ratios, and hence, it can provide valuable information for future space-based gravitational-wave observatories, like LISA, and even for advanced ground detectors. The local character in time of our multipolar post-Minkowskian self-force makes this scheme amenable to study the possible appearance of transient resonances in generic inspirals.

  12. Heat transfer analysis in internally-cooled fuel elements by means of a conformal mapping approach

    International Nuclear Information System (INIS)

    Sarmiento, G.S.; Laura, P.A.A.

    1981-01-01

    The present paper deals with an approximate solution of the steady-state heat conduction problem in internally cooled fuel elements of fast breeder reactors. Explicit expressions for the dimensionless temperature distribution in terms of the governing physical and geometrical parameters are determined by means of a coupled conformal mapping-variational approach. The results obtained are found to be in very good agreement with those calculated by means of a finite element code. (orig.)

  13. Wave propagation numerical models in damage detection based on the time domain spectral element method

    International Nuclear Information System (INIS)

    Ostachowicz, W; Kudela, P

    2010-01-01

    A Spectral Element Method is used for wave propagation modelling. A 3D solid spectral element is derived with shape functions based on Lagrange interpolation and Gauss-Lobatto-Legendre points. This approach is applied for displacement approximation suited for fundamental modes of Lamb waves as well as potential distribution in piezoelectric transducers. The novelty is the model geometry extension from flat to curved elements for application in shell-like structures. Exemplary visualisations of waves excited by the piezoelectric transducers in curved shell structure made of aluminium alloy are presented. Simple signal analysis of wave interaction with crack is performed. The crack is modelled by separation of appropriate nodes between elements. An investigation of influence of the crack length on wave propagation signals is performed. Additionally, some aspects of the spectral element method implementation are discussed.

  14. Simulation of Stress Concentration Problems in Laminated Plates by Quasi-Trefftz Finite Element Models

    Directory of Open Access Journals (Sweden)

    Flávio Luiz de Silva Bussamra

    Full Text Available Abstract Hybrid quasi-Trefftz finite elements have been applied with success to the analysis of laminated plates. Two independent fields are approximated by linearly independent, hierarchical polynomials: the stress basis in the domain, adapted from Papkovitch-Neuber solution of Navier equations, and the displacement basis, defined on element surface. The stress field that satisfies the Trefftz constraint a priori for isotropic material is adapted for orthotropic materials, which leads to the term "quasi". In this work, the hexahedral hybrid quasi-Trefftz stress element is applied to the modeling of nonsymmetric laminates and laminated composite plates with geometric discontinuities. The hierarchical p-refinement is exploited.

  15. Relativistic nuclear magnetic resonance J-coupling with ultrasoft pseudopotentials and the zeroth-order regular approximation

    International Nuclear Information System (INIS)

    Green, Timothy F. G.; Yates, Jonathan R.

    2014-01-01

    We present a method for the first-principles calculation of nuclear magnetic resonance (NMR) J-coupling in extended systems using state-of-the-art ultrasoft pseudopotentials and including scalar-relativistic effects. The use of ultrasoft pseudopotentials is allowed by extending the projector augmented wave (PAW) method of Joyce et al. [J. Chem. Phys. 127, 204107 (2007)]. We benchmark it against existing local-orbital quantum chemical calculations and experiments for small molecules containing light elements, with good agreement. Scalar-relativistic effects are included at the zeroth-order regular approximation level of theory and benchmarked against existing local-orbital quantum chemical calculations and experiments for a number of small molecules containing the heavy row six elements W, Pt, Hg, Tl, and Pb, with good agreement. Finally, 1 J(P-Ag) and 2 J(P-Ag-P) couplings are calculated in some larger molecular crystals and compared against solid-state NMR experiments. Some remarks are also made as to improving the numerical stability of dipole perturbations using PAW

  16. New elements. [Translated from Vestnik Akademii Nauk SSSR, 6 (1974)

    Energy Technology Data Exchange (ETDEWEB)

    Flerov, G

    1976-04-01

    The history is briefly described of the investigation of superheavy elements at the Joint Institute for Nuclear Research at Dubna. The significance of the investigation is assessed from the point of view of the nuclear structure study and major problems encountered in experimental efforts are indicated. Current experimental methods aiming at the discovery or the production of superheavy nuclei with Z approximately 114 are listed.

  17. Electronic structure and properties of disordered alloys of d-elements

    International Nuclear Information System (INIS)

    Demidenko, V.S.; Kal'yanov, A.P.

    1983-01-01

    On the basis of coherent potential approximation the fundamental characteristics in which transition element alloys differ have been established. Connection of the characteristics with position of the elements alloyed in the Mendeleev table is considered. It is confirmed by calculations that electronic structure and, consequently, physical properties of the alloys of a certain value potential disturbing matrix, change qualitatively. Results of the calculation of electron energy state density, diagrams of partial and average magnetic momenta in binary and ternary alloys of the first transition period, are presented. Besides, calculation results of bond energy in d-metals and energy of segregation formation in their alloys are also given. Comparison with experiment confirms the efficiency of concepts given in the paper

  18. Multilevel weighted least squares polynomial approximation

    KAUST Repository

    Haji-Ali, Abdul-Lateef

    2017-06-30

    Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi-optimal approximation in a given polynomial subspace scales, up to a logarithmic factor, linearly in the dimension of this space. However, in many applications, the computation of samples includes a numerical discretization error. Thus, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose a multilevel method that utilizes samples computed with different accuracies and is able to match the accuracy of single-level approximations with reduced computational cost. We derive complexity bounds under certain assumptions about polynomial approximability and sample work. Furthermore, we propose an adaptive algorithm for situations where such assumptions cannot be verified a priori. Finally, we provide an efficient algorithm for the sampling from optimal distributions and an analysis of computationally favorable alternative distributions. Numerical experiments underscore the practical applicability of our method.

  19. Improved Dutch Roll Approximation for Hypersonic Vehicle

    Directory of Open Access Journals (Sweden)

    Liang-Liang Yin

    2014-06-01

    Full Text Available An improved dutch roll approximation for hypersonic vehicle is presented. From the new approximations, the dutch roll frequency is shown to be a function of the stability axis yaw stability and the dutch roll damping is mainly effected by the roll damping ratio. In additional, an important parameter called roll-to-yaw ratio is obtained to describe the dutch roll mode. Solution shows that large-roll-to-yaw ratio is the generate character of hypersonic vehicle, which results the large error for the practical approximation. Predictions from the literal approximations derived in this paper are compared with actual numerical values for s example hypersonic vehicle, results show the approximations work well and the error is below 10 %.

  20. Regression with Sparse Approximations of Data

    DEFF Research Database (Denmark)

    Noorzad, Pardis; Sturm, Bob L.

    2012-01-01

    We propose sparse approximation weighted regression (SPARROW), a method for local estimation of the regression function that uses sparse approximation with a dictionary of measurements. SPARROW estimates the regression function at a point with a linear combination of a few regressands selected...... by a sparse approximation of the point in terms of the regressors. We show SPARROW can be considered a variant of \\(k\\)-nearest neighbors regression (\\(k\\)-NNR), and more generally, local polynomial kernel regression. Unlike \\(k\\)-NNR, however, SPARROW can adapt the number of regressors to use based...

  1. Critical experiments simulating accidental water immersion of highly enriched uranium dioxide fuel elements

    International Nuclear Information System (INIS)

    Ponomarev-Stepnoi, N.N.; Glushkov, L.S.

    2003-01-01

    The paper focuses on experimental analysis of nuclear criticality safety at accidental water immersion of fuel elements of the Russian TOPAZ-2 space nuclear power system reactor. The structure of water-moderated heterogeneous critical assemblies at the NARCISS facility is described in detail, including sizes, compositions, densities of materials of the main assembly components for various core configurations. Critical parameters of the assemblies measured for varying number of fuel elements, height of fuel material in fuel elements and their arrangement in the water moderator with a uniform or variable spacing are presented. It has been found from the experiments that at accidental water immersion of fuel elements involved, the minimum critical mass equal to approximately 20 kg of uranium dioxide is achieved at 31-37 fuel elements. The paper gives an example of a physical model of the water-moderated heterogeneous critical assembly with a detailed characterization of its main components that can be used for calculations using different neutronic codes, including Monte Carlo ones. (author)

  2. Rational approximation of vertical segments

    Science.gov (United States)

    Salazar Celis, Oliver; Cuyt, Annie; Verdonk, Brigitte

    2007-08-01

    In many applications, observations are prone to imprecise measurements. When constructing a model based on such data, an approximation rather than an interpolation approach is needed. Very often a least squares approximation is used. Here we follow a different approach. A natural way for dealing with uncertainty in the data is by means of an uncertainty interval. We assume that the uncertainty in the independent variables is negligible and that for each observation an uncertainty interval can be given which contains the (unknown) exact value. To approximate such data we look for functions which intersect all uncertainty intervals. In the past this problem has been studied for polynomials, or more generally for functions which are linear in the unknown coefficients. Here we study the problem for a particular class of functions which are nonlinear in the unknown coefficients, namely rational functions. We show how to reduce the problem to a quadratic programming problem with a strictly convex objective function, yielding a unique rational function which intersects all uncertainty intervals and satisfies some additional properties. Compared to rational least squares approximation which reduces to a nonlinear optimization problem where the objective function may have many local minima, this makes the new approach attractive.

  3. On Nash-Equilibria of Approximation-Stable Games

    Science.gov (United States)

    Awasthi, Pranjal; Balcan, Maria-Florina; Blum, Avrim; Sheffet, Or; Vempala, Santosh

    One reason for wanting to compute an (approximate) Nash equilibrium of a game is to predict how players will play. However, if the game has multiple equilibria that are far apart, or ɛ-equilibria that are far in variation distance from the true Nash equilibrium strategies, then this prediction may not be possible even in principle. Motivated by this consideration, in this paper we define the notion of games that are approximation stable, meaning that all ɛ-approximate equilibria are contained inside a small ball of radius Δ around a true equilibrium, and investigate a number of their properties. Many natural small games such as matching pennies and rock-paper-scissors are indeed approximation stable. We show furthermore there exist 2-player n-by-n approximation-stable games in which the Nash equilibrium and all approximate equilibria have support Ω(log n). On the other hand, we show all (ɛ,Δ) approximation-stable games must have an ɛ-equilibrium of support O(Δ^{2-o(1)}/ɛ2{log n}), yielding an immediate n^{O(Δ^{2-o(1)}/ɛ^2log n)}-time algorithm, improving over the bound of [11] for games satisfying this condition. We in addition give a polynomial-time algorithm for the case that Δ and ɛ are sufficiently close together. We also consider an inverse property, namely that all non-approximate equilibria are far from some true equilibrium, and give an efficient algorithm for games satisfying that condition.

  4. Environmental implications of element emissions from phosphate-processing operations in southeastern Idaho

    Science.gov (United States)

    Severson, R.C.; Gough, L.P.

    1979-01-01

    In order to assess the contribution to plants and soils of certain elements emitted by phosphate processing, we sampled sagebrush, grasses, and A- and C-horizon soils along upwind and downwind transects at Pocatello and Soda Springs, Idaho. Analyses for 70 elements in plants showed that, statistically, the concentration of 7 environmentally important elements, cadmium, chromium, fluorine, selenium, uranium, vanadium, and zinc, were related to emissions from phosphate-processing operations. Two additional elements, lithium and nickel, show probable relationships. The literature on the effects of these elements on plant and animal health is briefly surveyed. Relations between element content in plants and distance from the phosphate-processing operations were stronger at Soda Springs than at Pocatello and, in general, stronger in sagebrush than in the grasses. Analyses for 58 elements in soils showed that, statistically, beryllium, fluorine, iron, lead, lithium, potassium, rubidium, thorium, and zinc were related to emissions only at Pocatello and only in the A horizon. Moreover, six additional elements, copper, mercury, nickel, titanium, uranium, and vanadium, probably are similarly related along the same transect. The approximate amounts of elements added to the soils by the emissions are estimated. In C-horizon soils, no statistically significant relations were observed between element concentrations and distance from the processing sites. At Soda Springs, the nonuniformity of soils at the sampling locations may have obscured the relationship between soil-element content and emissions from phosphate processing.

  5. L∞-error estimates of a finite element method for the Hamilton-Jacobi-Bellman equations

    International Nuclear Information System (INIS)

    Bouldbrachene, M.

    1994-11-01

    We study the finite element approximation for the solution of the Hamilton-Jacobi-Bellman equations involving a system of quasi-variational inequalities (QVI). We also give the optimal L ∞ -error estimates, using the concepts of subsolutions and discrete regularity. (author). 7 refs

  6. Neutron radiography (NRAD) reactor 64-element core upgrade

    Energy Technology Data Exchange (ETDEWEB)

    Bess, John D. [Idaho National Lab. (INL), Idaho Falls, ID (United States)

    2014-03-01

    The neutron radiography (NRAD) reactor is a 250 kW TRIGA (registered) (Training, Research, Isotopes, General Atomics) Mark II , tank-type research reactor currently located in the basement, below the main hot cell, of the Hot Fuel Examination Facility (HFEF) at the Idaho National Laboratory (INL). It is equipped with two beam tubes with separate radiography stations for the performance of neutron radiography irradiation on small test components. The interim critical configuration developed during the core upgrade, which contains only 62 fuel elements, has been evaluated as an acceptable benchmark experiment. The final 64-fuel-element operational core configuration of the NRAD LEU TRIGA reactor has also been evaluated as an acceptable benchmark experiment. Calculated eigenvalues differ significantly (approximately ±1%) from the benchmark eigenvalue and have demonstrated sensitivity to the thermal scattering treatment of hydrogen in the U-Er-Zr-H fuel.

  7. Legendre-tau approximations for functional differential equations

    Science.gov (United States)

    Ito, K.; Teglas, R.

    1986-01-01

    The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.

  8. Approximate maximum parsimony and ancestral maximum likelihood.

    Science.gov (United States)

    Alon, Noga; Chor, Benny; Pardi, Fabio; Rapoport, Anat

    2010-01-01

    We explore the maximum parsimony (MP) and ancestral maximum likelihood (AML) criteria in phylogenetic tree reconstruction. Both problems are NP-hard, so we seek approximate solutions. We formulate the two problems as Steiner tree problems under appropriate distances. The gist of our approach is the succinct characterization of Steiner trees for a small number of leaves for the two distances. This enables the use of known Steiner tree approximation algorithms. The approach leads to a 16/9 approximation ratio for AML and asymptotically to a 1.55 approximation ratio for MP.

  9. Local density approximations for relativistic exchange energies

    International Nuclear Information System (INIS)

    MacDonald, A.H.

    1986-01-01

    The use of local density approximations to approximate exchange interactions in relativistic electron systems is reviewed. Particular attention is paid to the physical content of these exchange energies by discussing results for the uniform relativistic electron gas from a new point of view. Work on applying these local density approximations in atoms and solids is reviewed and it is concluded that good accuracy is usually possible provided self-interaction corrections are applied. The local density approximations necessary for spin-polarized relativistic systems are discussed and some new results are presented

  10. Interference effects of neutral MSSM Higgs bosons with a generalised narrow-width approximation

    International Nuclear Information System (INIS)

    Fuchs, Elina

    2014-11-01

    Mixing effects in the MSSM Higgs sector can give rise to a sizeable interference between the neutral Higgs bosons. On the other hand, factorising a more complicated process into production and decay parts by means of the narrow-width approximation (NWA) simplifies the calculation. The standard NWA, however, does not account for interference terms. Therefore, we introduce a generalisation of the NWA (gNWA) which allows for a consistent treatment of interference effects between nearly mass-degenerate particles. Furthermore, we apply the gNWA at the tree and 1-loop level to an example process where the neutral Higgs bosons h and H are produced in the decay of a heavy neutralino and subsequently decay into a fermion pair. The h-H propagator mixing is found to agree well with the approximation of Breit-Wigner propagators times finite wave-function normalisation factors, both leading to a significant interference contribution. The factorisation of the interference term based on on-shell matrix elements reproduces the full interference result within a precision of better than 1% for the considered process. The gNWA also enables the inclusion of contributions beyond the 1-loop order into the most precise prediction.

  11. A VNTR element associated with steroid sulfatase gene deletions stimulates recombination in cultured cells

    Energy Technology Data Exchange (ETDEWEB)

    Gong, Y.; Li, X.M.; Shapiro, L.J. [UCSF School of Medicine, San Francisco, CA (United States)] [and others

    1994-09-01

    Steroid sulfatase deficiency is a common genetic disorder, with a prevalence of approximately one in every 3500 males world wide. About 90% of these patients have complete gene deletions, which appear to result from recombination between members of a low-copy repeat family (CRI-232 is the prototype) that flank the gene. RU1 and RU2 are two VNTR elements found within each of these family members. RU1 consists of 30 bp repeating units and its length shows minimal variation among individuals. The RU2 element consists of repeating sequences which are highly asymmetric, with about 90% purines and no C`s on one strand, and range from 0.6 kb to over 23 kb among different individuals. We conducted a study to determine if the RU1 or RU2 elements can promote recombination in an in vivo test system. We inserted these elements adjacent to the neo gene in each of two pSV2neo derivatives, one of which has a deletion in the 5{prime} portion of the neo gene and the other having a deletion in the 3{prime} portion. These plasmids were combined and used to transfect EJ cells. Survival of cells in G418 indicates restoration of a functional neo gene by recombination between two deletion constructs. Thus counting G418 resistant colonies gives a quantitative measure of the enhancement of recombination by the inserted VNTR elements. The results showed no effect on recombination by the inserted RU1 element (compared to the insertion of a nonspecific sequence), while the RU2 element stimulated recombination by 3.5-fold (P<0.01). A separate set of constructs placed RU1 or RU2 within the intron of an exon trapping vector. Following tranfection of cells, recombination events were monitored by a PCR assay that detected the approximation of primer binding sites (as a result of recombination). These studies showed that, as in the first set of experiments, the highly variable RU2 element is capable of stimulating somatic recombination in mammalian cells.

  12. Some relations between entropy and approximation numbers

    Institute of Scientific and Technical Information of China (English)

    郑志明

    1999-01-01

    A general result is obtained which relates the entropy numbers of compact maps on Hilbert space to its approximation numbers. Compared with previous works in this area, it is particularly convenient for dealing with the cases where the approximation numbers decay rapidly. A nice estimation between entropy and approximation numbers for noncompact maps is given.

  13. Saddlepoint approximation methods in financial engineering

    CERN Document Server

    Kwok, Yue Kuen

    2018-01-01

    This book summarizes recent advances in applying saddlepoint approximation methods to financial engineering. It addresses pricing exotic financial derivatives and calculating risk contributions to Value-at-Risk and Expected Shortfall in credit portfolios under various default correlation models. These standard problems involve the computation of tail probabilities and tail expectations of the corresponding underlying state variables.  The text offers in a single source most of the saddlepoint approximation results in financial engineering, with different sets of ready-to-use approximation formulas. Much of this material may otherwise only be found in original research publications. The exposition and style are made rigorous by providing formal proofs of most of the results. Starting with a presentation of the derivation of a variety of saddlepoint approximation formulas in different contexts, this book will help new researchers to learn the fine technicalities of the topic. It will also be valuable to quanti...

  14. Approximating centrality in evolving graphs: toward sublinearity

    Science.gov (United States)

    Priest, Benjamin W.; Cybenko, George

    2017-05-01

    The identification of important nodes is a ubiquitous problem in the analysis of social networks. Centrality indices (such as degree centrality, closeness centrality, betweenness centrality, PageRank, and others) are used across many domains to accomplish this task. However, the computation of such indices is expensive on large graphs. Moreover, evolving graphs are becoming increasingly important in many applications. It is therefore desirable to develop on-line algorithms that can approximate centrality measures using memory sublinear in the size of the graph. We discuss the challenges facing the semi-streaming computation of many centrality indices. In particular, we apply recent advances in the streaming and sketching literature to provide a preliminary streaming approximation algorithm for degree centrality utilizing CountSketch and a multi-pass semi-streaming approximation algorithm for closeness centrality leveraging a spanner obtained through iteratively sketching the vertex-edge adjacency matrix. We also discuss possible ways forward for approximating betweenness centrality, as well as spectral measures of centrality. We provide a preliminary result using sketched low-rank approximations to approximate the output of the HITS algorithm.

  15. 9th International Conference on Boundary Elements

    CERN Document Server

    Wendland, W; Kuhn, G

    1987-01-01

    This book contains the edited versions of most of the papers presented at the 9th International Conference on Boundary Elements held at the University of Stuttgart, Germany from August 31st to September 4th, 1987, which was organized in co-operation with the Computational Mechanics Institute and GAMM (Society for Applied Mathematics and Mechanics). This Conference, as the previous ones, aimed to review the latest developments in technique and theory and point out new advanced future trends. The emphasis of the meeting was on the engineering advances versus mathematical formulations, in an effort to consolidate the basis of many new applications. Recently engineers have proposed different techniques to solve non-linear and time dependent problems and many of these formulations needed a better mathematical understanding. Furthermore, new approximate formulations have been proposed for boundary elements which appeared to work in engineering practice, but did not have a proper theoretical background. The Conferen...

  16. Quantitative assay of element mass inventories in single cell biological systems with micro-PIXE

    Energy Technology Data Exchange (ETDEWEB)

    Ogrinc, Nina [Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana (Slovenia); LOTRIČ Metrology, Selca 163, SI-4227 Selca (Slovenia); Pelicon, Primož, E-mail: primoz.pelicon@ijs.si [Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana (Slovenia); Vavpetič, Primož; Kelemen, Mitja; Grlj, Nataša; Jeromel, Luka [Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana (Slovenia); Tomić, Sergej [Medical Faculty of the Military Medical Academy, University of Defense, Crnotravska 17, Belgrade (Serbia); Čolić, Miodrag [Medical Faculty of the Military Medical Academy, University of Defense, Crnotravska 17, Belgrade (Serbia); Medical Faculty, University of Niš, Boulevard of Dr. Zoran Djindjić 81, 18000 Niš (Serbia); Beran, Alfred [Dipartimento di Oceanografia Biologica, Istituto Nazionale di Oceanografia e Geofisica Sperimentale, Via Auguste Piccard 54, 34151 Trieste (Italy)

    2013-07-01

    Elemental concentrations in micro-PIXE (Particle Induced X-ray Emission) maps of elements in biological tissue slices have been determined using auxiliary information on the sample matrix composition from EBS (Elastic Backscattering Spectroscopy) and STIM (Scanning Transmission Ion Microscopy). The thin sample approximation may be used for evaluating micro-PIXE data in cases, where X-ray absorption in the sample can be neglected and the mass of elements in a selected area can be estimated. The resulting sensitivity amounts to an impressive 10{sup −12} g of the selected elements. Two cases are presented as examples. In the first, we determined the total mass of gold nanoparticles internalized by human monocyte-derived dendritic cells (MDDC). In the second, an inventory of the mass of elements in the micro-particulate material adsorbed at the wall of the lorica of the microzooplankton species Tintinnopsis radix has been created.

  17. Quantitative assay of element mass inventories in single cell biological systems with micro-PIXE

    International Nuclear Information System (INIS)

    Ogrinc, Nina; Pelicon, Primož; Vavpetič, Primož; Kelemen, Mitja; Grlj, Nataša; Jeromel, Luka; Tomić, Sergej; Čolić, Miodrag; Beran, Alfred

    2013-01-01

    Elemental concentrations in micro-PIXE (Particle Induced X-ray Emission) maps of elements in biological tissue slices have been determined using auxiliary information on the sample matrix composition from EBS (Elastic Backscattering Spectroscopy) and STIM (Scanning Transmission Ion Microscopy). The thin sample approximation may be used for evaluating micro-PIXE data in cases, where X-ray absorption in the sample can be neglected and the mass of elements in a selected area can be estimated. The resulting sensitivity amounts to an impressive 10 −12 g of the selected elements. Two cases are presented as examples. In the first, we determined the total mass of gold nanoparticles internalized by human monocyte-derived dendritic cells (MDDC). In the second, an inventory of the mass of elements in the micro-particulate material adsorbed at the wall of the lorica of the microzooplankton species Tintinnopsis radix has been created

  18. Contact hyperfine field of the 4p and 4f series elements (rare-earths)

    International Nuclear Information System (INIS)

    Doi, I.

    1973-01-01

    The Coulomb correlation effect in the description of the contact hyperfine magnetic structure was analysed. The hyperfine magnetic structure was calculated from the spin polarized Hartree-Fock formalism, using the free electron gas approximation to the exchange-correlation energy of the 4p series atoms and some atoms and ions of the 4f series. No one of the analysed approximations to the exchange-correlation energy describes satisfactorily the contact hyperfine magnetic structure of the 4p and 4f series elements, which were studied [pt

  19. Reduced and selective integration techniques in the finite element analysis of plates

    International Nuclear Information System (INIS)

    Hughes, T.J.R.; Cohen, M.; Haroun, M.

    1978-01-01

    Efforts to develop effective plate bending finite elements by reduced integration techniques are described. The basis for the development is a 'thick' plate theory in which transverse shear strains are accounted for. The variables in the theory are all kinematic, namely, displacements and independent rotations. As only C 0 continuity is required, isoparametric elements may be employed, which result in several advantages over thin plate elements. It is shown that the avoidance of shear 'locking' may be facilitated by reduced integration techniques. Both uniform and selective schemes are considered. Conditions under which selective schemes are invariant are identified, and they are found to have an advantage over uniform schemes in the present situation. It is pointed out that the present elements are not subject to the difficulties encountered by thin plate theory elements, concerning boundary conditions. For example, the polygonal approximation of curved, simply supported edges is convergent. Other topics discussed are the equivalence with mixed methods, rank deficiency, convergence criteria and useful mass 'lumping' schemes for dynamics. Numerical results for several thin plate problems indicate the high degree of accuracy attainable by the present elements. (Auth.)

  20. Axiomatic Characterizations of IVF Rough Approximation Operators

    Directory of Open Access Journals (Sweden)

    Guangji Yu

    2014-01-01

    Full Text Available This paper is devoted to the study of axiomatic characterizations of IVF rough approximation operators. IVF approximation spaces are investigated. The fact that different IVF operators satisfy some axioms to guarantee the existence of different types of IVF relations which produce the same operators is proved and then IVF rough approximation operators are characterized by axioms.

  1. Approximation properties of fine hyperbolic graphs

    Indian Academy of Sciences (India)

    2016-08-26

    Aug 26, 2016 ... In this paper, we propose a definition of approximation property which is called the metric invariant translation approximation property for a countable discrete metric space. Moreover, we use ... Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209, People's Republic of China ...

  2. Efficient automata constructions and approximate automata

    NARCIS (Netherlands)

    Watson, B.W.; Kourie, D.G.; Ngassam, E.K.; Strauss, T.; Cleophas, L.G.W.A.

    2008-01-01

    In this paper, we present data structures and algorithms for efficiently constructing approximate automata. An approximate automaton for a regular language L is one which accepts at least L. Such automata can be used in a variety of practical applications, including network security pattern

  3. Efficient automata constructions and approximate automata

    NARCIS (Netherlands)

    Watson, B.W.; Kourie, D.G.; Ngassam, E.K.; Strauss, T.; Cleophas, L.G.W.A.; Holub, J.; Zdárek, J.

    2006-01-01

    In this paper, we present data structures and algorithms for efficiently constructing approximate automata. An approximate automaton for a regular language L is one which accepts at least L. Such automata can be used in a variety of practical applications, including network security pattern

  4. Approximation of the semi-infinite interval

    Directory of Open Access Journals (Sweden)

    A. McD. Mercer

    1980-01-01

    Full Text Available The approximation of a function f∈C[a,b] by Bernstein polynomials is well-known. It is based on the binomial distribution. O. Szasz has shown that there are analogous approximations on the interval [0,∞ based on the Poisson distribution. Recently R. Mohapatra has generalized Szasz' result to the case in which the approximating function is αe−ux∑k=N∞(uxkα+β−1Γ(kα+βf(kαuThe present note shows that these results are special cases of a Tauberian theorem for certain infinite series having positive coefficients.

  5. Rational approximations for tomographic reconstructions

    International Nuclear Information System (INIS)

    Reynolds, Matthew; Beylkin, Gregory; Monzón, Lucas

    2013-01-01

    We use optimal rational approximations of projection data collected in x-ray tomography to improve image resolution. Under the assumption that the object of interest is described by functions with jump discontinuities, for each projection we construct its rational approximation with a small (near optimal) number of terms for a given accuracy threshold. This allows us to augment the measured data, i.e., double the number of available samples in each projection or, equivalently, extend (double) the domain of their Fourier transform. We also develop a new, fast, polar coordinate Fourier domain algorithm which uses our nonlinear approximation of projection data in a natural way. Using augmented projections of the Shepp–Logan phantom, we provide a comparison between the new algorithm and the standard filtered back-projection algorithm. We demonstrate that the reconstructed image has improved resolution without additional artifacts near sharp transitions in the image. (paper)

  6. 'LTE-diffusion approximation' for arc calculations

    International Nuclear Information System (INIS)

    Lowke, J J; Tanaka, M

    2006-01-01

    This paper proposes the use of the 'LTE-diffusion approximation' for predicting the properties of electric arcs. Under this approximation, local thermodynamic equilibrium (LTE) is assumed, with a particular mesh size near the electrodes chosen to be equal to the 'diffusion length', based on D e /W, where D e is the electron diffusion coefficient and W is the electron drift velocity. This approximation overcomes the problem that the equilibrium electrical conductivity in the arc near the electrodes is almost zero, which makes accurate calculations using LTE impossible in the limit of small mesh size, as then voltages would tend towards infinity. Use of the LTE-diffusion approximation for a 200 A arc with a thermionic cathode gives predictions of total arc voltage, electrode temperatures, arc temperatures and radial profiles of heat flux density and current density at the anode that are in approximate agreement with more accurate calculations which include an account of the diffusion of electric charges to the electrodes, and also with experimental results. Calculations, which include diffusion of charges, agree with experimental results of current and heat flux density as a function of radius if the Milne boundary condition is used at the anode surface rather than imposing zero charge density at the anode

  7. Experiences during the exchange of fuel elements of the NS OTTO HAHN

    International Nuclear Information System (INIS)

    Scharge, J.; Manthey, H.J.; Schafstall, H.G.

    1977-01-01

    In the fall of 1972, the nuclear ship OTTO HAHN was taken out of service in order to exchange the fuel elements and to take care of necessary modifications. Up to this time, she travelled a total distance of 241 588 nautical miles on 79 trips. The reactor plant was in service for approximately 25 230 h. The fuel elements reached a burn-up of 570 days. The guaranteed burn-up was exceeded by 14%. At sea the reactor was available 99.7% during operation. Operational data proved the design of the reactor plant to be very conservative. The fuel elements were never damaged. This successful operation of the FDR-reactor and its first core demonstrated that a reactor of this type is suitable for shipboard use. (orig.) [de

  8. Modelling cohesive laws in finite element simulations via an adapted contact procedure in ABAQUS

    DEFF Research Database (Denmark)

    Feih, S.

    2004-01-01

    is not straightforward, and most existing publications consider theoretical and therefore simpler softening shapes. Two possible methods of bridging law approximation areexplained and compared in this report. The bridging laws were implemented in a numerical user subroutine in the finite element code ABAQUS. The main...

  9. Nonlinear approximation with general wave packets

    DEFF Research Database (Denmark)

    Borup, Lasse; Nielsen, Morten

    2005-01-01

    We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete...

  10. Approximations for stop-loss reinsurance premiums

    NARCIS (Netherlands)

    Reijnen, Rajko; Albers, Willem/Wim; Kallenberg, W.C.M.

    2005-01-01

    Various approximations of stop-loss reinsurance premiums are described in literature. For a wide variety of claim size distributions and retention levels, such approximations are compared in this paper to each other, as well as to a quantitative criterion. For the aggregate claims two models are

  11. Nuclear Matrix Elements for the $\\beta\\beta$ Decay of the $^{76}$Ge

    CERN Document Server

    Brown, B A; Horoi, M

    2015-01-01

    The nuclear matrix elements for two-neutrino double-beta (2 n$\\beta\\beta$ ) and zero-neutrino double-beta (0 n$\\beta\\beta$) decay of 76 Ge are evaluated in terms of the configuration interaction (CI), quasiparticle random phase approximation (QRPA) and interacting boson model (IBM) methods. We show that the decomposition of the matrix elements in terms of interemediate states in 74 Ge is dominated by ground state of this nucleus. We consider corrections to the CI results that arise from configurations admixtures involving orbitals out-side of the CI configuration space by using results from QRPA, many-body-perturbation theory, and the connections to related observables. The CI two-neutrino matrix element is reduced due to the inclusion of spin-orbit partners, and to many-body correlations connected with Gamow-Teller beta decay. The CI zero-neutrino matrix element for the heavy neutrino is enhanced due to particle-particle correlations that are connected with the odd-even oscillations in the nuclear masse...

  12. Stress recovery techniques for natural element method in 2-D solid mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Cho, Jin Rae [Dept. of Naval Architecture and Ocean Engineering, Hongik University, Sejong (Korea, Republic of)

    2016-11-15

    This paper is concerned with the stress recovery for the natural element method in which the problem domain is discretized with Delaunay triangles and the structural behavior is approximated with Laplace interpolation functions. Basically, the global and local patch recovery techniques based on the L2-projection method are adopted. For the local patch recovery, the local element patches are defined by the supports of each Laplace interpolation function. For the comparison purpose, the local stress recovery is also performed using Lagrange-type basis functions that are used for 3- and 6-node triangular elements. The stresses that are recovered by the present global and local recovery techniques are compared each other and compared with the available analytic solution, in terms of their spatial distributions and the convergence rates. As well, the dependence of the recovered stress field on the type of test basis functions that are used forbnov-Galerkin (BG) and Petrov-Galerkin (PG) natural element methods is also investigated.

  13. Transport and dispersion of pollutants in surface impoundments: a finite element model

    International Nuclear Information System (INIS)

    Yeh, G.T.

    1980-07-01

    A surface impoundment model in finite element (SIMFE) is presented to enable the simulation of flow circulations and pollutant transport and dispersion in natural or artificial lakes, reservoirs or ponds with any number of islands. This surface impoundment model consists of two sub-models: hydrodynamic and pollutant transport models. Both submodels are simulated by the finite element method. While the hydrodynamic model is solved by the standard Galerkin finite element scheme, the pollutant transport model can be solved by any of the twelve optional finite element schemes built in the program. Theoretical approximations and the numerical algorithm of SIMFE are described. Detail instruction of the application are given and listing of FORTRAN IV source program are provided. Two sample problems are given. One is for an idealized system with a known solution to show the accuracy and partial validation of the models. The other is applied to Prairie Island for a set of hypothetical input data, typifying a class of problems to which SIMFE may be applied

  14. Transport and dispersion of pollutants in surface impoundments: a finite element model

    Energy Technology Data Exchange (ETDEWEB)

    Yeh, G.T.

    1980-07-01

    A surface impoundment model in finite element (SIMFE) is presented to enable the simulation of flow circulations and pollutant transport and dispersion in natural or artificial lakes, reservoirs or ponds with any number of islands. This surface impoundment model consists of two sub-models: hydrodynamic and pollutant transport models. Both submodels are simulated by the finite element method. While the hydrodynamic model is solved by the standard Galerkin finite element scheme, the pollutant transport model can be solved by any of the twelve optional finite element schemes built in the program. Theoretical approximations and the numerical algorithm of SIMFE are described. Detail instruction of the application are given and listing of FORTRAN IV source program are provided. Two sample problems are given. One is for an idealized system with a known solution to show the accuracy and partial validation of the models. The other is applied to Prairie Island for a set of hypothetical input data, typifying a class of problems to which SIMFE may be applied.

  15. Convergence of a residual based artificial viscosity finite element method

    KAUST Repository

    Nazarov, Murtazo

    2013-02-01

    We present a residual based artificial viscosity finite element method to solve conservation laws. The Galerkin approximation is stabilized by only residual based artificial viscosity, without any least-squares, SUPG, or streamline diffusion terms. We prove convergence of the method, applied to a scalar conservation law in two space dimensions, toward an unique entropy solution for implicit time stepping schemes. © 2012 Elsevier B.V. All rights reserved.

  16. Approximation properties of haplotype tagging

    Directory of Open Access Journals (Sweden)

    Dreiseitl Stephan

    2006-01-01

    Full Text Available Abstract Background Single nucleotide polymorphisms (SNPs are locations at which the genomic sequences of population members differ. Since these differences are known to follow patterns, disease association studies are facilitated by identifying SNPs that allow the unique identification of such patterns. This process, known as haplotype tagging, is formulated as a combinatorial optimization problem and analyzed in terms of complexity and approximation properties. Results It is shown that the tagging problem is NP-hard but approximable within 1 + ln((n2 - n/2 for n haplotypes but not approximable within (1 - ε ln(n/2 for any ε > 0 unless NP ⊂ DTIME(nlog log n. A simple, very easily implementable algorithm that exhibits the above upper bound on solution quality is presented. This algorithm has running time O((2m - p + 1 ≤ O(m(n2 - n/2 where p ≤ min(n, m for n haplotypes of size m. As we show that the approximation bound is asymptotically tight, the algorithm presented is optimal with respect to this asymptotic bound. Conclusion The haplotype tagging problem is hard, but approachable with a fast, practical, and surprisingly simple algorithm that cannot be significantly improved upon on a single processor machine. Hence, significant improvement in computatational efforts expended can only be expected if the computational effort is distributed and done in parallel.

  17. Finite element and discontinuous Galerkin methods for transient wave equations

    CERN Document Server

    Cohen, Gary

    2017-01-01

    This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem ...

  18. Approximation for the adjoint neutron spectrum

    International Nuclear Information System (INIS)

    Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da

    2002-01-01

    The proposal of this work is the determination of an analytical approximation which is capable to reproduce the adjoint neutron flux for the energy range of the narrow resonances (NR). In a previous work we developed a method for the calculation of the adjoint spectrum which was calculated from the adjoint neutron balance equations, that were obtained by the collision probabilities method, this method involved a considerable quantity of numerical calculation. In the analytical method some approximations were done, like the multiplication of the escape probability in the fuel by the adjoint flux in the moderator, and after these approximations, taking into account the case of the narrow resonances, were substituted in the adjoint neutron balance equation for the fuel, resulting in an analytical approximation for the adjoint flux. The results obtained in this work were compared to the results generated with the reference method, which demonstrated a good and precise results for the adjoint neutron flux for the narrow resonances. (author)

  19. Operator approximant problems arising from quantum theory

    CERN Document Server

    Maher, Philip J

    2017-01-01

    This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.

  20. Confidence Estimation of Reliability Indices of the System with Elements Duplication and Recovery

    Directory of Open Access Journals (Sweden)

    I. V. Pavlov

    2017-01-01

    Full Text Available The article considers a problem to estimate a confidence interval of the main reliability indices such as availability rate, mean time between failures, and operative availability (in the stationary state for the model of the system with duplication and independent recovery of elements.Presents a solution of the problem for a situation that often arises in practice, when there are unknown exact values of the reliability parameters of the elements, and only test data of the system or its individual parts (elements, subsystems for reliability are known. It should be noted that the problems of the confidence estimate of reliability indices of the complex systems based on the testing results of their individual elements are fairly common function in engineering practice when designing and running the various engineering systems. The available papers consider this problem, mainly, for non-recovery systems.Describes a solution of this problem for the important particular case when the system elements are duplicated by the reserved elements, and the elements that have failed in the course of system operation are recovered (regardless of the state of other elements.An approximate solution of this problem is obtained for the case of high reliability or "fast recovery" of elements on the assumption that the average recovery time of elements is small as compared to the average time between failures.

  1. Non-Linear Approximation of Bayesian Update

    KAUST Repository

    Litvinenko, Alexander

    2016-01-01

    We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.

  2. Quirks of Stirling's Approximation

    Science.gov (United States)

    Macrae, Roderick M.; Allgeier, Benjamin M.

    2013-01-01

    Stirling's approximation to ln "n"! is typically introduced to physical chemistry students as a step in the derivation of the statistical expression for the entropy. However, naive application of this approximation leads to incorrect conclusions. In this article, the problem is first illustrated using a familiar "toy…

  3. Non-Linear Approximation of Bayesian Update

    KAUST Repository

    Litvinenko, Alexander

    2016-06-23

    We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.

  4. Design of JMTR high-performance fuel element

    International Nuclear Information System (INIS)

    Sakurai, Fumio; Shimakawa, Satoshi; Komori, Yoshihiro; Tsuchihashi, Keiichiro; Kaminaga, Fumito

    1999-01-01

    For test and research reactors, the core conversion to low-enriched uranium fuel is required from the viewpoint of non-proliferation of nuclear weapon material. Improvements of core performance are also required in order to respond to recent advanced utilization needs. In order to meet both requirements, a high-performance fuel element of high uranium density with Cd wires as burnable absorbers was adopted for JMTR core conversion to low-enriched uranium fuel. From the result of examination of an adaptability of a few group constants generated by a conventional transport-theory calculation with an isotropic scattering approximation to a few group diffusion-theory core calculation for design of the JMTR high-performance fuel element, it was clear that the depletion of Cd wires was not able to be predicted accurately using group constants generated by the conventional method. Therefore, a new generation method of a few group constants in consideration of an incident neutron spectrum at Cd wire was developed. As the result, the most suitable high-performance fuel element for JMTR was designed successfully, and that allowed extension of operation duration without refueling to almost twice as long and offer of irradiation field with constant neutron flux. (author)

  5. Nonlinear vibrations of thin arbitrarily laminated composite plates subjected to harmonic excitations using DKT elements

    Science.gov (United States)

    Chiang, C. K.; Xue, David Y.; Mei, Chuh

    1993-04-01

    A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite thin plates using the Discrete Kirchhoff Theory (DKT) triangular elements. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite triangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, triangular plates, different boundary conditions, lamination angles, number of plies, and uniform versus concentrated loads are presented.

  6. Approximations to camera sensor noise

    Science.gov (United States)

    Jin, Xiaodan; Hirakawa, Keigo

    2013-02-01

    Noise is present in all image sensor data. Poisson distribution is said to model the stochastic nature of the photon arrival process, while it is common to approximate readout/thermal noise by additive white Gaussian noise (AWGN). Other sources of signal-dependent noise such as Fano and quantization also contribute to the overall noise profile. Question remains, however, about how best to model the combined sensor noise. Though additive Gaussian noise with signal-dependent noise variance (SD-AWGN) and Poisson corruption are two widely used models to approximate the actual sensor noise distribution, the justification given to these types of models are based on limited evidence. The goal of this paper is to provide a more comprehensive characterization of random noise. We concluded by presenting concrete evidence that Poisson model is a better approximation to real camera model than SD-AWGN. We suggest further modification to Poisson that may improve the noise model.

  7. Diophantine approximation and Dirichlet series

    CERN Document Server

    Queffélec, Hervé

    2013-01-01

    This self-contained book will benefit beginners as well as researchers. It is devoted to Diophantine approximation, the analytic theory of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the book is divided into seven chapters, the first three of which present tools from commutative harmonic analysis, including a sharp form of the uncertainty principle, ergodic theory and Diophantine approximation to be used in the sequel. A presentation of continued fraction expansions, including the mixing property of the Gauss map, is given. Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of anal...

  8. Proceedings of the workshop on the nuclear sciences of the heaviest elements

    Energy Technology Data Exchange (ETDEWEB)

    Nagame, Yuichiro; Haba, Hiromitsu; Ikezoe, Hiroshi [eds.

    2000-03-01

    The workshop on the nuclear sciences of the heaviest elements took place on July 21-22, 1999 at the Japan Atomic Energy Research Institute (JAERI), Tokai. Approximately 40 scientists and 15 graduate students participated in the workshop which was organized by the Advanced Science Research Center, JAERI. The successful syntheses of three new super-heavy elements in 1999, Z=114 at the Joint Institute for Nuclear Research in Dubna, Russia, and Z=118 (with Z=116 following from {alpha}-decay of Z=118) at the Lawrence Berkeley National Laboratory (LBNL) in USA, are tremendous progress in the field of the heavy element research. The 1st International Conference on the Chemistry and Physics of the Transactinide Elements (TAN99) was held in Germany from September 26 to 30, 1999 to discuss in a larger context all scientific aspects of the heaviest elements. Thus, it was timely to hold the present domestic workshop to summarize what has been done in recent years, to see what has come true, and to discuss the perspectives in the near feature. The subjects in the workshop were classified into; (1) synthesis of heavy elements, (2) decay properties of heavy nuclei, (3) chemistry of the heaviest elements, and (4) future plans of the heavy element research in Japan. This volume contains the papers presented in the workshop. The 14 papers are indexed individually. (J.P.N.)

  9. APPROXIMATIONS TO PERFORMANCE MEASURES IN QUEUING SYSTEMS

    Directory of Open Access Journals (Sweden)

    Kambo, N. S.

    2012-11-01

    Full Text Available Approximations to various performance measures in queuing systems have received considerable attention because these measures have wide applicability. In this paper we propose two methods to approximate the queuing characteristics of a GI/M/1 system. The first method is non-parametric in nature, using only the first three moments of the arrival distribution. The second method treads the known path of approximating the arrival distribution by a mixture of two exponential distributions by matching the first three moments. Numerical examples and optimal analysis of performance measures of GI/M/1 queues are provided to illustrate the efficacy of the methods, and are compared with benchmark approximations.

  10. Exposure to Selected Geogenic Trace Elements (I, Li, and Sr from Drinking Water in Denmark

    Directory of Open Access Journals (Sweden)

    Denitza Dimitrova Voutchkova

    2015-02-01

    Full Text Available The naturally occurring geogenic elements iodine (I, lithium (Li, and strontium (Sr have a beneficial effect on human health. Iodine has an essential role in human metabolism while Li and Sr are used, respectively, as a treatment for various mental disorders and for post-menopausal osteoporosis. The aim here is to evaluate the potential for future epidemiological investigations in Denmark of lifelong and chronic exposure to low doses of these compounds. The drinking water data represents approximately 45% of the annual Danish groundwater abstraction for drinking water purposes, which supplies approximately 2.5 million persons. The spatial patterns were studied using inverse distance weighted interpolation and cluster analysis. The exposed population was estimated based on two datasets: (1 population density in the smallest census unit, the parishes, and (2 geocoded addresses where at least one person is residing. We found significant spatial variation in the exposure for all three elements, related mainly to geochemical processes. This suggests a prospective opportunity for future epidemiological investigation of long-term effects of I, Li, and Sr, either alone or in combinations with other geogenic elements such as Ca, Mg or F.

  11. Stochastic approximation Monte Carlo importance sampling for approximating exact conditional probabilities

    KAUST Repository

    Cheon, Sooyoung

    2013-02-16

    Importance sampling and Markov chain Monte Carlo methods have been used in exact inference for contingency tables for a long time, however, their performances are not always very satisfactory. In this paper, we propose a stochastic approximation Monte Carlo importance sampling (SAMCIS) method for tackling this problem. SAMCIS is a combination of adaptive Markov chain Monte Carlo and importance sampling, which employs the stochastic approximation Monte Carlo algorithm (Liang et al., J. Am. Stat. Assoc., 102(477):305-320, 2007) to draw samples from an enlarged reference set with a known Markov basis. Compared to the existing importance sampling and Markov chain Monte Carlo methods, SAMCIS has a few advantages, such as fast convergence, ergodicity, and the ability to achieve a desired proportion of valid tables. The numerical results indicate that SAMCIS can outperform the existing importance sampling and Markov chain Monte Carlo methods: It can produce much more accurate estimates in much shorter CPU time than the existing methods, especially for the tables with high degrees of freedom. © 2013 Springer Science+Business Media New York.

  12. Stochastic approximation Monte Carlo importance sampling for approximating exact conditional probabilities

    KAUST Repository

    Cheon, Sooyoung; Liang, Faming; Chen, Yuguo; Yu, Kai

    2013-01-01

    Importance sampling and Markov chain Monte Carlo methods have been used in exact inference for contingency tables for a long time, however, their performances are not always very satisfactory. In this paper, we propose a stochastic approximation Monte Carlo importance sampling (SAMCIS) method for tackling this problem. SAMCIS is a combination of adaptive Markov chain Monte Carlo and importance sampling, which employs the stochastic approximation Monte Carlo algorithm (Liang et al., J. Am. Stat. Assoc., 102(477):305-320, 2007) to draw samples from an enlarged reference set with a known Markov basis. Compared to the existing importance sampling and Markov chain Monte Carlo methods, SAMCIS has a few advantages, such as fast convergence, ergodicity, and the ability to achieve a desired proportion of valid tables. The numerical results indicate that SAMCIS can outperform the existing importance sampling and Markov chain Monte Carlo methods: It can produce much more accurate estimates in much shorter CPU time than the existing methods, especially for the tables with high degrees of freedom. © 2013 Springer Science+Business Media New York.

  13. Approximate Bayesian evaluations of measurement uncertainty

    Science.gov (United States)

    Possolo, Antonio; Bodnar, Olha

    2018-04-01

    The Guide to the Expression of Uncertainty in Measurement (GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty. This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand. The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists. We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.

  14. Generation of an approximately 2.4 Mb human X centromere-based minichromosome by targeted telomere-associated chromosome fragmentation in DT40.

    Science.gov (United States)

    Mills, W; Critcher, R; Lee, C; Farr, C J

    1999-05-01

    A linear mammalian artificial chromosome (MAC) will require at least three types of functional element: a centromere, two telomeres and origins of replication. As yet, our understanding of these elements, as well as many other aspects of structure and organization which may be critical for a fully functional mammalian chromosome, remains poor. As a way of defining these various requirements, minichromosome reagents are being developed and analysed. Approaches for minichromosome generation fall into two broad categories: de novo assembly from candidate DNA sequences, or the fragmentation of an existing chromosome to reduce it to a minimal size. Here we describe the generation of a human minichromosome using the latter, top-down, approach. A human X chromosome, present in a DT40-human microcell hybrid, has been manipulated using homologous recombination and the targeted seeding of a de novo telomere. This strategy has generated a linear approximately 2.4 Mb human X centromere-based minichromosome capped by two artificially seeded telomeres: one immediately flanking the centromeric alpha-satellite DNA and the other targeted to the zinc finger gene ZXDA in Xp11.21. The chromosome retains an alpha-satellite domain of approximately 1. 8 Mb, a small array of gamma-satellite repeat ( approximately 40 kb) and approximately 400 kb of Xp proximal DNA sequence. The mitotic stability of this minichromosome has been examined, both in DT40 and following transfer into hamster and human cell lines. In all three backgrounds, the minichromosome is retained efficiently, but in the human and hamster microcell hybrids its copy number is poorly regulated. This approach of engineering well-defined chromosome reagents will allow key questions in MAC development (such as whether a lower size limit exists) to be addressed. In addition, the 2.4 Mb minichromosome described here has potential to be developed as a vector for gene delivery.

  15. Production of porous filter elements from PEUAPM nanocomposites and silver nanoparticles

    International Nuclear Information System (INIS)

    Bizzo, M.A.; Hui, W.S.

    2014-01-01

    The production of filter elements for water based in polymers is widespread in the market, but has an undesirable characteristic: they are not efficient and able to retain or eliminate microorganisms at all times. This paper proposes to produce nanocomposite filters with biocidal properties composed of ultra-high molecular weight polyethylene(UHMWPE) and silver nanoparticles, the UHMWPE is responsible for the uniform porous structure of the filters and the silver nanoparticles incorporated on the polymer are responsible for the biocide action. Particulate polymer that presents a different particle size curve was used for sintering the filters. Samples of filter elements obtained in this work were characterized by the techniques of X-ray diffraction, scanning electron microscopy and EDS microanalysis. The results indicated a porosity of approximately 49% in the filter, and the formation of the nanocomposite. key-words: nanocomposites, silver, UHMWPE, filter elements. (author)

  16. Improved radiative corrections for (e,e'p) experiments: Beyond the peaking approximation and implications of the soft-photon approximation

    International Nuclear Information System (INIS)

    Weissbach, F.; Hencken, K.; Rohe, D.; Sick, I.; Trautmann, D.

    2006-01-01

    Analyzing (e,e ' p) experimental data involves corrections for radiative effects which change the interaction kinematics and which have to be carefully considered in order to obtain the desired accuracy. Missing momentum and energy due to bremsstrahlung have so far often been incorporated into the simulations and the experimental analyses using the peaking approximation. It assumes that all bremsstrahlung is emitted in the direction of the radiating particle. In this article we introduce a full angular Monte Carlo simulation method which overcomes this approximation. As a test, the angular distribution of the bremsstrahlung photons is reconstructed from H(e,e ' p) data. Its width is found to be underestimated by the peaking approximation and described much better by the approach developed in this work. The impact of the soft-photon approximation on the photon angular distribution is found to be minor as compared to the impact of the peaking approximation. (orig.)

  17. Trajectory averaging for stochastic approximation MCMC algorithms

    KAUST Repository

    Liang, Faming

    2010-10-01

    The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400-407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems and for general simulation and optimizations. In this paper, we first show that the trajectory averaging estimator is asymptotically efficient for the stochastic approximation MCMC (SAMCMC) algorithm under mild conditions, and then apply this result to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic approximation MLE algorithm for missing data problems, is also considered in the paper. © Institute of Mathematical Statistics, 2010.

  18. Toward a consistent random phase approximation based on the relativistic Hartree approximation

    International Nuclear Information System (INIS)

    Price, C.E.; Rost, E.; Shepard, J.R.; McNeil, J.A.

    1992-01-01

    We examine the random phase approximation (RPA) based on a relativistic Hartree approximation description for nuclear ground states. This model includes contributions from the negative energy sea at the one-loop level. We emphasize consistency between the treatment of the ground state and the RPA. This consistency is important in the description of low-lying collective levels but less important for the longitudinal (e,e') quasielastic response. We also study the effect of imposing a three-momentum cutoff on negative energy sea contributions. A cutoff of twice the nucleon mass improves agreement with observed spin-orbit splittings in nuclei compared to the standard infinite cutoff results, an effect traceable to the fact that imposing the cutoff reduces m * /m. Consistency is much more important than the cutoff in the description of low-lying collective levels. The cutoff model also provides excellent agreement with quasielastic (e,e') data

  19. Immiscible silicate liquids at high pressure: the influence of melt structure on elemental partitioning

    Energy Technology Data Exchange (ETDEWEB)

    Vicenzi, E [Princeton Materials Laboratory, Princeton, NJ (United States); Green, T H [Macquarie Univ., North Ryde, NSW (Australia); Sie, S H [Commonwealth Scientific and Industrial Research Organisation (CSIRO), North Ryde, NSW (Australia). Div. of Exploration Geoscience

    1994-12-31

    Micro-PIXE analyses have been applied to study partitioning of trace elements between immiscible silicate melts stabilised at 0.5 and 1.0 GPa over a temperature range of 1160-1240 deg C in the system SiO{sub 2}-FeO-Al{sub 2}0{sub 3}-K{sub 2}0 (+P{sub 2}0{sub 5}). The system was doped with a suite of trace elements of geochemical interest: Rb, Ba, Pb, Sr, La, Ce, Sm, Ho, Y, Lu, Th, U, Zr, Hf, Nb and Ta at approximately 200 ppm level for all elements except for the REE`s, Ba and Ta (600-1200 ppm). Trace element partitioning was found to be a complex function of cation field strength (charge/radius{sup 2}). Although field strength is important in determining the nature and degree of partitioning, the authors emphasised that it is only one component of the underlying mechanism for the way in which elements distribute themselves between two silicate liquids. 8 refs., 2 figs.

  20. Immiscible silicate liquids at high pressure: the influence of melt structure on elemental partitioning

    Energy Technology Data Exchange (ETDEWEB)

    Vicenzi, E. [Princeton Materials Laboratory, Princeton, NJ (United States); Green, T.H. [Macquarie Univ., North Ryde, NSW (Australia); Sie, S.H. [Commonwealth Scientific and Industrial Research Organisation (CSIRO), North Ryde, NSW (Australia). Div. of Exploration Geoscience

    1993-12-31

    Micro-PIXE analyses have been applied to study partitioning of trace elements between immiscible silicate melts stabilised at 0.5 and 1.0 GPa over a temperature range of 1160-1240 deg C in the system SiO{sub 2}-FeO-Al{sub 2}0{sub 3}-K{sub 2}0 (+P{sub 2}0{sub 5}). The system was doped with a suite of trace elements of geochemical interest: Rb, Ba, Pb, Sr, La, Ce, Sm, Ho, Y, Lu, Th, U, Zr, Hf, Nb and Ta at approximately 200 ppm level for all elements except for the REE`s, Ba and Ta (600-1200 ppm). Trace element partitioning was found to be a complex function of cation field strength (charge/radius{sup 2}). Although field strength is important in determining the nature and degree of partitioning, the authors emphasised that it is only one component of the underlying mechanism for the way in which elements distribute themselves between two silicate liquids. 8 refs., 2 figs.

  1. Handbook of the band structure of elemental solids from Z = 1 to Z = 112

    CERN Document Server

    Papaconstantopoulos, Dimitris A

    2015-01-01

    This handbook presents electronic structure data and tabulations of Slater-Koster parameters for the whole periodic table. This second edition presents data sets for all elements up to Z = 112, Copernicium, whereas the first edition contained only 53 elements. In this new edition, results are given for the equation of state of the elements together with the parameters of a Birch fit, so that the reader can regenerate the results and derive additional information, such as Pressure-Volume relations and variation of Bulk Modulus with Pressure. For each element, in addition to the equation of state, the energy bands, densities of states, and a set of tight-binding parameters is provided. For a majority of elements, the tight-binding parameters are presented for both a two- and three-center approximation. For the hcp structure, new three-center tight-binding results are given. Other new material in this edition include: energy bands and densities of states of all rare-earth metals, a discussion of the McMillan-Gas...

  2. Simulation of natural convection in a rectangular loop using finite elements

    International Nuclear Information System (INIS)

    Pepper, D.W.; Hamm, L.L.; Kehoe, A.B.

    1984-01-01

    A two-dimensional finite-element analysis of natural convection in a rectangular loop is presented. A psi-omega formulation of the Boussinesque approximation to the Navier-Stokes equation is solved by the false transient technique. Streamlines and isotherms at Ra = 10 4 are shown for three different modes of heating. The results indicate that corner effects should be considered when modeling flow patterns in thermosyphons

  3. Seismic wave extrapolation using lowrank symbol approximation

    KAUST Repository

    Fomel, Sergey

    2012-04-30

    We consider the problem of constructing a wave extrapolation operator in a variable and possibly anisotropic medium. Our construction involves Fourier transforms in space combined with the help of a lowrank approximation of the space-wavenumber wave-propagator matrix. A lowrank approximation implies selecting a small set of representative spatial locations and a small set of representative wavenumbers. We present a mathematical derivation of this method, a description of the lowrank approximation algorithm and numerical examples that confirm the validity of the proposed approach. Wave extrapolation using lowrank approximation can be applied to seismic imaging by reverse-time migration in 3D heterogeneous isotropic or anisotropic media. © 2012 European Association of Geoscientists & Engineers.

  4. Analysis of warping deformation modes using higher order ANCF beam element

    Science.gov (United States)

    Orzechowski, Grzegorz; Shabana, Ahmed A.

    2016-02-01

    Most classical beam theories assume that the beam cross section remains a rigid surface under an arbitrary loading condition. However, in the absolute nodal coordinate formulation (ANCF) continuum-based beams, this assumption can be relaxed allowing for capturing deformation modes that couple the cross-section deformation and beam bending, torsion, and/or elongation. The deformation modes captured by ANCF finite elements depend on the interpolating polynomials used. The most widely used spatial ANCF beam element employs linear approximation in the transverse direction, thereby restricting the cross section deformation and leading to locking problems. The objective of this investigation is to examine the behavior of a higher order ANCF beam element that includes quadratic interpolation in the transverse directions. This higher order element allows capturing warping and non-uniform stretching distribution. Furthermore, this higher order element allows for increasing the degree of continuity at the element interface. It is shown in this paper that the higher order ANCF beam element can be used effectively to capture warping and eliminate Poisson locking that characterizes lower order ANCF finite elements. It is also shown that increasing the degree of continuity requires a special attention in order to have acceptable results. Because higher order elements can be more computationally expensive than the lower order elements, the use of reduced integration for evaluating the stress forces and the use of explicit and implicit numerical integrations to solve the nonlinear dynamic equations of motion are investigated in this paper. It is shown that the use of some of these integration methods can be very effective in reducing the CPU time without adversely affecting the solution accuracy.

  5. Production of atomic negative ion beams of the Group IA elements

    International Nuclear Information System (INIS)

    Alton, G.D.; Mills, G.D.

    1988-01-01

    A method has been developed which enables the direct sputter generation of atomic negative ion beams of all members of the Group IA elements (Li, Na, K, Rb, and Cs). The method consists of the use of sputter samples formed by pressing mixtures of the carbonates of the Group IA elements and 10% (atomic) Cu, Ag, or other metal powder. The following intensities are typical of those observed from carbonate samples subjected to /approximately/3 KeV cesium ion bombardment: Li - : ≥0.5 μA; Na - : ≥0.5 μA; K - : ≥0.5 μA; Rb - : ≥0.5 μA; Cs - : ≥0.2 μA. 7 refs., 2 figs., 1 tab

  6. Approximation algorithms for guarding holey polygons ...

    African Journals Online (AJOL)

    Guarding edges of polygons is a version of art gallery problem.The goal is finding the minimum number of guards to cover the edges of a polygon. This problem is NP-hard, and to our knowledge there are approximation algorithms just for simple polygons. In this paper we present two approximation algorithms for guarding ...

  7. Approximation properties of fine hyperbolic graphs

    Indian Academy of Sciences (India)

    2010 Mathematics Subject Classification. 46L07. 1. Introduction. Given a countable discrete group G, some nice approximation properties for the reduced. C∗-algebras C∗ r (G) can give us the approximation properties of G. For example, Lance. [7] proved that the nuclearity of C∗ r (G) is equivalent to the amenability of G; ...

  8. Irradiation program of slightly enriched fuel elements at the Atucha I nuclear power plant

    International Nuclear Information System (INIS)

    Casario, J.A.; Cesario, R.H.; Perez, R.A.; Sidelnik, J.I.

    1987-01-01

    An irradiation program of fuel elements with slightly enriched uranium is implemented, tending to the homogenization of core at Atucha I nuclear power plant. The main benefits of the enrichment program are: a) to extend the average discharge burnup of fuel elements, reducing the number of elements used to generate the same amount of energy. This implies a smaller annual consumption of elements and consequently the reduction of transport and replacement operations and of the storage pool systems as well as that of radioactive wastes; b) the saving of uranium and structural materials (Zircaloy and others). In the initial stage of program an homogeneous core enrichment of 0.85% by weight of U-235 is anticipated. The average discharge burnup of fuel elements, as estimated by previous studies, is approximately 11.6 MW d/kg U. The annual consumption of fuel elements is reduced from 396 of natural uranium to 205, with a load factor of 0.85. It is intended to reach the next equilibrium steps with an enrichment of 1.00 and 1.20% in U-235. (Author)

  9. 17O(n,α)14C cross section from 25 meV to approximately 1 MeV

    International Nuclear Information System (INIS)

    Koehler, P.E.; Graff, S.M.

    1991-01-01

    We have measured the 17 O(n,α) 14 C cross section from thermal energy to approximately 1 MeV. A bump in the data near 3 keV could be fitted by a state whose properties are consistent with a known subthreshold J π =1 - level at E x =8.039 MeV. The cause of the 1/v cross section near thermal energy could not be determined although the known 2 + state at 8.213 MeV was found to be too narrow to contribute much to the thermal cross section. Our data are compared to measurements made via the inverse reaction. There are many differences between the two sets of data. The astrophysical reaction rate was calculated from the measured cross section. This reaction plays a role in the nucleosynthesis of heavy elements in nonstandard big-bang models. At big-bang temperatures, the experimental rate was found to be in fair agreement with the rate estimated from the previously known properties of states of 18 O in this region. Furthermore, using the available information from experiments, it was estimated that the 17 O(n,α) 14 C rate is approximately a factor of 10 3 --10 4 times larger than the 17 O(n,γ) 18 O rate at big-bang temperatures. As a result, there may be significant cycling between 14 C and 17 O resulting in a reduction of heavy-element nucleosynthesis

  10. Thermohydraulic analysis in pipelines using the finite element method

    International Nuclear Information System (INIS)

    Costa, L.E.; Idelsohn, S.R.

    1984-01-01

    The Finite Element Method (FEM) is employed for the numerical solution of fluid flow problems with combined heat transfer mechanisms. Boussinesq approximations are used for the solution of the governing equations. The application of the FEM leads to a set of simultaneous nonlinear equations. The development of the method, for the solution of bidimensional and axisymmetric problems, is presented. Examples of fluid flow in pipes, including natural and forced convection, are solved with the proposed method and discussed in the paper. (Author) [pt

  11. Approximate number word knowledge before the cardinal principle.

    Science.gov (United States)

    Gunderson, Elizabeth A; Spaepen, Elizabet; Levine, Susan C

    2015-02-01

    Approximate number word knowledge-understanding the relation between the count words and the approximate magnitudes of sets-is a critical piece of knowledge that predicts later math achievement. However, researchers disagree about when children first show evidence of approximate number word knowledge-before, or only after, they have learned the cardinal principle. In two studies, children who had not yet learned the cardinal principle (subset-knowers) produced sets in response to number words (verbal comprehension task) and produced number words in response to set sizes (verbal production task). As evidence of approximate number word knowledge, we examined whether children's numerical responses increased with increasing numerosity of the stimulus. In Study 1, subset-knowers (ages 3.0-4.2 years) showed approximate number word knowledge above their knower-level on both tasks, but this effect did not extend to numbers above 4. In Study 2, we collected data from a broader age range of subset-knowers (ages 3.1-5.6 years). In this sample, children showed approximate number word knowledge on the verbal production task even when only examining set sizes above 4. Across studies, children's age predicted approximate number word knowledge (above 4) on the verbal production task when controlling for their knower-level, study (1 or 2), and parents' education, none of which predicted approximation ability. Thus, children can develop approximate knowledge of number words up to 10 before learning the cardinal principle. Furthermore, approximate number word knowledge increases with age and might not be closely related to the development of exact number word knowledge. Copyright © 2014 Elsevier Inc. All rights reserved.

  12. Approximate Bayesian computation.

    Directory of Open Access Journals (Sweden)

    Mikael Sunnåker

    Full Text Available Approximate Bayesian computation (ABC constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology.

  13. Carbon nanotubes doped with trivalent elements by using back - scattering Raman spectroscopy

    Directory of Open Access Journals (Sweden)

    S. A. Babanejad

    2008-12-01

    Full Text Available  In this paper by using DC arc discharge method and acetylene gas, as the carbon source, and nitrogen, as the carrier gas, canrbon nanotubes, CNTs, doped with trivalent element boron, B, have been produced. The deposited CNTs on the cathod electrod, which have structural doped properties to boron element, have been collected and after purification have been investigated by back-scattering Raman spectroscopy. The results reveal that the high frequency G mode component in CNTs doped with electron acceptor element, B, shift to higher wavenumbers. The low frequency G mode component which can appear at approximately 1540–1570 cm-1 wavenumber region, called BWF mode, is a sign of metallic CNT. In the synthesized doped CNTs due to the presence of boron dopant, D mode has sharp peaks and has relatively high intensity in the Raman spectra .

  14. Pawlak algebra and approximate structure on fuzzy lattice.

    Science.gov (United States)

    Zhuang, Ying; Liu, Wenqi; Wu, Chin-Chia; Li, Jinhai

    2014-01-01

    The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to rough set theory. We also investigate molecule Pawlak algebra and obtain some related properties.

  15. Dynamical cluster approximation plus semiclassical approximation study for a Mott insulator and d-wave pairing

    Science.gov (United States)

    Kim, SungKun; Lee, Hunpyo

    2017-06-01

    Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.

  16. The model of interaction between the elements of construction and the layered medium

    Science.gov (United States)

    Fomin, V. G.

    2017-11-01

    The article considers the plane stress problem of the non-linear elasticity theory for a plate or a beam located in the aggressive medium which affects the physical properties of the material. In solving the problem we use the finite element method in combination with the successive approximations method and the variable elasticity parameters method.

  17. Methods of Fourier analysis and approximation theory

    CERN Document Server

    Tikhonov, Sergey

    2016-01-01

    Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.

  18. Optimization and approximation

    CERN Document Server

    Pedregal, Pablo

    2017-01-01

    This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.

  19. Finite cover method with mortar elements for elastoplasticity problems

    Science.gov (United States)

    Kurumatani, M.; Terada, K.

    2005-06-01

    Finite cover method (FCM) is extended to elastoplasticity problems. The FCM, which was originally developed under the name of manifold method, has recently been recognized as one of the generalized versions of finite element methods (FEM). Since the mesh for the FCM can be regular and squared regardless of the geometry of structures to be analyzed, structural analysts are released from a burdensome task of generating meshes conforming to physical boundaries. Numerical experiments are carried out to assess the performance of the FCM with such discretization in elastoplasticity problems. Particularly to achieve this accurately, the so-called mortar elements are introduced to impose displacement boundary conditions on the essential boundaries, and displacement compatibility conditions on material interfaces of two-phase materials or on joint surfaces between mutually incompatible meshes. The validity of the mortar approximation is also demonstrated in the elastic-plastic FCM.

  20. Multilevel Monte Carlo in Approximate Bayesian Computation

    KAUST Repository

    Jasra, Ajay

    2017-02-13

    In the following article we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given.